SPE93374_Performance Analysis of Compositional and Modified Black Oil Models for Rich Gas Condensate Reservoir

8/11/2019 SPE93374_Performance Analysis of Compositional and Modified Black Oil Models for Rich Gas Condensate Reservoir

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SPE 93374

Performance Analysis of Compositional and Modified Black-Oil Models for a Rich GasCondensate ReservoirB. Izgec and M.A. Barrufet, Texas A&M U.

Copyright 2005, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the 2005 SPE Western Regional Meeting held inIrvine, CA, U.S.A., 30 March 1 April 2005.

This paper was selected for presentation by an SPE Program Committee following review ofinformation contained in a proposal submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Society of Petroleum Engineers and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Society of Petroleum Engineers, its officers, or members. Papers presented atSPE meetings are subject to publication review by Editorial Committees of the Society ofPetroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paperfor commercial purposes without the written consent of the Society of Petroleum Engineers isprohibited. Permission to reproduce in print is restricted to a proposal of not more than 300words; illustrations may not be copied. The proposal must contain conspicuousacknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

Abst ractThe modified black-oil model (MBO) was tested against the

fully compositional model and performances of both models

were compared using various production and injectionscenarios for a rich gas condensate reservoir.

We evaluated the performance of MBO model by

investigating: the effects of black-oil PVT table generation

methods from a tuned equation-of-state, oil-gas ratio (OGR)

and saturation pressure versus depth as initialization methods,

uniform composition versus compositional gradient withdepth, location of the completions, production and injection

rates, kv/khratios, and vertical wells versus horizontal wells.Contrary to the common belief that OGR versus depth

initialization gives better representation of original fluids in

place, initializations with saturation pressure versus depth

gave closer original fluids in place considering the true initialfluids in place are given by the fully compositional model

initialized with compositional gradient.

Unrealistic vaporization in the MBO model was

encountered in both, production by natural depletion and gas

cycling. The changes in oil-gas ratio of the recyled gas showedthat, it is not possible to accurately represent the changing

PVT properties of the recycled gas with a single PVT table.Unrealistic vaporization also led to different arrival times forthe displacement fronts and different saturation profiles for the

near wellbore area and for the entire reservoir for the two

models even though the production performance of the models

was in good agreement.The MBO model representation of compositional

phenomena for a gas condensate reservoir proved to be

adequate for full pressure maintenance, reduced vertical

communication, vertical well with upper completions, and forhorizontal well producers.

IntroductionBlack-oil simulators represent a high percentage of al

simulation applications and they can model immiscible flowunder conditions such that fluid properties can be treated as

functions of pressure only.

However, gas condensate reservoirs exhibit a complexthermodynamic behavior that cannot be described by simple

pressure dependent functional relations. Compositions changecontinuously during production by natural depletion, or by

cycling above and below dew point pressures.

In another black-oil modeling approach reservoir fluidconsists of a gas component and vaporized oil which allows

the use of a simple and less expensive model.

According to this modified black-oil approach liquid

condenses from a condensate gas by retrograde condensationwhen the pressure is reduced isothermally from the dew point

and retrograde liquid is vaporized by dry gas.Coats1 presented radial well simulations of a gas

condensate that showed a modified black-oil PVT formulation

giving the same results as a fully compositional EOS PVT

formulation for natural depletion above and below dew point

Under certain conditions, he found that the modified black-oimodel could reproduce the results of compositional simulation

for cycling above the dew point. For cycling below the dew

point, the two-component simulation gave results that were

quite inaccurate.According to Fevang and Whitson2, results from Coats

example should be used with caution as EOS characterization

uses seven components with one C7+ fraction. With a moredetailed C7+ split, oil viscosity differences between black-oi

and compositional formulations often yield noticeable

differences in well deliverability.

Fevang et al.3 obtained results which mostly support the

conclusions by Coats.1However, they found differences in oi

recoveries predicted by compositional and MBO models whenthe reservoir is a very rich gas condensate and has increasing

permeability downwards. According to their final conclusionsa black oil simulator may be adequate where the effect of

gravity is negligible, and for gas injection studies black oil

model can only be used for lean to medium-rich gascondensate reservoirs undergoing cycling above dew point.

El-Banbi and McCain4, 5suggested that the MBO approach

could be used regardless of the complexity of the fluid. Their

paper presented the results of a full field simulation study for a

rich gas condensate reservoir. The MBO models performance

was compared with the performance of a compositional mode


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in the presence of water influx and also a field wide history

match study was conducted for above and below the dew

point. Their paper presents an accurate match of averagereservoir pressure and water production rates. However gas-oil

ratio and condensate saturation plots were not provided and

initial condensate production rates do not represent a clear

match for 500 days.

For the present study a representative gas condensate fluidwas selected and a fluid model was built by calibrating the

EOS to the available experimental data, which consisted ofconstant composition expansion (CCE) with relative volume,

liquid saturations and gas density values.

By using the calibrated EOS black-oil PVT tables were

generated for MBO model using Whitson and Torp6 and

Coats1methods.

The compositional model was run either with

compositional gradient or with uniform composition. The

compositional gradient in MBO model was given by depth

variation of OGR (Rv) and GOR (Rs) or saturation pressureversus depth tables.

Initially there was a discrepancy in saturation pressureswith depth in the MBO model which resulted in earlier

condensation and lower oil production rates whether it was

initialized with GOR / OGR or saturation pressure versus

depth tables.

For natural depletion cases as the reservoir gas becomes

leaner during production, the initial differences between themodels, due to saturation pressure changes with depth

disappear and a better match was obtained, especially for the

poor vertical communication.For the gas cycling cases the models were in good

agreement as long as the reservoir was produced with rates

high enough to minimize condensation. If the MBO model isinitialized with compositional gradient, lower production and

injection rates and bottom completions created differencesbetween the performances of the models.

Almost all the cases showed differences in condensate

saturation distribution around the wellbore area and the entirereservoir. The minimum difference between the models is 5 %

in terms of average field oil saturation and this was obtained

for a high rate gas injection case combined with reducedvertical communication.

However, the saturation differences between models

depend on the case and the time interval studied. As an

example, for gas injection with bottom completions, at 1000days, the condensate saturation difference between the two

models was as high as 60 % although they converged to a

close value at the end of the simulation.In MBO model, the runs with horizontal wells exhibited

closer performances with compositional model compared tothe runs with vertical wells.

The changes in oil-gas ratio of the cycling gas showed that,

it is not possible to accurately represent the changing PVTproperties of recycled gas with a single PVT table in the MBO

model since every time the produced gas passes through the

separators and is injected back into the reservoir its oil-gasratio and accordingly vaporization characteristics changes.

Fluid CharacterizationThe fluid selected for the study is a rich gas condensate taken

from Cusiana Field in Colombia.A compositional analysis with hydrocarbon components

that includes a heavy fraction of C30+, a set of experimenta

data obtained from a constant composition expansion and a

separator test were used to characterize the fluid. Table 1

presents the extended compositional description of the fluid.Following the procedure proposed by Whitson6, where the

groups are separated by molecular weight we used sixpseudocomponents and one non-hydrocarbon, CO2. The

pseudocomponents were defined as two pseudo-gases, GRP1

and GRP2, one gasoline group, GRP3 and three heavy

pseudocomponents, GRP4, GRP5 and GRP6. For the purpose

of CO2injection, this component was kept as a separate groupThe corresponding components for each pseudo componen

and the final molar compositions are given in Table 2.

Once the pseudocomponents were defined we proceeded

with the EOS tuning process. The variables used as regressionparameters were binary interaction coefficients, and shif

factors for selected groups. The final values for these variablesare presented in Table 3-4. Binary interaction coefficients

values after tuning are presented in Table 5.

Four parameter Peng-Robinson EOS was selected and

tuned to the data obtained from the constant composition

expansion at 254F, which includes the liquid saturation, gas

density and the relative volume. Figs. 1 through3illustrate the

match between the experimental and the simulated data.

Black-Oil PVT Table GenerationBlack-oil PVT properties in this study have been generatedwith an EOS model using the Whitson and Torp7procedure

Coats1 developed another black-oil PVT table generation

method. Instead of flashing the equilibrium liquid and vapor

compositions separately to obtain Bo, Rs, Bg, Rv directly asindicated by Whitson and Torp, Coats determines only one ofthese properties Rv, from flash separation and determines the

remaining three using equations that force the PVT properties

to satisfy mass conservation equations and yield correct

reservoir liquid density. In determining Rv from the surfaceseparation at each CVD pressure step Coats uses the surface

oil and gas molecular weights and densities obtained from the

separation of the original fluid mixture.McVay8 found better agreement between compositiona

and MBO simulations models if the surface oil, gas molecular

weights and densities are obtained from the separation of the

mixture at each CVD pressure step to calculate Rv at each

pressure. Also by using Coats method it is not possible toobtain the PVT properties of the liquid phase at the saturation

pressure. Coats defined the first CVD pressure step to be 0.1

or 1 psi below the saturation pressure and used the values

calculated at this pressure as the PVT properties at thesaturation pressure. Standard extrapolation of sub-dew poin

properties to dew point can lead to situations where the oil hasnon-physical negative compressibility.

Figs. 4 through 9 give the saturated oil, and gas PVT

properties obtained by Whitson and Torp and Coats methods

Notice that gas formation volume factors at lower pressure

values are quite different for the two methods.


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Coats method was not preferred for this study since it

created convergence problems in MBO model and the run was

automatically terminated due to number of errors encountered.

Initialization MethodsTo obtain the correct and consistent initial fluids in place for

black-oil and compositional models it is important to initialize

the models properly. The initial reservoir fluid composition iseither constant with depth or shows a vertical compositional

gradient where the effect of gravity is not negligible.Depending on the type of the reservoir fluid, the model should

be initialized either with solution GOR/ OGR versus depth or

saturation pressure versus depth to minimize the errors for

initial fluids in place.

Although initialization with saturation pressure versusdepth gives more accurate representation of fluids in place, at

the bottom of the reservoir where the amount of heavy fraction

increases, this initialization method provided higher

condensate saturations, especially for the gas cycling cases,compared to the MBO model initialized with GOR/OGR

versus depth and the compositional model.

Constant Composition with Depth. For the constant

composition case modified black-oil model was initialized

with either solution oil-gas ratio versus depth or saturation

pressure versus depth tables, which correspond to the

composition at a reference depth of 12,800 ft.The constant composition case was only run for the natural

depletion to show that initialization methods do not affect the

performance of the MBO model if compositional gradient isnot used and identical pressure, oil-gas ratio, recovery factor

and saturation plots can be obtained.

Also if the effect of gravity is negligible, both initializationmethods give the same initial fluids in place. The error in

initial fluids in place is calculated as 4 % for both initializationmethods. Table 6 shows the oil in places values for

compositional and MBO models initialized with two different

methods for the unifom composition case.

Compositional Gradient. Variation of the composition of C1-

N2 and C7+ with depth is presented in Figs. 10 and 11.

Corespondingly MBO model was initialized with solution gas-

oil and oil-gas ratio versus depth tables and saturation pressure

versus depth tables to investigate the effects of different

initialization methods. Table 7shows that when the black-oilmodel was initialized with saturation pressure versus depth, a

better representation of initial fluids in place could be

obtained. The error in initial fluids in place can be as low as 2% with saturation pressure initialization. With the use of

compositional gradient, different initialization methodsexhibited different initial fluids in place values.

Numerical SimulationA quarter of a 5-spot model with the description of a real gas

condensate fluid system was scaled to represent the entire

field. The top of the model is at 12,540 ft with an initialpressure of 5,868 psia at a reference depth of 12,800 ft. The

gas water contact is at 12,950 ft. The 359 ft total thickness is

represented by 18 layers having different porosity and

permeability values. Table 8 gives the thickness, porosity and

permeability values for each layer.

The injector and producer wells are located on the oppositecorners of the model. The producer operates under the

constraint of a fixed gas production rate of 3,000 Mscf/D unti

the minimum bottomhole pressure is reached. For the gas

cycling cases the optimum injection rate was chosen to be

2,500 Mscf/D and a three separators having 500, 30, 15 psiapressure and correspondingly 180, 150, 80 oF temperature

increments, were used on the surface.

Natural DepletionInitially a discrepancy in saturation pressures versus depth was

observed in MBO model for both uniform composition and

compositional grading with depth cases. The differences insaturation pressures versus depth for uniform and

compositional gradient initialization methods are given in Fig

12 and Fig. 13. The second figure shows that error in

saturation pressures increases with depth when thecompositional gradient is used.

The differences in saturation pressures resulted in earliercondensation and lower oil production rates in MBO mode

initialized with oil-gas ratio versus depth. On the other hand

saturation pressure versus depth table initialization made the

model more sensitive to pressure drop in the reservoir and the

model exhibited more condensate drop-out and higher oil

production rates at early times. However, it was observed thatthe error in saturation pressure versus depth had a little impac

on the production performance and recoveries and it

diminished as the reservoir was depleted.Oil production rate and the average field pressure for both

models are given by Fig. 14 andFig. 15.MBO model exhibits

slightly higher-pressures initially since early condensate dropout and accumulation around the wellbore reduces relative

permeability to gas and slows down the gas production and aswell as the pressure drop in the reservoir.

According to Fig. 16 andFig. 17 the effect of initialization

method on the performance of the MBO model is lesspronounced if the composition is not changing with depth.

Fig. 18 shows the comparison of two different

initialization methods for average saturation in each model. Byobserving the oil saturation values below critical saturation

that is 0.24, it can be concluded that a reduction in oi

saturation above this value is due to mobilization of liquid

phase and a reduction in oil saturation below this value is dueto revaporization. The liquid holding tendency of the gas in

modified black-oil model is dependent on the pressure. The

oil-gas ratio plot generated by the EOS determines therevaporization process in MBO model and this allows gas to

pick-up oil until it reaches to the value determined by the PVTtable. The tabulated values of oil-gas ratios at lower pressures

are very small. Accordingly the presence of more gas would

have caused excess amount of revaporization in MBO modeas will be seen gas cycling case.

The oil saturation distribution at the end of the simulation

time is given by Fig. 19 andFig. 20. In compositional modean additional condensate bank away from the producer is

observed. The same bank cannot be observed in the MBO

model. The wells are completed in the first nine layers and the

drainage of the fluids is faster from these layers in relation to


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completions and their higher permeability values. At the top of

the reservoir even though the gas is not as rich as in the

bottom layers because of compositional grading, condensationis still more effective due to faster drainage. At some distance

away from the producer, closer to the top of the reservoir

where no flow boundary conditions dominate, quick drainage,

pressure drop and lack of pressure support from the

neighboring layers in the region may form this kind ofbanking. If the injector well is completed inside this

additional bank or outside the bank but in the lower layers, itwill only be effective around the near wellbore region and

production from top layers will be negatively affected. The

size of the bank in the case of uniform composition is much

larger as can be seen in Fig. 21 since the percentage of heavy

components in the upper layers increases when the uniformcomposition is assumed.

For the natural depletion case two types of runs were

conducted to investigate the effect of completions. The first

one with the well completed in the first two layers and thesecond with the well completed in the last two layers. For the

two runs conducted average field pressure, oil production rate,saturation and gas-oil ratio comparison plots exhibited exactly

the same patterns as the previous examples. The differences in

recovery factors between compositional and MBO models for

upper and lower completions are given as 4 % and 7 % at the

end of the simulation time. The effect of the location of the

completions on the production performance is morepronounced for gas cycling cases and will be further

investigated in this section.

Gas CyclingTo investigate the effect of different parameters on

revaporization process, the producer is completed in the topnine layers and the injector is completed in the bottom nine

layers for all the cases except, the cases including theinvestigation of the effects of completion locations. By doing

so the bottom layers with high permeability and higher heavy

fractions are open to flow and also consequent channelingwith revaporization is expected to be maximized. Production

and injection rates are 3,000 and 2,500 Mscf/day.

Compositional model has the produced gas as injection gas,which gets leaner with time by passing through the three-stage

separator system and MBO model has the regular gas phase

option as an injection gas. The injected gas behavior in MBO

follows the gas PVT table characteristics obtained by Whitsonand Torp6method.

In compositional model the revaporization process begins

with the lighter ends of the oil and proceeds slowly with timesince the stripping of the liquid components is in inverse

proportion to their molecular weight. In MBO model the oiluptake of the injected gas is only a function of pressure which,

results in excess amount of revaporization. According to Fig.

22 andFig. 23 higher pressure dependent vaporization leavesless oil in the reservoir giving slightly higher oil production

rates for MBO model towards the end of the simulation.

The extent of vaporization occurring in both models can bequantified from Fig. 24through Fig. 28. According to the first

three plots, the third gridblock from the producer for layer

nine (23, 23, 9), gives zero condensate saturation at 5000 days,

which is not the case with compositional model and MBO

model initialized with saturation pressure versus depth table

The last two plots are the examples of unrealistic vaporization

in oil-gas ratio versus depth initialized MBO model forgridblocks at the producer in layer four and five. Higher oil

saturation is obtained from MBO model but as soon as the

displacement front arrives all the oil is vaporized. This type o

formulation allows dry gas to pick up oil until the gas becomes

saturated. Since miscibility cannot be represented in MBO, thearrival time of displacement front differs for both

compositional and MBO models and as well as for differentinitialization methods among the MBO models.

The liquid content of the initial gas composition and

different gas compositions obtained by flashing the origina

gas to different pressures is given in Fig. 29. The figure was

generated by flashing the original gas to 5,000, 4,000 and3,000 psia and generating black oil tables for each pressure

In fact, this process represents the changes in oil-gas ratio of

the injected gas during the cycling. According to the figure

especially at high pressures, it is not possible to accuratelyrepresent the continuously changing PVT properties of the

recycled gas with single PVT table in MBO model since everytime the produced gas passes through the separators and is

injected back into the reservoir its oil-gas ratio and

accordingly vaporization characteristics changes.

In the swept zone, the reservoir pressure is either above or

below its original dew point when the injection gas fron

arrives. If it is above the dew point a gas-gas miscibledisplacement will yield 100 % recovery of the curren

condensate in place, which is the case with higher production

and injection rates. If reservoir pressure is below the dew poinwhen the displacement front arrives, ultimate recovery of

condensate depends on both gas-gas miscible displacement o

the reservoir gas, and partial vaporization of the retrogradecondensate. The latter case is encountered with lower

production and injection rates and the amount of condensatedrop-out before gas-gas miscible displacement takes place is

determined by the fluid type. Fig. 30 shows the average oi

saturation obtained from both models for low production andinjection rates. The condensation times indicate the increasing

differences between the models with lower production and

injection rates.The richest part of the gas is located at the bottom of the

reservoir due to gravitational forces and the compositiona

effects, such as development of miscibility changes with

depth. Since miscibility cannot be represented with black-oimodels, more discrepancies are expected in the regions where

highly miscible processes take place i.e. around the bottom

completions. When the producer and injector were completedat the bottom part of the reservoir (layer 10 to 18), it has been

observed that saturation pressure versus depth initializationmethod resulted in extreme amounts of condensate

accumulation initially in MBO model. An unrealistic

vaporization of all the condensed oil follows in the swept zoneuntil the saturation becomes to the level given by the

compositional model. Fig. 31 andFig. 32 show the average oi

saturation and gas-oil ratio plots for the bottom completionscenario.

When kv/kh ratio is reduced to an extreme value of 10-4

which almost restricts the mass transfer between layers, it is

clearly observed that compositional and MBO models showed


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closer performances both for natural depletion and gas cycling

cases.

The reduced communication between layers prevented themixing of the leaner reservoir gas (relative to initial

conditions) with the oil formed after condensation. In the case

of good vertical communication; the leaner gas after the first

drop-out, tends to go up and at the same time vaporizes the oil

on its path during the continuing depletion process. Also theaccumulated condensate tends to go down under gravity

forces. Both scenarios are not possible with the restrictedvertical communication. Every layer is left with its own ability

to vaporize the condensate accumulated. In the case of

reduced vertical communication, condensate accumulation and

vaporization process for each layer is proportional to the

layers content of heavy and light component fractions.Compositional effects gain importance at the bottom part of

the model because of the isolated richer gas phase. Fig. 33 and

Fig. 34 show the oil production rate and gas-oil ratio plots for

reduced vertical communication.The lower drawdown pressure for horizontal well,

compared to the vertical well, for the same flow rate,considerably reduces retrograde condensation.9 Therefore

there is less condensate deposited near the horizontal wellbore.

This means lesser liquid drop-out and smaller amounts of

vaporization for MBO model, which in turn makes the models

give similar performances. Dehane and Tiab9 compared the

productivity of the horizontal and vertical wells for a gascondensate reservoir. According to their results the

productivity of the horizontal well outperforms the

productivity of the vertical well and drain hole length is themost important criteria for the productivity of a horizontal

well. Longer drain hole causes a lower drawdown and less

condensation around the wellbore, which is an importantfactor in duplicating the fully compositional model

performance with MBO model. In comparison with the runsthat had horizontal well completed in upper and bottom layers,

it can be concluded that MBO model performance with

horizontal well approaches to the compositional modelperformance if the well is placed closer to the area where fluid

sample is coming from, even if the sample is coming from the

bottom part of the reservoir. If the well is placed in the upperlayers also a good match can be obtained since the gas

becomes heavier with increasing depth. Also with the

horizontal well, error in dew point pressure versus depth is

almost eliminated for the gas cycling case and a betteragreement between the models has been obtained compared to

the vertical wells. Fig. 35 through Fig. 37 gives the oil

production rate, gas-oil ratio and recovery factors for gascycling with horizontal well set as a producer.

Conclusions1. The performance of the MBO model is not affected

by the initialization method if composition is constantwith depth. Also OOIP is the same for all

initialization methods if no compositional gradient is

used.2. Unrealistic vaporization in MBO model is not just

limited to gas cycling, it can also be encountered in

natural depletion to some degree depending on the

depletion scenario.

3. In natural depletion the gas present in MBO has alower capacity to hold liquid and more oil is left in

the reservoir.4. In gas cycling case, the injected gas in MBO can pick

up oil as a function of pressure and the oil left in the

reservoir is always lower than in the compositional

model.

5. Lower kv/khratios provide a better match between themodels.

6. The arrival time of displacement front differs for bothcompositional and MBO models and as well as for

different initialization methods among the MBO

models.

7. Due to reduced retrograde condensation and partialelimination of the error in dew point pressure versusdepth, MBO model with the horizontal wells exhibits

better agreement with compositional model.

8. Oil saturation distributions around the well andthroughout the reservoir may be quite different in twomodels regardless of a match with the production

performance.

References1. Coats, K.H.: Simulation of Gas Condensate Reservoir

Performance,JPT (October 1985), 5, 1870.

2. Fevang, O., and Whitson, C.H.: Modeling Gas CondensateDeliverability, paper SPE 30714 presented at the 1995SPE Annual Technical Conference and Exhibition, DallasTexas, 22-25 October.

3. Fevang, O., Singh, K., Whitson, C.H.: Guidelines forChoosing Compositional and Black-Oil Models for VolatileOil and Gas-Condensate Reservoirs, paper SPE 63087

presented at the 2000 SPE International Conference and

Exhibition, Dallas, Texas, 1-4 October.4. El-Banbi, A.H., and McCain, W.D.: Investigation of Wel

Productivity in Gas-Condensate Reservoirs, paper SPE59773 presented at the 2000 SPE/CERI Gas Technology

Symposium, Calgary, Alberta, Canada, 3-5 April.5. El-Banbi, A.H., McCain, W.D, Forrest, J.K., Fan, L.

Producing Rich Gas-Condensate Reservoirs-Case Historyand Comparison Between Compositional and Modified

Black-Oil Approaches, paper SPE 58988 presented at the2000 SPE International Conference and ExhibitionVillahermosa, Mexico, 1-3 February.

6. Whitson, C.H.: Characterizing Hydrocarbon PlusFractions, SPEJ (August 1983) 683; Trans., AIME, 27542.

7. Whitson, C.H., Torp, S.B.: Evaluating Constant VolumeDepletion Data, paper SPE 10067 presented at the 1981Annual Fall Technical SPE Conference and Exhibition, San

Antonio, Texas, 5-7 October.8. McVay, D.A.: Generation of PVT Properties for Modified

Black-Oil Simulation of Volatile Oil and Gas CondensateReservoirs, PhD Dissertation, Texas A&M UniversityCollege Station, Texas (1994).

9. Dehane, A., Tiab, D.: Comparison of Performance ofVertical and Horizontal Wells in Gas-Condensate

Reservoirs, paper SPE 63164 presented at the 2000 SPEAnnual Technical Conference and Exhibition, DallasTexas, 1-4 October.

10. Wattenbarger, R.A.: Practical Aspects of CompositionaSimulation, paper SPE 2800 presented at the 1970 SPESymposium on Numerical Simulation of ReservoiPerformance, Dallas, Texas, 5-6 February.


6/14

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11. Whitson, C.H., and Thomas, L.K.: CompositionalGradients in Petroleum Reservoirs, paper SPE 28000

presented at the 1994 SPE Annual Technical Conference

and Exhibition, Houston, Texas, 29-31 August.Joffe, J.,Schroeder, G.M., and Zudkevitch, D.: Vapor LiquidEquilibria with the Redlich Kwong Equation of State,

AIChE J. (May 1970) 2, 496.12. McCain, W.D. Jr.: The Properties of Petroleum Fluids,

Pennwell Books, Tulsa, Oklahoma (1990).13. Fevang, O., and Whitson, C.H.: Accurate in situ

Compositions in Petroleum Reservoirs, paper SPE 28829presented at the 1994 SPE European PetroleumConference, London, U.K, 25-27 October.

14. Jaramillo, J.M.: Vertical Composition Gradient Effects onOriginal Hydrocarbon in Place Volumes and LiquidRecovery for Volatile Oil and Gas Condensate Reservoirs,MS thesis, Texas A&M University, College Station, Texas(2000).

15. Coats, K.H., and Thomas, L.K.: Compositional and Black-Oil Reservoir Simulation, paper SPE 29111 presented atthe 1995 SPE Symposium on Reservoir Simulation, SanAntonio, Texas, 12-15 February.

16. Behrens, R.A., and Sandler, S.I.: The Use of

Semicontinuous Description to Model the C7+ Fraction inEquation of State Calculations, paper SPE 14925

presented at the 1986 SPE/DOE Symposium on EnhancedOil Recovery, Tulsa, Oklahoma, 23-23 April.

17. Kuenen, J.P.: On Retrograde Condensation and theCritical Phenomena of Two Substances, Commun. Phys.

Lab U. Leiden(1892) 4, 7.18. Whitson, C.H., and Thomas, L.K.: Simplified

Compositional Formulation for Modified Black-OilSimulators, paper SPE 18315 presented at the 1988 SPE

Annual Technical Conference and Exhibition, Houston,Texas, 2-5 October.

19.Nolen, J.S.: Numerical Simulation of CompositionalPhenomena in Petroleum Reservoirs, paper SPE 4274

presented at the 1973 SPE Symposium on Numerical

Simulation of Reservoir Performance, Houston, Texas, 11-12 January.

20. Spivak, A., Dixon, T.N.: Simulation of Gas-CondensateReservoirs, paper SPE 4271 presented at the 1973 SPESymposium on Numerical Simulation of ReservoirPerformance, Houston, Texas, 11-12 January.

21. Cook, A.B., Walker, C.J.: Realistic K Values of C7+Hydrocarbons for Calculating Oil Vaporization During GasCycling at High Pressures,JPT(July 1969), 2, 901.

22. Geoquest, PVTi Reference Manual 2001a, Geoquest,Houston (2001).

23. Schulte, A.M.: Compositional Variations within aHydrocarbon Column due to Gravity, paper SPE 9235

presented at the 1980 SPE Fall Technical Conference and

Exhibition, Dallas, Texas, 21-24 September.24. Hirschberg, A.: Role of Asphaltenes in CompositionalGrading of a Reservoirs Fluid Column, JPT (January1988), 5, 89.

25. Kenyon, D. E. and Behie, G.A.: Third SPE ComparativeSolution Project: Gas Cycling of Retrograde CondensateReservoirs, paper SPE 12278 presented at the 1983Reservoir Simulation Symposium, San Francisco, 15-18

November.26. Izgec, B.: Performance Analysis of Compositional and

Modified Black-Oil Models for Rich Gas CondensateReservoirs with Vertical and Horizontal Wells, MS

Thesis, Texas A&M University, College Station, Texas(2003).

Table 1 Extended mix ture composition

Com ponent Sym bol Mol %

Carbon Dioxide CO2

4.57

Nitrogen N2 0.52

Methane C1

68.97

Ethane C2

8.89

Propane C3

4.18

Isobutane iC4

0.99

N- Butane nC4 1.4

Isopentane iC5

0.71

N-Pentane nC5 0.6

Hexanes C6

0.99

Heptanes C7

1.02

Octanes C8

1.28

Nonanes C9

0.97

Decanes C10 0.73

Undecanes C11

0.53

Dodecanes C12 0.44

Tridecanes C13 0.48

Tetradecanes C14

0.41

Pentadecanes C15

0.36

Hexadecanes C16

0.28

Heptadecane C17

0.26

Octadecanes C18

0.24

Nonadecanes C19

0.19

Eicosanes C20

0.16

C21 's C21

0.13

C22 's C22 0.11

C23 's C23 0.1

C24 's C24

0.08

C25 's C25

0.07

C26 's C26

0.06

C27 's C27

0.06

C28 's C28 0.05

C29 's C29

0.04

C30+ C30+ 0.13

Table 2 Pseudocomponent grouping andcomposition

Ps eudocom ponent Com ponents Mol %

CO2

4.57

GRP1 N2-C

1 69.49

GRP2 C2-C

3 13.07

GRP3 C4-C

6 4.69

GRP4 C7-C

10 4

GRP5 C11

-C16

2.5

GRP6 C17-C34 1.68


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SPE 93374 7

Table 3 Pseudocomponent properties

Com ponent Molecular Weight Pc (ps ig) Tc (0F)

CO2 44.01 1056.6 88.79

GRP1 16.132 651.77 -117.46

GRP2 34.556 664.04 127.15

GRP3 67.964 490.47 350.279

GRP4 112.52 384.19 591.912

GRP5 178.79 269.52 781.912

GRP6 303.64 180.2 1001.13

Table 4 Pseudocomponent properties

Component ZC VC(ft3/lb-mo l) s-Shifts

CO2

0.27407 1.50573 -0.045792

GRP1 0.28471 1.56885 -0.144168

GRP2 0.28422 2.63712 -0.095027

GRP3 0.27197 4.67964 -0.041006

GRP4 0.25668 7.26188 0.003672

GRP5 0.23667 11.09534 0.00893404

GRP6 0.21972 17.67366 0.0115616

Table 5 Variation in parameters selected forregression

Parameter Ini tial Value Final Value % Change

BICGRP6-GRP1 0.0544 0.1231 -126.28BIC

GRP6-GRP2 0.01 0.0226 -126

BICGRP5-GRP1

0.0464 0.1052 -126.72

BICGRP5-GRP2

0.01 0.0226 -126

BICGRP4-GRP1

0.0377 0.0248 34.21

BICGRP4-GRP2

0.01 0.0066 34

BICCO2-GRP1 0.1 0.0657 34.3

BICCO2-GRP2 0.1 0.0657 34.3

BICCO2-GRP3

0.1 0.0657 34.3

BICCO2-GRP4

0.1 0.0657 34.3

BICCO2-GRP5

0.1 0.0657 34.3

BICCO2-GRP6

0.1 0.0657 34.3

SFCO2 0.0066 -0.0458 793.93SF

GRP4 0.0525 0.0037 92.95

SFGRP5

0.0714 0.0089 87.53

SFGRP6 0.095 0.0116 87.78

Table 6 Fluid in place and CPU time for uniformcomposition with depth

OOIP, s tb CPU, s ec. Er ror in OOIP, %

Compositional 999916.20 785.91 -

Rv vs Dept h 958733.40 64.47 4.11

Pd vs Depth 958733.40 65.00 4.11

Table 7 Fluid in place and CPU time withcompositional gradient

OOIP, s tb CPU, s ec. Er ror in OOIP, %

Compositional 941669.40 745.56 -

Rv vs Dept h 888033.20 72.22 5.69

Pd vs Depth 922730.10 64.28 2.01

Table 8 Reservoi r Propert ies

Layer Thickness Poros ity Perm eability (m d)

1 20 0.087 0.1

2 15 0.097 0.2

3 26 0.111 0.3

4 15 0.16 0.2

5 16 0.13 7

6 14 0.17 0.1

7 8 0.17 14

8 8 0.08 2

9 18 0.14 12

10 12 0.13 3

11 19 0.12 10

12 18 0.105 9

13 20 0.12 0.1

14 50 0.116 0.3

15 20 0.157 0.2

16 20 0.157 0.2

17 30 0.157 0.2

18 30 0.157 0.2

Table 9 CPU time in seconds for vertical wells

Com pos itional MBO MBO

Rvvs Depth Pdvs DepthNatural Depletio n

Constant Composition 785.91 64.47 65

Compositional Gradient 745.56 72.22 64.28

Bottom Completion 539.12 82.58 81.32

Top Completion 820.37 80.35 79.01

Reduced kv

985.45 106.35 103.2

Gas Cycling

Compositional Gradient 3021.78 597.77 582.49

Bottom Completion 3068.71 458.86 479.42

Top Completion 3296.56 531 603.04

Reduced kv

4743.82 363 453.81

Low Rates 1957.74 401.39 626.68


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8 SPE 93374

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 1000 2000 3000 4000 5000 6000 7000Pressure (psia)

RelativeVolu

me

Simulated

Experimental

Fig. 1 Simulated and experimental relative volume data from CCEat 254 F

0

0.05

0.1

0.15

0.2

0.25

0 1000 2000 3000 4000 5000 6000 7000

Pressure (psia)

LiquidSaturation

Simulated

Experimental

Fig. 2 Simulated and experimental liqu id saturation data from CCEat 254 F

0

5

10

15

20

25

30

0 1000 2000 3000 4000 5000 6000 7000

Pressure (psia)

GasDensity

(lb/ft3)

Simulated

Experim ental

Fig. 3 Simulated and experimental gas density data from CCE at254 F

0

0.5

1

1.5

2

2.5

3

0 1000 2000 3000 4000 5000 6000

Pressure, psia

GOR,M

scf/stb

Whitson and Torp Coats

Fig. 4 Gas-oil ratio comparison from Coats versus Whitson andTorp methods

0

0.5

1

1.5

2

2.5

3

0 1000 2000 3000 4000 5000 6000

Pressure, psia

Bo,rb/stb


Fig. 5 Oil formation volume factor comparison from Coats versusWhitson and Torp methods

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1000 2000 3000 4000 5000 6000

Pressure, psia

Viscosity,cp


Fig. 6 Oil viscosity comparison from Coats versus Whitson andTorp methods


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SPE 93374 9

Fig. 7 Oil-gas ratio comparison from Coats versus Whitson andTorp methods

Fig. 8 Gas formation volume factor comparison from Coatsversus Whitson and Torp methods

Fig. 9 Gas viscosity comparison generated from Coats versusWhitson and Torp methods

12500

12550

12600

12650

12700

12750

12800

12850

12900

12950

13000

0.6 0.62 0.64 0.66 0.68 0.7 0.72 0.74

Molar composit ion fraction

Depth(ft)

GWC

0

0.02

0.040.06

0.08

0.1

0.12

0.14

0.16

0.18

0 1000 2000 3000 4000 5000 6000

Pressure, psia

OG

R,stb/Mscf


Fig. 10 C1-N2compositional gradient

12500

12550

12600

12650

12700

12750

12800

12850

12900

12950

13000

0.04 0.06 0.08 0.1 0.12 0.14 0.16

Molar composit ion fraction

Depth(ft)

GWC

0

1

2

3

4

5

6

7

8

0 1000 2000 3000 4000 5000 6000

Pressure, psia

Bg,rb/Mscf


Fig. 11 C7+compositional gradient

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 1000 2000 3000 4000 5000 6000

Pressure, psia

Fig. 12 Change in dew-point pressure with depth, uniformcomposition case

Viscosity,cp


4000

4500

5000

5500

6000

12500 12550 12600 12650 12700 12750 12800 12850 12900

Depth, ft

Press

ure,psi

Compositional Model MBO Model


10/14

10 SPE 93374

Fig. 13 Change in dew-point pressure with depth, compositionalgradient case

Fig. 14 Oil production rate for the model initialized withcompositional gradient

Fig. 15 Average field pressure with composi tional gradient

0

100

200

300

400

500

600

0 500 1000 1500 2000

Time, days

ProductionRate,stb/day

MBO initialized w ith fixed RvCompositionalMBO initialized w ith fixed Pd

4000

4500

5000

5500

6000

12500 12550 12600 12650 12700 12750 12800 12850 12900

Depth, ft

Pressure,

psi


1044 psia900 psia

4000

4500

5000

5500

6000

12500 12550 12600 12650 12700 12750 12800 12850 12900

Depth, ft

Pressure,

psi


1044 psia900 psia

Fig. 16 Oil production rate for the natural depletion case, constancomposition

0

20

40

60

80

100

120

0 500 1000 1500 2000

Time, days

GOR,Mscf/stb

MBO initialized w ith fixed RvCompositionalMBO initialized w ith fixed Pd

0

100

200

300

400

500

0 500 1000 1500 2000

Time, days

ProdcutionRate,stb/day

MBO with Rv vs DepthCompositionalMBO with Pd vs Depth

Fig. 17 Gas oil ratio for the natural depletion case, constantcomposition

0

1000

2000

3000

4000

5000

6000

7000

0 500 1000 1500 2000

Time, days

Pres

sure,psia

MBO w ith Rv vs DepthCompositionalMBO w ith Pd vs Depth

0

0.05

0.1

0.15

0.2

0.25

0 500 1000 1500 2000

Time, days

Saturation


Fig. 18 Oil saturation distribution for the model initialized withcompositional gradient


11/14

SPE 93374 11

Fig. 19 Oil saturation distribution from compositional model withcompositional gradient

Fig. 20 Oil saturation distribution from MBO model withcompositional gradient

Fig. 21 Oil saturation distribution from compositional model foruniform composition

0

0.02

0.04

0.06

0.08

0.1

0.12

0 1000 2000 3000 4000 5000 6000

Time, days

Saturation

MBO w ith Rv vs DepthCompositionalMBO with Pd vs Depth

Fig. 22 Average oil saturation for gas cycling case

0

20

40

60

80

100

120

0 1000 2000 3000 4000 5000 6000

Time, days

GOR,Mscf/stb


Fig. 23 Gas-oil ratio for gas cyclin g case

0.05

0.1

0.15

0.2

0.25

0.3

1 2

Gridblock Number

Satura

tion

3

500 day s 1000 day s 1500 day s 2000 day s

2500 days 3000 days 4000 days 5000 days

Fig. 24 Saturation distributi on for compositional model for layer 9


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12 SPE 93374

Fig. 25 Saturation distr ibution for MBO model for layer 9

Fig. 26 Saturation distribution for MBO model (Pd versus depthiniti alization) for layer 9

Fig. 27 Saturation di stribu tion for MBO model gri dblock (25, 25, 4)

0

0.05

0.1

0.15

0.2

0.25

0.3

1 2 3

Gridblock Number

Satura

tion



0

0.05

0.1

0.15

0.2

0 1000 2000 3000 4000 5000 6000

Time, days

Saturation

CompositionalMBO with Rv vs Depth

Fig. 28 Saturation di stribut ion f or MBO model gri dblock (25, 25, 5)

Fig. 29 Oil-gas ratio versus pressure generated from differencompositions

Fig. 30 Average oil saturation for low production and injectionrates

0.1

0.15

0.2

0.25

0.3

1 2

Gridblock Number

Saturation

3

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 1000 2000 3000 4000 5000 6000

Pressure, psia

LiquidContentofGas,stb/Mscf Without flashing original gas

Flash to 5000 psiaFlash to 4000 psiaFlash to 3000 psia



0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 1000 2000 3000 4000 5000 6000

Time, days

Saturation

MBO w ith Rv vs DepthCompositionalMBO Pd vs Depth

0

0.05

0.1

0.15

0.2

0 1000 2000 3000 4000 5000 6000

Time, days

Saturation

Compositional

MBO with Rv vs Depth


13/14

SPE 93374 13

Fig. 31 Average oil saturation with wells completed at the bottomof the model

Fig. 32 Gas-oil ratio with wells completed at the bottom of themodel

Fig. 33 Oil productio n rate for kv/khratio of 0.0001

0

20

40

60

80

100

120

140

160

180

0 1000 2000 3000 4000 5000 6000

Time, days

GOR,Mscf/stb

MBO with Rv vs DepthCompositionalMBO with Pd vs Depth0

0.02

0.04

0.06

0.08

0.1

0 1000 2000 3000 4000 5000 6000

Time, days

Saturation


Fig. 34 Gas-oil ratio f or k v/khratio of 0.0001

0

50

100

150

200

0 1000 2000 3000 4000 5000 6000

Time, days

GOR,Mscf/stb

MBO w ith Rv vs DepthCompositionalMBO with Pd vs Depth

0

100

200

300

400

500

0 1000 2000 3000 4000 5000 6000

Time, days

Rate,stb/day

MBO Compositional

Fig. 35 Oil production rate for gas cycling with horizontal well

0

50

100

150

200

0 1000 2000 3000 4000 5000 6000

Time, days

GOR,M

scf/stb

MBO Compositional

0

50

100

150

200250

300

350

400

450

0 1000 2000 3000 4000 5000 6000

Time, days

ProductionRate,stb/day


Fig. 36 Gas-oil ratio for gas cycling with horizontal well


14/14

14 SPE 93374

0

0.1

0.2

0.3

0.4

0.5

0 1000 2000 3000 4000 5000 6000

Time, days

Recovery

Factor

MBO Compositional

Fig. 37 Recovery factor for gas cycling w ith hori zontal well

Documents

SPE93374_Performance Analysis of Compositional and Modified Black Oil Models for Rich Gas Condensate Reservoir