Reservoir Simulation Calvin C. Mattax, * SPE, and Robert L. Dalton SPE Exxon Production Research Co. u •• • the precision with which variations In reservoir properties can be modeled Is determined by the number of blocks In the model." Introduction In the past 30 years, reservoir simulation has evolved from a research area into one of the most flexible and widely used tools in reservoir engineering. Use of reservoir simulation has grown because of its ability to predict the future performance of oil and gas reservoirs over a wide range of operating conditions. Reservoir simulators use numerical methods and high-speed computers to model multidimensional fluid flow in reservoir rock. Reliable simulators and adequate computing capacity are available to most reservoir engineers, so simulation is usually practical for all reservoir sizes and all types of reservoir performance studies. Although the use of simulation frequently is optional, it may be the only reliable way to predict the performance of a large, complex reservoir, especially if such external considerations as government regulations influence the production schedule. Even for small reservoirs where simple calculations or extrapolations may be adequate, simulation is often faster, cheaper, and more reliable than alternative methods for predicting performance. Modeling Concepts A reservoir simulator models a reservoir as if it were divided into a number of individual blocks (gridblocks). Each block corresponds to a designated location in the reservoir and is assigned properties-porosity, permeability, relative permeability, etc.-believed to be representative of the reservoir at that location. In the simulator, fluids can flow between neighboring blocks at a rate determined by pressure differences between blocks and flow properties assigned to the interfaces between blocks. In essence, the mathematical problem is reduced to a calculation of flow between adjacent blocks. For every block-to-block interface, a set of equations must be solved to calculate the flow of all mobile phases. The equations generally incorporate Darcy's law and the concept of material balance and contain terms describing the permeability "between" blocks, fluid mobilities (relative per'Now retired. Copyright 1990 Society of Petroleum Engineers 692 ' , meability and viscosity), and rock and fluid compressibilities. Fig. 1 illustrates the most common types of models used in simulation. Models range in complexity from a single block, useful only for classical material-balance calculations, to fully 3D models capable of modeling all major factors that influence reservoir performance. Each gridblock in a model has only one set of properties; there is no variation in any property within a block. For example, phase saturations in a model block will be volumetric averages of the saturations in that part of the reservoir represented by the block. In this respect, a model block can be visualized as a well-stirred tank (Le., its contents are homogeneous) connected to adjacent tanks with pipes whose flow capacities are determined by reservoir flow properties. This visualization, although simplistic, demonstrates that the precision with which variations in reservoir properties can be modeled is determined by the number of blocks in the model. A simulator also divides the life of a reservoir into discrete increments. Changes in a reservoir (pressure, saturation, etc.) are computed over each of many time increments, or timesteps. Conditions are defined only at the beginning and end of each timestep; nothing is defined at any intermediate time within a time interval. The accuracy with which reservoir behavior can be calculated generally will be influenced by the length of the timesteps as well as the number of gridblocks. The preceding discussion implies that for any size gridblock and any length of timestep, there will always be abrupt changes in reservoir conditions from one block to the next and from one timestep to the next. Fig, 2 illustrates this point. At the top of Fig. 2 are plan views of a hypothetical two-well reservoir being waterflooded and a four-gridblock simulator model of the reservoir. The two plots show water-saturation distribution at a given time in both the reservoir and the model. In the reservoir, water saturation is a smooth function of distance but in the model, an abrupt drop in wate; saturation occurs between Blocks 1 and 2 and again between Blocks 2 and 3. A plot June 1990 • JPT sPETechnology Today a "The most useful way to determine whether a model adequately describes a reservoir Is to simulate past performance and to compare the simulation with the reservoir's actual performance history." c b SERIES /'/'/'/LL-;; ./" ( / ./" .J.x /" d -r--'--- ~ '- 9 Fig. 1-Types of models used In reservoir simulation: (a) tank (material balance), (b) 1D linear, (c) 1D radial, (d) 2D cross-sectional, (e) 2D areal, (f) radial cross-sectional, (g) 3D. of saturation vs. time in any block in the model would also be a "stair-step" curve, whereas a time/saturation plot for the corresponding location in the reservoir would be a continuous, smooth curve. The stairstep approximation approaches actual reservoir saturation distribution as the sizes of gridblocks and timesteps decrease. An important step in simulation clearly is the selection of the number of blocks in a model and the timestep size to use in calcuJPT • June 1990 lations. Increasing the number of blocks and timesteps will increase the time required to prepare input data and to interpret results and the cost of calculations. Other important model design steps are selecting model dimensions (10, 2D, or 3D) and determining whether conventional black-oil, compositional, miscible, chemical, or thermal treatment is needed. Designing the simplest model that will simulate the displacement process adequately is usually best. Although study results may be more credible to decision makers if the model is more complex than needed to solve the problem, added intricacy almost always increases the cost of a study. Usually, models are 2D or 3D and contain from 100 (for a simple 2D model) to 100,000 gridblocks (for a very complex 3D model) . Small models can be run on a personal computer or a standard mainframe computer, while the most complex ones re693 "For conventional primary and secondary recovery processes, the ability of reservoir simulators to predict performance Is determined largely by the quality of the reservoir and aquifer description and the model design." G_'_V o S i mulator Model Reservoir 75 75F-_--, 50 50 25 25 o~----~----~--~~--~ Distance a o~----~----~--~~--~ 4 b Block Number Fig. 2-A four-gridblock waterflood model: (a) hypothetical reservoir and Its watersaturation distribution at a given time In the waterflood and (b) four-grldblock model and simulated water-saturation distribution. quire a supercomputer. Computer time and costs for one simulation of reservoir performance can vary from a few minutes, costing less than $100, to many hours, costing thousands of dollars. major weaknesses in reservoir description or operating problems, such as casing leaks. Experience has shown that simulation can be a powerful reservoir-description tool. Testing Model Validity Reservoir simulators are most frequently used to predict future production from an entire reservoir or a major segment of a reservoir. Such full-field simulators normally predict oil, gas, and water production rates as a function of time from individual wells and from the total area modeled. In addition, the simulator may integrate wellbore constraints into predicted future performance by automatically implementing a logical sequence of well workovers, recompletions, replacements, and additions (infill drilling) to optimize economics. Several predictions will frequently be made to reflect different possible operating conditions or two or more equally probable reservoir descriptions . SPE Monograph Vol. 13, Reservoir Simulation, 1 discusses examples of this type of simulation. Simulation can be especially useful when uncertainty exists about the relative signifi- Simulation Applications The most useful way to determine whether a model adequately describes a reservoir is to simulate 'past performance and to compare the simulation with the reservoir's actual performance history. If the comparison is favorable, the model can be used with some confidence to predict the future. The simulation should match typical well histories as well as regional and overall reservoir performance. Pressure, saturation, GOR, and WOR should all match to within the precision needed to attain the objectives of the reservoir study. Usually, not enough is known about a reservoir to construct a model and to use it without some modification of permeability , porosity, continuity, and stratification. An unexpected benefit of simulation sometimes comes from discrepancies between actual and simulated performance that identify cance of major factors that influence performance. For example, results of a 3D, full-field reservoir simulation study of the Lower Brent reservoir of the Dunlin field in the U.K. North Sea by Exxon Production Research Co. demonstrated that faults dominate areal sweep and that vertical permeability distribution controls vertical sweep. As Fig. 3 shows, injected water has a tendency to "tongue" through the highquality Etive sands located approximately midreservoir. The study identified major targets for additional recovery (the Rannoch sands in the lower half of the section and the Lower Ness sands at the top of the section). On the basis of a similar 3D simulation and development study, 2 the field operator has already undertaken a program of dedicated Rannoch completions to improve recovery from this unit. A second interesting application of a fullfield simulator is the modeling 3 of the Troll field offshore Norway. Numerical simulation is the only practical way to study a large, complex field such as Troll. Note the major faulting illustrated in the cross section of the field (Fig. 4). The simulator used Fig. 3-Water-saturatlon distribution In the Dunlin, Lower Brent model after 9 years of water injection. WATER-INVADED RE&IION~ •• WATER - -- 694 - • OIL June 1990 • JPT 31/2-13 31/2-10 ':J 31/2-2 Authors 31/3-1 W ••----,t--+> E 1400 (j) ::; S 1600 ;:: 1800 Q. ~ 2000 o o SOGNEFJORO • HEATHER UNIT B FENSFJORO Fig. 4-Westleast cross section, Troll field. several special techniques to model all significant aspects of reservoir fluid dynamics, including flow through the faults and water and gas coning. Fig. 5 shows potential production profiles for two of several possible development plans. Engineers indicated that the model proved to be an efficient tool for comparing alternative development scenarios and for general reservoir management. Single-well models can be used to study flow at the sandface and in the region near a well. These models are usually radial, and gridblocks adjacent to the wellbore may be as small as 1 or 2 in. in radius. A radial cross-sectional model similar to that shown in Fig. I was used by Addington 4 to predict gas-coning behavior of Prudhoe Bay wells for a range of reservoir properties and perforation thicknesses and locations in the producing interval. With the model results, gas-coning correlations were developed for use in a 3D Prudhoe Bay field model to predict critical coning rates and GOR's of wells after cone arrival. Major heterogeneities usually must be represented in a reservoir model. Detailed representation of small-sized (a few inches to a few feet) reservoir heterogeneities seen in logs, cores, and outcrops, however, usually is not practical in simulation models because an excessive number of gridblocks would be needed. The influence of such small-sized heterogeneities should be included in a model through combined geologic and reservoir engineering studies that define the effective reservoir properties needed when a practical number of blocks is used. For example, Richardson et al. 5 derived effective vertical permeabilities .that would allow small, discontinuous shales to be modeled accurately in simulations of oil drainage with gridblocks larger than the shales. For conventional primary and secondary recovery processes, the ability of reservoir simulators to predict performance is determined largely by the quality of the reservoir and aquifer description and the model design. Our understanding of EOR processes is less advanced. These processes pose modeling difficulties, and industry has less experience in modeling them, as discussed in more detail in Reservoir Simulat{on. 1 Summary 1. Reservoir simulation is an effective technique that is now widely available for use in reservoir engineering. 2. Careful design of a simulation model is required to meet the objectives of a reser- 8.000 - - 01.. START-UP TROll EAST 1.000 - 01.., STAAT-UP TROlL WEST - - WATER. START-UP. TROLL EAST ! - - - WATER. STAAT-UP TROLl WEST 6,000 E ~ 5,000 I 4.000 w .... : 2.000 1.000 voir study and to control personnel and computer costs. 3. History matching, which is a vital part of a simulation study, can be a powerful reservoir-description tool. References 1. Mattax, C.C. and Dalton, R.L.: Reservoir Simulation, Monograph Series, SPE, Richardson, TX (1990) 13. 2. Braithwaite, C.I.M. et a!.: "Improving Recovery From the Dunlin Field, U.K. Northern North Sea, " paper SPE 19878 presented at the 1989 SPE Annual Technical Conference and Exhibition, San Antonio, Oct. 8-11. 3. Kydland, T. et a!.: "Application of Unconventional Techniques in Constructing an Integrated Reservoir Simulation of the Troll Field," SPERE (Aug. 1988) 967-76. 4. Addington, D.V.: "An Approach to Gas-Coning Correlations for a Large Grid Cell Reservoir Simulator," JPT (Nov. 1981) 2267-74. 5. Richardson, G.J. eta!.: "The Effect of Small, Discontinuous Shales on Oil Recovery," JPT (Nov. 1978) 1531-37. 51 Metric Conversion Factors r:::.----------- 3.000 Calvin C. MaUax, retired division manager from Exxon Production Research, is a consultant in Houston. He holds a BS degree from the U. of Tulsa and a PhD degree from Louisiana State U., both In chemistry. Mattax is editor and coauthor of the newest SPE Monograph, Reservoir Simulation, and is a member of a Technical Program Committee for the 1990 Annual Meeting. Robert L. Dalton, division manager at Exxon Production Research Co. in Houston, is editor and coauthor of Reservoir Simulation. He holds a BS degree in chemical engineering from Rice U. Dalton served on Technical Program committees for the 1974 and 1976 Annual Meetings and was a 1984-85 Distinguished Lecturer. He has been a member of the Editorial Review Committee since 1987 and is a 1989-90 Continuing Education Committee member. ;f """-------------------------------I bbl x 1.589 873 ft x. 3.048" in. x 2.54" E-Ol = m' E-Ol = m E+OO = em • Conversion factor is exact. TIME (years> This paper is SPE 20399. Technology Today Series arti· cles provide useful summary information on both classic and emerging concepts in pelroleum engineering. Purpose: To provide the general reader with a basic understanding of a significant concept, technique, or developmenl within a specific area of technology. Fig. 5-Productlon profiles, southern oil province, Troll field. JPT JPT • June 1990 695 Discussion of Reservoir Simulation Leendert Schenk, SPE, independent I read with interest the Technology Today Series article "Reservoir Simulation" by Mattax (retired) and Dalton of Exxon Production Research Co ., published in the June 1990 JPT (Pages 692-95). I have the following comments to make. 1. Am I really to accept the statement at the end of the Introduction: "Even for small reservoirs where simple calculations or extrapolations may be adequate, simulation is often faster, cheaper, and more reliable [my underlining] . .. "? Too bad that the article does not offer any proof. 2. In red at the top of Page 694 is the statement, "For conventional primary and secondary recovery processes, the ability of reservoir simulation to predict the performance is determined largely by the quality of the reservoir and aquifer description. .. ." The last sentence of Testing Model Validity says: "Experience has shown that simulation can be a powerful reservoir-description tool. " What a beautiful vicious circle: the simulator itself can "predict" what it needs to make predictions! 3. The examples given in the Simulation Applications section do not look very convincing for the needs of reservoir simulators . The third column on Page 694 says: JPT • November 1990 "For example, results of a 3D, full-field reservoir study of the Lower Brent reservoir of the Dunlin field in the U .K . North Sea by Exxon Production Research Co . demonstrates that faults dominate areal sweep and that vertical permeability distribution controls vertical sweep. As Fig. 3 shows, injected water has the tendency to tongue through the high-quality Etive sands. . . ." Does one really need simulators to draw the underlined conclusions? Or is it sometimes a relief to find that simulators can predict the obvious? Regarding the Troll field offshore Norway, the paper says: "Engineers indicated that the model proved to be an efficient tool for comparing alternative development scenarios and for general reservoir management." This sounds more like an article of faith* than a technical argument. 4. I was flabbergasted by a statement in the Modeling Concepts section at the bottom of Page 693: "Although study results may be more credible to decision ma"kefsif the model is more complex than needed to solve the problem, added intricacy almost always increases the cost of the study." What a concept this is! It gives rise to many questions . a. For example, how does it jibe with Point 2 of the Summary: "Careful design of a simulation mod~ quired to meet the objectives of a re'servoir study and to control personnel and computer costs." b . Does the statement hold only for the Exxon corporate culture or should it also extend to outside-Exxon decision makers-e.g., those in companies involved with joint ventures or in government agencies? c. Considering that " . .. added intricacy almost always increases the cost. . . ," what increase is considered advisable or permissible? Maybe 25 or 50% ? 5. Finally, I found it a great relief to read in the Introduction that" . .. the use of simulation frequently is optional . . . ." In conclusion, I am sad to have to say that I was disappointed to encounter the article in a journal of the caliber of the JPT, particularly in the Technology Today Series. JPT (SPE 21606) • The Devi/'s Dictionary by Ambrose Bierce gives this defi· nition: " Faith-belief without evidence . " 1447 Authors' Reply to Discussion of Reservoir Simulation Calvin C. Mattax,* SPE, and'Robert L. Dalton, SPE, Exxon Production Research Co. We wish to emphasize that simulation is a reservoir-management tool and only a tool; it should not be used as a substitute for engineering knowledge and skill. The quality of the results of any simulation and the ease with which those results can be obtained depend entirely on the skill and judgment of the engineer using the simulator. ** It is with this philosophy in mind that we offer the following comments in response to Schenk's five specific questions and remarks. 1. Whether simulation has an advantage over simple calculations or extrapolations depends on the engineer' s experience with simulation and with alternative methods. It also depends heavily on the reservoirmanagement issue being considered. Most alternative methods do not allow the reservoir engineer to consider directly the physics of the reservoir-depletion mechanism . We are aware of many situations where, in retrospect, starting with a simple , cheap, easy-to-run simulation model would have saved time and money because critical factors affecting reservoir performance were not well understood. An example of this is the reservoir study of the "Tom O'Connor 5,lOO-Ft Sand in South Texas." (A paper describing this study is planned for submittal to SPE for presentation at a general meeting.) This waterdrive gas reservoir began repressuring in the mid-1980's as a result of reduced purchaser takes . A reservoir study was needed to confirm and quantify reserve losses from continued water encroachment to secure Texas Railroad Commission approval for blowdown by special allowable . Initial attempts with simple, tank-type, material-balance calculations were unsuccessful in reproducing the repressuring observed in the 5,100-ft sand. It was concluded that conventional, material-balance methods could not properly account for the compression of the gas that was trapped with rep ressuring and, hence, could not be used to evaluate the influence of repressuring on 'Now retired . , 'Many excellent simulators are available for modeling conventional oil/gas/water displacements. For a large frac· tion of reservoir studies. the simulators can safely be assumed to solve the match correctly. The SPE Mono· graph Reservoir Simulation discusses exceptions to this general statement. 1448 water influx. The engineer found, however, that she could use a very simple, 1D model to simulate performance and to match the 5, 100-ft -sand pressure history. The model was used to estimate an optimal depletion rate and to demonstrate that reserves would be lost at lower rates. As a consequence, a special allowable was granted and the blowdown project was implemented immediately. Blowdown was completed late last year with a recovery very near that predicted by simulation. 2 and 3. There may be some misunderstanding about the use of history matching to improve reservoir description. In history matching, the engineer first attempts to model history by use of his best current description of the reservoir. If historical performance cannot be matched with current description, then either the description is wrong or the physics of the reservoir depletion mechanism is being modeled incorrectly. In either case, a better understanding of the reservoir is necessary if future performance is to be predicted reliably . Using a simulator is a practical way to consider the influence of acceptable changes in reservoir description on past performance. The Dunlin reservoir discussed in the Technology Today Series paper is an excellent example of the benefits of history matching. The prime question answered in that study was which faults were sealing and which were not. We know of no way to answer that question without developing a reservoir flow model and matching history with the model. Perhaps we were too superficial in our comments on the benefits of the Dunlin study . Certainly, with the reservoir description we now have, it is obvious that "faults dominate areal sweep ... ," etc. More specifically , however, what are the quantitative effects of faulting and vertical permeability and how much injected water will flow through the Etive? Only with a simulator can a reservoir engineer hope to study enough probable reservoir descriptions to develop rational answers to these questions . We point out here that in most reservoir simulations , results are qualitatively similar to prior expectations. There are seldom major "surprises," especially if geologists and engineers have attempted to develop an understanding of the reservoir. What a simulator provides is quantitative results that forecast timing of future events and produced and injected fluid volumes. These types of forecasts can provide invaluable information for planning depletion and developing operating strategies. Our experience and that of others (see the Reservoir Simulation monograph for references) suggest, however, that in many reservoirs with complex geology and where heterogeneity and multi phase fluid flow must be considered, prior expectations based on intuitive judgment are likely to be in error. 4. The degree of complexity needed for a reservoir-simulation model must be based first on what model design will provide an answer to the reservoir-management question being considered. Often, an important design factor concerns what simplifying assumptions will be accepted by the decision maker for whom the study is intended. When planning a simulation study , it is important to determine whether the cost of adding model complexity to lend credibility to study results can be justified. Frequently , in dealing with others who may not have an in-depth reservoir engineering background, it is cost-effective to construct a complex model rather than to do the work necessary to develop convincing evidence that simpler models are adequate. Of course, there is no answer to Schenk's question about how much intricacy is advisable. It depends on the objectives of the study . 5. In Reservoir Simulation, we repeatedly made the point that the reservoir engineer should use the fastest and cheapest engineering methods that will give adequate answers to the reservoir-management questions under consideration. If simulation is not needed, and if it is more costly than an alternative method, then by all means, don't use it. Our contention, however, is that in today's environment, computing power is often cheaper and faster than manpower and that simulation is a superb tool that every reservoir engineer should at least know how to evaluate. SI Metric Conversion Factor ft x 3.048* E-Ol : m 'Conversion factor is exact. (SPE 21620) JPT November 1990 • JPT