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Applied Reservoir Simulation by Dr. Tayyar Sezgin DALTABAN 1 - 1

Chapter 1 Introduction

1.1 Overview

Numerical simulators have come to play an increasingly important role in theoil industry. Knowledge of their use, strengths and limitations as tools for the

evaluation and prediction of reservoir performance is valuable for

understanding and m1anaging petroleum reservoirs.

Prior to simulation, hand calculation methods were the basis for reservoir

management. Essentially, this required that elements of the overall problem

were de-coupled. Zero dimensional material balances, one and two-

dimensional flow analyses in single and two-phase flow, well performance and

lift were studied as separate independent problems. Success in applying the

highly idealized models depended on the engineer's skill in recognizing the

degree and the effects of interdependence and integrated concept of the wholeoperation.

The advent of computer simulation, enabling full coupling of all elements of

the system, with increasingly detailed characterization of the reservoir, has

changed the situation dramatically. Now many difficult development scenarios

can be applied to several different geological interpretations so that key

uncertainties can be identified and data acquisition programs defined.

The situation has changed from one where much of the available data was used

only intuitively (through a highly personal 'expert system') to one where the

modern system can accommodate explicitly more data than is generally

available. This has the additional advantage that feed back is now possible, theoutcome or implications of particular interpretations can be fed back to

individual specialists for revision or confirmation. The continued

developments in mathematical methods of manipulating equations (Finite

1.


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Introduction


Figure 1-1:

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o o o o

C o r e

S e is m i c O u tc r o p P o r e S c a le

W e l l te s t W e l l L o g s

D a t a U p s c a l i n g / D o w n s c a l i n g

I n t e g r a t io n

, t )P (re

P (rw , t )

F in i te E le m e n t M e s h

F in i t e D if f e r e n c e M e s h

f o r M a c r o - F lo w

ii + 1


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Introduction

1 - 4 Applied Reservoir Simulation by Dr. Tayyar Sezgin DALTABAN

Figure 1-2:

Discovery 2D Standard Core Pressure PVT Well

Phase Seismic Well Log Measurements Measurements Analysis Tests

No?

Abandon

Field

Upscaling

ProductionPlanning

Reservoir

Simulation

O.K?

No!

Appraisal

Yes!Iterate?

Yes!

The Role of Simulation at Different Stages of Field Development

Appraisal 3D Production Interference Outcrop Tracer

Stage Seismic Logging Testing Surveys Testing

Upscaling

Revised

Production

Strategy

Update

Reservoir

Simulation

O.K?

No!

Appraisal

Yes!Iterate?

Yes!

No?

Abandon

Field


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Introduction


Figure 1-3:

Additional Data

Development 4D Well Tracer Predrilled

Phase Seismic? Logging(Sor) Testing(Sor) Production

Prediction?

Predrilled

Production Prediction

UpscalingUpdate

Reservoir

Simulation

O.K?

No!

Continue

with

Installing

Platform &

Implement

Production

Strategy

Yes!Revised

Production

StrategyYes!

Iterate?

No?

What is

the next step?


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Introduction


1.2 Aim of the Book

The book consists of a series of lectures, supported by carefully designed

tutorials. These will give participants the opportunity to vary key parameters in

the models and establish the impact on field performance.

This course intends to:

develop, a reasonable understanding of the mechanics of reservoir

simulation, which is one of the preconditions for the effective use of the

simulators by the engineers and geoscientists. Lack of this knowledge

and understanding means inputting information and getting results with-

out any appreciation of the relationship between them,

explain the limitations and the structural aspects of the models. If

these are not clearly understood, the users of the models will not be able

to prepare appropriate input data. discuss with and develop amongst participants a sufficient background

on engineering and geologic data acquisition techniques, data struc-

tures, and data processingtechniques,

review data scales and their interrelationships, soft data generation, and

in that respect, explain state of the art reservoir characterization and

reservoir model generationtechniques. Normally, reservoirmodels

are fine grid realizations of the reservoirs, and may comprise tens of

millions of grid blocks with currently available resources,

develop a sufficient background ongenerating reservoir models for

simulation. Due to restrictions in computational resources, the simula-

tion grid blocks are usually orders of magnitude greater than those usedin constructing fine grid reservoir models. This, therefore, requires

upscaling from a fine grid to a reservoir simulation grid. In depth dis-

cussion on the techniques used in single and multiphase case will be car-

ried out both under static and dynamic conditions. The accuracy of the

simulation model, therefore, depends strongly on the reservoir charac-

terization. As a consequence, incorrectly compiled data in building a

reservoir model, and improper use of upscaling procedures will yield

unacceptable results.

develop skills in conducting a simulation study, and framework for

checking the results, their quality and integrity. discuss the current modeling practices, the models available with

their unique features, and the degree of consistency among them.

form the necessary background on history matching using simulators.


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Introduction


1.3 Definitions and Descriptions

The dictionary meaning of the word 'simulate' is to give an appearance of',' to

make so as to resemble the real or genuine thing ' or in other words 'to imitate

or create the conditions of'. The word Simulation refers to 'utilization of a

model to obtain some insight into the behavior of a real system'. To simulateany physical process is, therefore, a means to investigate behavior through a

system necessary which is called a model. Models can be of two types,

namely:

1. Physical Model: It is essentially a scaled down reproduction of the origi-

nal.

2. Mathematical Model: It is a system of equations describing the physical

behavior of the process of concern.

The core of the reservoir simulator is the mathematical model and in this

context a reservoir simulator can be defined as:

'The process of inferring the behavior of a hydrocarbon reservoir from the

performance of a mathematical model of that reservoir'

The mathematical model of a reservoir simulator is a set of partial differen-

tial equations with appropriate boundary conditions sufficient to represent

the physical processes that may occur in a reservoir. These partial differen-

tial equations are always non-linear meaning that the primary unknowns of

the system such as saturation, pressure and concentration exhibit non-linear

A typical flow equation is given below:

(1)

where is formation volume factor, t is time, S is saturation, x, y and z are

cartesian co-ordinate directions, is porosity, flow potential. If there are

three phases in a given medium (oil + water + gas), then, there are three

similar partial differential equations. In the above equation, permeabilities,

porosities, flow potentials, formation volume factors, viscosities are to becalculated simultaneously.

Except in a few simple cases like Buckley-Leverett type displacement

problems, an analytical solution to the partial differential equations cannot

be found due to these non-linearities. This has tempted mathematicians to

x-----

x-------

y-----

x-------

z-----

z-------

+ + t----

S

------- =


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Introduction


explore approximate solution techniques to the full mathematical model

with complete reservoir description. These solutions are numerical in their

nature. Most frequently, there are two classes of numerical solutions used;

namely, finite element and finite difference methods. It follows from this

that a mathematical model should be translated into an approximate numer-

ical model. The reservoir simulator is then an implementation of numericalalgorithms on a computer in the form of software to find an approximate

solution to the mathematical model.

The approximate solutions to the flow equations are based on gridded real-

izations of the petroleum reservoirs. This is a final outcome of the efforts

summarized by Figure 1-1. For each node in the grid system, a value for

the following parameters is required:

Permeability

Porosity

Thickness

Elevation

Grid dimensions

Initial saturation for each phase

Initial pressure

Rock compressibility

Fluid characteristics are assigned by the following relationships:

Oil formation volume factor versus pressure Water formation volume factor versus pressure

Gas formation volume factor versus pressure

Oil viscosity versus pressure

Water viscosity versus pressure

Gas viscosity versus pressure

Solution gas-oil ratio versus pressure

Solution gas-water ratio versus pressure

Liquid to gas ratio versus pressure

Oil density Gas density

Water density

The interactions of forces between rock and fluids are given by the follow-

ing saturation dependent functions:


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Introduction


Relative permeability for each phase

Capillary pressure between oil and water

Capillary pressure between gas and oil

Additional data may come from wells and include:

Producing interval.

Oil production rate versus time

Water production rate versus time

Gas production rate versus time

Observed pressure versus time

1.4 Major Steps in a Simulation Study

These are:

1. Reservoir Description:Starting with a meaningful subdivision of a given

reservoir into hydraulic units; further discretization of hydraulic units into

grid blocks, and arriving at estimates of the parameters in the governing

flow equations describes the process as a function of spatial position. The

parameter estimates have the meaning of average or pseudo values at the

scale of grid block in the discretized version of a continuous reservoir. The

deliverable will be a reservoir model. The resolution of the reservoir model

may go up to hundreds of millions of mesh points.

2. Recovery Mechanism Identification: The decision has to be made concern-ing the method of recovery like water injection, gravity drainage, natural

depletion, gas injection, etc.

3. Mathematical Model: Selection of mathematical model is required here

which may be black oil formulation, compositional formulation, single

phase model, multi-phase model, single dimension, multi-dimension, etc.

4. Engineering Model: This is also called simulation model. The objective is

to generate an acceptable representation of the reservoir based on the reser-

voir model generated. Due to computational resource limitations, the grid

to be used for the engineering model can be much coarser than the reser-

voir model (on the order of tens of thousands or hundreds of thousands). Tothis end, some upscaling efforts are carried out.

5. Numerical Model: There are several different numerical models available

including: Finite Element Model, Finite Difference Model, Boundary Inte-

gral Model, and Streamlines Model. Among these, the Finite Difference


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Introduction


1.5 Classification of Simulators

1.5.1 Classification Based on Linearization

Due to strong non-linearity of Equation (1), it is necessary to

linearize it to obtain unknown parameters. Hence, the firstclassification of the simulators is based on the linearization technique

used. There are two generic techniques, namely:

IMPES: Implicit Pressure and Explicit Saturation. In this application,

flow equations of water, oil and gas are coupled and solved first for

pressure and then saturation. This technology assumes that the

change in capillary pressure over a time step should be negligible. In

addition, the pressures are calculated by the old time level saturation

and pressure dependent parameters. They are updated after pressures

and saturations are updated.

Fully Implicit: In this application, all of the unknowns are solved

simultaneously. The flow equations are linearized by using

Newtonian approach.

1.5.2 Classification Based on Fluid Characteristics

Simulators are classified based on fluid characterization as Black Oil

Simulators or Compositional Simulators.

1. Black Oil Simulators: This type of simulator treats hydrocarbons

as two components; gas and oil. They are applicable to dissolved

gas, medium gravity oil-bearing reservoirs under moderate reser-

voir pressures and temperatures. They can be applied to almost all

conventional water flooding simulation studies. If the oil forma-

tion volume factor is less than two, they can safely be applied to

solution-gas drive, gas cap expansion or gas injection studies.

Black oil simulators can also be used for some cases where the

formation volume factor is greater than 2. That is possible if oil

and gas formation volume factors, gas in solution, and oil and gas

viscosities, are plotted as a function of pressure and can be deter-

mined accurately by calculation or experiment.

2. Compositional Simulators: Compositional simulators are those

which use cubic Equations of State forms like Peng Robinson,

Soave-Redlich-Kwong, Redlich-Kwong, Schmidt Wenzel and Pa-

tel-Teja. Instead of tracking the phases, as in Black Oil Simula-

tors, track constituent components of hydrocarbons like Methane,

Ethane, Butane, Propane, Nitrogen, Carbon Dioxide, etc. Because


13/26

Introduction


of this multicomponent treatment of reservoir fluids, the simula-

tion is capable of handling:

Enhance Oil Recovery by carbon-Dioxide or enriched gas

injection, Multiple Contact Miscibility studies

Natural depletion and Injection of Gases such as Nitrogen orresidue gas into gas condensate reservoirs.

Natural Depletion or Gas Injection into Volatile Oil Reser-

voirs.

Re-evaporation of residual oil by injecting residual gas

Despite the excellent capability of simulating the compositional

phenomena in gas condensate reservoirs, compositional simulators

can be as much as 100 times more expensive than black oil

simulators. The main source of this additional computation cost is the

Equation of State (EOS) calculations (which may be up to 80% of the

total cost).

1.5.3 Classification Based on Temperature Dependence

Isothermal: Simulators that consider the temperature of the reser-

voir constant

Thermal: In this case the following equations are involved:

1. Energy equation.

2. Oxygen for in-situ conditions

3. Gas for in-situ conditions4. Hydrocarbon components: light, medium and heavy compo-

nents may be necessary

5. Phase: gas, liquid and solid phases (4 phase: oil + water + gas

+ solid)

1.5.4 Classification Based on Grid Dimensions and Types

(See Figures 1-4 to 1-8):

1-Dimensional: These models cannot be used for fieldwide

simulation applications because they cannot handle either arealsweep or the gravity effects. They can be used for sensitivity towards

some selected reservoir parameters prior to full-scale simulation. The

effect of viscous forces and mobility ratios on the recovery can be

tested. They are especially used for testing the accuracy of the

simulators against known analytic solutions like that of Buckley-

Leverett. Also, most of the finite difference techniques can be tested


14/26

Introduction


first with one-dimensional case and then their use can be extended to

multi-dimensions. They are also useful in assessing the heterogeneity

in the direction of flow.

1-Dimensional Cartesian - Horizontal.

1-Dimensional Cartesian -Vertical: These are usually used for

vertical equilibrium.

1-Dimensional Radial: In addition to general objectives as stated,

they are also used for assessing the productivity impairment in gas

condensate reservoirs as well as volatile oil reservoirs. They can also

simulate well testing (i.e. radial flow).

Figure 1-4: Grid Dimensions

X

(a) 1-D Linear

(b) 1-D Radial

Z

(c) 1-D VE

r


15/26

Introduction


2-Dimensional: These include areal cartesian, areal radial and cross-sectional

cartesian, and cross-sectional radial models.

2-Dimensional Cartesian Areal: Although petroleum reservoirs are three

dimensional, in some cases, especially for thin reservoirs where gravita-

tional effects are negligible, Z-direction may not be important. Under thecircumstances, these type of models are used when areal flow patterns

dominate the reservoir performance; and if the areal heterogeneities are im-

portant. Most areal models use pseudo functions to account for flow in ver-

tical direction. However, they are not necessary if the reservoir is thin and

stratification is not important. Under the circumstances, normal reservoir

engineering studies can be carried out with these models including well po-

sition optimization; distribution of injection and withdrawal rates; timing

for installation of artificial lift and modification of surface facilities.

2-Dimensional Radial Areal: This model investigates the effect of well

performance as in the case of 1-Dimensional radial models, with the addi-tion of areal heterogeneities.

2-Dimensional Cross-sectional Cartesian: In this case, instead of ne-

glecting flow in the vertical direction, one of the horizontal directions can

be discounted. This type of model can be used in cases where vertical flow

is dominant. A highly stratified reservoir is a typical case study for this

type of model. The effect of segregation and the effect of stratification are

the main focus areas in this type of modeling. They are also used in devel-

oping well functions, pseudo functions and coning functions; simulating

peripheral gas injection. Crestal gas injection, or other processes in which

frontal velocities toward producers are largely uniform help to justify sim-plification in modeling of entire fields or field segments. Studying miscible

processes to assess the gravity and heterogeneities on displacement effi-

ciency and the sweep efficiency are also candidates.

2-Dimensional Cross-Sectional Radial: This model is also applied to res-

ervoirs where gravity forces and stratification dominate the flow, and areal

property distribution of the reservoir is relatively homogeneous. This ap-

proach is used particularly to investigate the coning problem. They can also

be used to develop coning functions and well functions.


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Introduction



AREAL-CARTESIANCROSS-SECTIONAL CARTESIAN

AREAL-RADIAL

CROSS SECTIONAL RADIAL

2-DIMENSIONAL DOMAN

REALISATIONS


17/26

Introduction



7800

7400

7000

6600

6200

5800

7800

7400

7000

6600

6200

5800

Block Centered Geometry XZ plane

3000 4000 5000 6000

3000 4000 5000 6000

Corner point Geometry XZ plane

orner Point Geometry

lock Centered Geometry


18/26

Introduction


3-Dimensional Models: They can be Cartesian, Radial-Cylindrical or

Spherical.

3-Dimensional Cartesian: Reservoir geometry can sometimes be too

complex to be represented by two-dimension. For example, reservoirs hav-

ing shales or other flow barriers that are continuous over large areas, butwith permeable windows where crossflow occurs, are difficult, if not im-

possible, with two dimensions. Reservoir mechanics may be so complex

that two-dimensional realizations are difficult to analyze. Reservoirs which

are at a more advanced stage of depletion fall into this category and require

careful and precise modeling to distinguish between performances result-

ing from alternative depletion plans. The displacement to be studied may

be dominated by vertical flow as, for example, near wells where both cusp-

ing and coning may occur. Both areal and vertical details needed can be ob-

tained only in a 3D segment model. Occasionally 2-D studies are more

troublesome and expensive than 3-D modeling. Reservoirs with a complex

facies structure may require an excessive number of pseudoisations to berepresented with two dimensions.

3-Dimensional Cylindrical: This model has the same objectives as 1-D ra-

dial, 2-D Radial areal and 2-D radial cross-sectional models. In addition, it

is able to capture the impact of vertical and areal heterogeneities on the

flow.

3-Dimensional Spherical: This approach is used to investigate the partial

penetration effects on well testing results and to model minipermeametry

flow.


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Introduction


1.6 Benefits of Reservoir Simulators

The reason for using reservoir simulators is to estimate reservoir performance

under a variety of production schemes. We have only a single opportunity to

produce from an actual reservoir with a considerable expense whereas with

simulation we can test several alternatives and assess them prior to decidingthe actual field operation. The cost of simulation is considerably cheaper and

the time necessary is usually negligible to the actual operation. Some of the

applications and the benefits of the simulation can be summed up as follows:

1. The performance of a hydrocarbon reservoir under natural depletion, water

injection or cycling can be examined.

2. Type of water flooding can be judged. For example, it is possible to see the

relative merits of flank water injection and pattern waterflooding.

3. The effect of well location and spacing can be critically evaluated.

4. The effect of the production rate on the hydrocarbon recovery can be esti-

mated.

5. For a given number of wells at certain specified locations, it is possible to

predict total field gas deliverability.

6. In heterogeneous hydrocarbon reservoirs, it is possible to estimate the lea-

seline drainage.

7. To maximize hydrocarbon recovery, best methods of field development

and production schemes can be found.

8. Best Enhanced Oil Recovery (EOR) scheme and its implementation can be

determined.

9. The reasons why the reservoir behavior deviates from the earlier predic-

tions can be explained.

10. The ultimate economic hydrocarbon recovery can be predicted.

11. Laboratory and field data requirements and their subsequent effect on the

performance predictions can be assessed.

12. The best completion schemes for the wells can be established.


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Introduction


13. The section of reservoir from which the hydrocarbon is produced can be

identified.

14. Critical parameters to be measured from the field in an application of a re-

covery scheme can be identified.

15. It is possible to decide whether it is necessary to do physical model studies

of the reservoir and if so how can the findings can be scaled up for field ap-

plications.

1.7 ECLIPSE State of the Art Reservoir Simulator

Immense advances in the areas of data acquisition and integration, especially

in the last 10 years, dictate ever increasing complexities in reservoir

description in order to model reservoir behavior. The detail required by

reservoir management and the detail introduced by the integratedmultidisciplinary reservoir characterization efforts, require robust and fast

simulation technologies which are parallelisable and cost effective. These

technologies must be able to cope with all of the complexities of the field

production and operations and must be flexible to absorb new concepts. They

must be user friendly as the ever-growing demand for the simulators

encourages non-specialists to make use of them in their day to day field

management efforts. In this respect, the front-end processors of such

applications must be able to detect the physical inconsistencies in the input

data to a measurable degree. The increasing demand for the simulators also

dictates that simulation software be available for PC's as well as workstations.

The pre and post processing facilities must be extremely powerful so thatengineers and geoscientists can monitor their simulation studies efficiently.

Integration of various different data processing and simulation modules and

data transferability between them is another important aspect required within

the current reservoir management environment. In fact, the advances in data

exchange and integration between different disciplines in the recent years have

begun forming the firm and necessary basis for multi-disciplinary co-operation

and working.

ECLIPSE has been a leading state of the art software in the oil industry

dominating currently 70% of the market. Some of the main reasons for its

dominant role in the oil industry are its stability, robustness, and high degree ofmaterial conservation, mathematical accuracy and flexibility. The available

functions of the ECLIPSE are summarized in the form of need and solution:


22/26

Introduction


NEED SOLUTION

Handling multi-phase flow problems Eclipse 100, Eclipse 200 and Eclipse 300

Handling Complex Geometries Block-center geometry, Corner Point Geometry, Unstruc-

tured Gridding, Pebby/Voronoi Gridding, Non-Neighbor

Connections and Local Grid Refinement

Unconditional stability and robustness Fully Implicit

Compromise solution between accuracy and

computational speed

IMPES and Adaptive Implicit

Modeling Structural Geological Features like

faults

Non-Neighbor Connections

Flexibility in Model Size and Representation Run Time Dimensioning

Modeling Segregated flow in vertical direction Vertical Equilibrium

Fractured Reservoir Modeling Dual Porosity and Dual Porosity/permeability options

Relative Permeability and Capillary Pressure

Treatment

Directional Relative Permeabilities, Relative Permeability

and Capillary Pressure hysteresis, Saturation Table Scaling

Gas Field Operations, Gas Lift Optimization ECLIPSE 200

PVT Data ECLIPSE 100 and 200 for Black Oil data ECLIPSE 300

for Compositional data, API Tracking

Modeling Flow of Methane in Coalbed ECLIPSE 200

Collapse of pore channels due to change in the

pore pressure

Rock Compaction Option

Designing and modeling single well and inter-

well tracer testing

Tracer Tracking

Cold water injection into a reservoir cooling

effects need to be handled, energy conservation

must be maintained

Temperature Model

Modeling First Contact and Multiple Contract

Miscibilities

ECLIPSE 300 compositional formulation ECLIPSE 100/

200 three component model to handle First Contact Misci-

bility

Managing Field and Well schedules Individual Well Controls Group and Field Production Con-

trols Multi-Level Grouping Hierarchy Group Injection

Controls Sales Gas Production Control Crossflow and Co-

mingling in Wells Highly Deviated/Slanted and Horizontal

Wells Special Facilities for Gas Wells Surface Networks

Modeling Polymer, Surfactant and Foam ECLIPSE 200

Accurate Distribution of Initial Fluid in Place Fine Grid Equilibration

Aquifer Modeling Non-neighbor Connections Analytic Aquifers (Fetkovitch

and Carter Tracy) Numerical Aquifers

Interpolation of sparse data FILL Program

Flow in the Wellbore VFP Module comprising the following options:-Aziz,

Govier and Fogarasi Orkiszewski, Hagedorn and Brown,

Beggs and Brill Mukherjee and Brill, Gray

Pre and Post Processing Facility GRID, GRAF, and RT View


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Introduction


Well Test Interpretation and Analysis Well Test 200

Accurate and Efficient Preparation, Evaluation

and Quality Checking of the Well Production

and Completion Data

SCHEDULE

Relative Permeability and Capillary Pressure

Pseudoisations

PSEUDO

Coupling Multiple reservoirs and Paralleliza-

tion Compatibility

ECLIPSE 200

Between Different Modules YES

Automatic History Matching Sim Opt

NEED SOLUTION


24/26

Introduction


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Introduction


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Introduction

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