VARIABLE PRESSURE-DROP/FLOW-RATE SYSTEM ANALYSIS OF

i

The Pennsylvania State University

The Graduate School

John and Willie Leone Family Department of Energy and Mineral Engineering

VARIABLE PRESSURE-DROP/FLOW-RATE SYSTEM ANALYSIS OF

NATURAL GAS RESERVOIRS: A DENSITY-BASED APPROACH

A Thesis in

Energy and Mineral Engineering

by

Miao Zhang

© 2013 Miao Zhang

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

December 2013

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The thesis of Miao Zhang was reviewed and approved* by the following:

Luis F. Ayala H.

Associate Professor of Petroleum and Natural Gas Engineering

Associate Department Head for Graduate Education

Thesis Advisor

Russell T. Johns

Professor of Petroleum and Natural Gas Engineering

Li Li

Assistant Professor of Petroleum and Natural Gas Engineering

Shimin Liu

Assistant Professor of Energy and Mineral Engineering

*Signatures are on file in the Graduate School

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ABSTRACT

Conventional analytical methods analyzing gas well production data during boundary-dominated flow

(BDF) largely rely on the application of concepts such as pseudo-pressure, pseudo-time, and material

balance pseudo-time. Recently, Ayala H. and Ye (2012, 2013) introduced a density-based analytical

approximation that used a rescaled exponential model that proved successful in explicitly estimating

original-gas-in-place and forecasting constant bottomhole pressure (BHP) gas well BDF decline without

pseudo-variables. In this study, the rescaled exponential model is verified through a rigorous derivation

based on fundamental physical principles applied to BDF conditions and that leads to a rate-time equation

modeling gas rate decline in wells produced against a constant BHP specification. We further investigate

the applicability of this rate-time equation to the analysis of production data under varying BHP

conditions. The validity of rescaled exponential and density-based gas decline models for the analysis of

variable rate/pressure-drop is also verified and its successful performance against numerical data is

presented. We also demonstrate that the constant rate and constant BHP solutions given by the proposed

density-based decline models for gas wells under BDF are interchangeable. We propose a density-based

methodology that enables production data analysis of variable BHP/rate gas wells under BDF using

density variables and dimensionless viscosity-compressibility ratios. The proposed model uses actual

material-balance time and density variables and eliminates the need for the calculation of material balance

pseudo-time. Convenient and reliable OGIP calculations are successfully achieved via harmonic decline

type-curve or straight-line analysis. A number of field and numerical case studies are presented to

showcase the capabilities of the proposed approach. We finally extend the applicability of the rescaled

exponential and density-based decline models to high-pressure/high-formation-compressibility gas

reservoir systems. We formally derive the density-based analytical techniques rigorously capturing

formation compressibility effects during for the analysis of gas well BDF production data. The proposed

formulation proves to provide reliable gas rate forecasting for gas well under constant pressure-drop

specification and enable accurate calculation of OGIP by incorporating formation compressibility and the

change of reservoir pore volume effects applicable to both constant BHP, variable flow-rate/pressure-drop,

and constant rate systems.

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Table of Contents LIST OF FIGURES ..................................................................................................................................... vi

LIST OF TABLES ....................................................................................................................................... ix

NOMENCLATURE ..................................................................................................................................... x

ACKNOWLEDGEMENTS ....................................................................................................................... xiii

INTRODUCTION ........................................................................................................................................ 1

1 Gas Rate Forecasting in Boundary-Dominated Flow: Constant Bottomhole Pressure Decline

Analysis Using Rescaled Exponential Models ............................................................................................. 3

1.1 Chapter Summary ......................................................................................................................... 3

1.2 Background ................................................................................................................................... 3

1.3 Rate as a Function of Average Density in BDF ............................................................................ 8

1.4 Exponential Models for Gas Density and Rate Decline in BDF ................................................. 10

1.5 Case Studies – Revisited ............................................................................................................. 13

1.6 Concluding Remarks ................................................................................................................... 17

1.7 Chapter References ..................................................................................................................... 17

2 Rescaled Exponential and Density-Based Gas Decline Models: Extension to Variable Rate/Pressure-

Drawdown Conditions ................................................................................................................................ 19

2.1 Chapter Summary ....................................................................................................................... 19

2.2 Background ................................................................................................................................. 19

2.3 Rescaled Exponential Model for Variable Rate/Pressure-drop in BDF ...................................... 21

2.4 Case Studies ................................................................................................................................ 25



3 Variable Pressure-drop / Flow-rate Production Systems: Density-Based Straight-line and Type-

Curve Analyses ........................................................................................................................................... 36

3.1 Chapter Summary ....................................................................................................................... 36

3.2 Background ................................................................................................................................. 36

3.3 Density-Based Analysis for Variable qgsc/pwf systems in BDF ................................................... 38

3.4 Case Studies ................................................................................................................................ 41

Case Study 3-A: Field Case 1 - Ballycotton Gas Field (Chu et al., 2001) .......................................... 41

Case Study 3-B: Numerical Case 1 - Palacio and Blasingame (1993) Variable BHP Case ............... 44

Case Study 3-C: Field Case 2 - Palacio and Blasingame (1993) ........................................................ 46

Case Study 3-D: Numerical Case 2 - Variable qgsc schedule (Ibrahim et al.,2003) ............................ 48

Case Study 3-E: Field Case 3 - Mattar and Anderson (2003) ............................................................. 50

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Case Study 3-F: Field Case 4 - Palacio (1993) ................................................................................... 53

Case Study 3-G: Field Case 5 – Ibrahim et al. (2003) ........................................................................ 55

Case Study 3-H: Field Case 6 – Ibrahim et al. (2003) ........................................................................ 58



4 Decline Analysis for Gas Wells with Significant Rock Compressibility Effects ............................... 63

4.1 Chapter Summary ....................................................................................................................... 63

4.2 Background ................................................................................................................................. 63

4.3 Density-based Analysis for Systems with Significant Rock Compressibility Effects: Constant

BHP Case ................................................................................................................................................ 67

4.4 Constant BHP Production Examples: Rescaled Exponential Model .......................................... 69

4.5 Density-based Analysis for Systems with Significant Rock Compressibility Effects: Variable

qgsc/pwf Case ............................................................................................................................................. 77

4.6 Variable pwf/qgsc Examples: Straight-line/Type-curve Analysis .................................................. 78



Conclusions ................................................................................................................................................ 90

Appendix A: Diffusivity Equation for Gas System .................................................................................... 92

Appendix B: Derivation of Rate vs. Average Pseudo-pressure BDF Equation .......................................... 95

Appendix C: Derivation of the Rate vs. Pseudo-time BDF Equation ......................................................... 99

Appendix D: Derivation of the Rate vs. Material-balance Pseudo-time BDF Equation ........................... 101

Appendix E: Derivation of Rate vs. Material-balance Time Equation for Oil Well under BDF .............. 103

Appendix F: Relationship between Superposition Pseudo-Time and Material-Balance Pseudo-Time .... 107

Appendix G: Procedures for BDF Gas Rate Forecasting.......................................................................... 108

Appendix H: Production Data for Case Studies ........................................................................................ 110

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LIST OF FIGURES

Figure 1-1 Real Gas Pseudo-pressure vs. Density Graph ............................................................................. 9

Figure 1-2 Approximation between for , and .............................................................................. 12

Figure 1-3 Gas Rate Forecast for Case Study I in Ayala H. and Ye (2012) ............................................... 14

Figure 1-4 Gas Rate Forecast for Case Study II in Ayala H. and Ye (2012) .............................................. 15

Figure 1-5 Gas Rate Forecast for Case 2 in Ayala H. and Ye (2013) (Palacio and Blasingame, 1993) ..... 16

Figure 1-6 Gas Rate Forecast for Case 4 in Ayala H. and Ye (2013) (Fraim and Wattenbarger, 1987) .... 16

Figure 2-1 Gas rate forecast comparison between proposed analytical models and numerical simulation

for a variable pressure-drop/rate system (Case Study 2-A) ........................................................................ 26


for a variable pressure-drop/rate system (Case Study 2-B) ........................................................................ 27

Figure 2-3 pwf schedule for Case Study 2-C ................................................................................................ 28


for Case Study 2-C ...................................................................................................................................... 28

Figure 2-5 Density drawdown ratio forecast comparison between proposed analytical models and

numerical simulation for a constant rate system (Case Study 2-C(e)) ........................................................ 30

Figure 2-6 Density drawdown ratio forecast comparison between proposed analytical models and

numerical simulation for a variable pressure-drop/rate system (Case Study 2-D) ..................................... 31

Figure 2-7 Production history for Case Study 2-E - field data (Mattar and Anderson, 2003) .................... 32

Figure 2-8 Gas rate forecast comparison between proposed analytical models and reported data for Case

Study 2-E .................................................................................................................................................... 33

Figure 3-1 Production history of the Ballycotton gas field ......................................................................... 42

Figure 3-2 vs. straight-line analysis for the Ballycotton gas field .................................. 42

Figure 3-3 vs. straight-line analysis for the Ballycotton gas field ............................. 43

Figure 3-4 Harmonic type-curve match result for the Ballycotton gas field .............................................. 43

Figure 3-5 vs. straight-line analysis for Case Study 3-B ................................................. 44

Figure 3-6 vs. straight-line analysis for Case Study 3-B ............................................ 45

Figure 3-7 Harmonic type-curve match result for Case Study 3-B............................................................. 45

Figure 3-8 Production history for Case Study 3-C ..................................................................................... 46

Figure 3-9 vs. straight-line analysis for Case Study 3-C ................................................ 47

Figure 3-10 vs. straight-line analysis for Case Study 3-C .......................................... 47

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Figure 3-11 Harmonic type-curve match result for Case Study 3-C .......................................................... 48

Figure 3-12 vs. straight-line analysis for Case Study 3-D ............................................. 49

Figure 3-13 vs. straight-line analysis for Case Study 3-D.......................................... 49

Figure 3-14 Harmonic type-curve match for Case Study 3-D .................................................................... 50

Figure 3-15 Production history for Case Study 3-E .................................................................................... 51

Figure 3-16 vs. straight-line analysis for Case Study 3-E .............................................. 51

Figure 3-17 vs. straight-line analysis for Case Study 3-E ........................................... 52

Figure 3-18 Harmonic type-curve match result for Case Study 3-E ........................................................... 52

Figure 3-19 Production history for Case Study 3-F .................................................................................... 53

Figure 3-20 straight-line analysis for Case Study 3-F ............................................. 54

Figure 3-21 vs. straight-line analysis for Case Study 3-F ........................................... 54

Figure 3-22 Harmonic type-curve match result for Case Study 3-F ........................................................... 55

Figure 3-23 Production history of Case Study 3-G ..................................................................................... 56

Figure 3-24 straight-line analysis for Case Study 3-G ............................................. 56

Figure 3-25 vs. straight-line analysis result for Case Study 3-G ................................. 57

Figure 3-26 Harmonic type-curve match result for Case Study 3-G .......................................................... 57

Figure 3-27 Production history for Case Study 3-H ................................................................................... 58

Figure 3-28 straight-line analysis for Case Study 3-H ............................................ 59

Figure 3-29 vs. straight-line analysis result for Case Study 3-H ................................. 59

Figure 3-30 Harmonic type-curve match result for Case Study 3-H .......................................................... 60

Figure 4-1 Numerical simulation results for gas producing under different rock compressibility effects

(Case Study 4-A)......................................................................................................................................... 70

Figure 4-2 Comparison between numerical simulation result and flow rate prediction from rescaled

exponential model (Case Study 4-A) .......................................................................................................... 71

Figure 4-3 Trend of Changing with Pressure (Case Study 4-A) ............................................................ 72


(Case Study 4-B) ......................................................................................................................................... 73


exponential model (Case Study 4-B) .......................................................................................................... 74

Figure 4-6 Trend of Changing with Pressure (Case Study 4-B) ............................................................. 74


(Case Study 4-C) ......................................................................................................................................... 75

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exponential model (Case Study 4-C) .......................................................................................................... 76

Figure 4-9 Trend of Changing with Pressure (Case Study 4-C) ............................................................. 76


(Case Study 4-D)......................................................................................................................................... 79

Figure 4-11 Initial guess of OGIP prediction for cR=5*10-5

psi-1

scenario (Case Study 4-D) .................... 80

Figure 4-12 Straight-line analysis for cR=5*10-5

psi-1

scenario (Case Study 4-D) ...................................... 81

Figure 4-13 Type-curve analysis for cR=5*10-5

psi-1

scenario (Case Study 4-D) ....................................... 81

Figure 4-14 Comparison between the trend of and changing with pressure for cR=5*10-5

psi-1

scenario (Case Study 4-D) .......................................................................................................................... 82

Figure 4-15 Straight-line analysis using pseudo-functions for cR=5*10-5

psi-1

scenario (Case Study 4-D) 82

Figure 4-16 Straight-line analysis under different cR assumptions (Case Study 4-D) ................................ 83


(Case Study 4-E) ......................................................................................................................................... 84

Figure 4-18 Initial guess of OGIP prediction for cR=5*10-5

psi-1

scenario (Case Study 4-E) ..................... 85

Figure 4-19 Straight-line analysis for cR=5*10-5

psi-1

scenario (Case Study 4-E) ...................................... 86

Figure 4-20 Type-curve analysis for cR=5*10-5

psi-1

scenario (Case Study 4-E) ........................................ 86

Figure 4-21 Straight-line analysis results for different cR assumptions (Case Study 4-E) .......................... 87

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LIST OF TABLES

Table 2-1 pwf schedule for Case Study 2-A .................................................................................... 25

Table 2-2 pwf schedule for Case Study 2-B .................................................................................... 26

Table 2-3 Flow rate schedule for Case Study 2-D ......................................................................... 31

Table 4-1 pwf schedule for Case Study 4-E .................................................................................... 84

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NOMENCLATURE

A reservoir area, ft3

b D,PSS pseudosteady component

B dimensionless intrinsic dependency of viscosity-compressibility with density

average dimensionless intrinsic dependency of viscosity-compressibility with density

Bo oil formation volume factor, RB/STB

gas formation volume factor at initial conditions, RB/scf

CA Dietz’s reservoir shape factor

c fluid compressibility, 1/psi

co oil compressibility, 1/psi

cg gas compressibility, 1/psi

cgi gas compressibility at initial conditions, 1/psi

cR rock compressibility, 1/psi

ct total compressibility, 1/psi

total compressibility at average reservoir pressure, 1/psi

Die initial decline coefficient for rescaled exponential model, 1/day

Di initial decline rate for rescaled exponential model under full potential drawdown, 1/day

Gp cumulative production, scf

h reservoir net pay thickness, ft

k permeability, md

OGIP original gas in place, scf

m slope of straight-line

m(p) gas pseudo-pressure, psia2/cp

m*(p) normalized pseudo-pressure, psia

MW molecular weight, lb/lbmol

pi initial reservoir pressure, psia

p pressure, psia

pwf well bottom-hole pressure, psia

dimensionless flow rate

decline-curve dimensionless flow rate

qgi initial decline rate for rescaled exponential model, scf/D

qgie initial decline rate for rescaled exponential model under full potential drawdown, scf/D

qgsc gas flow rate at standard conditions, scf/D

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Qo oil cumulative production, STB

r reservoir radius, ft

rw wellbore radius, ft

re radial-cylindrical reservoir outer boundary, ft

rρ density drawdown ratio

R universal gas constant

modified density ratio term for variable BHP conditions,

t time, days

ta Palacio material balance pseudo-time, days

t'a Ibrahim material balance pseudo-time, days

tn Palacio pseudo-time, days

t’n Ibrahim pseudo-time, days

tMB material balance time, days

t dimensionless time definition for diffusivity equation based on wellbore radius

t decline-curve dimensionless time

T reservoir temperature, °F or °R

Z gas compressibility factor

Vp reservoir pore volume, ft3

Vpi reservoir pore volume at initial reservoir pressure, ft3

reservoir pore volume at average reservoir pressure, ft3

depletion-driven dimensionless time displacement factor for

depletion-driven dimensionless time displacement factor for

depletion-driven dimensionless time displacement factor modified for rock compressibility effects

Euler’s constant, 0.5772157749

dimensionless compressibility ratio

average dimensionless compressibility ratio

viscosity-compressibility dimensionless ratio

average viscosity-compressibility dimensionless ratio between average reservoir pressure and bottom-

hole pressure

average viscosity-compressibility dimensionless ratio between initial reservoir pressure and bottom-

hole pressure

fluid viscosity, cp

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oil viscosity, cp

gas viscosity, cp

gas viscosity at initial condition, cp

average fluid viscosity-compressibility between initial reservoir condition and bottom-hole

condition, cp/psi

( )

average fluid viscosity-compressibility between average reservoir condition and bottom-hole

condition, cp/psi

gas viscosity-compressibility at average reservoir pressure, cp/psi

porosity, faction

porosity at initial reservoir pressure, fraction

porosity at average reservoir pressure, fraction

3.141592653

fluid density

gas density at initial reservoir pressure, lbm/ft3

gas density at average reservoir pressure, lbm/ft3

gas density at standard condition, lbm/ft3

gas density at well bottom-hole pressure, lbm/ft3

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ACKNOWLEDGEMENTS

First, I would like to express my greatest gratitude to my advisor, Dr. Luis F. Ayala H. for his immense

knowledge and invaluable guidance that helped me finish this work. He had high standards for research

but also remained continuous supportive and patient, constantly looking for ways to help me move

forward.

I also would like to express my sincere thanks to my committee, Dr. Russell T. Johns, Dr. Li Li and Dr.

Shimin Liu, for their insightful comments and suggestions to improve this work.

My thanks also go to my colleague and friend, Mr. Pichit Vardcharragosad, for his generous help during

my two-year study and research in Penn State.

I want to give my special thanks to my parents and my boyfriend, Qian Sun, for giving me their

continuous support anytime at any place.

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INTRODUCTION

Natural gas plays an important role in energy supply around the world and consumption has increased

rapidly during the last 25 years. In 2011, for example, natural gas became the number one energy source

by providing 30 percentage of total world energy consumption (23.5 quadrillion Btu). With an increased

demand for natural gas, efficient development of natural gas reservoir systems has become essential.

Among all the factors affecting the management of gas reservoirs, two parameters are of utmost

importance: reliable estimation of gas reservoir reserves (original-gas-in-place, OGIP) and reliable

forecast of future performance of gas wells. These are key ingredients used in natural gas reservoir and

production engineering which can be obtained through production data analysis.

Production data analysis provides an alternative to volumetric and material-balance methods for reservoir

reserve estimation and it also a useful tool for gas well performance forecasting. Both predictions play a

crucial role in economic analysis of gas reservoir exploration and development expenditures.

Traditionally, production data analysis has been based on decline curve analysis and uses two parameters

representing the decline characteristic of a gas reservoir: initial decline rate and curvature of decline. The

classical method mainly involves a model-matching procedure, which is to match a production rate

function/rate-like function versus a time-like function against a decline model such as exponential

decline, hyperbolic decline and harmonic decline (i.e., Arps’ decline models) providing for different

curvature of decline. Exponential models are typical of volumetric liquid systems. For gas systems,

however, due to the effect of pressure-dependent properties such as viscosity and compressibility, the

conventional treatment is based on the use of empirical hyperbolic rate-time curve-fitting. It is also

possible and more rigorous to introduce pseudo-variables—such as pseudo-pressure and pseudo-time—

that replace pressure and time variables and make it possible to use liquid exponential decline stems to

analyze gas systems under constant bottomhole pressure (BHP) (Fraim and Wattenbarger,1987) and

harmonic decline stems to analyze variable pressure-drop/flow-rate systems (Palacio and

Blasingame,1993).

Most recently, Ayala H. and Ye (2012, 2013) has been demonstrated that an analytical decline equation

based on a density-approach rigorously models gas well producing under constant pressure-drop under

boundary-dominated-flow (BDF) without employing pseudo-functions or empirical concepts from Arps

decline analysis. In this density-based model, decline behavior of gas well under constant BHP is proved

to be described in terms of a “rescaled exponential model” for actual flow-rate versus actual time. While

decline analysis using pseudo-functions always involves an iteration procedure for OGIP estimation due

to pressure-dependent gas properties embedded in the definition of pseudo-pressure and pseudo-time, the

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rescaled exponential model eliminates the calculation of pseudo-functions and a new generation of gas

reserve analysis techniques providing explicit OGIP prediction is therefore presented. However, the

rescaled exponential model has limitations, one of which is the constraint of a constant BHP condition,

since in actual practice gas well BHP varies through declining life. It is of interest in this work to develop

an analytical equation applicable to gas well performance under variable pressure-drop/flow-rate

conditions on the basis of density-based approach. The proposed model in the presented work is

developed based on fundamental gas BDF equations and proved to successfully and effectively describe

the production performance of variable BHP/flow-rate system; the proposed methodology for OGIP

estimation allows for convenient and accurate reservoir reserve estimations for variable BHP/flow-rate

system, which will be verified with numerical and field cases. Another limitation of previous work on

density-based approach for gas decline analysis is that reservoir formation compressibility is always

neglected. This study includes the treatment needed for gas rate decline analysis under significant rock

compressibility effects and provides and validates the methodology accounting for such effect.

References

1. U.S. Energy Information Administration. Annual energy outlook 2013. 2013.

2. Arps, J.J. Analysis of decline curves. Trans AIME. 1945;160:228-47.

3. Ayala H., L.F. and Ye, P. Analysis of Unsteady Responses of Natural Gas Reservoirs via a

Universal Natural Gas Type-Curve Formulation. SPE paper 159956 presented at the SPE Annual

Technical Conference and Exhibition, San Antonio, TX, 8-10 October 2012.

4. Ayala H., L.F. and Ye, P. Unified Decline Type-Curve Analysis for Natural Gas Wells in

Boundary-Dominated Flow, SPE Journal, 2013; 18 (1): 97-113.

5. Fraim, M.L. and Wattenbarger, R.A. Gas reservoir decline-curve analysis using type curves with

real gas pseudopressure and normalized time. SPE Formation Evaluation.1987;2(4):671-82.

6. Palacio, J.C.and Blasingame, T.A. Decline curve analysis using type curves -analysis of gas well

production data. SPE paper 25909 presented at the SPE Rocky Mountain Regional / Low

Permeability Reservoirs Symposium, Denver, CO, April 12-14.1993.

3

1 Gas Rate Forecasting in Boundary-Dominated Flow: Constant Bottomhole

Pressure Decline Analysis Using Rescaled Exponential Models

1.1 Chapter Summary

Gas well performance forecasting during boundary-dominated flow (BDF) is largely based on the

application of pseudo-pressure, pseudo-time, and material balance pseudo-time concepts to rate, pressure,

and time data. Recently, Ayala H. and Ye (2012, 2013) and Ye and Ayala H. (2012) demonstrated the

convenience and importance of a rescaled exponential model that successfully forecasted gas well decline

in BDF and used density-based dimensionless parameters in lieu of pseudo-variables. In this study, the

interdependability and interchangeability of these methodologies is formally demonstrated with a rigorous

derivation for rescaled exponential models based on fundamental physical principles applicable to BDF

conditions. The rescaled exponential equation is demonstrated to be a rigorous rate-time equation

modeling gas rate decline in wells produced against a constant bottomhole pressure specification. The

proposed BDF decline equation is shown to be able to be expressed in terms of a dimensionless fluid

parameter ( ) that quantifies the dependency on density for the depletion process of interest, which

has been directly tied to the hyperbolic decline coefficient experienced by a declining gas well. Case

studies are presented to demonstrate the capabilities of the rescaled exponential model for gas rate

forecasting for wells producing at a constant bottomhole pressure and its performance is compared to all

other available models in the literature.

1.2 Background

Gas well deliverability in boundary-dominated flow (BDF) can be written in number of forms: 1) rate vs.

average pseudo-pressure; 2) rate vs. pseudo-time; and 3) rate vs. material balance pseudo-time

expressions. In 1966, Al-Hussainy et al. first derived the mathematical relationship relating gas rate to

average pseudo-pressure during BDF, later written by Palacio and Blasingame (1993) in the following

form:

( ( ) ( ))

Equation 1-1

where the coefficient is defined as:

(

)

Equation 1-2

4

and ( )is normalized pseudo-pressure defined as:

( )

∫

Equation 1-3

Equation 1-1 can be derived starting with the gas diffusivity equation (Appendix A) by taking its area-

averaged prediction for BDF conditions (as shown in Appendix B). In 1987, and on the basis of the

concept of pseudo-time originally introduced by Agarwal (1979) for the analysis of build-up bottomhole

pressure data, Fraim and Wattenbarger (1987) proved that the use of a normalized pseudo-time variable tn

such as:

∫

Equation 1-4

was able to collapse constant bottomhole flowing pressure (BHP), decline gas flow rate vs. time data into

an exponential model—just as it was known was the case for liquid flow rate vs. actual time data in

volumetric oil reservoirs.

Blasingame and Lee (1988) were the first to introduce the concept of a material-balance pseudo-time to

gas analysis based on the use of the normalized pseudo-time function combined with superposition

through material balance:

∫

∫

Equation 1-5

which extended earlier work by the authors aimed at analyzing variable-rate/variable pressure-drop data

for oil wells. Their work empirically showed, using numerical simulation verification, that a graph of

[( ( ) ( )) versus material balance pseudo-time ( ) yields a straight line from whose

slope reserves estimations could be extracted. In 1993, Palacio and Blasingame provided the analytical

proof of such relationship and presented it as:

( ) ( )

Equation 1-6

A detailed derivation of Equation 1-6 and a description of its variables are provided in Appendix D. An

equivalent form of Equation 1-6, rewritten in terms of the original pseudo-pressure definition by Al-

Hussainy et al. (1966), is also presented in Appendix D as Equation D-11. It should be noted that

5

Equation 1-6 implies the following dependency between rate and the material balance pseudo-time

variable:

( ) ( )

Equation 1-7

from where Palacio and Blasingame (1993) envisioned a significant insight for gas decline analysis:

( ) ( ) vs. data, when plotted in a log-log format, collapses to the harmonic decline stem in the

Fetkovich type-curve (Fetkovich, 1980).

In 2003, Mattar and Anderson rewrote the normalized rate vs. material-balance pseudo-time relationship

in terms of a cumulative production function (Qn) which yielded the following “flowing material balance”

equation:

( )

Equation 1-8

which is obtained by multiplying both sides of Equation D-11 by

( ) ( ) . In this equation, ( )

= ( ) ( ) using the original pseudo-pressure definition, is a normalized cumulative

production function defined as:

( )

( )∫

Equation 1-9

and

Equation 1-10

The implementation of Equation 1-8 instead of Equation 1-6 allows obtaining OGIP predictions by

extrapolating

( ) versus Qn straight-line BDF data towards the x- or Qn-axis—thus creating a

convenient analog to how OGIP is obtained in classical P/Z vs. Gp graphs. It should be noted that the rate

versus normalized pseudo-time relationship described by Fraim and Wattenbarger (1987) is strictly

applicable to wells producing at a constant bottomhole pressure. However, the normalized rate vs.

material balance pseudo-time relationship of Blasingame and Lee (1988) and Palacio and Blasingame

6

(1993) was shown to be applicable to variable pressure-drop/flow-rate producing systems. The use of an

exponential-decline model to describe variable pressure-drop/flow-rate producing systems had also been

attempted by Blasingame et al. (1991) using a constant-pressure analog time function.

The implementation of all expressions described above for gas rate forecasting during BDF (rate vs.

average pseudo-pressure; rate vs. pseudo-time; and rate vs. material balance pseudo-time) relies on the

simultaneous evaluation of average reservoir pressure or density , which would be obtained by

invoking zero-dimensional or tank material balance statements. For a volumetric dry gas reservoir, the

material balance statement is written as follows:

(

)

Equation 1-11

The coupled implementation of Equation 1-11 with gas rate forecasting expressions entails an iterative

process for the estimation of original-gas-in-place (OGIP) and the calculation of pressure-to-density-to-

pseudo variable transformations. In order to simplify such coupling, attempts has been made to develop

an approach providing more explicit calculations of OGIP. For instance, Thompson and Mattar (2000)

explored the feasibility of modifying a constant rate solution as an approximate solution to gas well

decline under BDF and at a fixed BHP. However, none of their proposed approximations were able to

account for the significant changes in gas viscosity and compressibility during BDF, from which they

confirmed that pseudo-time must be applied. More recently, Ayala H. and Ye (2012, 2013) proposed a

gas well deliverability equation based on the following analytical transformation for constant fixed

bottomhole flowing pressure solution:

( ) ( )

( )

Equation 1-12

based on the definition of the following dimensionless parameters, :

( )

Equation 1-13

and its time-averaged evolution :

∫

Equation 1-14

where dimensionless variables are defined as:

7

Equation 1-15

Equation 1-16

From where, on the basis of the well-known liquid exponential analytical model, the following rescaled

exponential decline equation for gas wells in boundary-dominated gas flow was first derived:

( )

Equation 1-17

where initial decline coefficient and initial decline rate were defined as:

Equation 1-18

( )

Equation 1-19

Ayala H. and Ye (2012, 2013) showed that it was possible to streamline the calculation of the and

variables through the definition of the strength of the coupling between gas viscosity and compressibility

product and density through the following dimensionless slope B:

( )

Equation 1-20

By identifying a suitable value of the average slope B within the interval of interest ( ), Equations 1-13

and 1-14 can be directly linked to the material balance statement stated in Equation 1-11 as shown below:

( ) (

)

(

)

Equation 1-21

Equation 1-21 provides a very useful approximation that, as demonstrated in Ayala H. and Ye (2012,

2013), led to explicit methods for the calculation of gas reserves (OGIP) that circumvented the explicit

calculation of pseudo-pressure and pseudo-time functions. In this study, we explore the interdependency

of all previous gas forecasting models and their relationship to and interchangeability with the rescaled

exponential model originally derived as presented in Equation 1-17.

8

1.3 Rate as a Function of Average Density in BDF

The first step to independently derive a rescaled exponential model for gas rate forecasting in BDF

conditions is explicitly recasting Equation 1-1 in terms of density. Such transformation would better

streamline the coupling between the gas deliverability equation and material balance statements (Equation

1-11), provide the foundation of variable flow-rate/pressure-drop analysis using the density approach, and

independently verify the validity of the gas well performance forecasting formulation in terms of the

rescaled exponential presented in Equation 1-17. It is first noted that we can readily quantify the

dependency of the gas viscosity-compressibility product with respect to average pressure by invoking a

modified version of the dimensionless viscosity-compressibility ratio concept ( ) originally introduced by

Carter (1985) and shown below in its modified version:

( )

( )

( ) ( )

( )

Equation 1-22

where:

Equation 1-23

This definition, when applied to Equation 1-1, yields the sought-after rate versus average density equation:

( )

Equation 1-24

Because the original pseudo-pressure definition of Al-Hussainy (1966) can be recast in terms of density

by substituting the definitions of gas density and isothermal compressibility, one writes:

( ) ∫

∫

∫

Equation 1-25

from where it follows that the ratio

is the tangent slope of any pseudo-pressure vs. density plot. This

is illustrated in Figure 1-1 at locations , , and .

9

Figure 1-1 Real Gas Pseudo-pressure vs. Density Graph

Note that the slope of the straight line connecting two points in Figure 1-1 gives the average value of the

viscosity-compressibility product between any such two points. For instance, the average value of the

viscosity-compressibility product between average reservoir and prevailing bottom-hole conditions—

namely, ( )

in Equation 1-22—can be expressed in terms the slope of the straight line ( )

connecting locations and illustrated in Figure 1-1 and calculated as:

( )

( ) ( )

Equation 1-26

Likewise, the average value of the viscosity-compressibility product between and would

be given by the straight line ( ) connecting those locations. This average value is highlighted in

Figure 1-1 as the product .

0 2 4 6 8 10 12 140

2

4

6

8

10

12

14x 10

8

(lb/ft3)

m(

) (p

si2

/cp

)

; ; i; wf

10

1.4 Exponential Models for Gas Density and Rate Decline in BDF

Starting with the material balance statement in Equation 1-11, the change of average fluid density with

time during boundary-dominated flow is given by:

Equation 1-27

By substituting the rate versus average density equation previously derived in Equation 1-24, this

derivative can be rewritten as:

( )

Equation 1-28

or,

( )

Equation 1-29

where is defined as initial decline coefficient for the rescaled exponential model, in close analogy to

the definition presented in Equation 1-18. This expression can be integrated by invoking the relationship

in direct analogy to their relationship in Equation 1-14 to yield:

∫

( )

∫ ( )

Equation 1-30

( )

Equation 1-31

which yields a very useful exponential model for density decline in BDF as a function of time:

(

)

Equation 1-32

Equation 1-32 is an important result because it demonstrates that changes in reservoir fluid density with

time during BDF can be written in terms of an exponential model just as it has been traditionally done

with flow rate versus time relationships. And while Equation 1-29 is applicable to variable-rate/variable-

pressure systems in BDF, Equation 1-32 is strictly applicable to constant BHP scenarios as per the

restrictions of the integration in Equation 1-30. For constant BHP conditions, Equation 1-30 becomes

interchangeable with the material balance statement in Equation 1-11.

11

More importantly, the substitution on Equation 1-32 into the rate versus average density expression in

Equation 1-24 directly leads to:

(

)

Equation 1-33

which analytically validates the functional form of the rescaled exponential model originally presented as

Equation 1-12 –which had been independently derived on the basis of Equation 1-12 using the density

diffusivity approximation proposed by Ye and Ayala H. (2012). In Equation 1-33, is the density

drawdown ratio defined as:

Equation 1-34

and is the initial decline rate in this exponential model defined as:

Equation 1-35

Equations 1-17 and 1-33 are two forms of the “rescaled exponential model”. By inspection of both forms,

the following equivalencies become apparent:

with

Equation 1-36

Equation 1-37

Equation 1-38

( ) ( )

Equation 1-39

Note that, while Equations 1-36 to 1-38 are derived by direct inspection, Equation 1-39 is obtained by

substituting the condition into Equation 1-22. This is because, at conditions and according

to Equation 1-21, =1 which leads to = (Equation 1-38). Notably, from this definition, it

becomes clear that the original Carter’s (Equation 4 in Carter, 1985) and share identical definitions.

Carter used it to quantify the drawdown effect on gas viscosity and compressibility and assumed that the

effect of this parameter would remain constant during BDF depletion. Equation 1-38 additionally honors

12

the fact that reservoir gas properties are time-dependent, especially during BDF gas well production when

fluid reservoir average pressure can significantly drop. It is now seen that Carter’s ( i.e., ) is

basically the slope of the straight-line connecting locations and in the pseudo-pressure

versus density plot presented in Figure 1-1.

The equivalency in Equation 1-38 is one of the most interesting results in this development

because it provides the bridge that allows expressing (defined in Equation 1-22) in terms of and thus

the dimensionless fluid parameter ( ) using Equation 1-21. The dimensionless fluid parameter ( )

attempts to quantify the strength of the dependency on density, which was directly tied in previous

studies to the hyperbolic decline coefficient to be experienced by a declining gas well and allowed the

formulation of universal type-curve formulations and straight-line analyses that led to explicit OGIP

determinations (Ayala H. and Ye, 2012; 2013). Equation 1-38 is clearly a useful transformation that

allows rewriting Equation 1-33 into Equation 1-17. The implementation of Equation 1-17 relies on the

validity of Equation 1-21. Equation 1-21 is an approximation in itself, which attempts to capture the

essence of the dependency on density for the fluid and process of interest in terms of the

dimensionless fluid parameter ( ).

Figure 1-2 Approximation between for , and

00.20.40.60.810

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Case Study I in Ayala and Ye (2012)

Case 2 in Ayala and Ye (2013)

[Palacio and Blasingame,1993]

Case 4 in Ayala and Ye (2013)

[Fraim and Wattenbarger,1987]

6(6 $ 6wf )

13

Figure 1-2 illustrates the performance of Equation 1-21 as an approximation in terms of the

equivalency . This figure revisits numerical cases that were analyzed in Ayala H. and Ye

(2012, 2013)—namely, Case Study I analyzed in Ayala H. and Ye (2012) and Cases 2 and 4 analyzed in

Ayala H. and Ye (2013)—which were originally investigated by Palacio and Blasingame (1993) and

Fraim and Wattenbarger (1987), respectively. It is important to note that Case Study I represents 3

different scenarios in one which considered same drawndown and fluid and reservoir properties but

different drainage area sizes. Figure 1-2 highlights that Equation 1-21 (and thus Equation 1-38) is not

only an approximation but also that it can be successful in capturing the overall behavior of with

depletion. This leads to the insight that the suitability or validity of any -value for any gas analysis

would be ultimately prescribed by its ability to successfully capture the overall behavior of with

depletion through the relationship illustrated in Figure 1-2. In other words, Equation 1-21

would represent, within this context, the very definition of or a means for its calculation. In the

following section, the ability of the underlying rescaled exponential model to successfully forecast gas

rates, either on the basis of or , is explored.

1.5 Case Studies – Revisited

In this final section, actual flow rate versus time data from all numerical results available in Ayala H. and

Ye (2012, 2013) are compared against predictions from all gas rate forecasting methods. Such predictions

do not only include the two forms of the rescaled exponential model (i.e., either based on or )

but also the more traditional rate vs. pseudo-pressure (Equation 1-1), rate vs. pseudo-time (Equation C-

13); rate versus material balance pseudo-time (Equation 1-7); and rate vs. density (Equation 1-24)

expressions. These comparisons further highlight the interchangeable nature of all these gas rate-

forecasting expressions.

Figure 1-3 reproduces the numerical data analyzed as Case Study I in Ayala H. and Ye(2012). This case

study considered three numerically-generated scenarios for a natural gas system of different sizes (re=175,

350, and 700 ft) producing at same bottomhole flowing pressure of 100 psia. As shown, gas well

performance under BDF for this case is being forecasted using all methods. In this figure, the last two

analytical curves use the rescaled exponential model in Equation 1-33 using the actual definition of and

its approximation. In this figure, the last two analytical curves use the rescaled exponential model

based on the rigorous definition (Equation 1-22) and its approximation (Equation 6) which uses

a constant value obtained for the best-fit match presented in Figure 1-2. In previous studies, -

14

values had been obtained through linear curve fitting result for

vs. in a log-log plot (Ye and Ayala,

2012) which may yield close but not necessarily identical values. By comparing analytical results with

numerical simulation result in Figure 1-3, it is clear that rescaled-exponential model provides identical,

accurate rate with the traditional gas-rate forecasting equations such as rate vs. density (rate-

pseudopressure equation), rate vs. pseudo-time and rate vs. material-balance pseudo-time; and that the

applicabiltiy of the equivalency of through the use of is also verified. Figure 1-4

reproduces the numerical data analyzed as Case Study II in Ayala H. and Ye (2012). The case study

considered three numerically-generated scenarios for a natural gas system of identical size (OGIP=6 Bcf)

but producing at different bottomhole flowing pressure specifications of 100, 1600 and 3200 psia.

Predicted results from rescaled-exponential model using both the definition and its

approximation are shown to be able to closely match for the constant values of , and

respectively. Clearly, the rescaled-exponential model, in any of its forms, was able to successfully match

both numerical and every other analytical forecasts during BDF.

Figure 1-3 Gas Rate Forecast for Case Study I in Ayala H. and Ye (2012)

10-2

10-1

100

101

102

103

104

104

105

106

107

t(days)

qgsc(S

CF

/D)

Numerical Simulat ion ResultRate vs. pseudo-pressure (Equat ion 1-1)

Rate vs. pseudo-t ime (Equat ion C-13)

Rate vs. material balance pseudo-t ime (Equat ion 1-7)

Rate vs. density (Equat ion 1-24)

Rescaled-exponent ial model with 6Rescaled-exponent ial model with 6 $ 6wf

re=175 ft

re=350 ft

re=700 ft

15

Figure 1-4 Gas Rate Forecast for Case Study II in Ayala H. and Ye (2012)

Figure 1-5 displays the numerical data presented as Case 2 in Ayala H. and Ye (2013) originally reported

by Palacio and Blasingame (1993). As with all numerical scanarios, input reservoir properties including

size, permeability and porosity are known and OGIP was reported to be 4.04 Bcf. Figure 1-5 presents the

gas rate forcast given by rescaled exponential model using definition and approximation with

best-fit constant value of 0.85, both of which yield the same gas rate during BDF as numerically-

simulated result and analytically-calculated result from traditional gas rate forecast methods (Equations 1-

1, C-13, 1-7, and 1-24). Figure 1-6 presents numerical results for Case 4 in Ayala H. and Ye (2013)—a

case study originally reported by Fraim and Wattenbarger (1987) with OGIP reported to be 61.5 Bcf.

Figure 1-6 also presents the corresponding analytical predictions, including that from the rescaled

exponential using the approximation with . From Figure 1-3 to Figure 1-6, it is evident

that recaled-exponential model is able to give reliable rate-forecasting results both using the definition

and its approximation through and Equation 1-21.

10-2

10-1

100

101

102

103

104

105

106

107

t(days)

qgsc(S

CF

/D)






pwf=1600 psia

pwf=3200 psia

pwf=100 psia

16

Figure 1-5 Gas Rate Forecast for Case 2 in Ayala H. and Ye (2013) (Palacio and Blasingame, 1993)

Figure 1-6 Gas Rate Forecast for Case 4 in Ayala H. and Ye (2013) (Fraim and Wattenbarger, 1987)

10-2

100

102

104

105

106

107

108

t(days)

qgsc(S

CF

/D)






10-2

100

102

104

106

107

108

t(days)

qgsc(S

CF

/D)






17

1.6 Concluding Remarks

It has been demonstrated through a rigorous analytical derivation that rescaled exponential models

describing gas rate decline for constant bottomhole pressure specifications can successfully undertake the

task of gas rate forecasting in boundary-dominated flow. Numerical cases were presented to demonstrate

that rescaled exponential models are able to successfully forecast gas well performance during BDF and

exactly match predictions from every other BDF analytical forecast models such as rate vs. pseudo-

pressure, rate vs. pseudo-time, and rate versus material balance pseudo-time equations. It was

demonstrated that the rescaled exponential model could be written in two forms, one that relies on a

rigorous definition of a dimensionless viscosity-compressibility ratio ( in Equation 1-22) or on its

approximation ( in Equation 1-38). This approximation further allows recasting the rescaled-

exponential model in terms of the dimensionless fluid parameter , which quantifies the strength of the

dependency on density for the fluid and depletion process of interest. The additional corroboration

of the applicability of the rescaled exponential model written in terms of the physically intuitive fluid

parameter is significant because it further substantiates, and the basis of the findings of Ayala H. and

Ye (2012, 2013), that: 1) a single-line, universal type-curve can be formulated for any gas well producing

under BDF at constant BHP, 2) iterationless, explicit calculation of reserves (OGIP) are possible using

this type-curve and associated straight-line analysis techniques, 3) no pseudo-pressure or pseudo-time

calculations are needed for such gas well performance calculations; and 4) that a direct link exists

between fluid properties ( ) and drawndown conditions and the hyperbolic coefficients experienced by

gas wells in decline.

1.7 Chapter References

1. Agarwal, R.G. “Real gas pseudo-time” - A New Function for Pressure Buildup Analysis of MHF

Gas Wells, SPE paper 8279 presented in 54th SPE Annual Technical Conference and Exhibition,

Las Vegas, Nevada. 1979.

2. Al-Hussainy, R., Ramey Jr, H.J., and Crawford, P.B. The Flow of Real Gases through Porous

Media. Journal of Petroleum Technology. 1966; 18(5):624-36.





Boundary-Dominated Flow, SPE Journal, 2013; 18 (1): 97-113.

18

5. Blasingame, T.A. and Lee, W.J. The Variable-Rate Reservoir Limits Testing Of Gas Wells. SPE

paper 17708 presented in SPE Gas Technology Symposium, Dallas, TX. 1988.

6. Blasingame, T.A., McCray, T.L., and Lee, W.J., Decline Curve Analysis for Variable Pressure

Drop/Variable Flowrate Systems. SPE paper 21513 presented at SPE Gas Technology

Symposium, Houston, TX, 23-24 January, 1991.

7. Carter, R.D. Type Curves for Finite Radial and Linear Gas-Flow Systems: Constant Terminal-

Pressure Case. SPE Journal. 1985; 25(5):719-28.

8. Fetkovich, M.J. Decline curve analysis using type curves. Journal of Petroleum Technology. 1980;

32(6):1065-77.


real gas pseudopressure and normalized time. SPE Formation Evaluation.1987; 2(4):671-82.

10. Ibrahim, M., Wattenbarger, R.A. and Helmy, W. Determination of OGIP for Wells in

Pseudosteady-State-Old Techniques, New Approaches. SPE paper 84286 presented at the SPE

Annual Technical Conference and Exhibition, Denver, Colorado, 5-8 October 2003.

11. Mattar, L. and Anderson, D.M. A Systematic and Comprehensive Method for Advanced Analysis

of Production Data. SPE paper 84472 presented at the SPE Annual Technical Conference and

Exhibition, Denver, Colorado, 5-8 October 2003.

12. Palacio-Uran, J.C. Analysis and Forecasting Of Gas Well Performance: A Rigorous Approach

Using Decline Curve Analysis. M.S. Thesis. Texas A & M University, M.S., August 1993.

13. Palacio, J.C. and Blasingame, T.A. Decline Curve Analysis Using Type Curves -Analysis Of Gas

Well Production Data. SPE paper 25909 presented at the SPE Rocky Mountain Regional /Low

Permeability Reservoirs Symposium, Denver, Colorado, 12-14 April.1993.

14. Thompson, T.W. and Mattar, L. Gas Rate Forecasting During Boundary-Dominated Flow. paper

2000-46 presented at Petroleum at the Petroleum Society’s Canadian International Petroleum

Conference, Calgary, Canada, 4-8 June, 2000.

15. Ye, P. and Ayala H., L.F. A Density Diffusivity Approach for the Unsteady State Analysis of

Natural Gas Reservoirs. J. Natural Gas Science and Engineering. 2012; v. 7:p.22-34.

19

2 Rescaled Exponential and Density-Based Gas Decline Models: Extension

to Variable Rate/Pressure-Drawdown Conditions

2.1 Chapter Summary

Constant bottomhole flowing pressure (BHP) solutions to the diffusivity equation are routinely used for

the analysis of well decline performance in boundary-dominated flow (BDF). Gas well performance

equations for constant BHP conditions may be written in a number of ways, including rate vs. pseudo-

pressure; rate vs. pseudo-time; rate versus material balance pseudo-time expressions; and more recently,

in terms of density-based rescaled exponential models (Ayala H. and Ye, 2012; 2013). A significant

constraint in some of these expressions, in special for the rescaled exponential model, is the assumption

that BHP conditions remain constant throughout the declining life of the well. However, the most realistic

well specification scenario is that in which both BHP and flow rate decline in time, i.e., a variable

pressure-drawdown/rate condition. In this study, we explore and prove the validity of rescaled

exponential and density-based gas decline models for the analysis of variable rate/pressure-drop gas

systems in BDF. We also demonstrate that the constant rate and constant BHP solutions given by the

proposed density-based decline models for gas wells under BDF are interchangeable.

2.2 Background

Rate-time decline analysis of variable flow-rate/pressure-drop system has traditionally relied on the use of

the superposition principle. Blasingame and Lee (1986) were the first to comprehensively study this

application for the case of rate-time analysis of volumetric oil reservoirs. They demonstrated that

variable-drawdown/rate oil production data during BDF can be modeled through the following equation

of a straight-line:

[

] [

(

)]

Equation 2-1

where , a superposition variable, is termed “material-balance-time” and is defined as:

∑

( )

Equation 2-2

20

where and represent cumulative oil production and flow rate at time step m, respectively.

Equation 2-1 is the straight-line version of Blasingame and Lee’s variable liquid rate/pressure-drop

system analysis approach derived in Appendix E. This expression may also be rewritten explicitly in

terms of oil rate versus material balance time to readily observe that

vs. BDF data follows the

harmonic decline (b=1) stem in Fetkovich type-curves (Fetkovich, 1980). Blasingame et al. (1991) later

showed that when a plotting time-like function tcp is used,

vs. tcp data collapse to Fetkovich’s

exponential decline stem instead. Blasingame et al. (1991) showed that the defining relation for tcp is

given by the expression:

∫

Equation 2-3

so that the long-time approximation for liquid reservoirs producing under constant BHP would be:

(

)

Equation 2-4

where m and for the liquid equations were identified in Equation 2-1. In 1988, Blasingame and Lee

had also empirically demonstrated that their method of analysis could be extended to gas wells if pressure

and material balance time in Equation 2-1 were to be replaced by pseudo-pressure and superposition

pseudo-time. Palacio and Blasingame (1993) later proved that this was indeed a rigorous conclusion and

that variable-drawdown/rate gas production data in BDF may be modeled through the following equation

of a straight-line:

( ) ( )

Equation 2-5

where ( ) is the normalized pseudo-pressure, ( ) ( )

is the rate-normalized pressure drop and

is a constant defined by Palacio and Blasingame (1993) as:

(

)

Equation 2-6

and is material balance pseudo-time is defined as:

∫

∑

( )

Equation 2-7

21

where is normalized pseudo-time, first proposed by Fraim and Wattenbarger (1987) for gas analysis,

defined as:

∫

Equation 2-8

Similarly, an inspection of Equation 2-5 shows that a log-log plot of

( ) ( ) vs. would follow the

trend of the harmonic decline stem in Fetkovich type-curves for boundary-dominated data

(Fetkovich,1980).

More recently, an analytical BDF decline model for gas wells based on a rescaled exponential function

(see Chapter 1; also, Ayala H. and Ye, 2012; 2013) has been proposed, which follows:

( )

Equation 2-9

where is the initial decline rate coefficient, is the initial flow rate, and and are dimensionless

rescaling parameters that quantify the effect that depletion-driven changes of gas viscosity and

compressibility have on the decline response of the system. Equation 2-9 was proven to be instrumental in

the formulation of successful universal, single-line type-curve and straight-line analysis techniques for the

analysis of gas wells producing at constant BHP, which yielded explicit reserve estimation and

circumvented the need for explicit calculation of pseudo-pressure or pseudo-time variables (Ayala H. and

Ye, 2012; 2013). A major restriction of Equation 2-9—which severely constrains its applicability to the

analysis of many other practical situations in gas production—is its built-in assumption of production

against a constant bottomhole pressure (BHP). In this study, we explore the possibility of extending the

applicability of rescaled exponential models to variable BHP conditions by deriving such expression

starting from fundamental physical principles consistent with boundary-dominated flow conditions. We

finally offer a number of test cases to prove the applicability of the methodology and the extension of the

rescaled exponential and density-based models to variable pressure-drawdown/rate situations.

2.3 Rescaled Exponential Model for Variable Rate/Pressure-drop in BDF

Palacio and Blasingame (1993) recast Al-Hussainy and Ramey (1966)’s gas deliverability forecasting

equation in BDF in terms of normalized pseudo-pressure as:

( ) ( )

22

Equation 2-10

Equation 2-10 can be written more explicitly in terms of density by introducing the use of modified

Carter’s viscosity-compressibility ratios (Carter, 1985) that are written in terms of the pseudo-pressure

concept proposed by Al-Hussainy (1966) such that:

( )

( )

( ) ( )

Equation 2-11

where

. The application of this version of Carter’s -ratio allows recasting the gas deliverability

forecasting expression in Equation 2-10 as shown:

( )

Equation 2-12

The tank material balance statement for volumetric dry gas reservoirs prescribes that the change in

average reservoir fluid density with time during BDF is given by:

Equation 2-13

from where a relationship between reservoir average density and time can be established by combining

Equations 2-12 and 2-13 to yield:

( )

Equation 2-14

where is the decline constant for this model defined by this equation. One may integrate Equation 2-

14 between any two arbitrary times t=tj and t=t and write:

∫

( )

∫ ( )

Equation 2-15

where is defined as the time averaged evolution of , in other words,

Equation 2-16

23

from where an insightful result can be derived: reservoir fluid density decline during BDF can be

expressed in terms of the following exponential model with time:

(

∫

) [ ( ( ) )]

Equation 2-17

provided that BHP remains constant within times t=tj and t=t. Please note that this integration

requirement does not constrain BHP to remain the same during the entire life of the well but rather more

narrowly within the stated time interval. For a well subjected to a variable BHP schedule, represents

the prevailing reservoir fluid density right at t=tj once the new BHP is imposed. This BHP remains the

same within the period tj < t < t. If the well were to be producing under a constant drawdown scenario,

Equation 2-17 would be simply reset from the start of production, i.e, tj=0 and , to give:

(

)

Equation 2-18

which upon substitution into Equation 2-12 leads to the following form of the gas deliverability equation:

(

)

Equation 2-19

which corresponds to the same functional form proposed by Ayala H. and Ye (2012; 2013)—i.e., the

rescaled exponential model for gas decline analysis in Equation 2-9. In Equation 2-19, is the initial

decline rate for this rescaled exponential model defined as:

Equation 2-20

and is the density drawdown ratio defined as:

Equation 2-21

It should be noted that if a specification changes to at time , the -value would be

written in terms of the prevailing value of pwf such that:

Equation 2-22

while the prevailing reservoir fluid density at time level ( ) would be prescribed by the material

balance equation:

24

(

)

Equation 2-23

where represents the cumulative production attained at time level . In order to obtain the flow

rate response following a BHP change at time , Equation 2-17 may be substituted into Equation 2-

12 to obtain:

( ) (

∫

)

Equation 2-24

where:

(

) (

)

Equation 2-25

where the stated definitions for

have been used (Equations 2-14 and 2-20). Therefore, the

rescaled exponential expression able to capture to variable, step-changes in BHP conditions may be

written as follows:

(

∫

)

Equation 2-26

where

. It should be noted that if the well were to be produced at a constant pwf at all

times, Equation 2-26 would readily collapse to Equation 2-19 given that , , and .

Equation 2-26 may be integrated to obtain the associated prediction for cumulative production during a

variable rate/pressure drawdown situation:

∫

∫ (

)

( )

( (

∫

))

(

)

Equation 2-27

from where an alternate gas rate decline model for the density-based approach is derived:

25

(

)

Equation 2-28

Equation 2-28 is the density-based decline forecasting model able to capture to variable rate and BHP

conditions. It is simple and rigorous yet does not employ pseudo-time or material balance pseudo-time

concepts to model variable flow-rate/pressure-drawdown systems. In the following sections, we evaluate

the applicability of these density-based decline models (Equation 2-26 and 2-28) to a variety of variable

pressure-drawdown/rate situations in order to assess their forecasting ability.

2.4 Case Studies

Case Study 2-A: Palacio and Blasingame (1993) variable pwf system

Figure 2-1 presents the numerical results of flow rate response vs. time generated for the variable qgsc-pwf

case study originally presented by Palacio and Blasingame (1993). This scenario follows the variable pwf-

schedule presented in Table 2-1. Figure 2-1 also displays the gas rate predicted by modified exponential

and density-based models (Equations 2-26 and 2-28). It is observed that the overlap between the reported

numerical data and the proposed analytical models is excellent for all boundary-dominated flow portions

of the data. As expected, prediction mismatches are only present within the early transient of infinite

acting period immediately following a bottomhole pressure change.

Table 2-1 pwf schedule for Case Study 2-A

t (days) pwf (psia)

0-365 4000

366-730 2000

731-1095 800

1096-2191 500

2192-3287 350

26

Figure 2-1 Gas rate forecast comparison between proposed analytical models and numerical simulation for a variable

pressure-drop/rate system (Case Study 2-A)

Case Study 2-B: Variable BHP: Ayala H. and Ye (2012) Case Study Ia reservoir system

Case Study B explores an identical reservoir system to that described in Case Study Ia in Ayala H. and Ye

(2012) but subjected to a variable BHP production schedule. The imposed pwf schedule is provided in

Table 2-2. Figure 2-2 displays the numerically-generated flow rate response when the reservoir has

experienced such variable-pwf schedule. The solid line in Figure 2-2 is analytically generated using

Equations 2-26 and 2-28. It is clear that both provide nearly identical flow rate predictions as those

generated by numerical simulation.

Table 2-2 pwf schedule for Case Study 2-B

t (days) pwf (psia)

0-300 3500

301-500 2500

501-1000 1000

1001-2000 500

2001-3000 300

3001-5000 100

10-2

100

102

104

105

106

107

t (day)

q (

scfD

)

Numerical data

Rescaled-exponential Model

27

Figure 2-2 Gas rate forecast comparison between proposed analytical models and numerical simulation for a variable

pressure-drop/rate system (Case Study 2-B)

Case Study 2-C: Constant BHP, variable BHP, and constant qgsc study

In Case Study 2-C, a reservoir and fluid system identical to that reported by Palacio and Blasingame

(1993)—previously examined as Case Study 2-A—has been used to further explore numerically

generated reservoir responses using a variety of different production specifications. Figure 2-3 displays

the designed bottomhole flowing pressure (BHP) specifications employed for the following five scenarios:

a) Case 2-C(a): Constant BHP case (production @ pwf = 350 psia)

b) Case 2-C(b): 2-step variable BHP case

c) Case 2-C(c): 3-step variable BHP case

d) Case 2-C(d): 15-step variable BHP case

e) Case 2-C(e): Constant flow rate production case (qgsc = 315 MSCFD, dash line in Figure 2-3).

Figure 2-4 displays the predicted gas rate for constant and variable BHP systems (scenarios 2-C(a), 2-

C(b), 2-C(c) and 2-C(d)) using the proposed analytical models (Equation 2-26 and 2-28). All of the five

scenarios run for the same simulated time and finish at the same bottomhole flowing pressure (pwf = 350

psia). It is evident in Figure 2-4 that the Equations 2-26 and 2-28 are able to fully capture every gas rate

jump due to BHP change and thus predict gas well performance at every BHP step. This further verifies

the validity of the proposed recaled-exponential and density-based models for variable BHP systems.

10-2

100

102

104

103

104

105

106

t(days)

qgsc(S

CF

/D)

Numerical simulation result

Rescaled-exponential model (Equation 2-23 and 2-25)

28

Figure 2-3 pwf schedule for Case Study 2-C

Figure 2-4 Gas rate forecast comparison between proposed analytical models and numerical simulation for Case Study 2-

C

0 2000 4000 6000 8000 100000

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

t (days)

pw

f (p

sia

)

Case Study C(a)

Case Study C(c)

Case Study C(e)

Case Study C(b)

Case Study C(d)

0 2000 4000 6000 8000 1000010

3

104

105

106

107

108

t(days)

qgsc(S

CF

/D)


Rescaled-exponential model (Equation 2-17)

Case Study C(a)

Case Study C(c)

Case Study C(d)

Case Study C(b)

29

Figure 2-4 omitted the flow rate information of Case Study 2-C(e) because the prediction target naturally

shifts from forecasting qgsc to predicting BHP changes in constant-qgsc situations. Scenarios 2-C(a) to 2-

C(d) in Figure 2-4 included a number of BHP changes with defined periods of constant BHP within times

. Equation 2-26 established that, within that time interval, rate decline is controlled by

an exponential term of the type ( ∫

) . Constant flow-rate production represents a

limiting case when BHP changes at every time and the time interval between two BHP

steps is negligible. Thus, for a constant qgsc case, , ( ∫

) , and Equation

2-26 directly collapses, in terms of or BHP predictions, to:

Equation 2-29

which is essentially Equation 2-28 originally derived for step-changes in BHP and constant BHP. The

further substitution of (constant qgsc) into Equation 2-29 yields the versus time governing

relationship for constant-flow rate production in BDF:

(

)

Equation 2-30

Equation 2-30 is an important result because it provides the solution for density drawdown ratio response

under constant flow rate production and demonstrates that constant rate solution and constant BHP

solution of gas well production given by rescaled exponential model are fully interchangeable for

boundary-dominated conditions. Figure 2-5 presents the constant rate scenario, 2-C(e), which produces at

the constant rate value of 315 MSCFD. The response under BDF given by constant-rate solution

(Equation 2-30) narrowly matches the calculated using pwf data reported by numerical simulation,

which illustrates the applicability of Equation 2-30 to gas wells producing at a constant flow rate.

30

Figure 2-5 Density drawdown ratio forecast comparison between proposed analytical models and numerical simulation

for a constant rate system (Case Study 2-C(e))

Case Study 2-D: Variable qgsc system - Ibrahim et al. (2003)

As previously shown, Equations 2-26 or 2-28 are generally applicable to the analysis of variable pressure

drawdown/flow rate systems in BDF. It was also illustrated that the rescaled-exponential model, which

was originally proposed as a constant BHP analytical model, can be transformed into a constant-rate BDF

equation. Equations 2-26 and 2-28 equations may be further recast as:

(

)

Equation 2-31

Note that Equation 2-31, which has general applicability, may be visualized as the constant-rate Equation

2-30 after actual production time t has been replaced by material-balance time “

”. Please further note

that this is not material balance pseudo-time—it is “actual” material-balance time. In order to further test

the validity of the proposed density-based forecasting model, Figure 2-6 presents BHP predictions (in

10-2

100

102

104

10-2

10-1

100

t(days)

r


qgsc

vs. Gp BDF equation

31

terms of -values) generated by numerical simulation of the variable rate system presented by Ibrahim et

al. (2003). Table 2-3 lists the reported flow rate schedule for this production system. Figure 2-6 also

shows the analytically calculated values of using Equation 2-31 (same equation as Equations 2-26 and

2-28). The match is excellent. It is clear that Equation 2-31 is able to predict the response of a

discontinuous rate production system and is able to provide identical results as those reported by

numerical simulation.

Table 2-3 Flow rate schedule for Case Study 2-D

t (days) qgsc (MSCF/D)

0-100 5000

101-200 4000

201-350 2000

351-400 3000

401-500 4000

501-650 1000

651-900 4000

901-1000 1000

1001-1200 3000

1201-1740 2000

Figure 2-6 Density drawdown ratio forecast comparison between proposed analytical models and numerical simulation

for a variable pressure-drop/rate system (Case Study 2-D)

200 400 600 800 1000 1200 1400 1600 1800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

t(days)

r


Constant rate BDF solution (Equation 2-27)

32

Case Study 2-E: Field Case, Mattar and Anderson (2003)

Figure 2-7 displays the production history of a field case reported by Mattar and Anderson (2003). In this

field case, both well rates and BHP change continuously and throughout well productive life. Figures 2-8

presents the analytical rate predictions of the density-based rescaled exponential model (Equations 2-26

and 2-28) using the reported BHP history. In Figure 2-8, analytical prediction results from the density-

based analytical model matches very well with field-reported rate within the BDF region. Departures are

found at early times, as expected, for early transient conditions. While the application of Equation 2-26 in

this case used the time difference between two neighboring BHP points as defined periods of constant

BHP within , Equation 2-28 directly yields the solution as a function of cumulative

production. In both cases, density-based analytical solutions required prior knowledge of original-gas-in-

place (24 BCF, used as reported by the authors) and a best-fit value (

in these

figures). On this basis, values are calculated using its definition (Equation 13) coupled with material-

balance statements (Equation 2-23). Work is underway to show that density-based models can be

rewritten to generate type-curves and straight-line analysis yielding these OGIP, , and

values

during the analysis of constant BHP, variable BHP-steps, constant-rate, and variable qgsc-steps cases.

Figure 2-7 Production history for Case Study 2-E - field data (Mattar and Anderson, 2003)

0 100 200 300 400 500 600 7000

1

2

3

4

5

6

7x 10

6

qgsc(S

CF

/D)

0 100 200 300 400 500 600 700600

700

800

900

1000

1100

1200

1300

BH

P(p

sia

)

t(days)

Flow rate

BHP

33

Figure 2-8 Gas rate forecast comparison between proposed analytical models and reported data for Case Study 2-E


We have studied the application of a density-based, rescaled exponential approach, originally devised for

constant BHP analysis, to variable flow-rate/pressure-drop gas systems and have provided their extension

to situations that fully incorporates the effect of changing bottom-hole pressure on the production rate.

Also, on the basis of this modified decline model, we proved that the constant rate solution and constant

BHP solution in the density-based approach are interchangeable for boundary-dominated flow analysis—

both being related through the concept of material-balance time. The proposed density-based decline-

forecasting models were fully validated and shown to be able to capture a variety of variable rate and

BHP conditions—including constant BHP, step-changes in BHP, constant flow-rate, and step-changes in

flow rate. The density-based model is simple and rigorous and can be written in a form that does not

employ pseudo-time or material balance pseudo-time concepts. The forecasting abilities of the proposed

models were fully verified.

0 100 200 300 400 500 600 7000

1

2

3

4

5

6

7x 10

6

t(days)

qgsc(S

CF

/D)

Reported flow rate

Proposed analytical model (Equations 2-26 and 2-28)

34



Gas Wells. SPE paper 8279 presented in 54th SPE Annual Technical Conference and Exhibition,


2. Al-Hussainy, R., Ramey Jr, H.J., and Crawford, P.B. The Flow of Real Gases through Porous


3. Al-Hussainy, R., and Ramey Jr., H.J., Application of the Real Gas Flow Theory to Well Testing

and Deliverability Forecasting, Journal of Petroleum Technology, 1966; 18(5):637-642.





Boundary-Dominated Flow. SPE Journal. 2013a; 18 (1): 97-113.

6. Ayala H., L.F. and Ye, P. Density-based decline performance analysis of natural gas reservoirs

using a universal type-curve, J. of Energy Resources Technology, in press, 2013b.

7. Blasingame, T.A, and Lee, W.J.: “Variable-Rate Reservoir Limits Testing,” paper SPE 15028

presented at the 1986 SPE Permian Basin Oil and Gas Recovery Conference, Midland, TX,

March 13-14, 1986.

8. Blasingame, T.A. and Lee, W.J. The Variable-Rate Reservoir Limits Testing Of Gas Wells. SPE

paper 17708 presented in SPE Gas Technology Symposium, Dallas, TX. 1988.

9. Blasingame, T.A., McCray, T.L., and Lee, W.J., Decline Curve Analysis for Variable Pressure

Drop/Variable Flowrate Systems. SPE paper 21513 presented at SPE Gas Technology

Symposium, Houston, TX, 23-24 January 1991.




32(6):1065-77.



13. Ibrahim, M., Wattenbarger, R.A. and Helmy, W. Determination of OGIP for Wells in

Pseudosteady-State-Old Techniques, New Approaches. SPE paper 84286 presented at the SPE


35

14. Mattar, L.and Anderson, D.M. A Systematic and Comprehensive Method for Advanced Analysis

of Production Data. SPE paper 84472 presented at the SPE Annual Technical Conference and

Exhibition, Denver, Colorado, 5-8 October 2003.

15. Palacio, J.C.and Blasingame, T.A. Decline Curve Analysis Using Type Curves -Analysis Of Gas

Well Production Data. SPE paper 25909 presented at the SPE Rocky Mountain Regional /Low

Permeability Reservoirs Symposium, Denver, Colorado, 12-14 April.1993.

36

3 Variable Pressure-drop / Flow-rate Production Systems: Density-Based

Straight-line and Type-Curve Analyses

3.1 Chapter Summary

This study demonstrates that production data analysis of variable bottomhole flowing pressure (BHP)/rate

gas wells under boundary-dominated flow (BDF) is possible using a density-based approach. In this

approach, governing equations are expressed in terms of density variables and dimensionless viscosity-

compressibility ratios. Recently, the methodology was successfully used to derive rescaled exponential

models for gas rate decline analysis of wells producing at constant bottomhole pressure (Ayala H. and Ye,

2012; 2013). For the case of natural gas systems experiencing BDF, gas well performance analysis has

been made largely possible—until now—by invoking the concept of pseudo-time, normalized pseudo-

time, or material balance pseudo-time. The density-based methodology rigorously derived in this study

does not employ any type of pseudo-time calculations even for variable rate/pressure drawdown cases.

The methodology enables straightforward OGIP calculations and gas well performance forecasting via

harmonic decline type-curves or straight-line analysis. A number of field and numerical case studies are

presented to showcase the capabilities of the proposed approach.

3.2 Background

Fetkovich (1980) pioneered modern decline curve analysis by placing the field of well decline analysis on

a more solid physical foundation. He developed a group of type curves in terms of dimensionless decline

variables (qDd and tDd) presented as a family of log-log stems used for decline prediction and reserve

estimations for constant bottomhole (BHP) production. Fetkovich demonstrated that it was possible to

justify Arps’ exponential and hyperbolic decline behaviors (Arps, 1945) on the basis of oil and gas

deliverability equations and material balance considerations and mapped those behaviors onto his type-

curves. In 1985, Carter used similar dimensionless rate and time variables as those used by Fetkovich in

order to extend his type-curve method of decline analysis to gas reservoirs. Carter (1985) presented

numerically generated type curves tailored to gas analysis that used a -depletion parameter quantifying

the impact of drawdown and changing gas viscosity-compressibility values—an effect neglected by

Fetkovich. Carter’s development was also restricted to constant BHP rate decline analysis.

Fraim and Wattenbarger (1987) proved both analytically and numerically that by manipulating production

data using normalized pseudo-time (“ ”) the decline character of gas reservoirs under constant bottom-

hole pressure could be captured by the Fetkovich’s exponential decline type-curve for oil wells. A key

37

insight in Fraim and Wattenbarger (1987) work was recognizing that the normalized pseudo-time variable

should be evaluated at average reservoir pressure for decline analysis as opposed to flowing bottomhole

pressure as originally proposed by Agarwal (1979) and Lee and Holditch (1982) in the context of build-up

analysis. Fraim and Wattenbarger’s “liquid equivalent” technique was limited to constant BHP production

scenario and was thus not applicable to the analysis of systems where both flow rate and BHP changed

with time.

Palacio and Blasingame (1993) provided a rigorous justification to the insight originally articulated by

Blasingame and Lee (1991) which recognized that BDF production data for variable pressure-drop/flow-

rate production systems may be readily analyzed through the concept “material balance” pseudo-time

(“ ”) introduced by the authors. The material-balance pseudo-time concept enabled decline type-curve

analysis of variable qgsc/pwf systems by converting variable-rate and pwf data into “equivalent constant-rate

liquid data” for boundary dominated analysis. Blasingame and Lee (1991) original insight showed that a

plot of rate-normalized pressure drop ( ( ) ( )

) versus produced a straight line whose slope

yielded original-gas-in-place (OGIP). Palacio and Blasingame (1993) showed that such relationship also

implied that a log-log plot of

( ) ( ) (“normalized rate”) vs. would match the harmonic decline

stem in Fetkovich’s type-curve. Later, Agarwal et al. (1999) also confirmed that solutions for constant

bottomhole pressure or constant rate production for gases and liquids may be converted to equivalent

constant rate liquid solutions and proposed decline type-curves in terms of well test dimensionless

variables and inverse-pressure-derivatives applicable to radial systems and vertically fractured wells with

infinite and finite conductivity fractures.

Ansah et al. (2000) captured the variation of the gas viscosity-compressibility product with pressure

drawdown via a dimensionless pressure variable. Based on the functional form of such dependence (linear

approximation applicable to low-pressures or exponential or higher-order polynomials for high pressures),

the authors developed a series of type-curves that directly used field variables instead of pseudo-functions

for decline curve analysis of gas well data. Their analysis did not require pseudo-time transformations and

yielded more explicit OGIP predictions but remained only applicable to constant-BHP production decline

situations.

Mattar and Anderson (2003) rewrote the normalized rate vs. material-balance pseudo-time relationship of

Blasingame and Lee (1991) and Palacio and Blasingame (1993) in terms of a cumulative production

function (Qn) and presented the “flowing material balance” methodology. By doing so, a linear

38

relationship was established between ( ) ( )

(“rate normalized pressure-drop”) vs. in a cartesian

plot—which conveniently yields OGIP as its x-axis intercept when extrapolated. Their calculation of the

cumulative production function (Qn) relies on the computation of material balance pseudo-time

transformations and also entails an iterative methodology.

More recently, Ayala H. and Ye (2012; 2013) proposed a density-based analytical BDF model for gas

wells that used a rescaled exponential function for gas rate decline modeling. The methodology

successfully provides explicit OGIP estimations without any explicit pseudo function calculations but was

restricted to constant BHP analysis. Their rescaled exponential decline model was expressed as:

( )

Equation 3-1

where is the initial decline rate coefficient, is the initial flow rate, and and were dimensionless

rescaling parameters quantifying the effect that depletion-driven changes of gas viscosity and

compressibility have on the decline response of the system. was presented by the authors as the time-

dependent version of Carter’s original depletion parameter (Carter, 1985), and as its time-averaged

value. The work by Ayala H. and Ye (2012; 2013) demonstrated that recasting gas flow unsteady

behavior in terms of density-based variables, while decoupling compressibility-viscosity effects through a

modified Carter’s depletion parameter, was able to bring significant advantages to decline analysis. In

particular, their work showed that neither pseudo-time nor pseudo-pressure calculations were required for

constant BHP analysis. In this study, we demonstrate that a density-based approach applied to the analysis

of variable rate/BHP systems in BDF is not only possible but also valuable—notably, no pseudo-time

transformations are no longer required to carry out variable BHP/qgsc analysis.

3.3 Density-Based Analysis for Variable qgsc/pwf systems in BDF

By introducing the following depletion-driven modification to Carter’s viscosity-compressibility ratio

(Carter, 1985) into decline analysis:

( )

Equation 3-2

with ( )

( ) ( ) and

, Al-Hussainy and Ramey (1966) deliverability equation

for BDF in gas reservoirs, in the form used by Palacio and Blasingame (1993), may be readily rewritten in

dimensionless form and in terms of density variables as shown:

39

(

)

Equation 3-3

where initial decline rate is being defined as:

Equation 3-4

The further definition of an initial decline rate coefficient :

Equation 3-5

also allows recasting the tank material balance equation for volumetric, single-phase gas reservoir as

follows:

Equation 3-6

where

. It is readily noted that the dimensionless Equation 3-2 now becomes:

(

)

Equation 3-7

where the definition of the density drawdown ratio introduced by Ayala H. and Ye (2012; 2013) has been

employed:

Equation 3-8

Equation 3-7 can be rearranged as a harmonic decline equation for log-log type curve analysis:

Equation 3-9

or as a straight-line equation for analysis on a cartesian graph:

Equation 3-10

40

Equation 3-9 and Equation 3-10 demonstrate that, by expressing variables in terms of density for this type

of variable pwf-qgsc BDF analysis, no pseudo-time calculation becomes necessary. It is noted that actual

material balance time (

) emerges from the density-based variable pwf-qgsc analysis rather than material-

balance pseudo-time. The following observations may also be made:

OGIP may be obtained from the slope of

vs.

in a cartesian graph;

OGIP may be obtained by matching

versus

data in a log-log format against a

harmonic decline type-curve. The resulting displacements in the x- and y-axes would yield

and

values, respectively, from where

;

For systems with relatively large values of ,

versus

plots may directly yield OGIP

estimates without any calculations or iterations. For all other systems,

versus

plots may

still generate good initial estimations of OGIP to initiate calculations in Equation 3-2;

Equation 3-10 can be recast in the following form:

Equation 3-11

which suggests that the x-axis extrapolation of the straight-line plot of

vs.

would

conveniently yields OGIP upon extrapolation towards the x-axis. We recommend Equation 3-10

over Equation 3-11 due to its use of inverted rates, which typically produces better-defined

straight lines during BDF in cartesian plots.

The associated methodology for OGIP estimation is detailed below:

a) Plot

vs.

data in a cartesian plot, obtain the best-fit straight line through BDF data points,

and calculate the reciprocal of the slope of the straight-line fit to obtain the first estimation of

OGIP;

b) Calculate the modified Carter’s viscosity-compressibility ratio for all data points:

( )

( )

( ) ( )

Equation 3-12

where:

41

Equation 3-13

c) Rescale all

vs.

data using ratios: calculate (

) vs. (

) for straight-line analysis

and/or (

) vs. (

) data for log-log type-curve matching. A new value of OGIP is

determined from the slope of the new cartesian plot and/or by calculating x- and y- axis

displacements required to match the log-log harmonic type-curve;

d) New values of OGIP are used to recalculate the ratios in (b). Data rescaling in (c) continues

until no meaningful OGIP improvement results from the analysis.

3.4 Case Studies

Case Study 3-A: Field Case 1 - Ballycotton Gas Field (Chu et al., 2001)

Ballycotton is an offshore gas field located in the Celtic Sea, Ireland, placed on production in July 1991

(Chu et al., 2001). Chu et al. (2001) presented a reserve estimation analysis on the basis of material

balance pseudo-time (pseudoequivalent time) calculations applied to the production data provided in and

reported an original-gas-in-place prediction of 62.57 Bcf. In order to illustrate the applicability and

practicality of the proposed density-based analysis, we first plot their digitized production data in Error!

eference source not found. in terms of

versus

. The resulting plot is presented in Figure 3-2. A

particular noteworthy feature of Figure 3-2 is how readily the Ballycotton production data—in the

absence of any calculation of viscosity, isothermal compressibility, pseudo-pressure, or pseudo-time

variables—neatly falls along a straight-line that closely crosses the origin. The best straight-line fit in

Figure 3-2 yields a slope of ; directly corresponding to an OGIP estimation of

61.77 BCF—which is consistent with the OGIP reported by Chu et al. (2001). Further refinement of this

OGIP estimation is obtained by pursuing the rescaling of the production data via ratios in Equation 3-12.

The resulting -rescaling produces Figure 3-3 (straight-line analysis) and Figure 3-4 (harmonic type-

curve match). The best straight-line fit in Figure 3-3 yields a slope of —leading to

an OGIP prediction of 62.62 BCF. The x- and y-axis displacements producing the match in Figure 3-4

correspond to and

( ) , or

.

The OGIP prediction resulting from the density-based approach is remarkably close to its reported

value—but no pseudo-time or pseudoequivalent time calculations were employed in the process.

42

Figure 3-1 Production history of the Ballycotton gas field

Figure 3-2

vs.

straight-line analysis for the Ballycotton gas field

0 500 1000 1500 2000 2500 30000

5

10x 10

7

t (days)

qgsc(S

CF

/D)

0 500 1000 1500 2000 2500 30000

500

1000

pw

f (p

sia

)

Flow rate

BHP

0 0.5 1 1.5 2 2.5 3

x 104

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

-7

43

Figure 3-3

vs.

straight-line analysis for the Ballycotton gas field

Figure 3-4 Harmonic type-curve match result for the Ballycotton gas field

0 1000 2000 3000 40000

1

2

3

4

5

6

7

8x 10

-8

10-4

10-2

100

102

104

10-3

10-2

10-1

100

Case 2 Numerical simulation result

Harmonic type-curve

44

Case Study 3-B: Numerical Case 1 - Palacio and Blasingame (1993) Variable BHP Case

The reservoir and fluid property data, and reported BHP schedule, for the variable BHP case presented by

Palacio and Blasingame (1993) were used for this numerically simulated case study. OGIP is exactly

known—reported by the simulator to be 4.04 BCF. As recommended in this study, the generated

production data is first analyzed in the

vs.

cartesian plot presented in Figure 3-5. The resulting

best-straight line fit does not yield an intercept crossing the origin, suggesting that this first OGIP

estimation needs to be refined. The slope in Figure 3-5 is for an OGIP estimation of

3.57 BCF. rescaling ratios are thus calculated and Figure 3-6 and Figure 3-7 are generated. Figure 3-6

yields a final OGIP estimate of 4.04 BCF, while Figure 3-7 yields and

(

) (OGIP = 4.04 BCF). It is observed that the reserve estimations resulting from the

proposed methodology are accurate.

Figure 3-5

vs.

straight-line analysis for Case Study 3-B

0 2000 4000 6000 8000 10000 12000 140000

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

-6

45

Figure 3-6

vs.

straight-line analysis for Case Study 3-B

Figure 3-7 Harmonic type-curve match result for Case Study 3-B

0 500 1000 1500 2000 25000

1

2

3

4

5

6

7

8x 10

-7

10-4

10-2

100

10-1

100

101


Harmonic type-curve

46

Case Study 3-C: Field Case 2 - Palacio and Blasingame (1993)

This field case was reported by Palacio and Blasingame (1993) for a low-permeability reservoir for which

an OGIP of 0.245 BCF resulted from their material-balance pseudo-time type-curve analysis. Figure 3-8

shows the production history as digitized from their original paper, where—as the authors point out—

BHP varies widely following no discernable pattern. For this case, the proposed

vs.

cartesian

plot analysis of the data is presented in Figure 3-9. Figure 3-9 generates a remarkable linear trend that

crosses the origin of the plot and yielding an OGIP prediction of 0.20 BCF. More remarkably, even after

rescaling (Figure 3-10 and Figure 3-11), the OGIP prediction remains the same (OGIP=0.20 BCF

from the slope of in Figure 3-10 and from x- and y-axis displacements--

and

(

) —obtained by type-curve match in Figure 3-11). It is

concluded that the resulting OGIP prediction from the density-based methodology is consistent and close

to the estimation originally reported by the authors.

Figure 3-8 Production history for Case Study 3-C

0 100 200 300 400 500 6000

1

2x 10

6

qgsc (

SC

F/D

)

t(days)

0 100 200 300 400 500 6000

1000

2000

pw

f (p

sia

)

Gas Flowrate

Bottomhole Pressure

Flow rate

BHP

47

Figure 3-9

vs.

straight-line analysis for Case Study 3-C

Figure 3-10

vs.

straight-line analysis for Case Study 3-C

0 6000 12000 180000

1

2

3

4

5

6

7

8

9x 10

-5

0 2000 4000 6000 80000

0.5

1

1.5

2

2.5

3

3.5

4x 10

-5

48

Figure 3-11 Harmonic type-curve match result for Case Study 3-C

Case Study 3-D: Numerical Case 2 - Variable qgsc schedule (Ibrahim et al.,2003)

Case Study 3-D is a numerically-generated variable rate production system based on the reservoir system

and properties reported by Ibrahim et al. (2003) as their Simulation Case 2. As a synthetic scenario, OGIP

is accurately known and is reported by the numerical simulator to be 8.5 BCF. The density-based analysis

starts with the Cartesian

vs.

plot shown in Figure 3-12. For this scenario based on step-changes

of specifications of constant rate, Figure 3-12 did not produce a good straight line fit—implying that an

iterative data rescaling process is needed via ratios (Equation 3-12). Figure 3-13 and Figure 3-14

display the resulting straight-line and type-curve matching analyses, respectively. OGIP prediction is

determined through inverse slope in Figure 3-13, which yields OGIP=8.4 BCF (slope =

). Figure 3-14 produces and

(

) for an

OGIP of 8.4 BCF. Both predictions are clearly accurate.

10-4

10-2

100

102

104

10-3

10-2

10-1

100

101

Case 3 field data

Harmonic type-curve

Field data

49

Figure 3-12

vs.

straight-line analysis for Case Study 3-D

Figure 3-13

vs.

straight-line analysis for Case Study 3-D

0 500 1000 1500 2000 2500 30000

1

2

3

4

5

6

7x 10

-7

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8x 10

-7

50

Figure 3-14 Harmonic type-curve match for Case Study 3-D

Case Study 3-E: Field Case 3 - Mattar and Anderson (2003)

Case Study 3-E is a field case reported and analyzed by Mattar and Anderson (2003) using the flowing

material balance method, which produced an OGIP prediction of 24 BCF. Their digitized production

history is shown in Figure 3-15. As in all previous cases, the

vs.

cartesian analysis plot is

generated for the available data and is presented in Figure 3-16. A first OGIP estimation of 26 BCF is

extracted from the best-fit straight-line slope of 3.85∙ in this figure. Subsequent rescaling

though calculation of associated ratios generate the

vs.

plot in Figure 3-17, which yields a

final OGIP prediction of 24.3 BCF (slope = ). Type-curve matching in Figure 3-18

generates the values and

(

) for an OGIP prediction of 24.3

BCF. OGIP predictions are clearly consistent with previously reported values and were obtained without

resorting to any pseudo-time transformations.

10-4

10-2

100

10-1

100

101


Harmonic type-curve

51

Figure 3-15 Production history for Case Study 3-E

Figure 3-16

vs.

straight-line analysis for Case Study 3-E

0 100 200 300 400 500 600 7000

1

2

3

4

5

6

7x 10

6

qgsc (

SC

F/D

)

t (days)

0 100 200 300 400 500 600 700600

700

800

900

1000

1100

1200

1300

pw

f ((p

sia

)

Flow rate

BHP

0 500 1000 15004

5

6

7

8

9

10

11

12

13

14x 10

-8

52

Figure 3-17

vs.

straight-line analysis for Case Study 3-E

Figure 3-18 Harmonic type-curve match result for Case Study 3-E

0 200 400 600 8002

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7x 10

-8

10-3

10-2

10-1

100

101

10-1

100

101

Case 5 field data

Harmonic type-curve

Field data

53

Case Study 3-F: Field Case 4 - Palacio (1993)

Field Case 4 is a field case presented as Gas Well B by Palacio (1993) in his master thesis, which was

reported to have OGIP value of 6.20 Bcf through pseudo-pressure and material-balance-time type-curve

match. Production history is displayed in Figure 3-19. As in all previous cases,

vs.

cartesian plot,

calculated from production data displayed in Figure 3-20 yields an initial guess of OGIP of 4.6 BCF.

The resulting straight-line analysis is presented in Figure 3-21, and OGIP prediction is 6.37 Bcf from the

slope of . In Figure 3-22, and

(

) are

obtained from type-curve matching analysis, from which OGIP is calculated as 6.37 Bcf.

Figure 3-19 Production history for Case Study 3-F

0 100 200 300 400 5000

5

10

15x 10

6

qgsc (

SC

F/D

)

t (days)

0 100 200 300 400 5001000

1500

2000

2500

pw

f (p

sia

)

Flow rate

BHP

54

Figure 3-20

vs.

straight-line analysis for Case Study 3-F

Figure 3-21

vs.

straight-line analysis for Case Study 3-F

0 200 400 600 800 1000 12000.5

1

1.5

2

2.5

3

3.5

4x 10

-7

0 50 100 150 200 250 300 3502

3

4

5

6

7

8

9

10

11

12x 10

-8

55

Figure 3-22 Harmonic type-curve match result for Case Study 3-F

Case Study 3-G: Field Case 5 – Ibrahim et al. (2003)

Field case 5 is a field case discussed by Ibrahim et al. (2003) as Well H58 with an initial pressure of

14,000 psia and an OGIP of 9.8 Bcf. Production history is provided in Figure 3-23. Initial guess of OGIP

is obtained as 7.9Bcf from the best-fit straight-line slope of

vs.

in Figure 3-24. Final OGIP

estimation is calculated to be 9.3 Bcf from the best-fit straight-line in Figure 3-25 after employing as

rescaling parameter to

and

. Similarly, Figure 3-26 shows harmonic type-curve match result after

iteration with and

(

) .

10-3

10-2

10-1

100

101

10-1

100

101

Field data

Harmonic type-curve

56

Figure 3-23 Production history of Case Study 3-G

Figure 3-24

vs.

straight-line analysis for Case Study 3-G

0 100 200 300 400 500 6000

2

4

6x 10

7

qgsc (

SC

F/D

)

0 100 200 300 400 500 6000

5000

10000

15000

pw

f (p

sia

)

t (days)

Flow rate

BHP

0 500 1000 1500 20000

0.5

1

1.5

2

2.5

3x 10

-7

57

Figure 3-25

vs.

straight-line analysis result for Case Study 3-G

Figure 3-26 Harmonic type-curve match result for Case Study 3-G

0 50 100 150 2000

0.5

1

1.5

2

2.5

3

3.5x 10

-8

10-3

10-2

10-1

100

101

10-1

100

101

Field data

Harmonic type-curve

58

Case Study 3-H: Field Case 6 – Ibrahim et al. (2003)

Ibrahim et al. (2003) also presented another field case is their paper. They analyzed the production data of

Well H60 (plotted in Figure 3-27) using material-balance pseudo-time and reported OGIP estimation to

be 7.3 Bcf. In our study, initial guess is calculated from

vs.

plot (Figure 3-28) as 5.9 Bcf. After

iteration based on Equation 3-22, best-fit straight-line in Figure 3-29 yields a final OGIP estimation of

7.0 Bcf . Alternatively, the same OGIP estimation can be obtained from harmonic type-curve match result

in Figure 3-30 with and

(

) .

Figure 3-27 Production history for Case Study 3-H

0 100 200 300 400 500 6000

1

2

3

4

5

6x 10

7

qgsc (

SC

F/D

)

0 100 200 300 400 500 6000

2000

4000

6000

8000

10000

12000

t (days)

ppw

f (p

sia

)

Flow rate)

BHP

59

Figure 3-28

vs.

straight-line analysis for Case Study 3-H

Figure 3-29

vs.

straight-line analysis result for Case Study 3-H

0 500 1000 1500 2000 25000

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

-7

0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5x 10

-8

60

Figure 3-30 Harmonic type-curve match result for Case Study 3-H


Density-based straight-line and type-curve methods of decline performance analysis have been rigorously

derived and proposed for the study of variable BHP/flow-rate gas systems in BDF. The methodologies are

based on the use of density variables coupled with the concept of depletion-driven viscosity-

compressibility ratios ( ) and eliminate the use of pseudo-time transformations during gas production

data analysis. Three field cases and two numerical cases were analyzed to demonstrate the validity and

practicality of the proposed methodologies. The proposed approach was demonstrated to reliably estimate

original-gas-in-place using BDF production data subjected to a variety of BHP and flow-rate

specifications.


1. Agarwal, R.G. Real gas pseudo-time: A New Function for Pressure Buildup Analysis of MHF

Gas Wells. SPE Paper 8279 presented in 54th SPE Annual Technical Conference and Exhibition,


2. Agarwal, R.G., Gardner, D.C., Kleinsteiber, SW., and Fussell, D.D.: Analyzing Well Production

10-2

10-1

100

101

10-1

100

101

Field data

Harmic type-curve

61

Data Using Combined-Type-Curve and Decline-Curve Analysis Concepts, SPEREE (Oct. 1999)

478-486.



4. Arps, J.J. Analysis of decline curves. Trans AIME. 1945; 160:228-47.


Universal Natural Gas Type-Curve Formulation. SPE Paper 159956 presented at the SPE Annual



Boundary-Dominated Flow. SPE Journal. 2013; 18 (1): 97-113.

7. Blasingame, T.A, and Lee, W.J.: The Variable-Rate Reservoir Limits Testing of Gas Wells, SPE

Paper 17708 presented at the SPE Gas Technology Symposium, held in Dallas, TX, June 13-15,

1988.




32(6):1065-77.

10. Fraim, M. L. and R. A. Wattenbarger (1987). Gas Reservoir Decline-Curve Analysis Using Type

Curves With Real Gas Pseudopressure and Normalized Time. SPE Formation Evaluation J. 2(4):

671-682.

11. Ibrahim, M., Wattenbarger, R., and Helmy, W., Determination of OGIP for Wells in

Pseudosteady-State—Old Techniques, New Approaches. SPE Paper 84286 presented at the SPE


12. Lee, W.J., and Holditch, S.A., Application of Pseudotime to Buildup Test Analysis of Low-

Permeability Gas Wells With Long-Duration Wellbore Storage Distortion, J. Petroleum

Technology, v. 34, n. 12, pp. 2877-2887, December 1982.

13. Mattar, L. and Anderson, D.M. A Systematic and Comprehensive Methodology for Advanced

Analysis of Production Data. SPE paper 84472 presented at SPE Annual Technical Conference

and Exhibition Held in Denver, Colorado,2003

14. Palacio, J.C. and Blasingame, T.A. Decline curve analysis using type curves -analysis of gas well

production data. SPE 25909 presented at the SPE Rocky Mountain Regional / Low Permeability

Reservoirs Symposium, Denver, CO, April 12-14. 1993.

62

15. Mattar, L.and Anderson, D.M. A Systematic and Comprehensive Methodology for Advance

Analysis of Production Data, SPE Paper 84472 presented at SPE Annual Technical Conference

and Exhibition, Denver, Colorado, 2003.

16. Chu, W., Fleming, C.H., and Carroll, K.M.: Determination of Original Gas in Place in

Ballycotton, Offshore Ireland, SPE Paper 69735, SPE Reservoir Evaluation & Engineering J., v.

4, n.1, pp. 11-15, February 2001.

63

4 Decline Analysis for Gas Wells with Significant Rock Compressibility

Effects

4.1 Chapter Summary

State-of-the-art analysis of production performance of gas wells relies on material balance concepts

combined with pseudo-pressure and pseudo-time for rate-time decline analysis and reserve estimations.

Customarily, rock compressibility and reservoir pore volume change are either neglected or accounted for

by replacing gas compressibility with total compressibility values. In this work, we extend the

applicability of a rescaled exponential and density-based decline analysis approach (Ayala H. and Ye,

2012, 2013a and 2013b) for the decline analysis of gas systems experiencing significant rock

compressibility effects. We formally derive the density-based analytical techniques that rigorously

capture formation compressibility effects during for the analysis of gas well production data during

boundary-dominated-flow (BDF), which proves crucially important for high-pressure and/or large-

formation-compressibility gas reservoir systems. The proposed formulations enable calculation of correct

prediction of well performance with depletion) and accurate value of original gas-in-place (OGIP) by

incorporating formation compressibility and the change of reservoir pore volume effects, which may

prove crucially important for high-pressure, highly-depleted, or large-formation-compressibility gas

reservoirs. We also present the associated straight-line analysis technique used for OGIP determination

based on the density approach and applicable to variable flow-rate/pressure-drop systems.

4.2 Background

In many practical cases in natural gas reservoir engineering, the effect of rock compressibility on

depletion performance may be considered negligible: gases are routinely at least one hundred thousand

times more compressible than the rock matrix. Accounting for formation compressibility, however, may

be important in high-pressure reservoirs or in formations with relatively large rock compressibility. In a

single-phase gas reservoir, total compressibility ct is calculated by adding the contribution of gas and rock

compressibility as follows:

Equation 4-1

where and represent gas and rock compressibility, respectively. When formation compressibility is

neglected, it is assumed that . In the context of gas decline and well performance analysis, the

effect of rock compressibility is typically accounted for by replacing gas compressibility with total

64

compressibility values during pseudo-time calculations. Fraim and Wattenbarger (1987) first proposed a

normalized pseudo-time function that extended the applicability of the pseudo-time concept originally

introduced by Agarwal (1979) to gas well performance analysis. In order to capture rock compressibility

effects in production data, Fraim and Wattenbarger (1987) defined their normalized pseudo-time function

in terms of total compressibility as shown below:

∫

Equation 4-2

In their work, Fraim and Wattenbarger proved that decline gas flow rate vs. normalized pseudo-time data

would collapse into an exponential model for gas wells producing under constant bottomhole pressure

(BHP) during BDF. Shortly after, Blasingame and Lee (1988) introduced the concept of a material-

balance pseudo-time to gas analysis based on the use of the normalized pseudo-time function combined

with superposition through material balance:

∫

∫

Equation 4-3

which extended earlier work by the authors aimed at analyzing variable-rate/variable pressure-drop data

for oil wells. In 1993, Palacio and Blasingame provided the analytical proof of Blasingame and Lee (1988)

relationship. In a later development, Ibrahim et al. (2003) proposed the following normalized pseudo-time

to take into account all the possible effect of properties change with average reservoir pressure:

∫

Equation 4-4

They also modified the straight-line equation for variable rate/pressure-drop gas system first proposed by

Blasingame and Lee (1988) on the basis of the superposition principle in terms of their normalized

pseudo-time definition:

∫

∑

(

)

65

Equation 4-5

where represents for the gas flow rate at time step m.

Agarwal (1979) first introduced by the pseudo-time definition as a means of linearizing the right hand

side (accumulation term) of the gas diffusivity equation for cases where viscosity and compressibility

changes with depletion were significant. The use of total compressibility values ( ) within the context of

pseudo-time calculation is typically justified on the basis of its presence on the accumulation term of the

gas diffusivity equation for systems with significant rock compressibility—which is the term that pseudo-

time attempts to linearize. An attempt at capturing rock compressibility effects without the explicit use of

pseudo-time was provided by Ansah et al (1996, 2000). Ansah et al (1996, 2000) rewrote their gas rate

deliverability equation in terms of total compressibility ( ) in order to capture significant formation

compressibility effects as shown:

∫

Equation 4-6

where dimensionless pressure is defined as:

Equation 4-7

Darcy’s law for a closed reservoir in BDF can be written as [Palacio and Blasingame (1993), Al-Hussainy

and Ramey (1966)]:

( ( ) ( ))

Equation 4-8

where ( ) is normalized pseudo-pressure defined as:

( )

∫

Equation 4-9

Since normalized pseudo-pressure in Equation 4-7 can be rewritten as:

( )

∫

∫

(

)

66

Equation 4-10

Ansah et al’s approach amounts to recasting Darcy’s law in terms of a different (pseudo-) pressure

gradient. Ansah et al’s approach calculates pseudo-pressure in terms of total compressibility ( ) instead

the traditional calculation of pseudo-pressure in terms of gas compressibility ( ) in Equation 4-10.

More recently, an analytical BDF decline model for gas wells based on a rescaled exponential function

has been proposed, through which explicit reservoir estimation for a fixed pressure-drawdown reservoir

can be obtained without calculation of pseudo-variables (Ayala H. and Ye; 2012, 2013a and 2013b). The

rescaled exponential model is expressed as:

( )

Equation 4-11

where is the initial decline rate coefficient, is the initial flow rate, and and are dimensionless

rescaling parameters that quantify the effect that depletion-driven changes of gas viscosity and

compressibility have on the decline response of the system. A rigorous derivation of Equation 4-11 was

provided in Chapter 1 along with the following definitions of the dimensionless variables and :

( )

Equation 4-12

∫

Equation 4-13

where ( )

( )

( ) ( ) and

. In Chapters 2 and 3, the application of rescaled-

exponential model to variable pressure-drop/rate system was presented. Chapter 2 derives the following

analytical model:

(

)

Equation 4-14

which is used for OGIP estimations in Chapter 3 in the following form:

67

Equation 4-15

where is the initial decline rate in this exponential model defined as:

Equation 4-16

4.3 Density-based Analysis for Systems with Significant Rock Compressibility Effects: Constant

BHP Case

Starting from a general material balance conservation statement ( where

and ), the following tank balance equation is derived for dry gas reservoirs of

evolving porosity:

(

)

Equation 4-17

Equation 4-17 can be easily transformed in the form in terms of p/z, which is discussed as the general

material balance equation by Fetkovich et al (1998) and by Moghadam et al (2011) for overpressured

single-phase gas reservoirs. Equation 4-17 leads to:

( )

Equation 4-18

Using the chain rule and rock and gas compressibility definitions, the left hand side of this equation can

be expressed as:

( )

(

)

Equation 4-19

which transforms Equation 4-18 into:

68

Equation 4-20

where:

(

)

(

) [ ( )

[ ( )

Equation 4-21

The -ratio is a dimensionless variable quantifying the effect that rock compressibility has on the gas

reservoir depletion, which collapses to unity when formation is considered incompressible and is

extremely small. In order to derive the extension of rescaled exponential model (Equation 4-11) in terms

of the depletion-driven dimensionless variables and , we rewrite the gas deliverability equation of Al-

Hussainy and Ramey (1966) and Palacio and Blasingame (1993)—written originally in terms of pseudo-

pressure—as follows:

( )

Equation 4-22

by using the following time-dependent version of Carter’s viscosity-compressibility ratio (Carter, 1985):

( )

Equation 4-23

where ( )

( )

( ) ( ) and

. The combination of Equations 4-20 and 4-22 leads to:

( )

Equation 4-24

For a constant BHP specification, the integration of this expression yields:

(

)

Equation 4-25

where:

69

Equation 4-26

and is the time-averaged value of the product:

∫

Equation 4-27

Equation 4-28

Substitution of Equation 4-25 into 4-22 yields the extension of the rescaled exponential model for the

analysis of gas rate decline in gas reservoirs with significant rock compressibility effects, given by:

(

)

Equation 4-29

where:

Equation 4-30

Equation 4-31

Equation 4-29 retains the same rescaled exponential functional form originally proposed by Ayala H. and

Ye (2012, 2013a and 2013b). The new dimensionless variable embedded in the new expression

quantifies the effect of the additional support given by rock expansion on the associated flow rate

response. It is further noted that, following their definitions, original gas-in-place is directly obtained by

taking the ratio of to

, as shown:

/

Equation 4-32

4.4 Constant BHP Production Examples: Rescaled Exponential Model

Case Study 4-A

70

Figure 4-1 reproduces the numerical scenarios presented by Ayala H. and Ye (2012) as their Case Study I.

System properties are kept identical except that the system is now initialized at a significantly higher

pressure (pi=10,000 psia) while rock compressibility effects are incorporated—an effect neglected in their

original study. As shown in the figure, the original case study considered three numerically-generated

scenarios for a natural gas system of different sizes (re=175, 350, and 700 ft) producing at same

bottomhole flowing pressure of 100 psia. Rock compressbiliy values of ,

and were studied—where is considered to represent gas systems

with a virtually incompressible rock. Figure 4-1 demonstrates that the cases and

overlap one another—illustrating that systems exhibiting those rock

compressibilities may be still considered incompressible. The figure further illustrates that differences in

behavior among the three systems are hardly noticeable at early times because depletion is not extensive.

However, once boundaries are felt and boundary-dominated flow starts, differences among flow rate

responses become noticeable. Higher flow rates can be sustained by the system with the largest rock

compressibility (cR= ) because formation expansion can provide significant extra support

in addition to gas expansion. As a consequence of this, the flow rate decline during late time BDF is

steeper for reservoirs with high rock compressibility due to the more extensive depletion caused by larger

values of cumulative production attained during early BDF.

Figure 4-1 Numerical simulation results for gas producing under different rock compressibility effects (Case Study 4-A)

100

101

102

103

104

103

104

105

106

107

t (days)

qgsc (

SC

F/D

)

cR

=5*10-5

psi-1

cR

=1*10-6

psi-1

cR

=1*10-12

psi-1

re350re175 re700

71

Figure 4-2 displays the predictions of the proposed exponential model (Equation 4-29) for the cR=

case. The matches are excellent for all reservoir sizes. It should be noted that typical values of

rock compressibility are found around 3 , whose effect could be considered negligible when

compared to typical values of natural gas compressibility. In this study, the significantly large value of

—while consistent with high values of used by Fetkovich et al.

(1998) for some field examples—was considered to more extensively verify the validity of Equation 4-19

as a rigorous rate forecast equation for a highly compressible gas reservoir.

Figure 4-2 Comparison between numerical simulation result and flow rate prediction from rescaled exponential model

(Case Study 4-A)

Figure 4-3 illustrates the behavior of the newly defined -ratio with respect to pressure for the case

under study and for a variety of rock compressibility values. The definition of is given by Equation 4-

12 as the variable accounting for rock compressibility effects in the rescaled exponential model. As per its

definition, its value equals one when rock compressibility is negligible. Therefore, in Figure 4-3, the

trend becomes flatter as rock compressibility decreases and becomes a fully horizontal line for virtually

incompressible formations ( ). It is noted that the and

trends are not significantly different, further explaining their similar flow rate responses in Figure 4-1. It

100

101

102

103

104

103

104

105

106

107

t (days)

qgsc


Rescaled-exponential model (Equation 4-19)

re175 re700re350

72

is interesting to note that values of are lower than unity at early times and larger than one at late times.

As per its definition and the presence of the (

) coefficient, the initial value of becomes

smaller as the contrasts between and is more significant. As depletion continues, the value of is

bound to increase with time.

Figure 4-3 Trend of Changing with Pressure (Case Study 4-A)

Case Study 4-B

Figure 4-4 displays the numerically-generated data for the gas well--originally reported by Palacio and

Blasingame (1993)--producing under a constant BHP condition, which is presented as Case 2 in Ayala H.

and Ye (2013a). As done in the previous case study, the numerical case has considered three different

rock compressibility values. Since this particular case was not a highly pressurized gas reservoir

(pi=4,800 psia), the highest cR is set to be so that the decline rate under effect of

significant rock compressibility can be observed. Figure 4-5 presents the gas rate forecast result given by

rescaled exponential model (Equation 4-19) for the case with the most compressible formation (

). From this figure, it is clear that the proposed model is able to capture the significant

associated rock compressibility effect by providing the same flow rate as numerical simulator for BDF

conditions. Figure 4-6 displays the trend of the -ratio with respect to pressure for this reservoir gas

system is provided under different rock compressibility effect, which shows the same information as

2000400060008000100000.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

p (psia)

c

cR=5*10

-5 psi

-1

cR=2*10

-5 psi

-1

cR=5*10

-6 psi

-1

cR=1*10

-6 psi

-1

cR=1*10

-12 psi

-1

73

previous case: the change of becomes more insignificant as rock compressibility is reduced and stays

equal to one for virtually incompressible formations ( ).

Figure 4-4 Numerical simulation results for gas producing under different rock compressibility effects (Case Study 4-B)

100

101

102

103

104

104

105

106

107

108

t (days)

qgsc (

SC

F/D

)

cR

=1*10-4

psi-1

cR

=1*10-6

psi-1

cR

=1*10-12

psi-1

74


(Case Study 4-B)

Figure 4-6 Trend of Changing with Pressure (Case Study 4-B)

100

101

102

103

104

103

104

105

106

107

t (days)

qgsc (

SC

F/D

)


Proposed rescaled-exponential model

100020003000400048000.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

p (psia)

c

cR=1*10

-4

cR=1*10

-5

cR=1*10

-6

cR=1*10

-12

75

Case Study 4-C

Case Study 3 explores an identical reservoir system to that described as a numerical simulation case by

Ibrahim et al. (2003) but producing at a constant BHP value of 350 psia and neglecting in-situ water

saturation by considering a single-phase gas reservoir. It is a highly-pressurized gas reservoir with initial

pressure of 12,300 psia. Figure 4-7 displays the numerically-generated flow rate response when the

system is exposed to different rock compressibility values, among which the scenario with

exhibits a clear deviation from the others due to a significant rock compressibility effect.

Figure 4-8 shows the prediction of the proposed model for this case. As shown below, the proposed

rescaled-exponential model (Equation 4-19) proves to fully capture rock compressibility effect by

matching with the reported flow rate for generated from numerical simulation. Also

the predicted trend of for different values for this particular reservoir gas is provided in Figure 4-9.

Figure 4-7 Numerical simulation results for gas producing under different rock compressibility effects (Case Study 4-C)

100

101

102

103

104

104

105

106

107

108

t (days)

qgsc (

SC

F/D

)

cR

=5*10-5

psi-1

cR

=1*10-6

psi-1

cR

=1*10-12

psi-1

76


(Case Study 4-C)

Figure 4-9 Trend of Changing with Pressure (Case Study 4-C)

100

101

102

103

104

104

105

106

107

108

t (days)

qgsc (

SC

F/D

)


Proposed rescaled-exponential model

200040006000800010000120000.2

1

1.5

2

2.5

p (psia)

c

cR=5*10

-5 psi

-1

cR=5*10

-6 psi

-1

cR=1*10

-6 psi

-1

cR=1*10

-12 psi

-1

77

4.5 Density-based Analysis for Systems with Significant Rock Compressibility Effects: Variable

qgsc/pwf Case

For gas system with significant rock compressibility effects, Equation 4-18 shows that flow rate can be

expressed as:

Equation 4-33

where the -ratio accounted for the rock compressibility effect. Upon integration:

∫

∫

Equation 4-34

which can be readily rearranged to give:

Equation 4-35

is the average value of the -ratio over the entire depletion interval of interest defined as:

∫

Equation 4-36

Given that Equation 4-22 can be rewritten as:

(

)

Equation 4-37

when combined with Equation 4-35, yields the following straight line relationship in terms of a material-

balance-time-like function:

Equation 4-38

Equation 4-38 retains a similar form to the proposed straight-line equation in Chapter 3 (Equation 4-15).

The only difference between the two formulations is that cumulative production term Gp is being replaced

78

by

—while the integration yields Gp when =1. It is also noted that OGIP may be obtained from

the slope of the straight line resulting from the application of Equation 4-38. Equation 4-38 can be

rearranged in terms of a harmonic decline type-curve form as shown:

Equation 4-39

from where OGIP may be determined from the x- and y- axis displacements against the

vs.

harmonic type-curve since

. The step-by-step procedure of OGIP estimation by employing

Equation 4-38 and 4-39 closely follows the procedure outlined in Chapter 3, reproduced below for

systems with significant rock compressibility:

a) Obtain an initial OGIP guess from the slope of the

vs.

plot;

b) Calculate reservoir average pressure/density for every data point through general material balance

equation for high-pressure gas reservoirs (Equation 4-17) and the corresponding –ratio

(Equation 4-21);

c) Calculate associated viscosity-compressibility ratios (Equation 4-23);

d) Generate the

vs

cartesian plot for straight-line analysis or

vs.

log-

log plot for type-curve match analysis. Obtain a value of OGIP through the inverse slope of the

straight-line plot, or the product of the displacements on x- and y- axis from the harmonic type-

curve match result;

e) Repeat step b) to d) until the change of OGIP value is negligible. For improved speed of

convergence when considerably large rock compressibility values are considered, a good practice

is the use of averaged OGIP values from the two most recent iterations.

4.6 Variable pwf/qgsc Examples: Straight-line/Type-curve Analysis

Case Study 4-D

Case Study 4-D reproduces the variable rate production scenario for the high-pressurized gas reservoir

presented and analyzed by Ibrahim et al.(2003)--previously investigated as Case Study 4-C--on the basis

of material-balance pseudo-time (Equation 4-5). Formation compressibility is reported as

79

and, since this is a synthetic case, OGIP is known to be equal to 8.4 BCF. Ibrahim et al.(2003) scenario

considers a series of successive constant-rate specifications and thus the simulation seeks the associated

well bottomhole pressure response. Figure 4-10 presents the predicted well bottomhole pressure data

numerically generated for the cases: , and

. The strongest rock compressibility effect is obviously observed for the

case, for which the extra support provided by the highly-compressible rock result in a smaller decreases

of BHP with time. The case is thus selected for analysis since it presents the most

substantial departure due to rock compressibility effects.

Figure 4-10 Numerical simulation results for gas producing under different rock compressibility effects (Case Study 4-D)

The reserve estimation procedure starts by obtaining an appropriate initial guess of OGIP from best-fit

straight-line in the

vs.

plot presented in Figure 4-11—which yields the starting value of

OGIP=12.8 BCF. Figure 4-12 presents the final converged result with a best-fit straight-line yielding

OGIP=8.7 BCF. The final matching result using the harmonic log-log type-curve is displayed in Figure

4-13, from which we get and

and OGIP is

0 500 1000 15000

2000

4000

6000

8000

10000

12000

t(days)

pw

f(psia

)

cR

=5*10-5

(psi)-1

cR

=4*10-6

(psi)-1

cR

=1*10-12

(psi)-1

80

calculated as

. Both estimations are excellent despite the very strong influence of

rock compressibility effects. Figure 4-14 illustrates the changes of average and with pressure

depletion. As a density-averaged evolution of , retains lower values but ratios start at same initial

value. In addition, the numerically-generated data is further analyzed in Figure 4-15 using pseudo-

pressure and modified pseudo-time model proposed by Ibrahim et al. (2003), where the best-fit straight-

line for the last iteration also yields a OGIP prediction of 8.7 BCF. This result is fully consistent with the

density-based methods analyses result from Figure 4-12 and 4-13, further verifying the applicability of

proposed methodology to variable BHP/flow-rate gas system with significant rock compressibility

effects..

Figure 4-11 Initial guess of OGIP prediction for cR=5*10-5 psi-1 scenario (Case Study 4-D)

0 500 1000 1500 2000 2500 3000 35000

0.5

1

1.5

2

2.5

3

3.5x 10

-7

81

Figure 4-12 Straight-line analysis for cR=5*10-5 psi-1 scenario (Case Study 4-D)

Figure 4-13 Type-curve analysis for cR=5*10-5 psi-1 scenario (Case Study 4-D)

0 200 400 600 8000

0.2

0.4

0.6

0.8

1

1.2

1.4x 10

-7

10-4

10-2

100

10-2

10-1

100

101


Harmonic type-curve

82

Figure 4-14 Comparison between the trend of and changing with pressure for cR=5*10-5 psi-1 scenario (Case Study

4-D)

Figure 4-15 Straight-line analysis using pseudo-functions for cR=5*10-5 psi-1 scenario (Case Study 4-D)

4000600080001000012000

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

pavg

(psia)

c

c

c

and

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

83

Figure 4-16 illustrates the situation when there is uncertainty about the appropriate formation

compressibility values for the case under study. For the case illustrated in Figures 4-11 to 4-13, is well

known and equal to . Figure 4-16 compares the OGIP best-fit straight-line results

when different formation compressibility assumptions are used to analyze the

scenario. The effect which is most evident is the significant change in slope, leading to significantly

different OGIP estimations, associated to different assumptions. In general, the smaller the value of the

assumption, the smaller or flatter the slope and the higher the OGIP prediction. For example, OGIP is

underestimated at 7.2 BCF for the largest value of being considered in Figure 4-16 (

) and OGIP is grossly overestimated at as much as 17 BCF when an incompressible formation

( ) is assumed. The effect of underestimating formation compressibility can be

significant, since a much larger initial hydrocarbon resource (OGIP) would be needed to artificially

counter balance the extra pressure support being experienced by the system. It should also be noted that

the straight-line fitting in Figure 4-16 is rather poor when incorrect values are used.

Figure 4-16 Straight-line analysis under different cR assumptions (Case Study 4-D)

0 500 1000 15000

0.2

0.4

0.6

0.8

1

1.2

1.4x 10

-7

cR

=8*10-5

(psi)-1

cR

=5*10-5

(psi)-1

cR

=1*10-5

(psi)-1

cR

=1*10-12

(psi)-1

84

Case Study 4-E

Case Study 4-E regenerates the Ibrahim et al. (2003) discussed previously but using a different production

specification: a series of successive step changes in BHP instead of successive step changes in rate. All

reservoir and fluid properties remain the same. The new prescribed BHP schedule is shown in Table 4-1

and the resulting rate decline response from the reservoir is presented in Figure 4-17 for two different

rock compressibility assumptions: and . Larger flow rates are

experienced by the system with extra pressure support due to rock compressibility effects.

Table 4-1 pwf schedule for Case Study 4-E

t (days) pwf (psia)

0-300 5000

301-500 2000

501-1000 800

1001-1200 2000

1201-1500 1000

Figure 4-17 Numerical simulation results for gas producing under different rock compressibility effects (Case Study 4-E)

0 500 1000 15000

2

4

6

8

10

12

14x 10

6

t(days)

qgsc(S

CF

/D)

cR

=5*10-5

(psi)-1

cR

=1*10-12

(psi)-1

85

To analyze the data with significant rock compressibility effects ( ), an initial guess of

OGIP of 8.6 BCF is determined from the inverse slope of

vs.

as shown in Figure 4-18. Figure 4-

19 shows that straight-line analysis using -rescaling for the data yields a final slope of

corresponding OGIP prediction is 8.5 BCF—consistent with the reported OGIP from

simulation. The harmonic type-curve match result is shown in Figure 4-20 yielding

, , and OGIP = 8.5 BCF. Figure 4-21 displays the converged results if

different assumptions of rock compressibility (other than ) were to be used in the

analysis. For this case, the incompressible formation assumption ( ) gives the worst

prediction of OGIP by overestimating it at 10.5 BCF, while places the estimation at

a smaller OGIP value of 8.0 BCF. Again, the best straight-line fit is obtained for the case where the

correct tock compressibility assumption was used.

Figure 4-18 Initial guess of OGIP prediction for cR=5*10-5 psi-1 scenario (Case Study 4-E)

0 1000 2000 3000 4000 50000

1

2

3

4

5

6

7x 10

-7

86

Figure 4-19 Straight-line analysis for cR=5*10-5 psi-1 scenario (Case Study 4-E)

Figure 4-20 Type-curve analysis for cR=5*10-5 psi-1 scenario (Case Study 4-E)

0 200 400 600 8000

0.2

0.4

0.6

0.8

1

1.2

1.4x 10

-7

10-4

10-2

100

10-2

10-1

100

101


Harmonic type-curve

87

Figure 4-21 Straight-line analysis results for different cR assumptions (Case Study 4-E)


In this study, we have extended the applicability of the rescaled exponential and density-based models to

gas systems with significant rock compressibility effects. The effect is captured through the definition of a

new compressibility coefficient, , which takes into account rock compressibility and corresponding

porosity change in gas reservoir producing under fixed BHP. -ratio is applied in rescaled exponential

model for constant BHP production system as well as straight-line/type-curve analyses for OGIP

estimation for variable BHP/flow-rate system. The proposed methods are rigorously derived from

physical principles and its validity was further confirmed via excellent matches against a number of

numerical simulation case studies which considered significantly large rock compressibility effects.



Gas Wells, paper SPE 8279 presented in 54th SPE Annual Technical Conference and Exhibition,


0 200 400 600 8000

0.2

0.4

0.6

0.8

1

x 10-7

cR

=8*10-5

(psi)-1

cR

=5*10-5

(psi)-1

cR

=1*10-12

(psi)-1

88

2. Al-Hussainy, R., Ramey Jr, H.J., and Crawford, P.B. The Flow of Real Gases Through Porous




4. Ansah, J., Knowles, R.S., and Blasingame, T.A.: A Semi-Analytical (p/z) Rate-Time Relation for

the Analysis and Prediction of Gas Well Performance. paper SPE 35268 presented at the SPE

Mid-Continent Gas Symposium, Amarillo, TX, 28–30 April 1996.

5. Ansah, J., Knowles, R.S., and Blasingame, T.A.: A Semi-Analytical (p/z) Rate-Time Relation for

the Analysis and Prediction of Gas Well Performance. SPE Reservoir Evaluation and Engineering.

2000; 3(6): 525-533.





Boundary-Dominated Flow. SPE Journal. 2013a; 18 (1): 97-113.

8. Ayala H., L.F. and Ye, P. Density-based decline performance analysis of natural gas reservoirs

using a universal type-curve, J. of Energy Resources Technology, in press, 2013b.

9. Blasingame, T.A, and Lee, W.J. The Variable-Rate Reservoir Limits Testing of Gas Wells. paper

SPE 17708 presented at the SPE Gas Technology Symposium, held in Dallas, TX, June 13-15,

1988.




32(6):1065-77.

12. Fetkovich, M.J., Vienot, M.E., Bradley, M.D., Kiesow, U.G. Decline Curve Analysis Using Type

Curves: Case Histories. SPE Formation Evaluation. 1987; 2(4):637-56.

13. Fetkovich, M. J., Reese, D. E. and Whitson, C.H., Application of a General Material Balance for

High-Pressure Gas Reservoirs. SPE Journal. 1998; 3(1):3-13.

14. Fraim, M.L and Wattenbarger, R. A. Gas reservoir decline-curve analysis using type curves with


15. Ibrahim, M., Wattenbarger, R. A. and Helmy, W. Determination of OGIP for Wells in

Pseudosteady-State-Old Techniques, New Approaches. paper SPE 84286 presented at the SPE

Annual Technical Conference and Exhibition, Denver, CO, 5-8 October 2003.

89

16. Moghadam, S., Jeje, O. and Mattar, L. Advanced Gas Material Balance in Simplified Format.

Journal of Canadian Petroleum Technology, 2011; 50(1):90-98

17. Palacio, J.C.a nd Blasingame, T.A. Decline curve analysis using type curves -analysis of gas well

production data. SPE Paper 25909 presented at the SPE Rocky Mountain Regional / Low

Permeability Reservoirs Symposium, Denver, CO, April 12-14. 1993.

90

Conclusions

A rigorous analytical derivation has been provided for the rescaled-exponential model originally

presented by Ayala H. and Ye (2012; 2013) which was used describe gas rate decline under a constant

bottomhole pressure (BHP) specification. This derivation provides a theoretical background for the new

generation of analysis techniques proposed by Ayala H. and Ye (2012; 2013) which enabled explicit

OGIP estimations by invoking the dimensionless viscosity-compressibility ratio approximation

as identified and documented in this work. This useful approximation connects the gas viscosity-

compressibility dependency with average reservoir density, material balance statements, and the

dimensionless parameter quantifying the strength of the coupling between viscosity and compressibility

values and fluid density. It also makes possible to circumvent the need for pseudo-pressure and pseudo-

time calculations during production data analysis for constant BHP data.

This study have also extended the applicability of the rescaled exponential model to variable flow-

rate/pressure-drop gas systems and provided the analytical expression modeling decline for varying

bottom-hole pressure conditions throughout the declining life of gas wells. By employing the proposed

equation, it is demonstrated that constant rate solution and constant BHP solution in the density-based

approach are interchangeable during BDF analysis. The proposed model is expressed in terms of density-

based variables and actual material-balance time rather than material-balance pseudo-time. Its ability to

forecast gas well performance under variable pressure-drop/flow-rate conditions was verified by applying

it to a number of numerical cases. Also, a density-based equation describing gas well performance under

variable flow-rate/pressure-drop specifications was also which eliminates the use of pseudo-time or

material-balance pseudo-time and provides convenient and reliable OGIP estimations. The proposed

production data analysis equation is written in two forms: straight-line and type-curve form and its

applicability to gas reservoir reserve estimation is fully verified by generating accurate OGIP estimation

for a number of numerical and field cases.

[1] Ayala H, L.F. and Ye, P. Analysis of Unsteady Responses of Natural Gas Reservoirs via a Universal Natural Gas Type-Curve

Formulation. SPE paper 159956 presented at the SPE Annual Technical Conference and Exhibition, San Antonio, TX, 8-10

October 2012.

[2] Ayala H, L.F. and Ye, P. Unified Decline Type-Curve Analysis for Natural Gas Wells in Boundary-Dominated Flow, SPE

Journal, 2013; 18 (1): 97-113.

91

In the last part of this work, we studied the applicability of the density-based methodologies to gas

systems with significant rock compressibility effects. On the basis of a modified material-balance

statement for gas reservoir with highly-compressible formation, we rigorously derive a compressibility

coefficient, , that can rigorously accounting for rock compressibility and corresponding porosity change

in gas reservoirs. The -ratio is a dimensionless parameter that incorporates the additional pressure

support provided by rock expansion. The validity of proposed -modified rescaled-exponential model is

further confirmed via gas rate forecasting result showing excellent matches against a number of numerical

simulation case studies which consider significantly large rock compressibility effects; and it is also

proved that the modified straight-line analysis employing provides accurate OGIP estimations for a

number of numerical simulation cases.

92

Appendix A: Diffusivity Equation for Gas System

For natural gas reservoirs, the analysis of production data is always performed under many constraints

because the significant changes of reservoir fluids properties under boundary-dominated flow. Some

efforts have been done to provide more accurate and rigorous modeling of these data. These authors

employed the concepts of “pseudo-functions” (pseudo-pressure and pseudo-time) to incorporate the

changes of gas viscosity and compressibility affected by depletion process. The mass conservation

equation for a single phase fluid flow through porous media is written as:

( )

( )

Equation A- 1

With the assumption that rock compressibility is negligible, combined this continuity equation and

Darcy’s law, the general diffusivity equation in terms of fluid density for a 1-D radial cylindrical system

can be written as:

(

)

Equation A- 2

For a constant viscosity and compressibility fluid, the general diffusivity equation becomes:

(

)

Equation A- 3

where represents for the fluid viscosity and compressibility that remains constant.

For liquid systems, Equation A-3 is linear and can be solved analytically in Laplacian space given by Van

Everdingen and Hurst (1949). For natural gas reservoirs, Equation A-2 cannot be easily solved because of

the strong dependence of gas viscosity and compressibility with pressure, especially during boundary-

dominated flow period when reservoir is in high level of depletion. To fully capture property changes of

reservoir gas and linearize Equation A-2, pseudo-pressure and pseudo-time are introduced and linearized

gas diffusivity equation is given by:

(

( )

)

( )

Equation A- 4

93

The pseudo-pressure m(p) function , first introduced by Al-Hussainy et al(1966)., is defined as:

( ) ∫

Equation A- 5

And pseudo-time, first introduced by Agarwal(1979) is defined as:

∫

Equation A- 6

The term is the product of reservoir gas viscosity and compressibility evaluated at the average

reservoir pressure at every time step. In the current petroleum and natural gas literature, is widely

treated as a weak non-linear term during infinite-acting period, and in this condition, , gas property

evaluated under initial condition and actual time are applied in modern well testing literature. However,

such approximation falls apart when boundary effects become significant and becomes a strong non-

linear term; thus, pseudo-time variable is introduced to rigorously linearize Equation A-2 with pseudo-

pressure so that gas diffusivity equation becomes analogous to liquid diffusivity equation (Equation A-3)

and can be solved analytically.

Additionally, several attempts have been made to make the pseudo-functions more convenient and avoid

weird units and magnitude by defining normalized pseudo-pressure and pseudo-time:

( )

∫

Equation A- 7

∫

Equation A- 8

which leads to the following linearization results of gas diffusivity equation:

(

( )

)

( )

Equation A- 9

94

With the re-defined pseudo-function variables, normalized pseudo-pressure and pseudo-time, the practice

of Equation A-9 become more convenient and friendlier with the normalized pseudo-function variables

share the same unit and magnitude of actual pressure and time. The disadvantage of using Equation A-9 is

the fact that it is required to calculate m(p) and as a function of pressure and actual time through

integration.

[1].Agarwal, R.G. “Real gas pseudo-time” - A New Function for Pressure Buildup Analysis of MHF Gas Wells, SPE paper 8279

presented in 54th SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada. 1979.

[2].Al-Hussainy, R., Ramey Jr., H.J., and Crawford, P.B. The Flow of Real Gases through Porous Media. Journal of Petroleum

Technology. 1966; 18(5):624-36.

[3].Van Everdingen, A.F. and Hurst, W. The application of the Laplace transformation to flow problems in reservoirs. Trans

AIME. 1949;186(12):305-24.

95

Appendix B: Derivation of Rate vs. Average Pseudo-pressure BDF Equation

The generalized density form of the diffusivity equation for the flow of fluids in porous media is:

( ) ( )

Equation B-1

After integrating Equation B-1 both sides over the entire reservoir volume, we have

∭ ( )

∭ ( )

Equation B-2

Gauss divergence theorem states that the volume integral of the divergence over the region inside the

surface is equal to the outward flux of a vector field through a closed surface. Thus, the left-hand-side of

Equation B-2 becomes:

∭ ( )

∬

Equation B-3

Applying Leibniz’s rule, the right-hand-side of Equation B-2 becomes:

∭ ( )

∭

( )

Equation B-4

where represents the volumetric-average density-porosity as

∭

. For volumetric gas

reservoir under BDF draining from the whole reservoir area, substitution of Equation B-4 into Equation

B-3 leads to the following equation for a radial-cylindrical system:

( )

(

)

Equation B-5

Introducing Darcy’s law and neglecting gravity effect, Equation B-1 can be written as:

96

(

)

( )

Equation B-6

Substituting the definition of pseudo-pressure defined in Equation A-5, Equation B-6 can be written as

following for a homogenous and isotropic system:

( )

( )

Equation B-7

where given ( )

. Combined with Equation B-4, integration of

Equation B-7 leads to:

∭ ( )

∭

( )

( )

Equation B- 3

For a 1-D radial-cylindrical system, ( )

(

( )

) and . Introducing boundary

conditions for BDF: ( ) @ and defining the system of study as the cylindrical volume

and surface between an arbitrary radius and , the left-hand-side of Equation B-5 becomes:

∭ ( )

∫

∫

∫

(

( )

)

( ) ( )

Equation B-8

In the meantime, the right-hand-side of Equation B-5 can be written as below given the defined system of

study has a time-invariant volume of ( ) :

( )

( )

[ (

)

Equation B-9

Substituting Equation B-8 and B-9 into Equation B-5

( )

( )

(

)

Equation B-10

Integration from wellbore to an arbitrary radius r leads to:

( ) ( )

( )

∫ (

)

( )

( )

[

(

)]

97

Equation B-11

Or integrating from wellbore to reservoir outer boundary,

( ) ( )

( )

∫ (

)

( )

( )

[

(

)]

Equation B-12

Substitute Equation B-5 in to right-hand side of Equation B-12 and applying , Equation B-12

becomes:

( ) ( )

[ (

)

]

Equation B-13

Thus, the gas BDF rate expression can be written in terms of ( ) and ( ) as:

[ (

) ]

( ( ) ( ))

Equation B-14

Alternatively, BDF rate expression can be written in terms of reservoir average condition ( ). The

average reservoir pseudo-pressure is defined as:

( )

∭ ( )

∫

∫

∫ ( )

∫ ( )

Equation B-15

Substituting Equation B-11 in to B-15,

( ) ( )

( )

∫ [

(

)]

Equation B-16

Substitution of Equation B-5 into B-16 and applying leads to:

( ) ( )

[ (

)

]

Equation B-17

which yields the BDF rate expression is:

[ (

) ]

( ( ) ( ))

Equation B-18

or,

98

[ (

) ]

( ( ) ( ))

Equation B-19

where is applied.

Introducing pseudo steady component bD,pss, rate-pseudo-pressure equation for gas well under BDF is

applied to any reservoir geometry:

( ( ) ( ))

Equation B-20

Equation B-20 can also be re written in terms of normalized pseudo-time as:

( ( ) ( ))

Equation B-21

99

Appendix C: Derivation of the Rate vs. Pseudo-time BDF Equation

Equation 1-1 can be written in terms of pseudo-pressure as follows (derivation provided in Appendix B):

( ( ) ( ))

Equation C- 1

where . Equation 1-27 states that the change of average fluid density with time during BDF

given by:

Equation C- 2

Substitution of Equation C-2 into Equation C-1 yields:

( ( ) ( ))

Equation C- 3

In the meantime, density derivative can be rewritten in terms of pseudo-pressure by invoking the

following transformation:

( )

Equation C- 4

Substitution of Equation C-4 into Equation C-3 leads to:

( )

( ( ) ( ))

Equation C- 5

( ) ( ) ( )

Equation C- 6

Integrating Equation C-6 from t=0 to t=t,

100

∫

( ) ( )

( )

( )

( )

∫

Equation C- 7

( ) ( )

( ) ( ) (

∫

)

Equation C- 8

Recall the definition of normalized pseudo-time given by Fraim and Wattenbarger (1987) given in

Equation 1-4:

∫

Equation C- 9

and by defining decline-curve dimensionless flow rate and dimensionless time as:

Equation C- 10

( ( ) ( ))

Equation C- 11

One arrives to Fraim and Wattenbarger’s key insight that gas production data should collapse to

Fetkovich’s liquid exponential stem (Fetkovich, 1980) when written in terms of normalized pseudo-time.

In dimensionless terms, the analytical expression is:

( )

Equation C- 12

which implies the following gas well deliverability in boundary-dominated flow (BDF) written in terms

of rate vs. pseudo-time:

( ( ) ( ))

(

)

Equation C- 13

[1].Fetkovich, M.J. Decline curve analysis using type curves. Journal of Petroleum Technology. 1980; 32(6):1065-77.

[2].Fraim, M.L.and Wattenbarger, R.A. Gas Reservoir Decline-Curve Analysis Using Type Curves with Real Gas Pseudo-

pressure And Normalized Time. SPE Formation Evaluation.1987; 2(4):671-82.

101

Appendix D: Derivation of the Rate vs. Material-balance Pseudo-time BDF

Equation

From the general material balance statement for volumetric gas reservoir, we have:

Equation D- 1

Equation D- 2

Recall the definition of pseudo-pressure in terms of gas density,

( ) ∫

Equation D- 3

Or:

( )

Equation D- 4

Substitution of Equation D-4 into Equation D-2 yields:

( )

Equation D- 5

Integration of Equation D-5 from t=0 to t=t leads to:

∫ ( ) ( )

( )

∫

Equation D- 6

Thus,

( ) ( )

∫

Equation D- 7

102

Or,

( ) ( )

∫

Equation D- 8

where ta represents for material-balance pseudo-time.

From gas rate BDF equation (Equation B-20):

( ( ) ( ))

Equation D- 9

Substitution of Equation D-9 into Equation D-7 leads to:

( ) ( )

Equation D- 10

Or Equation D-11 can be written in terms of normalized pseudo-pressure as follows:

( ) ( )

Equation D- 11

where

.

103

Appendix E: Derivation of Rate vs. Material-balance Time Equation for Oil

Well under BDF

The generalized density form of the diffusivity equation for the flow of fluids in porous media (gravity

effect is neglected) is:

( ) (

)

( )

Equation E- 1

The integration of this expression over the entire reservoir volume yields:

∭ ( )

∭ ( )

Equation E- 2

Gauss divergence theorem states that the volume integral of the divergence over the region inside the

surface is equal to the outward flux of a vector field through a closed surface. Thus, the left-hand-side of

Equation E-2 becomes:

∭ ( )

∬

Equation E-3

Applying Leibniz’s rule, the right-hand-side of Equation E-2 becomes:

∭ ( )

∭

( )

EquationE-4

where represents the volumetric-average density-porosity as

∭

. For volumetric oil

reservoir under BDF draining from the whole reservoir area, substitution of Equation E-4 into Equation

E-3 leads to the following equation for a radial-cylindrical system:

( )

(

)

Equation E-5

104

Assuming that fluid viscosity can be considered as a constant value (slightly compressible fluid),

Equation E-1 can be expressed as follows for a homogenous and isotropic reservoir:

( )

Equation E-6

Integration of Equation E-6 and combing Equation E-4, we have:

∭

∭

( )

( )

Equation E-7

For a 1-D radial-cylindrical system,

(

) and . Introducing boundary

conditions for BDF: @ and defining the system of study as the cylindrical volume and

surface between an arbitrary radius and , the left-hand-side of Equation E-7 is then written as:

∭

∫

∫

∫

(

)

( )

Equation E-8

In the meantime, the right-hand-side of Equation E-7 can be written as below given the defined system of

study has a time-invariant volume of ( ) :

( )

( )

[ (

)

Equation E-9

Combining Equation E-9 and Equation E-8:

( )

(

)

Equation E-10

Integration of Equation E-10 from wellbore to an arbitrary reservoir radius r leads to:

( )

∫ (

)

( )

[

(

)]

Equation E-11

In order to write Equation E-11 in terms of average reservoir conditions, average reservoir fluid density is

introduced as:

105

∭

∫

∫

∫

∫

Equation E-12

Substituting Equation E-11 in to E-12:

( )

∫ [

(

)]

Equation E- 13

Combining Equation E-5 and applying :

[ (

)

]

Equation E-14

To rewrite Equation E-14 in terms of reservoir pressure, divide both sides of Equation E-14 with average

reservoir fluid density :

[ (

)

]

Equation E-15

where applies. Considering a constant and small fluid compressibility (slightly compressible

fluid),

[ ( )], Equation E-15 then becomes:

[ (

)

]

Equation E-16

Rate BDF expression for oil system is then written as:

[ (

) ]

( )

Equation E-17

Introducing pseudo steady component bD,pss, Equation E-17 becomes:

( )

Equation E-18

106

In the meantime, applying definition of oil compressibility

(

) and rock compressibility

(

) , Equation E-5 becomes:

( )

Equation E-19

where total compressibility applies. Substituting of Equation E-19 into Equation E-5:

Equation E-20

Integration of Equation E-20 from t=0 to t=t:

∫

∫

( )

Equation E-21

Substitution of Equation E-21 into E-18 leads to:

Equation E-22

where .

107

Appendix F: Relationship between Superposition Pseudo-Time and Material-

Balance Pseudo-Time

Ibrahim’s pseudo-time (Ibrahim et al.,2003):

∫

Equation F-1

Ibrahim’s superposition pseudo-time (Ibrahim et al.,2003)::

∑

(

)

Equation F-2

Expand superposition pseudo-time as:

∑

(

)

[

( ) (

) ( )

(

) ( ) (

) ( )

(

)]

[

(

) (

)

(

)]

∫

Equation F-3

Thus, superposition pseudo-time is equivalent to material-balance pseudo-time.

[1].Ibrahim, M., Wattenbarger, R. A. and Helmy, W. Determination of OGIP for Wells in Pseudosteady-State-Old Techniques,

New Approaches. SPE paper 84286 presented at the SPE Annual Technical Conference and Exhibition, Denver, CO, 5-8

October 2003.

108

Appendix G: Procedures for BDF Gas Rate Forecasting

At time step 1, is calculated at initial reservoir condition,

( ) ( )

Equation G-1

And gas rate at time step 1 gas rate is given as:

( )

Equation G-2

Cumulative production at step 1 is calculated as:

Equation G-3

Calculate average reservoir density from material balance statement at time step 2:

(

)

Equation G-4

is calculated as:

( )

( ) ( )

Equation G-5

( )

Equation G-6

Continue the calculation as:

(

)

109

Equation G-7

( )

( ) ( )

Equation G-8

( )

Equation G-9

(

)( )

Equation G-10

110

Appendix H: Production Data for Case Studies

Chapter 1

Case Study I in Ayala H. and Ye (2012)

I(a) I(b) I(c)

pi=5000psia, pwf=100psia, T=200F, SG=0.55

t(day) qsc(SCFD) Gp(SCF) t(day) qsc(SCFD) Gp(SCF) t(day) qsc(SCFD) Gp(SCF)

0.01 2070849 20708.49 0.01 2072185 20721.85 0.01 2073500 20735

0.11 1193784 153856.8 0.11 1194252 153927.4 0.11 1194714 153997.1

0.22037 1089499 278434.6 0.220353 1089906 278533.3 0.220336 1090308 278630.7

0.434024 1005861 500146.5 0.433919 1006231 500235.8 0.433814 1006598 500323.6

0.892745 930278.7 940007.9 0.892372 930616.4 940001.5 0.892002 930950.4 939994.4

1.914333 861747.4 1846659 1.913179 862055.9 1846287 1.912037 862361.1 1845917

4.283673 799453.1 3795820 4.280261 799735.2 3794283 4.276874 800014.6 3792751

10.01054 742683.1 8169317 10.01138 742961.1 8172423 10.0014 743217.1 8167378

19.90399 699423.4 15259762 19.9268 702251.1 15291340 19.91568 702457.6 15287696

29.90399 669565.2 22085012 29.9268 680072.9 22183303 29.91568 680262.5 22181608

39.90399 643404.2 28634828 39.9268 665151.7 28897929 39.91568 665369.3 28898225

49.90399 619202.1 34934377 49.9268 653922.9 35485450 49.91568 654277.1 35488550

59.90399 596547.9 41000610 59.9268 644816.5 41973257 59.91568 645496.7 41981505

69.90399 575263 46847948 69.9268 637003.5 48377618 69.91568 638262.2 48395622

79.90399 555221.3 52489369 79.9268 630007.7 54708640 79.91568 632130.1 54743741

89.90399 536316.9 57936710 89.9268 623544.9 60972816 89.91568 626821.7 61035254

99.90399 518456.6 63200821 99.9268 617442.6 67174456 99.91568 622150.4 67277314

109.904 501557.1 68291679 109.9268 611595 73316542 109.9157 617985.8 73475538

119.904 485544.4 73218478 119.9268 605936.3 79401233 119.9157 614232.8 79634446

129.904 470351.5 77989710 129.9268 600425.4 85430177 129.9157 610820.1 85757748

139.904 455918.3 82613238 139.9268 595036.4 91404699 139.9157 607692.9 91848534

149.904 442190.4 87096357 149.9268 589752.3 97325919 149.9157 604807.8 97909411

159.904 429118.5 91445843 159.9268 584562.1 1.03E+08 159.9157 602129.9 1.04E+08

169.904 416658 95668009 169.9268 579458.2 1.09E+08 169.9157 599630.7 1.1E+08

179.904 404768.1 99768739 179.9268 574435.5 1.15E+08 179.9157 597286.6 1.16E+08

189.904 393411.5 1.04E+08 189.9268 569490 1.2E+08 189.9157 595077.7 1.22E+08

199.904 382554.4 1.08E+08 199.9268 564618.6 1.26E+08 199.9157 592987.2 1.28E+08

209.904 372165.5 1.11E+08 209.9268 559818.9 1.32E+08 209.9157 591000.8 1.34E+08

219.904 362216.4 1.15E+08 219.9268 555089 1.37E+08 219.9157 589106 1.4E+08

229.904 352680.5 1.19E+08 229.9268 550426.8 1.43E+08 229.9157 587292.2 1.46E+08

239.904 343533.8 1.22E+08 239.9268 545830.9 1.48E+08 239.9157 585550 1.51E+08

249.904 334753.9 1.25E+08 249.9268 541299.7 1.54E+08 249.9157 583871.4 1.57E+08

259.904 326320 1.29E+08 259.9268 536831.7 1.59E+08 259.9157 582249.3 1.63E+08

111

269.904 318213 1.32E+08 269.9268 532425.6 1.65E+08 269.9157 580677.4 1.69E+08

279.904 310415.1 1.35E+08 279.9268 528080.1 1.7E+08 279.9157 579150.4 1.75E+08

289.904 302909.8 1.38E+08 289.9268 523793.9 1.75E+08 289.9157 577663.4 1.8E+08

299.904 295681.8 1.41E+08 299.9268 519565.9 1.8E+08 299.9157 576212.3 1.86E+08

309.904 288716.8 1.44E+08 309.9268 515394.9 1.85E+08 309.9157 574793.3 1.92E+08

319.904 282001.4 1.47E+08 319.9268 511279.6 1.91E+08 319.9157 573403.1 1.98E+08

329.904 275523.2 1.5E+08 329.9268 507219.1 1.96E+08 329.9157 572039 2.03E+08

339.904 269270.5 1.52E+08 339.9268 503212.2 2.01E+08 339.9157 570698.4 2.09E+08

349.904 263232.5 1.55E+08 349.9268 499257.8 2.06E+08 349.9157 569378.9 2.15E+08

359.904 257399 1.58E+08 359.9268 495355.1 2.11E+08 359.9157 568078.7 2.21E+08

369.904 251760.3 1.6E+08 369.9268 491502.9 2.16E+08 369.9157 566795.9 2.26E+08

379.904 246307.5 1.63E+08 379.9268 487700.4 2.21E+08 379.9157 565529.1 2.32E+08

389.904 241032.1 1.65E+08 389.9268 483946.5 2.25E+08 389.9157 564276.9 2.38E+08

399.904 235926.2 1.68E+08 399.9268 480240.3 2.3E+08 399.9157 563037.9 2.43E+08

409.904 230982.3 1.7E+08 409.9268 476581.1 2.35E+08 409.9157 561811.3 2.49E+08

419.904 226193.3 1.72E+08 419.9268 472967.8 2.4E+08 419.9157 560595.9 2.54E+08

429.904 221552.7 1.74E+08 429.9268 469399.6 2.44E+08 429.9157 559391.1 2.6E+08

439.904 217054 1.77E+08 439.9268 465875.8 2.49E+08 439.9157 558195.9 2.66E+08

449.904 212691.3 1.79E+08 449.9268 462395.4 2.54E+08 449.9157 557009.9 2.71E+08

459.904 208459.1 1.81E+08 459.9268 458957.8 2.58E+08 459.9157 555832.2 2.77E+08

469.904 204352 1.83E+08 469.9268 455562.1 2.63E+08 469.9157 554662.6 2.82E+08

479.904 200365 1.85E+08 479.9268 452207.7 2.67E+08 479.9157 553500.3 2.88E+08

489.904 196493.2 1.87E+08 489.9268 448893.6 2.72E+08 489.9157 552345.2 2.93E+08

499.904 192732.3 1.89E+08 499.9268 445619.4 2.76E+08 499.9157 551196.7 2.99E+08

509.904 189077.8 1.91E+08 509.9268 442384.1 2.81E+08 509.9157 550054.7 3.04E+08

519.904 185525.6 1.93E+08 519.9268 439187.3 2.85E+08 519.9157 548918.6 3.1E+08

529.904 182072 1.94E+08 529.9268 436028.1 2.9E+08 529.9157 547788.4 3.15E+08

539.904 178713.2 1.96E+08 539.9268 432906 2.94E+08 539.9157 546663.7 3.21E+08

549.904 175445.6 1.98E+08 549.9268 429820.3 2.98E+08 549.9157 545544.4 3.26E+08

559.904 172266 2E+08 559.9268 426770.4 3.03E+08 559.9157 544430.3 3.32E+08

569.904 169171.2 2.02E+08 569.9268 423755.7 3.07E+08 569.9157 543321.2 3.37E+08

579.904 166158 2.03E+08 579.9268 420775.6 3.11E+08 579.9157 542216.9 3.43E+08

589.904 163223.6 2.05E+08 589.9268 417829.5 3.15E+08 589.9157 541117.3 3.48E+08

599.904 160365.3 2.06E+08 599.9268 414916.8 3.19E+08 599.9157 540022.3 3.53E+08

609.904 157580.4 2.08E+08 609.9268 412037.1 3.24E+08 609.9157 538931.8 3.59E+08

619.904 154866.3 2.1E+08 619.9268 409189.7 3.28E+08 619.9157 537845.7 3.64E+08

629.904 152220.6 2.11E+08 629.9268 406374.1 3.32E+08 629.9157 536763.8 3.7E+08

639.904 149641.1 2.13E+08 639.9268 403589.9 3.36E+08 639.9157 535686.1 3.75E+08

649.904 147125.5 2.14E+08 649.9268 400836.4 3.4E+08 649.9157 534612.6 3.8E+08

659.904 144671.7 2.16E+08 659.9268 398113.2 3.44E+08 659.9157 533543.1 3.86E+08

669.904 142277.7 2.17E+08 669.9268 395419.9 3.48E+08 669.9157 532477.6 3.91E+08

112

679.904 139941.5 2.18E+08 679.9268 392755.9 3.52E+08 679.9157 531416.1 3.96E+08

689.904 137661.2 2.2E+08 689.9268 390120.8 3.56E+08 689.9157 530358.4 4.02E+08

699.904 135435.2 2.21E+08 699.9268 387514.1 3.6E+08 699.9157 529304.5 4.07E+08

709.904 133261.6 2.23E+08 709.9268 384935.4 3.63E+08 709.9157 528254.4 4.12E+08

719.904 131138.8 2.24E+08 719.9268 382384.3 3.67E+08 719.9157 527208.1 4.17E+08

729.904 129065.2 2.25E+08 729.9268 379860.2 3.71E+08 729.9157 526165.4 4.23E+08

739.904 127039.4 2.26E+08 739.9268 377362.9 3.75E+08 739.9157 525126.4 4.28E+08

749.904 125059.8 2.28E+08 749.9268 374891.8 3.79E+08 749.9157 524091.1 4.33E+08

759.904 123125.1 2.29E+08 759.9268 372446.7 3.82E+08 759.9157 523059.3 4.38E+08

769.904 121233.9 2.3E+08 769.9268 370027 3.86E+08 769.9157 522031.1 4.44E+08

779.904 119385 2.31E+08 779.9268 367632.5 3.9E+08 779.9157 521006.4 4.49E+08

789.904 117577 2.33E+08 789.9268 365262.7 3.93E+08 789.9157 519985.3 4.54E+08

799.904 115808.7 2.34E+08 799.9268 362917.2 3.97E+08 799.9157 518967.6 4.59E+08

809.904 114079.1 2.35E+08 809.9268 360595.8 4.01E+08 809.9157 517953.3 4.64E+08

819.904 112386.9 2.36E+08 819.9268 358298 4.04E+08 819.9157 516942.5 4.7E+08

829.904 110731.2 2.37E+08 829.9268 356023.5 4.08E+08 829.9157 515935.1 4.75E+08

839.904 109110.8 2.38E+08 839.9268 353772 4.11E+08 839.9157 514931 4.8E+08

849.904 107524.8 2.39E+08 849.9268 351543.1 4.15E+08 849.9157 513930.4 4.85E+08

859.904 105972.3 2.4E+08 859.9268 349336.5 4.18E+08 859.9157 512933 4.9E+08

869.904 104452.2 2.41E+08 869.9268 347151.9 4.22E+08 869.9157 511939 4.95E+08

879.904 102963.8 2.42E+08 879.9268 344988.9 4.25E+08 879.9157 510948.3 5E+08

889.904 101506 2.43E+08 889.9268 342847.3 4.29E+08 889.9157 509960.8 5.06E+08

899.904 100078.2 2.44E+08 899.9268 340726.8 4.32E+08 899.9157 508976.6 5.11E+08

909.904 98679.41 2.45E+08 909.9268 338627 4.36E+08 909.9157 507995.7 5.16E+08

919.904 97308.96 2.46E+08 919.9268 336547.6 4.39E+08 919.9157 507017.9 5.21E+08

929.904 95966.05 2.47E+08 929.9268 334488.5 4.42E+08 929.9157 506043.4 5.26E+08

939.904 94649.97 2.48E+08 939.9268 332449.2 4.46E+08 939.9157 505072.1 5.31E+08

949.904 93360.01 2.49E+08 949.9268 330429.5 4.49E+08 949.9157 504103.9 5.36E+08

959.904 92095.48 2.5E+08 959.9268 328429.2 4.52E+08 959.9157 503138.9 5.41E+08

969.904 90855.73 2.51E+08 969.9268 326448 4.56E+08 969.9157 502177 5.46E+08

979.904 89640.12 2.52E+08 979.9268 324485.6 4.59E+08 979.9157 501218.2 5.51E+08

989.904 88448.04 2.53E+08 989.9268 322541.7 4.62E+08 989.9157 500262.6 5.56E+08

999.904 87278.87 2.54E+08 999.9268 320616.2 4.65E+08 999.9157 499310 5.61E+08

1009.904 86132.06 2.55E+08 1009.927 318708.7 4.68E+08 1009.916 498360.5 5.66E+08

1019.904 85007.03 2.56E+08 1019.927 316819 4.72E+08 1019.916 497414.1 5.71E+08

1029.904 83903.24 2.56E+08 1029.927 314946.9 4.75E+08 1029.916 496470.6 5.76E+08

1039.904 82820.17 2.57E+08 1039.927 313092.2 4.78E+08 1039.916 495530.3 5.81E+08

1049.904 81757.31 2.58E+08 1049.927 311254.6 4.81E+08 1049.916 494592.9 5.86E+08

1059.904 80714.16 2.59E+08 1059.927 309433.9 4.84E+08 1059.916 493658.5 5.91E+08

1069.904 79690.25 2.6E+08 1069.927 307629.8 4.87E+08 1069.916 492727.1 5.96E+08

1079.904 78685.1 2.6E+08 1079.927 305842.3 4.9E+08 1079.916 491798.7 6.01E+08

113

1089.904 77698.27 2.61E+08 1089.927 304070.9 4.93E+08 1089.916 490873.3 6.06E+08

1099.904 76729.33 2.62E+08 1099.927 302315.6 4.96E+08 1099.916 489950.7 6.11E+08

1109.904 75777.84 2.63E+08 1109.927 300576.1 4.99E+08 1109.916 489031.1 6.15E+08

1119.904 74843.39 2.63E+08 1119.927 298852.2 5.02E+08 1119.916 488114.4 6.2E+08

1129.904 73925.6 2.64E+08 1129.927 297143.7 5.05E+08 1129.916 487200.6 6.25E+08

1139.904 73024.06 2.65E+08 1139.927 295450.5 5.08E+08 1139.916 486289.7 6.3E+08

1149.904 72138.4 2.66E+08 1149.927 293772.3 5.11E+08 1149.916 485381.7 6.35E+08

1159.904 71268.26 2.66E+08 1159.927 292108.9 5.14E+08 1159.916 484476.5 6.4E+08

1169.904 70413.27 2.67E+08 1169.927 290460.2 5.17E+08 1169.916 483574.1 6.45E+08

1179.904 69573.11 2.68E+08 1179.927 288825.9 5.2E+08 1179.916 482674.6 6.49E+08

1189.904 68747.42 2.69E+08 1189.927 287205.9 5.23E+08 1189.916 481777.9 6.54E+08

1199.904 67935.88 2.69E+08 1199.927 285600.1 5.26E+08 1199.916 480884 6.59E+08

1209.904 67138.18 2.7E+08 1209.927 284008.2 5.29E+08 1209.916 479992.9 6.64E+08

1219.904 66354 2.71E+08 1219.927 282430 5.31E+08 1219.916 479104.5 6.69E+08

1229.904 65583.06 2.71E+08 1229.927 280865.5 5.34E+08 1229.916 478219 6.73E+08

1239.904 64825.05 2.72E+08 1239.927 279314.3 5.37E+08 1239.916 477336.1 6.78E+08

1249.904 64079.69 2.72E+08 1249.927 277776.5 5.4E+08 1249.916 476456.1 6.83E+08

1259.904 63346.71 2.73E+08 1259.927 276251.7 5.43E+08 1259.916 475578.7 6.88E+08

1269.904 62625.84 2.74E+08 1269.927 274739.9 5.45E+08 1269.916 474704 6.93E+08

1279.904 61916.81 2.74E+08 1279.927 273240.9 5.48E+08 1279.916 473832.1 6.97E+08

1289.904 61219.38 2.75E+08 1289.927 271754.5 5.51E+08 1289.916 472962.8 7.02E+08

1299.904 60533.29 2.76E+08 1299.927 270280.6 5.53E+08 1299.916 472096.2 7.07E+08

1309.904 59858.31 2.76E+08 1309.927 268819.1 5.56E+08 1309.916 471232.3 7.11E+08

1319.904 59194.2 2.77E+08 1319.927 267369.7 5.59E+08 1319.916 470371 7.16E+08

1329.904 58540.73 2.77E+08 1329.927 265932.4 5.62E+08 1329.916 469512.4 7.21E+08

1339.904 57897.68 2.78E+08 1339.927 264507 5.64E+08 1339.916 468656.4 7.26E+08

1349.904 57264.83 2.79E+08 1349.927 263093.4 5.67E+08 1349.916 467803 7.3E+08

1359.904 56641.97 2.79E+08 1359.927 261691.4 5.69E+08 1359.916 466952.2 7.35E+08

1369.904 56028.9 2.8E+08 1369.927 260300.9 5.72E+08 1369.916 466104 7.4E+08

1379.904 55425.41 2.8E+08 1379.927 258921.8 5.75E+08 1379.916 465258.3 7.44E+08

1389.904 54831.31 2.81E+08 1389.927 257553.9 5.77E+08 1389.916 464415.3 7.49E+08

1399.904 54246.41 2.81E+08 1399.927 256197.1 5.8E+08 1399.916 463574.8 7.53E+08

1409.904 53670.53 2.82E+08 1409.927 254851.2 5.82E+08 1409.916 462736.8 7.58E+08

1419.904 53103.47 2.82E+08 1419.927 253516.3 5.85E+08 1419.916 461901.4 7.63E+08

1429.904 52545.07 2.83E+08 1429.927 252192 5.87E+08 1429.916 461068.5 7.67E+08

1439.904 51995.15 2.83E+08 1439.927 250878.4 5.9E+08 1439.916 460238.1 7.72E+08

1449.904 51453.55 2.84E+08 1449.927 249575.2 5.92E+08 1449.916 459410.2 7.77E+08

1459.904 50920.09 2.84E+08 1459.927 248282.5 5.95E+08 1459.916 458584.8 7.81E+08

1469.904 50394.63 2.85E+08 1469.927 246999.9 5.97E+08 1469.916 457761.9 7.86E+08

1479.904 49877.01 2.85E+08 1479.927 245727.6 6E+08 1479.916 456941.4 7.9E+08

1489.904 49367.06 2.86E+08 1489.927 244465.2 6.02E+08 1489.916 456123.4 7.95E+08

114

1499.904 48864.65 2.86E+08 1499.927 243212.8 6.05E+08 1499.916 455307.8 7.99E+08

1509.904 48369.63 2.87E+08 1509.927 241970.1 6.07E+08 1509.916 454494.7 8.04E+08

1519.904 47881.85 2.87E+08 1519.927 240737.2 6.1E+08 1519.916 453684 8.09E+08

1529.904 47401.18 2.88E+08 1529.927 239513.9 6.12E+08 1529.916 452875.7 8.13E+08

1539.904 46927.49 2.88E+08 1539.927 238300 6.14E+08 1539.916 452069.8 8.18E+08

1549.904 46460.64 2.89E+08 1549.927 237095.6 6.17E+08 1549.916 451266.3 8.22E+08

1559.904 46000.5 2.89E+08 1559.927 235900.4 6.19E+08 1559.916 450465.1 8.27E+08

1569.904 45546.95 2.9E+08 1569.927 234714.4 6.21E+08 1569.916 449666.4 8.31E+08

1579.904 45099.86 2.9E+08 1579.927 233537.5 6.24E+08 1579.916 448870 8.36E+08

1589.904 44659.11 2.91E+08 1589.927 232369.6 6.26E+08 1589.916 448075.9 8.4E+08

1599.904 44224.6 2.91E+08 1599.927 231210.6 6.28E+08 1599.916 447284.2 8.45E+08

1609.904 43796.19 2.92E+08 1609.927 230060.3 6.31E+08 1609.916 446494.8 8.49E+08

1619.904 43373.78 2.92E+08 1619.927 228918.8 6.33E+08 1619.916 445707.7 8.53E+08

1629.904 42957.27 2.92E+08 1629.927 227785.9 6.35E+08 1629.916 444923 8.58E+08

1639.904 42546.53 2.93E+08 1639.927 226661.5 6.38E+08 1639.916 444140.5 8.62E+08

1649.904 42141.48 2.93E+08 1649.927 225545.6 6.4E+08 1649.916 443360.3 8.67E+08

1659.904 41742 2.94E+08 1659.927 224437.9 6.42E+08 1659.916 442582.4 8.71E+08

1669.904 41348 2.94E+08 1669.927 223338.6 6.44E+08 1669.916 441806.8 8.76E+08

1679.904 40959.38 2.95E+08 1679.927 222247.4 6.47E+08 1679.916 441033.4 8.8E+08

1689.904 40576.04 2.95E+08 1689.927 221164.3 6.49E+08 1689.916 440262.3 8.84E+08

1699.904 40197.88 2.95E+08 1699.927 220089.2 6.51E+08 1699.916 439493.4 8.89E+08

1709.904 39824.83 2.96E+08 1709.927 219022 6.53E+08 1709.916 438726.8 8.93E+08

1719.904 39456.78 2.96E+08 1719.927 217962.7 6.55E+08 1719.916 437962.4 8.98E+08

1729.904 39093.66 2.97E+08 1729.927 216911.1 6.58E+08 1729.916 437200.1 9.02E+08

1739.904 38735.36 2.97E+08 1739.927 215867.2 6.6E+08 1739.916 436440.1 9.06E+08

1749.904 38381.82 2.97E+08 1749.927 214830.9 6.62E+08 1749.916 435682.3 9.11E+08

1759.904 38032.95 2.98E+08 1759.927 213802.2 6.64E+08 1759.916 434926.6 9.15E+08

1769.904 37688.66 2.98E+08 1769.927 212780.9 6.66E+08 1769.916 434173.2 9.19E+08

1779.904 37348.89 2.98E+08 1779.927 211766.9 6.68E+08 1779.916 433421.9 9.24E+08

1789.904 37013.54 2.99E+08 1789.927 210760.3 6.7E+08 1789.916 432672.7 9.28E+08

1799.904 36682.56 2.99E+08 1799.927 209760.9 6.72E+08 1799.916 431925.7 9.32E+08

1809.904 36355.85 3E+08 1809.927 208768.6 6.75E+08 1809.916 431180.8 9.37E+08

1819.904 36033.36 3E+08 1819.927 207783.4 6.77E+08 1819.916 430438.1 9.41E+08

1829.904 35715.01 3E+08 1829.927 206805.3 6.79E+08 1829.916 429697.4 9.45E+08

1839.904 35400.73 3.01E+08 1839.927 205834.1 6.81E+08 1839.916 428958.9 9.5E+08

1849.904 35090.45 3.01E+08 1849.927 204869.7 6.83E+08 1849.916 428222.5 9.54E+08

1859.904 34784.11 3.01E+08 1859.927 203912.2 6.85E+08 1859.916 427488.2 9.58E+08

1869.904 34481.64 3.02E+08 1869.927 202961.4 6.87E+08 1869.916 426755.9 9.63E+08

1879.904 34182.98 3.02E+08 1879.927 202017.3 6.89E+08 1879.916 426025.8 9.67E+08

1889.904 33888.06 3.02E+08 1889.927 201079.8 6.91E+08 1889.916 425297.7 9.71E+08

1899.904 33596.82 3.03E+08 1899.927 200148.9 6.93E+08 1899.916 424571.6 9.75E+08

115

1909.904 33309.21 3.03E+08 1909.927 199224.4 6.95E+08 1909.916 423847.6 9.8E+08

1919.904 33025.17 3.03E+08 1919.927 198306.4 6.97E+08 1919.916 423125.6 9.84E+08

1929.904 32744.63 3.04E+08 1929.927 197394.7 6.99E+08 1929.916 422405.7 9.88E+08

1939.904 32467.54 3.04E+08 1939.927 196489.3 7.01E+08 1939.916 421687.8 9.92E+08

1949.904 32193.85 3.04E+08 1949.927 195590.2 7.03E+08 1949.916 420971.9 9.96E+08

1959.904 31923.5 3.05E+08 1959.927 194697.2 7.05E+08 1959.916 420258 1E+09

1969.904 31656.44 3.05E+08 1969.927 193810.4 7.07E+08 1969.916 419546.2 1E+09

1979.904 31392.62 3.05E+08 1979.927 192929.6 7.09E+08 1979.916 418836.3 1.01E+09

1989.904 31131.97 3.06E+08 1989.927 192054.9 7.11E+08 1989.916 418128.3 1.01E+09

1999.904 30874.47 3.06E+08 1999.927 191186.1 7.13E+08 1999.916 417422.4 1.02E+09

2009.904 30620.05 3.06E+08 2009.927 190323.1 7.14E+08 2009.916 416718.4 1.02E+09

2019.904 30368.66 3.07E+08 2019.927 189466.1 7.16E+08 2019.916 416016.4 1.03E+09

2029.904 30120.27 3.07E+08 2029.927 188614.8 7.18E+08 2029.916 415316.3 1.03E+09

2039.904 29874.82 3.07E+08 2039.927 187769.2 7.2E+08 2039.916 414618.2 1.03E+09

2049.904 29632.27 3.07E+08 2049.927 186929.3 7.22E+08 2049.916 413922 1.04E+09

2059.904 29392.57 3.08E+08 2059.927 186095.1 7.24E+08 2059.916 413227.7 1.04E+09

2069.904 29155.68 3.08E+08 2069.927 185266.4 7.26E+08 2069.916 412535.4 1.05E+09

2079.904 28921.56 3.08E+08 2079.927 184443.2 7.28E+08 2079.916 411844.9 1.05E+09

2089.904 28690.16 3.09E+08 2089.927 183625.6 7.29E+08 2089.916 411156.4 1.05E+09

2099.904 28461.44 3.09E+08 2099.927 182813.3 7.31E+08 2099.916 410469.7 1.06E+09

2109.904 28235.37 3.09E+08 2109.927 182006.4 7.33E+08 2109.916 409785 1.06E+09

2119.904 28011.9 3.09E+08 2119.927 181204.8 7.35E+08 2119.916 409102.1 1.07E+09

2129.904 27790.99 3.1E+08 2129.927 180408.6 7.37E+08 2129.916 408421.1 1.07E+09

2139.904 27572.61 3.1E+08 2139.927 179617.5 7.38E+08 2139.916 407741.9 1.08E+09

2149.904 27356.72 3.1E+08 2149.927 178831.6 7.4E+08 2149.916 407064.6 1.08E+09

2159.904 27143.28 3.11E+08 2159.927 178050.9 7.42E+08 2159.916 406389.2 1.08E+09

2169.904 26932.25 3.11E+08 2169.927 177275.2 7.44E+08 2169.916 405715.6 1.09E+09

2179.904 26723.6 3.11E+08 2179.927 176504.6 7.46E+08 2179.916 405043.8 1.09E+09

2189.904 26517.29 3.11E+08 2189.927 175739 7.47E+08 2189.916 404373.9 1.1E+09

2199.904 26313.29 3.12E+08 2199.927 174978.3 7.49E+08 2199.916 403705.8 1.1E+09

2209.904 26111.57 3.12E+08 2209.927 174222.6 7.51E+08 2209.916 403039.5 1.1E+09

2219.904 25912.09 3.12E+08 2219.927 173471.7 7.53E+08 2219.916 402374.9 1.11E+09

2229.904 25714.82 3.12E+08 2229.927 172725.6 7.54E+08 2229.916 401712.2 1.11E+09

2239.904 25519.73 3.13E+08 2239.927 171984.4 7.56E+08 2239.916 401051.3 1.12E+09

2249.904 25326.78 3.13E+08 2249.927 171247.8 7.58E+08 2249.916 400392.2 1.12E+09

2259.904 25135.95 3.13E+08 2259.927 170516 7.59E+08 2259.916 399734.8 1.12E+09

2269.904 24947.21 3.13E+08 2269.927 169788.8 7.61E+08 2269.916 399079.2 1.13E+09

2279.904 24760.52 3.14E+08 2279.927 169066.2 7.63E+08 2279.916 398425.4 1.13E+09

2289.904 24575.86 3.14E+08 2289.927 168348.2 7.65E+08 2289.916 397773.3 1.14E+09

2299.904 24393.19 3.14E+08 2299.927 167634.8 7.66E+08 2299.916 397123 1.14E+09

2309.904 24212.5 3.14E+08 2309.927 166925.8 7.68E+08 2309.916 396474.4 1.14E+09

116

2319.904 24033.74 3.15E+08 2319.927 166221.3 7.7E+08 2319.916 395827.6 1.15E+09

2329.904 23856.9 3.15E+08 2329.927 165521.2 7.71E+08 2329.916 395182.5 1.15E+09

2339.904 23681.95 3.15E+08 2339.927 164825.6 7.73E+08 2339.916 394539.1 1.16E+09

2349.904 23508.86 3.15E+08 2349.927 164134.2 7.75E+08 2349.916 393897.4 1.16E+09

2359.904 23337.6 3.16E+08 2359.927 163447.2 7.76E+08 2359.916 393257.4 1.16E+09

2369.904 23168.16 3.16E+08 2369.927 162764.4 7.78E+08 2369.916 392619.1 1.17E+09

2379.904 23000.5 3.16E+08 2379.927 162085.9 7.79E+08 2379.916 391982.6 1.17E+09

2389.904 22834.6 3.16E+08 2389.927 161411.5 7.81E+08 2389.916 391347.7 1.17E+09

2399.904 22670.44 3.16E+08 2399.927 160741.4 7.83E+08 2399.916 390714.5 1.18E+09

2409.904 22507.99 3.17E+08 2409.927 160075.3 7.84E+08 2409.916 390082.9 1.18E+09

2419.904 22347.23 3.17E+08 2419.927 159413.4 7.86E+08 2419.916 389453 1.19E+09

2429.904 22188.13 3.17E+08 2429.927 158755.5 7.87E+08 2429.916 388824.8 1.19E+09

2439.904 22030.68 3.17E+08 2439.927 158101.7 7.89E+08 2439.916 388198.3 1.19E+09

2449.904 21874.85 3.18E+08 2449.927 157451.8 7.91E+08 2449.916 387573.4 1.2E+09

2459.904 21720.62 3.18E+08 2459.927 156805.9 7.92E+08 2459.916 386950.1 1.2E+09

2469.904 21567.97 3.18E+08 2469.927 156163.9 7.94E+08 2469.916 386328.5 1.21E+09

2479.904 21416.87 3.18E+08 2479.927 155525.8 7.95E+08 2479.916 385708.5 1.21E+09

2489.904 21267.32 3.18E+08 2489.927 154891.6 7.97E+08 2489.916 385090.1 1.21E+09

2499.904 21119.27 3.19E+08 2499.927 154261.2 7.98E+08 2499.916 384473.4 1.22E+09

2509.904 20972.73 3.19E+08 2509.927 153634.6 8E+08 2509.916 383858.2 1.22E+09

2519.904 20827.66 3.19E+08 2519.927 153011.8 8.01E+08 2519.916 383244.7 1.23E+09

2529.904 20684.04 3.19E+08 2529.927 152392.8 8.03E+08 2529.916 382632.7 1.23E+09

2539.904 20541.87 3.19E+08 2539.927 151777.4 8.05E+08 2539.916 382022.4 1.23E+09

2549.904 20401.11 3.2E+08 2549.927 151165.7 8.06E+08 2549.916 381413.6 1.24E+09

2559.904 20261.75 3.2E+08 2559.927 150557.6 8.08E+08 2559.916 380806.5 1.24E+09

2569.904 20123.78 3.2E+08 2569.927 149953.2 8.09E+08 2569.916 380200.8 1.24E+09

2579.904 19987.17 3.2E+08 2579.927 149352.4 8.11E+08 2579.916 379596.8 1.25E+09

2589.904 19851.91 3.21E+08 2589.927 148755.1 8.12E+08 2589.916 378994.3 1.25E+09

2599.904 19717.97 3.21E+08 2599.927 148161.3 8.13E+08 2599.916 378393.4 1.26E+09

2609.904 19585.35 3.21E+08 2609.927 147571.1 8.15E+08 2609.916 377794 1.26E+09

2619.904 19454.02 3.21E+08 2619.927 146984.3 8.16E+08 2619.916 377196.2 1.26E+09

2629.904 19323.97 3.21E+08 2629.927 146401 8.18E+08 2629.916 376599.9 1.27E+09

2639.904 19195.19 3.21E+08 2639.927 145821.1 8.19E+08 2639.916 376005.2 1.27E+09

2649.904 19067.65 3.22E+08 2649.927 145244.5 8.21E+08 2649.916 375412 1.27E+09

2659.904 18941.34 3.22E+08 2659.927 144671.4 8.22E+08 2659.916 374820.3 1.28E+09

2669.904 18816.24 3.22E+08 2669.927 144101.6 8.24E+08 2669.916 374230.1 1.28E+09

2679.904 18692.35 3.22E+08 2679.927 143535.1 8.25E+08 2679.916 373641.4 1.29E+09

2689.904 18569.64 3.22E+08 2689.927 142971.9 8.27E+08 2689.916 373054.2 1.29E+09

2699.904 18448.1 3.23E+08 2699.927 142411.9 8.28E+08 2699.916 372468.6 1.29E+09

2709.904 18327.72 3.23E+08 2709.927 141855.2 8.29E+08 2709.916 371884.4 1.3E+09

2719.904 18208.47 3.23E+08 2719.927 141301.7 8.31E+08 2719.916 371301.7 1.3E+09

117

2729.904 18090.36 3.23E+08 2729.927 140751.4 8.32E+08 2729.916 370720.5 1.3E+09

2739.904 17973.35 3.23E+08 2739.927 140204.2 8.34E+08 2739.916 370140.8 1.31E+09

2749.904 17857.45 3.24E+08 2749.927 139660.2 8.35E+08 2749.916 369562.5 1.31E+09

2759.904 17742.63 3.24E+08 2759.927 139119.3 8.36E+08 2759.916 368985.7 1.32E+09

2769.904 17628.88 3.24E+08 2769.927 138581.5 8.38E+08 2769.916 368410.4 1.32E+09

2779.904 17516.2 3.24E+08 2779.927 138046.7 8.39E+08 2779.916 367836.5 1.32E+09

2789.904 17404.56 3.24E+08 2789.927 137515 8.41E+08 2789.916 367264.1 1.33E+09

2799.904 17293.95 3.24E+08 2799.927 136986.3 8.42E+08 2799.916 366693.1 1.33E+09

2809.904 17184.36 3.25E+08 2809.927 136460.6 8.43E+08 2809.916 366123.5 1.33E+09

2819.904 17075.79 3.25E+08 2819.927 135937.9 8.45E+08 2819.916 365555.4 1.34E+09

2829.904 16968.21 3.25E+08 2829.927 135418.1 8.46E+08 2829.916 364988.7 1.34E+09

2839.904 16861.61 3.25E+08 2839.927 134901.2 8.47E+08 2839.916 364423.5 1.34E+09

2849.904 16755.99 3.25E+08 2849.927 134387.3 8.49E+08 2849.916 363859.6 1.35E+09

2859.904 16651.33 3.25E+08 2859.927 133876.2 8.5E+08 2859.916 363297.2 1.35E+09

2869.904 16547.62 3.26E+08 2869.927 133368 8.51E+08 2869.916 362736.2 1.36E+09

2879.904 16444.84 3.26E+08 2879.927 132862.6 8.53E+08 2879.916 362176.6 1.36E+09

2889.904 16343 3.26E+08 2889.927 132360 8.54E+08 2889.916 361618.3 1.36E+09

2899.904 16242.07 3.26E+08 2899.927 131860.3 8.55E+08 2899.916 361061.5 1.37E+09

2909.904 16142.04 3.26E+08 2909.927 131363.3 8.57E+08 2909.916 360506.1 1.37E+09

2919.904 16042.91 3.26E+08 2919.927 130869 8.58E+08 2919.916 359952 1.37E+09

2929.904 15944.67 3.27E+08 2929.927 130377.5 8.59E+08 2929.916 359399.3 1.38E+09

2939.904 15847.3 3.27E+08 2939.927 129888.8 8.61E+08 2939.916 358848 1.38E+09

2949.904 15750.79 3.27E+08 2949.927 129402.7 8.62E+08 2949.916 358298.1 1.38E+09

2959.904 15655.14 3.27E+08 2959.927 128919.2 8.63E+08 2959.916 357749.5 1.39E+09

2969.904 15560.33 3.27E+08 2969.927 128438.5 8.65E+08 2969.916 357202.3 1.39E+09

2979.904 15466.36 3.27E+08 2979.927 127960.3 8.66E+08 2979.916 356656.4 1.4E+09

2989.904 15373.21 3.27E+08 2989.927 127484.8 8.67E+08 2989.916 356111.9 1.4E+09

2999.904 15280.88 3.28E+08 2999.927 127011.9 8.68E+08 2999.916 355568.7 1.4E+09

3009.904 15189.35 3.28E+08 3009.927 126541.6 8.7E+08 3009.916 355026.8 1.41E+09

3019.904 15098.62 3.28E+08 3019.927 126073.8 8.71E+08 3019.916 354486.3 1.41E+09

3029.904 15008.68 3.28E+08 3029.927 125608.5 8.72E+08 3029.916 353947.1 1.41E+09

3039.904 14919.51 3.28E+08 3039.927 125145.8 8.73E+08 3039.916 353409.3 1.42E+09

3049.904 14831.12 3.28E+08 3049.927 124685.6 8.75E+08 3049.916 352872.7 1.42E+09

3059.904 14743.48 3.29E+08 3059.927 124227.8 8.76E+08 3059.916 352337.5 1.42E+09

3069.904 14656.6 3.29E+08 3069.927 123772.5 8.77E+08 3069.916 351803.6 1.43E+09

3079.904 14570.46 3.29E+08 3079.927 123319.7 8.78E+08 3079.916 351271 1.43E+09

3089.904 14485.06 3.29E+08 3089.927 122869.3 8.8E+08 3089.916 350739.7 1.43E+09

3099.904 14400.39 3.29E+08 3099.927 122421.3 8.81E+08 3099.916 350209.6 1.44E+09

3109.904 14316.43 3.29E+08 3109.927 121975.7 8.82E+08 3109.916 349680.9 1.44E+09

3119.904 14233.19 3.29E+08 3119.927 121532.5 8.83E+08 3119.916 349153.5 1.44E+09

3129.904 14150.65 3.3E+08 3129.927 121091.7 8.84E+08 3129.916 348627.3 1.45E+09

118

3139.904 14068.81 3.3E+08 3139.927 120653.2 8.86E+08 3139.916 348102.4 1.45E+09

3149.904 13987.65 3.3E+08 3149.927 120217 8.87E+08 3149.916 347578.8 1.46E+09

3159.904 13907.17 3.3E+08 3159.927 119783.1 8.88E+08 3159.916 347056.5 1.46E+09

3169.904 13827.37 3.3E+08 3169.927 119351.6 8.89E+08 3169.916 346535.4 1.46E+09

3179.904 13748.23 3.3E+08 3179.927 118922.3 8.9E+08 3179.916 346015.6 1.47E+09

3189.904 13669.75 3.3E+08 3189.927 118495.2 8.92E+08 3189.916 345497 1.47E+09

3199.904 13591.92 3.31E+08 3199.927 118070.5 8.93E+08 3199.916 344979.7 1.47E+09

3209.904 13514.74 3.31E+08 3209.927 117647.9 8.94E+08 3209.916 344463.6 1.48E+09

3219.904 13438.19 3.31E+08 3219.927 117227.6 8.95E+08 3219.916 343948.8 1.48E+09

3229.904 13362.28 3.31E+08 3229.927 116809.4 8.96E+08 3229.916 343435.2 1.48E+09

3239.904 13286.98 3.31E+08 3239.927 116393.5 8.98E+08 3239.916 342922.9 1.49E+09

3249.904 13212.31 3.31E+08 3249.927 115979.7 8.99E+08 3249.916 342411.7 1.49E+09

3259.904 13138.24 3.31E+08 3259.927 115568.1 9E+08 3259.916 341901.8 1.49E+09

3269.904 13064.77 3.31E+08 3269.927 115158.6 9.01E+08 3269.916 341393.2 1.5E+09

3279.904 12991.91 3.32E+08 3279.927 114751.2 9.02E+08 3279.916 340885.7 1.5E+09

Case Study II in Ayala H. and Ye (2012)

II(b) II(c)

pi=5000psia, T=200F, SG=0.55

pwf=1600psia pwf=3200psia

t(day) qsc(SCFD) Gp(SCF) t(day) qsc(SCFD) Gp(SCF)

0.01 1775870 17758.7 0.01 1052698 10526.98

0.11 1032311 132747.6 0.112017 617021.2 80519.75

0.234018 936183.6 253260.9 0.372702 532763.4 226617.9

0.514355 855034.9 501393 1.420148 462969.6 735084.8

1.1939 782678.9 1051327 6.155704 404585.2 2737655

2.924358 717918.8 2334412 16.1557 373018.2 6581663

7.575083 659782.6 5500103 26.1557 358952.1 10227986

17.19333 616455.8 11585277 36.1557 350109.1 13766129

27.19333 594409.7 17618967 46.1557 343737.6 17230692

37.19333 580245.2 23480927 56.1557 338794 20639955

47.19333 569932.8 29224321 66.1557 334775.2 24005166

57.19333 561882.7 34877902 76.1557 331401.4 27333912

67.19333 555312.5 40459588 86.1557 328501.7 30631640

77.19333 549781.3 45981564 96.1557 325964.4 33902439

87.19333 545017.6 51452628 106.1557 323712.5 37149488

97.19333 540842.6 56879413 116.1557 321690.6 40375321

107.1933 537132.4 62267090 126.1557 319857.8 43582005

117.1933 533797.9 67619794 136.1557 318182.6 46771250

119

127.1933 530772.6 72940902 146.1557 316640.5 49944493

137.1933 528005.7 78233214 156.1557 315212 53102955

147.1933 525457.2 83499088 166.1557 313881 56247680

157.1933 523095.4 88740528 176.1557 312634.3 59379568

167.1933 520894.1 93959252 186.1557 311460.9 62499401

177.1933 518831.9 99156744 196.1557 310351.6 65607860

187.1933 516890.7 1.04E+08 206.1557 309298.2 68705539

197.1933 515055.4 1.09E+08 216.1557 308294 71792960

207.1933 513312.9 1.15E+08 226.1557 307333.2 74870582

217.1933 511652.1 1.2E+08 236.1557 306410.5 77938809

227.1933 510063.4 1.25E+08 246.1557 305521.5 80997998

237.1933 508538.3 1.3E+08 256.1557 304662.4 84048465

247.1933 507069.7 1.35E+08 266.1557 303829.8 87090489

257.1933 505651.2 1.4E+08 276.1557 303020.6 90124318

267.1933 504277.1 1.45E+08 286.1557 302232.4 93150172

277.1933 502942.7 1.5E+08 296.1557 301462.7 96168248

287.1933 501643.6 1.55E+08 306.1557 300709.7 99178721

297.1933 500376.1 1.6E+08 316.1557 299971.5 1.02E+08

307.1933 499136.9 1.65E+08 326.1557 299246.5 1.05E+08

317.1933 497923 1.7E+08 336.1557 298533.5 1.08E+08

327.1933 496731.9 1.75E+08 346.1557 297831.3 1.11E+08

337.1933 495561.3 1.8E+08 356.1557 297138.6 1.14E+08

347.1933 494409.3 1.85E+08 366.1557 296454.7 1.17E+08

357.1933 493274 1.9E+08 376.1557 295778.7 1.2E+08

367.1933 492153.9 1.95E+08 386.1557 295109.9 1.23E+08

377.1933 491047.6 2E+08 396.1557 294447.6 1.26E+08

387.1933 489953.9 2.05E+08 406.1557 293791.2 1.29E+08

397.1933 488871.8 2.1E+08 416.1557 293140.4 1.32E+08

407.1933 487800.2 2.15E+08 426.1557 292494.6 1.35E+08

417.1933 486738.4 2.19E+08 436.1557 291853.4 1.38E+08

427.1933 485685.6 2.24E+08 446.1557 291216.5 1.41E+08

437.1933 484641 2.29E+08 456.1557 290583.7 1.44E+08

447.1933 483604.3 2.34E+08 466.1557 289954.6 1.46E+08

457.1933 482574.7 2.39E+08 476.1557 289328.9 1.49E+08

467.1933 481551.9 2.44E+08 486.1557 288706.6 1.52E+08

477.1933 480535.5 2.48E+08 496.1557 288087.3 1.55E+08

487.1933 479525.1 2.53E+08 506.1557 287471 1.58E+08

497.1933 478520.3 2.58E+08 516.1557 286857.5 1.61E+08

507.1933 477520.9 2.63E+08 526.1557 286246.6 1.64E+08

517.1933 476526.6 2.68E+08 536.1557 285638.3 1.67E+08

527.1933 475537.3 2.72E+08 546.1557 285032.5 1.69E+08

120

537.1933 474552.6 2.77E+08 556.1557 284428.9 1.72E+08

547.1933 473572.4 2.82E+08 566.1557 283827.7 1.75E+08

557.1933 472596.6 2.87E+08 576.1557 283228.6 1.78E+08

567.1933 471625 2.91E+08 586.1557 282631.7 1.81E+08

577.1933 470657.4 2.96E+08 596.1557 282036.9 1.84E+08

587.1933 469693.8 3.01E+08 606.1557 281444.1 1.86E+08

597.1933 468734 3.05E+08 616.1557 280853.2 1.89E+08

607.1933 467778 3.1E+08 626.1557 280264.3 1.92E+08

617.1933 466825.7 3.15E+08 636.1557 279677.3 1.95E+08

627.1933 465876.9 3.19E+08 646.1557 279092.2 1.98E+08

637.1933 464931.6 3.24E+08 656.1557 278508.9 2E+08

647.1933 463989.8 3.29E+08 666.1557 277927.4 2.03E+08

657.1933 463051.4 3.33E+08 676.1557 277347.7 2.06E+08

667.1933 462116.4 3.38E+08 686.1557 276769.7 2.09E+08

677.1933 461184.6 3.43E+08 696.1557 276193.5 2.11E+08

687.1933 460256.1 3.47E+08 706.1557 275619 2.14E+08

697.1933 459330.7 3.52E+08 716.1557 275046.2 2.17E+08

707.1933 458408.6 3.56E+08 726.1557 274475.1 2.2E+08

717.1933 457489.5 3.61E+08 736.1557 273905.6 2.22E+08

727.1933 456573.6 3.66E+08 746.1557 273337.8 2.25E+08

737.1933 455660.7 3.7E+08 756.1557 272771.7 2.28E+08

747.1933 454750.9 3.75E+08 766.1557 272207.2 2.31E+08

757.1933 453844.1 3.79E+08 776.1557 271644.2 2.33E+08

767.1933 452940.2 3.84E+08 786.1557 271082.9 2.36E+08

777.1933 452039.3 3.88E+08 796.1557 270523.2 2.39E+08

787.1933 451141.4 3.93E+08 806.1557 269965.1 2.42E+08

797.1933 450246.4 3.97E+08 816.1557 269408.6 2.44E+08

807.1933 449354.2 4.02E+08 826.1557 268853.6 2.47E+08

817.1933 448465 4.06E+08 836.1557 268300.1 2.5E+08

827.1933 447578.6 4.11E+08 846.1557 267748.3 2.52E+08

837.1933 446695 4.15E+08 856.1557 267197.9 2.55E+08

847.1933 445814.3 4.2E+08 866.1557 266649.2 2.58E+08

857.1933 444936.4 4.24E+08 876.1557 266101.9 2.6E+08

867.1933 444061.2 4.29E+08 886.1557 265556.1 2.63E+08

877.1933 443188.9 4.33E+08 896.1557 265011.9 2.66E+08

887.1933 442319.2 4.37E+08 906.1557 264469.2 2.68E+08

897.1933 441452.4 4.42E+08 916.1557 263927.9 2.71E+08

907.1933 440588.2 4.46E+08 926.1557 263388.2 2.74E+08

917.1933 439726.8 4.51E+08 936.1557 262850 2.76E+08

927.1933 438868 4.55E+08 946.1557 262313.2 2.79E+08

937.1933 438012 4.59E+08 956.1557 261777.9 2.81E+08

121

947.1933 437158.6 4.64E+08 966.1557 261244.1 2.84E+08

957.1933 436307.8 4.68E+08 976.1557 260711.7 2.87E+08

967.1933 435459.8 4.73E+08 986.1557 260180.8 2.89E+08

977.1933 434614.3 4.77E+08 996.1557 259651.3 2.92E+08

987.1933 433771.5 4.81E+08 1006.156 259123.3 2.94E+08

997.1933 432931.2 4.86E+08 1016.156 258596.7 2.97E+08

1007.193 432093.6 4.9E+08 1026.156 258071.6 3E+08

1017.193 431258.5 4.94E+08 1036.156 257547.9 3.02E+08

1027.193 430426 4.98E+08 1046.156 257025.6 3.05E+08

1037.193 429596.1 5.03E+08 1056.156 256504.7 3.07E+08

1047.193 428768.7 5.07E+08 1066.156 255985.2 3.1E+08

1057.193 427943.8 5.11E+08 1076.156 255467.2 3.12E+08

1067.193 427121.4 5.16E+08 1086.156 254950.5 3.15E+08

1077.193 426301.6 5.2E+08 1096.156 254435.3 3.18E+08

1087.193 425484.3 5.24E+08 1106.156 253921.4 3.2E+08

1097.193 424669.4 5.28E+08 1116.156 253408.9 3.23E+08

1107.193 423857 5.33E+08 1126.156 252897.8 3.25E+08

1117.193 423047.1 5.37E+08 1136.156 252388 3.28E+08

1127.193 422239.6 5.41E+08 1146.156 251879.7 3.3E+08

1137.193 421434.6 5.45E+08 1156.156 251372.7 3.33E+08

1147.193 420632 5.5E+08 1166.156 250867 3.35E+08

1157.193 419831.8 5.54E+08 1176.156 250362.7 3.38E+08

1167.193 419034 5.58E+08 1186.156 249859.8 3.4E+08

1177.193 418238.7 5.62E+08 1196.156 249358.2 3.43E+08

1187.193 417445.7 5.66E+08 1206.156 248857.9 3.45E+08

1197.193 416655.1 5.7E+08 1216.156 248359 3.48E+08

1207.193 415866.8 5.75E+08 1226.156 247861.4 3.5E+08

1217.193 415080.9 5.79E+08 1236.156 247365.1 3.53E+08

1227.193 414297.4 5.83E+08 1246.156 246870.1 3.55E+08

1237.193 413516.1 5.87E+08 1256.156 246376.5 3.58E+08

1247.193 412737.3 5.91E+08 1266.156 245884.1 3.6E+08

1257.193 411960.7 5.95E+08 1276.156 245393.1 3.62E+08

1267.193 411186.4 5.99E+08 1286.156 244903.4 3.65E+08

1277.193 410414.4 6.04E+08 1296.156 244415 3.67E+08

1287.193 409644.7 6.08E+08 1306.156 243927.8 3.7E+08

1297.193 408877.3 6.12E+08 1316.156 243441.9 3.72E+08

1307.193 408112.1 6.16E+08 1326.156 242957.4 3.75E+08

1317.193 407349.2 6.2E+08 1336.156 242474.1 3.77E+08

1327.193 406588.6 6.24E+08 1346.156 241992 3.8E+08

1337.193 405830.1 6.28E+08 1356.156 241511.3 3.82E+08

1347.193 405073.9 6.32E+08 1366.156 241031.8 3.84E+08

122

1357.193 404319.9 6.36E+08 1376.156 240553.5 3.87E+08

1367.193 403568.2 6.4E+08 1386.156 240076.5 3.89E+08

1377.193 402818.6 6.44E+08 1396.156 239600.8 3.92E+08

1387.193 402071.2 6.48E+08 1406.156 239126.3 3.94E+08

1397.193 401325.9 6.52E+08 1416.156 238653 3.96E+08

1407.193 400582.9 6.56E+08 1426.156 238181 3.99E+08

1417.193 399842 6.6E+08 1436.156 237710.2 4.01E+08

1427.193 399103.2 6.64E+08 1446.156 237240.7 4.04E+08

1437.193 398366.6 6.68E+08 1456.156 236772.3 4.06E+08

1447.193 397632.2 6.72E+08 1466.156 236305.2 4.08E+08

1457.193 396899.8 6.76E+08 1476.156 235839.3 4.11E+08

1467.193 396169.6 6.8E+08 1486.156 235374.6 4.13E+08

1477.193 395441.4 6.84E+08 1496.156 234911.1 4.15E+08

1487.193 394715.4 6.88E+08 1506.156 234448.8 4.18E+08

1497.193 393991.4 6.92E+08 1516.156 233987.7 4.2E+08

1507.193 393269.6 6.96E+08 1526.156 233527.8 4.22E+08

1517.193 392549.8 7E+08 1536.156 233069.1 4.25E+08

1527.193 391832 7.04E+08 1546.156 232611.5 4.27E+08

1537.193 391116.3 7.08E+08 1556.156 232155.2 4.29E+08

1547.193 390402.7 7.12E+08 1566.156 231700 4.32E+08

1557.193 389691 7.16E+08 1576.156 231246 4.34E+08

1567.193 388981.5 7.19E+08 1586.156 230793.1 4.36E+08

1577.193 388273.9 7.23E+08 1596.156 230341.5 4.39E+08

1587.193 387568.3 7.27E+08 1606.156 229891 4.41E+08

1597.193 386864.8 7.31E+08 1616.156 229441.6 4.43E+08

1607.193 386163.2 7.35E+08 1626.156 228993.4 4.45E+08

1617.193 385463.6 7.39E+08 1636.156 228546.3 4.48E+08

1627.193 384766 7.43E+08 1646.156 228100.4 4.5E+08

1637.193 384070.3 7.46E+08 1656.156 227655.6 4.52E+08

1647.193 383376.7 7.5E+08 1666.156 227212 4.55E+08

1657.193 382684.9 7.54E+08 1676.156 226769.4 4.57E+08

1667.193 381995.1 7.58E+08 1686.156 226328 4.59E+08

1677.193 381307.3 7.62E+08 1696.156 225887.8 4.61E+08

1687.193 380621.4 7.66E+08 1706.156 225448.6 4.64E+08

1697.193 379937.4 7.69E+08 1716.156 225010.6 4.66E+08

1707.193 379255.3 7.73E+08 1726.156 224573.7 4.68E+08

1717.193 378575.1 7.77E+08 1736.156 224137.9 4.7E+08

1727.193 377896.8 7.81E+08 1746.156 223703.2 4.73E+08

1737.193 377220.4 7.85E+08 1756.156 223269.6 4.75E+08

1747.193 376545.9 7.88E+08 1766.156 222837 4.77E+08

1757.193 375873.2 7.92E+08 1776.156 222405.6 4.79E+08

123

1767.193 375202.5 7.96E+08 1786.156 221975.3 4.82E+08

1777.193 374533.5 8E+08 1796.156 221546 4.84E+08

1787.193 373866.5 8.03E+08 1806.156 221117.9 4.86E+08

1797.193 373201.2 8.07E+08 1816.156 220690.8 4.88E+08

1807.193 372537.8 8.11E+08 1826.156 220264.8 4.9E+08

1817.193 371876.3 8.14E+08 1836.156 219839.8 4.93E+08

1827.193 371216.5 8.18E+08 1846.156 219416 4.95E+08

1837.193 370558.6 8.22E+08 1856.156 218993.1 4.97E+08

1847.193 369902.5 8.26E+08 1866.156 218571.4 4.99E+08

1857.193 369248.2 8.29E+08 1876.156 218150.7 5.01E+08

1867.193 368595.6 8.33E+08 1886.156 217731.1 5.04E+08

1877.193 367944.9 8.37E+08 1896.156 217312.5 5.06E+08

1887.193 367295.9 8.4E+08 1906.156 216894.9 5.08E+08

1897.193 366648.7 8.44E+08 1916.156 216478.4 5.1E+08

1907.193 366003.3 8.48E+08 1926.156 216062.9 5.12E+08

1917.193 365359.6 8.51E+08 1936.156 215648.5 5.14E+08

1927.193 364717.7 8.55E+08 1946.156 215235.1 5.16E+08

1937.193 364077.5 8.59E+08 1956.156 214822.7 5.19E+08

1947.193 363439 8.62E+08 1966.156 214411.3 5.21E+08

1957.193 362802.3 8.66E+08 1976.156 214001 5.23E+08

1967.193 362167.3 8.7E+08 1986.156 213591.7 5.25E+08

1977.193 361534.1 8.73E+08 1996.156 213183.4 5.27E+08

1987.193 360902.5 8.77E+08 2006.156 212776.1 5.29E+08

1997.193 360272.6 8.8E+08 2016.156 212369.8 5.31E+08

2007.193 359644.4 8.84E+08 2026.156 211964.5 5.34E+08

2017.193 359017.9 8.88E+08 2036.156 211560.2 5.36E+08

2027.193 358393.1 8.91E+08 2046.156 211157 5.38E+08

2037.193 357770 8.95E+08 2056.156 210754.7 5.4E+08

2047.193 357148.6 8.98E+08 2066.156 210353.4 5.42E+08

2057.193 356528.8 9.02E+08 2076.156 209953 5.44E+08

2067.193 355910.6 9.05E+08 2086.156 209553.7 5.46E+08

2077.193 355294.1 9.09E+08 2096.156 209155.4 5.48E+08

2087.193 354679.3 9.13E+08 2106.156 208758 5.5E+08

2097.193 354066.1 9.16E+08 2116.156 208361.6 5.52E+08

2107.193 353454.5 9.2E+08 2126.156 207966.2 5.55E+08

2117.193 352844.5 9.23E+08 2136.156 207571.7 5.57E+08

2127.193 352236.2 9.27E+08 2146.156 207178.2 5.59E+08

2137.193 351629.5 9.3E+08 2156.156 206785.7 5.61E+08

2147.193 351024.3 9.34E+08 2166.156 206394.1 5.63E+08

2157.193 350420.8 9.37E+08 2176.156 206003.5 5.65E+08

2167.193 349818.9 9.41E+08 2186.156 205613.8 5.67E+08

124

2177.193 349218.5 9.44E+08 2196.156 205225.1 5.69E+08

2187.193 348619.8 9.48E+08 2206.156 204837.3 5.71E+08

2197.193 348022.6 9.51E+08 2216.156 204450.5 5.73E+08

2207.193 347427 9.55E+08 2226.156 204064.6 5.75E+08

2217.193 346832.9 9.58E+08 2236.156 203679.6 5.77E+08

2227.193 346240.4 9.62E+08 2246.156 203295.6 5.79E+08

2237.193 345649.5 9.65E+08 2256.156 202912.5 5.81E+08

2247.193 345060.1 9.68E+08 2266.156 202530.3 5.83E+08

2257.193 344472.2 9.72E+08 2276.156 202149.1 5.85E+08

2267.193 343885.9 9.75E+08 2286.156 201768.8 5.87E+08

2277.193 343301.1 9.79E+08 2296.156 201389.4 5.89E+08

2287.193 342717.8 9.82E+08 2306.156 201010.9 5.91E+08

2297.193 342136 9.86E+08 2316.156 200633.3 5.93E+08

2307.193 341555.8 9.89E+08 2326.156 200256.6 5.95E+08

2317.193 340977 9.92E+08 2336.156 199880.9 5.97E+08

2327.193 340399.8 9.96E+08 2346.156 199506 5.99E+08

2337.193 339824 9.99E+08 2356.156 199132 6.01E+08

2347.193 339249.7 1E+09 2366.156 198759 6.03E+08

2357.193 338676.9 1.01E+09 2376.156 198386.8 6.05E+08

2367.193 338105.6 1.01E+09 2386.156 198015.5 6.07E+08

2377.193 337535.8 1.01E+09 2396.156 197645.2 6.09E+08

2387.193 336967.4 1.02E+09 2406.156 197275.7 6.11E+08

2397.193 336400.5 1.02E+09 2416.156 196907 6.13E+08

2407.193 335835 1.02E+09 2426.156 196539.3 6.15E+08

2417.193 335271 1.03E+09 2436.156 196172.4 6.17E+08

2427.193 334708.5 1.03E+09 2446.156 195806.5 6.19E+08

2437.193 334147.3 1.03E+09 2456.156 195441.3 6.21E+08

2447.193 333587.7 1.04E+09 2466.156 195077.1 6.23E+08

2457.193 333029.4 1.04E+09 2476.156 194713.7 6.25E+08

2467.193 332472.5 1.04E+09 2486.156 194351.2 6.27E+08

2477.193 331917.1 1.05E+09 2496.156 193989.6 6.29E+08

2487.193 331363.1 1.05E+09 2506.156 193628.8 6.31E+08

2497.193 330810.5 1.05E+09 2516.156 193268.8 6.33E+08

2507.193 330259.3 1.06E+09 2526.156 192909.7 6.35E+08

2517.193 329709.5 1.06E+09 2536.156 192551.5 6.37E+08

2527.193 329161.1 1.06E+09 2546.156 192194.1 6.39E+08

2537.193 328614 1.07E+09 2556.156 191837.6 6.4E+08

2547.193 328068.4 1.07E+09 2566.156 191481.9 6.42E+08

2557.193 327524.1 1.07E+09 2576.156 191127 6.44E+08

2567.193 326981.2 1.08E+09 2586.156 190773 6.46E+08

2577.193 326439.7 1.08E+09 2596.156 190419.8 6.48E+08

125

2587.193 325899.5 1.08E+09 2606.156 190067.4 6.5E+08

2597.193 325360.7 1.09E+09 2616.156 189715.9 6.52E+08

2607.193 324823.2 1.09E+09 2626.156 189365.2 6.54E+08

2617.193 324287.1 1.09E+09 2636.156 189015.3 6.56E+08

2627.193 323752.3 1.1E+09 2646.156 188666.2 6.58E+08

2637.193 323218.9 1.1E+09 2656.156 188318 6.59E+08

2647.193 322686.8 1.1E+09 2666.156 187970.5 6.61E+08

2657.193 322156 1.11E+09 2676.156 187623.9 6.63E+08

2667.193 321626.5 1.11E+09 2686.156 187278.1 6.65E+08

2677.193 321098.4 1.11E+09 2696.156 186933.1 6.67E+08

2687.193 320571.6 1.11E+09 2706.156 186588.9 6.69E+08

2697.193 320046.1 1.12E+09 2716.156 186245.5 6.71E+08

2707.193 319521.8 1.12E+09 2726.156 185902.9 6.73E+08

2717.193 318998.9 1.12E+09 2736.156 185561.2 6.74E+08

2727.193 318477.3 1.13E+09 2746.156 185220.2 6.76E+08

2737.193 317957 1.13E+09 2756.156 184880 6.78E+08

2747.193 317437.9 1.13E+09 2766.156 184540.5 6.8E+08

2757.193 316920.1 1.14E+09 2776.156 184201.9 6.82E+08

2767.193 316403.7 1.14E+09 2786.156 183864.1 6.84E+08

2777.193 315888.4 1.14E+09 2796.156 183527 6.85E+08

2787.193 315374.5 1.15E+09 2806.156 183190.8 6.87E+08

2797.193 314861.8 1.15E+09 2816.156 182855.3 6.89E+08

2807.193 314350.4 1.15E+09 2826.156 182520.5 6.91E+08

2817.193 313840.2 1.16E+09 2836.156 182186.6 6.93E+08

2827.193 313331.2 1.16E+09 2846.156 181853.4 6.95E+08

2837.193 312823.6 1.16E+09 2856.156 181521 6.96E+08

2847.193 312317.1 1.17E+09 2866.156 181189.4 6.98E+08

2857.193 311811.9 1.17E+09 2876.156 180858.5 7E+08

2867.193 311307.9 1.17E+09 2886.156 180528.4 7.02E+08

2877.193 310805.2 1.17E+09 2896.156 180199.1 7.04E+08

2887.193 310303.6 1.18E+09 2906.156 179870.5 7.05E+08

2897.193 309803.3 1.18E+09 2916.156 179542.6 7.07E+08

2907.193 309304.2 1.18E+09 2926.156 179215.5 7.09E+08

2917.193 308806.4 1.19E+09 2936.156 178889.2 7.11E+08

2927.193 308309.7 1.19E+09 2946.156 178563.6 7.13E+08

2937.193 307814.2 1.19E+09 2956.156 178238.8 7.14E+08

2947.193 307319.9 1.2E+09 2966.156 177914.7 7.16E+08

2957.193 306826.8 1.2E+09 2976.156 177591.3 7.18E+08

2967.193 306334.9 1.2E+09 2986.156 177268.7 7.2E+08

2977.193 305844.2 1.21E+09 2996.156 176946.8 7.22E+08

2987.193 305354.7 1.21E+09 3006.156 176625.7 7.23E+08

126

2997.193 304866.3 1.21E+09 3016.156 176305.3 7.25E+08

3007.193 304379.1 1.21E+09 3026.156 175985.6 7.27E+08

3017.193 303893.1 1.22E+09 3036.156 175666.6 7.29E+08

3027.193 303408.3 1.22E+09 3046.156 175348.4 7.3E+08

3037.193 302924.6 1.22E+09 3056.156 175030.9 7.32E+08

3047.193 302442 1.23E+09 3066.156 174714.1 7.34E+08

3057.193 301960.7 1.23E+09 3076.156 174398 7.36E+08

3067.193 301480.4 1.23E+09 3086.156 174082.7 7.37E+08

3077.193 301001.4 1.24E+09 3096.156 173768 7.39E+08

3087.193 300523.4 1.24E+09 3106.156 173454.1 7.41E+08

3097.193 300046.6 1.24E+09 3116.156 173140.9 7.43E+08

3107.193 299570.9 1.24E+09 3126.156 172828.4 7.44E+08

3117.193 299096.4 1.25E+09 3136.156 172516.6 7.46E+08

3127.193 298623 1.25E+09 3146.156 172205.5 7.48E+08

3137.193 298150.7 1.25E+09 3156.156 171895.1 7.49E+08

3147.193 297679.5 1.26E+09 3166.156 171585.4 7.51E+08

3157.193 297209.4 1.26E+09 3176.156 171276.4 7.53E+08

3167.193 296740.4 1.26E+09 3186.156 170968.2 7.55E+08

3177.193 296272.6 1.27E+09 3196.156 170660.6 7.56E+08

3187.193 295805.8 1.27E+09 3206.156 170353.6 7.58E+08

3197.193 295340.2 1.27E+09 3216.156 170047.4 7.6E+08

3207.193 294875.6 1.27E+09 3226.156 169741.9 7.61E+08

3217.193 294412.2 1.28E+09 3236.156 169437 7.63E+08

3227.193 293949.8 1.28E+09 3246.156 169132.9 7.65E+08

3237.193 293488.5 1.28E+09 3256.156 168829.4 7.66E+08

3247.193 293028.3 1.29E+09 3266.156 168526.6 7.68E+08

3257.193 292569.2 1.29E+09 3276.156 168224.5 7.7E+08

3267.193 292111.1 1.29E+09 3286.156 167923 7.72E+08

3277.193 291654.1 1.3E+09 3296.156 167622.2 7.73E+08

3287.193 291198.2 1.3E+09 3306.156 167322.1 7.75E+08

Case Study 2 in Ayala H. and Ye (2013) Case Study 4 in Ayala H. and Ye (2013)

pi=4800 psia, pwf=500psia, T=200, SG=0.65 pi=5000 psia, pwf=3000psia, T=200, SG=0.601

t(day) qsc(SCFD) Gp(SCF) t(day) qsc(SCFD) Gp(SCF)

0.01 10779052 107790.5 0.01 35078844 350788.4

0.11 7578943 924152.8 0.122058 26214346 3475828

0.251279 7016451 1944595 0.569435 23358842 14320659

0.606439 6513132 4323200 3.060591 20890618 68213497

1.542825 6054512 10148257 12.20374 19202904 2.49E+08

4.13312 5635641 25135565 22.20374 18544974 4.37E+08

127

11.44481 5258589 64570974 32.20374 18154816 6.2E+08

21.44481 5037752 1.16E+08 42.20374 17867893 8E+08

31.44481 4886173 1.65E+08 52.20374 17627724 9.77E+08

41.44481 4753637 2.13E+08 62.20374 17410374 1.15E+09

51.44481 4629692 2.6E+08 72.20374 17205127 1.33E+09

61.44481 4511802 3.06E+08 82.20374 17007098 1.5E+09

71.44481 4399138 3.5E+08 92.20374 16814023 1.67E+09

81.44481 4291265 3.94E+08 102.2037 16624831 1.83E+09

91.44481 4187859 4.36E+08 112.2037 16438995 2E+09

101.4448 4088638 4.78E+08 122.2037 16256238 2.16E+09

111.4448 3993352 5.18E+08 132.2037 16076398 2.32E+09

121.4448 3901766 5.57E+08 142.2037 15899368 2.48E+09

131.4448 3813669 5.96E+08 152.2037 15725066 2.64E+09

141.4448 3728863 6.34E+08 162.2037 15553425 2.8E+09

151.4448 3647166 6.7E+08 172.2037 15384382 2.95E+09

161.4448 3568409 7.06E+08 182.2037 15217881 3.1E+09

171.4448 3492437 7.42E+08 192.2037 15053867 3.26E+09

181.4448 3419103 7.76E+08 202.2037 14892287 3.41E+09

191.4448 3348274 8.1E+08 212.2037 14733090 3.55E+09

201.4448 3279822 8.43E+08 222.2037 14576227 3.7E+09

211.4448 3213631 8.76E+08 232.2037 14421650 3.84E+09

221.4448 3149591 9.07E+08 242.2037 14269312 3.99E+09

231.4448 3087600 9.38E+08 252.2037 14119169 4.13E+09

241.4448 3027561 9.69E+08 262.2037 13971175 4.27E+09

251.4448 2969385 9.99E+08 272.2037 13825288 4.41E+09

261.4448 2912987 1.03E+09 282.2037 13681466 4.55E+09

271.4448 2858288 1.06E+09 292.2037 13539669 4.68E+09

281.4448 2805213 1.09E+09 302.2037 13399857 4.82E+09

291.4448 2753693 1.11E+09 312.2037 13261991 4.95E+09

301.4448 2703660 1.14E+09 322.2037 13126034 5.08E+09

311.4448 2655054 1.17E+09 332.2037 12991949 5.21E+09

321.4448 2607814 1.19E+09 342.2037 12859700 5.34E+09

331.4448 2561885 1.22E+09 352.2037 12729253 5.47E+09

341.4448 2517215 1.24E+09 362.2037 12600574 5.6E+09

351.4448 2473754 1.27E+09 372.2037 12473629 5.72E+09

361.4448 2431455 1.29E+09 382.2037 12348387 5.85E+09

371.4448 2390273 1.32E+09 392.2037 12224816 5.97E+09

381.4448 2350165 1.34E+09 402.2037 12102885 6.09E+09

391.4448 2311092 1.37E+09 412.2037 11982565 6.21E+09

401.4448 2273015 1.39E+09 422.2037 11863826 6.33E+09

411.4448 2235898 1.41E+09 432.2037 11746639 6.45E+09

128

421.4448 2199706 1.43E+09 442.2037 11630978 6.56E+09

431.4448 2164407 1.45E+09 452.2037 11516814 6.68E+09

441.4448 2129969 1.48E+09 462.2037 11404122 6.79E+09

451.4448 2096361 1.5E+09 472.2037 11292875 6.91E+09

461.4448 2063557 1.52E+09 482.2037 11183047 7.02E+09

471.4448 2031528 1.54E+09 492.2037 11074616 7.13E+09

481.4448 2000248 1.56E+09 502.2037 10967555 7.24E+09

491.4448 1969694 1.58E+09 512.2037 10861843 7.35E+09

501.4448 1939840 1.6E+09 522.2037 10757454 7.46E+09

511.4448 1910664 1.62E+09 532.2037 10654368 7.57E+09

521.4448 1882145 1.64E+09 542.2037 10552562 7.67E+09

531.4448 1854262 1.65E+09 552.2037 10452015 7.78E+09

541.4448 1826994 1.67E+09 562.2037 10352705 7.88E+09

551.4448 1800324 1.69E+09 572.2037 10254612 7.98E+09

561.4448 1774231 1.71E+09 582.2037 10157716 8.09E+09

571.4448 1748700 1.73E+09 592.2037 10061997 8.19E+09

581.4448 1723713 1.74E+09 602.2037 9967435 8.29E+09

591.4448 1699254 1.76E+09 612.2037 9874013 8.39E+09

601.4448 1675307 1.78E+09 622.2037 9781711 8.48E+09

611.4448 1651857 1.79E+09 632.2037 9690512 8.58E+09

621.4448 1628890 1.81E+09 642.2037 9600398 8.68E+09

631.4448 1606393 1.83E+09 652.2037 9511351 8.77E+09

641.4448 1584352 1.84E+09 662.2037 9423355 8.87E+09

651.4448 1562754 1.86E+09 672.2037 9336393 8.96E+09

661.4448 1541586 1.87E+09 682.2037 9250449 9.06E+09

671.4448 1520838 1.89E+09 692.2037 9165506 9.15E+09

681.4448 1500497 1.9E+09 702.2037 9081550 9.24E+09

691.4448 1480552 1.92E+09 712.2037 8998566 9.33E+09

701.4448 1460994 1.93E+09 722.2037 8916537 9.42E+09

711.4448 1441811 1.95E+09 732.2037 8835450 9.51E+09

721.4448 1422993 1.96E+09 742.2037 8755290 9.59E+09

731.4448 1404532 1.98E+09 752.2037 8676043 9.68E+09

741.4448 1386418 1.99E+09 762.2037 8597696 9.77E+09

751.4448 1368642 2.01E+09 772.2037 8520234 9.85E+09

761.4448 1351195 2.02E+09 782.2037 8443645 9.94E+09

771.4448 1334069 2.03E+09 792.2037 8367916 1E+10

781.4448 1317256 2.05E+09 802.2037 8293033 1.01E+10

791.4448 1300748 2.06E+09 812.2037 8218985 1.02E+10

801.4448 1284538 2.07E+09 822.2037 8145759 1.03E+10

811.4448 1268618 2.08E+09 832.2037 8073344 1.04E+10

821.4448 1252981 2.1E+09 842.2037 8001727 1.04E+10

129

831.4448 1237621 2.11E+09 852.2037 7930896 1.05E+10

841.4448 1222531 2.12E+09 862.2037 7860841 1.06E+10

851.4448 1207704 2.13E+09 872.2037 7791551 1.07E+10

861.4448 1193135 2.15E+09 882.2037 7723014 1.07E+10

871.4448 1178816 2.16E+09 892.2037 7655220 1.08E+10

881.4448 1164743 2.17E+09 902.2037 7588158 1.09E+10

891.4448 1150909 2.18E+09 912.2037 7521818 1.1E+10

901.4448 1137310 2.19E+09 922.2037 7456190 1.1E+10

911.4448 1123939 2.2E+09 932.2037 7391264 1.11E+10

921.4448 1110792 2.21E+09 942.2037 7327030 1.12E+10

931.4448 1097864 2.23E+09 952.2037 7263478 1.13E+10

941.4448 1085150 2.24E+09 962.2037 7200600 1.13E+10

951.4448 1072644 2.25E+09 972.2037 7138386 1.14E+10

961.4448 1060343 2.26E+09 982.2037 7076826 1.15E+10

971.4448 1048242 2.27E+09 992.2037 7015913 1.16E+10

981.4448 1036336 2.28E+09 1002.204 6955636 1.16E+10

991.4448 1024621 2.29E+09 1012.204 6895988 1.17E+10

1001.445 1013094 2.3E+09 1022.204 6836961 1.18E+10

1011.445 1001750 2.31E+09 1032.204 6778545 1.18E+10

1021.445 990585.9 2.32E+09 1042.204 6720732 1.19E+10

1031.445 979597 2.33E+09 1052.204 6663516 1.2E+10

1041.445 968779.9 2.34E+09 1062.204 6606887 1.2E+10

1051.445 958131.2 2.35E+09 1072.204 6550838 1.21E+10

1061.445 947647.3 2.36E+09 1082.204 6495361 1.22E+10

1071.445 937324.8 2.37E+09 1092.204 6440449 1.22E+10

1081.445 927160.5 2.38E+09 1102.204 6386095 1.23E+10

1091.445 917151.2 2.39E+09 1112.204 6332292 1.24E+10

1101.445 907293.6 2.4E+09 1122.204 6279031 1.24E+10

1111.445 897584.8 2.4E+09 1132.204 6226307 1.25E+10

1121.445 888021.7 2.41E+09 1142.204 6174112 1.25E+10

1131.445 878601.5 2.42E+09 1152.204 6122439 1.26E+10

1141.445 869321.4 2.43E+09 1162.204 6071282 1.27E+10

1151.445 860178.5 2.44E+09 1172.204 6020635 1.27E+10

1161.445 851170.3 2.45E+09 1182.204 5970491 1.28E+10

1171.445 842294.1 2.46E+09 1192.204 5920843 1.28E+10

1181.445 833547.3 2.46E+09 1202.204 5871686 1.29E+10

1191.445 824927.5 2.47E+09 1212.204 5823013 1.3E+10

1201.445 816432.2 2.48E+09 1222.204 5774819 1.3E+10

1211.445 808059 2.49E+09 1232.204 5727096 1.31E+10

1221.445 799805.7 2.5E+09 1242.204 5679840 1.31E+10

1231.445 791670 2.51E+09 1252.204 5633045 1.32E+10

130

1241.445 783649.6 2.51E+09 1262.204 5586705 1.32E+10

1251.445 775742.5 2.52E+09 1272.204 5540814 1.33E+10

1261.445 767946.5 2.53E+09 1282.204 5495367 1.34E+10

1271.445 760259.6 2.54E+09 1292.204 5450359 1.34E+10

1281.445 752679.7 2.54E+09 1302.204 5405784 1.35E+10

1291.445 745205 2.55E+09 1312.204 5361638 1.35E+10

1301.445 737833.4 2.56E+09 1322.204 5317914 1.36E+10

1311.445 730563.2 2.57E+09 1332.204 5274608 1.36E+10

1321.445 723392.5 2.57E+09 1342.204 5231715 1.37E+10

1331.445 716319.5 2.58E+09 1352.204 5189230 1.37E+10

1341.445 709342.5 2.59E+09 1362.204 5147148 1.38E+10

1351.445 702459.7 2.59E+09 1372.204 5105465 1.38E+10

1361.445 695669.6 2.6E+09 1382.204 5064175 1.39E+10

1371.445 688970.4 2.61E+09 1392.204 5023274 1.39E+10

1381.445 682360.6 2.62E+09 1402.204 4982758 1.4E+10

1391.445 675838.7 2.62E+09 1412.204 4942622 1.4E+10

1401.445 669403 2.63E+09 1422.204 4902862 1.41E+10

1411.445 663052.2 2.64E+09 1432.204 4863472 1.41E+10

1421.445 656784.6 2.64E+09 1442.204 4824450 1.42E+10

1431.445 650599 2.65E+09 1452.204 4785790 1.42E+10

1441.445 644494 2.66E+09 1462.204 4747489 1.43E+10

1451.445 638468 2.66E+09 1472.204 4709543 1.43E+10

1461.445 632519.9 2.67E+09 1482.204 4671947 1.44E+10

1471.445 626648.3 2.67E+09 1492.204 4634697 1.44E+10

1481.445 620851.9 2.68E+09 1502.204 4597790 1.45E+10

1491.445 615129.5 2.69E+09 1512.204 4561222 1.45E+10

1501.445 609479.9 2.69E+09 1522.204 4524988 1.46E+10

1511.445 603901.7 2.7E+09 1532.204 4489085 1.46E+10

1521.445 598393.9 2.71E+09 1542.204 4453510 1.46E+10

1531.445 592955.3 2.71E+09 1552.204 4418259 1.47E+10

1541.445 587584.8 2.72E+09 1562.204 4383327 1.47E+10

1551.445 582281.2 2.72E+09 1572.204 4348713 1.48E+10

1561.445 577043.5 2.73E+09 1582.204 4314411 1.48E+10

1571.445 571870.7 2.73E+09 1592.204 4280419 1.49E+10

1581.445 566761.6 2.74E+09 1602.204 4246733 1.49E+10

1591.445 561715.2 2.75E+09 1612.204 4213350 1.49E+10

1601.445 556730.6 2.75E+09 1622.204 4180266 1.5E+10

1611.445 551806.7 2.76E+09 1632.204 4147479 1.5E+10

1621.445 546942.7 2.76E+09 1642.204 4114984 1.51E+10

1631.445 542137.5 2.77E+09 1652.204 4082780 1.51E+10

1641.445 537390.2 2.77E+09 1662.204 4050862 1.52E+10

131

1651.445 532700 2.78E+09 1672.204 4019228 1.52E+10

1661.445 528065.9 2.78E+09 1682.204 3987875 1.52E+10

1671.445 523487.1 2.79E+09 1692.204 3956799 1.53E+10

1681.445 518962.7 2.79E+09 1702.204 3925997 1.53E+10

1691.445 514491.9 2.8E+09 1712.204 3895468 1.54E+10

1701.445 510073.8 2.8E+09 1722.204 3865207 1.54E+10

1711.445 505707.6 2.81E+09 1732.204 3835212 1.54E+10

1721.445 501392.7 2.81E+09 1742.204 3805480 1.55E+10

1731.445 497128.1 2.82E+09 1752.204 3776009 1.55E+10

1741.445 492913.1 2.82E+09 1762.204 3746795 1.55E+10

1751.445 488747 2.83E+09 1772.204 3717836 1.56E+10

1761.445 484629 2.83E+09 1782.204 3689129 1.56E+10

1771.445 480558.4 2.84E+09 1792.204 3660672 1.57E+10

1781.445 476534.5 2.84E+09 1802.204 3632462 1.57E+10

1791.445 472556.7 2.85E+09 1812.204 3604496 1.57E+10

1801.445 468624.2 2.85E+09 1822.204 3576772 1.58E+10

1811.445 464736.3 2.86E+09 1832.204 3549288 1.58E+10

1821.445 460892.5 2.86E+09 1842.204 3522041 1.58E+10

1831.445 457092 2.87E+09 1852.204 3495028 1.59E+10

1841.445 453334.3 2.87E+09 1862.204 3468247 1.59E+10

1851.445 449618.6 2.88E+09 1872.204 3441696 1.59E+10

1861.445 445944.5 2.88E+09 1882.204 3415372 1.6E+10

1871.445 442311.2 2.89E+09 1892.204 3389273 1.6E+10

1881.445 438718.3 2.89E+09 1902.204 3363398 1.6E+10

1891.445 435165.1 2.89E+09 1912.204 3337742 1.61E+10

1901.445 431651.1 2.9E+09 1922.204 3312305 1.61E+10

1911.445 428175.7 2.9E+09 1932.204 3287084 1.61E+10

1921.445 424738.3 2.91E+09 1942.204 3262077 1.62E+10

1931.445 421338.4 2.91E+09 1952.204 3237282 1.62E+10

1941.445 417975.6 2.92E+09 1962.204 3212697 1.62E+10

1951.445 414649.2 2.92E+09 1972.204 3188319 1.63E+10

1961.445 411358.8 2.92E+09 1982.204 3164146 1.63E+10

1971.445 408103.8 2.93E+09 1992.204 3140177 1.63E+10

1981.445 404883.8 2.93E+09 2002.204 3116410 1.64E+10

1991.445 401698.3 2.94E+09 2012.204 3092842 1.64E+10

2001.445 398546.8 2.94E+09 2022.204 3069471 1.64E+10

2011.445 395428.9 2.94E+09 2032.204 3046296 1.65E+10

2021.445 392344 2.95E+09 2042.204 3023315 1.65E+10

2031.445 389291.7 2.95E+09 2052.204 3000525 1.65E+10

2041.445 386271.6 2.96E+09 2062.204 2977925 1.65E+10

2051.445 383283.2 2.96E+09 2072.204 2955513 1.66E+10

132

2061.445 380326.2 2.96E+09 2082.204 2933288 1.66E+10

2071.445 377400 2.97E+09 2092.204 2911247 1.66E+10

2081.445 374504.3 2.97E+09 2102.204 2889388 1.67E+10

2091.445 371638.7 2.97E+09 2112.204 2867710 1.67E+10

2101.445 368802.7 2.98E+09 2122.204 2846211 1.67E+10

2111.445 365996 2.98E+09 2132.204 2824890 1.68E+10

2121.445 363218.2 2.99E+09 2142.204 2803744 1.68E+10

2131.445 360468.8 2.99E+09 2152.204 2782772 1.68E+10

2141.445 357747.6 2.99E+09 2162.204 2761972 1.68E+10

2151.445 355054.1 3E+09 2172.204 2741344 1.69E+10

2161.445 352388 3E+09 2182.204 2720884 1.69E+10

2171.445 349748.9 3E+09 2192.204 2700591 1.69E+10

2181.445 347136.4 3.01E+09 2202.204 2680464 1.69E+10

2191.445 344550.3 3.01E+09 2212.204 2660502 1.7E+10

2201.445 341990.2 3.01E+09 2222.204 2640702 1.7E+10

2211.445 339455.7 3.02E+09 2232.204 2621064 1.7E+10

2221.445 336946.5 3.02E+09 2242.204 2601585 1.7E+10

2231.445 334462.3 3.02E+09 2252.204 2582264 1.71E+10

2241.445 332002.8 3.03E+09 2262.204 2563100 1.71E+10

2251.445 329567.6 3.03E+09 2272.204 2544092 1.71E+10

2261.445 327156.4 3.03E+09 2282.204 2525237 1.72E+10

2271.445 324769 3.04E+09 2292.204 2506534 1.72E+10

2281.445 322405 3.04E+09 2302.204 2487982 1.72E+10

2291.445 320064.2 3.04E+09 2312.204 2469580 1.72E+10

2301.445 317746.2 3.05E+09 2322.204 2451326 1.73E+10

2311.445 315450.7 3.05E+09 2332.204 2433218 1.73E+10

2321.445 313177.6 3.05E+09 2342.204 2415256 1.73E+10

2331.445 310926.4 3.06E+09 2352.204 2397439 1.73E+10

2341.445 308696.9 3.06E+09 2362.204 2379763 1.73E+10

2351.445 306488.9 3.06E+09 2372.204 2362230 1.74E+10

2361.445 304302.1 3.07E+09 2382.204 2344836 1.74E+10

2371.445 302136.2 3.07E+09 2392.204 2327581 1.74E+10

2381.445 299991 3.07E+09 2402.204 2310464 1.74E+10

2391.445 297866.2 3.07E+09 2412.204 2293484 1.75E+10

2401.445 295761.5 3.08E+09 2422.204 2276638 1.75E+10

2411.445 293676.8 3.08E+09 2432.204 2259926 1.75E+10

2421.445 291611.7 3.08E+09 2442.204 2243347 1.75E+10

2431.445 289566.1 3.09E+09 2452.204 2226900 1.76E+10

2441.445 287539.7 3.09E+09 2462.204 2210582 1.76E+10

2451.445 285532.2 3.09E+09 2472.204 2194394 1.76E+10

2461.445 283543.5 3.09E+09 2482.204 2178334 1.76E+10

133

2471.445 281573.3 3.1E+09 2492.204 2162400 1.76E+10

2481.445 279621.4 3.1E+09 2502.204 2146593 1.77E+10

2491.445 277687.6 3.1E+09 2512.204 2130909 1.77E+10

2501.445 275771.6 3.11E+09 2522.204 2115349 1.77E+10

2511.445 273873.3 3.11E+09 2532.204 2099912 1.77E+10

2521.445 271992.4 3.11E+09 2542.204 2084596 1.77E+10

2531.445 270128.7 3.11E+09 2552.204 2069400 1.78E+10

2541.445 268282.1 3.12E+09 2562.204 2054323 1.78E+10

2551.445 266452.3 3.12E+09 2572.204 2039364 1.78E+10

2561.445 264639.1 3.12E+09 2582.204 2024522 1.78E+10

2571.445 262842.4 3.12E+09 2592.204 2009796 1.79E+10

2581.445 261061.9 3.13E+09 2602.204 1995185 1.79E+10

2591.445 259297.5 3.13E+09 2612.204 1980688 1.79E+10

2601.445 257548.9 3.13E+09 2622.204 1966304 1.79E+10

2611.445 255816.1 3.13E+09 2632.204 1952032 1.79E+10

2621.445 254098.7 3.14E+09 2642.204 1937871 1.79E+10

2631.445 252396.7 3.14E+09 2652.204 1923819 1.8E+10

2641.445 250709.8 3.14E+09 2662.204 1909877 1.8E+10

2651.445 249037.9 3.15E+09 2672.204 1896043 1.8E+10

2661.445 247380.8 3.15E+09 2682.204 1882316 1.8E+10

2671.445 245738.3 3.15E+09 2692.204 1868696 1.8E+10

2681.445 244110.4 3.15E+09 2702.204 1855180 1.81E+10

2691.445 242496.7 3.15E+09 2712.204 1841769 1.81E+10

2701.445 240897.2 3.16E+09 2722.204 1828462 1.81E+10

2711.445 239311.6 3.16E+09 2732.204 1815257 1.81E+10

2721.445 237739.9 3.16E+09 2742.204 1802154 1.81E+10

2731.445 236181.9 3.16E+09 2752.204 1789152 1.82E+10

2741.445 234637.4 3.17E+09 2762.204 1776249 1.82E+10

2751.445 233106.2 3.17E+09 2772.204 1763446 1.82E+10

2761.445 231588.3 3.17E+09 2782.204 1750741 1.82E+10

2771.445 230083.5 3.17E+09 2792.204 1738134 1.82E+10

2781.445 228591.6 3.18E+09 2802.204 1725623 1.82E+10

2791.445 227112.5 3.18E+09 2812.204 1713208 1.83E+10

2801.445 225646 3.18E+09 2822.204 1700888 1.83E+10

2811.445 224192.1 3.18E+09 2832.204 1688662 1.83E+10

2821.445 222750.5 3.19E+09 2842.204 1676529 1.83E+10

2831.445 221321.2 3.19E+09 2852.204 1664489 1.83E+10

2841.445 219903.9 3.19E+09 2862.204 1652541 1.83E+10

2851.445 218498.7 3.19E+09 2872.204 1640683 1.84E+10

2861.445 217105.2 3.19E+09 2882.204 1628916 1.84E+10

2871.445 215723.5 3.2E+09 2892.204 1617239 1.84E+10

134

2881.445 214353.4 3.2E+09 2902.204 1605650 1.84E+10

2891.445 212994.8 3.2E+09 2912.204 1594149 1.84E+10

2901.445 211647.5 3.2E+09 2922.204 1582735 1.84E+10

2911.445 210311.4 3.2E+09 2932.204 1571408 1.85E+10

2921.445 208986.4 3.21E+09 2942.204 1560167 1.85E+10

2931.445 207672.4 3.21E+09 2952.204 1549011 1.85E+10

2941.445 206369.2 3.21E+09 2962.204 1537939 1.85E+10

2951.445 205076.8 3.21E+09 2972.204 1526951 1.85E+10

2961.445 203795.1 3.21E+09 2982.204 1516045 1.85E+10

2971.445 202523.8 3.22E+09 2992.204 1505222 1.85E+10

2981.445 201263 3.22E+09 3002.204 1494481 1.86E+10

2991.445 200012.5 3.22E+09 3012.204 1483820 1.86E+10

3001.445 198772.2 3.22E+09 3022.204 1473240 1.86E+10

3011.445 197541.9 3.22E+09 3032.204 1462739 1.86E+10

3021.445 196321.7 3.23E+09 3042.204 1452318 1.86E+10

3031.445 195111.3 3.23E+09 3052.204 1441974 1.86E+10

3041.445 193910.7 3.23E+09 3062.204 1431708 1.87E+10

3051.445 192719.8 3.23E+09 3072.204 1421519 1.87E+10

3061.445 191538.4 3.23E+09 3082.204 1411407 1.87E+10

3071.445 190366.6 3.24E+09 3092.204 1401370 1.87E+10

3081.445 189204.1 3.24E+09 3102.204 1391408 1.87E+10

3091.445 188050.9 3.24E+09 3112.204 1381521 1.87E+10

3101.445 186906.8 3.24E+09 3122.204 1371708 1.87E+10

3111.445 185771.9 3.24E+09 3132.204 1361968 1.87E+10

3121.445 184646 3.25E+09 3142.204 1352301 1.88E+10

3131.445 183529 3.25E+09 3152.204 1342705 1.88E+10

3141.445 182420.8 3.25E+09 3162.204 1333182 1.88E+10

3151.445 181321.3 3.25E+09 3172.204 1323729 1.88E+10

3161.445 180230.5 3.25E+09 3182.204 1314346 1.88E+10

3171.445 179148.2 3.26E+09 3192.204 1305034 1.88E+10

3181.445 178074.4 3.26E+09 3202.204 1295790 1.88E+10

3191.445 177009 3.26E+09 3212.204 1286615 1.89E+10

3201.445 175951.9 3.26E+09 3222.204 1277508 1.89E+10

3211.445 174903 3.26E+09 3232.204 1268469 1.89E+10

3221.445 173862.3 3.26E+09 3242.204 1259497 1.89E+10

3231.445 172829.6 3.27E+09 3252.204 1250591 1.89E+10

3241.445 171804.9 3.27E+09 3262.204 1241752 1.89E+10

3251.445 170788.1 3.27E+09 3272.204 1232977 1.89E+10

3261.445 169779.1 3.27E+09 3282.204 1224268 1.89E+10

135

Chapter 2

Case Study 2-A Case Study 2-B

pi=4800 psia, T=200F, SG=0.65 pi=5000 psia,T=200F, SG=0.55

t(day) qsc(SCFD) Gp(SCF) pwf(psia) t(day) qsc(SCFD) Gp(SCF) Pwf(psia)

0.01 2626876 26268.76 4000 0.01 888250.1 8882.501 3500

0.246877 1735771 468292.5 4000 0.117118 518711.3 70653.49 3500

4.81919 1379744 7118124 4000 0.483704 438015.9 240393.6 3500

14.81919 1276022 20239680 4000 2.374525 373057.3 982720.9 3500

24.81919 1229354 32727804 4000 10.60727 326792.2 3793490 3500

34.81919 1192800 44816554 4000 20.60727 307912.4 6948565 3500

44.81919 1159124 56557870 4000 30.60727 294479.4 9952036 3500

54.81919 1126880 67970784 4000 40.60727 282405 12829708 3500

64.81919 1095745 79067482 4000 50.60727 271055.7 15590816 3500

74.81919 1065622 89858447 4000 60.60727 260299.8 18241752 3500

84.81919 1036460 1E+08 4000 70.60727 250084.6 20788137 3500

94.81919 1008219 1.11E+08 4000 80.60727 240372.4 23235165 3500

104.8192 980862.2 1.2E+08 4000 90.60727 231130.5 25587683 3500

114.8192 954356.5 1.3E+08 4000 100.6073 222329.1 27850229 3500

124.8192 928669.2 1.4E+08 4000 110.6073 213940.8 30027053 3500

134.8192 903769.7 1.49E+08 4000 120.6073 205940.5 32122149 3500

144.8192 879628.6 1.58E+08 4000 130.6073 198305.1 34139268 3500

154.8192 856217.9 1.66E+08 4000 140.6073 191013.2 36081939 3500

164.8192 833511.1 1.75E+08 4000 150.6073 184045 37953486 3500

174.8192 811482.7 1.83E+08 4000 160.6073 177382.2 39757046 3500

184.8192 790108.4 1.91E+08 4000 170.6073 171007.8 41495578 3500

194.8192 769365.1 1.99E+08 4000 180.6073 164905.9 43171877 3500

204.8192 749230.5 2.06E+08 4000 190.6073 159062 44788587 3500

214.8192 729683.5 2.14E+08 4000 200.6073 153462.4 46348214 3500

224.8192 710703.8 2.21E+08 4000 210.6073 148094.2 47853127 3500

234.8192 692271.9 2.28E+08 4000 220.6073 142945.6 49305575 3500

244.8192 674369.2 2.35E+08 4000 230.6073 138005.4 50707693 3500

254.8192 656977.9 2.41E+08 4000 240.6073 133263.3 52061506 3500

264.8192 640081 2.48E+08 4000 250.6073 128709.4 53368941 3500

274.8192 623661.9 2.54E+08 4000 260.6073 124334.6 54631829 3500

284.8192 607705.1 2.6E+08 4000 270.6073 120130.3 55851914 3500

294.8192 592195.4 2.66E+08 4000 280.6073 116088.4 57030856 3500

304.8192 577118.2 2.72E+08 4000 290.6073 112201.3 58170236 3500

314.8192 562459.8 2.78E+08 4000 300 108684.7 59205785 3500

324.8192 548206.6 2.83E+08 4000 300.1234 412759.4 59263100 2500

334.8192 534345.9 2.89E+08 4000 301.0148 345122.7 59586049 2500

136

344.8192 520865.2 2.94E+08 4000 308.1297 299593.7 61807268 2500

354.8192 507752.7 2.99E+08 4000 318.1297 282978.8 64702016 2500

364.8192 494996.9 3.04E+08 4000 328.1297 272427 67471695 2500

366.08 4700659 3.05E+08 2000 338.1297 263390.8 70145570 2500

366.3161 4190411 3.06E+08 2000 348.1297 254973.7 72732802 2500

367.4657 3756651 3.11E+08 2000 358.1297 246962.3 75238177 2500

373.4564 3396882 3.35E+08 2000 368.1297 239293.5 77665353 2500

383.4564 3234387 3.68E+08 2000 378.1297 231939.3 80017589 2500

393.4564 3137786 4E+08 2000 388.1297 224880.2 82297920 2500

403.4564 3057920 4.31E+08 2000 398.1297 218099.9 84509206 2500

413.4564 2984154 4.61E+08 2000 408.1297 211583.6 86654154 2500

423.4564 2913809 4.9E+08 2000 418.1297 205317.7 88735326 2500

433.4564 2846121 5.19E+08 2000 428.1297 199289.2 90755156 2500

443.4564 2780809 5.47E+08 2000 438.1297 193486.3 92715951 2500

453.4564 2717717 5.74E+08 2000 448.1297 187897.9 94619905 2500

463.4564 2656728 6.01E+08 2000 458.1297 182513.4 96469105 2500

473.4564 2597738 6.28E+08 2000 468.1297 177323.1 98265536 2500

483.4564 2540653 6.53E+08 2000 478.1297 172317.8 1E+08 2500

493.4564 2485385 6.78E+08 2000 488.1297 167489 1.02E+08 2500

503.4564 2431851 7.03E+08 2000 498.1297 162828.4 1.03E+08 2500

513.4564 2379974 7.27E+08 2000 500.081 499400.2 1.04E+08 1000

523.4564 2329681 7.5E+08 2000 500.4399 430054.8 1.04E+08 1000

533.4564 2280903 7.73E+08 2000 503.2073 377009.1 1.05E+08 1000

543.4564 2233575 7.96E+08 2000 512.871 346551.4 1.08E+08 1000

553.4564 2187638 8.18E+08 2000 522.871 333029.9 1.12E+08 1000

563.4564 2143032 8.4E+08 2000 532.871 323010.4 1.15E+08 1000

573.4564 2099703 8.61E+08 2000 542.871 314186.5 1.18E+08 1000

583.4564 2057601 8.82E+08 2000 552.871 305937.2 1.21E+08 1000

593.4564 2016676 9.02E+08 2000 562.871 298073.1 1.24E+08 1000

603.4564 1976882 9.22E+08 2000 572.871 290527.5 1.27E+08 1000

613.4564 1938176 9.42E+08 2000 582.871 283269.8 1.3E+08 1000

623.4564 1900515 9.61E+08 2000 592.871 276280.9 1.33E+08 1000

633.4564 1863861 9.8E+08 2000 602.871 269545.9 1.36E+08 1000

643.4564 1828176 9.98E+08 2000 612.871 263051.6 1.38E+08 1000

653.4564 1793425 1.02E+09 2000 622.871 256785.9 1.41E+08 1000

663.4564 1759573 1.03E+09 2000 632.871 250737.7 1.43E+08 1000

673.4564 1726588 1.05E+09 2000 642.871 244896.5 1.46E+08 1000

683.4564 1694440 1.07E+09 2000 652.871 239252.6 1.48E+08 1000

693.4564 1663100 1.09E+09 2000 662.871 233796.7 1.51E+08 1000

703.4564 1632539 1.1E+09 2000 672.871 228520.3 1.53E+08 1000

713.4564 1602731 1.12E+09 2000 682.871 223415.2 1.55E+08 1000

137

723.4564 1573650 1.13E+09 2000 692.871 218473.8 1.57E+08 1000

731.02 3339737 1.14E+09 800 702.871 213688.9 1.6E+08 1000

731.3095 2898047 1.15E+09 800 712.871 209053.7 1.62E+08 1000

736.5301 2613192 1.16E+09 800 722.871 204561.8 1.64E+08 1000

746.5301 2516524 1.19E+09 800 732.871 200207.2 1.66E+08 1000

756.5301 2457880 1.21E+09 800 742.871 195984.2 1.68E+08 1000

766.5301 2409971 1.24E+09 800 752.871 191887.3 1.7E+08 1000

776.5301 2366454 1.26E+09 800 762.871 187911.4 1.72E+08 1000

786.5301 2325196 1.28E+09 800 772.871 184051.8 1.74E+08 1000

796.5301 2285415 1.31E+09 800 782.871 180303.7 1.75E+08 1000

806.5301 2246807 1.33E+09 800 792.871 176662.8 1.77E+08 1000

816.5301 2209237 1.35E+09 800 802.871 173124.9 1.79E+08 1000

826.5301 2172633 1.37E+09 800 812.871 169686.2 1.81E+08 1000

836.5301 2136948 1.39E+09 800 822.871 166342.9 1.82E+08 1000

846.5301 2102145 1.42E+09 800 832.871 163091.4 1.84E+08 1000

856.5301 2068192 1.44E+09 800 842.871 159928.3 1.86E+08 1000

866.5301 2035058 1.46E+09 800 852.871 156850.3 1.87E+08 1000

876.5301 2002716 1.48E+09 800 862.871 153854.5 1.89E+08 1000

886.5301 1971137 1.5E+09 800 872.871 150937.9 1.9E+08 1000

896.5301 1940297 1.52E+09 800 882.871 148097.6 1.92E+08 1000

906.5301 1910172 1.54E+09 800 892.871 145331 1.93E+08 1000

916.5301 1880737 1.56E+09 800 902.871 142635.5 1.95E+08 1000

926.5301 1851971 1.57E+09 800 912.871 140008.7 1.96E+08 1000

936.5301 1823853 1.59E+09 800 922.871 137448.3 1.97E+08 1000

946.5301 1796361 1.61E+09 800 932.871 134952 1.99E+08 1000

956.5301 1769476 1.63E+09 800 942.871 132517.7 2E+08 1000

966.5301 1743180 1.65E+09 800 952.871 130143.3 2.01E+08 1000

976.5301 1717454 1.66E+09 800 962.871 127826.9 2.03E+08 1000

986.5301 1692282 1.68E+09 800 972.871 125566.6 2.04E+08 1000

996.5301 1667646 1.7E+09 800 982.871 123360.5 2.05E+08 1000

1006.53 1643530 1.71E+09 800 992.871 121207.1 2.06E+08 1000

1016.53 1619920 1.73E+09 800 1000.02 197680.9 2.07E+08 500

1026.53 1596801 1.75E+09 800 1001.767 157015.7 2.08E+08 500

1036.53 1574158 1.76E+09 800 1011.767 148074.7 2.09E+08 500

1046.53 1551978 1.78E+09 800 1021.767 144388.1 2.11E+08 500

1056.53 1530248 1.79E+09 800 1031.767 141490.7 2.12E+08 500

1066.53 1508955 1.81E+09 800 1041.767 138912.4 2.13E+08 500

1076.53 1488086 1.82E+09 800 1051.767 136501.9 2.15E+08 500

1086.53 1467632 1.84E+09 800 1061.767 134195.9 2.16E+08 500

1096 1744093 1.85E+09 500 1071.767 131965.7 2.17E+08 500

1100.102 1578240 1.86E+09 500 1081.767 129797.5 2.19E+08 500

138

1110.102 1547774 1.87E+09 500 1091.767 127684.4 2.2E+08 500

1120.102 1524242 1.89E+09 500 1101.767 125622.3 2.21E+08 500

1130.102 1502725 1.9E+09 500 1111.767 123608.6 2.23E+08 500

1140.102 1482242 1.92E+09 500 1121.767 121641.2 2.24E+08 500

1150.102 1462425 1.93E+09 500 1131.767 119718.6 2.25E+08 500

1160.102 1443112 1.95E+09 500 1141.767 117839.3 2.26E+08 500

1170.102 1424222 1.96E+09 500 1151.767 116002 2.27E+08 500

1180.102 1405716 1.98E+09 500 1161.767 114205.4 2.28E+08 500

1190.102 1387569 1.99E+09 500 1171.767 112448.3 2.3E+08 500

1200.102 1369766 2E+09 500 1181.767 110729.6 2.31E+08 500

1210.102 1352296 2.02E+09 500 1191.767 109048.1 2.32E+08 500

1220.102 1335149 2.03E+09 500 1201.767 107402.8 2.33E+08 500

1230.102 1318316 2.04E+09 500 1211.767 105792.6 2.34E+08 500

1240.102 1301789 2.06E+09 500 1221.767 104216.6 2.35E+08 500

1250.102 1285560 2.07E+09 500 1231.767 102673.8 2.36E+08 500

1260.102 1269622 2.08E+09 500 1241.767 101163.2 2.37E+08 500

1270.102 1253967 2.1E+09 500 1251.767 99684.08 2.38E+08 500

1280.102 1238590 2.11E+09 500 1261.767 98235.45 2.39E+08 500

1290.102 1223483 2.12E+09 500 1271.767 96816.52 2.4E+08 500

1300.102 1208639 2.13E+09 500 1281.767 95426.48 2.41E+08 500

1310.102 1194053 2.14E+09 500 1291.767 94064.56 2.42E+08 500

1320.102 1179719 2.16E+09 500 1301.767 92730.01 2.43E+08 500

1330.102 1165630 2.17E+09 500 1311.767 91422.1 2.44E+08 500

1340.102 1151782 2.18E+09 500 1321.767 90140.15 2.45E+08 500

1350.102 1138168 2.19E+09 500 1331.767 88883.46 2.46E+08 500

1360.102 1124783 2.2E+09 500 1341.767 87651.39 2.46E+08 500

1370.102 1111622 2.21E+09 500 1351.767 86443.31 2.47E+08 500

1380.102 1098680 2.22E+09 500 1361.767 85258.59 2.48E+08 500

1390.102 1085952 2.24E+09 500 1371.767 84096.65 2.49E+08 500

1400.102 1073433 2.25E+09 500 1381.767 82956.92 2.5E+08 500

1410.102 1061119 2.26E+09 500 1391.767 81838.83 2.51E+08 500

1420.102 1049005 2.27E+09 500 1401.767 80741.84 2.51E+08 500

1430.102 1037087 2.28E+09 500 1411.767 79665.44 2.52E+08 500

1440.102 1025361 2.29E+09 500 1421.767 78609.12 2.53E+08 500

1450.102 1013822 2.3E+09 500 1431.767 77572.39 2.54E+08 500

1460.102 1002466 2.31E+09 500 1441.767 76554.77 2.55E+08 500

1470.102 991290.5 2.32E+09 500 1451.767 75555.79 2.55E+08 500

1480.102 980290.5 2.33E+09 500 1461.767 74575.03 2.56E+08 500

1490.102 969462.6 2.34E+09 500 1471.767 73612.03 2.57E+08 500

1500.102 958803.3 2.35E+09 500 1481.767 72666.37 2.58E+08 500

1510.102 948309 2.36E+09 500 1491.767 71737.66 2.58E+08 500

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1520.102 937976.4 2.37E+09 500 1501.767 70825.49 2.59E+08 500

1530.102 927802.1 2.38E+09 500 1511.767 69929.48 2.6E+08 500

1540.102 917783 2.39E+09 500 1521.767 69049.24 2.6E+08 500

1550.102 907915.9 2.39E+09 500 1531.767 68184.43 2.61E+08 500

1560.102 898197.7 2.4E+09 500 1541.767 67334.69 2.62E+08 500

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1590.102 869907.3 2.43E+09 500 1571.767 64872.47 2.64E+08 500

1600.102 860755.8 2.44E+09 500 1581.767 64079.65 2.64E+08 500

1610.102 851739.1 2.45E+09 500 1591.767 63300.28 2.65E+08 500

1620.102 842854.6 2.46E+09 500 1601.767 62534.06 2.66E+08 500

1630.102 834099.6 2.46E+09 500 1611.767 61780.7 2.66E+08 500

1640.102 825471.8 2.47E+09 500 1621.767 61039.92 2.67E+08 500

1650.102 816968.6 2.48E+09 500 1631.767 60311.44 2.68E+08 500

1660.102 808587.8 2.49E+09 500 1641.767 59594.99 2.68E+08 500

1670.102 800326.9 2.5E+09 500 1651.767 58890.32 2.69E+08 500

1680.102 792183.8 2.5E+09 500 1661.767 58197.18 2.69E+08 500

1690.102 784156.2 2.51E+09 500 1671.767 57515.32 2.7E+08 500

1700.102 776241.9 2.52E+09 500 1681.767 56844.49 2.7E+08 500

1710.102 768438.9 2.53E+09 500 1691.767 56184.48 2.71E+08 500

1720.102 760745.1 2.54E+09 500 1701.767 55535.04 2.72E+08 500

1730.102 753158.5 2.54E+09 500 1711.767 54895.96 2.72E+08 500

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1750.102 738299.1 2.56E+09 500 1731.767 53648.03 2.73E+08 500

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1790.102 709783.2 2.59E+09 500 1771.767 51267.36 2.75E+08 500

1800.102 702894.6 2.59E+09 500 1781.767 50695.07 2.76E+08 500

1810.102 696098.6 2.6E+09 500 1791.767 50131.56 2.76E+08 500

1820.102 689393.7 2.61E+09 500 1801.767 49576.66 2.77E+08 500

1830.102 682778.3 2.62E+09 500 1811.767 49030.2 2.77E+08 500

1840.102 676250.8 2.62E+09 500 1821.767 48492 2.78E+08 500

1850.102 669809.7 2.63E+09 500 1831.767 47961.91 2.78E+08 500

1860.102 663453.4 2.64E+09 500 1841.767 47439.77 2.79E+08 500

1870.102 657180.7 2.64E+09 500 1851.767 46925.42 2.79E+08 500

1880.102 650989.9 2.65E+09 500 1861.767 46418.72 2.8E+08 500

1890.102 644879.8 2.65E+09 500 1871.767 45919.5 2.8E+08 500

1900.102 638848.8 2.66E+09 500 1881.767 45427.64 2.81E+08 500

1910.102 632895.8 2.67E+09 500 1891.767 44942.99 2.81E+08 500

1920.102 627019.4 2.67E+09 500 1901.767 44465.41 2.82E+08 500

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1930.102 621218.3 2.68E+09 500 1911.767 43994.76 2.82E+08 500

1940.102 615491.2 2.69E+09 500 1921.767 43530.93 2.82E+08 500

1950.102 609836.9 2.69E+09 500 1931.767 43073.77 2.83E+08 500

1960.102 604254.3 2.7E+09 500 1941.767 42623.17 2.83E+08 500

1970.102 598742 2.7E+09 500 1951.767 42178.99 2.84E+08 500

1980.102 593299.1 2.71E+09 500 1961.767 41741.13 2.84E+08 500

1990.102 587924.2 2.72E+09 500 1971.767 41309.47 2.85E+08 500

2000.102 582616.5 2.72E+09 500 1981.767 40883.89 2.85E+08 500

2010.102 577374.6 2.73E+09 500 1991.767 40464.28 2.85E+08 500

2020.102 572197.6 2.73E+09 500 2000.01 67287.31 2.86E+08 300

2030.102 567084.5 2.74E+09 500 2004.578 47643.64 2.86E+08 300

2040.102 562034.2 2.75E+09 500 2014.578 46339.05 2.86E+08 300

2050.102 557045.7 2.75E+09 500 2024.578 45611.54 2.87E+08 300

2060.102 552118 2.76E+09 500 2034.578 45022.27 2.87E+08 300

2070.102 547250.2 2.76E+09 500 2044.578 44496.4 2.88E+08 300

2080.102 542441.3 2.77E+09 500 2054.578 44007.22 2.88E+08 300

2090.102 537690.3 2.77E+09 500 2064.578 43541.92 2.89E+08 300

2100.102 532996.5 2.78E+09 500 2074.578 43093.38 2.89E+08 300

2110.102 528358.9 2.78E+09 500 2084.578 42657.4 2.89E+08 300

2120.102 523776.6 2.79E+09 500 2094.578 42231.36 2.9E+08 300

2130.102 519248.7 2.79E+09 500 2104.578 41813.65 2.9E+08 300

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2205.459 529885.8 2.83E+09 350 2184.578 38696.05 2.94E+08 300

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2305.459 485026.4 2.88E+09 350 2284.578 35249.99 2.97E+08 300

2315.459 481073.7 2.89E+09 350 2294.578 34929.6 2.98E+08 300

2325.459 477168.4 2.89E+09 350 2304.578 34613.31 2.98E+08 300

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2335.459 473308.7 2.9E+09 350 2314.578 34301.07 2.98E+08 300

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2375.459 458305.2 2.92E+09 350 2354.578 33091.14 3E+08 300

2385.459 454659 2.92E+09 350 2364.578 32798.1 3E+08 300

2395.459 451053.3 2.93E+09 350 2374.578 32508.71 3E+08 300

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2425.459 440473.1 2.94E+09 350 2404.578 31661.9 3.01E+08 300

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2505.459 413900.6 2.97E+09 350 2484.578 29550.51 3.04E+08 300

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2535.459 404512 2.98E+09 350 2514.578 28809.84 3.05E+08 300

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2625.459 378065.7 3.02E+09 350 2604.578 26738.57 3.07E+08 300

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2655.459 369785.8 3.03E+09 350 2634.578 26094.7 3.08E+08 300

2665.459 367081.9 3.03E+09 350 2644.578 25884.92 3.08E+08 300

2675.459 364405.5 3.04E+09 350 2654.578 25677.5 3.08E+08 300

2685.459 361756.2 3.04E+09 350 2664.578 25472.41 3.09E+08 300

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2705.459 356537.3 3.05E+09 350 2684.578 25069.08 3.09E+08 300

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2725.459 351422.7 3.06E+09 350 2704.578 24674.65 3.1E+08 300

2735.459 348903.6 3.06E+09 350 2714.578 24480.7 3.1E+08 300

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2745.459 346409.5 3.06E+09 350 2724.578 24288.88 3.1E+08 300

2755.459 343940.2 3.07E+09 350 2734.578 24099.16 3.1E+08 300

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2775.459 339074.4 3.07E+09 350 2754.578 23725.91 3.11E+08 300

2785.459 336677.3 3.08E+09 350 2764.578 23542.32 3.11E+08 300

2795.459 334303.7 3.08E+09 350 2774.578 23360.71 3.11E+08 300

2805.459 331953.3 3.08E+09 350 2784.578 23181.06 3.12E+08 300

2815.459 329625.8 3.09E+09 350 2794.578 23003.34 3.12E+08 300

2825.459 327320.9 3.09E+09 350 2804.578 22827.52 3.12E+08 300

2835.459 325038.4 3.09E+09 350 2814.578 22653.57 3.12E+08 300

2845.459 322777.8 3.1E+09 350 2824.578 22481.48 3.12E+08 300

2855.459 320539.1 3.1E+09 350 2834.578 22311.21 3.13E+08 300

2865.459 318321.8 3.1E+09 350 2844.578 22142.74 3.13E+08 300

2875.459 316125.8 3.11E+09 350 2854.578 21976.04 3.13E+08 300

2885.459 313950.7 3.11E+09 350 2864.578 21811.09 3.13E+08 300

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2905.459 309662.5 3.12E+09 350 2884.578 21486.35 3.14E+08 300

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2935.459 303381 3.13E+09 350 2914.578 21011.77 3.14E+08 300

2945.459 301326.5 3.13E+09 350 2924.578 20856.83 3.15E+08 300

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2965.459 297274.9 3.13E+09 350 2944.578 20551.7 3.15E+08 300

2975.459 295277.3 3.14E+09 350 2954.578 20401.46 3.15E+08 300

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2995.459 291337.7 3.14E+09 350 2974.578 20105.56 3.16E+08 300

3005.459 289395.2 3.15E+09 350 2984.578 19959.85 3.16E+08 300

3015.459 287470.5 3.15E+09 350 2994.578 19815.6 3.16E+08 300

3025.459 285563.6 3.15E+09 350 3000.068 27424.93 3.16E+08 100

3035.459 283674.1 3.15E+09 350 3008.003 23393.79 3.16E+08 100

3045.459 281801.8 3.16E+09 350 3018.003 22945.61 3.17E+08 100

3055.459 279946.7 3.16E+09 350 3028.003 22662.52 3.17E+08 100

3065.459 278108.4 3.16E+09 350 3038.003 22433.07 3.17E+08 100

3075.459 276286.7 3.17E+09 350 3048.003 22230.32 3.17E+08 100

3085.459 274481.5 3.17E+09 350 3058.003 22043.67 3.17E+08 100

3095.459 272692.6 3.17E+09 350 3068.003 21867.82 3.18E+08 100

3105.459 270919.8 3.17E+09 350 3078.003 21699.71 3.18E+08 100

3115.459 269162.9 3.18E+09 350 3088.003 21537.4 3.18E+08 100

3125.459 267421.7 3.18E+09 350 3098.003 21379.6 3.18E+08 100

3135.459 265696 3.18E+09 350 3108.003 21225.43 3.19E+08 100

3145.459 263985.7 3.18E+09 350 3118.003 21074.24 3.19E+08 100

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3155.459 262290.5 3.19E+09 350 3128.003 20925.6 3.19E+08 100

3165.459 260610.4 3.19E+09 350 3138.003 20779.17 3.19E+08 100

3175.459 258945.1 3.19E+09 350 3148.003 20634.74 3.19E+08 100

3185.459 257294.4 3.19E+09 350 3158.003 20492.11 3.2E+08 100

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3205.459 254036.4 3.2E+09 350 3178.003 20211.83 3.2E+08 100

3215.459 252428.8 3.2E+09 350 3188.003 20074 3.2E+08 100

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3235.459 249255.3 3.21E+09 350 3208.003 19802.67 3.21E+08 100

3245.459 247689.3 3.21E+09 350 3218.003 19669.09 3.21E+08 100

3255.459 246136.7 3.21E+09 350 3228.003 19536.85 3.21E+08 100

3265.459 244597.5 3.21E+09 350 3238.003 19405.92 3.21E+08 100

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3508.003 16305.53 3.26E+08 100

3518.003 16204.94 3.26E+08 100

3528.003 16105.25 3.26E+08 100

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3538.003 16006.45 3.26E+08 100

3548.003 15908.53 3.27E+08 100

3558.003 15811.48 3.27E+08 100

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3918.003 12821.55 3.32E+08 100

3928.003 12750.65 3.32E+08 100

3938.003 12680.32 3.32E+08 100

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3948.003 12610.55 3.32E+08 100

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4318.003 10377.08 3.37E+08 100

4328.003 10324.96 3.37E+08 100

4338.003 10273.23 3.37E+08 100

4348.003 10221.87 3.37E+08 100

146

4358.003 10170.88 3.37E+08 100

4368.003 10120.26 3.37E+08 100

4378.003 10070.01 3.37E+08 100

4388.003 10020.12 3.37E+08 100

4398.003 9970.59 3.37E+08 100

4408.003 9921.415 3.37E+08 100

4418.003 9872.593 3.38E+08 100

4428.003 9824.12 3.38E+08 100

4438.003 9775.993 3.38E+08 100

4448.003 9728.208 3.38E+08 100

4458.003 9680.763 3.38E+08 100

4468.003 9633.653 3.38E+08 100

4478.003 9586.877 3.38E+08 100

4488.003 9540.431 3.38E+08 100

4498.003 9494.311 3.38E+08 100

4508.003 9448.515 3.38E+08 100

4518.003 9403.041 3.38E+08 100

4528.003 9357.884 3.39E+08 100

4538.003 9313.042 3.39E+08 100

4548.003 9268.512 3.39E+08 100

4558.003 9224.291 3.39E+08 100

4568.003 9180.377 3.39E+08 100

4578.003 9136.767 3.39E+08 100

4588.003 9093.457 3.39E+08 100

4598.003 9050.446 3.39E+08 100

4608.003 9007.73 3.39E+08 100

4618.003 8965.307 3.39E+08 100

4628.003 8923.174 3.39E+08 100

4638.003 8881.328 3.4E+08 100

4648.003 8839.768 3.4E+08 100

4658.003 8798.49 3.4E+08 100

4668.003 8757.491 3.4E+08 100

4678.003 8716.771 3.4E+08 100

4688.003 8676.325 3.4E+08 100

4698.003 8636.151 3.4E+08 100

4708.003 8596.248 3.4E+08 100

4718.003 8556.612 3.4E+08 100

4728.003 8517.242 3.4E+08 100

4738.003 8478.135 3.4E+08 100

4748.003 8439.288 3.41E+08 100

4758.003 8400.7 3.41E+08 100

147

4768.003 8362.368 3.41E+08 100

4778.003 8324.29 3.41E+08 100

4788.003 8286.463 3.41E+08 100

4798.003 8248.886 3.41E+08 100

4808.003 8211.557 3.41E+08 100

4818.003 8174.472 3.41E+08 100

4828.003 8137.631 3.41E+08 100

4838.003 8101.031 3.41E+08 100

4848.003 8064.67 3.41E+08 100

4858.003 8028.545 3.41E+08 100

4868.003 7992.655 3.42E+08 100

4878.003 7956.999 3.42E+08 100

4888.003 7921.573 3.42E+08 100

4898.003 7886.376 3.42E+08 100

4908.003 7851.405 3.42E+08 100

4918.003 7816.66 3.42E+08 100

4928.003 7782.138 3.42E+08 100

4938.003 7747.838 3.42E+08 100

4948.003 7713.756 3.42E+08 100

4958.003 7679.892 3.42E+08 100

4968.003 7646.244 3.42E+08 100

4978.003 7612.81 3.42E+08 100

4988.003 7579.587 3.42E+08 100

4998.003 7546.575 3.43E+08 100

Case 2-C(a) Case 2-C(b)

pi=4800 psia, T=200F, SG=0.65

t(day) qsc(SCFD) Gp(SCF) Pwf(psia) t(day) qsc(SCFD) Gp(SCF) Pwf(psia)

0.01 10882556 108825.6 350 0.01 6957340 69573.4 2575

0.249885 7082064 1952312 350 0.393896 4384120 1892456 2575

1.510208 6116949 10039066 350 6.70354 3544496 25513369 2575

11.09237 5314630 63263127 350 26.70354 3219178 92294135 2575

31.09237 4932679 1.65E+08 350 46.70354 3041933 1.55E+08 2575

51.09237 4673307 2.61E+08 350 66.70354 2883056 2.14E+08 2575

71.09237 4440451 3.52E+08 350 86.70354 2736172 2.7E+08 2575

91.09237 4227147 4.38E+08 350 106.7035 2599836 3.23E+08 2575

111.0924 4030838 5.21E+08 350 126.7035 2472981 3.74E+08 2575

131.0924 3849542 6E+08 350 146.7035 2354691 4.22E+08 2575

151.0924 3681586 6.75E+08 350 166.7035 2244162 4.68E+08 2575

171.0924 3525543 7.47E+08 350 186.7035 2140691 5.12E+08 2575

148

191.0924 3380185 8.16E+08 350 206.7035 2043658 5.54E+08 2575

211.0924 3244453 8.82E+08 350 226.7035 1952514 5.94E+08 2575

231.0924 3117423 9.45E+08 350 246.7035 1866771 6.32E+08 2575

251.0924 2998290 1.01E+09 350 266.7035 1785993 6.68E+08 2575

271.0924 2886347 1.07E+09 350 286.7035 1709792 7.03E+08 2575

291.0924 2780969 1.12E+09 350 306.7035 1637816 7.37E+08 2575

311.0924 2681604 1.18E+09 350 326.7035 1569752 7.69E+08 2575

331.0924 2587760 1.23E+09 350 346.7035 1505316 7.99E+08 2575

351.0924 2498999 1.28E+09 350 366.7035 1444248 8.29E+08 2575

371.0924 2414928 1.33E+09 350 386.7035 1386317 8.57E+08 2575

391.0924 2335196 1.38E+09 350 406.7035 1331309 8.84E+08 2575

411.0924 2259485 1.42E+09 350 426.7035 1279030 9.1E+08 2575

431.0924 2187507 1.47E+09 350 446.7035 1229302 9.35E+08 2575

451.0924 2119003 1.51E+09 350 466.7035 1181964 9.59E+08 2575

471.0924 2053737 1.55E+09 350 486.7035 1136866 9.83E+08 2575

491.0924 1991493 1.59E+09 350 506.7035 1093872 1E+09 2575

511.0924 1932077 1.63E+09 350 526.7035 1052854 1.03E+09 2575

531.0924 1875308 1.67E+09 350 546.7035 1013696 1.05E+09 2575

551.0924 1821021 1.71E+09 350 566.7035 976290.7 1.07E+09 2575

571.0924 1769067 1.74E+09 350 586.7035 940538.2 1.09E+09 2575

591.0924 1719306 1.78E+09 350 606.7035 906345.9 1.1E+09 2575

611.0924 1671610 1.81E+09 350 626.7035 873628.1 1.12E+09 2575

631.0924 1625861 1.84E+09 350 646.7035 842304.8 1.14E+09 2575

651.0924 1581949 1.88E+09 350 666.7035 812301.6 1.16E+09 2575

671.0924 1539773 1.91E+09 350 686.7035 783549.3 1.17E+09 2575

691.0924 1499239 1.94E+09 350 706.7035 755983.2 1.19E+09 2575

711.0924 1460259 1.97E+09 350 726.7035 729542.7 1.2E+09 2575

731.0924 1422753 2E+09 350 746.7035 704171.3 1.22E+09 2575

751.0924 1386644 2.02E+09 350 766.7035 679816 1.23E+09 2575

771.0924 1351862 2.05E+09 350 786.7035 656427.1 1.24E+09 2575

791.0924 1318340 2.08E+09 350 806.7035 633957.9 1.26E+09 2575

811.0924 1286018 2.1E+09 350 826.7035 612364.5 1.27E+09 2575

831.0924 1254836 2.13E+09 350 846.7035 591605.9 1.28E+09 2575

851.0924 1224741 2.15E+09 350 866.7035 571643.1 1.29E+09 2575

871.0924 1195682 2.18E+09 350 886.7035 552439.6 1.3E+09 2575

891.0924 1167610 2.2E+09 350 906.7035 533960.8 1.31E+09 2575

911.0924 1140482 2.22E+09 350 926.7035 516174.4 1.33E+09 2575

931.0924 1114254 2.25E+09 350 946.7035 499049.4 1.34E+09 2575

951.0924 1088887 2.27E+09 350 966.7035 482556.9 1.34E+09 2575

149

971.0924 1064343 2.29E+09 350 986.7035 466669.4 1.35E+09 2575

991.0924 1040586 2.31E+09 350 1006.704 451360.7 1.36E+09 2575

1011.092 1017583 2.33E+09 350 1026.704 436606.3 1.37E+09 2575

1031.092 995302.4 2.35E+09 350 1046.704 422382.8 1.38E+09 2575

1051.092 973713.8 2.37E+09 350 1066.704 408668 1.39E+09 2575

1071.092 952788.7 2.39E+09 350 1086.704 395440.7 1.4E+09 2575

1091.092 932500.3 2.41E+09 350 1106.704 382681.1 1.41E+09 2575

1111.092 912823 2.43E+09 350 1126.704 370370.1 1.41E+09 2575

1131.092 893732.5 2.45E+09 350 1146.704 358489.7 1.42E+09 2575

1151.092 875205.9 2.46E+09 350 1166.704 347022.5 1.43E+09 2575

1171.092 857221.1 2.48E+09 350 1186.704 335952.2 1.43E+09 2575

1191.092 839757.3 2.5E+09 350 1206.704 325263.3 1.44E+09 2575

1211.092 822794.8 2.52E+09 350 1226.704 314940.7 1.45E+09 2575

1231.092 806314.6 2.53E+09 350 1246.704 304970.4 1.45E+09 2575

1251.092 790298.9 2.55E+09 350 1266.704 295338.8 1.46E+09 2575

1271.092 774730.4 2.56E+09 350 1286.704 286032.9 1.46E+09 2575

1291.092 759592.9 2.58E+09 350 1306.704 277040.5 1.47E+09 2575

1311.092 744870.7 2.59E+09 350 1326.704 268349.7 1.48E+09 2575

1331.092 730549 2.61E+09 350 1346.704 259949.2 1.48E+09 2575

1351.092 716613.6 2.62E+09 350 1366.704 251828.3 1.49E+09 2575

1371.092 703050.8 2.64E+09 350 1386.704 243976.6 1.49E+09 2575

1391.092 689847.7 2.65E+09 350 1406.704 236384.3 1.5E+09 2575

1411.092 676991.9 2.66E+09 350 1426.704 229042 1.5E+09 2575

1431.092 664471.5 2.68E+09 350 1446.704 221940.5 1.51E+09 2575

1451.092 652275.2 2.69E+09 350 1466.704 215071.1 1.51E+09 2575

1471.092 640391.9 2.7E+09 350 1486.704 208425.7 1.51E+09 2575

1491.092 628811.3 2.72E+09 350 1506.704 201996.1 1.52E+09 2575

1511.092 617523.4 2.73E+09 350 1526.704 195774.8 1.52E+09 2575

1531.092 606518.5 2.74E+09 350 1546.704 189754.4 1.53E+09 2575

1551.092 595787.5 2.75E+09 350 1566.704 183927.8 1.53E+09 2575

1571.092 585321.6 2.77E+09 350 1586.704 178288.4 1.53E+09 2575

1591.092 575112.2 2.78E+09 350 1606.704 172829.5 1.54E+09 2575

1611.092 565151.2 2.79E+09 350 1626.704 167544.9 1.54E+09 2575

1631.092 555430.8 2.8E+09 350 1646.704 162428.7 1.54E+09 2575

1651.092 545943.5 2.81E+09 350 1666.704 157475.1 1.55E+09 2575

1671.092 536682 2.82E+09 350 1686.704 152678.6 1.55E+09 2575

1691.092 527639.3 2.83E+09 350 1706.704 148033.7 1.55E+09 2575

1711.092 518808.9 2.84E+09 350 1726.704 143535.4 1.56E+09 2575

1731.092 510184.2 2.85E+09 350 1746.704 139178.7 1.56E+09 2575

150

1751.092 501759.1 2.86E+09 350 1766.704 134958.9 1.56E+09 2575

1771.092 493527.6 2.87E+09 350 1786.704 130871.4 1.56E+09 2575

1791.092 485483.9 2.88E+09 350 1806.704 126911.8 1.57E+09 2575

1811.092 477622.6 2.89E+09 350 1826.704 123075.8 1.57E+09 2575

1831.092 469938.2 2.9E+09 350 1846.704 119359.5 1.57E+09 2575

1851.092 462425.7 2.91E+09 350 1866.704 115758.7 1.57E+09 2575

1871.092 455080 2.92E+09 350 1886.704 112269.7 1.58E+09 2575

1891.092 447896.5 2.93E+09 350 1906.704 108888.9 1.58E+09 2575

1911.092 440870.4 2.94E+09 350 1926.704 105612.8 1.58E+09 2575

1931.092 433997.4 2.95E+09 350 1946.704 102437.8 1.58E+09 2575

1951.092 427273.1 2.96E+09 350 1966.704 99360.85 1.58E+09 2575

1971.092 420693.3 2.96E+09 350 1986.704 96378.63 1.59E+09 2575

1991.092 414254.2 2.97E+09 350 2006.704 93488.13 1.59E+09 2575

2011.092 407951.8 2.98E+09 350 2026.704 90686.38 1.59E+09 2575

2031.092 401782.3 2.99E+09 350 2046.704 87970.56 1.59E+09 2575

2051.092 395742.1 3E+09 350 2066.704 85337.9 1.59E+09 2575

2071.092 389827.9 3E+09 350 2086.704 82785.76 1.6E+09 2575

2091.092 384036 3.01E+09 350 2106.704 80311.56 1.6E+09 2575

2111.092 378363.4 3.02E+09 350 2126.704 77912.84 1.6E+09 2575

2131.092 372806.9 3.03E+09 350 2146.704 75587.2 1.6E+09 2575

2151.092 367363.3 3.03E+09 350 2166.704 73332.33 1.6E+09 2575

2171.092 362029.8 3.04E+09 350 2186.704 71145.99 1.6E+09 2575

2191.092 356803.4 3.05E+09 350 2206.704 69026.04 1.6E+09 2575

2211.092 351681.4 3.06E+09 350 2226.704 66970.38 1.61E+09 2575

2231.092 346661.1 3.06E+09 350 2246.704 64977 1.61E+09 2575

2251.092 341739.9 3.07E+09 350 2266.704 63043.95 1.61E+09 2575

2271.092 336915.3 3.08E+09 350 2286.704 61169.35 1.61E+09 2575

2291.092 332184.8 3.08E+09 350 2306.704 59351.36 1.61E+09 2575

2311.092 327546.1 3.09E+09 350 2326.704 57588.25 1.61E+09 2575

2331.092 322996.9 3.1E+09 350 2346.704 55878.28 1.61E+09 2575

2351.092 318535 3.1E+09 350 2366.704 54219.83 1.61E+09 2575

2371.092 314158.1 3.11E+09 350 2386.704 52611.3 1.62E+09 2575

2391.092 309864.3 3.12E+09 350 2406.704 51051.13 1.62E+09 2575

2411.092 305651.4 3.12E+09 350 2426.704 49537.85 1.62E+09 2575

2431.092 301517.6 3.13E+09 350 2446.704 48070 1.62E+09 2575

2451.092 297460.9 3.13E+09 350 2466.704 46646.19 1.62E+09 2575

2471.092 293479.4 3.14E+09 350 2486.704 45265.06 1.62E+09 2575

2491.092 289571.4 3.15E+09 350 2506.704 43925.31 1.62E+09 2575

2511.092 285735.1 3.15E+09 350 2526.704 42625.66 1.62E+09 2575

151

2531.092 281968.8 3.16E+09 350 2546.704 41364.9 1.62E+09 2575

2551.092 278270.9 3.16E+09 350 2566.704 40141.83 1.62E+09 2575

2571.092 274639.8 3.17E+09 350 2586.704 38955.3 1.62E+09 2575

2591.092 271073.9 3.17E+09 350 2606.704 37804.2 1.63E+09 2575

2611.092 267571.7 3.18E+09 350 2626.704 36687.44 1.63E+09 2575

2631.092 264131.7 3.18E+09 350 2646.704 35604 1.63E+09 2575

2651.092 260752.6 3.19E+09 350 2666.704 34552.85 1.63E+09 2575

2671.092 257432.9 3.19E+09 350 2686.704 33533.01 1.63E+09 2575

2691.092 254171.3 3.2E+09 350 2706.704 32543.53 1.63E+09 2575

2711.092 250966.5 3.2E+09 350 2726.704 31583.51 1.63E+09 2575

2731.092 247817.2 3.21E+09 350 2746.704 30652.03 1.63E+09 2575

2751.092 244722.1 3.21E+09 350 2766.704 29748.25 1.63E+09 2575

2771.092 241680.2 3.22E+09 350 2786.704 28871.32 1.63E+09 2575

2791.092 238690.1 3.22E+09 350 2806.704 28020.44 1.63E+09 2575

2811.092 235750.7 3.23E+09 350 2826.704 27194.82 1.63E+09 2575

2831.092 232861 3.23E+09 350 2846.704 26393.7 1.63E+09 2575

2851.092 230019.9 3.24E+09 350 2866.704 25616.35 1.63E+09 2575

2871.092 227226.3 3.24E+09 350 2886.704 24862.04 1.63E+09 2575

2891.092 224479.1 3.25E+09 350 2906.704 24130.09 1.63E+09 2575

2911.092 221777.5 3.25E+09 350 2926.704 23419.82 1.63E+09 2575

2931.092 219120.3 3.26E+09 350 2946.704 22730.59 1.64E+09 2575

2951.092 216506.8 3.26E+09 350 2966.704 22061.76 1.64E+09 2575

2971.092 213935.8 3.27E+09 350 2986.704 21412.73 1.64E+09 2575

2991.092 211406.7 3.27E+09 350 3006.704 20782.9 1.64E+09 2575

3011.092 208918.4 3.27E+09 350 3026.704 20171.69 1.64E+09 2575

3031.092 206470.2 3.28E+09 350 3046.704 19578.56 1.64E+09 2575

3051.092 204061.1 3.28E+09 350 3066.704 19002.95 1.64E+09 2575

3071.092 201690.5 3.29E+09 350 3086.704 18444.36 1.64E+09 2575

3091.092 199357.4 3.29E+09 350 3106.704 17902.26 1.64E+09 2575

3111.092 197061.2 3.29E+09 350 3126.704 17376.17 1.64E+09 2575

3131.092 194801 3.3E+09 350 3146.704 16865.61 1.64E+09 2575

3151.092 192576.3 3.3E+09 350 3166.704 16370.12 1.64E+09 2575

3171.092 190386.1 3.31E+09 350 3186.704 15889.25 1.64E+09 2575

3191.092 188229.9 3.31E+09 350 3206.704 15422.56 1.64E+09 2575

3211.092 186107 3.31E+09 350 3226.704 14969.64 1.64E+09 2575

3231.092 184016.7 3.32E+09 350 3246.704 14530.07 1.64E+09 2575

3251.092 181958.3 3.32E+09 350 3266.704 14103.45 1.64E+09 2575

3271.092 179931.2 3.32E+09 350 3286.704 13689.41 1.64E+09 2575

3291.092 177934.9 3.33E+09 350 3306.704 13287.57 1.64E+09 2575

152

3311.092 175968.7 3.33E+09 350 3326.704 12897.57 1.64E+09 2575

3331.092 174032 3.33E+09 350 3346.704 12519.05 1.64E+09 2575

3351.092 172124.3 3.34E+09 350 3366.704 12151.67 1.64E+09 2575

3371.092 170245 3.34E+09 350 3386.704 11795.11 1.64E+09 2575

3391.092 168393.5 3.34E+09 350 3406.704 11449.05 1.64E+09 2575

3411.092 166569.3 3.35E+09 350 3426.704 11113.17 1.64E+09 2575

3431.092 164772 3.35E+09 350 3446.704 10787.17 1.64E+09 2575

3451.092 163000.9 3.35E+09 350 3466.704 10470.77 1.64E+09 2575

3471.092 161255.7 3.36E+09 350 3486.704 10163.67 1.64E+09 2575

3491.092 159535.7 3.36E+09 350 3506.704 9865.597 1.64E+09 2575

3511.092 157840.6 3.36E+09 350 3526.704 9576.291 1.64E+09 2575

3531.092 156169.9 3.37E+09 350 3546.704 9295.491 1.64E+09 2575

3551.092 154523.1 3.37E+09 350 3566.704 9022.945 1.64E+09 2575

3571.092 152899.8 3.37E+09 350 3586.704 8758.409 1.64E+09 2575

3591.092 151299.5 3.38E+09 350 3606.704 8501.646 1.64E+09 2575

3611.092 149721.8 3.38E+09 350 3626.704 8252.428 1.64E+09 2575

3631.092 148166.4 3.38E+09 350 3646.704 8010.531 1.64E+09 2575

3651.092 146632.8 3.39E+09 350 3666.704 7775.74 1.65E+09 2575

3671.092 145120.6 3.39E+09 350 3686.704 7547.845 1.65E+09 2575

3691.092 143629.5 3.39E+09 350 3706.704 7326.642 1.65E+09 2575

3711.092 142158.9 3.39E+09 350 3726.704 7111.934 1.65E+09 2575

3731.092 140708.7 3.4E+09 350 3746.704 6903.531 1.65E+09 2575

3751.092 139278.4 3.4E+09 350 3766.704 6701.245 1.65E+09 2575

3771.092 137867.7 3.4E+09 350 3786.704 6504.897 1.65E+09 2575

3791.092 136476.2 3.41E+09 350 3806.704 6314.312 1.65E+09 2575

3811.092 135103.6 3.41E+09 350 3826.704 6129.321 1.65E+09 2575

3831.092 133749.6 3.41E+09 350 3846.704 5949.757 1.65E+09 2575

3851.092 132413.8 3.41E+09 350 3866.704 5775.463 1.65E+09 2575

3871.092 131095.9 3.42E+09 350 3886.704 5606.282 1.65E+09 2575

3891.092 129795.6 3.42E+09 350 3906.704 5442.064 1.65E+09 2575

3911.092 128512.6 3.42E+09 350 3926.704 5282.664 1.65E+09 2575

3931.092 127246.6 3.42E+09 350 3946.704 5127.939 1.65E+09 2575

3951.092 125997.4 3.43E+09 350 3966.704 4977.751 1.65E+09 2575

3971.092 124764.5 3.43E+09 350 3986.704 4831.969 1.65E+09 2575

3991.092 123547.9 3.43E+09 350 4006.704 4690.461 1.65E+09 2575

4011.092 122347.1 3.43E+09 350 4026.704 4553.102 1.65E+09 2575

4031.092 121161.9 3.44E+09 350 4046.704 4419.771 1.65E+09 2575

4051.092 119992.1 3.44E+09 350 4066.704 4290.349 1.65E+09 2575

4071.092 118837.4 3.44E+09 350 4086.704 4164.721 1.65E+09 2575

153

4091.092 117697.5 3.44E+09 350 4106.704 4042.775 1.65E+09 2575

4111.092 116572.2 3.45E+09 350 4126.704 3924.404 1.65E+09 2575

4131.092 115461.3 3.45E+09 350 4146.704 3809.503 1.65E+09 2575

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8971.092 19424.43 3.69E+09 350 8958.799 95014.84 3.49E+09 350

8991.092 19306.37 3.69E+09 350 8978.799 94168.2 3.49E+09 350

9011.092 19189.13 3.69E+09 350 8998.799 93331.51 3.5E+09 350

9031.092 19072.72 3.69E+09 350 9018.799 92504.61 3.5E+09 350

9051.092 18957.12 3.69E+09 350 9038.799 91687.36 3.5E+09 350

9071.092 18842.32 3.69E+09 350 9058.799 90879.61 3.5E+09 350

9091.092 18728.33 3.69E+09 350 9078.799 90081.23 3.5E+09 350

9111.092 18615.14 3.7E+09 350 9098.799 89292.06 3.51E+09 350

9131.092 18502.73 3.7E+09 350 9118.799 88511.98 3.51E+09 350

9151.092 18391.1 3.7E+09 350 9138.799 87740.84 3.51E+09 350

9171.092 18280.25 3.7E+09 350 9158.799 86978.53 3.51E+09 350

9191.092 18170.16 3.7E+09 350 9178.799 86224.9 3.51E+09 350

9211.092 18060.84 3.7E+09 350 9198.799 85479.83 3.51E+09 350

9231.092 17952.27 3.7E+09 350 9218.799 84743.2 3.52E+09 350

9251.092 17844.46 3.7E+09 350 9238.799 84014.88 3.52E+09 350

9271.092 17737.38 3.7E+09 350 9258.799 83294.75 3.52E+09 350

9291.092 17631.04 3.7E+09 350 9278.799 82582.69 3.52E+09 350

9311.092 17525.43 3.7E+09 350 9298.799 81878.59 3.52E+09 350

9331.092 17420.55 3.7E+09 350 9318.799 81182.33 3.52E+09 350

9351.092 17316.39 3.7E+09 350 9338.799 80493.81 3.53E+09 350

9371.092 17212.93 3.7E+09 350 9358.799 79812.9 3.53E+09 350

9391.092 17110.19 3.7E+09 350 9378.799 79139.51 3.53E+09 350

9411.092 17008.14 3.7E+09 350 9398.799 78473.52 3.53E+09 350

9431.092 16906.8 3.7E+09 350 9418.799 77814.83 3.53E+09 350

9451.092 16806.14 3.7E+09 350 9438.799 77163.34 3.53E+09 350

9471.092 16706.16 3.7E+09 350 9458.799 76518.95 3.54E+09 350

9491.092 16606.86 3.7E+09 350 9478.799 75881.55 3.54E+09 350

9511.092 16508.24 3.7E+09 350 9498.799 75251.05 3.54E+09 350

9531.092 16410.28 3.7E+09 350 9518.799 74627.36 3.54E+09 350

160

9551.092 16312.99 3.7E+09 350 9538.799 74010.38 3.54E+09 350

9571.092 16216.35 3.7E+09 350 9558.799 73400.01 3.54E+09 350

9591.092 16120.37 3.7E+09 350 9578.799 72796.18 3.54E+09 350

9611.092 16025.03 3.7E+09 350 9598.799 72198.77 3.55E+09 350

9631.092 15930.33 3.7E+09 350 9618.799 71607.72 3.55E+09 350

9651.092 15836.26 3.7E+09 350 9638.799 71022.93 3.55E+09 350

9671.092 15742.83 3.7E+09 350 9658.799 70444.32 3.55E+09 350

9691.092 15650.02 3.71E+09 350 9678.799 69871.79 3.55E+09 350

9711.092 15557.84 3.71E+09 350 9698.799 69305.28 3.55E+09 350

9731.092 15466.27 3.71E+09 350 9718.799 68744.71 3.55E+09 350

9751.092 15375.31 3.71E+09 350 9738.799 68189.98 3.56E+09 350

9771.092 15284.96 3.71E+09 350 9758.799 67641.02 3.56E+09 350

9791.092 15195.2 3.71E+09 350 9778.799 67097.76 3.56E+09 350

9811.092 15106.05 3.71E+09 350 9798.799 66560.12 3.56E+09 350

9831.092 15017.48 3.71E+09 350 9818.799 66028.02 3.56E+09 350

9851.092 14929.51 3.71E+09 350 9838.799 65501.4 3.56E+09 350

Case Study 2-C(c) Case Study 2-C(d)

pi=4800 psia, T=200F, SG=0.65

t(day) qsc(SCFD) Gp(SCF) Pwf(psia) t(day) qsc(SCFD) Gp(SCF) Pwf(psia)

0.01 4784279 47842.79 3318 0.01 982488.7 9824.887 4503

0.787142 2860153 2447308 3318 1.425055 567826.1 863199.5 4503

15.62955 2309099 38644536 3318 12.42506 483996.6 6433669 4503

35.62955 2162443 83172789 3318 32.42506 449987.7 15718875 4503

55.62955 2045188 1.25E+08 3318 52.42506 424689.4 24449167 4503

75.62955 1936875 1.65E+08 3318 72.42506 401134 32693202 4503

95.62955 1835943 2.03E+08 3318 92.42506 378968.1 40480922 4503

115.6295 1741693 2.38E+08 3318 112.4251 358093 47839020 4503

135.6295 1653538 2.72E+08 3318 132.4251 338426.2 54792435 4503

155.6295 1570959 3.04E+08 3318 152.4251 319891.4 61364523 4503

175.6295 1493495 3.35E+08 3318 172.4251 302418 67577172 4503

195.6295 1420733 3.64E+08 3318 192.4251 285940.3 73450914 4503

215.6295 1352302 3.92E+08 3318 212.4251 270397.1 79005011 4503

235.6295 1287872 4.18E+08 3318 232.4251 255731.6 84257551 4503

255.6295 1227142 4.43E+08 3318 252.4251 241890.7 89225525 4503

275.6295 1169841 4.67E+08 3318 272.4251 228825 93924901 4503

295.6295 1115725 4.9E+08 3318 292.4251 216488.4 98370691 4503

315.6295 1064569 5.12E+08 3318 312.4251 204837.6 1.03E+08 4503

335.6295 1016172 5.33E+08 3318 332.4251 193832.5 1.07E+08 4503

355.6295 970346.5 5.52E+08 3318 352.4251 183435.2 1.1E+08 4503

161

375.6295 926924.1 5.71E+08 3318 372.4251 173610.5 1.14E+08 4503

395.6295 885748.9 5.89E+08 3318 392.4251 164325.2 1.17E+08 4503

415.6295 846678.4 6.07E+08 3318 412.4251 155548.5 1.2E+08 4503

435.6295 809580.9 6.23E+08 3318 432.4251 147251.1 1.23E+08 4503

455.6295 774335.6 6.39E+08 3318 452.4251 139405.9 1.26E+08 4503

475.6295 740830.5 6.54E+08 3318 472.4251 131987.1 1.29E+08 4503

495.6295 708962.3 6.69E+08 3318 492.4251 124970.8 1.32E+08 4503

515.6295 678635.3 6.83E+08 3318 512.4251 118334.2 1.34E+08 4503

535.6295 649760.6 6.96E+08 3318 532.4251 112056.2 1.36E+08 4503

555.6295 622255.9 7.09E+08 3318 552.4251 106116.7 1.39E+08 4503

575.6295 596044.2 7.21E+08 3318 572.4251 100497 1.41E+08 4503

595.6295 571054.4 7.32E+08 3318 592.4251 95179.24 1.43E+08 4503

615.6295 547219.6 7.44E+08 3318 612.4251 90146.81 1.44E+08 4503

635.6295 524477.8 7.54E+08 3318 632.4251 85383.99 1.46E+08 4503

655.6295 502770.9 7.65E+08 3318 652.4251 80875.97 1.48E+08 4503

675.6295 482044.5 7.74E+08 3318 663.409 582199.7 1.52E+08 4206

695.6295 462247.6 7.84E+08 3318 683.409 530066.7 1.63E+08 4206

715.6295 443332.6 7.93E+08 3318 703.409 501426.9 1.73E+08 4206

735.6295 425254.6 8.02E+08 3318 723.409 475236.1 1.83E+08 4206

755.6295 407971.5 8.1E+08 3318 743.409 450546.4 1.92E+08 4206

775.6295 391443.9 8.18E+08 3318 763.409 427227.2 2.01E+08 4206

795.6295 375634.5 8.25E+08 3318 783.409 405192 2.09E+08 4206

815.6295 360508.2 8.33E+08 3318 803.409 384362.3 2.17E+08 4206

835.6295 346032 8.4E+08 3318 823.409 364665.3 2.25E+08 4206

855.6295 332174.7 8.47E+08 3318 843.409 346033.1 2.32E+08 4206

875.6295 318906.9 8.53E+08 3318 863.409 328402.7 2.39E+08 4206

895.6295 306200.8 8.59E+08 3318 883.409 311715.2 2.45E+08 4206

915.6295 294030.3 8.65E+08 3318 903.409 295915.9 2.51E+08 4206

935.6295 282370.3 8.71E+08 3318 923.409 280953.4 2.57E+08 4206

955.6295 271197.5 8.77E+08 3318 943.409 266779.8 2.62E+08 4206

975.6295 260489.5 8.82E+08 3318 963.409 253350.4 2.68E+08 4206

995.6295 250225.2 8.87E+08 3318 983.409 240623.3 2.72E+08 4206

1015.63 240384.7 8.92E+08 3318 1003.409 228559.1 2.77E+08 4206

1035.63 230948.9 8.97E+08 3318 1023.409 217121.1 2.82E+08 4206

1055.63 221899.9 9.01E+08 3318 1043.409 206274.5 2.86E+08 4206

1075.63 213220.6 9.06E+08 3318 1063.409 195987.1 2.9E+08 4206

1095.63 204894.6 9.1E+08 3318 1083.409 186228.2 2.94E+08 4206

1115.63 196906.5 9.14E+08 3318 1103.409 176969.3 2.97E+08 4206

1135.63 189241.7 9.18E+08 3318 1123.409 168183.3 3.01E+08 4206

1155.63 181886.1 9.21E+08 3318 1143.409 159844.9 3.04E+08 4206

1175.63 174826.5 9.25E+08 3318 1163.409 151930.1 3.07E+08 4206

162

1195.63 168050.1 9.28E+08 3318 1183.409 144416.5 3.1E+08 4206

1215.63 161545 9.32E+08 3318 1203.409 137282.8 3.13E+08 4206

1235.63 155299.5 9.35E+08 3318 1223.409 130509.1 3.16E+08 4206

1255.63 149302.8 9.38E+08 3318 1243.409 124076.3 3.18E+08 4206

1275.63 143544.4 9.41E+08 3318 1263.409 117966.8 3.21E+08 4206

1295.63 138014.3 9.44E+08 3318 1283.409 112163.7 3.23E+08 4206

1315.63 132702.9 9.46E+08 3318 1303.409 106651 3.25E+08 4206

1335.63 127601.3 9.49E+08 3318 1314.764 690874.3 3.27E+08 3909

1355.63 122700.6 9.51E+08 3318 1334.395 558775.5 3.38E+08 3909

1375.63 117992.7 9.54E+08 3318 1354.395 528819.8 3.49E+08 3909

1395.63 113469.6 9.56E+08 3318 1374.395 502978.6 3.59E+08 3909

1415.63 109123.8 9.58E+08 3318 1394.395 478635.8 3.69E+08 3909

1435.63 104947.9 9.6E+08 3318 1414.395 455568.2 3.79E+08 3909

1455.63 100935.1 9.63E+08 3318 1434.395 433693.1 3.87E+08 3909

1475.63 97078.86 9.64E+08 3318 1454.395 412941 3.96E+08 3909

1495.63 93372.71 9.66E+08 3318 1474.395 393247.4 4.04E+08 3909

1515.63 89810.65 9.68E+08 3318 1494.395 374552.2 4.12E+08 3909

1535.63 86386.88 9.7E+08 3318 1514.395 356799.2 4.19E+08 3909

1555.63 83095.85 9.72E+08 3318 1534.395 339936.1 4.26E+08 3909

1575.63 79932.25 9.73E+08 3318 1554.395 323913.8 4.32E+08 3909

1595.63 76890.99 9.75E+08 3318 1574.395 308686.3 4.39E+08 3909

1615.63 73967.2 9.76E+08 3318 1594.395 294210.5 4.45E+08 3909

1635.63 71156.22 9.78E+08 3318 1614.395 280446 4.51E+08 3909

1655.63 68453.56 9.79E+08 3318 1634.395 267355 4.56E+08 3909

1675.63 65854.94 9.81E+08 3318 1654.395 254901.7 4.61E+08 3909

1695.63 63356.26 9.82E+08 3318 1674.395 243052.7 4.66E+08 3909

1715.63 60953.57 9.83E+08 3318 1694.395 231776.5 4.71E+08 3909

1735.63 58643.1 9.84E+08 3318 1714.395 221043.3 4.75E+08 3909

1755.63 56421.22 9.85E+08 3318 1734.395 210825.3 4.8E+08 3909

1775.63 54284.47 9.87E+08 3318 1754.395 201096 4.84E+08 3909

1795.63 52229.52 9.88E+08 3318 1774.395 191830.6 4.88E+08 3909

1815.63 50253.16 9.89E+08 3318 1794.395 183005.7 4.92E+08 3909

1835.63 48352.33 9.9E+08 3318 1814.395 174599.1 4.95E+08 3909

1855.63 46524.09 9.91E+08 3318 1834.395 166589.8 4.99E+08 3909

1875.63 44765.61 9.91E+08 3318 1854.395 158958 5.02E+08 3909

1895.63 43074.19 9.92E+08 3318 1874.395 151685.2 5.05E+08 3909

1915.63 41447.23 9.93E+08 3318 1894.395 144753.4 5.08E+08 3909

1935.63 39882.23 9.94E+08 3318 1914.395 138146.1 5.11E+08 3909

1955.63 38376.78 9.95E+08 3318 1934.395 131847.4 5.13E+08 3909

1975.63 36928.6 9.96E+08 3318 1954.395 125842.1 5.16E+08 3909

1995.63 35535.47 9.96E+08 3318 1971.03 909437.8 5.18E+08 3612

163

2015.63 34195.26 9.97E+08 3318 1985.383 581423 5.27E+08 3612

2035.63 32905.95 9.98E+08 3318 2005.383 547794.8 5.38E+08 3612

2055.63 31665.56 9.98E+08 3318 2025.383 522616.2 5.49E+08 3612

2075.63 30472.23 9.99E+08 3318 2045.383 499133.3 5.59E+08 3612

2095.63 29324.14 9.99E+08 3318 2065.383 476825.4 5.69E+08 3612

2115.63 28219.56 1E+09 3318 2085.383 455597.2 5.78E+08 3612

2135.63 27156.83 1E+09 3318 2105.383 435387.5 5.87E+08 3612

2155.63 26134.33 1E+09 3318 2125.383 416141 5.95E+08 3612

2175.63 25150.53 1E+09 3318 2145.383 397805.9 6.04E+08 3612

2195.63 24203.95 1E+09 3318 2165.383 380333.9 6.11E+08 3612

2215.63 23293.17 1E+09 3318 2185.383 363679.5 6.19E+08 3612

2235.63 22416.82 1E+09 3318 2205.383 347800.2 6.26E+08 3612

2255.63 21573.58 1E+09 3318 2225.383 332656.1 6.33E+08 3612

2275.63 20762.21 1E+09 3318 2245.383 318209.5 6.39E+08 3612

2295.63 19981.47 1E+09 3318 2265.383 304425 6.45E+08 3612

2315.63 19230.21 1E+09 3318 2285.383 291269.4 6.51E+08 3612

2335.63 18507.31 1.01E+09 3318 2305.383 278711.2 6.57E+08 3612

2355.63 17811.68 1.01E+09 3318 2325.383 266721 6.62E+08 3612

2375.63 17142.29 1.01E+09 3318 2345.383 255270.8 6.68E+08 3612

2395.63 16498.15 1.01E+09 3318 2365.383 244334.2 6.73E+08 3612

2415.63 15878.28 1.01E+09 3318 2385.383 233886.3 6.77E+08 3612

2435.63 15281.78 1.01E+09 3318 2405.383 223903.7 6.82E+08 3612

2455.63 14707.76 1.01E+09 3318 2425.383 214364 6.86E+08 3612

2475.63 14155.37 1.01E+09 3318 2445.383 205246.2 6.91E+08 3612

2495.63 13623.78 1.01E+09 3318 2465.383 196530.4 6.95E+08 3612

2515.63 13112.2 1.01E+09 3318 2485.383 188197.6 6.98E+08 3612

2535.63 12619.89 1.01E+09 3318 2505.383 180230 7.02E+08 3612

2555.63 12146.11 1.01E+09 3318 2525.383 172610.5 7.06E+08 3612

2575.63 11690.16 1.01E+09 3318 2545.383 165323.1 7.09E+08 3612

2595.63 11251.36 1.01E+09 3318 2565.383 158352.5 7.12E+08 3612

2615.63 10829.07 1.01E+09 3318 2585.383 151684.1 7.15E+08 3612

2635.63 10422.67 1.01E+09 3318 2605.383 145304.1 7.18E+08 3612

2655.63 10031.55 1.01E+09 3318 2625.383 139199.5 7.21E+08 3612

2675.63 9655.132 1.01E+09 3318 2636.374 608069.7 7.27E+08 3315

2695.63 9292.87 1.01E+09 3318 2656.374 564077.4 7.39E+08 3315

2715.63 8944.224 1.01E+09 3318 2676.374 539173.8 7.5E+08 3315

2735.63 8608.683 1.01E+09 3318 2696.374 516698.1 7.6E+08 3315

2755.63 8285.751 1.01E+09 3318 2716.374 495351.5 7.7E+08 3315

2775.63 7974.953 1.01E+09 3318 2736.374 474975.4 7.8E+08 3315

2795.63 7675.832 1.01E+09 3318 2756.374 455511 7.89E+08 3315

2815.63 7387.947 1.01E+09 3318 2776.374 436910.9 7.98E+08 3315

164

2835.63 7110.875 1.01E+09 3318 2796.374 419131.4 8.07E+08 3315

2855.63 6844.21 1.01E+09 3318 2816.374 402131.5 8.15E+08 3315

2875.63 6587.558 1.01E+09 3318 2836.374 385872.4 8.23E+08 3315

2895.63 6340.543 1.01E+09 3318 2856.374 370317.9 8.3E+08 3315

2915.63 6102.802 1.01E+09 3318 2876.374 355433.6 8.38E+08 3315

2935.63 5873.987 1.01E+09 3318 2896.374 341187.3 8.44E+08 3315

2955.63 5653.76 1.01E+09 3318 2916.374 327548.6 8.51E+08 3315

2975.63 5441.8 1.01E+09 3318 2936.374 314488.6 8.58E+08 3315

2995.63 5237.794 1.01E+09 3318 2956.374 301980.1 8.64E+08 3315

3015.63 5041.445 1.01E+09 3318 2976.374 289997.6 8.7E+08 3315

3035.63 4852.464 1.01E+09 3318 2996.374 278516.6 8.75E+08 3315

3055.63 4670.573 1.01E+09 3318 3016.374 267514.1 8.81E+08 3315

3075.63 4495.507 1.01E+09 3318 3036.374 256968.4 8.86E+08 3315

3095.63 4327.009 1.01E+09 3318 3056.374 246858.8 8.91E+08 3315

3115.63 4164.832 1.01E+09 3318 3076.374 237165.6 8.96E+08 3315

3135.63 4008.738 1.01E+09 3318 3096.374 227870.3 9.01E+08 3315

3155.63 3858.499 1.01E+09 3318 3116.374 218955.2 9.05E+08 3315

3175.63 3713.896 1.01E+09 3318 3136.374 210403.6 9.09E+08 3315

3195.63 3574.715 1.01E+09 3318 3156.374 202199.5 9.13E+08 3315

3215.63 3440.754 1.01E+09 3318 3176.374 194327.7 9.17E+08 3315

3235.63 3311.817 1.01E+09 3318 3196.374 186773.8 9.21E+08 3315

3255.63 3187.715 1.01E+09 3318 3216.374 179524.2 9.25E+08 3315

3275.63 3068.266 1.01E+09 3318 3236.374 172565.7 9.28E+08 3315

3286.097 2950761 1.01E+09 1835 3256.374 165886 9.32E+08 3315

3290.583 2137686 1.02E+09 1835 3276.374 159473.2 9.35E+08 3315

3310.583 1902670 1.06E+09 1835 3287.368 661310.2 9.38E+08 3018

3330.583 1819599 1.1E+09 1835 3307.368 578545 9.5E+08 3018

3350.583 1752396 1.14E+09 1835 3327.368 552838 9.61E+08 3018

3370.583 1689844 1.17E+09 1835 3347.368 531368.9 9.72E+08 3018

3390.583 1630465 1.2E+09 1835 3367.368 511126.8 9.83E+08 3018

3410.583 1573912 1.24E+09 1835 3387.368 491765.2 9.93E+08 3018

3430.583 1519986 1.27E+09 1835 3407.368 473211.7 1E+09 3018

3450.583 1468519 1.3E+09 1835 3427.368 455424.2 1.01E+09 3018

3470.583 1419359 1.33E+09 1835 3447.368 438366 1.02E+09 3018

3490.583 1372366 1.35E+09 1835 3467.368 422002.8 1.03E+09 3018

3510.583 1327412 1.38E+09 1835 3487.368 406302 1.04E+09 3018

3530.583 1284378 1.41E+09 1835 3507.368 391233.2 1.05E+09 3018

3550.583 1243154 1.43E+09 1835 3527.368 376767.4 1.05E+09 3018

3570.583 1203638 1.46E+09 1835 3547.368 362877.3 1.06E+09 3018

3590.583 1165738 1.48E+09 1835 3567.368 349537 1.07E+09 3018

3610.583 1129364 1.5E+09 1835 3587.368 336722 1.07E+09 3018

165

3630.583 1094436 1.52E+09 1835 3607.368 324409.2 1.08E+09 3018

3650.583 1060877 1.55E+09 1835 3627.368 312576.6 1.09E+09 3018

3670.583 1028619 1.57E+09 1835 3647.368 301203.2 1.09E+09 3018

3690.583 997593.2 1.59E+09 1835 3667.368 290269.4 1.1E+09 3018

3710.583 967739.6 1.61E+09 1835 3687.368 279756.2 1.11E+09 3018

3730.583 939000.2 1.63E+09 1835 3707.368 269645.9 1.11E+09 3018

3750.583 911320.9 1.64E+09 1835 3727.368 259921.3 1.12E+09 3018

3770.583 884651.3 1.66E+09 1835 3747.368 250566.5 1.12E+09 3018

3790.583 858943.6 1.68E+09 1835 3767.368 241565.9 1.13E+09 3018

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4430.583 362042.8 2.04E+09 1835 4398.368 272550.9 1.35E+09 2721

166

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5250.583 134893.8 2.23E+09 1835 5209.376 229952.8 1.63E+09 2424

167

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5970.583 59277.41 2.3E+09 1835 5913.24 710576.2 1.89E+09 1830

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6010.583 56666.19 2.3E+09 1835 5951.435 540885.2 1.91E+09 1830

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6070.583 52968.17 2.3E+09 1835 6011.435 497752 1.94E+09 1830

168

6090.583 51791.11 2.3E+09 1835 6031.435 484813.4 1.95E+09 1830

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6769.718 830424.1 2.51E+09 350 6722.518 451459.4 2.22E+09 1534

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6869.718 751494.3 2.59E+09 350 6822.518 402070.2 2.26E+09 1534

169

6889.718 736992.8 2.6E+09 350 6842.518 392964.5 2.27E+09 1534

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7629.718 392493.6 3E+09 350 7573.608 374012.8 2.52E+09 1238

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7669.718 380920.4 3.02E+09 350 7613.608 359226.7 2.53E+09 1238

7689.718 375311.7 3.02E+09 350 7633.608 352094.6 2.54E+09 1238

170

7709.718 369817.2 3.03E+09 350 7653.608 345129.7 2.55E+09 1238

7729.718 364434.2 3.04E+09 350 7673.608 338327.3 2.55E+09 1238

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7829.718 339090.6 3.07E+09 350 7773.608 306593.8 2.59E+09 1238

7849.718 334317.8 3.08E+09 350 7793.608 300673.6 2.59E+09 1238

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8389.718 234164.9 3.23E+09 350 8324.922 318962.8 2.79E+09 942

8409.718 231301.9 3.24E+09 350 8344.922 313486.7 2.8E+09 942

8429.718 228486.9 3.24E+09 350 8364.922 308125.6 2.8E+09 942

8449.718 225718.8 3.25E+09 350 8384.922 302876.5 2.81E+09 942

8469.718 222996.6 3.25E+09 350 8404.922 297736.4 2.82E+09 942

8489.718 220319.4 3.25E+09 350 8424.922 292702.5 2.82E+09 942

8509.718 217686.2 3.26E+09 350 8444.922 287772.1 2.83E+09 942

171

8529.718 215096.1 3.26E+09 350 8464.922 282942.6 2.83E+09 942

8549.718 212548.1 3.27E+09 350 8484.922 278211.3 2.84E+09 942

8569.718 210041.4 3.27E+09 350 8504.922 273575.7 2.84E+09 942

8589.718 207575.1 3.28E+09 350 8524.922 269033.6 2.85E+09 942

8609.718 205148.4 3.28E+09 350 8544.922 264582.4 2.86E+09 942

8629.718 202760.4 3.28E+09 350 8564.922 260220 2.86E+09 942

8649.718 200410.4 3.29E+09 350 8576.217 431012.1 2.86E+09 646

8669.718 198097.6 3.29E+09 350 8596.217 405083.2 2.87E+09 646

8689.718 195821.2 3.3E+09 350 8616.217 394883.2 2.88E+09 646

8709.718 193580.5 3.3E+09 350 8636.217 387229.3 2.89E+09 646

8729.718 191374.7 3.3E+09 350 8656.217 380517.1 2.9E+09 646

8749.718 189203.2 3.31E+09 350 8676.217 374235.1 2.9E+09 646

8769.718 187065.3 3.31E+09 350 8696.217 368194 2.91E+09 646

8789.718 184960.3 3.32E+09 350 8716.217 362320.6 2.92E+09 646

8809.718 182887.5 3.32E+09 350 8736.217 356585 2.93E+09 646

8829.718 180846.3 3.32E+09 350 8756.217 350974 2.93E+09 646

8849.718 178836.2 3.33E+09 350 8776.217 345480.7 2.94E+09 646

8869.718 176856.4 3.33E+09 350 8796.217 340100.5 2.95E+09 646

8889.718 174906.4 3.33E+09 350 8816.217 334830 2.95E+09 646

8909.718 172985.6 3.34E+09 350 8836.217 329666 2.96E+09 646

8929.718 171093.4 3.34E+09 350 8856.217 324605.8 2.97E+09 646

8949.718 169229.4 3.34E+09 350 8876.217 319646.7 2.97E+09 646

8969.718 167392.9 3.35E+09 350 8896.217 314786 2.98E+09 646

8989.718 165583.5 3.35E+09 350 8916.217 310021.3 2.99E+09 646

9009.718 163800.6 3.35E+09 350 8936.217 305350.1 2.99E+09 646

9029.718 162043.7 3.36E+09 350 8956.217 300770.1 3E+09 646

9049.718 160312.3 3.36E+09 350 8976.217 296279.1 3E+09 646

9069.718 158606 3.36E+09 350 8996.217 291874.8 3.01E+09 646

9089.718 156924.3 3.37E+09 350 9016.217 287555 3.01E+09 646

9109.718 155266.7 3.37E+09 350 9036.217 283317.8 3.02E+09 646

9129.718 153632.8 3.37E+09 350 9056.217 279161.2 3.03E+09 646

9149.718 152022.1 3.38E+09 350 9076.217 275083 3.03E+09 646

9169.718 150434.3 3.38E+09 350 9096.217 271081.6 3.04E+09 646

9189.718 148868.8 3.38E+09 350 9116.217 267155 3.04E+09 646

9209.718 147325.4 3.38E+09 350 9136.217 263301.4 3.05E+09 646

9229.718 145803.5 3.39E+09 350 9156.217 259519.2 3.05E+09 646

9249.718 144302.9 3.39E+09 350 9176.217 255806.6 3.06E+09 646

9269.718 142823 3.39E+09 350 9196.217 252162.1 3.06E+09 646

9289.718 141363.7 3.4E+09 350 9208.977 353285.7 3.07E+09 350

9309.718 139924.4 3.4E+09 350 9228.977 341738.4 3.07E+09 350

9329.718 138504.8 3.4E+09 350 9248.977 335021.7 3.08E+09 350

172

9349.718 137104.7 3.4E+09 350 9268.977 329567.3 3.09E+09 350

9369.718 135723.5 3.41E+09 350 9288.977 324655.9 3.09E+09 350

9389.718 134361.1 3.41E+09 350 9308.977 320023.4 3.1E+09 350

9409.718 133017.1 3.41E+09 350 9328.977 315558.8 3.11E+09 350

9429.718 131691.1 3.42E+09 350 9348.977 311213.4 3.11E+09 350

9449.718 130382.9 3.42E+09 350 9368.977 306965.1 3.12E+09 350

9469.718 129092.1 3.42E+09 350 9388.977 302803.1 3.13E+09 350

9489.718 127818.4 3.42E+09 350 9408.977 298721.8 3.13E+09 350

9509.718 126561.6 3.43E+09 350 9428.977 294717.5 3.14E+09 350

9529.718 125321.4 3.43E+09 350 9448.977 290787.7 3.14E+09 350

9549.718 124097.5 3.43E+09 350 9468.977 286930.4 3.15E+09 350

9569.718 122889.5 3.43E+09 350 9488.977 283143.7 3.16E+09 350

9589.718 121697.3 3.44E+09 350 9508.977 279425.9 3.16E+09 350

9609.718 120520.5 3.44E+09 350 9528.977 275775.3 3.17E+09 350

9629.718 119359 3.44E+09 350 9548.977 272190.4 3.17E+09 350

9649.718 118212.4 3.44E+09 350 9568.977 268669.6 3.18E+09 350

9669.718 117080.5 3.44E+09 350 9588.977 265211.5 3.18E+09 350

9689.718 115963.1 3.45E+09 350 9608.977 261814.5 3.19E+09 350

9709.718 114860 3.45E+09 350 9628.977 258477.5 3.19E+09 350

9729.718 113770.8 3.45E+09 350 9648.977 255198.8 3.2E+09 350

9749.718 112695.4 3.45E+09 350 9668.977 251977.3 3.2E+09 350

9769.718 111633.5 3.46E+09 350 9688.977 248811.7 3.21E+09 350

9789.718 110584.9 3.46E+09 350 9708.977 245700.7 3.21E+09 350

9809.718 109549.5 3.46E+09 350 9728.977 242643.1 3.22E+09 350

9829.718 108527 3.46E+09 350 9748.977 239637.7 3.22E+09 350

9849.718 107517.1 3.47E+09 350 9768.977 236683.4 3.23E+09 350

9788.977 233779 3.23E+09 350

9808.977 230923.5 3.24E+09 350

9828.977 228115.8 3.24E+09 350

9848.977 225354.9 3.25E+09 350

Case Study 2-C(e)

pi=4800 psia, T=200F, SG=0.65

t(day) Qsc(SCFD) Gp(SCF) Pwf(psia) t(day) Qsc(SCFD) Gp(SCF) Pwf(psia)

0.01 315400 3154 4705.025 4914.471 315400 1.55E+09 2453.125

1.471303 315400 464048.9 4637.016 4934.471 315400 1.56E+09 2445.687

7.471303 315400 2356449 4615.129 4954.471 315400 1.56E+09 2438.254

14.4713 315400 4564249 4606.347 4974.471 315400 1.57E+09 2430.825

34.4713 315400 10872249 4593.03 4994.471 315400 1.58E+09 2423.401

54.4713 315400 17180249 4582.009 5014.471 315400 1.58E+09 2415.982

173

74.4713 315400 23488249 4571.132 5034.471 315400 1.59E+09 2408.567

94.4713 315400 29796249 4560.286 5054.471 315400 1.59E+09 2401.157

114.4713 315400 36104249 4549.466 5074.471 315400 1.6E+09 2393.75

134.4713 315400 42412249 4538.671 5094.471 315400 1.61E+09 2386.349

154.4713 315400 48720249 4527.901 5114.471 315400 1.61E+09 2378.951

174.4713 315400 55028249 4517.155 5134.471 315400 1.62E+09 2371.558

194.4713 315400 61336249 4506.434 5154.471 315400 1.63E+09 2364.168

214.4713 315400 67644249 4495.737 5174.471 315400 1.63E+09 2356.783

234.4713 315400 73952249 4485.065 5194.471 315400 1.64E+09 2349.401

254.4713 315400 80260249 4474.417 5214.471 315400 1.64E+09 2342.024

274.4713 315400 86568249 4463.793 5234.471 315400 1.65E+09 2334.65

294.4713 315400 92876249 4453.193 5254.471 315400 1.66E+09 2327.279

314.4713 315400 99184249 4442.616 5274.471 315400 1.66E+09 2319.913

334.4713 315400 1.05E+08 4432.064 5294.471 315400 1.67E+09 2312.55

354.4713 315400 1.12E+08 4421.535 5314.471 315400 1.68E+09 2305.19

374.4713 315400 1.18E+08 4411.029 5334.471 315400 1.68E+09 2297.834

394.4713 315400 1.24E+08 4400.547 5354.471 315400 1.69E+09 2290.481

414.4713 315400 1.31E+08 4390.089 5374.471 315400 1.7E+09 2283.131

434.4713 315400 1.37E+08 4379.653 5394.471 315400 1.7E+09 2275.784

454.4713 315400 1.43E+08 4369.241 5414.471 315400 1.71E+09 2268.44

474.4713 315400 1.5E+08 4358.851 5434.471 315400 1.71E+09 2261.1

494.4713 315400 1.56E+08 4348.485 5454.471 315400 1.72E+09 2253.762

514.4713 315400 1.62E+08 4338.141 5474.471 315400 1.73E+09 2246.427

534.4713 315400 1.69E+08 4327.82 5494.471 315400 1.73E+09 2239.094

554.4713 315400 1.75E+08 4317.521 5514.471 315400 1.74E+09 2231.765

574.4713 315400 1.81E+08 4307.245 5534.471 315400 1.75E+09 2224.438

594.4713 315400 1.87E+08 4296.992 5554.471 315400 1.75E+09 2217.113

614.4713 315400 1.94E+08 4286.76 5574.471 315400 1.76E+09 2209.791

634.4713 315400 2E+08 4276.551 5594.471 315400 1.76E+09 2202.471

654.4713 315400 2.06E+08 4266.363 5614.471 315400 1.77E+09 2195.153

674.4713 315400 2.13E+08 4256.198 5634.471 315400 1.78E+09 2187.838

694.4713 315400 2.19E+08 4246.054 5654.471 315400 1.78E+09 2180.524

714.4713 315400 2.25E+08 4235.932 5674.471 315400 1.79E+09 2173.213

734.4713 315400 2.32E+08 4225.832 5694.471 315400 1.8E+09 2165.903

754.4713 315400 2.38E+08 4215.753 5714.471 315400 1.8E+09 2158.595

774.4713 315400 2.44E+08 4205.695 5734.471 315400 1.81E+09 2151.289

794.4713 315400 2.51E+08 4195.659 5754.471 315400 1.81E+09 2143.985

814.4713 315400 2.57E+08 4185.644 5774.471 315400 1.82E+09 2136.682

834.4713 315400 2.63E+08 4175.65 5794.471 315400 1.83E+09 2129.381

854.4713 315400 2.7E+08 4165.678 5814.471 315400 1.83E+09 2122.081

874.4713 315400 2.76E+08 4155.726 5834.471 315400 1.84E+09 2114.782

174

894.4713 315400 2.82E+08 4145.794 5854.471 315400 1.85E+09 2107.485

914.4713 315400 2.88E+08 4135.884 5874.471 315400 1.85E+09 2100.188

934.4713 315400 2.95E+08 4125.994 5894.471 315400 1.86E+09 2092.893

954.4713 315400 3.01E+08 4116.125 5914.471 315400 1.87E+09 2085.599

974.4713 315400 3.07E+08 4106.276 5934.471 315400 1.87E+09 2078.305

994.4713 315400 3.14E+08 4096.447 5954.471 315400 1.88E+09 2071.012

1014.471 315400 3.2E+08 4086.638 5974.471 315400 1.88E+09 2063.72

1034.471 315400 3.26E+08 4076.85 5994.471 315400 1.89E+09 2056.429

1054.471 315400 3.33E+08 4067.081 6014.471 315400 1.9E+09 2049.137

1074.471 315400 3.39E+08 4057.333 6034.471 315400 1.9E+09 2041.847

1094.471 315400 3.45E+08 4047.604 6054.471 315400 1.91E+09 2034.556

1114.471 315400 3.52E+08 4037.895 6074.471 315400 1.92E+09 2027.266

1134.471 315400 3.58E+08 4028.206 6094.471 315400 1.92E+09 2019.976

1154.471 315400 3.64E+08 4018.536 6114.471 315400 1.93E+09 2012.686

1174.471 315400 3.7E+08 4008.886 6134.471 315400 1.93E+09 2005.396

1194.471 315400 3.77E+08 3999.255 6154.471 315400 1.94E+09 1998.105

1214.471 315400 3.83E+08 3989.643 6174.471 315400 1.95E+09 1990.815

1234.471 315400 3.89E+08 3980.05 6194.471 315400 1.95E+09 1983.524

1254.471 315400 3.96E+08 3970.476 6214.471 315400 1.96E+09 1976.232

1274.471 315400 4.02E+08 3960.922 6234.471 315400 1.97E+09 1968.94

1294.471 315400 4.08E+08 3951.386 6254.471 315400 1.97E+09 1961.648

1314.471 315400 4.15E+08 3941.869 6274.471 315400 1.98E+09 1954.354

1334.471 315400 4.21E+08 3932.37 6294.471 315400 1.99E+09 1947.06

1354.471 315400 4.27E+08 3922.89 6314.471 315400 1.99E+09 1939.764

1374.471 315400 4.34E+08 3913.429 6334.471 315400 2E+09 1932.468

1394.471 315400 4.4E+08 3903.986 6354.471 315400 2E+09 1925.17

1414.471 315400 4.46E+08 3894.562 6374.471 315400 2.01E+09 1917.871

1434.471 315400 4.52E+08 3885.155 6394.471 315400 2.02E+09 1910.571

1454.471 315400 4.59E+08 3875.767 6414.471 315400 2.02E+09 1903.269

1474.471 315400 4.65E+08 3866.397 6434.471 315400 2.03E+09 1895.965

1494.471 315400 4.71E+08 3857.044 6454.471 315400 2.04E+09 1888.66

1514.471 315400 4.78E+08 3847.71 6474.471 315400 2.04E+09 1881.353

1534.471 315400 4.84E+08 3838.393 6494.471 315400 2.05E+09 1874.044

1554.471 315400 4.9E+08 3829.094 6514.471 315400 2.05E+09 1866.733

1574.471 315400 4.97E+08 3819.813 6534.471 315400 2.06E+09 1859.419

1594.471 315400 5.03E+08 3810.549 6554.471 315400 2.07E+09 1852.104

1614.471 315400 5.09E+08 3801.302 6574.471 315400 2.07E+09 1844.786

1634.471 315400 5.16E+08 3792.073 6594.471 315400 2.08E+09 1837.465

1654.471 315400 5.22E+08 3782.861 6614.471 315400 2.09E+09 1830.142

1674.471 315400 5.28E+08 3773.666 6634.471 315400 2.09E+09 1822.816

1694.471 315400 5.34E+08 3764.488 6654.471 315400 2.1E+09 1815.487

175

1714.471 315400 5.41E+08 3755.328 6674.471 315400 2.11E+09 1808.155

1734.471 315400 5.47E+08 3746.184 6694.471 315400 2.11E+09 1800.82

1754.471 315400 5.53E+08 3737.056 6714.471 315400 2.12E+09 1793.482

1774.471 315400 5.6E+08 3727.946 6734.471 315400 2.12E+09 1786.14

1794.471 315400 5.66E+08 3718.852 6754.471 315400 2.13E+09 1778.795

1814.471 315400 5.72E+08 3709.775 6774.471 315400 2.14E+09 1771.446

1834.471 315400 5.79E+08 3700.714 6794.471 315400 2.14E+09 1764.094

1854.471 315400 5.85E+08 3691.67 6814.471 315400 2.15E+09 1756.737

1874.471 315400 5.91E+08 3682.641 6834.471 315400 2.16E+09 1749.377

1894.471 315400 5.98E+08 3673.629 6854.471 315400 2.16E+09 1742.012

1914.471 315400 6.04E+08 3664.633 6874.471 315400 2.17E+09 1734.643

1934.471 315400 6.1E+08 3655.654 6894.471 315400 2.17E+09 1727.27

1954.471 315400 6.16E+08 3646.69 6914.471 315400 2.18E+09 1719.892

1974.471 315400 6.23E+08 3637.742 6934.471 315400 2.19E+09 1712.509

1994.471 315400 6.29E+08 3628.809 6954.471 315400 2.19E+09 1705.122

2014.471 315400 6.35E+08 3619.893 6974.471 315400 2.2E+09 1697.729

2034.471 315400 6.42E+08 3610.992 6994.471 315400 2.21E+09 1690.332

2054.471 315400 6.48E+08 3602.106 7014.471 315400 2.21E+09 1682.929

2074.471 315400 6.54E+08 3593.236 7034.471 315400 2.22E+09 1675.52

2094.471 315400 6.61E+08 3584.382 7054.471 315400 2.22E+09 1668.106

2114.471 315400 6.67E+08 3575.542 7074.471 315400 2.23E+09 1660.686

2134.471 315400 6.73E+08 3566.718 7094.471 315400 2.24E+09 1653.261

2154.471 315400 6.8E+08 3557.909 7114.471 315400 2.24E+09 1645.829

2174.471 315400 6.86E+08 3549.115 7134.471 315400 2.25E+09 1638.391

2194.471 315400 6.92E+08 3540.336 7154.471 315400 2.26E+09 1630.946

2214.471 315400 6.98E+08 3531.571 7174.471 315400 2.26E+09 1623.495

2234.471 315400 7.05E+08 3522.822 7194.471 315400 2.27E+09 1616.038

2254.471 315400 7.11E+08 3514.087 7214.471 315400 2.28E+09 1608.573

2274.471 315400 7.17E+08 3505.367 7234.471 315400 2.28E+09 1601.101

2294.471 315400 7.24E+08 3496.661 7254.471 315400 2.29E+09 1593.622

2314.471 315400 7.3E+08 3487.97 7274.471 315400 2.29E+09 1586.136

2334.471 315400 7.36E+08 3479.294 7294.471 315400 2.3E+09 1578.642

2354.471 315400 7.43E+08 3470.631 7314.471 315400 2.31E+09 1571.14

2374.471 315400 7.49E+08 3461.983 7334.471 315400 2.31E+09 1563.631

2394.471 315400 7.55E+08 3453.349 7354.471 315400 2.32E+09 1556.113

2414.471 315400 7.62E+08 3444.729 7374.471 315400 2.33E+09 1548.587

2434.471 315400 7.68E+08 3436.123 7394.471 315400 2.33E+09 1541.052

2454.471 315400 7.74E+08 3427.531 7414.471 315400 2.34E+09 1533.508

2474.471 315400 7.8E+08 3418.953 7434.471 315400 2.34E+09 1525.956

2494.471 315400 7.87E+08 3410.388 7454.471 315400 2.35E+09 1518.394

2514.471 315400 7.93E+08 3401.837 7474.471 315400 2.36E+09 1510.823

176

2534.471 315400 7.99E+08 3393.3 7494.471 315400 2.36E+09 1503.243

2554.471 315400 8.06E+08 3384.776 7514.471 315400 2.37E+09 1495.652

2574.471 315400 8.12E+08 3376.266 7534.471 315400 2.38E+09 1488.052

2594.471 315400 8.18E+08 3367.769 7554.471 315400 2.38E+09 1480.442

2614.471 315400 8.25E+08 3359.285 7574.471 315400 2.39E+09 1472.82

2634.471 315400 8.31E+08 3350.815 7594.471 315400 2.4E+09 1465.189

2654.471 315400 8.37E+08 3342.358 7614.471 315400 2.4E+09 1457.546

2674.471 315400 8.44E+08 3333.914 7634.471 315400 2.41E+09 1449.892

2694.471 315400 8.5E+08 3325.482 7654.471 315400 2.41E+09 1442.227

2714.471 315400 8.56E+08 3317.064 7674.471 315400 2.42E+09 1434.55

2734.471 315400 8.62E+08 3308.658 7694.471 315400 2.43E+09 1426.861

2754.471 315400 8.69E+08 3300.266 7714.471 315400 2.43E+09 1419.16

2774.471 315400 8.75E+08 3291.886 7734.471 315400 2.44E+09 1411.447

2794.471 315400 8.81E+08 3283.518 7754.471 315400 2.45E+09 1403.72

2814.471 315400 8.88E+08 3275.163 7774.471 315400 2.45E+09 1395.981

2834.471 315400 8.94E+08 3266.821 7794.471 315400 2.46E+09 1388.229

2854.471 315400 9E+08 3258.491 7814.471 315400 2.46E+09 1380.463

2874.471 315400 9.07E+08 3250.173 7834.471 315400 2.47E+09 1372.683

2894.471 315400 9.13E+08 3241.867 7854.471 315400 2.48E+09 1364.889

2914.471 315400 9.19E+08 3233.574 7874.471 315400 2.48E+09 1357.08

2934.471 315400 9.26E+08 3225.292 7894.471 315400 2.49E+09 1349.257

2954.471 315400 9.32E+08 3217.023 7914.471 315400 2.5E+09 1341.419

2974.471 315400 9.38E+08 3208.765 7934.471 315400 2.5E+09 1333.565

2994.471 315400 9.44E+08 3200.52 7954.471 315400 2.51E+09 1325.695

3014.471 315400 9.51E+08 3192.286 7974.471 315400 2.52E+09 1317.81

3034.471 315400 9.57E+08 3184.064 7994.471 315400 2.52E+09 1309.907

3054.471 315400 9.63E+08 3175.853 8014.471 315400 2.53E+09 1301.989

3074.471 315400 9.7E+08 3167.654 8034.471 315400 2.53E+09 1294.052

3094.471 315400 9.76E+08 3159.467 8054.471 315400 2.54E+09 1286.099

3114.471 315400 9.82E+08 3151.291 8074.471 315400 2.55E+09 1278.127

3134.471 315400 9.89E+08 3143.126 8094.471 315400 2.55E+09 1270.137

3154.471 315400 9.95E+08 3134.972 8114.471 315400 2.56E+09 1262.129

3174.471 315400 1E+09 3126.83 8134.471 315400 2.57E+09 1254.101

3194.471 315400 1.01E+09 3118.699 8154.471 315400 2.57E+09 1246.053

3214.471 315400 1.01E+09 3110.579 8174.471 315400 2.58E+09 1237.986

3234.471 315400 1.02E+09 3102.469 8194.471 315400 2.58E+09 1229.898

3254.471 315400 1.03E+09 3094.371 8214.471 315400 2.59E+09 1221.789

3274.471 315400 1.03E+09 3086.284 8234.471 315400 2.6E+09 1213.659

3294.471 315400 1.04E+09 3078.207 8254.471 315400 2.6E+09 1205.507

3314.471 315400 1.05E+09 3070.141 8274.471 315400 2.61E+09 1197.332

3334.471 315400 1.05E+09 3062.085 8294.471 315400 2.62E+09 1189.135

177

3354.471 315400 1.06E+09 3054.04 8314.471 315400 2.62E+09 1180.914

3374.471 315400 1.06E+09 3046.006 8334.471 315400 2.63E+09 1172.669

3394.471 315400 1.07E+09 3037.982 8354.471 315400 2.64E+09 1164.4

3414.471 315400 1.08E+09 3029.968 8374.471 315400 2.64E+09 1156.105

3434.471 315400 1.08E+09 3021.965 8394.471 315400 2.65E+09 1147.785

3454.471 315400 1.09E+09 3013.971 8414.471 315400 2.65E+09 1139.439

3474.471 315400 1.1E+09 3005.988 8434.471 315400 2.66E+09 1131.065

3494.471 315400 1.1E+09 2998.015 8454.471 315400 2.67E+09 1122.664

3514.471 315400 1.11E+09 2990.052 8474.471 315400 2.67E+09 1114.235

3534.471 315400 1.11E+09 2982.098 8494.471 315400 2.68E+09 1105.777

3554.471 315400 1.12E+09 2974.155 8514.471 315400 2.69E+09 1097.289

3574.471 315400 1.13E+09 2966.221 8534.471 315400 2.69E+09 1088.77

3594.471 315400 1.13E+09 2958.297 8554.471 315400 2.7E+09 1080.221

3614.471 315400 1.14E+09 2950.382 8574.471 315400 2.7E+09 1071.639

3634.471 315400 1.15E+09 2942.477 8594.471 315400 2.71E+09 1063.025

3654.471 315400 1.15E+09 2934.582 8614.471 315400 2.72E+09 1054.377

3674.471 315400 1.16E+09 2926.695 8634.471 315400 2.72E+09 1045.694

3694.471 315400 1.17E+09 2918.818 8654.471 315400 2.73E+09 1036.976

3714.471 315400 1.17E+09 2910.951 8674.471 315400 2.74E+09 1028.222

3734.471 315400 1.18E+09 2903.092 8694.471 315400 2.74E+09 1019.43

3754.471 315400 1.18E+09 2895.243 8714.471 315400 2.75E+09 1010.6

3774.471 315400 1.19E+09 2887.403 8734.471 315400 2.75E+09 1001.731

3794.471 315400 1.2E+09 2879.571 8754.471 315400 2.76E+09 992.8205

3814.471 315400 1.2E+09 2871.749 8774.471 315400 2.77E+09 983.8688

3834.471 315400 1.21E+09 2863.935 8794.471 315400 2.77E+09 974.8743

3854.471 315400 1.22E+09 2856.13 8814.471 315400 2.78E+09 965.8357

3874.471 315400 1.22E+09 2848.334 8834.471 315400 2.79E+09 956.7518

3894.471 315400 1.23E+09 2840.546 8854.471 315400 2.79E+09 947.6211

3914.471 315400 1.23E+09 2832.767 8874.471 315400 2.8E+09 938.4424

3934.471 315400 1.24E+09 2824.997 8894.471 315400 2.81E+09 929.214

3954.471 315400 1.25E+09 2817.234 8914.471 315400 2.81E+09 919.9346

3974.471 315400 1.25E+09 2809.48 8934.471 315400 2.82E+09 910.6025

3994.471 315400 1.26E+09 2801.735 8954.471 315400 2.82E+09 901.2161

4014.471 315400 1.27E+09 2793.997 8974.471 315400 2.83E+09 891.7735

4034.471 315400 1.27E+09 2786.268 8994.471 315400 2.84E+09 882.273

4054.471 315400 1.28E+09 2778.546 9014.471 315400 2.84E+09 872.7127

4074.471 315400 1.29E+09 2770.833 9034.471 315400 2.85E+09 863.0905

4094.471 315400 1.29E+09 2763.128 9054.471 315400 2.86E+09 853.4043

4114.471 315400 1.3E+09 2755.43 9074.471 315400 2.86E+09 843.6518

4134.471 315400 1.3E+09 2747.74 9094.471 315400 2.87E+09 833.8308

4154.471 315400 1.31E+09 2740.058 9114.471 315400 2.87E+09 823.9388

178

4174.471 315400 1.32E+09 2732.383 9134.471 315400 2.88E+09 813.973

4194.471 315400 1.32E+09 2724.716 9154.471 315400 2.89E+09 803.9309

4214.471 315400 1.33E+09 2717.056 9174.471 315400 2.89E+09 793.8093

4234.471 315400 1.34E+09 2709.404 9194.471 315400 2.9E+09 783.6053

4254.471 315400 1.34E+09 2701.759 9214.471 315400 2.91E+09 773.3156

4274.471 315400 1.35E+09 2694.122 9234.471 315400 2.91E+09 762.9366

4294.471 315400 1.35E+09 2686.491 9254.471 315400 2.92E+09 752.4647

4314.471 315400 1.36E+09 2678.868 9274.471 315400 2.93E+09 741.8958

4334.471 315400 1.37E+09 2671.252 9294.471 315400 2.93E+09 731.2259

4354.471 315400 1.37E+09 2663.643 9314.471 315400 2.94E+09 720.4503

4374.471 315400 1.38E+09 2656.04 9334.471 315400 2.94E+09 709.5642

4394.471 315400 1.39E+09 2648.445 9354.471 315400 2.95E+09 698.5625

4414.471 315400 1.39E+09 2640.856 9374.471 315400 2.96E+09 687.4396

4434.471 315400 1.4E+09 2633.274 9394.471 315400 2.96E+09 676.1894

4454.471 315400 1.4E+09 2625.698 9414.471 315400 2.97E+09 664.8056

4474.471 315400 1.41E+09 2618.13 9434.471 315400 2.98E+09 653.2811

4494.471 315400 1.42E+09 2610.567 9454.471 315400 2.98E+09 641.6083

4514.471 315400 1.42E+09 2603.011 9474.471 315400 2.99E+09 629.779

4534.471 315400 1.43E+09 2595.461 9494.471 315400 2.99E+09 617.7842

4554.471 315400 1.44E+09 2587.918 9514.471 315400 3E+09 605.614

4574.471 315400 1.44E+09 2580.381 9534.471 315400 3.01E+09 593.2577

4594.471 315400 1.45E+09 2572.85 9554.471 315400 3.01E+09 580.7033

4614.471 315400 1.46E+09 2565.325 9574.471 315400 3.02E+09 567.9378

4634.471 315400 1.46E+09 2557.806 9594.471 315400 3.03E+09 554.9465

4654.471 315400 1.47E+09 2550.292 9614.471 315400 3.03E+09 541.7133

4674.471 315400 1.47E+09 2542.785 9634.471 315400 3.04E+09 528.2199

4694.471 315400 1.48E+09 2535.283 9654.471 315400 3.05E+09 514.446

4714.471 315400 1.49E+09 2527.788 9674.471 315400 3.05E+09 500.3683

4734.471 315400 1.49E+09 2520.297 9694.471 315400 3.06E+09 485.9605

4754.471 315400 1.5E+09 2512.813 9714.471 315400 3.06E+09 471.1925

4774.471 315400 1.51E+09 2505.333 9734.471 315400 3.07E+09 456.0293

4794.471 315400 1.51E+09 2497.859 9754.471 315400 3.08E+09 440.4301

4814.471 315400 1.52E+09 2490.391 9774.471 315400 3.08E+09 424.347

4834.471 315400 1.52E+09 2482.928 9794.471 315400 3.09E+09 407.723

4854.471 315400 1.53E+09 2475.469 9814.471 315400 3.1E+09 390.4893

4874.471 315400 1.54E+09 2468.016 9834.471 315400 3.1E+09 372.5616

4894.471 315400 1.54E+09 2460.568 9854.471 315400 3.11E+09 353.835

179

Chapter 3

Case Study 3-A Case Study 3-C Case Study 3-E

pi=1200 psia, T=87F, SG=0.68 pi=2625 psia, T=275F, SG=0.72 pi=1335 psia, T=125F, SG=0.6

t(days) qsc(SCFD) pwf(psia) t(Day) qsc(SCFD) pwf(psia) t(Day) qsc(SCFD) pwf(psia)

177.741 53603300 981.029465 1.604647 772521.602 624.2504 7.30552 2282.05 1143.01

181.523 51436800 965.37293 1.851375 814196.11 512.1123 12.9876 2098.277 1152.8

234.467 49386200 902.777 2.199854 873057.17 741.5538 14.611 2166.67 1211.54

253.376 52579900 896.156942 3.431634 1018698.07 629.664 16.2345 3615.38 1079.37

257.157 51097600 895.054175 5.24585 851644.5 778.6625 22.7283 891.0267 1265.38

268.503 49843600 891.745 5.874 921544.469 483.8291 23.54 923.077 1250.7

276.066 49501800 872.4075 9.267798 849500.517 441.3482 36.5276 4038.46 1130.77

283.629 49045900 868.728432 13.29666 825740.268 410.2282 37.3393 4423.08 1050

287.411 48361900 867.809621 16.20906 399746.042 521.0732 39.7745 5948.72 895.804

294.975 47906000 865.972 17.0999 798081.4 498.8527 42.2097 5858.97 886.014

302.538 47108100 861.371804 19.51317 694220.695 1184.829 47.08 6081.185 851.748

306.32 47678400 859.071402 20.68344 794978.181 1252.939 47.8918 6217.95 832.168

313.883 47336600 851.247 22.95627 990662.844 1364.486 51.9504 6042.733 844.406

317.665 46196400 850.020892 23.85483 573697.537 1011.542 52.7621 5970.087 815.035

321.447 45398300 848.794784 26.03042 1056938 1330.38 55.1973 6384.62 805.245

325.228 45056300 847.569 26.79384 1078236.64 875.7636 58.4442 6166.668 810.14

329.01 44486300 799.677 26.95611 1059944.15 802.0082 61.6911 6158.115 815.035

332.792 45284700 840.206 28.07178 836500.514 594.9397 64.938 5836.543 822.378

340.355 43916500 835.298216 28.33336 900404.1 1118.665 66.5614 5637.829 861.538

344.137 44258800 832.844 29.46678 976460.609 507.5845 68.1849 5942.305 788.112

351.701 43460800 819.954 30.04833 831564.3 892.1029 69.8083 6262.825 800.35

359.264 43917300 821.801162 31.77141 867550.761 413.4582 72.2435 6081.194 802.797

366.827 43119300 818.121615 32.13028 850591.457 386.1362 73.867 6038.46 810.14

370.609 42549300 816.281743 34.53603 889091 440.3609 78.7373 5999.999 797.902

378.173 41637300 812.602 36.68971 838253.73 389.475 81.1725 5794.87 822.378

389.518 42207900 805.240026 38.94414 425364.137 421.1543 82.7959 5982.896 797.902

397.081 40725700 795.574598 39.50926 357066.956 796.6015 85.2311 6025.642 800.35

400.863 39471500 793.274196 45.19956 742995.374 1135.896 86.8546 5974.36 797.902

408.426 20541900 788.674 45.58533 783051.609 1035.029 87.6663 6068.377 788.112

415.99 37305400 782.538 46.99431 730085 1106.482 90.1015 6192.306 773.427

419.772 42779200 779.47 47.10239 826845.717 869.1769 94.1601 6014.957 797.902

438.68 37078200 770.271 47.87684 629670.27 795.3805 99.0304 6089.733 788.112

446.244 37078500 773.959513 48.14986 666240.7 1086.313 102.277 6247.891 770.979

453.807 36508600 762.912 48.8949 1179810.55 447.1519 109.583 5064.1 795.455

457.589 36052600 766.5985 49.65477 960915.619 385.4699 113.641 5474.36 795.455

465.152 35140600 762.919 50.84513 991051.3 716.529 117.7 5935.9 788.112

180

468.934 35825000 777.658 51.91508 1196586 579.0639 120.947 5942.31 780.769

476.497 34798900 760.470758 56.31086 659506.7 357.2174 123.382 5967.952 778.322

480.279 34571000 751.876 56.37995 577855.457 328.8754 127.441 6128.21 763.636

484.061 33886900 757.404 56.53318 833934.4 336.9057 129.064 6205.114 753.846

491.624 33545100 759.251 57.16191 675636.5 334.8914 129.876 6243.59 741.608

495.406 39247000 748.201 59.44295 721139.99 436.742 133.935 6416.708 726.923

499.188 26247200 755.572 60.18546 700909.872 418.6377 135.558 6500 700

502.97 27159600 747.283404 61.40345 841430.146 378.5226 139.617 6301.26 709.79

506.751 32519400 738.997 61.67233 459578.491 390.5712 142.052 6320.51 724.476

510.533 31949400 867.947 62.76846 740988.2 397.937 143.675 6256.41 739.161

529.442 34915000 750.064 64.03406 467865.4 370.8785 144.487 6423.08 746.503

533.223 32520400 726.119 64.52974 590779.591 524.7934 146.11 6692.31 702.448

537.005 35713500 731.648 65.6512 601600.9 400.625 151.793 6730.77 673.077

540.787 36968100 715.071 69.60391 586503.5 525.3172 155.039 6429.51 687.762

544.569 35143600 707.704026 70.70155 552562.223 518.7338 159.91 4346.19 883.566

548.35 37424500 700.339 75.21961 595562.897 501.7126 163.968 4397.451 898.252

552.132 33433400 727.973 77.93137 460690.074 535.0537 165.592 4397.444 878.671

555.914 36626500 715.999917 78.35303 555653.982 542.1088 168.027 4512.82 981.469

559.695 36056500 704.03 79.52955 641110.675 607.3821 176.956 4401.701 878.671

567.259 31609400 710.175333 83.58469 725007.797 350.4071 183.45 4440.173 886.014

571.041 30925400 713.248 86.81581 759150.725 429.1998 187.508 4358.991 895.804

582.386 30355600 702.202 87.74956 743505.004 471.3868 194.002 4294.87 898.252

586.168 29215400 706.810109 88.65301 728366.912 360.7677 200.496 4198.72 903.147

597.513 28759700 676.422 89.83312 705114.5 418.0033 203.743 4121.795 912.937

605.076 28075800 705.9 92.11523 615162.241 326.9356 208.613 4064.104 922.727

608.858 26593500 694.85 94.37377 635528.8 326.7934 215.919 4153.85 905.594

612.64 29786600 692.396117 97.26468 588325.774 346.7665 216.731 4243.59 934.965

616.421 32067400 689.942883 97.99961 601731.112 312.7396 219.166 4205.086 910.49

620.203 34348300 687.489 98.59127 653808.692 360.6934 223.224 4006.414 925.175

623.985 30129100 663.544 99.68012 638397.368 448.9456 230.53 3928.209 930.07

627.766 27734500 681.9672 102.5348 597993.275 380.9129 233.777 3833.33 934.965

642.893 25454400 681.976 104.5332 604058.3 366.9705 237.024 3739.299 944.755

646.675 24542300 686.584 104.6374 447063.389 295.8596 241.082 3676.929 949.65

654.239 25682900 686.588391 107.3011 371154.602 442.1992 245.141 3641.03 956.993

658.02 17358500 681.986 107.5818 432765.529 457.6243 248.388 3615.392 944.755

661.802 25341100 670.9355 108.3743 616659.518 364.2836 256.505 3576.92 949.65

673.147 26025800 668.731566 109.0891 801213.482 372.55 259.752 3608.975 954.545

680.711 26824300 677.579302 109.6181 937773.683 432.1358 264.622 3435.9 961.888

684.492 24201600 682.002 110.6724 1209948.38 436.7328 266.246 3401.699 966.783

692.056 25684400 658.9805 111.5795 550591.389 440.6881 273.551 3393.166 971.678

699.619 26026800 659.906 113.0716 442943.597 328.3569 275.986 3401.71 976.573

181

707.183 23518300 652.542 113.466 483224.358 483.2815 281.669 3423.08 969.231

710.964 23062300 665.439 114.77 441055.9 351.5302 285.727 3371.79 971.678

722.31 23746900 645.183 115.0794 614213.61 349.9824 288.974 3336.536 974.126

729.873 21694600 655.012667 115.8018 906675.701 321.629 296.28 3307.69 976.573

733.655 23063200 642.734333 116.9181 628819.9 351.8776 301.15 3227.564 981.469

737.437 21238700 630.456 118.3802 1508556.69 512.386 305.209 3141.03 983.916

741.218 25458200 648.879 120.3285 356348.064 364.2785 307.644 3094.01 979.021

748.782 28537400 634.147 120.4703 360257.2 365.5877 315.761 3201.92 986.364

756.345 25800900 623.099 121.7858 594794.314 301.8982 323.067 3166.663 981.469

760.127 29336100 608.365 123.0922 680370.4 502.414 323.878 3153.852 979.021

763.909 23634500 597.314 123.2023 470769.7 486.3328 331.184 3108.971 986.364

767.69 20213600 607.44666 123.9329 441409.117 526.0573 340.113 3056.414 991.259

771.472 27626000 617.582 124.9988 368608.6 295.3203 347.418 3076.928 983.916

775.254 26371800 613.9 125.8996 666447.951 361.3975 349.853 3054.482 983.916

782.817 28880800 586.273 127.0531 646067.2 482.3618 355.536 3021.362 991.259

786.599 24661700 597.328 127.9368 489586.583 506.2844 358.782 2990.679 991.259

794.162 26828600 578.912 128.2697 477140.4 363.1462 366.088 2948.72 996.154

797.944 28083200 581.370333 130.043 389011.241 519.173 371.77 2923.08 1003.5

809.289 15083600 578.921 131.1933 342673.772 526.2118 373.393 2913.474 991.259

816.853 29110200 569.715171 131.7909 354057.491 554.5933 377.452 2871.799 1003.5

820.635 28540200 567.875342 134.6245 605741.351 466.7104 383.134 2690.483 1018.18

824.416 29452600 566.036 135.6757 638011.596 400.5661 387.193 2809.517 1005.94

831.98 28882700 556.83 137.0291 610118.319 273.8537 392.875 2811.96 996.154

835.761 27742500 545.78 137.2084 622040.2 502.0888 395.31 2787.176 1008.39

843.325 26716500 548.854621 139.7129 354051.547 254.0527 397.745 2764.104 1018.18

854.67 27401100 543.335333 140.3385 493566.756 302.9028 404.239 2756.41 1008.39

858.452 26831100 546.407667 141.8959 347744.3 275.835 410.733 2649.58 1015.73

873.579 26033400 558.698 143.7213 373123.035 396.2554 413.98 2717.971 1010.84

877.36 25349400 547.648961 144.6156 471825.6 346.0914 419.662 2636.75 1010.84

881.142 24779300 536.597 146.9063 420455 339.5703 422.909 2581.185 1025.52

884.924 25805800 573.444914 147.3842 561608 338.2098 428.591 2538.46 1030.42

888.706 22613000 610.292829 147.4442 558877.619 346.0117 430.214 2538.46 1023.08

896.269 24893900 654.501 147.6786 362649.126 368.3611 435.896 2528.221 1020.63

900.051 25920400 663.714 149.0704 483738.797 501.0603 441.578 2397.443 1027.97

907.614 26490900 538.456 149.9052 452261.065 421.6454 444.825 2576.92 1030.42

911.396 25806800 527.405 152.0471 369533.5 501.7703 451.319 2397.44 1035.31

915.178 22842000 534.776975 153.5595 344469.623 511.5462 456.189 2429.486 1030.42

918.959 23298300 542.147 154.7223 420118.688 503.6933 460.248 2461.54 1042.66

922.741 21473900 518.202 156.3495 392097.591 492.7045 461.06 2358.97 1030.42

934.086 24553300 525.577829 159.9403 365605.9 522.6023 464.307 2366.296 1035.31

937.868 22158700 523.738 160.2411 368664.898 523.993 468.365 2410.26 1035.31

182

945.431 23983500 536.637 161.5819 390175.8 540.5036 470.8 2417.951 1035.31

949.213 26264400 520.0605 164.1264 378923.812 558.1182 476.483 2326.94 1032.87

952.995 21247000 503.484 167.2129 395377.7 557.6375 479.729 2288.472 1035.31

960.558 20677100 488.752 168.0866 364417.3 558.2025 485.411 2282.05 1040.21

964.34 19194800 540.333 172.3372 374677.865 549.2011 488.658 2323.071 1035.31

975.685 20221500 505.34 174.7182 366712.512 544.1592 494.34 2205.13 1042.66

987.03 18967600 520.543665 176.2739 344630 541.4569 501.646 2269.23 1042.66

994.594 15774900 488.773 179.9048 356664.03 586.8227 504.893 2384.62 1045.1

998.376 23187300 503.512 182.1202 354086.896 593.5796 512.198 2047.005 1054.9

1002.16 18968200 505.972067 186.4615 345433.172 606.8204 517.069 2128.221 1057.34

1005.94 17371800 508.429533 187.5726 346352.5 605.2685 520.316 2198.718 1050

1009.72 22389500 510.887 190.3593 554172.436 635.2721 525.186 2143.167 1047.55

1013.5 18740500 521.942 193.2117 342658.6 625.9112 527.621 2149.576 1050

1024.85 17714700 508.1335 194.2633 294526.553 660.8871 533.303 2188.646 1047.55

1028.63 17258700 518.267 198.8672 284260.3 665.3475 535.738 2210.622 1047.55

1032.41 15548300 479.586 202.0714 265754.381 712.117 542.232 2186.814 1050

1036.19 15662500 451.956 204.5145 273885.5 698.3531 545.479 2153.85 1052.45

1039.97 25241600 494.327 207.9241 251047.3 715.4498 551.161 2108.975 1052.45

1043.76 19425900 475.908 210.9223 233363.299 745.5708 557.655 2025.64 1057.34

1058.88 22049300 498.023 212.4647 227567.9 738.1887 561.714 1946.152 1059.79

1062.66 18058200 483.301315 216.4011 233310.8 753.8538 567.396 1903.854 1067.13

1066.45 20909200 468.540685 217.4629 284801.5 758.4859 575.513 1841.026 1067.13

1074.01 21479700 472.243 218.7335 230335.295 782.9655 580.383 1897.44 1074.48

1077.79 17944800 468.561 220.3457 233402.5 773.792 582.818 1878.193 1069.58

1081.57 22278200 464.879 221.4106 14787.5289 922.4576 590.124 1942.31 1072.03

1085.36 13269600 473.181954 221.5623 179170.2 781.0353 595.806 1858.97 1064.69

1089.14 17717100 481.463 222.3967 16356.001 919.1938 599.053 1858.97 1074.48

1096.7 19199900 472.257 223.3095 24949.9651 959.3774 603.923 2000 1067.13

1100.48 22621100 466.733 223.4906 26654.3791 964.3309 608.794 1798.065 1069.58

1104.26 17147500 461.209 223.9321 40863.3021 976.4119 612.041 1602.56 1084.27

1108.05 18516100 453.833269 224.3983 67399.9504 979.2648 616.099 1660.255 1084.27

1111.83 17718000 446.477 225.1981 10207.705 984.1586 618.534 1769.23 1076.92

1123.17 20569300 457.079455 226.8408 10386.04 948.8469 622.593 1630.344 1094.06

1126.95 18630800 451.098911 227.2457 8130.79268 997.0115 625.84 1610.253 1094.06

1134.52 20227600 439.122 229.1188 7353.94352 1019.075 630.71 1615.38 1089.16

1138.3 21140100 434.05875 230.3278 7200.972 997.3158 637.204 1557.673 1091.61

1142.08 22052500 428.9955 231.1043 24216.98 1012.375 638.016 1592.942 1101.4

1149.64 20684300 418.869 231.357 23052.6182 1027.551 641.263 1681.628 1081.82

1160.99 18518100 527.56 231.8028 203411.084 1006.909 646.945 1555.501 1089.16

1164.77 20000700 520.194 232.9656 270160.616 953.0705 647.756 1487.18 1096.5

1176.12 21141500 409.6742 234.1629 346615.053 929.5858 650.192 1423.08 1101.4

183

1179.9 18975000 407.8344 235.4462 342403.3 1035.401 655.874 1582.049 1084.27

1191.24 19887700 402.315 237.6078 224516.777 949.7359 658.309 1589.74 1091.61

1195.03 17265000 404.163502 237.8974 98210.4592 953.8048 662.368 1580.59 1094.06

1202.59 17835500 407.850751 239.1254 152245.554 971.0614 666.426 1663 1091.61

1210.15 20572600 411.538 239.8541 161906.933 939.8713 670.485 1641.034 1084.27

1213.93 18634200 409.330968 241.7719 134881.796 985.4487 672.92 1676.28 1084.27

1221.5 16923900 404.911065 242.3632 140715.722 999.4991 674.543 1644.24 1089.16

1225.28 18976700 402.704032 243.5921 154497.3 962.4093 677.79 1608.975 1094.06

1232.84 19547200 391.288 244.0218 270593.086 1045.857 681.037 1589.74 1094.06

1240.41 18293100 415.24 246.4732 381836.196 931.5015 685.908 1529.889 1094.06

1247.97 17381100 416.473333 247.0708 406518.037 959.883

1255.53 16013000 400.513 248.3031 98376.8999 986.5422

1259.31 12820100 389.463 249.0642 248979.6 919.9309

1263.1 17723800 383.009486 249.2843 132259.2 923.8253

1274.44 16811900 385.173667 250.8188 288956.216 1056.417

1278.22 19092800 389.474 251.7572 353466.142 1047.22

1285.79 16128200 415.269 252.7821 593574.58 921.7249

1289.57 15216000 393.166 253.5916 581647.469 696.1919

1293.35 16926700 387.028 254.4139 637990.7 1015.571

1297.13 16356700 380.89 256.7326 575364.889 683.2609

1308.48 14646600 398.704 257.2926 566046.1 747.7532

1316.04 13848600 389.498 259.5202 352933.919 689.5653

1323.6 15217300 380.292 260.852 366060.748 696.3464

1327.39 15673600 391.361604 261.3839 356666.6 654.974

1331.17 13507100 402.402 262.1699 349363.674 661.2833

1334.95 14533500 391.352 263.5188 279341.922 700.8098

1338.73 10656500 411.617 265.1597 568719.369 716.5136

1353.86 10086900 387.064667 267.3041 638016.054 463.8596

1361.42 12710000 396.894 268.1389 624404.876 384.4447

1368.98 11912000 403.658408 268.5505 587256.9 618.6861

1372.77 14649000 397.509592 269.5151 584278.949 358.9421

1376.55 13280700 391.377 271.5888 420952.475 316.433

1384.11 13965200 415.329 274.2223 478272 318.9567

1387.89 12368900 389.542 274.8687 368353.562 625.7226

1406.8 13053800 397.446637 275.5494 146275.989 426.0727

1414.37 11001500 400.611 276.1779 209394.745 330.715

1418.15 13966500 382.192 277.7256 357202.7 486.5375

1421.93 12256200 368.379 278.3875 348829.576 602.8615

1425.71 13054600 354.566 283.5835 354161.695 595.5512

1437.06 7011130 388.654545 284.1779 355121.747 594.715

1440.84 7809520 393.259 286.2353 265977.6 589.8166

184

1444.62 6213180 387.735 286.7388 434744.556 628.755

1448.4 14081700 382.211 287.1893 682841.539 580.594

1452.18 13169600 365.635 287.6853 592346.4 611.1293

1459.75 11801500 376.692 288.205 297182.777 439.2943

1467.31 12600000 370.249 288.6936 345315.046 342.3288

1486.22 11802500 365.661827 290.7444 349451.194 478.784

1497.56 11004700 355.841785 291.0341 363816.213 478.5489

1501.35 12259200 351.538215 292.3034 410808.7 482.9658

1512.69 14426300 334.356 292.9648 294362.2 484.6642

1516.47 11917700 343.102465 293.8583 468701.481 381.3762

1520.25 13514300 351.848931 295.3189 356686.236 331.1223

1527.82 10891800 369.365 296.0162 293204.526 420.4406

1531.6 12716500 366.297333 298.0404 290811.7 414.8605

1535.38 8611390 363.229667 299.2198 365113.934 477.2325

1542.94 9980100 371.217 299.6633 570878.317 439.9527

1550.51 12603200 390.571417 300.518 273301.248 368.1123

1554.29 8270000 396.556709 302.5268 289230.634 451.696

1558.07 9524530 402.542 304.8512 280755.659 498.701

1561.85 8840470 370.3075 308.7593 280314.8 523.2624

1573.2 7358450 347.288 309.3591 239272.715 549.8607

1576.98 10551600 342.380331 310.5884 185006.9 529.2474

1592.11 10666200 322.736669 311.4937 198439.209 779.6934

1595.89 13403200 317.829 314.0651 208857 810.9538

1599.67 9754200 328.884 315.2167 213522.249 887.574

1607.23 12263300 303.099 319.6996 231683.847 950.0807

1614.8 12263500 339.0245 320.5282 251794.218 873.5026

1618.58 7588250 314.158 322.0105 341221.774 799.7753

1626.14 11465700 331.356 322.6082 355183.365 828.1568

1633.71 10553700 367.647406 322.7777 358636.7 924.0728

1641.27 9869820 360.225 325.1336 254029.4 826.5113

1645.05 9299790 308.648 326.0501 230573.957 808.7507

1671.52 8616600 311.245156 326.6183 279662.837 805.5471

1675.3 11809700 309.774734 327.7668 388881.988 785.5965

1701.78 6679160 308.67522 328.956 382155.9 767.0407

1720.69 9872860 293.964829 329.1523 72812.7307 853.828

1728.25 10899500 301.331 331.7425 49288.6399 876.5781

1739.59 9645520 301.367877 331.8174 41864.29 837.1522

1743.38 11014100 284.762 331.9193 29426.67 840.1244

1747.16 7251070 287.220333 333.0002 93595.647 904.9737

1758.5 8505890 314.245 334.2566 400804.104 792.3054

1762.28 9646380 324.0695 335.0242 343643.017 723.4737

185

1766.07 9190390 326.5325 335.3229 677522.803 696.6829

1769.85 7480010 328.989 335.7874 299432.5 852.796

1781.19 8278690 299.522 337.1982 800759.013 496.999

1788.76 6682490 309.335856 338.3318 743273.6 769.9342

1792.54 9533510 300.749428 339.294 583628.207 436.4975

1796.32 7481020 292.163 339.5038 603469.71 349.0837

1800.1 5314500 309.479835 340.512 698829.383 445.2118

1803.88 6454990 312.05967 341.1406 352477.727 505.1469

1807.66 5770930 314.639505 341.3968 413173.118 471.5886

1819.01 9762590 297.703 343.1252 288488.7 436.3767

1826.57 6455860 306.919 344.0928 461131.005 363.3657

1830.36 8508640 271.921 345.2529 440313.7 438.3911

1837.92 8965070 281.750333 346.8065 259233.734 497.0201

1841.7 7482760 286.665 347.7847 398298.069 485.4301

1853.05 6114770 295.882 348.0521 291158.195 469.4632

1856.83 10790400 291.73975 349.3045 342568.265 394.6823

1860.61 8737870 287.5975 351.9446 429863.967 394.7384

1864.39 7825730 283.45525 353.0837 376440.727 477.0322

1868.17 10334600 279.313 354.4974 354518.893 434.5091

1875.74 6913880 308.791 357.7351 295481.685 462.9468

1879.52 7484200 283.004 358.4785 279137.497 497.8657

1883.3 3036980 272.567667 362.4359 248867.695 524.4749

1890.86 8967090 251.695 365.4745 345699.628 545.3809

1894.64 4976010 263.353719 367.6419 345078.306 460.3207

1898.43 10335800 275.043281 368.905 267670.094 418.5303

1909.77 4976590 303.286 372.1436 271039.218 514.3171

1913.55 8169720 296.539949 374.0737 265456.168 537.0532

1921.12 6687550 283.03 378.0514 245882.829 558.9232

1928.68 4863280 264.613 380.6253 260498.738 587.267

1936.24 6117950 310.671 382.6542 469028.155 537.2358

1940.03 9653190 299.598589 384.3344 403756.313 368.4952

1947.59 8741190 277.512196 385.5128 296549.774 438.0059

1951.37 7030810 266.469 386.2602 367681.974 398.3054

1966.5 7943670 264.637 389.6614 341630.495 382.1048

1977.84 8628320 260.9595 392.3191 264807.531 344.5336

1989.19 9084890 250.8345 393.0304 236098.71 346.6

1996.75 7488690 262.808128 395.6595 223193.504 354.2369

2019.44 7831660 246.248 396.8292 293239.347 333.4038

2027.01 5893360 248.085266 399.542 282952.802 361.7086

2034.57 6805930 237.047 400.8279 239745.894 412.1661

2038.35 8402560 227.839 401.9287 376293.334 455.3615

186

2042.13 9885160 218.631 403.9625 346730.06 482.1422

2045.91 10341400 253.630085 406.1736 374241.459 347.6653

2049.7 9201240 257.322915 407.5177 165317.362 332.2101

2057.26 7262940 249.955667 408.8824 350812.586 316.5173

2061.04 7947290 238.905333 410.411 355536.179 320.9575

2072.39 8631940 251.814808 412.88 344194.982 299.581

2083.73 7606050 244.446 415.6001 366249.728 321.4502

2091.29 8404590 224.556578 416.9559 356489.611 326.3749

2102.64 7264670 220.141422 418.1666 220803.275 296.8566

2113.98 5896680 240.796559 422.8555 190743.874 265.7507

2117.77 8519640 231.572 423.4469 350359.761 296.969

2121.55 6581180 234.029416 424.7948 294440.012 312.9375

2136.68 7380010 243.865584 426.9504 35168.5466 277.2741

2140.46 6125770 246.323 428.6335 165475.066 339.6325

2144.24 8064510 222.378 430.0735 251289.959 299.8912

2148.02 8178690 222.789546 431.9097 13475.4653 296.7853

2155.58 8863190 223.612637 434.7202 38197.8762 292.0313

2166.93 7039060 224.848363 437.0597 70917.8869 267.8422

2174.49 3048120 225.671454 437.4137 364964.027 249.0392

2178.27 7267570 226.083 438.882 255918.034 481.6946

2185.84 3960840 296.088 440.2219 87670.2115 322.8569

2197.18 6812150 268.478008 443.4392 95151.3856 313.7642

2200.96 7382470 259.274678 444.2367 352156.608 311.5106

2216.09 5558490 218.73665 445.4823 285509.143 481.835

2227.44 6243130 229.80035 447.6608 237939.061 348.2397

2231.22 7725730 233.485 451.1122 57469.1569 323.0895

2238.78 4419000 221.208333 452.172 259433.968 329.575

2242.56 6357750 215.07 453.3831 353541.15 336.9861

2246.35 5445610 242.704 454.8975 201254.445 338.5661

2250.13 7840490 233.496 458.0942 225166.317 315.7741

2253.91 6928360 224.288 460.6405 252393.413 323.1706

2276.6 6359050 217.302781 463.6341 224848.349 331.8666

2291.73 6929800 222.092233 465.2482 225393.651 316.617

2310.63 6360350 207.742063 466.3304 206315.667 306.392

2321.98 7159030 191.172 467.8151 242044.762 322.0949

2329.54 5448790 192.404123 471.7863 210317.059 319.429

2333.32 6247180 193.020185 473.0111 245705.836 321.1322

2340.89 7387820 194.253938 475.1001 185835.633 337.9278

2348.45 6817940 198.094118 478.2554 225807.665 337.3702

2352.23 5677730 201.318235 479.632 193752.695 331.5384

2363.58 6020270 202.865 481.4589 249546.264 331.6994

187

2371.14 6590740 193.045 484.1569 204894.758 351.6385

2382.49 6135030 195.508724 486.6825 239263.65 339.166

2386.27 5336930 196.329241 488.7094 205024.371 345.1023

2405.18 5679760 200.434 490.7295 178788.685 376.8075

2416.52 5224050 192.708288 493.2795 194056.836 358.0293

2424.09 5680480 187.551 493.3792 162827.255 359.3542

2427.87 4654310 190.009667 497.2124 186397.381 389.4379

2439.21 5795100 207.824 499.2807 148640.865 395.4459

2442.99 4996990 203.775742 501.1063 191804.359 400.749

2454.34 6023740 191.620258 505.8077 233148.438 363.9696

2461.9 4883680 196.785 506.9747 184117.606 357.0637

2465.69 3971550 186.64262 510.8424 197286.648 323.0175

2469.47 5454150 176.527 511.4101 233379.441 320.152

2477.03 4200050 188.505 515.0919 185604.148 344.309

2484.59 4998590 200.483 517.1219 161990.944 321.6571

2492.16 4428700 190.658674 518.6606 192136.025 334.028

2503.5 5455450 188.826645

2514.85 4315530 193.441178

2518.63 4999890 194.978

2526.19 1693160 187.614

2529.97 5798570 195.440074

2537.54 4088330 211.112926

2541.32 3518300 218.939

2545.1 3062310 185.784

2552.66 5115230 222.611029

2556.45 1580280 237.37

2560.23 3747090 217.109

2567.79 2949140 210.670758

2582.92 4204100 204.228667

2598.05 3976610 190.23157

2601.83 4660970 187.287928

2620.74 5003800 193.199

2624.52 5688150 192.833

2635.86 3864020 191.735

2639.64 4548380 191.369

2658.55 4777170 169.893324

2662.34 4321180 167.435

2685.03 4664150 176.66

2707.72 4208880 172.579163

2715.28 4551270 171.765641

2737.97 4096000 169.324

188

2756.88 2386200 186.8355

2760.66 4324940 185.917

2775.79 4667620 171.803667

2779.57 2843210 174.262333

2794.7 4782380 176.723602

2802.26 4212500 173.046534

2809.82 2730330 160.158

2824.95 3301080 177.36

2828.73 3871400 174.906

2851.42 3188060 177.376667

2866.55 4328990 171.246

Case Study 3-F Case Study 3-G Case Study 3-H

pi=6900 psia, T=200F, SG=0.67 pi=14000 psia, T=200F, SG=0.55 pi=14000 psia, T=200F, SG=0.55

t(Day) qsc(SCFD) pwf(psia) t(Day) qsc(SCFD) pwf(psia) t(Day) qsc(SCFD) pwf(psia)

5.34759 10938.6 2500 1.85185 37642700 12396.8 2.22222 36749500 11327.3

7.35294 7990.93 2445.413 3.08642 51694300 10334.2 3.7037 37774200 11100

9.35829 11103.4 2399.56 4.32099 54272600 9302.85 4.44444 36180300 10986.35

13.369 10938.6 2097.24 4.93827 51307600 9045.027 5.18519 45060700 10872.7

18.0481 10616.3 2100.437 6.17284 54272600 8271.55 5.92593 47110100 10456.04

21.3904 8483.43 2684.973 7.40741 52854500 7820.348 7.40741 37888000 9622.73

22.7273 9419.46 2559.851 8.02469 58655600 7626.98 8.14815 46426900 10077.29

24.7326 10776.2 2027.544 9.25926 48342500 6466.76 9.62963 36635700 10986.4

30.0802 10616.3 1868.726 10.4938 54659300 5693.28 10.3704 44833000 8372.73

37.4332 10303.6 1687.722 11.1111 57108700 5435.45 11.1111 50184100 7293.258

39.4385 8111.31 1655.908 11.7284 56721900 5177.62 12.5926 52461100 5872.745

43.4492 9705.39 1814.906 12.963 55303900 4404.14 13.3333 42214400 5531.851

49.4652 9419.46 1837.893 14.1975 54401500 4017.4 14.0741 43239100 5190.91

54.8128 9141.95 1824.417 14.8148 54530400 3824.03 15.5556 34244800 5645.45

60.1604 9419.46 1824.253 16.0494 51823200 3501.75 16.2963 50525600 4281.82

64.8396 8611.22 1804.97 17.284 48729300 3243.92 17.037 51436400 3770.49

69.5187 8233.5 1754.382 17.9012 46408800 3115.02 18.5185 49273200 3145.458

73.5294 9006.28 1693.292 19.1358 44733000 2986.1 19.2593 42783700 3031.812

78.877 8611.22 1664.308 20.3704 43443800 2986.1 20 43694500 2918.18

84.2246 8611.22 1637.992 20.9877 41896900 2857.175 21.4815 41759000 2766.663

90.2406 8611.22 1605.122 22.2222 40994500 2685.3 22.2222 40165100 2690.91

96.9251 8483.43 1594.874 23.4568 40092100 2599.36 22.963 37774200 2539.38

101.604 7990.93 1546.138 24.0741 39060800 2556.384 24.4444 34927900 2236.36

108.957 7755.51 1752.255 25.3086 38029500 2470.44 25.1852 27072100 3088.693

189

110.294 6579.33 1760.887 25.9259 36869200 2470.44 25.9259 32992400 3940.91

112.299 6385.5 1773.83 27.1605 35966900 2470.44 27.4074 24908900 3789.393

114.973 8111.31 1758.294 28.3951 35064500 2470.44 28.1481 31967700 3713.64

120.321 7415.32 1852.218 29.0123 34419900 2470.44 28.8889 31740000 3145.417

124.332 7990.93 1835.508 30.2469 33646400 2470.44 30.3704 30487700 2463.627

127.674 7415.32 1819.353 30.8642 33259700 2470.44 31.1111 33675500 2350

132.353 7415.32 1745.974 33.3333 32357300 2341.53 31.8519 34017100 2236.357

136.364 7415.32 1745.847 33.9506 31454900 2341.53 33.3333 31967700 2236.357

141.043 7415.32 1730.489 35.1852 31197100 2341.53 34.0741 30487700 2350

143.717 7305.27 1730.406 36.4198 28489900 2341.53 35.5556 29804600 2577.27

147.059 7305.27 1730.306 37.037 30294700 2341.53 37.037 27641400 2406.801

151.07 7305.27 1730.186 38.2716 29521200 2341.53 38.5185 24908900 2776.135

154.412 7196.86 1730.086 39.5062 29134400 2341.53 39.2593 24567400 2861.371

157.754 7090.05 1729.98 40.1235 28747700 2341.53 41.4815 27641400 3088.641

160.428 7090.05 1732.899 41.358 28489900 2341.53 42.2222 26616700 3145.455

163.102 7090.05 1742.946 42.5926 27845300 2341.53 42.963 26389000 3202.276

165.775 7090.05 1738.062 43.8272 27329700 2126.676 44.4444 24112000 2690.91

169.786 7090.05 1723.017 45.679 26556200 2244.848 45.1852 25136600 2350

175.134 6881.17 1714.237 46.2963 25911600 2277.075 46.6667 24908900 2259.091

180.481 6984.83 1714.071 47.5309 25653800 2341.53 47.4074 24112000 2213.639

183.824 6881.17 1703.08 49.3827 24880300 2341.53 48.8889 23656500 2122.73

187.166 5581.53 1630.501 51.2346 24364600 2341.53 49.6296 23201100 1952.287

187.834 6678.44 1584.317 53.0864 24493600 2341.53 50.3704 22859600 1781.82

192.513 6197.38 1290.617 54.321 24106800 2212.615 51.8519 22404200 2009.09

197.193 6984.83 1260.775 54.9383 23849000 2083.7 53.3333 21948800 2009.09

197.861 5417.09 1275.875 56.1728 23462200 2083.7 54.0741 21493400 2009.09

201.872 6779.05 1366.557 58.0247 22946600 2083.7 55.5556 15573100 2009.09

207.888 7415.32 1395.448 59.8765 22946600 2083.7 56.2963 20241000 2009.09

214.572 7415.32 1405.098 61.1111 22430900 2083.7 57.037 20810200 2009.09

222.594 7196.86 1422.137 62.963 21915300 2083.7 58.5185 20127100 2009.09

225.267 6290.73 1381.431 64.8148 21528500 2083.7 59.2593 18760900 2009.09

226.604 5257.5 1384.445 66.6667 21270700 2083.7 60 19102500 2009.09

230.615 6481.69 1875.115 68.5185 20884000 2212.62 61.4815 20582500 1971.208

233.957 6678.44 2326.821 69.7531 20497200 2161.05 62.2222 19671700 1933.332

239.305 6779.05 2159.497 70.9877 20110500 2109.481 62.963 17963900 1895.45

243.316 6481.69 1613.635 73.4568 19981600 2083.7 63.7037 19216300 1933.328

247.995 6385.5 1568.903 75.3086 19723800 1997.762 65.1852 18874800 2009.09

251.337 6385.5 1574.959 76.5432 19337000 1954.79 66.6667 18305500 2084.852

255.348 6481.69 1567.15 79.0123 19208100 1954.79 68.1481 17963900 2122.73

190

259.358 6481.69 1559.499 80.8642 18950300 1825.87 69.6296 17736200 2122.73

264.037 6385.5 1559.357 82.0988 20497200 1825.87 70.3704 17280800 2122.73

269.385 6014.79 1559.19 83.9506 19981600 1793.643 71.1111 16939300 2122.73

273.396 6197.38 1548.888 84.5679 19465900 1761.415 72.5926 16711600 2122.73

276.738 6197.38 1531.883 87.037 19208100 1782.898 73.3333 16483900 2122.73

280.08 5925.53 1521.658 88.8889 19079200 1568.05 74.8148 16256200 2065.91

284.091 5925.53 1517.431 90.1235 18821400 1653.995 77.037 16142300 2009.09

288.77 5837.59 1549.778 91.358 18563500 1664.733 78.5185 15800800 2009.09

294.118 5498.7 1748.936 93.8272 18305700 1568.05 80 15686900 1952.274

297.46 4878.79 1977.568 95.0617 18047900 1568.05 81.4815 15003800 1838.636

298.128 3957.33 1996.429 95.679 17790100 1568.05 83.7037 14889900 1781.82

300.802 5837.59 1786.584 96.9136 17532200 1568.05 85.1852 14548400 1781.82

307.487 5750.96 1471.182 98.1481 17532200 1568.05 86.6667 14434500 2009.09

316.176 5498.7 1549.405 100 17403300 1568.05 88.1481 14206800 1923.858

322.193 5336.7 1527.152 100.617 17274400 1482.153 90.3704 14093000 2009.09

326.872 5417.09 1560.154 101.235 16758700 1396.117 92.5926 13979100 2009.09

331.551 5417.09 1581.458 103.086 16758700 1310.22 93.3333 13751400 2009.09

335.561 5102.61 1572.392 104.938 16500900 1310.22 94.8148 13296000 1918.181

340.909 5102.61 1572.233 105.556 16372000 1310.22 95.5556 13865300 1872.723

345.588 5179.47 1583.226 106.79 14438300 1310.22 97.7778 13296000 1781.82

350.267 5026.88 1578.965 108.025 15856400 1310.22 100 12954500 1781.82

354.947 5102.61 1571.803 109.259 16629800 1310.22 102.222 12840600 1781.82

360.294 5026.88 1571.643 110.494 16372000 1310.22 103.704 12726800 1781.82

364.973 4806.38 1553.771 111.728 16243100 1374.649 105.926 12499100 1696.6

366.979 3115.35 1544.581 112.963 15985300 1439.13 108.148 12499100 1668.18

368.984 4077.46 1531.692 114.198 15082900 1374.649 108.889 12157500 1668.18

372.995 4595.55 1501.131 115.432 14438300 1310.22 109.63 11929800 1668.18

377.674 5026.88 1495.027 116.049 15727400 1310.22 111.111 11815900 1724.981

381.684 4952.28 1486.347 117.284 15598500 1310.22 112.593 11702100 1781.82

385.027 4806.38 1471.032 118.519 15598500 1310.22 114.074 11702100 1725.019

389.037 4878.79 1449.763 119.753 15469600 1310.22 116.296 11360500 1696.561

396.39 4952.28 1433.586 120.988 15340700 1310.22 117.778 11246700 1753.4

401.738 3511.19 1446.329 122.222 15082900 1310.22 120 10905120 1781.82

403.075 5179.47 1448.604 124.691 15082900 1232.899 121.481 10905120 1781.82

408.422 4735.05 1448.437 125.926 14954000 1181.31 122.963 10677420 1781.82

413.102 4735.05 1433.67 127.16 14825000 1202.783 124.444 10677420 1781.82

417.781 4735.05 1432.935 128.395 14696100 1245.765 126.667 10677420 1781.82

421.123 4460.16 1432.835 129.012 14567200 1267.238 128.889 10563570 1781.82

424.465 4460.16 1432.735 130.864 13922700 1284.446 131.111 10335860 1781.82

191

427.807 4460.16 1432.635 131.481 13535900 1258.673 133.333 10335860 1781.82

431.15 4460.16 1425.437 133.951 14180500 1224.326 134.815 10335860 1781.82

435.829 4595.55 1417.171 134.568 13407000 1267.273 137.037 10108160 1781.82

442.513 4595.55 1432.186 135.802 14051600 1278.006 138.519 9994310 1781.82

447.861 4460.16 1446.061 137.654 13793700 1181.31 140.741 9880460 1781.82

451.203 4264.52 1431.916 139.506 13793700 1181.31 141.481 9538900 1781.82

455.882 4264.52 1431.776 141.358 13793700 1052.394 143.704 9538900 1743.923

461.23 4328.76 1416.397 142.593 13407000 987.9114 145.926 9425050 1668.18

464.572 4328.76 1449.904 144.444 13407000 987.8853 148.889 9425050 1668.18

145.679 13020300 1052.394 150.37 9311200 1724.981

148.765 12504600 1052.394 152.593 9197340 1781.82

150.617 12762400 1052.394 154.815 9197340 1781.82

153.086 12762400 1052.394 156.296 9425050 1668.223

154.321 12504600 1052.394 157.778 9197340 1554.55

156.173 12504600 1052.394 160 8969640 1592.444

158.642 12504600 1052.394 162.222 8741940 1668.18

159.877 12246800 1052.394 164.444 8741940 1645.472

162.346 12117900 1052.394 166.667 8855790 1577.258

163.58 12117900 1052.394 167.407 9766600 1554.55

165.432 11989000 1052.394 168.148 10222010 1554.55

167.284 11860000 1052.394 169.63 10108160 1554.55

169.753 11731100 966.452 171.111 9880460 1554.55

172.222 10442000 923.481 171.852 9538900 1554.55

172.84 10828700 923.481 173.333 6920300 1554.55

174.074 10442000 923.481 174.815 9083490 1668.18

175.309 9926340 949.2887 177.037 9538900 1753.4

175.926 11344400 975.0546 177.778 9311200 1781.82

177.16 11473300 1026.586 179.259 9083490 1781.82

178.395 11344400 1052.394 180.741 8969640 1759.086

179.63 11215500 1052.394 182.963 8741940 1690.914

181.481 11086600 1052.394 185.185 8628080 1781.82

182.716 10957600 1052.394 185.926 8058820 1781.82

183.951 11086600 1052.394 187.407 8628080 1781.82

185.185 10957600 1052.394 189.63 8514230 1781.82

187.037 10957600 1052.394 191.111 8514230 1781.82

188.889 11731100 1052.394 193.333 8400380 1696.6

190.123 11215500 1052.394 195.556 8172680 1668.18

191.358 10957600 1052.394 198.519 8172680 910.2644

192.593 10699800 1052.394 201.481 8172680 531.818

193.21 10313100 1052.394 202.963 8172680 531.818

192

195.062 10055200 1052.394 205.185 7944970 531.818

196.296 10184200 1052.394 208.148 7717270 531.818

198.148 7734810 1052.394 211.111 7603420 531.818

198.765 8121550 1052.394 214.074 7603420 531.818

200 8508290 1052.394 217.778 7489560 456.0607

201.235 9539590 1009.377 220.741 7489560 418.182

202.469 10442000 923.481 222.963 7489560 503.3994

203.704 10184200 923.481 224.444 7148010 531.818

204.321 9926340 923.481 227.407 7375710 531.818

205.556 9797420 923.481 228.148 5440230 531.818

206.79 9539590 923.481 229.63 7603420 531.818

208.642 9539590 923.481 231.852 7375710 418.182

210.494 9668510 923.481 233.333 6578750 418.182

211.728 9281770 987.9114 237.037 7148010 418.182

214.198 9539590 1052.394 240 6920300 418.182

215.432 9281770 1052.394 241.481 6123340 190.9605

216.667 8895030 1052.394 242.963 7148010 109.753

219.136 8379370 1009.423 244.444 6806450 174.669

219.753 9023940 966.452 246.667 6464900 272.1089

220.988 8895030 923.481 249.63 6578750 475.0573

222.222 8637200 923.481 251.852 5554080 588.6557

224.074 8895030 923.481 253.333 5212520 645.455

225.309 8637200 923.481 254.074 6578750 617.0362

226.543 8379370 923.481 256.296 7034160 531.818

227.778 8250460 966.4984 258.519 6351040 361.3057

229.63 8250460 1052.394 261.481 6123340 304.545

230.864 7863720 1052.394 263.704 5895640 531.818

232.716 8508290 1052.394 265.185 6464900 456.0777

234.568 8379370 1052.394 266.667 6464900 418.182

235.802 8250460 1052.394 268.148 6578750 418.182

237.037 8250460 1052.394 271.111 6351040 418.182

238.272 8121550 1052.394 271.852 5440230 446.6006

240.123 8121550 1052.394 272.593 6237190 475.0192

241.975 8250460 1052.394 275.556 6237190 531.818

243.827 8379370 1052.394 278.519 6237190 531.818

245.679 8250460 1052.394 280 6123340 531.818

248.148 8121550 1052.394 282.222 5895640 531.818

250 7992630 955.6962 285.926 5781780 531.818

251.235 7863720 923.481 286.667 6009490 531.818

252.469 7863720 923.481 290.37 5895640 645.455

254.938 7734810 923.481 292.593 6009490 418.182

193

257.407 7734810 923.481 293.333 4984820 418.182

259.877 7734810 923.481 296.296 5667930 418.182

261.111 6832410 923.481 297.778 6009490 531.818

262.963 7992630 923.481 300.741 5781780 759.091

264.198 7734810 923.481 304.444 5781780 463.5998

264.815 7348070 923.481 305.926 4643260 554.5581

266.049 7734810 923.481 307.407 5895640 645.455

267.901 7476980 923.481 308.889 5667930 645.455

269.136 5414360 923.481 311.111 5667930 509.1157

270.37 6703500 923.481 313.333 5212520 418.182

271.605 7734810 923.481 315.556 5326380 418.182

274.074 7734810 923.481 317.778 5440230 531.818

275.926 7605890 923.481 319.259 4529410 531.818

277.16 7348070 923.481 320.741 5895640 645.4929

278.395 7090240 923.481 321.481 5212520 702.2536

280.247 7476980 923.481 322.963 3049340 787.5103

281.481 7348070 1181.168 325.185 5895640 872.73

283.333 7219150 923.481 326.667 5781780 796.9366

285.802 7219150 923.481 328.889 5326380 713.6243

287.654 7219150 923.481 330.37 3390890 668.1883

289.506 7219150 923.481 331.111 4984820 645.455

291.358 7219150 923.481 331.852 5440230 702.273

293.21 7219150 923.481 333.333 5667930 683.4015

295.679 6703500 923.481 336.296 5554080 607.559

297.531 6445670 923.481 337.778 4415560 645.455

299.383 6961330 923.481 339.259 5212520 683.2996

301.235 7219150 923.481 341.481 5326380 759.091

303.704 6703500 1000.846 342.222 3960150 759.091

305.556 6961330 1052.394 343.704 5895640 730.6724

307.407 6961330 1052.394 344.444 4984820 702.2922

309.877 6961330 1052.394 345.926 5554080 645.455

311.728 7090240 1052.394 347.407 5326380 645.455

314.198 6832410 1310.22 348.889 5212520 645.455

316.049 5543280 1181.342 352.593 4984820 607.559

317.284 6445670 1095.353 355.556 5098670 486.3513

319.136 6058930 1116.878 356.296 5326380 463.6487

320.37 6961330 1181.31 357.778 5098670 418.182

322.222 6961330 1084.649 358.519 4415560 418.182

325.309 6445670 1052.394 361.481 5212520 607.4042

327.16 6316760 1052.394 363.704 5098670 759.091

329.012 8379370 1052.394 364.444 4643260 730.7108

194

329.63 7992630 1052.394 365.926 5098670 673.8736

330.864 6703500 1052.394 369.63 5098670 554.527

331.481 7992630 1052.394 370.37 4074000 531.818

332.716 7734810 987.9375 371.852 5212520 486.3513

333.951 7476980 923.481 374.074 4984820 418.182

335.802 7219150 923.481 376.296 4074000 673.835

337.654 6574590 923.481 377.037 5098670 759.091

338.272 7090240 923.481 379.259 5098670 418.182

340.741 7090240 923.481 381.481 4870970 418.182

342.593 6961330 923.481 382.222 3846300 446.6006

345.062 6832410 923.481 384.444 5212520 531.818

346.914 6832410 987.9549 385.926 5440230 531.818

349.383 6703500 1052.394 388.148 4187860 645.455

351.235 6058930 1052.394 389.63 4643260 645.455

351.852 6703500 1052.394 391.852 3732450 872.73

353.704 6445670 1052.394 394.074 5212520 645.455

355.556 6316760 1052.394 396.296 5212520 617.0745

357.407 6058930 1052.394 397.778 4643260 560.2368

358.642 5801100 1052.394 400 5098670 531.818

361.111 5672190 1052.394 402.222 4757120 531.818

362.963 5543280 1052.394 402.963 5098670 503.3994

363.58 4383060 1052.394 405.185 4757120 418.182

364.815 6187850 1052.394 406.667 4643260 509.0847

366.667 5156540 1052.394 410.37 4757120 418.182

367.901 4511970 1052.394 413.333 4757120 418.182

369.136 4640880 1052.394 416.296 4529410 531.818

370.37 5027620 1052.394 419.259 3732450 531.7161

373.457 5156540 1052.394 420 4529410 645.4035

375.309 4769800 1129.76 420.741 4187860 759.091

377.16 5027620 1181.31 422.222 4643260 645.455

379.012 5285450 1181.31 424.444 3732450 645.455

381.481 5414360 1181.31 425.926 4757120 509.0542

383.333 4769800 1181.31 428.889 4415560 304.545

384.568 5414360 1267.273 431.111 4074000 531.818

386.42 5543280 1310.22 431.852 3390890 531.818

387.037 5285450 1310.22 433.333 4643260 531.818

388.889 5801100 1267.25 434.815 4529410 531.818

390.741 5930020 1155.502 437.037 4187860 531.818

393.21 5930020 1052.394 438.519 4529410 531.818

395.062 5801100 1052.394 440.741 4529410 531.818

396.914 5801100 1052.394 443.704 4301710 531.818

195

399.383 5801100 1052.394 446.667 4187860 531.818

401.235 5672190 1052.394 449.63 3960150 531.818

402.469 5414360 1052.394 452.593 4187860 531.818

404.321 5414360 1116.852 456.296 4074000 446.6006

406.173 5543280 1245.765 460 3960150 361.3635

408.642 5543280 1568.05 462.963 3960150 418.182

411.111 5543280 1245.79 467.407 3960150 418.182

412.963 5543280 1052.394 470.37 3846300 418.182

415.432 4769800 1568.05 472.593 3960150 418.182

416.667 5543280 1052.394 477.037 3960150 418.182

418.519 5414360 1052.394 480 3960150 361.3635

421.605 5543280 1052.394 482.963 3390890 531.818

424.074 5543280 1052.394 484.444 4074000 531.818

426.543 4511970 1310.22 487.407 3732450 721.0415

429.012 5414360 1439.13 490.37 4074000 645.455

430.247 5543280 1310.218 493.333 3960150 645.455

432.716 5414360 1181.307 497.037 3163190 797.0382

433.333 4898710 1245.711 497.778 3960150 645.455

435.185 5285450 1439.13 500.741 3960150 929.5258

437.654 5543280 1482.153 502.222 3504740 872.73

440.123 5414360 1224.326 502.963 3960150 730.6358

441.975 5414360 1095.412 504.444 2821630 446.6392

443.827 5285450 923.481 505.185 4187860 304.545

445.679 5285450 794.567 506.667 3846300 475.0575

448.148 5156540 794.567 508.889 3504740 683.3507

450.617 5156540 794.567 512.593 3504740 673.8352

452.469 5027620 794.567 516.296 3618600 418.1431

455.556 5027620 880.5329 519.259 3732450 327.254

458.025 5027620 1052.394 522.963 3504740 456.0777

459.259 5027620 1052.394 525.926 3390890 531.818

461.728 5027620 1052.394 527.407 3618600 456.1285

462.963 4898710 1181.307 530.37 3163190 361.3443

464.198 4511970 1310.22 531.852 3504740 418.182

466.049 4898710 1310.22 534.074 3504740 486.3513

469.136 4898710 1116.879 537.037 3390890 531.818

470.988 4898710 923.481 540.741 3163190 531.818

472.84 4769800 923.481 543.704 3390890 531.818

474.691 4769800 923.481 547.407 3390890 531.818

477.16 4898710 923.481 551.111 3163190 531.818

479.012 4898710 1052.394 554.815 3277040 486.3513

481.481 4769800 1052.394 557.778 3163190 418.182

196

483.333 4898710 1052.394 560 3277040 418.182

485.802 4898710 1052.394 562.222 3277040 418.182

487.037 4898710 1052.394 565.185 3049340 440.9153

488.272 4769800 1052.394 567.407 3277040 509.0847

490.741 4769800 1052.394 569.63 3163190 531.818

492.593 4640880 1052.394 572.593 2935480 531.818

495.062 4640880 1052.394 574.074 3049340 531.818

497.531 4511970 1052.394 577.037 3163190 815.909

499.383 4511970 1052.394 578.519 3390890 531.818

501.852 4511970 1052.394 581.481 3390890 531.818

503.704 4511970 1052.394 584.444 3163190 418.2328

505.556 4511970 1052.394 585.926 3163190 372.7454

507.407 4383060 1052.394 588.889 3049340 645.455

509.259 4383060 1052.394 591.111 2593930 475.0194

510.494 4383060 1052.394 591.852 2935480 418.182

511.728 4383060 1052.394 593.333 3049340 361.3827

512.963 4383060 1052.394 594.815 3163190 304.545

514.198 4383060 1052.394 598.519 3163190 332.9638

516.049 4383060 1052.394 600 2935480 389.7632

517.901 4383060 1052.394

520.37 4254140 1052.394

522.84 4383060 1052.394

525.309 4383060 1052.394

526.543 3738490 1052.394

527.778 3996320 1052.394

529.63 4254140 1052.394

531.481 4125230 1052.394

Chapter 4

Case Study 4-A (re=175 ft)

pi=10,000 psia, T=200F, SG=0.55

Cr=5.00E-05 1/psi Cr=1.00E-06 1/psi Cr=1.00E-12 1/psi


1.5 2419343 4029073 2 2205392 4865019 2 2201274 4855526

21 1865720 43195716 22 1685380 42027512 22 1679512 41929400

41 1689136 78600712 42 1434904 72976608 42 1427648 72742376

61 1534312 1.11E+08 62 1246816 99617736 62 1239472 99236376

81 1395552 1.4E+08 82 1099672 1.23E+08 82 1092872 1.22E+08

101 1270864 1.67E+08 102 980960 1.44E+08 102 974816 1.43E+08

197

121 1159104 1.91E+08 122 884176 1.62E+08 122 878656 1.61E+08

141 1059056 2.13E+08 142 802736 1.79E+08 142 797984 1.78E+08

161 968864 2.33E+08 162 733968 1.94E+08 162 729696 1.93E+08

181 888496 2.52E+08 182 674032 2.08E+08 182 670368 2.07E+08

201 815840 2.69E+08 202 623072 2.21E+08 202 619840 2.2E+08

221 751104 2.84E+08 222 577696 2.33E+08 222 574816 2.32E+08

241 692064 2.99E+08 242 537152 2.44E+08 242 534640 2.43E+08

261 639392 3.12E+08 262 501856 2.55E+08 262 499696 2.54E+08

281 591712 3.24E+08 282 470288 2.64E+08 282 468384 2.63E+08

301 548000 3.36E+08 302 441376 2.74E+08 302 439712 2.72E+08

321 508736 3.46E+08 322 415008 2.82E+08 322 413536 2.81E+08

341 473376 3.56E+08 342 391072 2.9E+08 342 389824 2.89E+08

361 440768 3.65E+08 362 369792 2.98E+08 362 368736 2.96E+08

381 410752 3.73E+08 382 350336 3.05E+08 382 349408 3.04E+08

401 383456 3.81E+08 402 332256 3.12E+08 402 331488 3.1E+08

421 358976 3.89E+08 422 315456 3.18E+08 422 314784 3.17E+08

441 336384 3.96E+08 442 299808 3.24E+08 442 299296 3.23E+08

461 315360 4.02E+08 462 285280 3.3E+08 462 284800 3.29E+08

481 295968 4.08E+08 482 271776 3.36E+08 482 271424 3.34E+08

501 278016 4.14E+08 502 259360 3.41E+08 502 259104 3.4E+08

521 261504 4.19E+08 522 248000 3.46E+08 522 247808 3.45E+08

541 246496 4.25E+08 542 237376 3.51E+08 542 237248 3.49E+08

561 232704 4.29E+08 562 227392 3.56E+08 562 227360 3.54E+08

581 219776 4.34E+08 582 217984 3.6E+08 582 217984 3.59E+08

601 207680 4.38E+08 602 209088 3.64E+08 602 209152 3.63E+08

621 196480 4.42E+08 622 200768 3.68E+08 622 200832 3.67E+08

641 185920 4.46E+08 642 192832 3.72E+08 642 192960 3.71E+08

661 176160 4.5E+08 662 185344 3.76E+08 662 185504 3.75E+08

681 167008 4.53E+08 682 178272 3.8E+08 682 178432 3.78E+08

701 158400 4.56E+08 702 171584 3.83E+08 702 171744 3.82E+08

721 150528 4.59E+08 722 165216 3.87E+08 722 165504 3.85E+08

741 143200 4.62E+08 742 159232 3.9E+08 742 159456 3.88E+08

761 136288 4.65E+08 762 153568 3.93E+08 762 153824 3.92E+08

781 129824 4.68E+08 782 148288 3.96E+08 782 148576 3.95E+08

801 123776 4.7E+08 802 143264 3.99E+08 802 143552 3.97E+08

821 118080 4.73E+08 822 138464 4.02E+08 822 138784 4E+08

841 112704 4.75E+08 842 133920 4.04E+08 842 134272 4.03E+08

861 107648 4.77E+08 862 129568 4.07E+08 862 129920 4.06E+08

881 102912 4.79E+08 882 125440 4.1E+08 882 125760 4.08E+08

901 98432 4.81E+08 902 121472 4.12E+08 902 121824 4.11E+08

921 94176 4.83E+08 922 117696 4.15E+08 922 118080 4.13E+08

198

941 90176 4.85E+08 942 114112 4.17E+08 942 114464 4.15E+08

961 86432 4.87E+08 962 110624 4.19E+08 962 111040 4.18E+08

981 82880 4.88E+08 982 107296 4.21E+08 982 107712 4.2E+08

1001 79488 4.9E+08 1002 104160 4.23E+08 1002 104544 4.22E+08

1021 76256 4.92E+08 1022 101120 4.25E+08 1022 101472 4.24E+08

1041 73248 4.93E+08 1042 98208 4.27E+08 1042 98624 4.26E+08

1061 70368 4.95E+08 1062 95424 4.29E+08 1062 95840 4.28E+08

1081 67680 4.96E+08 1082 92736 4.31E+08 1082 93152 4.3E+08

1101 65088 4.97E+08 1102 90176 4.33E+08 1102 90560 4.32E+08

1121 62624 4.99E+08 1122 87712 4.35E+08 1122 88064 4.33E+08

1141 60288 5E+08 1142 85312 4.37E+08 1142 85760 4.35E+08

1161 58112 5.01E+08 1162 83008 4.38E+08 1162 83424 4.37E+08

1181 56000 5.02E+08 1182 80832 4.4E+08 1182 81280 4.39E+08

1201 53952 5.03E+08 1202 78752 4.41E+08 1202 79136 4.4E+08

1221 52064 5.04E+08 1222 76704 4.43E+08 1222 77120 4.42E+08

1241 50240 5.05E+08 1242 74720 4.45E+08 1242 75136 4.43E+08

1261 48480 5.06E+08 1262 72832 4.46E+08 1262 73280 4.45E+08

1281 46880 5.07E+08 1282 71040 4.47E+08 1282 71392 4.46E+08

1301 45312 5.08E+08 1302 69248 4.49E+08 1302 69696 4.48E+08

1321 43840 5.09E+08 1322 67520 4.5E+08 1322 68000 4.49E+08

1341 42368 5.1E+08 1342 65920 4.52E+08 1342 66304 4.5E+08

1361 40992 5.11E+08 1362 64320 4.53E+08 1362 64736 4.52E+08

1381 39680 5.12E+08 1382 62784 4.54E+08 1382 63168 4.53E+08

1401 38464 5.12E+08 1402 61312 4.55E+08 1402 61728 4.54E+08

1421 37280 5.13E+08 1422 59872 4.57E+08 1422 60320 4.55E+08

1441 36128 5.14E+08 1442 58496 4.58E+08 1442 58880 4.57E+08

1461 35040 5.15E+08 1462 57184 4.59E+08 1462 57568 4.58E+08

1481 33952 5.15E+08 1482 55904 4.6E+08 1482 56256 4.59E+08

1501 32992 5.16E+08 1502 54688 4.61E+08 1502 55072 4.6E+08

1521 32000 5.17E+08 1522 53408 4.62E+08 1522 53824 4.61E+08

1541 31072 5.17E+08 1542 52288 4.63E+08 1542 52640 4.62E+08

1561 30176 5.18E+08 1562 51168 4.64E+08 1562 51520 4.63E+08

1581 29344 5.18E+08 1582 50048 4.65E+08 1582 50432 4.64E+08

1601 28512 5.19E+08 1602 49024 4.66E+08 1602 49376 4.65E+08

1621 27712 5.2E+08 1622 47968 4.67E+08 1622 48320 4.66E+08

1641 26976 5.2E+08 1642 46944 4.68E+08 1642 47328 4.67E+08

1661 26272 5.21E+08 1662 46016 4.69E+08 1662 46336 4.68E+08

1681 25568 5.21E+08 1682 45088 4.7E+08 1682 45408 4.69E+08

1701 24864 5.22E+08 1702 44160 4.71E+08 1702 44512 4.7E+08

1721 24224 5.22E+08 1722 43296 4.72E+08 1722 43616 4.71E+08

1741 23584 5.23E+08 1742 42432 4.73E+08 1742 42752 4.72E+08

199

1761 23040 5.23E+08 1762 41568 4.74E+08 1762 41952 4.72E+08

1781 22432 5.24E+08 1782 40800 4.74E+08 1782 41152 4.73E+08

1801 21856 5.24E+08 1802 40000 4.75E+08 1802 40320 4.74E+08

1821 21344 5.24E+08 1822 39232 4.76E+08 1822 39584 4.75E+08

1841 20800 5.25E+08 1842 38464 4.77E+08 1842 38784 4.76E+08

1861 20288 5.25E+08 1862 37792 4.78E+08 1862 38048 4.76E+08

1881 19808 5.26E+08 1882 37024 4.78E+08 1882 37408 4.77E+08

1901 19296 5.26E+08 1902 36384 4.79E+08 1902 36672 4.78E+08

1921 18848 5.26E+08 1922 35712 4.8E+08 1922 36064 4.79E+08

1941 18464 5.27E+08 1942 35104 4.8E+08 1942 35392 4.79E+08

1961 17984 5.27E+08 1962 34432 4.81E+08 1962 34752 4.8E+08

1981 17536 5.27E+08 1982 33824 4.82E+08 1982 34112 4.81E+08

2001 17152 5.28E+08 2002 33248 4.82E+08 2002 33536 4.81E+08

2021 16736 5.28E+08 2022 32608 4.83E+08 2022 32960 4.82E+08

2041 16352 5.29E+08 2042 32096 4.84E+08 2042 32384 4.83E+08

2061 15968 5.29E+08 2062 31552 4.84E+08 2062 31808 4.83E+08

2081 15616 5.29E+08 2082 31008 4.85E+08 2082 31296 4.84E+08

2101 15232 5.29E+08 2102 30464 4.86E+08 2102 30752 4.85E+08

2121 14912 5.3E+08 2122 29920 4.86E+08 2122 30208 4.85E+08

2141 14560 5.3E+08 2142 29472 4.87E+08 2142 29728 4.86E+08

2161 14272 5.3E+08 2162 28960 4.87E+08 2162 29248 4.86E+08

2181 13952 5.31E+08 2182 28480 4.88E+08 2182 28800 4.87E+08

2201 13632 5.31E+08 2202 28032 4.89E+08 2202 28320 4.88E+08

2221 13376 5.31E+08 2222 27584 4.89E+08 2222 27840 4.88E+08

2241 13056 5.31E+08 2242 27136 4.9E+08 2242 27424 4.89E+08

2261 12832 5.32E+08 2262 26720 4.9E+08 2262 27008 4.89E+08

2281 12544 5.32E+08 2282 26272 4.91E+08 2282 26560 4.9E+08

2301 12288 5.32E+08 2302 25888 4.91E+08 2302 26144 4.9E+08

2321 12032 5.32E+08 2322 25472 4.92E+08 2322 25696 4.91E+08

2341 11776 5.33E+08 2342 25088 4.92E+08 2342 25312 4.91E+08

2361 11552 5.33E+08 2362 24704 4.93E+08 2362 24960 4.92E+08

2381 11296 5.33E+08 2382 24288 4.93E+08 2382 24544 4.92E+08

2401 11104 5.33E+08 2402 23936 4.94E+08 2402 24224 4.93E+08

2421 10880 5.34E+08 2422 23616 4.94E+08 2422 23840 4.93E+08

2441 10656 5.34E+08 2442 23232 4.95E+08 2442 23488 4.94E+08

2461 10432 5.34E+08 2462 22880 4.95E+08 2462 23136 4.94E+08

2481 10272 5.34E+08 2482 22560 4.96E+08 2482 22816 4.95E+08

2501 10080 5.34E+08 2502 22272 4.96E+08 2502 22496 4.95E+08

2521 9888 5.35E+08 2522 21920 4.96E+08 2522 22144 4.96E+08

2541 9696 5.35E+08 2542 21600 4.97E+08 2542 21856 4.96E+08

2561 9536 5.35E+08 2562 21280 4.97E+08 2562 21568 4.96E+08

200

2581 9312 5.35E+08 2582 20992 4.98E+08 2582 21184 4.97E+08

2601 9184 5.35E+08 2602 20672 4.98E+08 2602 20928 4.97E+08

2621 9024 5.36E+08 2622 20416 4.99E+08 2622 20576 4.98E+08

2641 8832 5.36E+08 2642 20128 4.99E+08 2642 20320 4.98E+08

2661 8704 5.36E+08 2662 19808 4.99E+08 2662 20064 4.99E+08

2681 8544 5.36E+08 2682 19552 5E+08 2682 19776 4.99E+08

2701 8384 5.36E+08 2702 19264 5E+08 2702 19520 4.99E+08

2721 8224 5.36E+08 2722 18976 5.01E+08 2722 19232 5E+08

2741 8096 5.37E+08 2742 18752 5.01E+08 2742 19008 5E+08

2761 8000 5.37E+08 2762 18528 5.01E+08 2762 18752 5E+08

2781 7808 5.37E+08 2782 18272 5.02E+08 2782 18464 5.01E+08

2801 7680 5.37E+08 2802 18016 5.02E+08 2802 18240 5.01E+08

2821 7552 5.37E+08 2822 17792 5.02E+08 2822 17984 5.02E+08

2841 7424 5.37E+08 2842 17536 5.03E+08 2842 17728 5.02E+08

2861 7296 5.38E+08 2862 17280 5.03E+08 2862 17504 5.02E+08

2881 7168 5.38E+08 2882 17056 5.03E+08 2882 17280 5.03E+08

2901 7104 5.38E+08 2902 16800 5.04E+08 2902 17056 5.03E+08

2921 6912 5.38E+08 2922 16608 5.04E+08 2922 16800 5.03E+08

2941 6848 5.38E+08 2942 16416 5.04E+08 2942 16608 5.04E+08

2961 6784 5.38E+08 2962 16160 5.05E+08 2962 16352 5.04E+08

2981 6592 5.38E+08 2982 15968 5.05E+08 2982 16160 5.04E+08

3001 6592 5.38E+08 3002 15776 5.05E+08 3002 15936 5.05E+08

3021 6464 5.39E+08 3022 15520 5.06E+08 3022 15776 5.05E+08

3041 6336 5.39E+08 3042 15328 5.06E+08 3042 15520 5.05E+08

3061 6208 5.39E+08 3062 15168 5.06E+08 3062 15328 5.06E+08

3081 6144 5.39E+08 3082 14944 5.07E+08 3082 15136 5.06E+08

3101 6080 5.39E+08 3102 14784 5.07E+08 3102 14944 5.06E+08

3121 5952 5.39E+08 3122 14592 5.07E+08 3122 14784 5.06E+08

3141 5824 5.39E+08 3142 14400 5.08E+08 3142 14592 5.07E+08

3161 5760 5.39E+08 3162 14240 5.08E+08 3162 14400 5.07E+08

3181 5760 5.4E+08 3182 14048 5.08E+08 3182 14208 5.07E+08

3201 5632 5.4E+08 3202 13888 5.08E+08 3202 14048 5.08E+08

3221 5504 5.4E+08 3222 13728 5.09E+08 3222 13888 5.08E+08

3241 5440 5.4E+08 3242 13568 5.09E+08 3242 13728 5.08E+08

3261 5440 5.4E+08 3262 13376 5.09E+08 3262 13568 5.08E+08

3281 5312 5.4E+08 3282 13216 5.09E+08 3282 13408 5.09E+08

3301 5248 5.4E+08 3302 13088 5.1E+08 3302 13216 5.09E+08

3321 5120 5.4E+08 3322 12896 5.1E+08 3322 13056 5.09E+08

3341 5120 5.4E+08 3342 12736 5.1E+08 3342 12928 5.1E+08

3361 4928 5.41E+08 3362 12608 5.11E+08 3362 12800 5.1E+08

3381 4992 5.41E+08 3382 12448 5.11E+08 3382 12640 5.1E+08

201

3401 4864 5.41E+08 3402 12320 5.11E+08 3402 12480 5.1E+08

3421 4800 5.41E+08 3422 12192 5.11E+08 3422 12352 5.11E+08

3441 4736 5.41E+08 3442 12032 5.11E+08 3442 12192 5.11E+08

3461 4672 5.41E+08 3462 11904 5.12E+08 3462 12064 5.11E+08

3481 4544 5.41E+08 3482 11776 5.12E+08 3482 11904 5.11E+08

3501 4544 5.41E+08 3502 11648 5.12E+08 3502 11808 5.11E+08

3521 4480 5.41E+08 3522 11520 5.12E+08 3522 11648 5.12E+08

3541 4480 5.41E+08 3542 11360 5.13E+08 3542 11520 5.12E+08

3561 4352 5.41E+08 3562 11264 5.13E+08 3562 11392 5.12E+08

3581 4288 5.42E+08 3582 11104 5.13E+08 3582 11264 5.12E+08

3601 4288 5.42E+08 3602 11040 5.13E+08 3602 11136 5.13E+08

3621 4160 5.42E+08 3622 10912 5.14E+08 3622 11040 5.13E+08

3641 4160 5.42E+08 3642 10784 5.14E+08 3642 10912 5.13E+08

3661 4096 5.42E+08 3662 10624 5.14E+08 3662 10752 5.13E+08

3681 4032 5.42E+08 3682 10560 5.14E+08 3682 10688 5.14E+08

3701 3968 5.42E+08 3702 10432 5.14E+08 3702 10528 5.14E+08

3721 3968 5.42E+08 3722 10304 5.15E+08 3722 10464 5.14E+08

3741 3904 5.42E+08 3742 10208 5.15E+08 3742 10336 5.14E+08

3761 3840 5.42E+08 3762 10112 5.15E+08 3762 10240 5.14E+08

3781 3776 5.42E+08 3782 9984 5.15E+08 3782 10144 5.15E+08

3801 3776 5.42E+08 3802 9888 5.15E+08 3802 10016 5.15E+08

3821 3648 5.43E+08 3822 9760 5.16E+08 3822 9920 5.15E+08

3841 3648 5.43E+08 3842 9664 5.16E+08 3842 9824 5.15E+08

3861 3584 5.43E+08 3862 9568 5.16E+08 3862 9696 5.15E+08

3881 3520 5.43E+08 3882 9504 5.16E+08 3882 9632 5.16E+08

3901 3520 5.43E+08 3902 9408 5.16E+08 3902 9504 5.16E+08

3921 3520 5.43E+08 3922 9280 5.17E+08 3922 9440 5.16E+08

3941 3456 5.43E+08 3942 9216 5.17E+08 3942 9312 5.16E+08

3961 3392 5.43E+08 3962 9120 5.17E+08 3962 9216 5.16E+08

3981 3328 5.43E+08 3982 9056 5.17E+08 3982 9152 5.16E+08

4001 3328 5.43E+08 4002 8928 5.17E+08 4002 9088 5.17E+08

4021 3264 5.43E+08 4022 8864 5.17E+08 4022 8960 5.17E+08

4041 3264 5.43E+08 4042 8768 5.18E+08 4042 8864 5.17E+08

4061 3200 5.43E+08 4062 8640 5.18E+08 4062 8800 5.17E+08

4081 3200 5.43E+08 4082 8576 5.18E+08 4082 8704 5.17E+08

4101 3136 5.43E+08 4102 8512 5.18E+08 4102 8640 5.18E+08

4121 3136 5.44E+08 4122 8448 5.18E+08 4122 8544 5.18E+08

4141 3072 5.44E+08 4142 8352 5.19E+08 4142 8448 5.18E+08

4161 3008 5.44E+08 4162 8288 5.19E+08 4162 8352 5.18E+08

4181 3008 5.44E+08 4182 8192 5.19E+08 4182 8320 5.18E+08

4201 2944 5.44E+08 4202 8096 5.19E+08 4202 8224 5.18E+08

202

4221 2880 5.44E+08 4222 8064 5.19E+08 4222 8160 5.19E+08

4241 2816 5.44E+08 4242 7968 5.19E+08 4242 8064 5.19E+08

4261 2880 5.44E+08 4262 7904 5.19E+08 4262 7968 5.19E+08

4281 2880 5.44E+08 4282 7840 5.2E+08 4282 7904 5.19E+08

4301 2752 5.44E+08 4302 7744 5.2E+08 4302 7840 5.19E+08

4321 2752 5.44E+08 4322 7648 5.2E+08 4322 7776 5.19E+08

4341 2752 5.44E+08 4342 7616 5.2E+08 4342 7712 5.19E+08

4361 2752 5.44E+08 4362 7552 5.2E+08 4362 7616 5.2E+08

4381 2688 5.44E+08 4382 7456 5.2E+08 4382 7552 5.2E+08

4401 2688 5.44E+08 4402 7392 5.21E+08 4402 7488 5.2E+08

4421 2624 5.44E+08 4422 7328 5.21E+08 4422 7424 5.2E+08

4441 2624 5.44E+08 4442 7232 5.21E+08 4442 7392 5.2E+08

4461 2560 5.44E+08 4462 7232 5.21E+08 4462 7296 5.2E+08

4481 2560 5.45E+08 4482 7136 5.21E+08 4482 7232 5.21E+08

4501 2496 5.45E+08 4502 7040 5.21E+08 4502 7168 5.21E+08

4521 2496 5.45E+08 4522 7040 5.21E+08 4522 7104 5.21E+08

4541 2496 5.45E+08 4542 6912 5.22E+08 4542 7008 5.21E+08

4561 2432 5.45E+08 4562 6912 5.22E+08 4562 6976 5.21E+08

4581 2432 5.45E+08 4582 6816 5.22E+08 4582 6944 5.21E+08

4601 2368 5.45E+08 4602 6784 5.22E+08 4602 6880 5.21E+08

4621 2368 5.45E+08 4622 6688 5.22E+08 4622 6784 5.22E+08

4641 2368 5.45E+08 4642 6624 5.22E+08 4642 6720 5.22E+08

4661 2304 5.45E+08 4662 6592 5.22E+08 4662 6656 5.22E+08

4681 2304 5.45E+08 4682 6528 5.22E+08 4682 6656 5.22E+08

4701 2304 5.45E+08 4702 6464 5.23E+08 4702 6560 5.22E+08

4721 2240 5.45E+08 4722 6400 5.23E+08 4722 6496 5.22E+08

4741 2240 5.45E+08 4742 6368 5.23E+08 4742 6464 5.22E+08

4761 2176 5.45E+08 4762 6272 5.23E+08 4762 6368 5.22E+08

4781 2176 5.45E+08 4782 6272 5.23E+08 4782 6336 5.23E+08

4801 2112 5.45E+08 4802 6208 5.23E+08 4802 6304 5.23E+08

4821 2176 5.45E+08 4822 6144 5.23E+08 4822 6240 5.23E+08

4841 2112 5.45E+08 4842 6080 5.24E+08 4842 6240 5.23E+08

4861 2112 5.45E+08 4862 6048 5.24E+08 4862 6144 5.23E+08

4881 2112 5.45E+08 4882 6016 5.24E+08 4882 6112 5.23E+08

4901 2048 5.46E+08 4902 5920 5.24E+08 4902 6048 5.23E+08

4921 2048 5.46E+08 4922 5952 5.24E+08 4922 6016 5.23E+08

4941 1984 5.46E+08 4942 5888 5.24E+08 4942 5984 5.24E+08

4961 1984 5.46E+08 4962 5824 5.24E+08 4962 5888 5.24E+08

4981 1984 5.46E+08 4982 5760 5.24E+08 4982 5856 5.24E+08

5001 1984 5.46E+08 5002 5696 5.24E+08 5002 5792 5.24E+08

203


pi=10,000 psia, T=200F, SG=0.55



0.002 45921416 107616.2 0.002 40707580 94051.55 0.002 40547712 93709.81

0.039384 26404132 1211297 0.047853 23452676 1287547 0.048243 23364472 1292561

1.487214 17572952 28680544 2 15923256 34726516 2 15888996 34648408

11 14669408 1.76E+08 12 13687504 1.78E+08 12 13659408 1.78E+08

21 13924320 3.18E+08 22 12945824 3.11E+08 22 12910496 3.1E+08

41 13173696 5.88E+08 42 11839680 5.58E+08 42 11786944 5.56E+08

61 12621504 8.45E+08 62 10911680 7.84E+08 62 10849536 7.82E+08

81 12113280 1.09E+09 82 10113088 9.94E+08 82 10046336 9.9E+08

101 11627136 1.33E+09 102 9419008 1.19E+09 102 9349632 1.18E+09

121 11161216 1.56E+09 122 8809728 1.37E+09 122 8742016 1.36E+09

141 10715520 1.78E+09 142 8268800 1.54E+09 142 8201856 1.53E+09

161 10286976 1.99E+09 162 7785984 1.7E+09 162 7722112 1.69E+09

181 9878016 2.19E+09 182 7353600 1.85E+09 182 7291776 1.84E+09

201 9483776 2.38E+09 202 6959744 2E+09 202 6901504 1.98E+09

221 9105920 2.57E+09 222 6608896 2.13E+09 222 6554240 2.12E+09

241 8746496 2.74E+09 242 6286336 2.26E+09 242 6234112 2.25E+09

261 8401152 2.92E+09 262 5988608 2.38E+09 262 5938944 2.37E+09

281 8068352 3.08E+09 282 5718272 2.5E+09 282 5672960 2.48E+09

301 7751680 3.24E+09 302 5471232 2.61E+09 302 5427968 2.59E+09

321 7448576 3.39E+09 322 5240320 2.72E+09 322 5198848 2.7E+09

341 7156736 3.54E+09 342 5023488 2.82E+09 342 4984064 2.8E+09

361 6878208 3.68E+09 362 4822016 2.92E+09 362 4785664 2.9E+09

381 6614528 3.81E+09 382 4638720 3.01E+09 382 4605184 2.99E+09

401 6361344 3.94E+09 402 4467968 3.1E+09 402 4436224 3.08E+09

421 6117632 4.07E+09 422 4305664 3.19E+09 422 4275712 3.17E+09

441 5884928 4.18E+09 442 4151808 3.28E+09 442 4123392 3.25E+09

461 5664256 4.3E+09 462 4005632 3.36E+09 462 3979008 3.34E+09

481 5453312 4.41E+09 482 3868416 3.44E+09 482 3843328 3.41E+09

501 5250560 4.52E+09 502 3740416 3.51E+09 502 3717632 3.49E+09

521 5055488 4.62E+09 522 3622656 3.59E+09 522 3600896 3.56E+09

541 4868096 4.72E+09 542 3510528 3.66E+09 542 3490304 3.63E+09

561 4691456 4.82E+09 562 3403520 3.73E+09 562 3384064 3.7E+09

581 4524032 4.91E+09 582 3300352 3.79E+09 582 3282176 3.77E+09

601 4362240 5E+09 602 3201792 3.86E+09 602 3184640 3.83E+09

621 4207104 5.08E+09 622 3107584 3.92E+09 622 3091200 3.9E+09

641 4057088 5.16E+09 642 3016960 3.98E+09 642 3001856 3.96E+09

661 3912704 5.24E+09 662 2930688 4.04E+09 662 2916608 4.02E+09

204

681 3776000 5.32E+09 682 2848768 4.1E+09 682 2835712 4.07E+09

701 3647488 5.4E+09 702 2771968 4.16E+09 702 2759424 4.13E+09

721 3523584 5.47E+09 722 2700032 4.21E+09 722 2688512 4.18E+09

741 3404800 5.54E+09 742 2631168 4.26E+09 742 2620672 4.24E+09

761 3289600 5.6E+09 762 2565120 4.32E+09 762 2555136 4.29E+09

781 3179008 5.67E+09 782 2501120 4.37E+09 782 2491904 4.34E+09

801 3072512 5.73E+09 802 2439168 4.42E+09 802 2430464 4.39E+09

821 2970112 5.79E+09 822 2379264 4.46E+09 822 2371584 4.44E+09

841 2870784 5.85E+09 842 2321920 4.51E+09 842 2314240 4.48E+09

861 2777600 5.91E+09 862 2265088 4.56E+09 862 2258944 4.53E+09

881 2689536 5.96E+09 882 2211840 4.6E+09 882 2204672 4.57E+09

901 2605056 6.01E+09 902 2159104 4.64E+09 902 2153472 4.62E+09

921 2523648 6.06E+09 922 2108928 4.69E+09 922 2103296 4.66E+09

941 2445312 6.11E+09 942 2060288 4.73E+09 942 2055168 4.7E+09

961 2369024 6.16E+09 962 2013184 4.77E+09 962 2008064 4.74E+09

981 2295296 6.21E+09 982 1967616 4.81E+09 982 1963520 4.78E+09

1001 2224640 6.25E+09 1002 1925120 4.85E+09 1002 1920512 4.82E+09

1021 2156032 6.3E+09 1022 1883648 4.89E+09 1022 1880064 4.86E+09

1041 2089472 6.34E+09 1042 1844224 4.92E+09 1042 1840640 4.89E+09

1061 2025984 6.38E+09 1062 1806848 4.96E+09 1062 1803776 4.93E+09

1081 1965056 6.42E+09 1082 1769984 5E+09 1082 1767424 4.97E+09

1101 1906176 6.46E+09 1102 1734656 5.03E+09 1102 1733120 5E+09

1121 1850880 6.5E+09 1122 1700864 5.07E+09 1122 1698304 5.04E+09

1141 1798656 6.53E+09 1142 1667072 5.1E+09 1142 1666048 5.07E+09

1161 1747968 6.57E+09 1162 1634816 5.13E+09 1162 1633280 5.1E+09

1181 1698304 6.6E+09 1182 1602560 5.16E+09 1182 1601536 5.14E+09

1201 1650688 6.64E+09 1202 1571840 5.2E+09 1202 1570816 5.17E+09

1221 1604608 6.67E+09 1222 1541632 5.23E+09 1222 1541120 5.2E+09

1241 1560064 6.7E+09 1242 1511936 5.26E+09 1242 1511936 5.23E+09

1261 1517056 6.73E+09 1262 1483776 5.29E+09 1262 1483776 5.26E+09

1281 1475584 6.76E+09 1282 1456128 5.32E+09 1282 1456128 5.29E+09

1301 1433600 6.79E+09 1302 1428992 5.35E+09 1302 1428992 5.32E+09

1321 1395200 6.82E+09 1322 1402880 5.37E+09 1322 1402880 5.34E+09

1341 1357312 6.85E+09 1342 1376768 5.4E+09 1342 1377792 5.37E+09

1361 1320448 6.87E+09 1362 1352192 5.43E+09 1362 1352192 5.4E+09

1381 1285120 6.9E+09 1382 1327104 5.46E+09 1382 1328128 5.43E+09

1401 1250816 6.92E+09 1402 1303552 5.48E+09 1402 1304064 5.45E+09

1421 1217536 6.95E+09 1422 1280512 5.51E+09 1422 1281536 5.48E+09

1441 1185792 6.97E+09 1442 1257984 5.53E+09 1442 1259008 5.5E+09

1461 1153536 7E+09 1462 1235968 5.56E+09 1462 1236992 5.53E+09

1481 1123840 7.02E+09 1482 1214976 5.58E+09 1482 1216000 5.55E+09

205

1501 1095168 7.04E+09 1502 1193984 5.61E+09 1502 1195008 5.58E+09

1521 1068544 7.06E+09 1522 1174016 5.63E+09 1522 1174528 5.6E+09

1541 1041920 7.08E+09 1542 1153536 5.65E+09 1542 1155584 5.62E+09

1561 1016832 7.1E+09 1562 1134592 5.68E+09 1562 1136640 5.65E+09

1581 991232 7.12E+09 1582 1116160 5.7E+09 1582 1117696 5.67E+09

1601 967680 7.14E+09 1602 1097728 5.72E+09 1602 1100288 5.69E+09

1621 944128 7.16E+09 1622 1080832 5.74E+09 1622 1082880 5.71E+09

1641 921600 7.18E+09 1642 1064448 5.76E+09 1642 1065472 5.74E+09

1661 899584 7.2E+09 1662 1047040 5.79E+09 1662 1049600 5.76E+09

1681 878080 7.22E+09 1682 1031168 5.81E+09 1682 1033216 5.78E+09

1701 857600 7.24E+09 1702 1015296 5.83E+09 1702 1017344 5.8E+09

1721 837120 7.25E+09 1722 999936 5.85E+09 1722 1002496 5.82E+09

1741 818176 7.27E+09 1742 984576 5.87E+09 1742 987136 5.84E+09

1761 799232 7.29E+09 1762 970240 5.89E+09 1762 972288 5.86E+09

1781 780288 7.3E+09 1782 955904 5.91E+09 1782 958464 5.88E+09

1801 761856 7.32E+09 1802 941568 5.93E+09 1802 944128 5.9E+09

1821 744960 7.33E+09 1822 928256 5.94E+09 1822 930816 5.91E+09

1841 727552 7.35E+09 1842 914432 5.96E+09 1842 916992 5.93E+09

1861 711168 7.36E+09 1862 901120 5.98E+09 1862 904192 5.95E+09

1881 695296 7.37E+09 1882 887808 6E+09 1882 891392 5.97E+09

1901 679936 7.39E+09 1902 875520 6.02E+09 1902 878080 5.99E+09

1921 665088 7.4E+09 1922 862720 6.03E+09 1922 865792 6E+09

1941 649728 7.42E+09 1942 850944 6.05E+09 1942 852992 6.02E+09

1961 636416 7.43E+09 1962 838144 6.07E+09 1962 841216 6.04E+09

1981 622080 7.44E+09 1982 826368 6.08E+09 1982 829952 6.06E+09

2001 608768 7.45E+09 2002 815616 6.1E+09 2002 818176 6.07E+09

2021 595456 7.46E+09 2022 803840 6.12E+09 2022 806912 6.09E+09

2041 582144 7.48E+09 2042 793088 6.13E+09 2042 796160 6.1E+09

2061 569856 7.49E+09 2062 781824 6.15E+09 2062 785408 6.12E+09

2081 558592 7.5E+09 2082 771072 6.16E+09 2082 774656 6.14E+09

2101 546304 7.51E+09 2102 760832 6.18E+09 2102 764416 6.15E+09

2121 535040 7.52E+09 2122 750080 6.19E+09 2122 753664 6.17E+09

2141 523776 7.53E+09 2142 740352 6.21E+09 2142 743936 6.18E+09

2161 513024 7.54E+09 2162 730624 6.22E+09 2162 734208 6.2E+09

2181 502784 7.55E+09 2182 720896 6.24E+09 2182 724480 6.21E+09

2201 492032 7.56E+09 2202 712192 6.25E+09 2202 714752 6.22E+09

2221 482304 7.57E+09 2222 702464 6.27E+09 2222 705024 6.24E+09

2241 472576 7.58E+09 2242 693248 6.28E+09 2242 696320 6.25E+09

2261 463360 7.59E+09 2262 684032 6.29E+09 2262 687616 6.27E+09

2281 454144 7.6E+09 2282 675328 6.31E+09 2282 678912 6.28E+09

2301 444928 7.61E+09 2302 666624 6.32E+09 2302 670208 6.29E+09

206

2321 436736 7.62E+09 2322 657920 6.33E+09 2322 661504 6.31E+09

2341 428032 7.63E+09 2342 650240 6.35E+09 2342 653312 6.32E+09

2361 419840 7.63E+09 2362 642048 6.36E+09 2362 644608 6.33E+09

2381 411648 7.64E+09 2382 633344 6.37E+09 2382 636928 6.35E+09

2401 403968 7.65E+09 2402 625664 6.39E+09 2402 629248 6.36E+09

2421 396288 7.66E+09 2422 618496 6.4E+09 2422 621056 6.37E+09

2441 388608 7.67E+09 2442 609792 6.41E+09 2442 613376 6.38E+09

2461 381952 7.67E+09 2462 602624 6.42E+09 2462 605696 6.4E+09

2481 374272 7.68E+09 2482 595456 6.43E+09 2482 599040 6.41E+09

2501 368128 7.69E+09 2502 588288 6.45E+09 2502 591872 6.42E+09

2521 360960 7.7E+09 2522 580608 6.46E+09 2522 584704 6.43E+09

2541 354304 7.7E+09 2542 573952 6.47E+09 2542 577536 6.44E+09

2561 348160 7.71E+09 2562 567296 6.48E+09 2562 570368 6.45E+09

2581 342016 7.72E+09 2582 560640 6.49E+09 2582 563200 6.47E+09

2601 335872 7.73E+09 2602 553472 6.5E+09 2602 557056 6.48E+09

2621 329728 7.73E+09 2622 547328 6.51E+09 2622 550912 6.49E+09

2641 324096 7.74E+09 2642 540672 6.53E+09 2642 543744 6.5E+09

2661 317952 7.74E+09 2662 534528 6.54E+09 2662 537600 6.51E+09

2681 312320 7.75E+09 2682 527872 6.55E+09 2682 531456 6.52E+09

2701 306688 7.76E+09 2702 522240 6.56E+09 2702 525312 6.53E+09

2721 302080 7.76E+09 2722 516096 6.57E+09 2722 519168 6.54E+09

2741 296960 7.77E+09 2742 510976 6.58E+09 2742 513536 6.55E+09

2761 291328 7.78E+09 2762 504832 6.59E+09 2762 508416 6.56E+09

2781 286720 7.78E+09 2782 498688 6.6E+09 2782 502272 6.57E+09

2801 281600 7.79E+09 2802 493568 6.61E+09 2802 496640 6.58E+09

2821 276992 7.79E+09 2822 487936 6.62E+09 2822 491008 6.59E+09

2841 271360 7.8E+09 2842 482304 6.63E+09 2842 485888 6.6E+09

2861 267776 7.8E+09 2862 477184 6.64E+09 2862 480768 6.61E+09

2881 263168 7.81E+09 2882 472064 6.65E+09 2882 475648 6.62E+09

2901 259072 7.81E+09 2902 467456 6.66E+09 2902 470016 6.63E+09

2921 254976 7.82E+09 2922 461824 6.67E+09 2922 465408 6.64E+09

2941 250368 7.82E+09 2942 457216 6.67E+09 2942 459776 6.65E+09

2961 246784 7.83E+09 2962 451584 6.68E+09 2962 455168 6.66E+09

2981 242176 7.83E+09 2982 446464 6.69E+09 2982 450560 6.67E+09

3001 238080 7.84E+09 3002 442368 6.7E+09 3002 445440 6.68E+09

3021 234496 7.84E+09 3022 437760 6.71E+09 3022 441344 6.69E+09

3041 231424 7.85E+09 3042 433664 6.72E+09 3042 436736 6.69E+09

3061 227328 7.85E+09 3062 429056 6.73E+09 3062 431616 6.7E+09

3081 223744 7.86E+09 3082 424448 6.74E+09 3082 428032 6.71E+09

3101 220160 7.86E+09 3102 419840 6.74E+09 3102 423424 6.72E+09

3121 217088 7.87E+09 3122 415232 6.75E+09 3122 419328 6.73E+09

207

3141 212992 7.87E+09 3142 411136 6.76E+09 3142 414720 6.74E+09

3161 209920 7.87E+09 3162 407040 6.77E+09 3162 410112 6.74E+09

3181 206848 7.88E+09 3182 402944 6.78E+09 3182 406528 6.75E+09

3201 203264 7.88E+09 3202 398848 6.79E+09 3202 402432 6.76E+09

3221 200192 7.89E+09 3222 395264 6.79E+09 3222 398336 6.77E+09

3241 197632 7.89E+09 3242 391168 6.8E+09 3242 394240 6.78E+09

3261 194048 7.89E+09 3262 387072 6.81E+09 3262 389632 6.78E+09

3281 192512 7.9E+09 3282 382976 6.82E+09 3282 386560 6.79E+09

3301 188416 7.9E+09 3302 378880 6.82E+09 3302 382464 6.8E+09

3321 186880 7.91E+09 3322 375808 6.83E+09 3322 378880 6.81E+09

3341 183296 7.91E+09 3342 372224 6.84E+09 3342 375296 6.82E+09

3361 180736 7.91E+09 3362 368128 6.85E+09 3362 371200 6.82E+09

3381 177664 7.92E+09 3382 364544 6.85E+09 3382 367616 6.83E+09

3401 175616 7.92E+09 3402 360960 6.86E+09 3402 364032 6.84E+09

3421 173056 7.92E+09 3422 357376 6.87E+09 3422 360960 6.84E+09

3441 169984 7.93E+09 3442 354816 6.88E+09 3442 357376 6.85E+09

3461 167936 7.93E+09 3462 351232 6.88E+09 3462 354304 6.86E+09

3481 165376 7.93E+09 3482 347648 6.89E+09 3482 350720 6.87E+09

3501 163328 7.94E+09 3502 344576 6.9E+09 3502 347136 6.87E+09

3521 160768 7.94E+09 3522 340480 6.9E+09 3522 344064 6.88E+09

3541 158720 7.94E+09 3542 337920 6.91E+09 3542 340992 6.89E+09

3561 156672 7.95E+09 3562 334336 6.92E+09 3562 337920 6.89E+09

3581 155136 7.95E+09 3582 331264 6.92E+09 3582 334848 6.9E+09

3601 152064 7.95E+09 3602 328704 6.93E+09 3602 331264 6.91E+09

3621 150016 7.96E+09 3622 325632 6.94E+09 3622 328704 6.91E+09

3641 147968 7.96E+09 3642 322560 6.94E+09 3642 325632 6.92E+09

3661 146432 7.96E+09 3662 320000 6.95E+09 3662 322048 6.93E+09

3681 144384 7.96E+09 3682 316928 6.96E+09 3682 318976 6.93E+09

3701 141824 7.97E+09 3702 313856 6.96E+09 3702 316416 6.94E+09

3721 140800 7.97E+09 3722 310784 6.97E+09 3722 314368 6.95E+09

3741 138240 7.97E+09 3742 308224 6.97E+09 3742 310784 6.95E+09

3761 136192 7.98E+09 3762 305664 6.98E+09 3762 307712 6.96E+09

3781 134144 7.98E+09 3782 302592 6.99E+09 3782 305152 6.96E+09

3801 133120 7.98E+09 3802 300032 6.99E+09 3802 303104 6.97E+09

3821 131072 7.98E+09 3822 296960 7E+09 3822 300032 6.98E+09

3841 129536 7.99E+09 3842 294912 7.01E+09 3842 297472 6.98E+09

3861 128000 7.99E+09 3862 292352 7.01E+09 3862 294912 6.99E+09

3881 125952 7.99E+09 3882 289792 7.02E+09 3882 292352 6.99E+09

3901 124416 7.99E+09 3902 287232 7.02E+09 3902 289280 7E+09

3921 122880 8E+09 3922 284160 7.03E+09 3922 287232 7.01E+09

3941 120832 8E+09 3942 282112 7.03E+09 3942 284672 7.01E+09

208

3961 119808 8E+09 3962 279552 7.04E+09 3962 282624 7.02E+09

3981 118272 8E+09 3982 276480 7.04E+09 3982 279552 7.02E+09

4001 116736 8.01E+09 4002 274944 7.05E+09 4002 277504 7.03E+09

4021 115200 8.01E+09 4022 272384 7.06E+09 4022 274432 7.03E+09

4041 113664 8.01E+09 4042 269824 7.06E+09 4042 272896 7.04E+09

4061 112640 8.01E+09 4062 267776 7.07E+09 4062 270336 7.04E+09

4081 110592 8.02E+09 4082 265728 7.07E+09 4082 267776 7.05E+09

4101 109568 8.02E+09 4102 263168 7.08E+09 4102 265728 7.06E+09

4121 108032 8.02E+09 4122 261120 7.08E+09 4122 263680 7.06E+09

4141 106496 8.02E+09 4142 259072 7.09E+09 4142 261632 7.07E+09

4161 105472 8.02E+09 4162 256512 7.09E+09 4162 259584 7.07E+09

4181 103936 8.03E+09 4182 253952 7.1E+09 4182 257024 7.08E+09

4201 102400 8.03E+09 4202 251904 7.1E+09 4202 254464 7.08E+09

4221 101376 8.03E+09 4222 250368 7.11E+09 4222 253440 7.09E+09

4241 99840 8.03E+09 4242 248832 7.11E+09 4242 250880 7.09E+09

4261 98816 8.03E+09 4262 246272 7.12E+09 4262 249344 7.1E+09

4281 97280 8.04E+09 4282 244736 7.12E+09 4282 246784 7.1E+09

4301 96256 8.04E+09 4302 242176 7.13E+09 4302 244736 7.11E+09

4321 95232 8.04E+09 4322 240640 7.13E+09 4322 242176 7.11E+09

4341 94208 8.04E+09 4342 238080 7.14E+09 4342 240640 7.12E+09

4361 93184 8.04E+09 4362 236544 7.14E+09 4362 239104 7.12E+09

4381 92160 8.05E+09 4382 234496 7.15E+09 4382 236544 7.13E+09

4401 90112 8.05E+09 4402 232448 7.15E+09 4402 235520 7.13E+09

4421 90112 8.05E+09 4422 230912 7.16E+09 4422 233472 7.14E+09

4441 88576 8.05E+09 4442 228864 7.16E+09 4442 231424 7.14E+09

4461 88064 8.05E+09 4462 227328 7.17E+09 4462 229376 7.14E+09

4481 86528 8.05E+09 4482 225792 7.17E+09 4482 227840 7.15E+09

4501 85504 8.06E+09 4502 223232 7.17E+09 4502 226304 7.15E+09

4521 84480 8.06E+09 4522 221696 7.18E+09 4522 224256 7.16E+09

4541 82944 8.06E+09 4542 220160 7.18E+09 4542 222720 7.16E+09

4561 81920 8.06E+09 4562 218624 7.19E+09 4562 220672 7.17E+09

4581 81408 8.06E+09 4582 217088 7.19E+09 4582 219136 7.17E+09

4601 80384 8.06E+09 4602 215040 7.2E+09 4602 217600 7.18E+09

4621 79360 8.07E+09 4622 214016 7.2E+09 4622 215552 7.18E+09

4641 78336 8.07E+09 4642 211456 7.2E+09 4642 214528 7.18E+09

4661 77824 8.07E+09 4662 209920 7.21E+09 4662 212480 7.19E+09

4681 77312 8.07E+09 4682 208384 7.21E+09 4682 211456 7.19E+09

4701 76288 8.07E+09 4702 207360 7.22E+09 4702 208896 7.2E+09

4721 75264 8.07E+09 4722 205312 7.22E+09 4722 207872 7.2E+09

4741 74752 8.08E+09 4742 203776 7.23E+09 4742 206336 7.21E+09

4761 73216 8.08E+09 4762 202240 7.23E+09 4762 204288 7.21E+09

209

4781 72704 8.08E+09 4782 201216 7.23E+09 4782 203264 7.21E+09

4801 71680 8.08E+09 4802 199168 7.24E+09 4802 201728 7.22E+09

4821 71168 8.08E+09 4822 197632 7.24E+09 4822 200192 7.22E+09

4841 70144 8.08E+09 4842 196608 7.25E+09 4842 198144 7.23E+09

4861 69632 8.08E+09 4862 195072 7.25E+09 4862 197632 7.23E+09

4881 68608 8.09E+09 4882 193536 7.25E+09 4882 195072 7.23E+09

4901 68096 8.09E+09 4902 192000 7.26E+09 4902 194560 7.24E+09

4921 66560 8.09E+09 4922 190976 7.26E+09 4922 193024 7.24E+09

4941 66048 8.09E+09 4942 189440 7.26E+09 4942 191488 7.25E+09

4961 65536 8.09E+09 4962 187392 7.27E+09 4962 189952 7.25E+09

4981 65024 8.09E+09 4982 186880 7.27E+09 4982 188928 7.25E+09

5001 64512 8.09E+09 5002 185344 7.28E+09 5002 187392 7.26E+09


pi=10,000 psia, T=200F, SG=0.55



0.01875 4705882 99308.46 0.0375 3842075 159826.6 0.0375 3831127 159403.2

0.548103 2779742 1716345 1.5 2334780 3870570 1.5 2330337 3862966

8 2100512 18506752 11 1931056 23260182 11 1928052 23220610

18 1952340 38578476 21 1828240 41940644 21 1825484 41872552

28 1880780 57678348 31 1772112 59892948 31 1769524 59798348

48 1800608 94368264 51 1705696 94574320 51 1703272 94429928

68 1752672 1.3E+08 71 1664232 1.28E+08 71 1661896 1.28E+08

88 1718912 1.65E+08 91 1634224 1.61E+08 91 1631920 1.61E+08

108 1692880 1.99E+08 111 1610336 1.94E+08 111 1607984 1.93E+08

128 1671904 2.32E+08 131 1589968 2.26E+08 131 1587536 2.25E+08

148 1654368 2.66E+08 151 1571760 2.57E+08 151 1569184 2.57E+08

168 1639264 2.98E+08 171 1554880 2.88E+08 171 1552128 2.88E+08

188 1625952 3.31E+08 191 1538848 3.19E+08 191 1535936 3.19E+08

208 1614016 3.63E+08 211 1523520 3.5E+08 211 1520320 3.49E+08

228 1603040 3.96E+08 231 1508544 3.8E+08 231 1505184 3.8E+08

248 1592832 4.28E+08 251 1493984 4.1E+08 251 1490464 4.1E+08

268 1583232 4.59E+08 271 1479744 4.4E+08 271 1476032 4.39E+08

288 1574080 4.91E+08 291 1465888 4.7E+08 291 1462016 4.69E+08

308 1565312 5.22E+08 311 1452352 4.99E+08 311 1448288 4.98E+08

328 1556736 5.54E+08 331 1439040 5.28E+08 331 1434816 5.27E+08

348 1548480 5.85E+08 351 1425920 5.56E+08 351 1421568 5.55E+08

368 1540416 6.15E+08 371 1412992 5.85E+08 371 1408512 5.83E+08

388 1532416 6.46E+08 391 1400384 6.13E+08 391 1395648 6.11E+08

408 1524544 6.77E+08 411 1387904 6.41E+08 411 1383040 6.39E+08

210

428 1516800 7.07E+08 431 1375616 6.68E+08 431 1370624 6.67E+08

448 1509120 7.37E+08 451 1363456 6.96E+08 451 1358464 6.94E+08

468 1501504 7.67E+08 471 1351552 7.23E+08 471 1346496 7.21E+08

488 1493952 7.97E+08 491 1339840 7.5E+08 491 1334720 7.48E+08

508 1486464 8.27E+08 511 1328512 7.76E+08 511 1323136 7.74E+08

528 1478976 8.57E+08 531 1317248 8.03E+08 531 1311936 8.01E+08

548 1471616 8.86E+08 551 1306176 8.29E+08 551 1300672 8.27E+08

568 1464320 9.16E+08 571 1295296 8.55E+08 571 1289792 8.53E+08

588 1457088 9.45E+08 591 1284480 8.81E+08 591 1278848 8.79E+08

608 1449920 9.74E+08 611 1273920 9.06E+08 611 1268224 9.04E+08

628 1442688 1E+09 631 1263488 9.32E+08 631 1257792 9.29E+08

648 1435520 1.03E+09 651 1253120 9.57E+08 651 1247360 9.54E+08

668 1428416 1.06E+09 671 1242944 9.82E+08 671 1237184 9.79E+08

688 1421312 1.09E+09 691 1232896 1.01E+09 691 1227008 1E+09

708 1414272 1.12E+09 711 1223104 1.03E+09 711 1217216 1.03E+09

728 1407360 1.15E+09 731 1213312 1.06E+09 731 1207424 1.05E+09

748 1400320 1.17E+09 751 1203840 1.08E+09 751 1197952 1.08E+09

768 1393408 1.2E+09 771 1194496 1.1E+09 771 1188480 1.1E+09

788 1386368 1.23E+09 791 1185280 1.13E+09 791 1179392 1.12E+09

808 1379712 1.26E+09 811 1176192 1.15E+09 811 1170304 1.15E+09

828 1372672 1.28E+09 831 1167232 1.17E+09 831 1161344 1.17E+09

848 1366016 1.31E+09 851 1158528 1.2E+09 851 1152512 1.19E+09

868 1359232 1.34E+09 871 1149696 1.22E+09 871 1143680 1.22E+09

888 1352576 1.37E+09 891 1141248 1.24E+09 891 1135232 1.24E+09

908 1345792 1.39E+09 911 1132672 1.27E+09 911 1126784 1.26E+09

928 1339264 1.42E+09 931 1124352 1.29E+09 931 1118080 1.28E+09

948 1332608 1.45E+09 951 1115904 1.31E+09 951 1110016 1.31E+09

968 1325952 1.47E+09 971 1107968 1.33E+09 971 1101568 1.33E+09

988 1319552 1.5E+09 991 1099904 1.36E+09 991 1093632 1.35E+09

1008 1313024 1.53E+09 1011 1091968 1.38E+09 1011 1085696 1.37E+09

1028 1306752 1.55E+09 1031 1084032 1.4E+09 1031 1077888 1.39E+09

1048 1300224 1.58E+09 1051 1076224 1.42E+09 1051 1070208 1.42E+09

1068 1293952 1.6E+09 1071 1068544 1.44E+09 1071 1062656 1.44E+09

1088 1287424 1.63E+09 1091 1061248 1.46E+09 1091 1055360 1.46E+09

1108 1281152 1.66E+09 1111 1053952 1.48E+09 1111 1047936 1.48E+09

1128 1275008 1.68E+09 1131 1046784 1.51E+09 1131 1040640 1.5E+09

1148 1268608 1.71E+09 1151 1039616 1.53E+09 1151 1033472 1.52E+09

1168 1262336 1.73E+09 1171 1032448 1.55E+09 1171 1026560 1.54E+09

1188 1256320 1.76E+09 1191 1025408 1.57E+09 1191 1019648 1.56E+09

1208 1250048 1.78E+09 1211 1018368 1.59E+09 1211 1012480 1.58E+09

1228 1243904 1.81E+09 1231 1011712 1.61E+09 1231 1005824 1.6E+09

211

1248 1237760 1.83E+09 1251 1004800 1.63E+09 1251 998912 1.62E+09

1268 1231744 1.86E+09 1271 998144 1.65E+09 1271 992384 1.64E+09

1288 1225728 1.88E+09 1291 991744 1.67E+09 1291 985728 1.66E+09

1308 1219712 1.91E+09 1311 985088 1.69E+09 1311 979200 1.68E+09

1328 1213696 1.93E+09 1331 978560 1.71E+09 1331 972544 1.7E+09

1348 1207936 1.95E+09 1351 972160 1.73E+09 1351 966272 1.72E+09

1368 1202048 1.98E+09 1371 965760 1.75E+09 1371 959872 1.74E+09

1388 1196160 2E+09 1391 959488 1.77E+09 1391 953600 1.76E+09

1408 1190272 2.03E+09 1411 953216 1.79E+09 1411 947456 1.78E+09

1428 1184512 2.05E+09 1431 947072 1.8E+09 1431 941440 1.8E+09

1448 1178752 2.07E+09 1451 941184 1.82E+09 1451 935552 1.82E+09

1468 1172992 2.1E+09 1471 935296 1.84E+09 1471 929664 1.83E+09

1488 1167360 2.12E+09 1491 929536 1.86E+09 1491 923776 1.85E+09

1508 1161600 2.14E+09 1511 923904 1.88E+09 1511 918272 1.87E+09

1528 1156096 2.17E+09 1531 918016 1.9E+09 1531 912640 1.89E+09

1548 1150720 2.19E+09 1551 912384 1.92E+09 1551 907008 1.91E+09

1568 1145088 2.21E+09 1571 906880 1.93E+09 1571 901376 1.93E+09

1588 1139456 2.24E+09 1591 901376 1.95E+09 1591 895872 1.94E+09

1608 1134080 2.26E+09 1611 896000 1.97E+09 1611 890496 1.96E+09

1628 1128448 2.28E+09 1631 890624 1.99E+09 1631 885120 1.98E+09

1648 1123072 2.3E+09 1651 885248 2.01E+09 1651 879872 2E+09

1668 1117440 2.33E+09 1671 879872 2.02E+09 1671 874624 2.01E+09

1688 1112320 2.35E+09 1691 874752 2.04E+09 1691 869376 2.03E+09

1708 1107200 2.37E+09 1711 869632 2.06E+09 1711 864128 2.05E+09

1728 1101568 2.39E+09 1731 864512 2.08E+09 1731 859008 2.07E+09

1748 1096448 2.41E+09 1751 859264 2.09E+09 1751 853888 2.08E+09

1768 1090816 2.44E+09 1771 854272 2.11E+09 1771 848768 2.1E+09

1788 1085696 2.46E+09 1791 849152 2.13E+09 1791 843776 2.12E+09

1808 1080576 2.48E+09 1811 844288 2.14E+09 1811 838912 2.13E+09

1828 1075712 2.5E+09 1831 839424 2.16E+09 1831 834048 2.15E+09

1848 1070080 2.52E+09 1851 834304 2.18E+09 1851 829440 2.17E+09

1868 1065472 2.54E+09 1871 829696 2.19E+09 1871 824576 2.18E+09

1888 1060096 2.57E+09 1891 825088 2.21E+09 1891 819712 2.2E+09

1908 1054976 2.59E+09 1911 820224 2.23E+09 1911 815104 2.22E+09

1928 1050112 2.61E+09 1931 815616 2.24E+09 1931 810752 2.23E+09

1948 1045248 2.63E+09 1951 811008 2.26E+09 1951 806144 2.25E+09

1968 1040384 2.65E+09 1971 806656 2.28E+09 1971 801536 2.27E+09

1988 1035264 2.67E+09 1991 802048 2.29E+09 1991 797440 2.28E+09

2008 1030400 2.69E+09 2011 797696 2.31E+09 2011 792832 2.3E+09

2028 1025536 2.71E+09 2031 793344 2.32E+09 2031 788480 2.31E+09

2048 1020928 2.73E+09 2051 788992 2.34E+09 2051 784384 2.33E+09

212

2068 1016064 2.75E+09 2071 784896 2.36E+09 2071 780032 2.35E+09

2088 1011200 2.77E+09 2091 780544 2.37E+09 2091 775936 2.36E+09

2108 1006336 2.79E+09 2111 776448 2.39E+09 2111 771584 2.38E+09

2128 1001728 2.81E+09 2131 772608 2.4E+09 2131 767232 2.39E+09

2148 996864 2.83E+09 2151 768000 2.42E+09 2151 763392 2.41E+09

2168 992256 2.85E+09 2171 764160 2.43E+09 2171 759296 2.42E+09

2188 987392 2.87E+09 2191 760064 2.45E+09 2191 755200 2.44E+09

2208 982784 2.89E+09 2211 755968 2.46E+09 2211 751360 2.45E+09

2228 978432 2.91E+09 2231 752128 2.48E+09 2231 747520 2.47E+09

2248 973568 2.93E+09 2251 747776 2.49E+09 2251 743168 2.48E+09

2268 969216 2.95E+09 2271 744192 2.51E+09 2271 739840 2.5E+09

2288 964096 2.97E+09 2291 740352 2.52E+09 2291 735744 2.51E+09

2308 959744 2.99E+09 2311 736512 2.54E+09 2311 731648 2.53E+09

2328 955136 3.01E+09 2331 732416 2.55E+09 2331 727808 2.54E+09

2348 950784 3.03E+09 2351 728576 2.57E+09 2351 724480 2.56E+09

2368 946176 3.05E+09 2371 724992 2.58E+09 2371 720384 2.57E+09

2388 941824 3.07E+09 2391 721408 2.6E+09 2391 716800 2.58E+09

2408 937472 3.08E+09 2411 717568 2.61E+09 2411 713216 2.6E+09

2428 933120 3.1E+09 2431 713472 2.63E+09 2431 709376 2.61E+09

2448 929024 3.12E+09 2451 709888 2.64E+09 2451 705536 2.63E+09

2468 924672 3.14E+09 2471 706560 2.65E+09 2471 702208 2.64E+09

2488 920320 3.16E+09 2491 702976 2.67E+09 2491 698624 2.66E+09

2508 915968 3.18E+09 2511 699136 2.68E+09 2511 695296 2.67E+09

2528 911872 3.2E+09 2531 695808 2.7E+09 2531 691712 2.68E+09

2548 907776 3.21E+09 2551 692224 2.71E+09 2551 688384 2.7E+09

2568 903424 3.23E+09 2571 689152 2.72E+09 2571 684544 2.71E+09

2588 899328 3.25E+09 2591 685312 2.74E+09 2591 681472 2.72E+09

2608 895232 3.27E+09 2611 681984 2.75E+09 2611 678144 2.74E+09

2628 891136 3.29E+09 2631 678912 2.76E+09 2631 674816 2.75E+09

2648 887040 3.3E+09 2651 675584 2.78E+09 2651 671744 2.76E+09

2668 882944 3.32E+09 2671 672256 2.79E+09 2671 668416 2.78E+09

2688 878848 3.34E+09 2691 669184 2.8E+09 2691 665344 2.79E+09

2708 874752 3.36E+09 2711 666112 2.82E+09 2711 662016 2.8E+09

2728 870912 3.37E+09 2731 663040 2.83E+09 2731 658688 2.82E+09

2748 867072 3.39E+09 2751 659712 2.84E+09 2751 656128 2.83E+09

2768 862720 3.41E+09 2771 656384 2.86E+09 2771 652544 2.84E+09

2788 858880 3.43E+09 2791 653568 2.87E+09 2791 649472 2.86E+09

2808 855296 3.44E+09 2811 650496 2.88E+09 2811 646656 2.87E+09

2828 850944 3.46E+09 2831 647680 2.9E+09 2831 643584 2.88E+09

2848 847104 3.48E+09 2851 644352 2.91E+09 2851 640512 2.9E+09

2868 843264 3.49E+09 2871 641536 2.92E+09 2871 637440 2.91E+09

213

2888 839424 3.51E+09 2891 638464 2.94E+09 2891 634880 2.92E+09

2908 835584 3.53E+09 2911 635136 2.95E+09 2911 632064 2.93E+09

2928 831744 3.54E+09 2931 632576 2.96E+09 2931 629248 2.95E+09

2948 828160 3.56E+09 2951 629760 2.97E+09 2951 626176 2.96E+09

2968 824064 3.58E+09 2971 626688 2.99E+09 2971 623360 2.97E+09

2988 820480 3.59E+09 2991 624128 3E+09 2991 620544 2.98E+09

3008 817152 3.61E+09 3011 621056 3.01E+09 3011 617472 3E+09

3028 813056 3.63E+09 3031 618496 3.02E+09 3031 614656 3.01E+09

3048 809472 3.64E+09 3051 615424 3.04E+09 3051 611840 3.02E+09

3068 805888 3.66E+09 3071 612864 3.05E+09 3071 609024 3.03E+09

3088 802048 3.67E+09 3091 610048 3.06E+09 3091 606464 3.05E+09

3108 798464 3.69E+09 3111 607232 3.07E+09 3111 603648 3.06E+09

3128 794880 3.71E+09 3131 604416 3.08E+09 3131 600832 3.07E+09

3148 791552 3.72E+09 3151 601600 3.1E+09 3151 598272 3.08E+09

3168 787968 3.74E+09 3171 598784 3.11E+09 3171 595712 3.09E+09

3188 784384 3.75E+09 3191 595968 3.12E+09 3191 593152 3.11E+09

3208 781312 3.77E+09 3211 593920 3.13E+09 3211 590592 3.12E+09

3228 777472 3.78E+09 3231 591104 3.14E+09 3231 587776 3.13E+09

3248 774144 3.8E+09 3251 588544 3.16E+09 3251 585216 3.14E+09

3268 770816 3.82E+09 3271 585728 3.17E+09 3271 582656 3.15E+09

3288 767488 3.83E+09 3291 583168 3.18E+09 3291 579840 3.16E+09

3308 763648 3.85E+09 3311 580352 3.19E+09 3311 577536 3.18E+09

3328 760064 3.86E+09 3331 578048 3.2E+09 3331 574976 3.19E+09

3348 757248 3.88E+09 3351 575488 3.21E+09 3351 572160 3.2E+09

3368 753664 3.89E+09 3371 573184 3.23E+09 3371 569856 3.21E+09

3388 750336 3.91E+09 3391 570880 3.24E+09 3391 567296 3.22E+09

3408 747008 3.92E+09 3411 568320 3.25E+09 3411 564736 3.23E+09

3428 743680 3.94E+09 3431 565504 3.26E+09 3431 562176 3.24E+09

3448 740352 3.95E+09 3451 562944 3.27E+09 3451 559872 3.26E+09

3468 737024 3.97E+09 3471 560896 3.28E+09 3471 557568 3.27E+09

3488 733696 3.98E+09 3491 558336 3.29E+09 3491 555008 3.28E+09

3508 730624 4E+09 3511 556032 3.3E+09 3511 553216 3.29E+09

3528 727552 4.01E+09 3531 553728 3.32E+09 3531 550912 3.3E+09

3548 724224 4.02E+09 3551 551424 3.33E+09 3551 548352 3.31E+09

3568 720896 4.04E+09 3571 549120 3.34E+09 3571 546304 3.32E+09

3588 717824 4.05E+09 3591 546816 3.35E+09 3591 544000 3.33E+09

3608 714496 4.07E+09 3611 544768 3.36E+09 3611 541952 3.34E+09

3628 711424 4.08E+09 3631 542464 3.37E+09 3631 539648 3.35E+09

3648 707840 4.1E+09 3651 540416 3.38E+09 3651 537600 3.36E+09

3668 705024 4.11E+09 3671 537856 3.39E+09 3671 535296 3.38E+09

3688 701952 4.12E+09 3691 536064 3.4E+09 3691 533248 3.39E+09

214

3708 699136 4.14E+09 3711 533504 3.41E+09 3711 531200 3.4E+09

3728 695808 4.15E+09 3731 531712 3.42E+09 3731 528640 3.41E+09

3748 692736 4.17E+09 3751 529664 3.44E+09 3751 526592 3.42E+09

3768 689664 4.18E+09 3771 527360 3.45E+09 3771 524544 3.43E+09

3788 686848 4.19E+09 3791 525312 3.46E+09 3791 522752 3.44E+09

3808 684032 4.21E+09 3811 523264 3.47E+09 3811 520704 3.45E+09

3828 680960 4.22E+09 3831 521216 3.48E+09 3831 518656 3.46E+09

3848 677632 4.24E+09 3851 519424 3.49E+09 3851 516352 3.47E+09

3868 674816 4.25E+09 3871 517120 3.5E+09 3871 514304 3.48E+09

3888 672256 4.26E+09 3891 515072 3.51E+09 3891 512000 3.49E+09

3908 669184 4.28E+09 3911 513024 3.52E+09 3911 510208 3.5E+09

3928 666368 4.29E+09 3931 511232 3.53E+09 3931 508160 3.51E+09

3948 663552 4.3E+09 3951 508672 3.54E+09 3951 506368 3.52E+09

3968 660992 4.32E+09 3971 506880 3.55E+09 3971 504320 3.53E+09

3988 657920 4.33E+09 3991 504832 3.56E+09 3991 502272 3.54E+09

4008 655360 4.34E+09 4011 502784 3.57E+09 4011 500480 3.55E+09

4028 652288 4.35E+09 4031 500992 3.58E+09 4031 498432 3.56E+09

4048 649728 4.37E+09 4051 498944 3.59E+09 4051 496384 3.57E+09

4068 646656 4.38E+09 4071 496896 3.6E+09 4071 494592 3.58E+09

4088 644096 4.39E+09 4091 495104 3.61E+09 4091 492800 3.59E+09

4108 641536 4.41E+09 4111 493312 3.62E+09 4111 490496 3.6E+09

4128 638464 4.42E+09 4131 491264 3.63E+09 4131 488960 3.61E+09

4148 635904 4.43E+09 4151 489472 3.64E+09 4151 486656 3.62E+09

4168 633344 4.44E+09 4171 487680 3.65E+09 4171 484864 3.63E+09

4188 630784 4.46E+09 4191 485376 3.66E+09 4191 483328 3.64E+09

4208 628224 4.47E+09 4211 483840 3.67E+09 4211 481280 3.65E+09

4228 625152 4.48E+09 4231 481792 3.68E+09 4231 479488 3.66E+09

4248 622592 4.5E+09 4251 480000 3.69E+09 4251 477696 3.67E+09

4268 620032 4.51E+09 4271 478208 3.7E+09 4271 475904 3.68E+09

4288 616960 4.52E+09 4291 476160 3.71E+09 4291 473856 3.69E+09

4308 614400 4.53E+09 4311 474368 3.72E+09 4311 472064 3.7E+09

4328 612352 4.54E+09 4331 472576 3.73E+09 4331 470272 3.71E+09

4348 609280 4.56E+09 4351 471040 3.73E+09 4351 468736 3.72E+09

4368 606720 4.57E+09 4371 468992 3.74E+09 4371 466688 3.73E+09

4388 604672 4.58E+09 4391 467200 3.75E+09 4391 464896 3.73E+09

4408 602112 4.59E+09 4411 465664 3.76E+09 4411 463360 3.74E+09

4428 599040 4.6E+09 4431 463872 3.77E+09 4431 461312 3.75E+09

4448 596992 4.62E+09 4451 461824 3.78E+09 4451 459776 3.76E+09

4468 594432 4.63E+09 4471 460288 3.79E+09 4471 457984 3.77E+09

4488 591872 4.64E+09 4491 458496 3.8E+09 4491 456192 3.78E+09

4508 589312 4.65E+09 4511 456960 3.81E+09 4511 454656 3.79E+09

215

4528 587264 4.66E+09 4531 455168 3.82E+09 4531 452864 3.8E+09

4548 584704 4.68E+09 4551 453632 3.83E+09 4551 451328 3.81E+09

4568 582144 4.69E+09 4571 451840 3.84E+09 4571 449536 3.82E+09

4588 579584 4.7E+09 4591 450048 3.85E+09 4591 447744 3.83E+09

4608 577024 4.71E+09 4611 448512 3.85E+09 4611 445952 3.84E+09

4628 574464 4.72E+09 4631 446976 3.86E+09 4631 444672 3.84E+09

4648 571904 4.73E+09 4651 444928 3.87E+09 4651 443136 3.85E+09

4668 569344 4.75E+09 4671 443648 3.88E+09 4671 441088 3.86E+09

4688 567808 4.76E+09 4691 441856 3.89E+09 4691 439808 3.87E+09

4708 565760 4.77E+09 4711 440576 3.9E+09 4711 438016 3.88E+09

4728 562688 4.78E+09 4731 438784 3.91E+09 4731 436480 3.89E+09

4748 560640 4.79E+09 4751 437248 3.92E+09 4751 434944 3.9E+09

4768 558080 4.8E+09 4771 435456 3.92E+09 4771 433664 3.91E+09

4788 555520 4.81E+09 4791 433920 3.93E+09 4791 432128 3.91E+09

4808 553472 4.82E+09 4811 432384 3.94E+09 4811 430592 3.92E+09

4828 551424 4.83E+09 4831 430848 3.95E+09 4831 428800 3.93E+09

4848 549376 4.85E+09 4851 429312 3.96E+09 4851 427520 3.94E+09

4868 546816 4.86E+09 4871 428032 3.97E+09 4871 425984 3.95E+09

4888 544768 4.87E+09 4891 426752 3.98E+09 4891 424704 3.96E+09

4908 542208 4.88E+09 4911 424960 3.99E+09 4911 423424 3.97E+09

4928 540160 4.89E+09 4931 423424 3.99E+09 4931 421632 3.97E+09

4948 538624 4.9E+09 4951 422144 4E+09 4951 420352 3.98E+09

4968 536064 4.91E+09 4971 420864 4.01E+09 4971 418560 3.99E+09

4988 534016 4.92E+09 4991 419328 4.02E+09 4991 417536 4E+09

5008 531456 4.93E+09 5011 417792 4.03E+09 5011 416256 4.01E+09

Case Study 4-B

pi=4800 psia, pwf=500 psia, T=200F, SG=0.65


TIME(day) qsc(SCFD) Gp(SCF) TIME(day) qsc(SCFD) Gp(SCF) TIME(day) qsc(SCFD) Gp(SCF)

0.003061 14633209 50275.89 0.002996 13768060 46227.51 0.002996 13757130 46183.14

2 6662673 14300550 3 6181474 19920280 3 6178550 19910272

12 5698200 73952016 13 5477424 76846184 13 5475048 76811048

22 5448744 1.29E+08 23 5246288 1.3E+08 23 5243736 1.3E+08

32 5302048 1.83E+08 33 5082768 1.82E+08 33 5079696 1.82E+08

52 5092672 2.87E+08 53 4802752 2.8E+08 53 4798496 2.8E+08

72 4913088 3.87E+08 73 4553568 3.74E+08 73 4548448 3.74E+08

92 4743456 4.83E+08 93 4324960 4.62E+08 93 4319136 4.62E+08

112 4581760 5.76E+08 113 4116608 5.47E+08 113 4110400 5.46E+08

132 4426048 6.66E+08 133 3924224 6.27E+08 133 3917760 6.26E+08

152 4275968 7.53E+08 153 3746048 7.04E+08 153 3739264 7.03E+08

216

172 4132608 8.37E+08 173 3582528 7.77E+08 173 3575744 7.76E+08

192 3994624 9.18E+08 193 3429504 8.47E+08 193 3422720 8.46E+08

212 3861376 9.97E+08 213 3286336 9.14E+08 213 3279616 9.13E+08

232 3733312 1.07E+09 233 3154048 9.78E+08 233 3147456 9.77E+08

252 3611136 1.15E+09 253 3030272 1.04E+09 253 3023808 1.04E+09

272 3492992 1.22E+09 273 2913408 1.1E+09 273 2907008 1.1E+09

292 3379072 1.29E+09 293 2803072 1.16E+09 293 2796928 1.15E+09

312 3269504 1.35E+09 313 2700288 1.21E+09 313 2694144 1.21E+09

332 3164544 1.42E+09 333 2603904 1.26E+09 333 2598016 1.26E+09

352 3064064 1.48E+09 353 2512000 1.32E+09 353 2506368 1.31E+09

372 2966656 1.54E+09 373 2424832 1.36E+09 373 2419328 1.36E+09

392 2872704 1.6E+09 393 2341888 1.41E+09 393 2336640 1.41E+09

412 2782080 1.65E+09 413 2264192 1.46E+09 413 2258816 1.46E+09

432 2695552 1.71E+09 433 2190464 1.5E+09 433 2185728 1.5E+09

452 2612224 1.76E+09 453 2120448 1.55E+09 453 2115968 1.54E+09

472 2531712 1.81E+09 473 2053376 1.59E+09 473 2048896 1.59E+09

492 2454144 1.86E+09 493 1989376 1.63E+09 493 1985024 1.63E+09

512 2378880 1.91E+09 513 1928192 1.67E+09 513 1923968 1.66E+09

532 2306432 1.96E+09 533 1869696 1.71E+09 533 1865728 1.7E+09

552 2237184 2E+09 553 1814400 1.74E+09 553 1810560 1.74E+09

572 2170752 2.05E+09 573 1761664 1.78E+09 573 1758080 1.77E+09

592 2106112 2.09E+09 593 1711232 1.81E+09 593 1707648 1.81E+09

612 2043776 2.13E+09 613 1662720 1.85E+09 613 1659264 1.84E+09

632 1983488 2.17E+09 633 1616000 1.88E+09 633 1612800 1.88E+09

652 1925120 2.21E+09 653 1571072 1.91E+09 653 1567872 1.91E+09

672 1868800 2.25E+09 673 1527936 1.94E+09 673 1524864 1.94E+09

692 1815040 2.29E+09 693 1486592 1.97E+09 693 1483648 1.97E+09

712 1762816 2.32E+09 713 1446656 2E+09 713 1444096 2E+09

732 1712640 2.36E+09 733 1408640 2.03E+09 733 1406080 2.03E+09

752 1664000 2.39E+09 753 1372288 2.06E+09 753 1369856 2.05E+09

772 1617152 2.42E+09 773 1337216 2.08E+09 773 1334656 2.08E+09

792 1571328 2.45E+09 793 1303424 2.11E+09 793 1301120 2.11E+09

812 1527296 2.49E+09 813 1270656 2.14E+09 813 1268608 2.13E+09

832 1484800 2.52E+09 833 1238784 2.16E+09 833 1236992 2.16E+09

852 1443584 2.54E+09 853 1208576 2.19E+09 853 1206528 2.18E+09

872 1403392 2.57E+09 873 1179136 2.21E+09 873 1177088 2.21E+09

892 1365504 2.6E+09 893 1150464 2.23E+09 893 1148928 2.23E+09

912 1328384 2.63E+09 913 1123072 2.26E+09 913 1121280 2.25E+09

932 1292288 2.65E+09 933 1096448 2.28E+09 933 1094656 2.27E+09

952 1257728 2.68E+09 953 1070848 2.3E+09 953 1069312 2.3E+09

972 1224192 2.7E+09 973 1046016 2.32E+09 973 1044480 2.32E+09

217

992 1191168 2.73E+09 993 1022208 2.34E+09 993 1020928 2.34E+09

1012 1160192 2.75E+09 1013 998912 2.36E+09 1013 997632 2.36E+09

1032 1129216 2.77E+09 1033 976640 2.38E+09 1033 975104 2.38E+09

1052 1099520 2.8E+09 1053 954624 2.4E+09 1053 953600 2.4E+09

1072 1070848 2.82E+09 1073 933888 2.42E+09 1073 932864 2.42E+09

1092 1042944 2.84E+09 1093 913152 2.44E+09 1093 912640 2.43E+09

1112 1016064 2.86E+09 1113 893696 2.46E+09 1113 892928 2.45E+09

1132 990208 2.88E+09 1133 874496 2.47E+09 1133 873472 2.47E+09

1152 965120 2.9E+09 1153 855808 2.49E+09 1153 855296 2.49E+09

1172 940544 2.92E+09 1173 837632 2.51E+09 1173 836608 2.5E+09

1192 916992 2.94E+09 1193 819968 2.52E+09 1193 819456 2.52E+09

1212 893952 2.96E+09 1213 803072 2.54E+09 1213 802304 2.54E+09

1232 871424 2.97E+09 1233 786432 2.56E+09 1233 785920 2.55E+09

1252 850176 2.99E+09 1253 770560 2.57E+09 1253 769792 2.57E+09

1272 828928 3.01E+09 1273 754688 2.59E+09 1273 753920 2.58E+09

1292 808704 3.02E+09 1293 739328 2.6E+09 1293 739072 2.6E+09

1312 788736 3.04E+09 1313 724736 2.62E+09 1313 724224 2.61E+09

1332 769536 3.06E+09 1333 710400 2.63E+09 1333 709888 2.63E+09

1352 750848 3.07E+09 1353 696320 2.65E+09 1353 696064 2.64E+09

1372 732672 3.09E+09 1373 683008 2.66E+09 1373 682496 2.66E+09

1392 715008 3.1E+09 1393 669440 2.67E+09 1393 669184 2.67E+09

1412 698112 3.11E+09 1413 656640 2.69E+09 1413 656384 2.68E+09

1432 681472 3.13E+09 1433 644352 2.7E+09 1433 643840 2.69E+09

1452 665344 3.14E+09 1453 632064 2.71E+09 1453 632064 2.71E+09

1472 649984 3.15E+09 1473 620288 2.72E+09 1473 620032 2.72E+09

1492 634624 3.17E+09 1493 608768 2.74E+09 1493 608512 2.73E+09

1512 620032 3.18E+09 1513 597504 2.75E+09 1513 597248 2.74E+09

1532 605696 3.19E+09 1533 586752 2.76E+09 1533 586240 2.76E+09

1552 591872 3.2E+09 1553 575744 2.77E+09 1553 576000 2.77E+09

1572 578304 3.22E+09 1573 565248 2.78E+09 1573 564992 2.78E+09

1592 564992 3.23E+09 1593 555264 2.79E+09 1593 555264 2.79E+09

1612 552448 3.24E+09 1613 545024 2.81E+09 1613 545280 2.8E+09

1632 539904 3.25E+09 1633 535296 2.82E+09 1633 535296 2.81E+09

1652 527872 3.26E+09 1653 526080 2.83E+09 1653 525824 2.82E+09

1672 516096 3.27E+09 1673 516608 2.84E+09 1673 517120 2.83E+09

1692 504832 3.28E+09 1693 507904 2.85E+09 1693 508160 2.84E+09

1712 493568 3.29E+09 1713 498944 2.86E+09 1713 499200 2.85E+09

1732 482816 3.3E+09 1733 490240 2.87E+09 1733 490496 2.86E+09

1752 472320 3.31E+09 1753 481792 2.88E+09 1753 482560 2.87E+09

1772 462080 3.32E+09 1773 474112 2.89E+09 1773 474368 2.88E+09

1792 452096 3.33E+09 1793 465920 2.9E+09 1793 466176 2.89E+09

218

1812 442368 3.34E+09 1813 458240 2.91E+09 1813 458496 2.9E+09

1832 432640 3.35E+09 1833 450560 2.91E+09 1833 450560 2.91E+09

1852 423680 3.35E+09 1853 443136 2.92E+09 1853 443392 2.92E+09

1872 414464 3.36E+09 1873 435968 2.93E+09 1873 435968 2.93E+09

1892 405760 3.37E+09 1893 428800 2.94E+09 1893 429056 2.94E+09

1912 397312 3.38E+09 1913 421888 2.95E+09 1913 421888 2.95E+09

1932 388864 3.39E+09 1933 414720 2.96E+09 1933 414976 2.95E+09

1952 380928 3.39E+09 1953 408064 2.97E+09 1953 408320 2.96E+09

1972 372736 3.4E+09 1973 401664 2.97E+09 1973 401664 2.97E+09

1992 365312 3.41E+09 1993 395264 2.98E+09 1993 395264 2.98E+09

2012 357632 3.42E+09 2013 388864 2.99E+09 2013 389120 2.99E+09

2032 350208 3.42E+09 2033 382464 3E+09 2033 383232 2.99E+09

2052 343296 3.43E+09 2053 376832 3.01E+09 2053 376832 3E+09

2072 336384 3.44E+09 2073 370944 3.01E+09 2073 371200 3.01E+09

2092 329472 3.44E+09 2093 365056 3.02E+09 2093 365312 3.02E+09

2112 322816 3.45E+09 2113 359424 3.03E+09 2113 359680 3.02E+09

2132 316672 3.46E+09 2133 353792 3.03E+09 2133 354304 3.03E+09

2152 310272 3.46E+09 2153 348416 3.04E+09 2153 348928 3.04E+09

2172 304128 3.47E+09 2173 343296 3.05E+09 2173 343808 3.04E+09

2192 297984 3.48E+09 2193 338176 3.06E+09 2193 338432 3.05E+09

2212 292352 3.48E+09 2213 333056 3.06E+09 2213 333568 3.06E+09

2232 286720 3.49E+09 2233 328192 3.07E+09 2233 328448 3.06E+09

2252 281344 3.49E+09 2253 323328 3.08E+09 2253 323840 3.07E+09

2272 275968 3.5E+09 2273 318464 3.08E+09 2273 318720 3.08E+09

2292 270592 3.5E+09 2293 313856 3.09E+09 2293 314368 3.08E+09

2312 265728 3.51E+09 2313 309248 3.09E+09 2313 309760 3.09E+09

2332 260352 3.51E+09 2333 305152 3.1E+09 2333 305152 3.1E+09

2352 255488 3.52E+09 2353 300544 3.11E+09 2353 301056 3.1E+09

2372 250624 3.52E+09 2373 296192 3.11E+09 2373 296448 3.11E+09

2392 246016 3.53E+09 2393 291840 3.12E+09 2393 292352 3.11E+09

2412 241664 3.53E+09 2413 287744 3.12E+09 2413 288000 3.12E+09

2432 237056 3.54E+09 2433 283648 3.13E+09 2433 284160 3.13E+09

2452 232704 3.54E+09 2453 280064 3.14E+09 2453 280064 3.13E+09

2472 228352 3.55E+09 2473 276224 3.14E+09 2473 276224 3.14E+09

2492 224256 3.55E+09 2493 272128 3.15E+09 2493 272640 3.14E+09

2512 220160 3.56E+09 2513 268288 3.15E+09 2513 268544 3.15E+09

2532 216320 3.56E+09 2533 264704 3.16E+09 2533 265216 3.15E+09

2552 212224 3.57E+09 2553 261120 3.16E+09 2553 261376 3.16E+09

2572 208384 3.57E+09 2573 257280 3.17E+09 2573 257792 3.16E+09

2592 204544 3.57E+09 2593 253952 3.17E+09 2593 254208 3.17E+09

2612 200960 3.58E+09 2613 250624 3.18E+09 2613 251392 3.17E+09

219

2632 197376 3.58E+09 2633 247296 3.18E+09 2633 247808 3.18E+09

2652 193536 3.59E+09 2653 243712 3.19E+09 2653 244224 3.18E+09

2672 189952 3.59E+09 2673 240384 3.19E+09 2673 241152 3.19E+09

2692 186624 3.59E+09 2693 237312 3.2E+09 2693 237824 3.19E+09

2712 183552 3.6E+09 2713 234496 3.2E+09 2713 234752 3.2E+09

2732 180224 3.6E+09 2733 231424 3.21E+09 2733 231680 3.2E+09

2752 176896 3.61E+09 2753 228352 3.21E+09 2753 228352 3.21E+09

2772 173824 3.61E+09 2773 225280 3.22E+09 2773 225536 3.21E+09

2792 171008 3.61E+09 2793 222464 3.22E+09 2793 222464 3.22E+09

2812 167680 3.62E+09 2813 219392 3.22E+09 2813 219904 3.22E+09

2832 165120 3.62E+09 2833 216576 3.23E+09 2833 216832 3.23E+09

2852 162048 3.62E+09 2853 214016 3.23E+09 2853 214272 3.23E+09

2872 159744 3.63E+09 2873 210944 3.24E+09 2873 211712 3.23E+09

2892 156672 3.63E+09 2893 208384 3.24E+09 2893 208896 3.24E+09

2912 154112 3.63E+09 2913 205568 3.25E+09 2913 205824 3.24E+09

2932 151296 3.63E+09 2933 203008 3.25E+09 2933 203520 3.25E+09

2952 148992 3.64E+09 2953 200704 3.25E+09 2953 200960 3.25E+09

2972 146432 3.64E+09 2973 197888 3.26E+09 2973 198400 3.25E+09

2992 144128 3.64E+09 2993 195072 3.26E+09 2993 195840 3.26E+09

3012 141312 3.65E+09 3013 192768 3.27E+09 3013 193536 3.26E+09

3032 139264 3.65E+09 3033 190208 3.27E+09 3033 190976 3.27E+09

3052 136960 3.65E+09 3053 187904 3.27E+09 3053 188672 3.27E+09

3072 134912 3.65E+09 3073 185856 3.28E+09 3073 186112 3.27E+09

3092 132864 3.66E+09 3093 183552 3.28E+09 3093 183808 3.28E+09

3112 130304 3.66E+09 3113 181248 3.28E+09 3113 181760 3.28E+09

3132 128256 3.66E+09 3133 179200 3.29E+09 3133 179456 3.28E+09

3152 126464 3.67E+09 3153 176640 3.29E+09 3153 177152 3.29E+09

3172 124160 3.67E+09 3173 174592 3.3E+09 3173 175104 3.29E+09

3192 122368 3.67E+09 3193 172544 3.3E+09 3193 173056 3.29E+09

3212 120576 3.67E+09 3213 170496 3.3E+09 3213 171008 3.3E+09

3232 118272 3.67E+09 3233 168448 3.31E+09 3233 168960 3.3E+09

3252 116480 3.68E+09 3253 166400 3.31E+09 3253 166656 3.31E+09

3272 114688 3.68E+09 3273 164608 3.31E+09 3273 164608 3.31E+09

3292 112640 3.68E+09 3293 162304 3.32E+09 3293 162816 3.31E+09

3312 111104 3.68E+09 3313 160512 3.32E+09 3313 160768 3.31E+09

3332 109312 3.69E+09 3333 158720 3.32E+09 3333 158720 3.32E+09

3352 107776 3.69E+09 3353 156416 3.33E+09 3353 156928 3.32E+09

3372 105984 3.69E+09 3373 154880 3.33E+09 3373 155392 3.32E+09

3392 104192 3.69E+09 3393 153088 3.33E+09 3393 153600 3.33E+09

3412 102656 3.69E+09 3413 151296 3.33E+09 3413 151552 3.33E+09

3432 101120 3.7E+09 3433 149760 3.34E+09 3433 150016 3.33E+09

220

3452 99840 3.7E+09 3453 147968 3.34E+09 3453 148224 3.34E+09

3472 98048 3.7E+09 3473 145920 3.34E+09 3473 146688 3.34E+09

3492 96512 3.7E+09 3493 144384 3.35E+09 3493 144896 3.34E+09

3512 95232 3.7E+09 3513 142592 3.35E+09 3513 143104 3.35E+09

3532 93696 3.71E+09 3533 141312 3.35E+09 3533 141568 3.35E+09

3552 92416 3.71E+09 3553 139520 3.35E+09 3553 140288 3.35E+09

3572 90880 3.71E+09 3573 137984 3.36E+09 3573 138496 3.35E+09

3592 89600 3.71E+09 3593 136448 3.36E+09 3593 136704 3.36E+09

3612 88320 3.71E+09 3613 135168 3.36E+09 3613 135680 3.36E+09

3632 87040 3.72E+09 3633 133632 3.37E+09 3633 133632 3.36E+09

3652 85504 3.72E+09 3653 131840 3.37E+09 3653 132352 3.36E+09

3672 84480 3.72E+09 3673 130560 3.37E+09 3673 131072 3.37E+09

3692 82944 3.72E+09 3693 128768 3.37E+09 3693 129536 3.37E+09

3712 81920 3.72E+09 3713 127744 3.38E+09 3713 128000 3.37E+09

3732 80384 3.72E+09 3733 126464 3.38E+09 3733 126464 3.37E+09

3752 79616 3.73E+09 3753 124672 3.38E+09 3753 125184 3.38E+09

3772 78336 3.73E+09 3773 123648 3.38E+09 3773 123904 3.38E+09

3792 77056 3.73E+09 3793 121856 3.39E+09 3793 122624 3.38E+09

3812 76032 3.73E+09 3813 120576 3.39E+09 3813 121088 3.38E+09

3832 74752 3.73E+09 3833 119552 3.39E+09 3833 119808 3.39E+09

3852 73984 3.73E+09 3853 118016 3.39E+09 3853 118528 3.39E+09

3872 72704 3.73E+09 3873 116992 3.4E+09 3873 117504 3.39E+09

3892 71680 3.74E+09 3893 115712 3.4E+09 3893 116224 3.39E+09

3912 70400 3.74E+09 3913 114432 3.4E+09 3913 114688 3.4E+09

3932 69632 3.74E+09 3933 113408 3.4E+09 3933 113408 3.4E+09

3952 68864 3.74E+09 3953 111872 3.4E+09 3953 112384 3.4E+09

3972 67840 3.74E+09 3973 110848 3.41E+09 3973 111360 3.4E+09

3992 66816 3.74E+09 3993 109568 3.41E+09 3993 110336 3.41E+09

4012 65792 3.74E+09 4013 108800 3.41E+09 4013 108544 3.41E+09

4032 64768 3.75E+09 4033 107520 3.41E+09 4033 107776 3.41E+09

4052 64256 3.75E+09 4053 106496 3.42E+09 4053 106752 3.41E+09

4072 62976 3.75E+09 4073 105472 3.42E+09 4073 105728 3.41E+09

4092 62208 3.75E+09 4093 103936 3.42E+09 4093 104448 3.42E+09

4112 61184 3.75E+09 4113 102912 3.42E+09 4113 103424 3.42E+09

4132 60416 3.75E+09 4133 101632 3.42E+09 4133 102400 3.42E+09

4152 59904 3.75E+09 4153 100864 3.43E+09 4153 101376 3.42E+09

4172 58880 3.75E+09 4173 99840 3.43E+09 4173 100096 3.42E+09

4192 58112 3.76E+09 4193 99072 3.43E+09 4193 99072 3.43E+09

4212 57088 3.76E+09 4213 98048 3.43E+09 4213 98304 3.43E+09

4232 56320 3.76E+09 4233 97024 3.43E+09 4233 97024 3.43E+09

4252 55808 3.76E+09 4253 96000 3.44E+09 4253 96512 3.43E+09

221

4272 54784 3.76E+09 4273 94464 3.44E+09 4273 95488 3.43E+09

4292 54016 3.76E+09 4293 94208 3.44E+09 4293 94464 3.44E+09

4312 53504 3.76E+09 4313 92928 3.44E+09 4313 93440 3.44E+09

4332 52480 3.76E+09 4333 92160 3.44E+09 4333 92416 3.44E+09

4352 51968 3.76E+09 4353 91136 3.45E+09 4353 91648 3.44E+09

4372 50944 3.77E+09 4373 90112 3.45E+09 4373 90368 3.44E+09

4392 50176 3.77E+09 4393 89344 3.45E+09 4393 89600 3.45E+09

4412 49664 3.77E+09 4413 88320 3.45E+09 4413 88832 3.45E+09

4432 49152 3.77E+09 4433 87552 3.45E+09 4433 87808 3.45E+09

4452 48384 3.77E+09 4453 86784 3.45E+09 4453 87040 3.45E+09

4472 47872 3.77E+09 4473 85760 3.46E+09 4473 86272 3.45E+09

4492 47104 3.77E+09 4493 84992 3.46E+09 4493 85248 3.45E+09

4512 46336 3.77E+09 4513 84224 3.46E+09 4513 84736 3.46E+09

4532 45568 3.77E+09 4533 83200 3.46E+09 4533 83968 3.46E+09

4552 44800 3.77E+09 4553 82688 3.46E+09 4553 83200 3.46E+09

4572 44544 3.77E+09 4573 81920 3.46E+09 4573 81920 3.46E+09

4592 44032 3.78E+09 4593 80896 3.47E+09 4593 81408 3.46E+09

4612 43264 3.78E+09 4613 80128 3.47E+09 4613 80640 3.46E+09

4632 42752 3.78E+09 4633 79360 3.47E+09 4633 79616 3.47E+09

4652 41984 3.78E+09 4653 78592 3.47E+09 4653 78848 3.47E+09

4672 41472 3.78E+09 4673 78080 3.47E+09 4673 78336 3.47E+09

4692 40960 3.78E+09 4693 77056 3.47E+09 4693 77312 3.47E+09

4712 40448 3.78E+09 4713 76288 3.48E+09 4713 76800 3.47E+09

4732 39680 3.78E+09 4733 75520 3.48E+09 4733 76032 3.47E+09

4752 39424 3.78E+09 4753 75008 3.48E+09 4753 75264 3.47E+09

4772 38656 3.78E+09 4773 74496 3.48E+09 4773 74496 3.48E+09

4792 38400 3.78E+09 4793 73216 3.48E+09 4793 73984 3.48E+09

4812 37888 3.78E+09 4813 72960 3.48E+09 4813 73216 3.48E+09

4832 37376 3.79E+09 4833 72192 3.48E+09 4833 72448 3.48E+09

4852 36608 3.79E+09 4853 71424 3.49E+09 4853 71936 3.48E+09

4872 36352 3.79E+09 4873 70912 3.49E+09 4873 71168 3.48E+09

4892 35840 3.79E+09 4893 70144 3.49E+09 4893 70400 3.49E+09

4912 35328 3.79E+09 4913 69632 3.49E+09 4913 70144 3.49E+09

4932 34560 3.79E+09 4933 68864 3.49E+09 4933 68864 3.49E+09

4952 34560 3.79E+09 4953 68096 3.49E+09 4953 68352 3.49E+09

4972 33792 3.79E+09 4973 67584 3.49E+09 4973 67840 3.49E+09

4992 33536 3.79E+09 4993 66816 3.5E+09 4993 67584 3.49E+09

222

Case Study 4-C

pi=12,300 psia, pwf=350 psia, T=200F, SG=0.55



0.001 61694792 61694.79 0.001 53343972 53343.97 0.001 53162096 53162.1

0.028598 27596630 926498.8 0.033931 24495450 961039 0.03418 24405358 963987.1

1 18257416 20118748 1.5 16363308 26764888 1.5 16327032 26703910

10 14786592 1.61E+08 11 13786560 1.65E+08 11 13758928 1.64E+08

20 13978016 3.04E+08 21 13009216 2.98E+08 21 12974912 2.97E+08

40 13203712 5.75E+08 41 11890240 5.46E+08 41 11838176 5.44E+08

60 12647808 8.33E+08 61 10954624 7.74E+08 61 10892800 7.71E+08

80 12138112 1.08E+09 81 10150080 9.84E+08 81 10083456 9.8E+08

100 11651072 1.32E+09 101 9451648 1.18E+09 101 9382528 1.17E+09

120 11183872 1.55E+09 121 8838400 1.36E+09 121 8770432 1.36E+09

140 10737536 1.76E+09 141 8294528 1.53E+09 141 8227328 1.52E+09

160 10307840 1.98E+09 161 7808640 1.69E+09 161 7744896 1.68E+09

180 9897728 2.18E+09 181 7374080 1.85E+09 181 7312256 1.83E+09

200 9503232 2.37E+09 201 6978304 1.99E+09 201 6919936 1.98E+09

220 9124608 2.56E+09 221 6625536 2.12E+09 221 6570880 2.11E+09

240 8764416 2.74E+09 241 6302208 2.25E+09 241 6249472 2.24E+09

260 8417792 2.91E+09 261 6002944 2.38E+09 261 5953024 2.36E+09

280 8084736 3.07E+09 281 5731328 2.49E+09 281 5685760 2.48E+09

300 7767040 3.23E+09 301 5483264 2.61E+09 301 5440256 2.59E+09

320 7463168 3.38E+09 321 5251072 2.71E+09 321 5209856 2.69E+09

340 7171072 3.53E+09 341 5033728 2.82E+09 341 4994816 2.8E+09

360 6891776 3.67E+09 361 4831488 2.91E+09 361 4795392 2.89E+09

380 6627328 3.8E+09 381 4647168 3.01E+09 381 4613888 2.99E+09

400 6373632 3.93E+09 401 4475904 3.1E+09 401 4444160 3.08E+09

420 6129664 4.06E+09 421 4313600 3.19E+09 421 4283392 3.17E+09

440 5895936 4.18E+09 441 4159232 3.27E+09 441 4130560 3.25E+09

460 5675008 4.29E+09 461 4013312 3.35E+09 461 3986176 3.33E+09

480 5463552 4.41E+09 481 3875328 3.43E+09 481 3849984 3.41E+09

500 5260288 4.51E+09 501 3746816 3.51E+09 501 3723520 3.49E+09

520 5064704 4.62E+09 521 3628032 3.58E+09 521 3606784 3.56E+09

540 4877824 4.72E+09 541 3515904 3.65E+09 541 3495424 3.63E+09

560 4700160 4.81E+09 561 3408384 3.72E+09 561 3389440 3.7E+09

580 4531712 4.9E+09 581 3305472 3.79E+09 581 3287296 3.76E+09

600 4370432 4.99E+09 601 3206912 3.85E+09 601 3189504 3.83E+09

620 4214784 5.08E+09 621 3112192 3.92E+09 621 3095808 3.89E+09

640 4064256 5.16E+09 641 3021568 3.98E+09 641 3005952 3.95E+09

660 3920384 5.24E+09 661 2935040 4.04E+09 661 2920704 4.01E+09

223

680 3782144 5.32E+09 681 2852864 4.1E+09 681 2839552 4.07E+09

700 3652608 5.39E+09 701 2775552 4.15E+09 701 2763520 4.13E+09

720 3529728 5.46E+09 721 2703104 4.21E+09 721 2692096 4.18E+09

740 3410432 5.53E+09 741 2634496 4.26E+09 741 2624000 4.23E+09

760 3295744 5.6E+09 761 2568192 4.31E+09 761 2558464 4.29E+09

780 3184640 5.66E+09 781 2504192 4.36E+09 781 2494976 4.34E+09

800 3077120 5.73E+09 801 2442240 4.41E+09 801 2434048 4.39E+09

820 2974208 5.79E+09 821 2382336 4.46E+09 821 2374144 4.43E+09

840 2876416 5.85E+09 841 2324480 4.51E+09 841 2316800 4.48E+09

860 2782208 5.9E+09 861 2268672 4.55E+09 861 2261504 4.53E+09

880 2694144 5.96E+09 881 2214400 4.6E+09 881 2207744 4.57E+09

900 2610176 6.01E+09 901 2162176 4.64E+09 901 2156032 4.61E+09

920 2528256 6.06E+09 921 2111488 4.69E+09 921 2105344 4.66E+09

940 2448896 6.11E+09 941 2062848 4.73E+09 941 2057216 4.7E+09

960 2373120 6.16E+09 961 2015744 4.77E+09 961 2011136 4.74E+09

980 2299392 6.21E+09 981 1970688 4.81E+09 981 1966592 4.78E+09

1000 2228224 6.25E+09 1001 1926656 4.85E+09 1001 1922560 4.82E+09

1020 2159104 6.3E+09 1021 1885184 4.88E+09 1021 1881600 4.86E+09

1040 2093568 6.34E+09 1041 1846272 4.92E+09 1041 1843200 4.89E+09

1060 2029568 6.38E+09 1061 1808384 4.96E+09 1061 1805824 4.93E+09

1080 1968128 6.42E+09 1081 1772032 4.99E+09 1081 1769984 4.97E+09

1100 1909248 6.46E+09 1101 1736704 5.03E+09 1101 1734144 5E+09

1120 1853952 6.5E+09 1121 1701888 5.06E+09 1121 1700352 5.03E+09

1140 1800704 6.53E+09 1141 1668608 5.1E+09 1141 1666560 5.07E+09

1160 1750528 6.57E+09 1161 1635840 5.13E+09 1161 1634304 5.1E+09

1180 1701376 6.6E+09 1181 1604608 5.16E+09 1181 1603072 5.13E+09

1200 1653248 6.64E+09 1201 1573888 5.19E+09 1201 1572352 5.17E+09

1220 1607168 6.67E+09 1221 1543168 5.23E+09 1221 1541632 5.2E+09

1240 1562624 6.7E+09 1241 1513984 5.26E+09 1241 1512960 5.23E+09

1260 1518592 6.73E+09 1261 1485824 5.29E+09 1261 1484800 5.26E+09

1280 1476608 6.76E+09 1281 1457664 5.32E+09 1281 1457664 5.29E+09

1300 1437184 6.79E+09 1301 1430016 5.34E+09 1301 1431040 5.32E+09

1320 1397248 6.82E+09 1321 1403904 5.37E+09 1321 1403392 5.34E+09

1340 1358848 6.85E+09 1341 1378304 5.4E+09 1341 1377792 5.37E+09

1360 1322496 6.87E+09 1361 1353216 5.43E+09 1361 1353728 5.4E+09

1380 1286656 6.9E+09 1381 1329152 5.46E+09 1381 1329664 5.43E+09

1400 1251840 6.92E+09 1401 1305088 5.48E+09 1401 1305600 5.45E+09

1420 1218048 6.95E+09 1421 1281536 5.51E+09 1421 1282048 5.48E+09

1440 1186304 6.97E+09 1441 1259520 5.53E+09 1441 1260032 5.5E+09

1460 1155584 7E+09 1461 1236992 5.56E+09 1461 1238528 5.53E+09

1480 1125376 7.02E+09 1481 1214976 5.58E+09 1481 1216512 5.55E+09

224

1500 1097728 7.04E+09 1501 1194496 5.61E+09 1501 1196544 5.58E+09

1520 1069568 7.06E+09 1521 1174016 5.63E+09 1521 1176064 5.6E+09

1540 1042944 7.08E+09 1541 1154560 5.65E+09 1541 1156096 5.62E+09

1560 1017344 7.1E+09 1561 1135104 5.68E+09 1561 1136640 5.65E+09

1580 993280 7.12E+09 1581 1116160 5.7E+09 1581 1118720 5.67E+09

1600 968704 7.14E+09 1601 1098752 5.72E+09 1601 1099776 5.69E+09

1620 945152 7.16E+09 1621 1081344 5.74E+09 1621 1082880 5.71E+09

1640 922624 7.18E+09 1641 1064448 5.76E+09 1641 1067008 5.73E+09

1660 900608 7.2E+09 1661 1048064 5.78E+09 1661 1049600 5.76E+09

1680 879104 7.22E+09 1681 1032192 5.81E+09 1681 1034240 5.78E+09

1700 858624 7.23E+09 1701 1016832 5.83E+09 1701 1018368 5.8E+09

1720 838144 7.25E+09 1721 1000448 5.85E+09 1721 1003520 5.82E+09

1740 818176 7.27E+09 1741 986112 5.87E+09 1741 988160 5.84E+09

1760 799232 7.28E+09 1761 971264 5.89E+09 1761 973824 5.86E+09

1780 780800 7.3E+09 1781 956928 5.91E+09 1781 958976 5.88E+09

1800 763392 7.32E+09 1801 942592 5.92E+09 1801 945152 5.9E+09

1820 745984 7.33E+09 1821 928256 5.94E+09 1821 930816 5.91E+09

1840 729088 7.35E+09 1841 914944 5.96E+09 1841 917504 5.93E+09

1860 712704 7.36E+09 1861 901632 5.98E+09 1861 904704 5.95E+09

1880 696832 7.37E+09 1881 888832 6E+09 1881 890880 5.97E+09

1900 680448 7.39E+09 1901 875520 6.01E+09 1901 878592 5.99E+09

1920 665600 7.4E+09 1921 863744 6.03E+09 1921 866304 6E+09

1940 650752 7.41E+09 1941 850944 6.05E+09 1941 854528 6.02E+09

1960 636416 7.43E+09 1961 839168 6.07E+09 1961 841728 6.04E+09

1980 622592 7.44E+09 1981 827904 6.08E+09 1981 830464 6.05E+09

2000 609280 7.45E+09 2001 815616 6.1E+09 2001 818688 6.07E+09

2020 595968 7.46E+09 2021 804864 6.12E+09 2021 807424 6.09E+09

2040 583168 7.48E+09 2041 793088 6.13E+09 2041 796672 6.1E+09

2060 571392 7.49E+09 2061 782848 6.15E+09 2061 785408 6.12E+09

2080 558592 7.5E+09 2081 772096 6.16E+09 2081 775168 6.13E+09

2100 546304 7.51E+09 2101 761856 6.18E+09 2101 764416 6.15E+09

2120 535040 7.52E+09 2121 751616 6.19E+09 2121 754688 6.17E+09

2140 524288 7.53E+09 2141 741376 6.21E+09 2141 743936 6.18E+09

2160 513536 7.54E+09 2161 731136 6.22E+09 2161 734720 6.2E+09

2180 503296 7.55E+09 2181 721408 6.24E+09 2181 724992 6.21E+09

2200 492544 7.56E+09 2201 711680 6.25E+09 2201 715264 6.22E+09

2220 482816 7.57E+09 2221 702976 6.27E+09 2221 706560 6.24E+09

2240 473600 7.58E+09 2241 693248 6.28E+09 2241 696832 6.25E+09

2260 463872 7.59E+09 2261 684544 6.29E+09 2261 687616 6.27E+09

2280 455168 7.6E+09 2281 675840 6.31E+09 2281 678912 6.28E+09

2300 445952 7.61E+09 2301 666624 6.32E+09 2301 670720 6.29E+09

225

2320 437248 7.62E+09 2321 658944 6.33E+09 2321 662016 6.31E+09

2340 428544 7.63E+09 2341 650240 6.35E+09 2341 653312 6.32E+09

2360 420864 7.63E+09 2361 641536 6.36E+09 2361 645632 6.33E+09

2380 412672 7.64E+09 2381 634368 6.37E+09 2381 637440 6.35E+09

2400 404480 7.65E+09 2401 625664 6.39E+09 2401 629248 6.36E+09

2420 396800 7.66E+09 2421 617984 6.4E+09 2421 621568 6.37E+09

2440 389632 7.67E+09 2441 610816 6.41E+09 2441 613376 6.38E+09

2460 381952 7.67E+09 2461 603136 6.42E+09 2461 606720 6.4E+09

2480 375296 7.68E+09 2481 595456 6.43E+09 2481 599040 6.41E+09

2500 368128 7.69E+09 2501 588288 6.45E+09 2501 591360 6.42E+09

2520 360960 7.7E+09 2521 581632 6.46E+09 2521 584704 6.43E+09

2540 354816 7.7E+09 2541 574464 6.47E+09 2541 578048 6.44E+09

2560 348160 7.71E+09 2561 567296 6.48E+09 2561 570880 6.45E+09

2580 341504 7.72E+09 2581 560640 6.49E+09 2581 564736 6.47E+09

2600 335872 7.72E+09 2601 553984 6.5E+09 2601 557568 6.48E+09

2620 329728 7.73E+09 2621 547328 6.51E+09 2621 550912 6.49E+09

2640 324096 7.74E+09 2641 540672 6.52E+09 2641 544768 6.5E+09

2660 318976 7.74E+09 2661 534528 6.54E+09 2661 538624 6.51E+09

2680 313344 7.75E+09 2681 528384 6.55E+09 2681 532480 6.52E+09

2700 307200 7.76E+09 2701 522752 6.56E+09 2701 526336 6.53E+09

2720 302080 7.76E+09 2721 516608 6.57E+09 2721 519680 6.54E+09

2740 296448 7.77E+09 2741 509952 6.58E+09 2741 514048 6.55E+09

2760 291328 7.77E+09 2761 504320 6.59E+09 2761 508416 6.56E+09

2780 286208 7.78E+09 2781 499200 6.6E+09 2781 502272 6.57E+09

2800 281600 7.79E+09 2801 493568 6.61E+09 2801 496640 6.58E+09

2820 277504 7.79E+09 2821 487936 6.62E+09 2821 491520 6.59E+09

2840 272384 7.8E+09 2841 482304 6.63E+09 2841 485888 6.6E+09

2860 268288 7.8E+09 2861 477696 6.64E+09 2861 480768 6.61E+09

2880 263168 7.81E+09 2881 472064 6.65E+09 2881 475136 6.62E+09

2900 259072 7.81E+09 2901 467456 6.66E+09 2901 471040 6.63E+09

2920 254976 7.82E+09 2921 462336 6.66E+09 2921 464896 6.64E+09

2940 250880 7.82E+09 2941 457216 6.67E+09 2941 460288 6.65E+09

2960 246272 7.83E+09 2961 452608 6.68E+09 2961 455680 6.66E+09

2980 243200 7.83E+09 2981 448000 6.69E+09 2981 451072 6.67E+09

3000 238592 7.84E+09 3001 442368 6.7E+09 3001 445952 6.68E+09

3020 235520 7.84E+09 3021 437760 6.71E+09 3021 441344 6.68E+09

3040 230912 7.85E+09 3041 433152 6.72E+09 3041 436736 6.69E+09

3060 227840 7.85E+09 3061 429056 6.73E+09 3061 432128 6.7E+09

3080 223744 7.86E+09 3081 424960 6.74E+09 3081 427520 6.71E+09

3100 220672 7.86E+09 3101 419840 6.74E+09 3101 423424 6.72E+09

3120 217088 7.87E+09 3121 415744 6.75E+09 3121 418816 6.73E+09

226

3140 213504 7.87E+09 3141 411648 6.76E+09 3141 414720 6.74E+09

3160 210432 7.87E+09 3161 407552 6.77E+09 3161 410624 6.74E+09

3180 207360 7.88E+09 3181 402432 6.78E+09 3181 406016 6.75E+09

3200 204288 7.88E+09 3201 398848 6.79E+09 3201 401920 6.76E+09

3220 201216 7.89E+09 3221 394752 6.79E+09 3221 398336 6.77E+09

3240 197632 7.89E+09 3241 390656 6.8E+09 3241 394752 6.78E+09

3260 195072 7.89E+09 3261 387072 6.81E+09 3261 390656 6.78E+09

3280 191488 7.9E+09 3281 382976 6.82E+09 3281 386560 6.79E+09

3300 189440 7.9E+09 3301 379904 6.82E+09 3301 382976 6.8E+09

3320 185856 7.91E+09 3321 375808 6.83E+09 3321 378880 6.81E+09

3340 183296 7.91E+09 3341 371712 6.84E+09 3341 375296 6.82E+09

3360 180736 7.91E+09 3361 368640 6.85E+09 3361 371712 6.82E+09

3380 178176 7.92E+09 3381 365056 6.85E+09 3381 368640 6.83E+09

3400 175616 7.92E+09 3401 361472 6.86E+09 3401 364544 6.84E+09

3420 172544 7.92E+09 3421 358400 6.87E+09 3421 361472 6.84E+09

3440 170496 7.93E+09 3441 354304 6.88E+09 3441 357888 6.85E+09

3460 168448 7.93E+09 3461 350720 6.88E+09 3461 354304 6.86E+09

3480 166400 7.93E+09 3481 347136 6.89E+09 3481 351232 6.87E+09

3500 163328 7.94E+09 3501 344064 6.9E+09 3501 347648 6.87E+09

3520 161280 7.94E+09 3521 341504 6.9E+09 3521 344064 6.88E+09

3540 158720 7.94E+09 3541 337920 6.91E+09 3541 340992 6.89E+09

3560 156672 7.95E+09 3561 334848 6.92E+09 3561 337920 6.89E+09

3580 154112 7.95E+09 3581 331776 6.92E+09 3581 334848 6.9E+09

3600 152576 7.95E+09 3601 328192 6.93E+09 3601 331776 6.91E+09

3620 150016 7.96E+09 3621 326144 6.94E+09 3621 328192 6.91E+09

3640 148480 7.96E+09 3641 322560 6.94E+09 3641 325632 6.92E+09

3660 145408 7.96E+09 3661 318976 6.95E+09 3661 323072 6.93E+09

3680 143872 7.96E+09 3681 316416 6.96E+09 3681 320000 6.93E+09

3700 142336 7.97E+09 3701 313856 6.96E+09 3701 316928 6.94E+09

3720 140288 7.97E+09 3721 311808 6.97E+09 3721 313344 6.95E+09

3740 138752 7.97E+09 3741 307712 6.97E+09 3741 311296 6.95E+09

3760 136704 7.98E+09 3761 305152 6.98E+09 3761 308736 6.96E+09

3780 135168 7.98E+09 3781 302592 6.99E+09 3781 305664 6.96E+09

3800 133120 7.98E+09 3801 300032 6.99E+09 3801 302592 6.97E+09

3820 131072 7.98E+09 3821 297472 7E+09 3821 300544 6.98E+09

3840 129536 7.99E+09 3841 294400 7E+09 3841 297472 6.98E+09

3860 128000 7.99E+09 3861 291840 7.01E+09 3861 295424 6.99E+09

3880 126464 7.99E+09 3881 289280 7.02E+09 3881 292352 6.99E+09

3900 124416 7.99E+09 3901 286720 7.02E+09 3901 289792 7E+09

3920 122368 8E+09 3921 284672 7.03E+09 3921 286720 7.01E+09

3940 121856 8E+09 3941 282112 7.03E+09 3941 284672 7.01E+09

227

3960 119808 8E+09 3961 279552 7.04E+09 3961 282624 7.02E+09

3980 117760 8E+09 3981 277504 7.04E+09 3981 280576 7.02E+09

4000 116736 8.01E+09 4001 274432 7.05E+09 4001 277504 7.03E+09

4020 114688 8.01E+09 4021 272384 7.06E+09 4021 275968 7.03E+09

4040 113664 8.01E+09 4041 270336 7.06E+09 4041 272896 7.04E+09

4060 111616 8.01E+09 4061 267776 7.07E+09 4061 270848 7.04E+09

4080 110592 8.02E+09 4081 265216 7.07E+09 4081 268288 7.05E+09

4100 109568 8.02E+09 4101 263680 7.08E+09 4101 266240 7.06E+09

4120 108032 8.02E+09 4121 261120 7.08E+09 4121 264192 7.06E+09

4140 106496 8.02E+09 4141 259072 7.09E+09 4141 261632 7.07E+09

4160 105472 8.02E+09 4161 257024 7.09E+09 4161 260096 7.07E+09

4180 103936 8.03E+09 4181 254976 7.1E+09 4181 257536 7.08E+09

4200 102400 8.03E+09 4201 252416 7.1E+09 4201 255488 7.08E+09

4220 101376 8.03E+09 4221 250880 7.11E+09 4221 252928 7.09E+09

4240 99840 8.03E+09 4241 247808 7.11E+09 4241 250880 7.09E+09

4260 98816 8.03E+09 4261 246272 7.12E+09 4261 248320 7.1E+09

4280 97792 8.04E+09 4281 243712 7.12E+09 4281 247808 7.1E+09

4300 96256 8.04E+09 4301 242688 7.13E+09 4301 245248 7.11E+09

4320 95232 8.04E+09 4321 240128 7.13E+09 4321 243712 7.11E+09

4340 94208 8.04E+09 4341 238592 7.14E+09 4341 241152 7.12E+09

4360 92672 8.04E+09 4361 236544 7.14E+09 4361 239616 7.12E+09

4380 91648 8.05E+09 4381 234496 7.15E+09 4381 237568 7.13E+09

4400 91136 8.05E+09 4401 232960 7.15E+09 4401 235008 7.13E+09

4420 89600 8.05E+09 4421 230400 7.16E+09 4421 233472 7.14E+09

4440 88064 8.05E+09 4441 229376 7.16E+09 4441 231936 7.14E+09

4460 87552 8.05E+09 4461 226816 7.17E+09 4461 229888 7.14E+09

4480 86528 8.05E+09 4481 225280 7.17E+09 4481 228352 7.15E+09

4500 84992 8.06E+09 4501 223744 7.17E+09 4501 226304 7.15E+09

4520 84480 8.06E+09 4521 221696 7.18E+09 4521 224256 7.16E+09

4540 83968 8.06E+09 4541 219648 7.18E+09 4541 222208 7.16E+09

4560 82432 8.06E+09 4561 218624 7.19E+09 4561 221184 7.17E+09

4580 81408 8.06E+09 4581 216576 7.19E+09 4581 219136 7.17E+09

4600 80896 8.06E+09 4601 215552 7.2E+09 4601 217600 7.18E+09

4620 79872 8.07E+09 4621 213504 7.2E+09 4621 216064 7.18E+09

4640 78336 8.07E+09 4641 211968 7.2E+09 4641 214016 7.18E+09

4660 77312 8.07E+09 4661 210432 7.21E+09 4661 212992 7.19E+09

4680 76800 8.07E+09 4681 209408 7.21E+09 4681 210944 7.19E+09

4700 75776 8.07E+09 4701 206336 7.22E+09 4701 209920 7.2E+09

4720 75264 8.07E+09 4721 205312 7.22E+09 4721 207872 7.2E+09

4740 74240 8.08E+09 4741 203776 7.23E+09 4741 206336 7.21E+09

4760 73728 8.08E+09 4761 202240 7.23E+09 4761 205312 7.21E+09

228

4780 72704 8.08E+09 4781 200704 7.23E+09 4781 203776 7.21E+09

4800 72192 8.08E+09 4801 199680 7.24E+09 4801 201728 7.22E+09

4820 71168 8.08E+09 4821 197632 7.24E+09 4821 200192 7.22E+09

4840 70144 8.08E+09 4841 196608 7.25E+09 4841 199168 7.23E+09

4860 69120 8.08E+09 4861 195072 7.25E+09 4861 197120 7.23E+09

4880 68608 8.09E+09 4881 193536 7.25E+09 4881 196096 7.23E+09

4900 67584 8.09E+09 4901 192000 7.26E+09 4901 194560 7.24E+09

4920 67072 8.09E+09 4921 190464 7.26E+09 4921 193024 7.24E+09

4940 66560 8.09E+09 4941 188928 7.26E+09 4941 191488 7.25E+09

4960 65536 8.09E+09 4961 188416 7.27E+09 4961 190464 7.25E+09

4980 65024 8.09E+09 4981 186880 7.27E+09 4981 188928 7.25E+09

5000 64000 8.09E+09 5001 184832 7.28E+09 5001 186880 7.26E+09

Case Study 4-D

pi=12,300 psia, T=200F, SG=0.55


t(day) qsc(SCFD) pwf(psia) t(day) qsc(SCFD) pwf(psia) t(day) qsc(SCFD) pwf(psia)

1 5000000 9433.33 1 5000000 9215.77 1 5000000 9185.39

11 4999996 8739.1 11 4999996 8520.15 11 4999996 8488.69

21 5000000 8552.84 21 5000000 8313 21 5000000 8272.24

31 5000000 8438.66 31 5000000 8148.65 31 5000000 8092.67

41 5000000 8349.96 41 5000000 7991.19 41 5000000 7918.62

51 5000000 8271.21 51 5000000 7835.46 51 5000000 7746.64

61 5000000 8196.4 61 5000000 7681.06 61 5000000 7577.83

71 5000032 8123.09 71 5000032 7529.67 71 5000032 7414.08

81 5000000 8050.25 81 5000000 7381.46 81 5000000 7252.52

91 5000000 7977.53 91 5000000 7234.36 91 5000000 7092.05

101 4000000 8459.77 101 4000000 7676.02 101 4000000 7524.43

111 4000000 8551.66 110 4000000 7711.96 110 4000000 7552.05

121 4000000 8516.42 120 4000000 7611.6 120 4000000 7444.23

131 4000000 8466.7 130 4000000 7501.48 130 4000000 7327.55

141 4000000 8411.89 140 4000000 7391.75 140 4000000 7209.73

151 4000000 8355.23 150 4000000 7282.41 150 4000000 7092.08

161 4000000 8298.03 160 3999936 7173.29 160 3999936 6974.86

171 4000000 8240.58 170 4000064 7064.41 170 4000064 6858.69

181 4000000 8182.97 180 4000000 6955.9 180 4000000 6744.1

191 4000000 8125.2 190 4000000 6848.17 190 4000000 6632.75

201 2000000 9176.31 200 4000000 6741.65 200 4000000 6523.59

210 2000000 9440.45 209 2000000 8136.68 209 2000000 7923.76

220 2000000 9462.88 219 2000000 8125.52 219 2000000 7908.13

230 1999936 9452.36 229 2000064 8083.61 229 2000064 7861.96

229

240 2000000 9430.61 239 2000000 8035.35 239 2000000 7810.08

250 2000000 9404.48 249 2000000 7985.69 249 2000000 7757.17

260 2000000 9376.58 259 2000000 7935.74 259 2000000 7704.17

270 2000000 9347.96 269 1999936 7885.73 269 1999936 7651.35

280 2000000 9319.05 279 2000000 7835.73 279 2000000 7598.83

290 2000000 9290.02 289 2000000 7785.77 289 2000000 7546.74

300 2000000 9260.94 299 2000000 7735.9 299 2000000 7495.28

310 2000000 9231.84 309 2000000 7686.15 309 2000000 7444.99

320 2000000 9202.75 319 2000000 7636.59 319 2000000 7396.08

330 2000000 9173.69 329 2000000 7587.28 329 2000000 7347.65

340 2000000 9144.67 339 2000000 7538.33 339 2000000 7299.34

350 2000000 9115.73 349 2000000 7489.93 349 2000000 7251.06

359 3000064 8383.52 358 3000064 6711.8 358 3000064 6467.17

369 2999936 8311.52 368 2999936 6616.01 368 2999936 6368.91

379 2999936 8258.2 378 3000064 6540.43 378 3000064 6290.22

389 3000064 8211.02 388 3000064 6469.43 388 3000064 6215.88

399 2999936 8166.21 398 2999936 6399.57 398 2999936 6142.77

408 3999872 7422.74 407 4000000 5594.66 407 4000000 5328.73

418 4000000 7331.15 417 4000000 5467.67 417 4000000 5197.7

428 4000000 7261.32 427 4000000 5365.51 427 4000000 5092.51

438 4000000 7198.31 437 4000000 5269.2 437 4000000 4994.39

448 3999872 7137.87 447 4000128 5174.81 447 4000128 4900.2

458 4000000 7078.35 457 4000000 5081.31 457 4000000 4807.72

468 4000000 7019.09 467 4000000 4989.31 467 4000000 4715.67

478 4000000 6959.91 477 4000000 4899.46 477 4000000 4623.71

488 4000000 6900.73 487 3999872 4810.7 487 3999872 4531.32

498 4000000 6841.53 497 4000000 4722.16 497 4000000 4439.06

507 1000064 8877.53 506 1000064 6846.96 506 1000064 6582

517 1000064 8973.73 516 999936 6947.34 516 999936 6679.96

527 999936 8996.21 526 999936 6955.52 526 999936 6688.93

537 999936 8996.55 536 999936 6942.99 536 999936 6676.44

547 999936 8988.28 546 999936 6924.67 546 999936 6657.99

557 999936 8976.52 556 1000064 6904.69 556 1000064 6637.97

567 1000064 8963.32 566 1000064 6884.24 566 1000064 6617.67

577 1000192 8949.52 576 999936 6863.65 576 999936 6597.56

587 1000064 8935.47 586 1000064 6843.04 586 1000064 6577.96

597 1000064 8921.32 596 1000064 6822.42 596 1000064 6558.76

607 999936 8907.11 606 999936 6801.81 606 999936 6539.71

617 999936 8892.88 616 999936 6781.23 616 999936 6520.7

627 999936 8878.63 626 999936 6760.68 626 999936 6501.71

637 999936 8864.36 636 999936 6740.17 636 999936 6482.72

230

647 999936 8850.08 646 1000064 6719.71 646 1000064 6463.72

656 4000000 6775.55 655 3999872 4531.93 655 3999872 4250.6

666 4000000 6584.55 665 4000000 4286.13 665 4000000 4000.81

676 4000000 6483.44 675 4000000 4158.6 675 4000000 3871.96

686 4000000 6407.85 685 4000000 4059.7 685 4000000 3771.53

696 4000000 6341.94 695 4000000 3970.72 695 4000000 3679.3

706 4000128 6279.83 705 4000000 3884.88 705 4000000 3589.8

716 4000000 6219.03 715 4000000 3799.9 715 4000000 3501.11

726 4000000 6158.74 725 4000000 3714.4 725 4000000 3412.38

736 4000000 6098.6 735 4000000 3628.55 735 4000000 3323.31

746 4000000 6038.47 745 4000000 3542.47 745 4000000 3234.44

756 4000000 5978.3 755 4000000 3456.18 755 4000000 3145.66

766 4000000 5918.05 765 4000000 3369.15 765 4000000 3058.1

776 4000000 5857.99 775 4000000 3282.01 775 4000000 2971.77

786 4000000 5798.25 785 4000000 3194.89 785 4000000 2885.24

796 4000000 5738.61 795 4000000 3108.11 795 4000000 2797.73

806 4000000 5678.91 805 4000000 3022.58 805 4000000 2709.43

816 4000000 5619.01 815 4000256 2937.87 815 4000256 2620.23

826 4000000 5558.9 825 4000000 2852.02 825 4000000 2529.98

836 4000000 5498.57 835 4000000 2765.42 835 4000000 2437.73

846 4000000 5437.95 845 4000000 2677.94 845 4000000 2344.38

856 4000000 5376.96 855 4000000 2589.52 855 4000000 2249.74

866 3999744 5315.77 865 4000000 2499.64 865 4000000 2153.53

876 4000000 5254.41 875 4000000 2408.02 875 4000000 2056.17

886 3999744 5192.89 885 4000256 2315.3 885 4000256 1956.2

896 4000000 5131.18 895 4000000 2221 895 4000000 1855.36

905 999936 7167.5 904 999936 4641.31 904 999936 4390.28

915 1000192 7305.42 914 999680 4831.67 914 999680 4598.56

925 999936 7337.29 924 999936 4872.26 924 999936 4644.55

935 1000192 7341.46 934 999936 4878.76 934 999936 4654.08

945 999680 7334.94 944 1000192 4872.8 944 1000192 4649.56

955 999936 7324.02 954 1000192 4861.8 954 1000192 4639.1

965 999936 7311.25 964 999936 4848.64 964 999936 4626.08

975 999680 7297.71 974 1000192 4834.56 974 1000192 4611.97

985 999936 7283.84 984 999936 4820.07 984 999936 4597.37

995 999680 7269.82 994 1000192 4805.42 994 1000192 4582.56

1004 3000064 5909.85 1003 3000064 3308.55 1003 3000064 3052.1

1014 3000064 5739.01 1013 3000064 3052.62 1013 3000064 2781.1

1024 3000064 5658.82 1023 3000064 2943.87 1023 3000064 2665.9

1034 3000064 5600.34 1033 2999808 2866.37 1033 2999808 2583.77

1044 2999808 5550.04 1043 3000064 2800.95 1043 3000064 2514.43

231

1054 3000064 5502.93 1053 3000064 2740.51 1053 3000064 2450.32

1064 3000064 5457.03 1063 3000064 2681.56 1063 3000064 2388.34

1074 3000064 5411.58 1073 3000064 2623.14 1073 3000064 2326.92

1084 3000064 5366.24 1083 2999808 2564.76 1083 2999808 2265.53

1094 3000064 5320.89 1093 2999808 2505.9 1093 2999808 2203.83

1104 2999552 5275.38 1103 3000064 2446.59 1103 3000064 2141.64

1114 3000064 5229.75 1113 3000064 2386.77 1113 3000064 2078.28

1124 3000064 5184.04 1123 3000064 2326.33 1123 3000064 2014.44

1134 2999808 5138.23 1133 3000064 2265.35 1133 3000064 1950.25

1144 3000064 5092.35 1143 2999808 2203.8 1143 2999808 1886

1154 2999808 5046.45 1153 3000064 2141.61 1153 3000064 1821.97

1164 3000064 5000.58 1163 3000064 2078.15 1163 3000064 1757.43

1174 3000064 4954.86 1173 3000064 2014.16 1173 3000064 1691.68

1184 3000064 4909.5 1183 3000064 1949.75 1183 3000064 1624.8

1194 3000064 4864.34 1193 2999808 1885.23 1193 2999808 1556.55

1203 2000128 5509.88 1202 1999872 2762.47 1202 1999872 2508.96

1213 1999872 5560.53 1212 2000384 2882.12 1212 2000384 2640.04

1223 2000128 5551.76 1222 2000128 2885.32 1222 2000128 2646.23

1233 2000128 5530.58 1232 1999872 2868.94 1232 1999872 2630.75

1243 1999872 5504.69 1242 1999872 2844.74 1242 1999872 2606.62

1253 1999872 5476.8 1252 1999872 2816.8 1252 1999872 2578.31

1263 1999872 5448.03 1262 1999872 2786.92 1262 1999872 2547.82

1273 1999872 5418.82 1272 1999872 2755.98 1272 1999872 2516.16

1283 2000128 5389.4 1282 2000128 2724.49 1282 2000128 2483.83

1293 2000128 5359.85 1292 2000128 2692.58 1292 2000128 2451.08

1303 1999872 5330.18 1302 2000384 2660.41 1302 2000384 2418.04

1313 2000128 5300.45 1312 2000128 2628.02 1312 2000128 2384.78

1323 2000128 5270.64 1322 1999872 2595.44 1322 1999872 2351.34

1333 1999872 5240.77 1332 1999872 2562.67 1332 1999872 2317.73

1343 1999872 5210.83 1342 1999872 2529.74 1342 1999872 2283.97

1353 1999872 5180.85 1352 1999872 2496.63 1352 1999872 2250.03

1363 1999872 5150.82 1362 2000128 2463.35 1362 2000128 2215.71

1373 2000128 5120.76 1372 2000128 2429.91 1372 2000128 2181.25

1383 2000384 5090.67 1382 1999872 2396.31 1382 1999872 2146.68

1393 2000128 5060.58 1392 2000128 2362.54 1392 2000128 2112.01

1403 2000128 5030.49 1402 1999872 2328.61 1402 1999872 2077.27

1413 1999872 5000.43 1412 1999872 2294.53 1412 1999872 2042.48

1423 1999872 4970.43 1422 1999872 2260.31 1422 1999872 2007.58

1433 1999872 4940.55 1432 1999872 2225.68 1432 1999872 1972.63

1443 1999872 4910.93 1442 1999872 2190.87 1442 1999872 1937.96

1453 2000128 4881.59 1452 2000128 2155.92 1452 2000128 1903.51

232

1463 2000128 4852.38 1462 2000128 2120.86 1462 2000128 1869.08

1473 1999872 4823.18 1472 2000384 2085.7 1472 2000384 1834.35

1483 2000128 4793.94 1482 2000128 2050.48 1482 2000128 1799.38

1493 2000128 4764.6 1492 1999872 2015.18 1492 1999872 1764.12

1503 1999872 4735.13 1502 1999872 1979.72 1502 1999872 1728.43

1513 1999872 4705.57 1512 1999872 1944.5 1512 1999872 1692.31

1523 1999872 4675.93 1522 1999872 1909.53 1522 1999872 1655.77

1533 1999872 4646.2 1532 2000128 1874.6 1532 2000128 1618.7

1543 2000128 4616.36 1542 2000128 1839.39 1542 2000128 1581.14

1553 1999872 4586.37 1552 1999872 1803.92 1552 1999872 1543.02

1563 1999872 4556.29 1562 2000384 1768.15 1562 2000384 1504.34

1573 1999872 4526.13 1572 2000384 1731.95 1572 2000384 1465.04

1583 1999872 4495.83 1582 2000384 1695.27 1582 2000384 1425.1

1593 1999872 4465.45 1592 1999872 1658.17 1592 1999872 1384.46

1603 2000384 4434.96 1602 1999872 1620.52 1602 1999872 1342.99

1613 1999872 4404.38 1612 1999872 1582.36 1612 1999872 1300.47

1623 1999872 4373.7 1622 1999872 1543.61 1622 1999872 1257.07

1633 1999872 4342.95 1632 1999872 1504.27 1632 1999872 1212.74

1643 1999872 4312.11 1642 2000384 1464.28 1642 2000384 1167.41

1653 1999872 4281.2 1652 1999872 1423.63 1652 1999872 1121

1663 1999872 4250.23 1662 1999872 1382.24 1662 1999872 1073.42

1673 1999872 4219.2 1672 1999872 1339.96 1672 1999872 1024.55

1683 1999872 4188.14 1682 2000384 1296.59 1682 2000384 974.06

1693 1999872 4157.05 1692 1999872 1252.31 1692 1999872 921.77

1703 2000384 4125.96 1702 1999872 1207.05 1702 1999872 867.72

1713 2000384 4094.9 1712 1999872 1160.73 1712 1999872 811.72

1723 2000384 4063.92 1722 1999872 1113.27 1722 1999872 753.52

1733 1999872 4033.11 1732 1999872 1064.56 1732 1999872 692.66

1743 1999872 4002.63 1742 2000384 1014.48 1742 2000384 628.75

1753 1999872 3972.36 1752 1999872 962.59 1752 1999872 561.52

1763 1999872 3942.13 1762 2000384 908.87 1762 2000384 490.4

1773 2000384 3911.75 1772 2000384 853.27 1772 2000384 414.45

1783 2000384 3881.28 1782 1999872 795.55 1782 1999872 332.84

1793 2000384 3850.7 1792 1999872 735.47 1792 1999872 244.55

Case Study 4-E

pi=12,300 psia, T=200F, SG=0.55

Cr=5.00E-05 1/psi Cr=1.00E-012 1/psi

t(day) qsc(SCFD) Gp(SCF) pwf(psia) t(day) qsc(SCFD) Gp(SCF) pwf(psia)

1 12293744 13464423 5000 1 11380937 12397046 5000

5 10660156 57822764 5000 5 9964124 53754020 5000

233

10 10063496 1.09E+08 5000 10 9433792 1.02E+08 5000

15 9747776 1.58E+08 5000 15 9130320 1.48E+08 5000

20 9536208 2.07E+08 5000 20 8893792 1.93E+08 5000

30 9246304 3E+08 5000 30 8483200 2.8E+08 5000

40 9030784 3.91E+08 5000 40 8110496 3.62E+08 5000

50 8843104 4.81E+08 5000 50 7767840 4.42E+08 5000

60 8667264 5.68E+08 5000 60 7446016 5.17E+08 5000

70 8497664 6.54E+08 5000 70 7144320 5.9E+08 5000

80 8331968 7.38E+08 5000 80 6865216 6.6E+08 5000

90 8170048 8.2E+08 5000 90 6602496 7.27E+08 5000

100 8011904 9.01E+08 5000 100 6353216 7.92E+08 5000

110 7857088 9.8E+08 5000 110 6118016 8.54E+08 5000

120 7705024 1.06E+09 5000 120 5899328 9.14E+08 5000

130 7555712 1.13E+09 5000 130 5693184 9.72E+08 5000

140 7409024 1.21E+09 5000 140 5496384 1.03E+09 5000

150 7265152 1.28E+09 5000 150 5308288 1.08E+09 5000

160 7124096 1.35E+09 5000 160 5129472 1.13E+09 5000

170 6986368 1.42E+09 5000 170 4961152 1.18E+09 5000

180 6851584 1.49E+09 5000 180 4803584 1.23E+09 5000

190 6719488 1.56E+09 5000 190 4652800 1.28E+09 5000

200 6589440 1.63E+09 5000 200 4507648 1.33E+09 5000

210 6461824 1.69E+09 5000 210 4368256 1.37E+09 5000

220 6336640 1.76E+09 5000 220 4234240 1.41E+09 5000

230 6213632 1.82E+09 5000 230 4105984 1.45E+09 5000

240 6093312 1.88E+09 5000 240 3984256 1.5E+09 5000

250 5975936 1.94E+09 5000 250 3869824 1.53E+09 5000

260 5861376 2E+09 5000 260 3760896 1.57E+09 5000

270 5748992 2.06E+09 5000 270 3655936 1.61E+09 5000

280 5638272 2.12E+09 5000 280 3554048 1.65E+09 5000

290 5529856 2.17E+09 5000 290 3455744 1.68E+09 5000

300 5423360 2.23E+09 5000 300 3360512 1.71E+09 5000

304 9037056 2.26E+09 2000 304 6872704 1.74E+09 2000

314 8551936 2.35E+09 2000 314 6409728 1.81E+09 2000

324 8312576 2.44E+09 2000 324 6186752 1.87E+09 2000

334 8125952 2.52E+09 2000 334 6011008 1.93E+09 2000

344 7959552 2.6E+09 2000 344 5854720 1.99E+09 2000

354 7801856 2.68E+09 2000 354 5708672 2.05E+09 2000

364 7650048 2.75E+09 2000 364 5568768 2.11E+09 2000

374 7500800 2.83E+09 2000 374 5433856 2.16E+09 2000

384 7355392 2.9E+09 2000 384 5303552 2.21E+09 2000

394 7212288 2.98E+09 2000 394 5178112 2.27E+09 2000

234

404 7072768 3.05E+09 2000 404 5057280 2.32E+09 2000

414 6936832 3.12E+09 2000 414 4941824 2.37E+09 2000

424 6804224 3.19E+09 2000 424 4833024 2.42E+09 2000

434 6674176 3.25E+09 2000 434 4728832 2.46E+09 2000

444 6546176 3.32E+09 2000 444 4628224 2.51E+09 2000

454 6420736 3.38E+09 2000 454 4530688 2.56E+09 2000

464 6297600 3.45E+09 2000 464 4436224 2.6E+09 2000

474 6177024 3.51E+09 2000 474 4343808 2.65E+09 2000

484 6058752 3.57E+09 2000 484 4254208 2.69E+09 2000

494 5943552 3.63E+09 2000 494 4167168 2.73E+09 2000

503 6779392 3.69E+09 800 503 4989952 2.77E+09 800

513 6551552 3.75E+09 800 513 4790272 2.82E+09 800

523 6405632 3.82E+09 800 523 4674560 2.87E+09 800

533 6275328 3.88E+09 800 533 4576768 2.91E+09 800

543 6152192 3.94E+09 800 543 4487936 2.96E+09 800

553 6033664 4E+09 800 553 4403712 3E+09 800

563 5917952 4.06E+09 800 563 4322560 3.05E+09 800

573 5804800 4.12E+09 800 573 4243200 3.09E+09 800

583 5694464 4.18E+09 800 583 4166656 3.13E+09 800

593 5587456 4.24E+09 800 593 4091648 3.17E+09 800

603 5483520 4.29E+09 800 603 4018688 3.21E+09 800

613 5381632 4.35E+09 800 613 3947264 3.25E+09 800

623 5281792 4.4E+09 800 623 3878144 3.29E+09 800

633 5183488 4.45E+09 800 633 3810816 3.33E+09 800

643 5087232 4.5E+09 800 643 3745536 3.37E+09 800

653 4992512 4.55E+09 800 653 3682048 3.41E+09 800

663 4900352 4.6E+09 800 663 3620864 3.44E+09 800

673 4809216 4.65E+09 800 673 3562496 3.48E+09 800

683 4720640 4.7E+09 800 683 3506432 3.51E+09 800

693 4633088 4.75E+09 800 693 3451904 3.55E+09 800

703 4550144 4.79E+09 800 703 3398656 3.58E+09 800

713 4468224 4.84E+09 800 713 3347200 3.62E+09 800

723 4388352 4.88E+09 800 723 3296000 3.65E+09 800

733 4311040 4.92E+09 800 733 3246080 3.68E+09 800

743 4234240 4.97E+09 800 743 3197184 3.71E+09 800

753 4158464 5.01E+09 800 753 3149568 3.75E+09 800

763 4084736 5.05E+09 800 763 3102720 3.78E+09 800

773 4012032 5.09E+09 800 773 3056384 3.81E+09 800

783 3940352 5.13E+09 800 783 3012096 3.84E+09 800

793 3871232 5.17E+09 800 793 2967808 3.87E+09 800

803 3802624 5.21E+09 800 803 2924800 3.9E+09 800

235

813 3735040 5.25E+09 800 813 2882560 3.93E+09 800

823 3670016 5.28E+09 800 823 2841344 3.95E+09 800

833 3606016 5.32E+09 800 833 2801152 3.98E+09 800

843 3544064 5.35E+09 800 843 2761728 4.01E+09 800

853 3484160 5.39E+09 800 853 2723328 4.04E+09 800

863 3425280 5.42E+09 800 863 2685952 4.06E+09 800

873 3367424 5.46E+09 800 873 2650112 4.09E+09 800

883 3311616 5.49E+09 800 883 2615040 4.12E+09 800

893 3255808 5.52E+09 800 893 2580992 4.14E+09 800

903 3201024 5.56E+09 800 903 2548480 4.17E+09 800

913 3147776 5.59E+09 800 913 2516224 4.19E+09 800

923 3095552 5.62E+09 800 923 2484736 4.22E+09 800

933 3043328 5.65E+09 800 933 2453760 4.24E+09 800

943 2991616 5.68E+09 800 943 2423040 4.27E+09 800

953 2942464 5.71E+09 800 953 2393344 4.29E+09 800

963 2893824 5.74E+09 800 963 2363904 4.32E+09 800

973 2845696 5.77E+09 800 973 2334720 4.34E+09 800

983 2798080 5.8E+09 800 983 2306048 4.36E+09 800

993 2752000 5.82E+09 800 993 2278912 4.39E+09 800

1001 1767824 5.84E+09 2000 1000.492 1199797 4.4E+09 2000

1011 1928192 5.86E+09 2000 1010 1473024 4.42E+09 2000

1021 1924096 5.88E+09 2000 1020 1491456 4.43E+09 2000

1031 1904128 5.9E+09 2000 1030 1488384 4.45E+09 2000

1041 1879040 5.92E+09 2000 1040 1478144 4.46E+09 2000

1051 1852928 5.94E+09 2000 1050 1464832 4.48E+09 2000

1061 1825792 5.96E+09 2000 1060 1449984 4.49E+09 2000

1071 1798144 5.98E+09 2000 1070 1434112 4.5E+09 2000

1081 1771008 5.99E+09 2000 1080 1418240 4.52E+09 2000

1091 1744896 6.01E+09 2000 1090 1401856 4.53E+09 2000

1101 1718784 6.03E+09 2000 1100 1385472 4.55E+09 2000

1111 1692672 6.05E+09 2000 1110 1370112 4.56E+09 2000

1121 1667584 6.06E+09 2000 1120 1354752 4.57E+09 2000

1131 1641984 6.08E+09 2000 1130 1339392 4.59E+09 2000

1141 1616896 6.1E+09 2000 1140 1323520 4.6E+09 2000

1151 1592832 6.11E+09 2000 1150 1309184 4.61E+09 2000

1161 1568256 6.13E+09 2000 1160 1293824 4.63E+09 2000

1171 1545216 6.14E+09 2000 1170 1279488 4.64E+09 2000

1181 1522176 6.16E+09 2000 1180 1265152 4.65E+09 2000

1191 1499136 6.17E+09 2000 1190 1251328 4.67E+09 2000

1201 2558464 6.19E+09 1000 1200 1237504 4.68E+09 1000

1210 2101760 6.21E+09 1000 1209 1893376 4.7E+09 1000

236

1220 2043392 6.23E+09 1000 1219 1837056 4.71E+09 1000

1230 2001920 6.25E+09 1000 1229 1802240 4.73E+09 1000

1240 1967616 6.27E+09 1000 1239 1775616 4.75E+09 1000

1250 1935360 6.29E+09 1000 1249 1751552 4.77E+09 1000

1260 1905664 6.31E+09 1000 1259 1730560 4.79E+09 1000

1270 1875968 6.33E+09 1000 1269 1710592 4.8E+09 1000

1280 1847296 6.35E+09 1000 1279 1691648 4.82E+09 1000

1290 1819648 6.36E+09 1000 1289 1673216 4.84E+09 1000

1300 1792512 6.38E+09 1000 1299 1655808 4.85E+09 1000

1310 1765376 6.4E+09 1000 1309 1638400 4.87E+09 1000

1320 1739776 6.42E+09 1000 1319 1622528 4.89E+09 1000

1330 1714176 6.43E+09 1000 1329 1606144 4.9E+09 1000

1340 1689088 6.45E+09 1000 1339 1590272 4.92E+09 1000

1350 1664512 6.47E+09 1000 1349 1574400 4.93E+09 1000

1360 1640448 6.48E+09 1000 1359 1558528 4.95E+09 1000

1370 1617920 6.5E+09 1000 1369 1543680 4.96E+09 1000

1380 1594880 6.52E+09 1000 1379 1528832 4.98E+09 1000

1390 1572864 6.53E+09 1000 1389 1513984 5E+09 1000

1400 1551872 6.55E+09 1000 1399 1499136 5.01E+09 1000

1410 1530368 6.56E+09 1000 1409 1484800 5.03E+09 1000

1420 1508864 6.58E+09 1000 1419 1470464 5.04E+09 1000

1430 1487872 6.59E+09 1000 1429 1456640 5.05E+09 1000

1440 1466368 6.61E+09 1000 1439 1441792 5.07E+09 1000

1450 1447424 6.62E+09 1000 1449 1428992 5.08E+09 1000

1460 1426944 6.64E+09 1000 1459 1414656 5.1E+09 1000

1470 1406976 6.65E+09 1000 1469 1401344 5.11E+09 1000

1480 1387520 6.67E+09 1000 1479 1388032 5.13E+09 1000

1490 1369600 6.68E+09 1000 1489 1375232 5.14E+09 1000

1500 1350656 6.69E+09 1000 1499 1362432 5.15E+09 1000

Documents

VARIABLE PRESSURE-DROP/FLOW-RATE SYSTEM ANALYSIS OF