RRRRReeeeesssssererererervvvvvoir Engoir Engoir Engoir Engoir Engininininineeeeeering for Gering for Gering for Gering for Gering for GeeeeeolooloolooloologggggistsistsistsistsistsArticle 14 - Reservoir Simulation by: Ray Mireault, P. Eng.; Nick Esho; and Lisa Dean, P. Geol.; Fekete Associates Inc.

In Fekete’s experience, a well performedreservoir simulation represents the ultimateintegration of geology, geophysics,petrophysics, production data, and reservoirengineering. Through simulation, the flow ofmultiple fluids in heterogeneous rock overtime can be quantitatively estimated to gaininsights into reservoir performance notavailable by any other means.

Initially, reservoir simulation was reservedfor large reservoirs requiring large capitalinvestments that justified costly, intensivestudies such as offshore developments.However, simulation of more modest-sizedreservoirs has increased as simulationsoftware and computer capability havebecome more readily available. Oilfieldsunder primary production, waterflood, andEOR typically qualify for reservoir simulationbut its usage is not uncommon for gas fields,unconventional reservoirs, or poolsundergoing CO

2 injection.

In broad terms, the geologist / geophysicist /petrophysicist’s role in reservoir simulationis to reliably approximate the (a) stratigraphy,(b) structure, and (c) geometry of thereservoir flow unit(s) and the initial fluiddistributions throughout. The aim of theexercise is to quantify and manage thesubsurface knowledge and uncertainties. Inthe practical sense, a good model is the onethat is f it- for-purpose uti l iz ing soundgeological reasoning and at the same timesupports reservoir dynamics (e.g., fluid flow,history matching).

Geological data is often characterized bysparseness, high uncertainty, and unevendistribution, thus various methods ofstochastic s imulation of discrete andcontinuous variables are usually employed.The final product will be a combination of:

• observation of real data (deterministiccomponent),

• education, training, and experience(geology, geophysics, andpetrophysics), and

• formalized guessing (geostatistics).

The first step is the geologist’s conceptualdepositional model which (s)he must be ableto sketch and explain to the other membersof the team. The conceptual model should bebroadly compared and tested with eachdiscipline’s observations and data (e.g., core

permeability versus well-test permeability,core porosity versus log-derived values) untilthe team has a consistent explanation of thereservoir’s pre- through post-depositionalhistory. Hydrocarbon reservoirs are toocomplex to develop a completeunderstanding “in one afternoon” so theprocess should be viewed as a series ofongoing discussions.

The next step is to define, test, and prioritizethe uncertainties to be modeled and theirimpact on the overall dimensions of themodel. For example, a gridblock height thatis too large to reflect the layering in thinbeds will introduce significant errors in theflow net-to-gross pay estimates as well asflow pathways. It is essential to agree upfronton the level of resolution and details to becaptured in the model. The appropriate levelof detail can be different for each reservoirand is also dependent on the purpose of thesimulation, sometimes testing and iterationsmaybe necessary.

Next comes selecting the appropriate gridtype (regular or faulted) to model thepresent day structure of the reservoir.Components to be modeled include the topof structure, faults, internal baffles to flow,and any areal variation in thickness and rockproperties. The objective is to replicate theorientation, geometry, and effect of thestructural imprint as it affects flow withinthe model. It is imperative to validate thefault-horizon network to ensure it isgeologically feasible and to ascertain theabsence of structural distortion and otherproblems.

Facies modeling is the next step inconstruction. Where available , the bestpractice is to integrate core data and outcropanalogues to constrain and refine logderivedfacies type and property estimates.Understanding the facies distributionprovides a tool for predicting reservoirquality away from the known datapoints. Thegeometry (length, width, thickness, anddirection) of each facies body will affect theway heterogeneit ies in porosity andpermeability are modeled. Attribute analysis(inversion/QI) and geobodies extracted fromseismic data are also useful to further refinethe geological model.

It is important to quality check at each step

of development to ensure consistency in theinterpretation and reaff irm that thedeveloping model is fit-for-purpose. A verydetailed geological model may be unable toaddress the question(s) that the simulationteam is attempting to answer.

The engineer’s role in the process is toreliably simulate the performance of thegeological model for the productionscenario(s) under consideration by historymatching a producing field and / or forecastingfuture performance. While it may seem thatreservoir s imulation would bestraightforward if we only knew all theinputs, that perception is incorrect. Limitedinformation unquestionably complicates thetask but the most fundamental (andunavoidable) issue is the error introducedby approximating overwhelmingly complexphysical geometries / interactions withsimpler but manageable mathematicalrelationships.

Of necessity, simulation uses a sequence ofthree-dimensional gridblocks as a proxy forreservoir rock volume (see Figure 1). Inorder to keep the time, cost, and computingrequirements of a simulation manageable, thetotal number of gridblocks is generallylimited to less than 500,000, with a smallsimulation requiring less than 100,000gridblocks. For either large or small projects,

Figure 14.1. Typical reservoir simulation models (a)tank, (b) ID, (c) ID radial, (d) cross-sectional, (e)areal, (f) radial cross-sectional, and (g) 3D;Mattax and Dalton, 1990.

a gridblock may represent a “unit” rockvolume of one or more acres in areal extentand several feet thick (Figure 14.2).

While fluid saturations and / or otherproperties can vary significantly over an acreand / or several feet of reservoir (e.g., anoil-water transition zone), each gridblockhas only a single value for each property (e.g.,porosity, saturation of water, oil and gas,permeability, capillary pressure) of thegridblock. When the true variation in thereservoir is too great to be comfortablyrepresented by a single average value, thesolution may be to (iteratively) increase thedensity of the gridblocks (“fine grid”) in aspecific area of the reservoir. Alternatively,a separate, smaller simulation may be runand the results provided as input to thelarger study, as when modeling fluid andpressure behaviour at the wellbore sandface.

Similarly, simulation must approximate thecontinuous movement of fluids and theresulting changes in fluid saturations withcalculations performed at discrete timesteps.Though it does not occur in the real world,there can be abrupt changes in a gridblock’sfluid saturation(s) as fluids move into or outof the gridblock. The usual solution is to limitthe magnitude of the change to tolerablelevels through (iterative) selection of smallertimesteps.

The use of discrete timesteps and discretegridblocks with a single value for eachproperty also leads to the dilemma of whatvalues to use in modeling the f luidproperties for f low between adjacentgridblocks and adjacent timesteps. Thisartifact of numerical simulation also hasconsequences on calculated performancethat do not exist in reality. For furtherdiscussion, see Chapter 2 of the SPEMonograph Volume 13. Though there is nocompletely satisfactory answer to theproblem, workable approximations for flowacross gridblock boundaries and betweensubsequent timesteps exist. The choice ofwhich to use in a particular situation oftencomes down to experience and iteration.

Figure 14.3. Rock and fluid properties (Mattaxand Dalton, 1990).

Figure 14.2. Example of 3D gridblocks.

DDDDDAAAAATTTTTA REA REA REA REA REQUIREQUIREQUIREQUIREQUIREMEMEMEMEMENNNNNTTTTTSSSSSThe rock and fluid properties required forreservoir simulation are summarized inFigure 14.3. Collecting the data and puttingit into a form that can be imported in areservoir simulator can be a major effort initself.

ASSIGNMENT OF GRIDBLOCKASSIGNMENT OF GRIDBLOCKASSIGNMENT OF GRIDBLOCKASSIGNMENT OF GRIDBLOCKASSIGNMENT OF GRIDBLOCKPROPERTIESPROPERTIESPROPERTIESPROPERTIESPROPERTIESChapter 4 and 5 of SPE Monograph 13provide further discussion on the challengesof assigning representative average valuesfor rock and f luid properties to eachgridblock in a simulation model and the sizeof gridblocks and timesteps to use. Thechoices are interrelated and influenced by:

• the areal and vertical variation in theobserved rock and fluid properties,

• the type of physical processes beingmodeled, and

• the solution techniques being used.

Often, the best approach is to select thesmallest gridblock size and number of layersneeded to accurately describe the changesin reservoir facies, reservoir geometry, andfluid distribution. For example, f luidsaturation changes in an oil-water transitionzone might require gridblocks with anunusually small height of one foot or less toadequately represent the change in saturationthrough the transition zone with the seriesof single values avai lable to “stacked”gridblocks. Production and injection wells

and internal no-flow boundaries such asshale deposits or non-conducting faults areother features that can be the determiningfactor in selecting gridblock size.

Porosity and permeability distribution arenearly always important and are often thekeys to reservoir performance. Sensitivitystudies generally indicate that if the faciesdistributions through the reservoir arecorrectly modeled and each facies is assignedthe correct order of magnitude forpermeability, the relatively small errors inthe absolute value of permeability assignedto each gridblock are insignificant, since theyare compensated for by the large area offlow that is available for fluid movement.

Constructing the entire reservoir modelwith a minimum size of gridblock capturesthe level of detai l needed for crit icalaspect(s) of the reservoir simulation butover-compensates in non-critical areas.Subsequent inspection of the model, keepingin mind the physical processes (i.e., thermalprocesses) and solution techniques that willbe used to model fluid flow, will identify areasof the reservoir that do not require the levelof detail that was built into the originalmodel. The process of subsequently selectingand reducing the number of gridblocks usedto model the non-critical areas is referredto as “upscaling.”

Selection of the appropriate timestep isgenerally left to last, because the pore

volume of a gridblock and rate of fluid flow(production) both influence the rate ofchange in a gridblock’s fluid saturations overtime. Limits on the rate of saturation changethat are developed from experience, aregenerally used to determine the largesttimestep size that will present apparentlysmooth results when mapped or graphed.This process is done internally by thesimulator to ensure smoothness of results.

SIMULSIMULSIMULSIMULSIMULAAAAATION OUTION OUTION OUTION OUTION OUTPTPTPTPTPUUUUUTTTTTSince it is not possible to individually inspectthe mil l ions of calculat ions that areperformed in a simulation, editing andgraphical presentation of the output iscrucial to assessing the consistency andreliability of the results. As a minimum, theoutput graphs should include:

• oil, water and gas production rates,• producing gas-oil ratio;• producing water cut or water oil ratio,

and• bottomhole flowing pressures.

Maps / movies of f luid saturation andreservoir pressure trends are alsoinvaluable to assessing the quality andconsistency of the output. For example,inconsistent pressure behaviour – relatedto negative cell volumes – may indicate thatthere is an issue with the gridding and / orassigned transmissibility of gridblocks alonga fault zone.

UUUUUSESESESESES AND LS AND LS AND LS AND LS AND LIMITIMITIMITIMITIMITAAAAATIONS OFTIONS OFTIONS OFTIONS OFTIONS OFSIMULSIMULSIMULSIMULSIMULAAAAATIONTIONTIONTIONTIONAs computing power and software capabilityhave developed, the “art” of reservoirsimulation has proven to be a valuablecomplement to other methods of reservoiranalysis. To the geologist, a threedimensionalmodel is the ultimate tool for visualizing andthen communicating the reservoirinterpretation to others (Figure 14.4). As aworking tool, it integrates the partialinterpretations provided by each disciplineand allows for an unsurpassed level ofconsistency checks.

To the reservoir engineer, modern-dayreservoir simulation software provides thecapabil ity to visualize and present themovement of f luids through rock inaccordance with physical principals. With itwe can:

• comparatively assess the hydrocarbonrecovery eff ic iency of variousproduction systems that could beconsidered for a given reservoir priorto their implementation and

• more closely monitor producingreservoir trends and more quickly

Figure 14.4. Visualization of 3D model.

identi fy the probable causes ofdeviations from forecastedperformance, particularly during theearly life of a reservoir.

Prior to production, Monte Carlo volumetricestimates are still the best tool to quantifythe uncertainty in the gas or oil-in-placewithin a deposit. But reservoir simulational lows comparison of productionperformance over the probable volumetricrange at a level not previously available.Simulation sensitivity studies are invaluablein identifying the uncertainties that can havea significant impact on production / financialperformance and in focusing efforts toacquire additional information and / ormodify development plans to mitigatepotential impacts.

For a producing reservoir, material balancestill provides the most accurate estimatesof oil- and / or gas-in-place. Accordingly,tuning the in-place volumes in the simulatorto the material balance results improves thediagnoses of well performance and allowsfor better reservoir management.

REFERENCESREFERENCESREFERENCESREFERENCESREFERENCESMattax, C.C. and Dalton R.L. 1990. ReservoirSimulation. Society of Petroleum Engineers, HenryL. Doherty Series, Monograph Vol. 13.