The Role of Reservoir Simulation in Optimal Reservoir Management

8/19/2019 The Role of Reservoir Simulation in Optimal Reservoir Management

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SPE 14129

The Role of Reservoir Simulation in Optimal

Reservoir Management

by G.W. Thomas, Scientific Software-intercomp

SPE Member

Copyright

1X, Sockty of

PetroleumEnginaara

This paperwas proaantd at theSPE 19SSInternationalMeeting

on petroleumEngineeringheld in Beijing,CMa

March

17-20,

19SS.The materialis

subjecttocorrectionbythe author.PermissiontoCOPYsrestrictedto an ab.str~ OfMt morethan300 words,WriteSPE. P.O. SoxS33S3S,Richardson.

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SIMULATIONANDVIRGINRESERVOIR DEVELOPMENT

When a reservoir simulator is employed to assist in

ABSTRACT

ptenning the development of a virgin reservoir, the

reservoir description is typically limited. Consequ@ly,

This paper discusses the role reservoir simulators only a minimal degree

of

optimisat ion is poa%ible.

play in formulating initial development plans, history

Nevertheless, some useful insights can be cbtained with

matching and optimizing future production and in planning

the aid of a simulator that can minimise the number of

and designing enhanced oil recovery projects. The Hibernia

decisions one must make in planning field development.

Field in Canada and the Hassi R’Mel in AIgeria illustrate how

In perticuter, the simulator can end should be used to

simulation can be used to asdst in initial reservoir

a$sesa sensitivity in computed results to uncertainties in

development. The Lookout Butte F.undle (Alberta) and others

the reservoir description and rock-fluid data.

It is

are cited to exemplify Optimhsl,fon of future production

surprising how often variations

input data over

plans with the aid of simutetion. Finally, applications to

reasonable ranges of uncertainty, for some reservoirs,

several reported EOR projects are briefly discussed with

yield modest changes in the computed results. On the

major emptux~is concentrating on the Bati Raman Field in

Turkey.

other hand, it is useful to know, in the early stages of

development, where the greatest effort should be

concentrated to obtain those data that affect calculated

INTRODUCTION

performance the most.

‘he purpose of this paper is to provide an overview

Simulation studies at the development stage

on the role of reservoir simulation in managing hydrocarbon

because of the uncertainties involved, are regarded as

reservoirs. As pointed out by Coatsl , reservoir simulation, in

the broad sense, has been practiced since the 1930%, when

preliminary. Npically, they are periodically updated as

more information becomes available; This means that

some

of

the first calculetionaI procedures were deveIoped to

early development plans arising from the first sim’? ation

predict reservoir performance. Here, however, we take a

studies should be sufficiently flexible to accom mudate

narrower view, and restrict our discussion to applications of

future contingencies as one learns more about the

numerical reservoir simulation. ‘his involves solving targe reservoir. This presents a severe challenge where the

s~ algebraic equations on digitaI computers to

reservoir in question is highIy complex, large in extent or

approximate transient, multiphaee

or

muIticomponent flow in in a hostiIe environment - all of which may require large

heterogeneous media. ‘I?tis technoIgy started in the mid to

investments to put it on production.

late 1950%and, within the last twenty years, has played an

increasingly important-role in the development, planning and

In cases where the reservoir description and roek-

management of gas and oiI reservoirs.

fluid properties are reasonably defined, one can we a

simutetor to plan well locations and densities aswtming

In the folluwing, we first discus~ the role of

voidege replacement by injection to maintain pres..ure.

reservoir simulation as a tool in planning the initia 1 Such strategies can be compared to primary depletion

development of a reservoir. The discussion then turns to through the same number of wells to arrive at the best

their uses as predictive tools when investigating various

development policy for the reservoir.

future operating strategies.

Finally, some attention is

devoted to their utility in planning and executing enhanced Arwlication to the Hibcrnia FieId

oil recovery schemes. Illustrations in the form of case

histories are provided, albeit these are necessarily not

To illustrate, we cite the Hibernia Field off the

detailed because of space limitations.

Neverthele$w,

3fIStePn Ccest of Canada2. me fjeId lies abut 32tI km

sufficient references to recent literature on the subject are

southeast of St. John%, Newfoundland in a water depth of

given for the interested reader.

80 m. Five welts were drilIed to confirm the existence of

substantial hydrocarbon reserves

in at least two

reservoirs, the Avalon and the Hibernia sendstones. The

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THEROLEOF RZSEPSfOIR SIMULATIONN OPTIMALRSSERVOIRNANAGENENT

SPE 14129

Avalon reservoir appears to be heterogeneous with wide

Applications to Gas Condensate Systems

variations in the porosity and permeability, whereas the

deeper Hibernia is more homogeneous. Correlations of the

In the Hibernia Field, a black-oil reservoir simulator

limited porosity - permeabili ty data were used to extrapolate

was employed to arrive at preliminary development

into areas where data were lacking.

Correlations of decisions.

This 1s frequently done even though the

verticaI/horizontal permeability ratios were used in a similar

reservoir may contain fluids that undergo substantial

manner. A porosity cutoff of 13% was used to define the net

compositional changes during production. The motivation

pay in the Avalon while 10% was employed in the Hibernia.

for doing so is most often due to lack of data precisely

Average connate and residual oil saturations in the Avalon

defining the compositional behaviour of the fluids in the

were estimated at 25%.

For the Hibernia, connate water

early development stages. Moreover, black-il simulators

varied from 11 to 15% while 30% average residual oil

can still provide usefuI information in such systems at

saturation was assumed.

substantially lea.. cost than a compositional simuIator5.

EventuaNy, however, resources must be devoted early on

AH evidence indicates that the two reservoirs are

to the correct characterisation of the fluids and definition

non-cornmunicating.

The Avalon ccntains an apparent

of their phase behaviour.

undersaturated crude oil with a relative density of 0.873. PVT

properties for the hydrocarbon were obtained from a drill stem

As exampIes, we cite two large gas condensate

test fluid sample.

The Hibernia reservoir has more

reservoirs.

The first, the Has..i R’Mel is located in

complicated fluid propties in two separate fault blocks. In

Algeria6. The field was discovered in 1953 and contained

one, a saturated crude, probably a volatile oil, of relative

about 1.7 x 1012 mS

of

retrograde condensate gas at

density, 0.825, is apparently overlain by what appears to be a

32x10S kPa.

The reservoir has a surface area of 4800

gas condensate with a liquid gas content of 0.001 m /m*. For

km’.

Because of its vast reserves and closeness to ports,

this block the fluid properties

were generated using an ambitious development plan was executed in the earIy

correlations assuming an initial seturat ion pressure of 40x10

1970%baaed on a bleck-oit simulation study. At the time,

end a sclut ion gasail ratio of 356 m ‘/m’. In the other fault

only 20 wells had been drilIed and the geological

block, the oil appears to be undersaturated having a relative description was limited. Consequently, full continuity of

density of 0.850, there again, a drill stem test fluid was

the reservoir was assumed. The objective was to produce

analysed to determine the PVTproperties.

a fixed daily rate of rich gas, extract the condensate,

market scma of the- dry gas end reinject the rest to

The first simulation runs involved 2-dimensional

recover any condensate dropout that might occur.

For

cross-sect ions to generate pseudo functions3~4 for subsequent

this purpose, a line drive gas injection scheme was

use in 3+3imensional model% For the Avalon and Hibernia, 21-

implemented.

and 5-layer models, respectively, were used to generate

pseudo relative permeabiIities.

These subsequently were

Haaei R’Mel now has about 200 welLs and giant

employed in a 28 x 23 x 2 AvaIon model and a 24 x 20 x 2

plants for ga? treatment and gas injection. production to-

Hibernia model. h each case, square grid blocks 569 m on a

date is 5 to 6% of the initial gas reserves. During the

side were employed. Well locations were originally selected to development drilling, en oil ring of 0.82 relative density

give reasonable pettern coverage over thoseregions where the and 15.2 m thickness was discovered - hence Haasi RIMel

oil accumulations were considered to be greatest . Completion

can be regarded as a volatile oil reservoir with a huge rich

intervals for producers and injectors were selected such that

gas cap. A fault system was also discovered that was

oil production would be favoured while production of gas and subsequently better defined by seismic investigation.

water, where pert inent, was minimised.

Some revisions were made in the geological description of

the field when 100 weUa were in place. The subsequent

Four production/injection

scenarios were

need is to @rform a major update using information from

investigated in the Avalon while four and five were considered

all welt., the production history, the seismic surveys and

for each of the fault blocks in the Hibernia reservoir. Some of

state-of-the-art simulation tooLs.

In particular, the

the results of the study are shown in Figs. 1-3. In the~

effects of the faults and retrograde condensation and

figures W.I. and G.I. refer to flank water and crestal gas

revapourisation need to be examined in detail. The

injection, respectively.

It is seen that in the AvaIon,

appropriatenes~ of the line drive is aLscin question.

differences in the water and gas injection cases were

insignificant with the present geological description of the In such an update, one first determines to what

reservoir. In the Hibernia, it was found that an ultimate

extent, if any, he can use previous seismic, geological and

recovery level of 50% of the original oil-in-place may be

petrophysical interpretations.

With regard to a

achieved through an optimised production/injection strategy.

retrograde condensate, the effect of liquid dropout on

The uncertainties in these reauIts are linked to the geological well deliverability is also an important issue. Moreover,

model. As”the latter is improved in the early development

where cycling is performed, one would like to know what

planning process, optimum recovery schemes can be desigiwd the .~timum is to maximise Iiquid revapouriaation.

to account for the reservoir complexities.

Again, in reservoirs with thin oil zones overlain by

massive gas reserves - and possibly underlying water - the

probebitity of coning can be high should producing weila

be completed in the oil zone. The question arises, can the

oil be recovered through displacement or vapouriaat ion by

selective completion of dry gas injection welLs, as an

alternative to producing directly from the oil zone?

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SPE 14129

G.w. Thomas

Finally, given a certain well pattern - like the line drive in

development. Here we’ve just conveyed the flavour for

the Has$i R’Mel -

is it the optimum in view of possible

some particular cases. The approach one takes is of

geological discontinu{ties such as faults, pinchouts etc?

course problem+ependent and may be unique for a given

These and similar issues constitute the natural province for

reservoir. (2) The devebpment plan, even though aided by

reservoir simulators and sometimes definitive answers can

sophisticated tools, should be regarded as tentative.

emerge from carefully constructed models.

Effort should be made, during the early stages, to endow

it with maximum flexibility and continually upd&te it with

The issues of lSquid dropout, revapourisation, etc.

additional simulation studies as new data are obtained.

may at some point require application of a compositional

wimulator. Such simulators internaUy generate the PVT SIMULATORS AS PREDICTIVE TOOLS IN DEVELOPED

characteristics of the hydrocarbon fluids using a “tuned”

RESERVOIRS.

phase behaviour package. me ‘tuning” as performed prior to

the simulations by adjusting certain coefficients and/or

In a sense, development of a reservoir is an on-going

parameters in the phase behaviour package such that it

process that continues over its productive life. However,

reproduces, within acceptable limits? the results of a

one can divide reservoirs into two categories - those with

particular laboratory experiment on the hydrocarbon fluid.

little or no productive history, end those that have

The coefficient adjustment is accomplished using regression

produced for some period of time. ‘Ihe distinction is

analysis5 or trial-and+rror computer runs. It is important in

particularly clear with regard to reservoir simulation. In

such applications that data errors (from sampling, laboratory

the former case, the simulator is applied in a qualitative

analysis, etc) be kept to en absolute minimum. Furthermore,

sense, i.e., it is not a priori calibrated to a particular

fluid samples from different wells wiU, hopeful~y, have

reservoir% characteristics, since these are largely

similar or neer+imilar characteristics such that a

unknown. In the latter, the response of the reservoir to

representative or several regional representatives can be

some predecided development plan is presumably known,

used to typify the whole. Unfortunately, this is not always

and effort is first devoted to the task of calibrating the

the case.

simulator such that it reproduces the response i.e. the

past production history. This history matching involves

For

example, h Fig. 4’we djspley plots of retrograde

trial-end-error runs with the simulator in which input data

liquid dropout (as percentage of hydrocarbon pore volume) as

adjustments are made within reasonable bounds until a

functions of pressure for several fluid samples taken from a

satisfactory match is achieved. *

large (2000 km*) lean gas retrograde condensate reservoir

(the name and location are witheld for proprietary reasons).

TypicaUy, one seeks to reproduce the field-wide pressure,

Such data are derived from constant volume depletion

water-oil ratio and ges+il tatio performance and also

experiments under controUed laboratory conditions on what

match individual weU behaviour for the asme vnriables.

presumably are representative fluid semples7. Obviously,

Unfortunately, the procedure frequently involves iu-

from Fig. 4 one cannot easily decide which well sample is conditioned systems, and unique results are not

representative.

The proper choke becomes even more

guaranteed.

As a consequence, it can be time

cIouded given the poasibititiea for eempting errora

consuming, coatty, and, at times, frustrating. However, a

(contamination, fluid 10ss, long dMsnce transport, etc.).

reaourcefuI engineer with in-depth understanding of

However, in development planning, one frequently empIoye a

reservoir behaviour can achieve meaningful matches.

simulator in worst caee/beet case scenarios.

An effort is

then made to determine the most likely case between these

Performing Evaluation of the

extremes (this could be the average

of the

extremes), and

Lookout Eutte RundleA Pool

then plan the development around the latter. In this context.

if one considers depletion without cycling, men the data from Once a satisfactory match is achieved, the

WeUe 1 and 6 clearly define the worat and best cases,

simutator is used in a predictive mode to investigate

respectively, assuming retrograde liquid condensation occurs

various production alternatives. Here again, the objective

in the reservoir prior to fluid entry into the welLs. The phase

is to optimise future operations of the reservoir. As an

behaviour package is then tuned to each situation, i.e. an example of such an appUcation, we cite the Lookout Butte

effort is made to reproduce the curves in Fig. 4 for WeUs 1

Rundle A Pool located in Alberta, Canada~4. The

end 6 to characterise the hydrocarbon properties for the

reservoir is a tight, interbedded limestone having an

worst end best case situations. Should the resuIts from the

average porosity of 6.5% and permeabilities in the range

subsequent simulations for each scenario not differ

0.1 to 0.3 md. fie reservoir dips to the west end north

subetant. ‘Jly, then one need not concern himself about and is delineated by en extensive aquifer on the west, and

defining the most likely case since averages from the

a fault on the east (see Fig 5). It contains a dry gas

eXtrema would be sufficient. Otherwise, one might take

some curve weighted in favour of the pIots that are closest

together in Fig. 4 (shown by the dashed line), fit the phase

beheviour package to this, end w this tuned result in the

*Efforts have been made to deveIop software

simulator for the moat Iikely scenario.

~ams that automate the history matching t-e=.

However, these have not found Iairge scale use on a

In concluding this section we emphasise two things: commerical basis to+ate.

(1) ‘llIere are many different waya in which a reservoir

simulator can play a vital role in optimum reservoir

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THEROLE RJZSERVOIRIMULATIONN OPTIMALWSERVOIRMANAGEMENT

SPE 141

condensate underIain by the aquifer. GeoIogicaI and core

northern and southern parts. Moreover, it is aIso regarded

data indicate the reservoir is extensively fractured and that

ashight’isk since it is near to Well 4-32 which was shut i

vertical fractures dominate.

In late 1963 production

because of high water production. The 13-32 location

commenced by depletion coupled with gaa cycling. Dry gas

gives the highest cumulative gas production and increase

was injected into one weU(We114-13 in Fig. 5)untiIlate 1967

field deliverability 3.4 x 106 m:/D over the productivity

at which time it was converted to a producer and blowdown

in 1972 (the year the study was performed). This well

started.

Prior

to this, only minor amounts of water, were

in communication with some other wetls in the field an

produced. However,

thereafter four producing welL~

was considered as a future drilling location. There wa

experienced water production that increased steadily until

however, some concern because of its proximity to th

the water-gas ratio averaged 1 x 10-5 m‘/m 1 by June, 1972. fault on the east.

The objectives of the study were to determine the

The utility of a reservoir simulator should b

mechanisms causing the water production, develop an

recognised in this brief case history.

It provide

optimum depIetion plan for the reservoir, and evaIuate the

engineering answers to certain questions that one migh

surface facilities required to carry out the depletion plan. To

pose regarding future exploitation of a reservoir. I

determine if water production was caused by water coning or

however, cannot make the decision as to which possibilit

fingering, two types of modeI studies were executed:

is the optimum. This remains within the realm of huma

Individual well coning studies using a radial gas-water

judgment (thankfully). The judgment, in this case, wa

simulator, and crossaectional studies to evaluate fingering.

that Well 5-21, because of Iow risk, should be drilled

t

Both invoked history matching the performance data. In

recover gas from the southern portion of the reservoir

addition, the adequacy of the reservoir description required

Moreover, Well 14-13 shouId be drilled even though

to match the history was evaluated. Finally, calibration of

constitutes a high risk because of substantial water influx

the simulator was accomplished by matching the pressure

However, without it, gas in the North may be trapped

history of the entire

field and the individual well

otherwise by the incoming water.

FinalIy, one shouI

performances. The results of the history match were used to

abandon Well 15-29 as a poasibilit y and re+vaIuate

determine the distribution of gas-in-place and the water

drilling of Well 13-32 after more history become

influx in the prediction and optimisation phases of the study.

available.

In addition the reservoir simulator, after history matching,

was coupled with a gas gathering system simulator to

Other interesting case histories involving histor

optimise the surface faciUtiea15. The latter exercise

matching and predictions have appeared in the recen

involved examining various possible effective line diameters

literature. One involves the Leroy Gas Storge Facility i

and welI connections to yield a maximum in deliverability. In

Wyoming16. A simulator wqa used to match the pressur

Figs. 6 and 7 we show typical matches of pressure and water- history of the reservoir incIuding the effect of a time-and

gas ratio for one of the wells in the field.

pressure-dependent leak to the surface. The simulato

was a useful tool in the ccmprehensi /e analysis required

It was concluded from the history match runs that

to understand, monitor and control the leakage. The cas

water coning was the cause

of

the water production in the

history is significant in that it documents how reIevan

reservoir. The prediction phase

of

the study involved computer simulations can, with other engineering studies

choosing one or more optimum infill drilling locations from lead to safe and economic gas storage operations. Tw

among the four possible sites indicated by the arrows in Fig.

other recent studies akc are of interest. One describe

5. A base case, with no infiU drilling was also run. The total

application of a black OK simulator to the El Gueri

field deliverability for each case is shown in Fig. 8. For the

reservoir in the Ashstart Field

of offshore Tunisia17. Th

predictions, both the reservoir and surface system were other treats the Sawtelle Field in California 18, The E

simulated simultaneously. The field was produced at the

Gueria is a moderately to highly fractured nummulitic

maximum of the production facilities. Wells were shut in

limestone originaUy containing an undersaturated oil o

when their production declined below 0.15 x 106 m‘/D or

0.88 relative density. The reservoir is produced wit

when the gas-water contact reached the bottom perforations. injection of seawater to maint~in pressure above th

bubblepoint pressure. A three+imensional model wa

Well 14-13 initially increased the field deliverability

constructed to perform the history match and predictions

about 3 x 106 m ‘/D over the other cases and 5.8 x 106 ma/D ‘Ihe model was also augmented by wellbore hydraulic

over the base case. Because the gas-water contact had been

routines to simulate vertical

or

inclined flow to th

depressed by gas-injection in the proximity of this location, surface. fie Sawtell study employed a two+imensional,

the water influx rate was very high as the contact rebounded.

three-phase black oil model and is of interest since

As a result, the well watered out at Lfie end of 1978.

involves a complex and unusually shaped reservoir

Consequently, this is regarded as a high risk well. Well 5-21

Finally, we cite the simulation study of the East Velm

presents a low risk end is necessary to drain gas from the West Block Sims Sand Unit in 0klahoma19. This study

tighter portions of the reservoir in the south. The 15-29 weIl

of intereat since it involves a rather old reservoir fo

is located in that part of the reservoir which is poorly

which

few data exists for the primary production phas

defined.

This region has limited communication with the

(1949-1962). The history match of field pressures, gas

and water+il ratios was largely for the secondary

recovery phase (1962-1972) in which water was injected

Predictions included the possibility of continue

waterflood operations and inject ion of carbon dioxide.

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SPE 14129

G.K.

Thomas

APPLICATIONS TO EOR PROJECTS

Sometimes reservoir simulators are used to assess

the relative merits of various enhanced oil recovery (EOR)

schemes. In such cases, the simulator is used in a predictive

mode both with or without prior history matching. In

particular, Aydelotte and Pope20 and George, et a121 report

on the novel use of reservoir simulators to validate and assist

in the development of simplified, reliable inexpensive

predictive- modeLs for steamfloodin

~ and micell

ar~lymer

flooding. Recently, Frazier and Todd 2 employed a simulator

to design and evaluate an application of Iiquified petroleum

gas (LPG) in a reservoir that had previously been

waterflooded. The choice was to either abandon the field or

attempt an EOR process. The simulation study indicated that

an additional 7% of the original oil in-place could be

recovered from a miscible LPG flood.

me predictions

involved use of the best available reservoir description, i.e.

no history match runs were employed to calibrate the

simutator. l%e project was initiated in the field with propane

injection in three wells starting in July, 1980.

As of

December 1981, it appeared as though the process was

working as predicted by the simulation study.

Simulation has been used to design, monitor and

evaluate several steam in”ection projects23-27. The

A

Georgsdorf Field in Germany 7 presents an interesting case

history. Here, production history over 10 years, including six

with

steam injection,

was

satisfactorily

matched.

Considering the usual reservoir complexities and the

difficulties associated with nonisothermaI operations, the

matches are remarkably good. Predictions were then made

to determine steam requirements in certain portions of the

reservoir, to arrive at a plan for future project expansion,

and to ascertain where new injection welLs and infill

producers should be located.

A very interesting application of the use of

reservoir simulators in the management of reservoirs is

provided by the Bati Raman Field in Turkey 28. The reservoir

contains substantial reserves (2.9 x 108 m‘) of a heavy crude

oil (relative density = 0.986) with a bubble point pressure of

1103 kPa, The amount of gas in solution at the bubble point

pressure is quite low, i.e. 3.2 m ‘/m 1. There is no natural

water intlux into the reservoir.

At discovery in 1961 the

reservoir prewre was 11,032 kPa. Currently, it is 2,758 kPa.

There are 103 wells - all pumping - with a total production

rate of 413 m‘/D. The estimated primary recovery is 1.5%

of the original oil in-place. A pilot waterflood indicated that

an additional 3.5% could be recovered by this means. The

reservoir presents an intriguing and difficult challenge for

two reasons: (1) lt is Turkey??largest single oil reserve; (2) It

has essentially no internal energy to as..ist production, i.e.

recovery must rely almost entirely on external means.

A suite of simulation studies were executed to

screen various EOR processes. Simulation of water flooding

led to a prediction of 5% recovery, confirming the field pilot

tests. ‘fhe reservoir presents other complexities in that it is

fractured and displays dual porosity29 characteristics in .aome

parts. Simulation of steam flooding indicates 32% recovery if

the system behaves like a single poiosity system whereas only

half

this amount is recoverable by steam if it is indeed a dual

system throughout.

Nevertheless, this process and

immiscibIe carbon dioxide injection appear the most

favorable. From an economic viewpoint, the latter

process is the most feasible because of a nearby carbon

dioxide gas reserve and the high initiaI investment

requirements for steam injection. Currently, a large

reservoir simuiat ion study using a fractured reservoir

simuIator capable of handling carbon dioxide diffusion

into the heavy oil is being executed. At the same time a

field pilot project is being planned to assist in optimum

development of the reservoir. Early indications are that

17- 32% recovery can be expected.

CONCLUSIONS

Reservoir simulators play an active and important

role in the optimum management of oil and gas reservoirs.

They prGvide insights which could not otherwise be

obtained, especially in complex systems where simpler

reservoir engineering methods are found wanting. We

have seen how they can be used in the infancy, maturity

and final days of a reservoir% life. Indeed, in some

instances, they have indicated the existence of additional

oil reserves which were later ‘discovered” by subsequent

driIling30. However, we emphasise that there is no

substitute for sound engineering judgment. Ultimately,

the opt imisation must be done on that level. A reservoir

simulator is just another tool in the engineer% arsenal

that, hopefully, enables him to probe deeper, and gain a

larger measure of “understanding.

REFERENCES

1.

Coats, K.H.: “Reservoir Simulation: State~f-the-

Artn, J. Pet. Tech (Aug., 1982) 1633-1642.

2. Handyside, D.D. and Chipman, W.I.: “A Preliminary

Study of the Hibernia Fieldw, Paper No. 82-32-24,

Presented at the 33rd Annual Technical Meeting of

the PetroIeum Sociey of CIM, Calgary, Cmada 6-9

June, 1982.

3.

Costs, K.H., Dempsey, J.R. and Henderson, J. H.:

‘me Use of VerticaI Equilibrium in Two-

Dimensional Simulation of Three-DimensionaI

Reservoir Performance”, Sot. Pet. Eng. J. (March,

1971), 63.

4. Kyte, J.R. and Berry, D.W.: “New Pseudo Functions

To Control Numericai Dispersion”, Sot. Pet. Eng. J.

(August, 1975), 269.

5.

Coats, K.H.:

‘Simulation of Gas Condensate

Reservoir Performance”, Paper SPE 10512, Sixth

SPE Symposium on Reservoir Simulation, 31 Jan, -3

Feb., 1982, New Orleans, La.

R Gondouin, M., Iffly, R, and Husson, J.: “An Attempt

to Predict the Time Dependence of Wet

Deliverability in Gas Condensate Fields,” Sot. Pet.

Eng. J. (June, 1967), 113-124.

. ..

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THE ROLE OF RESERVOIR SIMULATION IN OPTIMAL RESERVOIR MANAGEMENT

SPE 14129

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8.

9.

10.

11.

12.

13.

1.4.

15.

16.

17.

18.

19,

Whitson, C.H., and Torp, S.B.: ’’Evacuating Constant

volume DepIetion Data”, J/of Pet, Tech. (March,

1973),610-620.

Chavent, C. Dupuy, M. and Lemonnier, P.: “History

Matching by Use of Optimal Control Theory,” ~

Pet, Eng. J., (February 1975) 74-86, AIME, Vol 259.

Wasserman, M.L., Emanuel, A.S., and Seinfeld, J.H.:

tlpra~tical Applications of optimal Control Theory

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Documents

The Role of Reservoir Simulation in Optimal Reservoir Management