26 Oilfield Review

Improving the Virtual Reservoir

John O. AfilakaCaracas, Venezuela

Jamal Bahamaish Abu Dhabi Company for Onshore OperationsAbu Dhabi, UAE

Garfield BowenKyrre BratvedtJonathan A. HolmesTommy MillerAbingdon, England

Paul FjerstadDubai, United Arab Emirates

George GrinestaffBPAberdeen, Scotland

Younes JalaliCharles LucasRosharon, Texas, USA

Zulay JimenezPDVSA E&PCaracas, Venezuela

Tony LolomariEdward MayHouston, Texas

Edy RandallBPWareham, England

Waterflood, gas flood or drill infill wells? Using a desktop laboratory, engineers can

test reservoir-development scenarios, evaluating tens or even hundreds of possible

well paths and iterating to a best solution before rig costs begin to mount.

Understanding a reservoir is much like unravelingthe mysteries of the stars—both are far awayand accessible only to remote-sensing technol-ogy. Astronomers ascend to their telescopes andarrays of antennae, and by careful study of cap-tured optical, radio and X-ray frequencies, theycharacterize a small proportion of vast space,mostly major features like galaxies and nebulae,or stars within our own galaxy. The situation isnot so different for geoscientists and engineers,who rely on remote sensing to understand majorsubsurface features such as formation bound-aries and faults. Like our upward-looking col-leagues who send rockets into space to obtaindetailed data from a tiny fraction of the universe,in the oil industry, we obtain detailed informationnear wellbores sunk into the reservoir.

Whether from outer space or underground,the data provide a limited picture of remote envi-ronments. To understand the cosmos, scientistsdevise models, simulations of the way they thinkthe universe behaves, and test those modelsagainst reality—represented by the captureddata. In our industry, we do the same with, forexample, basin, geomechanical and reservoirmodeling. We test the models against seismicdata, rock cuttings and cores, well logs, and ulti-mately hydrocarbon production.

In 1949, Morris Muskat indicated that he wasworking on a computer simulation to determineoptimal well spacing.1 The first simple reservoir

simulators appeared in the 1950s as solutions of differential equations for fluid flow in a homogeneous material with simple geometry.Later, computers were programmed to modelflow through blocks of the earth.2 During the1960s, improved algorithms solved equationsfaster and more accurately. The models becamelarger and more complex as computing speed,memory and algorithm sophistication improved.More physics was added, extending solutionsfrom flowing a single phase to flowing threephases—gas, oil and water—then allowing thecomposition of the gas and oil to change withpressure and temperature. Methods for solvingirregular geometries eliminated the need tomodel reservoir blocks using rectangular grids.

Until recently, simulators resolved the reser-voir into blocks hundreds of meters across—significantly larger than the resolution of theseismic and well-log information used in geo-logic modeling. Today, reservoir simulators canhandle more gridblocks and model more compli-cated geology, allowing closer adherence to geo-logic models. Incorporating complex geologicinput makes a more realistic reservoir model,which can be used to match historical productiondata to confirm or improve the geologic model.

Simulation software also has changed as aresult of improvements in drilling technology.Multilateral and extended-reach wells allow moreoptions for draining reservoirs.3 A multilateral well

For help in preparation of this article, thanks to Jonathan P.Cox, Kirsty Foster, Jonathan Morris and Terry Stone, Abingdon,England; Neil Goldsworthy, Miri, Sarawak, Malaysia;Thomas Graf, Aubrey O’Callaghan and Raul Tovar, Caracas,Venezuela; Omer Gurpinar, Denver, Colorado, USA; Ramdas Narayanan, Abu Dhabi, UAE; Roger Pollock,Clamart, France; Ian Raw, Rosharon, Texas, USA; Jeb Tyrie,Aberdeen, Scotland; and Johan Warmedal, Bergen,Norway. Thanks also to student interns Rakesh Kumar,Shekhar Sinha, Leonardo Vega and Burak Yeten for theirwork on the dual-drive reservoir studies.

ECLIPSE, ECLIPSE100, ECLIPSE300, ECLIPSE Office, FloGrid,FrontSim, GRID, Peep, PVTi, SCAL, Schedule, SimOPT, VFPi,Weltest 200 and WRFC are marks of Schlumberger. VIP is a mark of Landmark Graphics Corporation. STARS is a markof CMG, Computer Modelling Group Ltd. UNIX is a registeredtrademark of The Open Group. Windows NT is a mark ofMicrosoft Corporation. LoadLeveler and RS/6000 are marksof IBM, International Business Machines Corporation.

Spring 2001 27

splits deep in the subsurface to drain multiplehorizons or provide several entries into the sameformation to improve areal reach and recovery.Engineers must decide the optimal placement ofthese well branches. The ability to model thesereservoirs prior to drilling becomes extremelyimportant. Since hydrocarbons may come fromdifferent zones with vastly different fluid proper-ties, models also must be able to account forthese difficulties.

The ability to solve complex models now islargely the result of incredible improvements incomputer processing speeds. A common maxi-mum desired run time for a large reservoir simu-lation is “overnight,” so improvements in

computer speed often translate into larger orincreasingly complex models, or both—so longas the result is ready the next morning. Recentadvances in parallel computing have increasedsimulator speed, but, as described later, doublingthe number of processors generally does nothalve the run time.

When computer simulation of reservoirsbegan, it was the province of specialists who bothdesigned the computer programs and ran the mod-els, and software development was mostly donewithin larger oil companies. The simulator oftenwas reprogrammed for each new situation toaccount for differences in the reservoirs.Improvements in a model tended to parallel

company asset-development strategy: for exam-ple, dual-porosity models were developed forlarge, fractured reservoirs. As the technologygrew, so did the team of specialists, eventuallydistinguishing those who developed the programcode from those who ran the models. The two dis-ciplines typically maintained close ties, and oftenboth were in a centralized technical support group.

Eventually, demand for reservoir simulationincreased and companies began installing copiesof the simulators outside the centralized facility.With programs and users remote from developers,software documentation—and ease of use—became much more important. Since reservoir-simulator developers in large oil companies oftenwere not skilled in designing user interfaces, theera of vendor-supplied simulation software began.Although in-house reservoir modeling programsstill exist, the trend is away from simulatorsowned and maintained by individual oil companiesand toward third-party software suppliers. Today,the goal is to make the program simple to use,with automatic grid generation, easy import ofgeologic, fluid and formation data, and graphicaloutput of the results end-users require.

Currently, the two dominant vendor simula-tors are the ECLIPSE model from SchlumbergerGeoQuest and the VIP simulator from LandmarkGraphics. Both packages include black oil andcompositional models—without and with mixingof gas and oil—which are described in moredetail later in this article. Other simulators arestrong in niches—the Computer ModellingGroup, Ltd., STARS model simulates thermal pro-cesses such as steamflooding.

This article shows how simulation softwarecan build, manage and display results from avirtual reservoir. Unprecedented simulator tech-nology allows more realistic wells in the model,each with multiple segments, such as branched ormultilateral wells, complicated completions andinclusion of intelligent downhole controls withinthe simulation. Case studies illustrate advances incurrent reservoir engineering practice. One of thecase studies has a complex computational sce-nario—a model using a fluid description withmany components executed using parallel pro-cessing. Finally, a different kind of simulator isdescribed that uses a front-tracking methodinstead of the usual finite-difference method.

> Reservoirs and stars. Reservoir data at fine scale are now used in simula-tors to study reservoir life. Similarly, the Hubble space telescope providesastrophysicists with more details for cosmic models. The National Aeronauticsand Space Administration (NASA) photographed this old star cluster in theTarantula Nebula.

1. Muskat M: Physical Principles of Oil Production. NewYork, New York, USA: McGraw-Hill, 1949: 812-813.

2. For an overview of the history of reservoir simulation:Watts JW: “Reservoir Simulation: Past, Present, andFuture,” paper SPE 38441, presented at the SPEReservoir Simulation Symposium, Dallas, Texas, USA,June 8-11, 1997.

3. Bosworth S, El-Sayed HS, Ismail G, Ohmer H, Stracke M,West C and Retnanto A: “Key Issues in MultilateralTechnology,” Oilfield Review 10, no. 4 (Winter 1998): 14-28.

The Virtual Reservoir EnvironmentImagine drilling a well into a reservoir and pro-ducing from it for five years, then deciding youmight have produced more by shifting the well toanother location. You wind back the clock, drillthe second option and produce again. And maybea third trajectory looks promising (right).

The power of reservoir simulation is the abil-ity to investigate all these options before a drillbit touches earth. Multiple scenarios can beexamined inside the model’s virtual reservoir—changing well locations, reservoir geology, pro-duction limitations or any combination of inputsto the model. Just as cosmologists observe starformation to improve their models, leading topredictions of new phenomena, engineersdevelop reservoirs in stages—starting withexploration and ending with field abandon-ment—with models based on data from onestage influencing the next stage.4

In the exploration phase, reservoir geology isuncertain. Multiple geostatistical realizationscan be fed into a reservoir simulator. Givenenough realizations, statistically meaningfulhigh-, mean- and low-production cases can beexamined to show economic variability.

More wells delineate the field during devel-opment drilling, adding information about theformation. Production results from early wellscan be used to tune the reservoir model, furtherdecreasing uncertainties about reservoir proper-ties.5 Well trajectories result from informeddecisions. The reservoir model provides esti-mates of hydrocarbons in place and recoverablehydrocarbons, which are needed for manage-ment decisions and for reporting to regulatorybodies. When contracts specify delivery require-ments for supplying gas, models can include the cyclic nature of gas demand, including rein-jection options.

Later in field life, reservoir engineers usemodels to study candidates for improved recov-ery in great detail. The virtual reservoir is a cost-effective way to examine multiple infill-drillingstrategies, water- or gas-flooding scenarios andother, perhaps more exotic, recovery methods.

Managing the Virtual Reservoir Reservoir modeling is not an exact science. Evenwith the best geologic interpretation and years ofproduction data to provide guidance, many possi-ble virtual scenarios might describe the reservoir.Until recently, reservoir engineers operating amodel had to have special expertise, includingdesigning grids and upscaling—converting froma fine-scale geologic model to a reservoir model with larger gridblocks—populating thegridblocks with appropriate data, adjustingparameters to match production history, schedul-ing drilling wells within the model and devisingdepletion schemes.

The need for specialized training restrictedmodeling to economically important reservoirs,leaving many smaller reservoirs to be managedwith less sophisticated engineering methods.Within the past few years, new tools have beendeveloped to put some of these expert capabilitiesinto the hands of less experienced, even novice,users. New software tools expand the reservoir

simulation user base to include geoscientists,completions engineers and drilling engineers.

The ECLIPSE Office software provides a singleinterface to tools that help the user design andexecute a reservoir simulation. Buttons acrossthe top of the Case Manager screen activate sub-programs that help users set up a reservoir model(next page). Program modules, activated by thebuttons on the left of the screen, guide usersthrough the simulation process.

The Data Manager module in the ECLIPSEOffice suite accesses a series of screens orga-nized around logically consistent groups of data.FloGrid and GRID geologic modeling and simula-tion grid design software can input model geom-etry, or a user can create it interactively. FloGridsoftware has the additional power of generatingan upscaled reservoir grid that retains the geo-logic model’s important features, such as faults,formation layers or channels.

One reservoir gridblock may comprise severalgeologic model gridblocks, which provide inputdata for reservoir parameters such as porosityand permeability. Although averaging values ofporosity is a reasonable way to upscale, averag-ing permeability values may conceal geologiccomplexity, such as preferential flow direction.The FloGrid module can simulate flow throughthe geologic blocks composing a reservoir blockto determine an upscaled permeability tensor.

Rock and fluid properties to populate grid-blocks can be developed from laboratory datausing SCAL special core analysis managementsoftware and PVTi pressure-volume-temperatureanalysis software, respectively. Alternatively,correlations for rock and fluid properties can be obtained through panels in the Data Man-ager module.

Often the simulator has to match surface pro-duction data, not data at reservoir conditions.Converting from bottomhole pressure to tubing-head pressure depends on flow conditions inwells, which can vary. Gas lift, downhole pumps,gas compression and surface chokes affect flow,as do undulating and nonvertical wellbore sections. Some flow constraints come from sur-face facilities, so the simulator must know howwells connect to those facilities and honor theconstraints. The VFPi vertical-flow-performanceprogram simulates the reservoir-to-tubing-head

28 Oilfield Review

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> A question of economics. Reservoir modelingprovides economic input for choosing amongpossible wellbore locations.

4. For a more complete view of reservoir simulation at dif-ferent stages of field life: Adamson G, Crick M, Gane B,Gurpinar O, Hardiman J and Ponting D: “SimulationThroughout the Life of a Reservoir,” Oilfield Review 8, no. 2 (Summer 1996): 16-27.

5. Bouska J, Cooper M, O’Donovan A, Corbett D,Malinverno A, Prange M and Ryan S: “ValidatingReservoir Models to Improve Recovery,” Oilfield Review11, no. 2 (Summer 1998): 21-35.

Spring 2001 29

flow. The Schedule well-data transformationsoftware can import and manipulate the flow andpressure history and define well groupings.

These tools in the ECLIPSE Office softwarework together to allow users to create data sets,without having to know the specifics of format-ting and organizing data and keywords in inputfiles. The Data Manager application can creategraphical displays of data in relevant formats,such as grid-based contour maps or line plots.

If the field has already produced, the engineercan compare predictions to actual production todate and adjust parameters to optimize themodel. This process—called history matching—improves confidence in future model predictions.The Run Manager routine allows the user to startand stop the simulator while monitoring selecteddata. For example, when simulating a waterfloodpilot, the water cut of the producer might bemonitored to ensure water breakthrough occursat the correct time compared with the pilot his-tory. If it occurs too early or too late, the user canabort the run and reset input parameters.

The Case Manager module provides visualbookkeeping of multiple runs or cases. The usercould generate a hierarchy of cases to develop a reservoir with water injectors, gas injectors, or both working together. In a complex reservoir,the engineer may have hundreds of cases totrack. The Case Manager software alters only thedata files that differ among cases, to keep filesfrom proliferating.

Another subprogram, the SimOPT modelcalibration software, can help in the history-matching process by determining which inputparameters have a major impact on the results. Itprovides an interface for defining input variableranges, runs multiple cases based on user-selected variables and displays the output. Theprogram can automatically look for a best solu-tion, or it can allow the user to control whichvariables to evaluate. Although it may not findthe optimal solution, the SimOPT program helpsthe user determine whether a history match ispossible within the range of values that the userconsiders credible.

Simulators generate predictions of pressure,saturation and other parameters for each grid-block, which the Result Viewer routine can dis-play in two- or three-dimensional views. The usercan query the values of any gridblock at any timethrough the graphical interface, and obtain presentation plots from run data. Some data arebetter displayed as x-y plots, such as gridblocksaturation, or water, oil and gas production at awell as a function of time.

Simulation results must be documented. TheReport Generator creates simplified summaryreports and shows warnings and error messagesin meaningful language, and users can definecustom reports. Simulation results can beexported to the Peep economic analysis program,a standard asset management package in thepetroleum industry.

The Calculator—another feature of ECLIPSEOffice software—allows customized calculationsusing any parameters within the model. Userscan define their own conditions, greatly expand-ing the possibilities for illustrating results. A but-ton links the user to the Weltest 200 analysissoftware, which uses the simulation power ofECLIPSE software to numerically solve well tests,rather than relying on analytical models.

Better Well Modeling with Segments Wells today are much more complicated than theywere only a few years ago. Wellbores may havemultiple branches, enabling a single well to drain alarger portion of the formation or to contact a num-ber of isolated productive regions. Downhole sen-sors can monitor the conditions—temperature,pressure, density, flow rate and water and gas frac-tions—at selected locations within the well, whilesurface-activated flow-control devices can pro-gressively reduce or shut off production from highwater-cut or high gas/oil ratio (GOR) areas. TheECLIPSE family of reservoir simulators has addedthe multisegment well (MSW) option to help modelconditions in these advanced wellbores.

Early reservoir simulators used simple wellmodels, allowing fluid flow to and from the forma-tion but using simplistic flow physics within thewellbore. The wellbore pressure gradient typicallywas based on a mixture density that did not allowfor slip between phases—the tendency of individ-ual fluids to flow with different velocities.Moreover, the model treated the fluid within awellbore as completely mixed and uniform. Withthe advent of extended-reach and horizontal wells,some simulators included a refinement to accountfor friction, which can be a significant part of the

> ECLIPSE Office Case Manager screen. Users call up various programs to help set up a grid, populateit with data, run it and analyze results. This screen (top) shows a base case with no injection. The subordinate cases are for gas injection only, water injection only and both gas and water injection.The line plot (insert) shows oil production rates for the base case (black line) and the gas- and water-injection case (blue line). The improved recovery from gas and water flooding obtained from the Calculator module is shown as the shaded area. At 1800 days, the ECLIPSE simulation shut off highwater-cut zones, forcing water through oil-filled zones and increasing oil production.

energy losses of fluids flowing in a horizontal sec-tion. This still did not allow the contents of thewellbore to vary with location, nor did it properlycalculate the density of the flowing mixture.

The MSW option overcomes these limita-tions, allowing the reservoir modeler to divide awellbore into segments and define the set ofvariables describing fluids in each one. In thisone-dimensional grid of segments, wellbore contents and fluid-mixture properties can varywith location (see “Flowing Wells,” next page). A branching network of these segments definesmultilateral well geometry.

Well segments representing perforated linersconnect to the reservoir grid, allowing fluid pas-sage. Other model elements can be defined withpressure-drop characteristics of flow-controldevices such as valves, chokes and pumps.

The segmented structure follows the well tra-jectory independent of the reservoir grid. Thewell model can incorporate sections of unperfo-rated tubing extending outside the grid andallows branches of multilateral wells to join out-side the grid. This would not be possible with aconventional well model—without the MSWfacility, the simulator defines the well path by thesequence of grid cells it intersects.

Controlling a Dual-Lateral Well in Wytch Farm FieldWytch Farm field has the world’s first downholeflow-control completion in an extended-reachmultilateral well.6 The largest onshore oil field inEurope, Wytch Farm field lies in the south of England near Poole Harbor and extends intothe English Channel (above). The operator, BP, developed the field using an ongoing pro-gram of extended-reach wells, some exceeding10 km [6 miles].7

The M-15 well has two branches that drain apart of the Sherwood sandstone formation. Thenorthern branch lies in a faulted area, so it wascased and perforated, whereas the southern lat-eral is an openhole completion. The potentialproblems were quite different. BP anticipatedearly water breakthrough in the northern, faultedarea, and they felt drawdown had to be con-trolled to avoid borehole collapse in the southern, openhole completion.

While sharing a parent wellbore, the two later-als require different production strategies—highdrawdown was desired in the northern branch, atleast until water influx increased, but high draw-down was not possible in the southern. Downholeflow-control valves separately controlling produc-tion from the two laterals rectified the problem.

BP drilled and completed the well with threeWRFC-H hydraulic, wireline-retrievable flow-control valves. Expected flow rates were higherin the northern lateral, so two valves wereinstalled to allow more flow. The third valve con-trolled the southern lateral.

To determine optimal operating conditions forthe control valves, the Completions TechnologyGroup at the Schlumberger Reservoir Com-pletions (SRC) Center developed a black-oilECLIPSE100 reservoir model. They used theMSW option to model the parent well and thetwo laterals. Elements with inflow-control devicecharacteristics modeled control valves.

30 Oilfield Review

>Wytch Farm field in southern England. The M-15 well was drilled fromonshore and completed in the Sherwood Formation in the location shown.At the scale shown, the two branches cannot be distinguished.

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> Model prediction of Wytch Farm production. Oil production from commingled zones of Well M-15(green curve) was substantially improved by the addition of subsurface control valves (blue curve).The abrupt slope change in oil production rate (shaded curves) from both conventional and advancedcompletion relates to choking back flow to control water production.

6. Gai H, Davies J, Newberry P, Vince S and Al-Mashgari A:“World’s First Downhole Flow Control Completion of anExtended-Reach, Multilateral Well at Wytch Farm,”paper IADC/SPE 59211, presented at the IADC/SPEDrilling Conference, New Orleans, Louisiana, USA,February 23-25, 2000.

7. Allen F, Tooms P, Conran G, Lesso B and Van de Slijke P:“Extended-Reach Drilling: Breaking the 10-km Barrier,”Oilfield Review 9, no. 4 (Winter 1997): 32-47.

8. Algeroy J and Pollock R: “Equipment and Operation of Advanced Completions in the M-15 Wytch FarmMultilateral Well,” paper SPE 62951, presented at theSPE Annual Technical Conference and Exhibition, Dallas,Texas, USA, October 1-4, 2000.

Spring 2001 31

The ECLIPSE multisegment well (MSW) facilityoffers several options for modeling multiphaseflow in the wellbore. The simplest option is ahomogeneous flow model in which all phasesflow with the same velocity.

A second option uses a simple “drift flux”model to represent slip between the phases.This type of model allows rapid calculation, andits results are continuous over a wide range offlowing conditions. It is valid with countercur-rent flow, where the heavy and light phases flowin opposite directions. It also can be used tomodel phase separation within a wellbore, forexample, when a well is shut in during a builduptest. Phase separation influences the wellbore-storage response, which must be understood toproperly model test results.

A third option uses precalculated tables—similar to the vertical-flow performance tableswidely used to model wellbore-pressure lossesbetween the formation and the tubing head—to determine pressure drop across a segment.This option allows use of more complex and

computationally expensive multiphase flowmodels, if their results are first translated intotabular form. Obtaining the pressure drop byinterpolating the table is rapid and computa-tionally efficient. Tables also provide an effi-cient way of representing pressure losses incertain flow-control devices such as chokes,because pressure-drop calculations for moreaccurate models of these devices require morecomputing time.

The ability to manipulate subsurface controldevices is an important addition to the ECLIPSEMSW facility. The simulation engineer canchange choke settings at any time during a sim-ulator run by switching to a different table.Built-in models are available for certain devicessuch as subcritical valves, allowing “manual”changes to settings such as constriction area.Other device models are designed to operateautomatically in response to a changing watercut or GOR, or to limit the flow rate of oil, wateror gas to a specified maximum value.

Flowing wellbore conditions are representedin the black-oil simulator by four variables foreach segment: pressure, total flow rate throughthe segment, and flowing fractions of water andgas. These variables allow computation of fluid-mixture properties and the pressure gradient.Four equations apply in each segment: thematerial conservation equations for oil, waterand gas, and a relation for pressure drop alongthe segment. The compositional simulator usesadditional variables for the molar density ofeach fluid component and additional material-conservation equations for each component (see “Composing Pseudofluids,” page 44). Theseequations and those describing conditions inthe reservoir grid are solved simultaneously—a computational technique known as implicitcoupling. This ensures that the combined sys-tem of well plus reservoir remains stable overthe timesteps chosen by the simulator. Computa-tional stability is important since changes inflow conditions propagate through the well in a fraction of one timestep.

Flowing Wells

Conventional recovery—without subsurfacecontrol valves—allowed two options: producefirst one lateral then the other, or produce bothsimultaneously. The ECLIPSE model showed that,of the two, producing simultaneously generatedmore oil over the five-year study period. To con-trol high water cut in this scenario, productionfrom the entire well was choked back.

Adding separate control valves for eachbranch provided significant additional production(previous page, bottom). The northern branchcould be choked back without decreasing produc-tion from the other branch.

The well went on production in February1999. The northern lateral produced alone for sixmonths at over 10,000 B/D [1600 m3/d] of liquid.At the end of this period, only about 3000 B/D[477 m3/d] were oil. Then the operator shut inthis lateral and opened the southern lateral. Oilproduction was the same as that provided by thenorthern lateral, but with significantly lowerwater production. After five months of productionfrom this leg with increasing water cut, both lat-erals were produced simultaneously.8

Reservoir engineers used the ECLIPSE modelto history-match field production. A comparisonof cases with and without downhole controls in

the M-15 well indicates an expected incrementalrecovery of more than one million barrels[160,000 m3] of oil after five years.

Recently, a downhole pump failed and BPdecided to replace it with a larger one to increaseflow rate, so the downhole flow-control valvescan no longer be adjusted. However, the resultsfrom this well encouraged BP to continue usingmultilateral wells with downhole control inWytch Farm field. An electric, tubing-retrievableflow-control valve (TRFC-E ) was installed in WellF-22 in September 2000.

Modeling Isolated ZonesSchlumberger studied a series of delta-plainchannel sands braided with coal beds, targetingthree isolated sand bodies. The gas-oil contact(GOC) intersected the upper sand, Zone 1, andthe water-oil contact (WOC) probably fell withinthe lower sand, Zone 3, but the WOC locationwas uncertain. The ECLIPSE100 black-oil reser-voir model assumed that the reservoirs were laterally extensive, but there was no flow com-munication between them. A segmented well-bore connected the three zones in the model toevaluate wellbore fluid interactions (right).

The GOC in Zone 1 implies a potentially rapidincrease in GOR from that zone. Uncertaintyabout the WOC in Zone 3 meant there was a pos-sibility of substantial water production. Withsuch diverse influx, the model had to account forcomplex fluid interactions within the wellbore.Downhole controls might be needed to chokeback water or gas production.

32 Oilfield Review

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> Multisegment well (MSW) model of three sand bodies. Influx from eachzone is controlled with a downhole flow-control valve. Three separated setsof gridblocks modeled behavior in the zones using the MSW option, whichallows well segments outside reservoir gridblocks.

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> Production improvement with flow control. Production using flow-control valves (blue line) greatly exceedsserial production with no valves in the completion (green line). The shaded green flow-rate curve for the serialcase shows rate decline for the lowest zone until it is shut off and middle zone production begins. The rapidchanges in production rate (shaded blue) are a result of controlling gas influx with flow-control valves.

Spring 2001 33

Without downhole flow-control devices, moreoil is produced in the five-year model period bycompleting the well sequentially from the bottomsand up, rather than producing all three simulta-neously. However, with downhole flow-controlvalves, the most productive case examined com-mingled production from all three zones. As GORfrom Zone 1 increased, flow through the uppervalve was restricted to limit gas rate. The lowervalve controlled water influx. Another combina-tion allowed the upper valve to be opened to pro-vide gas for artificial lift, which might becomenecessary if water from Zone 3 could not bechoked back without losing significant oil produc-tion. Compared with a conventional productionapproach, the advanced completion scheme notonly extends the well life, but increases produc-tion rate throughout the five-year life of the study(previous page, bottom).

Downhole Control in Dual-Drive ReservoirsSimple models can illuminate flow responsesthat may be hidden in more complex reservoirs.To understand simultaneous gas drive and waterdrive toward horizontal wellbores, engineers atSRC modeled a simple, homogeneous reser-voir.9,10 The first case uses one well perforatedthroughout the straight, horizontal section fromthe bend leading to the vertical section, calledthe heel, to the wellbore termination, or toe(above). The fluid velocity inside the 6-in. linerincreases from almost zero in the toe segment toabout 10 feet per second [3 m/sec] at the heel.

At initial conditions and with only oil flowinginto the wellbore, the greatest pressure draw-down occurs at the heel. For the geometry andproperties of this model, the difference in draw-down between heel and toe is only 40 psi [275 kPa], but that causes almost 3000 B/D [477 m3/d] greater influx at the heel.

> Simple horizontal-well reservoir model with one gas layer, 13 oil layers and one water layer. The modelhas 25 blocks in the direction of the well and 17 transverse, with the well between the seventh andeighth. The well is 4000 ft [1220 m] long, with a 6-in. ID liner and flows 16,000 B/D [2540 m3/d] of oil. Pres-sure (pink), oil influx (blue) and flow rate (white) profiles within the horizontal wellbore are indicated inthis cutaway view of the model.

9. Sinha S, Kumar R, Vega L and Jalali Y: “Flow EquilibrationTowards Horizontal Wells Using Downhole Valves,”paper SPE 68635, presented at the SPE Asia Pacific Oiland Gas Conference and Exhibition, Jakarta, Indonesia,April 17-19, 2001.

10. Yeten B and Jalali Y: “Effectiveness of IntelligentCompletions in a Multiwell Development Context,” paperSPE 68077, presented at the 2001 SPE Middle East OilShow, Bahrain, March 17-20, 2001.

34 Oilfield Review

Gas saturation

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> Snapshots of fluid fronts. Without downhole flow-control valves, drawdown is greatest at the heel ofthe well, preferentially drawing water up and gasdown in that region. Water breaks through first inthis model, shown as two gridblocks touching thewellbore (top). Two years after water breakthrough,there is still poor recovery near the toe (bottom).Gridblocks retaining original oil saturation have beenomitted from the illustrations.

Spring 2001 35

The higher drawdown and flow rate at theheel will draw water up from the WOC and pullgas down from the GOC (previous page). Twoyears after breakthrough at the heel, there is stillconsiderable unswept oil near the toe. If waterbreakthrough occurred first at the toe, watered-out zones could be shut off with a packer, but set-ting a packer at the heel would kill all production.

An intelligent completion lessens theseproblems by dividing the horizontal section into two parts with a packer and moving the maximum pressure drawdown point to the mid-dle of each segment (top). Putting a surface-controllable valve in the heel section provides a

capability to optimize the pressure profile andmatch the drawdown in the toe.

Creating a zoned reservoir by adding a valvewill not prevent gas or water breakthrough, butcan delay it and at the same time improve sweepefficiency along the length of a wellbore (above).The degree of postponement depends on a number of factors, such as wellbore friction, vertical location of the horizontal well within areservoir and total flow rate. Greater wellborefriction—possibly due to undulations in the wellbore—steepens the slope of the pressuredrawdown along the wellbore and exacerbatesthe sweep problem. This makes the completion

with a valve more profitable, because as frictionlosses along the wellbore increase, incrementalrecovery from addition of a valve also increases.

Cumulative oil production provides a betterassessment of well placement between the gasand water zones than breakthrough time. Optimalwell placement within the oil zone depends onthe liquid production rate—at higher flow rates,the well should be closer to the water layer. Ofcourse, real reservoirs are not homogeneous, andrelative sweep efficiencies for water and gas dis-placing oil will affect results.

A B

Valve Packer Sleeve opening

Pres

sure

/flo

w ra

te

Annular pressure/flow profile

> Completion assembly with a packer dividing the horizontal section into two parts (A and B). Fluidfrom the reservoir flows either through a sleeve opening into the liner in the toe section or through asurface-controllable valve in the heel section. Maximum drawdown occurs at the sleeve opening orthe valve. With proper control of the valve, pressure drawdown or flow rate can be equalizedbetween the two sections (pink curve).

Gas saturation

Oil saturation

Water saturation

Well

> Improved sweep with intelligent control. Dividingthe well into two zones and controlling the upstreamzone with a control valve to achieve the same draw-down profile as the downstream zone improvessweep efficiency at breakthrough, as more grid-blocks near the toe have been swept by water orgas. Gridblocks retaining original oil saturationhave been omitted from the illustration.

Sometimes, reservoir geology or surface facil-ity constraints dictate placing horizontal wells soclose that they may interfere with one another’sproduction. To examine this situation, a second,parallel horizontal well was added to the simplereservoir model with gas cap and aquifer drive(above). Both wells can enter the reservoir fromthe same side, that is, heel-to-heel, or from oppo-site sides, heel-to-toe. The wells have a downholecontrol valve in the heel section that can beenabled or disabled. Six cases were examined:neither well instrumented, one well instrumentedor both wells instrumented, with each case in bothheel-to-heel and heel-to-toe configurations.

The heel-to-heel, uninstrumented case hasthe least recovery, so it is considered the base case. Sweep efficiency is poor, particu-larly in the toe region of the model (right). Oil recovery after five years is 30.2 million barrels[4.8 million m3], representing 34.5% of the original oil in place. Switching the orientation ofone well improves sweep between the wells by

172,000 barrels [27,400 m3], because in this configuration, the strong drawdown at the heelof one well complements the weaker drawdownat the toe of the other well.

Adding a control valve in one well improvesrecovery for both wells. The instrumented well inthe heel-to-toe configuration has a greaterimprovement than in the heel-to-heel case, with-out significantly affecting recovery in the unin-strumented well. With a control valve in bothwells, the recovery is even higher. The pressuredrawdown also is more uniform, making theconfiguration—heel-to-heel or heel-to-toe—less important.

These two examples show the power of simple models to help engineers understandmore complex reservoir cases and develop completion strategies.

36 Oilfield Review

> Parallel well model similar to the single-well case, but made wider to accommodate a second well.Well 1 and Well 2 can either be heel-to-toe, as shown here, with flow along the horizontal sections inopposite directions, or heel-to-heel, with both wells flowing in the same direction.

30.16million bbl

+263thousand bbl

+448thousand bbl

+172thousand bbl

+318thousand bbl

+454thousand bbl

None instrumented None instrumented

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Both instrumented Both instrumented

+86

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+86

> Dual-well gas cusping. These snapshots, taken early in the simulation of areservoir layer above the horizontal well, indicate interference of gas sweep(red) between the wells. The top row represents conventional, uninstrumentedwells. In the middle, Well 1 is instrumented, and both wells are instrumentedin the bottom row. The left-hand figures are heel-to-heel, and the right-handones are heel-to-toe. Sweep efficiency is improved when flow is controlledusing downhole valves. Total recovery in the heel-to-heel, uninstrumentedcase is 30.16 million bbl [4.8 million m3] of oil. Incremental recovery beyond thisis shown for other cases (beside each snapshot), with recovery improvementalso shown for each well in each case (within the snapshot).

Spring 2001 37

Parallel Processing in Venezuela Many of today’s reservoir models are huge—perhaps comprising millions of gridblocks—to capture as much relevant geologic data as pos-sible. Models with so many more gridblocks thanthose of a decade ago require significantly moretime to solve. Historical production data spanningseveral decades and hundreds of wells add evenmore simulation complexity and solution time.

One computer processor may not solve amega-gridblock problem overnight, but by divid-ing the model into parts, several processors canwork simultaneously. Versions of both the VIPsimulator and the ECLIPSE simulator use parallelprocessing this way.

Ideally, doubling the number of processorsworking in parallel would halve the solution time.However, inefficient problem splitting and pro-cessor-to-processor communication curtail thatlevel of speedup.

Parallel processors do not start a new stepuntil they all complete the previous one. Properdivision of the problem to equalize work amongprocessors is necessary to optimize speedup.

Dividing the problem requires communicationbetween processors. This includes transfer offlow and pressure information between adjacentgridblocks that are in different processors andbetween surface facilities and wells in separateprocessors. Dividing the problem along naturalbreaks helps control internal communicationtime—for example, a large fracture that conductsfluid should be completely within one processor.

Petróleos de Venezuela, S. A. (PDVSA) stud-ied parallel-processing speedup to identify thebest processor configurations and the balancebetween computer central processing unit (CPU)power and memory use. In 1998, initial PDVSAstudies indicated four processors solved a varietyof problems in about half the time of one proces-sor. However, internal communications used aslow bus—computer communications link—onan older UNIX network. PDVSA engineersbelieved newer machines could achieve betterspeed. The study of efficient job distribution con-tinued on new, more powerful IBM RS/6000machines, using IBM’s LoadLeveler load-management software.

LoadLeveler software makes parallel nodesbehave as a single machine. It manages alljobs—serial or parallel—assigning each newrequest to the least-used processor or proces-sors. When a particular job needs more nodesthan are currently available, the managementsoftware puts it on hold until enough nodes areready. Once a reservoir model begins running,CPU use will be uninterrupted, making compar-isons between runs possible. These studies showsignificant speedups with parallel processors—afactor of six for eight machines and a factor ofalmost four for four machines (left).

PC processor speed has also improved sincethe 1998 study. Schlumberger evaluated a heavy-oil reservoir in the East Venezuela basin using aversion of parallel ECLIPSE software on two PCsrunning the Windows NT operating system. Thereservoir geology comprises prodeltaic shales andmouth bars, occasionally cut or overlain by fluvialchannels. Part of the field was a major channelcomplex, probably feeding into the delta. To cap-ture geologic uncertainties, the reservoir modelused a stochastic—or probabilistic—realizationbased on facies and stratigraphic features.

In this heavy-oil reservoir, water is about 50 times more mobile than oil, so water does notdisplace oil as a uniform front. Instead, it fingers, orcreates narrow channels through the oil.Numerical cross-section and sector models indi-cated that a fine vertical resolution was needed toaccurately model this displacement behavior. Thesimulation incorporated a fine grid, with a resolu-tion in vertical direction of 1- to 3-ft [0.3- to 1-m]layers. The gridblocks were the same size as thosein the stochastic model—50 m [164 ft] on a side—to maintain geologic heterogeneity. The numericalmodel had some 880,000 grid cells. A two-node PCsystem using the Windows NT operating systemran the simulation in 62 hours, compared with 119 hours on one PC. Doubling the number of processors sped simulation by 1.9 times.

Number of grid cells

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Reservoir A B C

> Speedups obtained for Venezuela reservoirs. In Reservoir C, the heavy-oil reservoir, aspeedup of 1.9 was achieved for the large stochastic model.

A second realization of this reservoir upscaledto a coarser grid—150 m [492 ft] on a side—had only 94,080 gridblocks (above). This smallersize allowed a global history match with reason-able computing efforts. On a single-processor PCwith 1 gigabyte of RAM running at 900 MHz, sim-ulation took about six hours. With parallelECLIPSE simulation on two processors of thesame specifications, run time decreased to aboutthree hours—an almost ideal speedup factorclose to two.

Simulating Complex Fluid BehaviorThe ECLIPSE simulator was used to model aMiddle East carbonate reservoir. It is a foreslopedepositional environment, thickening and improv-ing in reservoir quality to the south. Cyclicchanges in sea level led to an alternating seriesof porous and dense limestones, which can beidentified from wireline log response. The field isdivided into a low-permeability northern area anda higher permeability southern area (next page).The northern part, termed the pattern area, had1.7 billion barrels [270 million m3] original oil in

place and the southern, or extension, area origi-nally had 3.4 billion barrels [540 million m3].

The Abu Dhabi Company for OnshoreOperations, ADCO, began production from thefield shortly after discovery in 1962, but significantproduction did not start until 1986. The field hashad peripheral water injection since 1974.Extension-area oil production peaked at about13,000 B/D [2000 m3/d] in the late 1980s. Theaddition of twelve gas injectors in the poorerquality pattern area in 1996 led to a productionpeak at about that same rate in 1999 and 2000,while the extension area continued to contributeabout 3000 B/D of oil.

ADCO initiated a study of two producingzones to determine future production scenarios.There were three concerns. First was uneven gasinjection due to injection-well placement, whichcreated a pressure differential between the pat-tern area and extension area and caused oil tomigrate a great distance to the south. Alternatingtight and permeable layers in the pattern areacomplicate fluid displacement.

The second concern was that pressure draw-down near producing wells was too great. Thiscan cause gas to evolve from the liquid hydrocar-bon near the well, reducing relative permeabilityfor oil flow, thereby decreasing productivity.Finally, poor reservoir quality in the northern partof the pattern area caused low productivity andinjectivity, which ADCO hoped to improvethrough a new reservoir-depletion plan.

The injected gas was expected to be miscible,that is, to go into solution with the oil uponcontact. This change in oil composition alters its properties, including density and viscosity, so engineers used the ECLIPSE300 simulator,which can model compositional changes (see“Composing Pseudofluids,” page 44 ).

The two zones needed 37 layers to accountfor vertical heterogeneity. A grid of 55 by 45 hor-izontal blocks, each 500 m [1640 ft] on a side,was sufficient to cover the field, but this wouldnot allow an adequate number of gridblocksbetween wells in the center of the field.Separation by several gridblocks is necessary todefine the saturation gradient between injectorsand producers.

38 Oilfield Review

Rock type

31 2 64 5

> Stochastic model of a Venezuela reservoir. This heavy-oil reservoir needed thin layers to deal withwater flow and small grids to deal with a complex geology. The fine-grid realization had 880,000 cells.The colors designate six gridblock rock types representing six classifications of relative permeabilityand capillary properties.

0

0 1 2 3 4 5 miles

1.5 3.0 4.5 6.0 7.5 km

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Spring 2001 39

The solution was to use local grid refine-ment—making smaller gridblocks in a portion ofthe model. In this case, the central blocks, 15 inthe north-south direction by 11 in the east-westdirection, were divided into cells 100 m [328 ft]on a side, leaving larger blocks in the flanks. In

conjunction with the local grid refinement in thecenter of the field, ADCO used a feature of theECLIPSE300 simulator called adaptive implicitmethod, or AIM (see “Coupling Space and Time,”next page).

This model has about 238,000 cells. Whilenot large for a Middle Eastern field study, amodel with so many gridblocks will executeslowly, particularly when the fluid compositionchanges, as in this case. ADCO increased simu-lation speed by using 12 parallel processors.

< Structure map of carbonate field.Known faults are shown in red.The large purple square delimitsthe simulation model area, and theblue box encloses the region oflocal grid refinement. Within thelocal grid refinement, the boxesoutlined in gray form the patternarea, while the blocks below arethe extension area. Locations ofproducing Well P and gas injectorWell I are indicated.

40

The essential problem in simulation isadvancing the state of a reservoir throughtime, affected by external changes such as oilproduction, or internal change, such as fluidphase transitions. Reservoir properties arestored in the computer as matrices, with acombination of properties defining each grid-block in a model. A change in one gridblockaffects surrounding blocks, just as sucking on astraw drains a drink from the nearest crushedice, causing fluid from ice farther away to flowtoward the straw.

Variables in the reservoir model are gas, oiland water saturation and pressure. The definingequations are based on a material balance—matter is neither created nor destroyed in theprocess—and force balance, which is essen-tially Newton’s second law, F = ma, expressedin terms of pressure rather than force. Theequations are partial differential equations thatcannot be solved analytically, so the problem isbroken into pieces based on a grid and solvedas a set of equations expressing the differencebetween blocks.1 The system seeks equilibrium,but since fluid flow is not instantaneous, timemust be factored into the problem. Time also isdivided into discrete steps.

The mathematics within a simulator takesconditions within every gridblock and stepsforward in time, solving for conditions at thatnew time. Different procedures have beentried, but today the two most common aretermed fully implicit and IMPES—implicitpressure, explicit saturation. Fully implicitmodels solve for both pressure and saturationat the end of a timestep, while IMPES usessaturation values from the beginning of atimestep to solve for pressures at its end. Eachhas advantages and disadvantages, and majorcommercial simulators can be set to useeither method.

IMPES is computationally faster, since fluidsaturations are solved in one matrix calcula-tion. The simulator then iterates a number oftimes until pressures in the gridblocks have aninternally consistent solution. However, a solu-tion may be difficult to achieve if saturation,which the IMPES method assumes is constant

within a timestep, actually changes rapidlyduring that step. Such models account for thisby decreasing the size of the timestep, but thenumber of timesteps the model uses can growquite large, or the model may not converge toa solution.

The fully implicit procedure is more stable.Saturation and pressure are obtained simulta-neously, so the disparity between one timestep and the next is less important. Timesteps can be larger than those in the IMPES method.The price is additional processing time toachieve a simultaneous solution for pressureand saturation. When the reservoir changesrapidly, a fully implicit method often can solvethe model faster, even though each iterationmay take longer.

The Landmark VIP simulator has a useroption that compromises between these twomethods. The grid can be divided into twoparts, one using the IMPES method and theother a fully implicit solution.

The ECLIPSE300 reservoir simulator has afeature called AIM, the adaptive implicitmethod, which takes a flexible approach. Theprogram finds the parts of the model whereproperties change rapidly and the IMPESmethod may not converge easily, and the simu-lator sets them to solve implicitly. AIM seeks atimestep size that is optimal for both solutionmethods. The user can specify the maximumpercentage of the model to be solved implicitly.If that proportion exceeds 10 to 20%, it is proba-bly faster to solve the whole model using theimplicit method.

1. Mattax CC: “Modeling Concepts,” in Mattax CC andDalton RL: Reservoir Simulation, SPE Monograph, Vol 13. Richardson, Texas, USA: Society of PetroleumEngineers, 1990.

Model parameters were adjusted to optimizethe history match—correlating model outputwith production data recorded since the field wasput on production. The primary data included thereservoir pressure at producing wells and tubing-head pressure at injectors (next page, left). A goodhistory match allowed ADCO to evaluate futureproduction scenarios with greater confidence.

The first recommendation from this reservoirstudy was to convert 24 vertical wells in the pat-tern area in the north of the field, including bothinjectors and producers, to horizontal comple-tions by redrilling. This extended the productionplateau and increased ultimate recovery com-pared with previous development plans (nextpage, top right). Surface facility constraintsrestricted liquid production from the pattern areato 30,000 B/D [4800 m3/d]. The ECLIPSE simula-tor allows wells to be grouped, applying the lim-its to the whole group. Based on user-definedinput, the simulator selects which wells to chokeback to maintain production within field con-straints. ADCO considers this ability to controlgroups a crucial feature of the simulator.

Converting the wells to a horizontal geometryalso decreased long-distance oil migration to theextension area, since these wells allow moreproduction from the pattern area. The flux, ormigration rate, declines rapidly, whereas themodel of the business plan showed continuedflux out of the pattern area (next page, bottomright). The simulator handles the resulting hys-teresis, or increase in saturation of a fluid phasewhen it had been decreasing, caused by the flowdirection reversal in the pattern area.

The simulation study continued with a com-parison of further field development with different injector-well patterns. In addition toevaluating gas injection, this study included eval-uations of water injection, water-alternating-gasinjection, and combined water and gas injectionthat are beyond the scope of this article.

Oilfield Review

Coupling Space and Time

Spring 2001 41

Streamline SimulationThe ECLIPSE reservoir simulators, like mostothers, use finite-difference methodology.Saturation fronts are difficult to follow in a finite-difference model since the virtual reservoir isdivided into blocks. As soon as the water satura-tion in a gridblock exceeds the minimum mobilesaturation, flow into adjacent gridblocks willinclude some water. This effect—called numeri-cal dispersion—occurs in the model even ifwater in the reservoir could not possibly havetraveled from one side of the block to the other in the time since it entered. Modelers oftenresort to pseudofunctions—altered relative-permeability curves—to delay the transmissionof water from one cell into another.

An alternative approach is to solve the prob-lem using streamlines. The simplest visualizationof a streamline is the path taken by a stream ofdye carried along by flowing water. More complexpatterns include the Gulf Stream, a flow of warmwater from the tropics that passes along the eastcoast of the USA on its way to the North AtlanticOcean, and the jet stream, a flow of high-speedair in the upper stratosphere or troposphere.

A flowing fluid moves within an energy field.The Gulf and jet streams are driven by a combi-nation of forces, including rotation of the earthand convective heat transfer in either the air orthe ocean. Gravity, density difference created bya temperature or composition difference, andpressure difference drive fluids in a reservoir.Lines of constant potential energy can be deter-mined, like elevation contours on a topographic

0

-4

-8

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-201980 1990 2000 2010

Year2020 2030 2040 2050

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, 100

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D

> Flux-rate decline. Adding horizontal wells to the pattern area decreasesthe amount of oil flowing from the pattern area into the extension area in thelower zone of the Middle East reservoir (purple) compared with the previousplan (green). Negative flux is movement out of the pattern area.

35

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01980 1990 2000 2010

Year2020 2030 2040 2050

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> Impact of horizontal wells. Converting 24 wells to horizontal completionsincreases recovery significantly from the pattern area (purple), comparedwith the previous plan (green) for the Middle East field. The plateau, extendingto 2017, is restricted by a 30,000 B/D [4800 m3/d] facilities limitation, which thereservoir simulator handles as a group limitation on the wells.

6000

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1990 1992 1994 1996 1998 2000

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> History match for two wells. Simulation pressure results(orange) matched field data (purple dots) for tubing-headpressure of injector Well I (top) and for bottomhole shut-inpressure of production Well P (bottom). Injection andproduction flow rates (light blue) are shown but were nothistory-matched.

map and isobars on a weather or reservoir map(below). Fluid is driven from a high-energy con-tour surface towards a lower one. In a reservoir,there may be several forces acting—gravity,thermal gradients, differential burial rates acrossa basin, and fluid injection or production. Astreamline is always at right angles to the linesof constant drive force.

Streamlines are mathematical entities—aninfinite number exist for a given force field.However, to make this concept practical for solv-ing flow problems, a limited number of stream-lines are considered, and the fluid surrounding astreamline is considered one stream. The situa-tion can be extended to three dimensions, wherestreamlines become streamtubes, defining dis-tinct volumes of fluid flowing together.

Since fluid does not pass from one streamlineto another, flow within one stream can be con-sidered independently of any other stream. This

essentially uncouples the complex relationship offlow and material balance that finite-differencesimulators must deal with. The problem can besolved as a series of independent, quasi-one-dimensional flow regimes. This avoids the prob-lem of numerical dispersion and allows a cleardefinition of flood fronts or passage of a fluid slugthrough the reservoir. In addition, the source offluid flowing to a producing well can be deter-mined, whether it is from one of several injectorwells, a bottom- or edge-drive aquifer or the oilcolumn. Streamlines can also identify areaswithin a field that have been bypassed, or wellswith inefficient injection, such as water or gasthat is continuously sweeping the same part of areservoir without moving additional oil.

Streamline simulators are not a replacementfor standard reservoir simulators. When condi-tions change rapidly, a streamline simulator maygive incorrect results or may not converge to asolution. The streamline simulator solves the

pressure field, assuming negligible gravitationaland thermal effects, as a first step toward solvingthe flow problem. This solution scheme assumespressure changes are slow, so it is better suitedto a pressure-maintenance situation than a rapid-depletion case. In addition, when the pressurefield changes significantly because of addition ofinjectors or producers, streamline models mayneed to be history-matched again. Streamlinesimulators also neglect capillary forces.

On the other hand, streamline simulators canbe very fast. The size of a timestep—the timeperiod between solution steps in a model—isrestricted in finite-difference simulators. Themore grid cells and the smaller they are, themore CPU time is required in a step. Streamlinesimulators do not have the same timestep con-straint, and can take large timesteps if neces-sary. As a consequence, the simulator is capableof handling large models with many wells orlarge geologic models, which might be difficult orimpossible for a finite-difference simulator tosolve in a reasonable time.

The FrontSim streamline simulator can usethe same gridding and property assignment, suchas porosity and permeability, as an ECLIPSEreservoir model. Changes to the underlying geo-logic model made in one simulator can be carriedimmediately into the other.

In most cases, the geologic model developedfor a field is considerably more detailed than thereservoir model. These high-density models areusually upscaled to decrease the number of cellsbefore reservoir modeling is done. With stream-line simulation, upscaling is not necessary—thelarge number of cells in a geologic model can beevaluated for production potential.

42 Oilfield Review

11. Idrobo EA, Choudhary MK and Datta-Gupta A: “SweptVolume Calculations and Ranking of GeostatisticalReservoir Models Using Streamline Simulation,” paper SPE 62557, presented at the SPE/AAPG WesternRegional Meeting, Long Beach, California, USA, June 19-23, 2000.

12. Lolomari T, Bratvedt K, Crane M, Milliken WJ and TyrieJJ: “The Use of Streamline Simulation in ReservoirManagement: Methodology and Case Studies,” paperSPE 63157, presented at the SPE Annual TechnicalConference and Exhibition, Dallas, Texas, USA, October 1-4, 2000.

13. Lolomari et al, reference 12.14. Grinestaff GH and Caffrey DJ: “Waterflood Management:

A Case Study of the Northwest Fault Block Area ofPrudhoe Bay, Alaska, Using Streamline Simulation andTraditional Waterflood Analysis,” paper SPE 63152, pre-sented at the SPE Annual Technical Conference andExhibition, Dallas, Texas, USA, October 1-4, 2000.

P3

I2

> Streamlines flow from Injector I2 to Producer P3. For a horizontal reservoirat constant temperature, pressure drives flow. Lines of constant pressuredecrease from high pressure (yellow) to low pressure (orange) around theproducer. The injector-producer pair influences an existing pressure field,gradually decreasing from left to right. Streamlines are perpendicular to thepressure field, with color designating the decreasing proportion of waterflowing out from the injector (blue, shading to green then yellow), with oilflow in most of the model (purple). The underlying gridblocks (light gray) contain reservoir property definitions.

Spring 2001 43

The speed of streamline simulators makesthem useful for ranking multiple geostatisticalrealizations of a reservoir. After many cases arerun, those with—for example—a high, a meanand a low recovery factor can be further evalu-ated.11 This can improve the economic evaluationof prospective reservoirs.

Schlumberger used the FrontSim streamlinereservoir model on a structurally complex, three-dimensional, faulted geologic model of a Gulf ofMexico sandstone field. The cell properties wereassigned using a geostatistical approach basedon a related seismic attribute. Permeability wasassigned based on a relationship to porosity.FloGrid software was used to create a FrontSimmodel with the same dimensions as the geologicmodel, with twelve production and two injectionwells. The million-cell FrontSim model executedin about six hours, much faster than a finite-difference model would have run.12

The model was upscaled to obtain a finite-difference case of about 120,000 cells, usingharmonically averaged permeability and arith-metically averaged porosity (right). This smaller version was run using a finite-differencemodel. After nine years of simulated production,the pressure difference between the streamlineand finite-difference models was about one psiout of almost 5200 psi [35.8 MPa]. The fieldwater cut differed by only about 0.1% of liquidproduction.13 The excellent agreement validatedthe upscaling method.

Flow Streams in Prudhoe Bay FieldSome reservoirs are difficult to simulate with afinite-difference model. Large reservoirs mayneed millions of gridblocks to define faults orother complex geology. Water and gas floodingadd dynamic movement of flood fronts, which

may need to be tracked closely. There may bemany wells, each with a production or injectionhistory to match. The time required to solve sucha model can be beyond the budget of a companyand the patience of a reservoir engineer.

Prudhoe Bay field, on the north slope ofAlaska, USA, provided just such a problem for theoperator, BP. This large field—26 billion barrels[4 billion m3] of oil in place—now has more than23 years of production history, including waterand water-alternating-gas injection in the water-flood areas. Simulating over 1000 wells penetrat-ing the reservoir is difficult.

In the Northwest Fault Block (NWFB) area ofPrudhoe Bay field, a finite-difference simulatorwith over 200,000 gridblocks was abandonedafter 10 months because it was unable toachieve a detailed history match of the more than200 wells included (left). The operator evaluatedalternatives to a finite-difference model anddecided to use the FrontSim streamline model.14

The geologic complexity could be maintained, ascould the large number of wells, and sufficientgridblocks could be included to adequately coverthe reservoir. One engineer using the FrontSimmodel matched the complex production historyof the NWFB in only six months.

0.03 0.11 0.19 0.27 0.35

Porosity

> Gulf of Mexico sandstone model for steamline simulator in two gridblock sizes. The front part of thisfigure is half of the million-cell case and the back is half of the 120,000-cell upscaled version, illustratingthe difference in gridblock size. Both are color-coded by porosity.

Oil saturation

0.37500.18750.0000 0.75000.5625

> Prudhoe Bay Northwest Fault Block (NWFB). The FrontSim model of the NWFB indicates the oilsaturation in 2001. Some wells shown in the model are no longer active.

(continued on page 46)

44

The simplest reservoir model would use a singlefluid. Although a single-component model isuseful for describing aquifers, it is not adequatefor hydrocarbon production, which can havethree flowing phases—gas, oil and water. Three-component models, called black-oil models, areactually simple compositional models withwater and two hydrocarbon phases, because gascan go in and out of solution with the oil. Thegas and oil components have defined properties,such as density and viscosity, and the gas-oilphase behavior is treated as a two-componentsystem. This means that any gas evolved fromthe oil or present as a free-gas cap will have a set composition. The only variable is howmuch of the gas is still dissolved in the oil.

However, gas in a reservoir is not a singlecomponent, but a combination of many com-ponents such as methane, ethane, propane,

butane and so forth. The amount of each compo-nent in the gas phase is given by the pressure-volume-temperature, or PVT, relationship of themixture.1 It is important to note the differencebetween a component, such as pentane, and a phase, such as gas.

Water at atmospheric pressure has a simplephase relationship. It is a single phase that goesfrom solid to liquid to gas—ice to water to watervapor. Chill water to the freezing point and itbegins to convert to ice. Two phases coexist atthat temperature, and we can speak of the per-centage of each phase that is present at any time,but both the solid and liquid phases are still H2O.

In a two-component system, such as propane[C3H8] and hexadecane [C16H34], the picturegets more complicated. At reservoir temperatureand pressure conditions, the two-componentsystem can be all gas, all liquid, or gas and

liquid together. But now, not only do the per-centages of the gas and liquid phases dependon conditions, so does the amount of propane orhexadecane in each phase. Starting in the gasphase and decreasing pressure, there comes a point when drops of liquid begin to appear. At this “dewpoint,” the first drops of liquid arericher in hexadecane, the heavier component.With decreasing pressure, more of both compo-nents move from gas to liquid. The last bubbleof gas to transform to liquid is richer in propane,the lighter phase. The final state is all liquid,with the same mixture of the two componentsas the original gas.

Oilfield Review

Composing Pseudofluids

1. For a complete description of hydrocarbon fluid proper-ties: Muskat M: “The Physical Properties and Behavior ofPetroleum Fluids,” in Muskat M: Physical Principles of OilProduction. Boston, Massachusetts, USA: IHRDC, 1981.

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B

C

D

10% gas

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30%

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80%

Hydrocarbon phase envelope. The phaseenvelope is bounded by the bubblepointand dewpoint curves, which meet at thecritical point. Under pressure and tempera-ture conditions at Point A, the fluid is allliquid. Depletion decreases the pressure,and at Point B, bubbles of gas begin form-ing. Continued depletion increases the pro-portion of free gas in the system, crossinglines of constant composition. At a highertemperature, such as Point C, depletionintersects the dewpoint curve at Point D,where liquid begins to drop out of the gas.Lines of constant gas-to-liquid ratio meet atthe critical point. By following a path from B to A to C to D, first increasing pressure,then increasing temperature and finallydecreasing pressure, a fluid can be takenfrom liquid to gas without going through a phase transition.

>

Spring 2001 45

A reservoir hydrocarbon is a more complexmixture of components, ranging from those withone carbon atom to compounds with perhapsmore than 40. The phase diagram is similar to a two-phase case, but now there is a broaderdistribution of components that can be in eitherphase. The phase diagram of reservoir oil froma field in the Middle East indicates some of theimportant characteristics of phase behavior(previous page). The phase diagram shows thefluid behavior as pressure and temperaturechange at constant volume, going from a singlephase outside the diagram to two phases inside.The fluid is a liquid above the bubblepointcurve, where bubbles first form as pressuredecreases, and a gas above the dewpoint curve,where liquid droplets first form as pressuredecreases. The point where the bubblepoint anddewpoint curves meet is the critical point. Linesof constant composition inside the diagram allmeet at the critical point. At the critical point,intensive properties, such as density, are identicalfor both gas and liquid phases. Near the criticalpoint, small changes in pressure or temperatureyield large changes in phase composition.

Fluid composition defines phase-envelopeshape, position of the critical point on the enve-lope and location of the constant-compositioncurves. Since hydrocarbon fluids may have 40 or more components, modeling behaviorwould be an enormous problem if each compo-nent were included. To simplify the problem,the concept of lumping or creating pseudocom-ponents was developed. One common groupingputs all components heavier than hexane into a C7+ pseudocomponent. The lighter compo-nents may also be lumped into two or moregroups. Tools such as the PVTi software help in defining pseudocomponents.

Fluid physical properties are described by an equation of state. When using pseudocom-ponents, the inputs to the equation must beestablished for each lumped group. The fluidbehavior—determined in laboratory tests suchas constant-composition expansion tests, sepa-rator tests and oil-swelling tests—is used totune the equation of state, which is then usedin the compositional reservoir model (above).

So long as the specific composition of the gasphase is not crucial to the reservoir situation,the black-oil model can work well. The engineermust determine how important the effect ofchanging composition is on fluid properties, andultimately on the revenue stream from a field.

A compositional model may be required in thefollowing situations:• gas injection, due to gas stripping• miscible flooding, as the injection gas goes

into solution with oil• carbon dioxide flooding with the gas soluble

in both oil and water• thick reservoirs with a compositional gradient

due to gravity• reservoirs with areal variations in fluid

composition• reservoirs near the critical point• high-pressure, high-temperature reservoirs.

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35

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42

Liqu

id d

ensi

ty, l

bm/f

t3

Gas, mole percent

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

4750

4500

4250

4000

3750

3500

3250

3000

2750

2500

Satu

ratio

n pr

essu

re, p

sia

> Equation-of-state modeling. Parameters describing pseudocomponents are tuned by comparinglaboratory measurements (blocks) to pseudocomponent model output (lines). Hydrocarbon liquiddensity (green) and saturation pressure (purple) are shown as functions of gas composition.

The operator sought to understand in detailthe relationship between injectors and producersto allocate water injection and manage thewaterfloods. A well-by-well examination usingthe NWFB model can identify problems withwater influx, illustrating whether water comesfrom the aquifer or a nearby injection well(above). Based on such an analysis, BP alteredthe injection program, including redrilling wellsand adjusting injection allocation. After thesechanges, flow patterns were more localized, andwater injection was reduced by 40% (next page).

BP maintains FrontSim reservoir models forall Prudhoe Bay waterflood areas, consideringthem an important tool for day-to-day reservoirmanagement. These models run in one or twohours, making them useful in assessing new welllocations for waterflooding and in predictingenhanced oil recovery.

Managing Reservoirs from Cradle to GraveRadical ups and downs in oil prices drive theindustry toward two extremes of reservoir man-agement. Some operators in mature areas wantto produce as much oil and gas as possible withminimal expenditure of capital and engineeringresources. They seek simple engineering solu-tions. Although reservoir simulation may neverbe possible “on the back of an envelope,” theseusers drive the need for an intuitive user inter-face. Therefore, to succeed, future computer pro-grams must have intelligent defaults so noviceusers can obtain reasonable solutions quickly.

At the other end of the spectrum are largefields, both under production or still in delineationand exploration phases, where huge capital invest-ments must be protected with the best engineeringavailable. Developers will improve algorithms andinternal design of simulators to satisfy the vora-cious need for more gridblocks, more complexityand more speed to solve large problems.

Parallel processing has been an option in reser-voir simulators for several years, but in the future,it will become the default method, particularly formodels with multimillion gridblocks. This requiresimprovements in the way processors communicatewith one another and better tools that divide simu-lation models into sections that are logically con-sistent and easy for the program to handle.

The modeler faces two major tasks that needimproved automation. First, the user must designthe grid, which can be made easier through auto-mated links with geologic models and improvedimportation of gridblock data from geologic toreservoir models. Closer linking of these twotypes of models will help geologists use reservoirmodels when assessing prospects.

Second, the modeler must match the produc-tion history of the field. Complete automation ofhistory matching is probably far in the future, butin the near term, optimization routines will help

46 Oilfield Review

Water saturation

0.6250 0.8125 1.00000.2500 0.4375

> Source of water influx. In this timestep from 1983, streamtubes leading to a single well illustrate a distinction between pure water flowing from the aquifer (dark blue), and water and oil flowing fromupper layers (light blue). Streamtubes indicate some water travels past many other wells (magenta)before being produced.

Spring 2001 47

users focus their efforts on identifying variableswith the greatest influence on solutions.Engineering judgment will continue to play a keyrole. However, improved history-matching rou-tines could revolutionize simulator algorithms.

Most of the preceding discussion relates touser interfaces or the way models will changeinternally. With improvements, other disciplineswill find reservoir simulators more useful. Alreadyavailable, the Weltest 200 module provides engi-neers with a numerical tool for evaluating welltests. In addition, the MSW option of ECLIPSEsoftware provides new possibilities for comple-tion engineers to analyze multilateral wells andsome intelligent downhole control devices.

Efforts are under way to improve models in thenear-well region. Greater flexibility in well place-ment within models will help optimize future welllocations, not just to the level of one gridblock ver-sus another, but to define well location within afew meters. Engineers and geoscientists will beable to evaluate the influence of faults and naturalfractures, sand or shale lenses, and zone pinch-outs, to cite a few geologic examples, as well asinteraction of existing wellbores and flood fronts.

Today, reservoir simulators include simplerelations to earth stresses. Modeling of stresschanges is done using rock mechanical models.The future will see simulators capable of solvingflow and earth-stress models simultaneously.Reservoirs with significant compaction and subsi-dence need these integrated solutions to ensurereservoir energies are assessed correctly.Permeability increase or decrease due to com-paction must be related to stress changes. Moreproduction practices will be included in reservoirmodels as modules are added to numerically han-dle fracturing and sand production and control.Further in the future, drilling-bit interaction withformations may become a standard part of mod-els, accounting for formation damage and drilling-fluid invasion as well as breakouts and cave-ins.

Until a few years ago, astronomers and astro-physicists didn’t have the ability to detect planetsaround other stars, but they improved detectiontechniques and planetary-system models. Now itseems every few months more new planetaryobjects are found. In our industry, the idea of asingle program providing discovery-to-abandon-ment modeling for a reservoir is a dream for thedistant future, but the elements exist to make ithappen sooner rather than later. —MAA

1997

2001

> Simulation results for 1997 and 2001. Prior to changes in the injection program, streamtubes originatedoutside the productive area, such as the long green tubes in the foreground (top). Model predictionsafterward show flowstreams remain within the productive area (bottom). The tubes are color-coded byinjection source, and the length of the tube is the distance fluid travels in about three years.