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Reservoir simulation applications

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Reservoir simulation is a widely used tool for making decisions on the development of new fields, the location of infill wells, and the implementation of enhanced recovery projects. It is the focal point of an integrated effort of geosciences, petrophysics, reservoir, production and facilities engineering, computer science, and economics.

Overview

Geoscientists using seismic, well-log, outcrop analog data and mathematical models are able to develop geological models containing millions of cells. These models characterize complex geological features including faults, pinchouts, shales, and channels. Simulation of the reservoir at the fine geologic scale, however, is usually not undertaken except in limited cases. Generally, the fine-scaled geological model is partially integrated or "upscaled" to a coarse-grid model, which is computationally more tractable. The grid of the upscaled model is designed to capture the principal geological features of the geologic model to simulate the fluid flow. The grid may also be designed to capture the effects of complex wells. In the upscaling process, the laboratory relative-permeability and capillary-pressure functions may be upscaled to "pseudofunctions." These pseudofunctions attempt to capture fluid-flow behavior that is lost because of the integration of fine-scale geologic features in the upscaling process. Phase-behavior treatment can range from simple black-oil PVT to compositional and thermal processes.

The reservoir simulation model may either be used directly to forecast the performance of a new reservoir or adjusted so that it reasonably models the historical behavior of an existing reservoir and wells. This adjustment process is called history matching. Programs called "preprocessors" and "post-processors" enable the engineer to prepare data, manipulate the model, and view results. Once a history-matched model is obtained, then forecasts are made under a variety of operating conditions. These results are combined together with economic models to enable the engineer to make decisions concerning the operation of the reservoir.

Development of the geological model

A sound understanding of the structural elements of the reservoir and the depositional environment under which the sediments were deposited is critical to the development of an accurate geologic model. Today, the geologic model is frequently constructed as a numerical representation of the reservoir and adjacent aquifer and is referred to as a static, or geocellular, model. This model provides the vehicle to capture and combine the seismic structural interpretation and well petrophysical data in a numerically consistent way with known depositional characteristics.[1][2] Petrophysical properties such as porosity, permeability, and water saturation can be distributed throughout the interwell 3D volume using various techniques, many of which rely on geostatistics.[3] Efforts are also underway to condition these numerical, static models with production[4] and well test[5] data to further reduce geologic uncertainty. The construction of a geocellular model represents a significant collaborative effort between geoscientists, petrophysicists, and reservoir engineers.

Geocellular models today may consist of over 25 to 50 million cells on large and/or geologically complex reservoirs. The ability to build static geologic models of this magnitude has outstripped the reservoir engineer’s ability to simulate an equal number of cells in a full physics reservoir simulator (and will continue to do so). Classical development geologic efforts have focused on defining and describing the reservoir geology using 2D maps, which depict the most likely interpretation of the depositional environment and the variability of the reservoir parameters between wells. These interpretations have historically been referred to as "deterministic" reservoir descriptions. With the advent of geocellular models and the application of such technologies as geostatistics, it is now possible for geoscientists to generate multiple reservoir descriptions for the reservoir engineer to simulate. In some cases, one of these descriptions may be selected to represent the "deterministic" model. Regardless if one or several static models are handed over for reservoir simulation, it is generally necessary to reduce the cell count to run the problem with existing reservoir simulators. Significant effort is being spent improving techniques to reduce the number of reservoir cells in the areal and vertical dimension while maintaining the essential geologic character that impacts the recovery process under consideration. This approach is referred to as upscaling, and it will be discussed in greater detail in the following section. To date, the largest reservoir simulators consist of reservoir descriptions of 2 million grid cells and are run using massively parallel processing power.

Upscaling geological model to reservoir flow model

Geological models, which contain the complex structural features of large oil and gas reservoirs, commonly have tens of millions of cells. These models, which contain pinchouts, faults, and other significant information including lithology and facies distributions, are upscaled in both the vertical and areal directions to tens or hundreds of thousands of cells for reservoir simulation.[6]

Several upscaling methods have been developed over the last several years including analytical techniques, local flow-based methods, and global flow-based methods. Analytical methods use arithmetic, harmonic, power law, and geometric averaging to calculate effective properties for each reservoir model gridblock. Local flow-based methods calculate effective gridblock properties by performing single-phase flow simulations in each direction across the upscaled block.[7] The diagonal permeability tensor is calculated by sealing the boundaries perpendicular to the applied pressure gradient. The full-permeability tensor can be calculated in a similar manner by leaving the boundaries normal to the imposed pressure gradient open and applying periodic boundary conditions. Global flow-based methods use pressure gradients across the entire field subject to a specific set of wells to calculate the permeability tensor. Local and global flow-based techniques can be used to compute upscaled transmissibilities directly.

Inclusion of faults in reservoir flow model

Faults and pinchouts of geological layers are incorporated in geological models to capture the complex geometry of many reservoirs. This information is then upscaled into the reservoir model, and it results in both neighbor and non-neighbor connections across the faults and non-neighbor connections across the pinchouts. In Cartesian coordinates, the trace of a fault may need to be represented by a "stair-stepped" line, while a somewhat better representation of faults can be made with corner-point grids. Perpendicular bisector (PEBI) grids, which will be discussed subsequently, are best suited to accurately model fault geometry.

Models for calculating the transmissibility across the fault and parallel to the fault have been developed based on fault type, displacement, geochemical deposition, and whether open joints occur along the fault.[8] In general, transmissibilities across a fault can be at least an order of magnitude lower than those parallel to the fault. Inclusion of this information in a reservoir model is frequently a key parameter in reservoir description.

A recent paper describes the analysis that was performed to calculate fluid flow through conductive faults in the Khafji oil field in the Arabian Gulf.[9] Two sandstone reservoirs separated by a thick continuous shale are both connected to the same large aquifer and had the same initial water-oil contact (WOC). The top reservoir has edgewater drive, while the deeper reservoir is bottomwater drive. Early water breakthrough in the upper sand was determined to be a function of supplemental water influx from the aquifer of the lower sand through conductive faults.

Development of pseudofunctions for multiphase flow

Pseudorelative permeability curves are developed for upscaled reservoir models to match multiphase fluid flow at the fine-grid level. Several methods for performing these calculations have been presented in the literature.[10] In the "10th SPE Comparative Solution Project: A Comparison of Upscaling Techniques," the fine-scale geological model was chosen to be sufficiently detailed such that it would be difficult to run the fine grid and use classical pseudoization methods.[11] Several participants, however, used some level of fine-grid simulation to develop pseudorelative permeability curves, with two of the participants adjusting the exponents of the Corey equations to effect a reasonable match. This approach can be done manually or with an automated history-matching algorithm.

Gridding techniques

The majority of reservoir simulation studies conducted today use Cartesian or corner-point structured grids with some application of local grid refinement to evaluate infill well locations or to more accurately calculate water and/or gas coning in a well. In a structured grid, cell locations are specified using a 3D, i, j, k, indexing system. This allows for ready access either numerically or visually, using pre- and post-processing software, to multilayer well information or data and calculated results at any physical location in the reservoir model.

A more flexible approach for modeling reservoirs with complex geometries that still relies on structured gridding was presented by Jenny et al.[12] Here, a hexahedral multiblock grid is used which is unstructured globally, but maintains an i, j, k structure on each subgrid.

PEBI grids[13] are now being used on a limited basis to simulate reservoirs with complex geological features that have been developed with nonconventional wells to maximize recovery.[14] These grids are unstructured and are described internally in a simulator with a 1D index, i, that ranges from one to the number of nonzero pore volume cells in a model. Evaluation of simulator input and results relies heavily on pre- and post-processing software that allows the user to visually look at the model and make changes during the history-matching phase of a study.

Simulation of nonconventional and intelligent wells

Nonconventional wells are routinely used to maximize production rates and ultimate recovery in oil and gas reservoirs. Wells in this category include deviated, horizontal, horizontal and vertical multilaterals, and multilateral fishbone designs. This latter well type is especially effective in low-permeability or heavy oil reservoirs.

Simulation of nonconventional wells can be approached in several ways. First, the productivity of each perforation in a conventional model can be approximated by applying the appropriate skin and Peaceman’s equation.[15] Second, simulation grids can be constructed that closely follow the well path and allow a more accurate calculation of well rates.[16] Another approach, which is quite appealing, is based on a semi-analytical method.[17] It results in a good approximation for productivity indexes (PIs) in nonconventional wells and incorporates the near-wellbore skin because of heterogeneity in this region as well as mechanical skin. This method, which is very efficient, can also include wellbore hydraulic effects.

Nonconventional wells coupled with intelligent completions can be used to improve sweep efficiency and optimize recovery.[18] One example of this technology is the use of surface-controlled, downhole-adjustable chokes, which can be used to apply different pressure drawdowns to separate zones along the well. This allows a more uniform inflow in the well and control of early water or gas breakthrough. Real-time measurements of wellbore pressures and temperatures are being made for use in conjunction with production logging tool (PLT) tests for inflow performance analysis.

Integrated reservoir and surface facilities models

Integration of reservoir and surface facilities simulation can result in improved production forecasts and allows optimization of the surface facilities structure and operating conditions. An integrated reservoir, well flow string, and surface network model of the Prudhoe Bay oil field was built and successfully applied to a facility optimization study.[19] Production costs as a result of this effort were reduced by defining the optimum number of separator stages and their connections, and defining the optimum separator operating conditions and by using excess capacity in the Prudhoe Bay facilities to process production from satellite fields. Procedures for the simultaneous solution of the reservoir and surface pipeline network flow equations are described in Quandalle[20] and Killough.[21]

In the Ekofisk field in the Norwegian sector of the North Sea, integrated reservoir and facilities simulations have been made to optimize throughput in existing surface facilities and to forecast production from planned expansion of current facilities.[22] This optimization project has resulted in sustained high production of approximately 300,000 STB/D over the last several years. Another important aspect in the management of this field is the inclusion of compaction logic in the model based on both stress and water saturation changes during depletion and waterflooding.[23] Treatment of geomechanical effects in stress-sensitive reservoirs has received increased attention throughout the industry in recent years.

Simulation of multiple reservoirs

Simulation of multiple fields producing into a common production facility is routinely practiced to capture the interplay between well deliverability, water and gas injection, operating constraints, and contract rates. In the J-Block area fields, in the UK sector of the North Sea, an integrated reservoir study was conducted that included a gas condensate reservoir with gas cycling that was simultaneously modeled with volatile oil reservoirs.[24] The fields were developed with a single platform and one subsea manifold completion and a combination of vertical and horizontal wells. Four separate PVT regions were used to describe the fluid behavior. The integrated model used in this study results in an efficient reservoir management tool for making development and operating decisions.

Another example of reservoir management of multiple fields with shared facilities is the Gannet cluster, located in the UK sector of the North Sea, which connects four fields.[25] Wells from one of the fields are directly linked to the production platform, and the other three fields are subsea tiebacks to the platform. Three of the four fields are oil fields and the fourth is a gas field. An integrated model was built to simulate the interaction of the subsurface and surface processes. The well-management objective on this project was to maximize hydrocarbon recovery while simultaneously meeting a long-term gas contract.

Use of larger models

The maximum practical model size has increased from tens of thousands to hundreds of thousands of cells at essentially a linear rate vs. time during the last decade. This trend has developed as a result of the dramatic increase in computer hardware speed accompanied with larger memory and cache. Both high-speed UNIX workstations and high-end PCs are used for reservoir simulation, with a close race developing between the two platforms in regard to run times. Additional advances in computing speed for megamodels have been achieved using parallel hardware along with the necessary developments in model software, discussed in a previous section. An example application of this technology was recently presented in a simulation study of complex water encroachment in a large carbonate reservoir in Saudi Arabia.[26]

History matching and production forecasting

Once a reservoir simulation model has been constructed, the validity of the model is examined by using it to simulate the performance of a field under past operating conditions. This is usually done by specifying historical controlling rates, such as oil rate in an oil reservoir vs. time, and then making a comparison of the nonspecified performance such as gas/oil ratio (GOR), water/oil ratio (WOR), and reservoir pressure with measured data. If there are significant differences between the calculated performance and the known performance of the well/reservoir system, then adjustments to the reservoir simulation model are made to reduce this difference. This process is called history matching. These adjustments should be made in a geologically consistent manner.[5] Modification of those parameters that have the highest degree of uncertainty will give the maximum reduction in the error. The history-matching process should be approached in a consistent manner to minimize the effort.[27] In addition to well rates and bottomhole pressures, and reservoir pressures measured at the time the well is drilled, production logs, long-term pressure gauges, and time-lapse seismic data enable the engineer to better constrain the model during the history-matching process. Time-lapse (4D) seismic[28][29] is becoming an integral part of the field performance monitoring and history matching. Streamline models together with reservoir simulators[30][4] can be used to improve the history-matching process, especially in waterflood operations. Tools to assist in the history-matching process consist of the use of parallel computers, sensitivity analysis, and gradient techniques.[31][32]

Once a history match is obtained, then forecasts of future well/reservoir performance under various operating scenarios are made. Models of multiphase flow in the wellbore and production lines are used to constrain the production rate. These models may include subsea completions[33] with very long gathering lines or complex surface facilities with reinjection of produced fluids.[34] Because of the uncertainty in the geological and reservoir simulation models for new fields, often multiple forecasts[34] with different reservoir parameters are made to determine the uncertainty in the forecasts. Multiple history-matched models based on multiple geological models,[35] and experimental design[36] may also be used to characterize the uncertainty in production forecasts.

References

  1. ↑ Guerberoff, D., Zucchi, H., Victoria, M. et al. 2001. Lateral Delineation of Sandstone Bodies Guided by Seismic and Petrophysical Data Using Geocellular Model: Geocellular Model: Canadon Secon Formation, San Jorge Basin, Argentina. Presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, Buenos Aires, Argentina, 25-28 March 2001. SPE-69487-MS. http://dx.doi.org/10.2118/69487-MS
  2. ↑ Agarwal, B., Hermansen, H., Sylte, J.E. et al. 2000. Reservoir Characterization of Ekofisk Field: A Giant, Fractured Chalk Reservoir in the Norwegian North Sea—History Match. SPE Res Eval & Eng 3 (6): 534-543. SPE-68096-PA. http://dx.doi.org/10.2118/68096-PA
  3. ↑ Caers, J., Avseth, P., and Mukerji, T. 2001. Geostatistical integration of rock physics, seismic amplitudes and geological models in North-Sea turbidite systems. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 30 September-3 October 2001. SPE-71321-MS. http://dx.doi.org/10.2118/71321-MS
  4. ↑ 4.0 4.1 Qassab, H.M.A., Rahmeh, B.A., Khalifa, M.A.A. et al. 2001. Conditioning Integrated Geological Models to Dynamic Flow Data of Giant Saudi Arabian Reservoir. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 30 September-3 October 2001. SPE-71319-MS. http://dx.doi.org/10.2118/71319-MS Cite error: Invalid <ref> tag; name "r4" defined multiple times with different content
  5. ↑ 5.0 5.1 Raghavan, R., Dixon, T.N., Robinson, S.W. et al. 2000. Integration of Geology, Geophysics, and Numerical Simulation in the Interpretation of A Well Test in a Fluvial Reservoir. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, 1-4 October 2000. SPE-62983-MS. http://dx.doi.org/10.2118/62983-MS
  6. ↑ Durlofsky, L.J. 2005. Upscaling and gridding of fine-scale geological models for flow simulation. Proc., 2005 Intl. Forum on Reservoir Simulation, Stresa, Italy, 20–25 June.
  7. ↑ Peaceman, D.W. 1997. Effective Transmissibilities of a Gridblock by Upscaling - Comparison of Direct Methods with Renormalization. SPE J. 2 (3): 338-349. SPE-36722-PA. http://dx.doi.org/10.2118/36722-PA
  8. ↑ Flodin, E.A., Aydin, A., Durlofsky, L.J. et al. 2001. Representation of fault zone permeability in reservoir flow models. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 30 September–3 October. SPE-71617-MS. http://dx.doi.org/10.2118/71617-MS
  9. ↑ Nishikiori, N. and Hayashida, Y. 2000. Investigation of Fluid Conductive Faults and Modeling of Complex Water Influx in the Khafji Oil Field, Arabian Gulf. SPE Res Eval & Eng 3 (5): 401-407. SPE-66223-PA. http://dx.doi.org/10.2118/66223-PA
  10. ↑ Barker, J.W. and Thibeau, S. 1997. A Critical Review of the Use of Pseudorelative Permeabilities for Upscaling. SPE Res Eng 12 (2): 138–143. SPE-35491-PA. http://dx.doi.org/10.2118/35491-PA
  11. ↑ Christie, M.A. and Blunt, M.J. 2001. Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques. SPE Res Eval & Eng 4 (4): 308–317. SPE-72469-PA. http://dx.doi.org/10.2118/72469-PA
  12. ↑ Jenny, P., Wolfsteiner, C., Lee, S.H. et al. 2002. Modeling Flow in Geometrically Complex Reservoirs Using Hexahedral Multiblock Grids. SPE J. 7 (2): 149-157. SPE-78673-PA. http://dx.doi.org/10.2118/78673-PA
  13. ↑ Aziz, K. 1993. Reservoir Simulation Grids: Opportunities and Problems. J Pet Technol 45 (7): 658-663. SPE-25233-PA. http://dx.doi.org/10.2118/25233-PA
  14. ↑ Beckner, B.L., Hutfilz, J.M., Ray, M.B. et al. 2001. EMpower: New Reservoir Simulation System. Presented at the SPE Middle East Oil Show, Bahrain, 17–20 March. SPE-68116-MS. http://dx.doi.org/10.2118/68116-MS
  15. ↑ Peaceman, D.W. 1983. Interpretation of Well-Block Pressures in Numerical Reservoir Simulation With Nonsquare Grid Blocks and Anisotropic Permeability. SPE J. 23 (3): 531–543. SPE-10528-PA. http://dx.doi.org/10.2118/10528-PA
  16. ↑ Mlacnik, M.J. and Heinemann, Z.E. 2003. Using Well Windows in Full Field Reservoir Simulation. SPE Res Eval & Eng 6 (4): 275–285. SPE-85709-PA. http://dx.doi.org/10.2118/85709-PA
  17. ↑ Wolfsteiner, C., Durlofsky, L.J., and Aziz, K. 2000. Approximate Model for Productivity of Nonconventional Wells in Heterogeneous Reservoirs. SPE J. 5 (2): 218–226. SPE-56754-PA. http://dx.doi.org/10.2118/62812-PA
  18. ↑ Valvatne, P.H., Durlofsky, L.J., and Aziz, K. 2001. Semi-Analytical Modeling of the Performance of Intelligent Well Completions. Presented at the SPE Reservoir Simulation Symposium, Houston, Texas, 11-14 February 2001. SPE-66368-MS. http://dx.doi.org/10.2118/66368-MS
  19. ↑ Litvak, M.L., Clark, A.J., Fairchild, J.W. et al. 1997. Integration of Prudhoe Bay Surface Pipeline Network and Full Field Reservoir Models. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 5-8 October. SPE 38885. http://dx.doi.org/10.2118/38885-MS
  20. ↑ Fang, W.Y. and Lo, K.K. 1996. A Generalized Well-Management Scheme for Reservoir Simulation. SPE Res Eng 11 (2): 116–120. SPE-29124-PA. http://dx.doi.org/10.2118/29124-PA.
  21. ↑ Litvak, M.L. and Wang, C.H. 2000. Simplified Phase-Equilibrium Calculations in Integrated Reservoir and Surface-Pipeline-Network Models. SPE J. 5 (2): 236-241. SPE-64498-PA. http://dx.doi.org/10.2118/64498-PA
  22. ↑ Hermansen, H., Thomas, L.K., Sylte, J.E. et al. 1997. Twenty Five years of Ekofisk Reservoir Management. Presented at the Annual Technical Conference and Exhibition, San Antonio, Texas, 5–8 October. SPE-38927-MS. http://dx.doi.org/10.2118/38927-MS
  23. ↑ Sylte, J.E., Thomas, L.K., Rhett, D.W. et al. 1999. Water Induced Compaction in the Ekofisk Field. Presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 3–6 October. SPE-56426-MS. http://dx.doi.org/10.2118/56426-MS
  24. ↑ Ashton, K., Sylte, J.E., Thomas, L.K. et al. 1998. Judy/Joanne Field Development. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 27-30 September 1998. SPE-49128-MS. http://dx.doi.org/10.2118/49128-MS
  25. ↑ Pieters, J. and Por, G.J.A. 1995. Total system modelling - a tool for effective reservoir management of multiple fields with shared facilities. Presented at the Offshore Europe, Aberdeen, United Kingdom, 5-8 September 1995. SPE-30442-MS. http://dx.doi.org/10.2118/30442-MS
  26. ↑ Pavlas Jr., E.J. 2001. MPP Simulation of Complex Water Encroachment in a Large Carbonate Reservoir in Saudi Arabia. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 30 September-3 October 2001. SPE-71628-MS. http://dx.doi.org/10.2118/71628-MS
  27. ↑ Williams, M.A., Keating, J.F., and Barghouty, M.F. 1998. The Stratigraphic Method: A Structured Approach to History-Matching Complex Simulation Models. SPE Res Eval & Eng 1 (2): 169-176. SPE-38014-PA. http://dx.doi.org/10.2118/38014-PA
  28. ↑ Ditzhuijzen, R.v., Oldenziel, T., and Kruijsdijk, C.P.J.W.v. 2001. Geological Parameterization of a Reservoir Model for History Matching Incorporating Time-Lapse Seismic Based on a Case Study of the Statfjord Field. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 30 September-3 October 2001. SPE-71318-MS. http://dx.doi.org/10.2118/71318-MS
  29. ↑ Bogan, C., Johnson, D., Litvak, M. et al. 2003. Building Reservoir Models Based on 4D Seismic & Well Data in Gulf of Mexico Oil Fields. Presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, 5-8 October 2003. SPE-84370-MS. http://dx.doi.org/10.2118/84370-MS
  30. ↑ Milliken, W.J., Emanuel, A.S., and Chakravarty, A. 2000. Applications of 3D Streamline Simulation to Assist History Matching. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, 1-4 October 2000. SPE-63155-MS. http://dx.doi.org/10.2118/63155-MS
  31. ↑ Schulze-Riegert, R.W., Axmann, J.K., Haase, O. et al. 2001. Optimization Methods for History Matching of Complex Reservoirs. Presented at the SPE Reservoir Simulation Symposium, Houston, 11-14 February. SPE 66393. http://dx.doi.org/10.2118/66393-MS
  32. ↑ Grussaute, T. and Gouel, P. 1998. Computer Aided History Matching of a Real Field Case. Presented at the European Petroleum Conference, The Hague, Netherlands, 20-22 October 1998. SPE-50642-MS. http://dx.doi.org/10.2118/50642-MS
  33. ↑ Zapata, V.J., Brummett, W.M., Osborne, M.E. et al. 2001. Advances in Tightly Coupled Reservoir/Wellbore/Surface-Network Simulation. SPE Res Eval & Eng 4 (2): 114–120. SPE-71120-PA. http://dx.doi.org/10.2118/71120-PA
  34. ↑ 34.0 34.1 Gorell, S. and Bassett, R. 2001. Trends in Reservoir Simulation: Big Models, Scalable Models? Will you Please Make up Your Mind? Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 30 September-3 October 2001. SPE-71596-MS. http://dx.doi.org/10.2118/71596-MS
  35. ↑ Zabalza-Mezghani, I., Mezghani, M., and Blanc, G. 2001. Constraining Reservoir Facies Models to Dynamic Data - Impact of Spatial Distribution Uncertainty on Production Forecasts. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 30 September-3 October 2001. SPE-71335-MS. http://dx.doi.org/10.2118/71335-MS
  36. ↑ Manceau, E., Mezghani, M., Zabalza-Mezghani, I. et al. 2001. Combination of Experimental Design and Joint Modeling Methods for Quantifying the Risk Associated With Deterministic and Stochastic Uncertainties—An Integrated Test Study. Presented at the SPE Annual Conference and Technical Exhibition, New Orleans, Louisiana, 30 September–3 October. SPE-71620-MS. http://dx.doi.org/10.2118/71620-MS

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See also

Reservoir simulation

Gridding in reservoir simulation

Upscaling of grid properties in reservoir simulation

Phase behavior in reservoir simulation

Streamline simulation

PEH:Reservoir_Simulation

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