Efficient Design of Reservoir Simulation Studies for Development and Optimization
- Subhash Kalla (Louisiana State U.) | Christopher David White (Louisiana State U.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- December 2007
- Document Type
- Journal Paper
- 629 - 637
- 2007. Society of Petroleum Engineers
- 5.5.5 Evaluation of uncertainties, 5.7.2 Recovery Factors, 2.2.2 Perforating, 5.5 Reservoir Simulation, 2.4.3 Sand/Solids Control, 5.1 Reservoir Characterisation, 3.1 Artificial Lift Systems, 3.3.6 Integrated Modeling, 2 Well Completion, 5.1.5 Geologic Modeling, 4.1.2 Separation and Treating, 7.6.2 Data Integration, 1.6 Drilling Operations
- 0 in the last 30 days
- 1,317 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
Development studies examine geologic, engineering, and economic factors to formulate and optimize production plans. If there are many factors, these studies are prohibitively expensive unless simulation runs are chosen efficiently.
Experimental design and response models improve study efficiency and have been widely applied in reservoir engineering. To approximate nonlinear oil and gas reservoir responses, designs must consider factors at more than two levels—not just high and low values. However, multilevel designs require many simulations, especially if many factors are being considered. Partial factorial and mixed designs are more efficient than full factorials, but multilevel partial factorial designs are difficult to formulate. Alternatively, orthogonal arrays (OAs) and nearly-orthogonal arrays (NOAs) provide the required design properties and can handle many factors. These designs span the factor space with fewer runs, can be manipulated easily, and are appropriate for computer experiments.
The proposed methods were used to model a gas well with water coning. Eleven geologic factors were varied while optimizing three engineering factors. An NOA was specified with three levels for eight factors and four levels for the remaining six factors. The proposed design required 36 simulations compared to 26,873,856 runs for a full factorial design. Kriged response surfaces are compared to polynomial regression surfaces. Polynomial-response models are used to optimize completion length, tubinghead pressure, and tubing diameter for a partially penetrating well in a gas reservoir with uncertain properties.
OAs, Hammersley sequences (HSs), and response models offer a flexible, efficient framework for reservoir simulation studies.
Complexity of Reservoir Studies
Reservoir studies require integration of geologic properties, drilling and production strategies, and economic parameters. Integration is complex because parameters such as permeability, gas price, and fluid saturations are uncertain.
In exploration and production decisions, alternatives such as well placement, artificial lift, and capital investment must be evaluated. Development studies examine these alternatives, as well as geologic, engineering, and economic factors to formulate and optimize production plans (Narayanan et al. 2003). Reservoir studies may require many simulations to evaluate the many factor effects on reservoir performance measures, such as net present value (NPV) and breakthrough time.
Despite the exponential growth of computer memory and speed, computing accurate sensitivities and optimizing production performance is still expensive, to the point that it may not be feasible to consider all alternative models. Thus, simulation runs should be chosen as efficiently as possible. Experimental design addresses this problem statistically, and along with response models, it has been applied in engineering science (White et al. 2001; Peng and Gupta 2004; Peake et al. 2005; Sacks et al. 1989a) to
- Minimize computational costs by choosing a small but statistically representative set of simulation runs for predicting responses (e.g., recovery)
- Decrease expected error compared with nonoptimal simulation designs (i.e., sets of sample points)
- Evaluate sensitivity of responses to varying factors
- Translate uncertainty in input factors to uncertainty in predicted performance (i.e., uncertainty analysis)
- Estimate value of information to focus resources on reducing uncertainty in factors that have the most significant effect on response uncertainty to help optimize engineering factors.
|File Size||1 MB||Number of Pages||9|
Armenta, M. 2003. Mechanisms and Control of Water Inflow to Wells in GasReservoirs with Bottom Water Drive. PhD dissertation, Louisiana State U., BatonRouge, Louisiana.
Armenta, M., White. C.D., and Wojtanowicz. A.K. 2003.Completion LengthOptimization in Gas Wells. Paper presented at the Canadian InternationalPetroleum Conference, Calgary, June 10-12.
Aslett, R., Buck, R.J., and Duvall, S.G. 1998. Circuit Optimization viaSequential Computer Experiments: Design of an Output Buffer. AppliedStatistics 47 (1): 31-48
Box, G.E.P. and Hunter, J.S. 1961. The 2(k-p) Fractional Factorial Designs,Part I, Technometrics 3 (3): 311-351
Box, G.E.P., Hunter, W.G., and Hunter, J.S. 1978. Statistics forExperimenters: An Introduction to Design, Data Analysis, and ModelBuilding. New York City: John Wiley & Sons.
CMG Technologies Launcher, Version 2002.1, Revision 4, Computer ModelingGroup, 1978-2002, Calgary.
Deutsch, C.V. and Journel, A.G. 1998. GSLIB: Geostatistical SoftwareLibrary and User's Guide. New York City: Oxford.
Efron, B. and Tibshirani, R.J. 1993. An Introduction to theBootstrap. New York: Chapman & Hall.
Giunta, A.A. and Watson, L.T. 1998. A Comparison of Approximation ModelingTechniques: Polynomial versus Interpolating Models. Paper AIAA-1998-4758presented at the 7th AIAA/USAF/NASA/ISSMO Symposium on MultidisciplinaryAnalysis and Optimization, St. Louis, Missouri, 2-4 September.
Giunta, A.A., Wojtkiewicz, S.F., and Eldred, M.S. 2003. Overview of ModernDesign of Experiments Methods for Computer Simulations. Paper AIAA-2003-649presented at the Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 6-9January.
Goovaerts, P. 1997. Geostatistics for Natural Resources Evaluation.New York City: Oxford.
Halton, J.H. 1960. On the Efficiency of Certain Quasi-Random Sequences ofPoints in Evaluating Multi-Dimensional Integrals. Numerische Mathematik2 (1): 84-90.
Hedayat, A.S., Sloane, N.J.A., and Stufken, J. 1999. Orthogonal Arrays:Theory and Applications. Springer Series, New York.
Iman, R.L. and Conover, W.J. 1982. A Distribution-Free Approach to InducingRank Correlation among Input Variables. Communications in Statistics11 (3): 311-334.
Informatics and Mathematical Modeling. 2002. Design and Analysis ofComputer Experiments, Version 2.0, Lyngby, Denmark.
Jin, R., Chen, W., and Simpson, W.T. 2001. Comparative Studies ofMetamodeling Techniques under Multiple Modeling Criteria. Structural andMultidisciplinary Optimization 23 (1), 1-13
Kalagnanam, J.R. and Diwekar, U.M. 1997. An Efficient Sampling Technique forOff-Line Quality Control. Technometrics 39 (3): 308-319.McKay,M.D., Conover, W.J., and Beckman, R.J. 1979. A Comparison of Three Methods forSelecting Values of Output Variables in the Analysis of Output from a ComputerCode. Technometrics 21 (2): 239-245
McMullan, J.H. and Bassiouni, Z.A. 2000. Optimization of Gas-Well Completionand Production Practices. Paper SPE 58983 presented at the SPEInternational Petroleum Conference and Exhibition in Mexico, Villahermosa,Mexico, 1-3 February. DOI: 10.2118/58983-MS.
Montgomery, D.C. 2001. Introduction to Linear Regression Analysis.New York City: Wiley.
Myers, R.H. and Montgomery, D.C. 1995. Response Surface Methodology:Process and Product Optimization Using Designed Experiments. New York City:Wiley.
Narayanan, K. 1999. Applications for Response Surfaces in ReservoirEngineering. MS thesis, U. of Texas, Austin, Texas.
Narayanan, K., Cullick, A.S., and Bennett, M. 2003. Better Field Development Decisionsfrom Multiscenario, Interdependent Reservoir, Well, and FacilitySimulations. Paper 79703 presented at the SPE Reservoir SimulationSymposium, Houston, 3-5 February. DOI: 10.2118/79703-MS.
Peake, W.T., Abadah, M., and Skander, L. 2005. Uncertainty Assessment usingExperimental Design: Minagish Oolite Reservoir. Paper SPE 91820 presentedat the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 31 January-2February. DOI: 10.2118/91820-MS.
Peng, C.Y. and Gupta, R. 2004. Experimental Design and AnalysisMethods in Multiple Deterministic Modeling for Quantifying Hydrocarbon In-PlaceProbability Distribution Curve. Paper SPE 87002 presented at the SPE AsiaPacific Conference on Integrated Modeling for Asset Management, Kuala Lumpur,Malaysia, 29-30 March. DOI: 10.2118/87002-MS.
Sacks, J., Welch, W.J., Mitchell, T.J., and Wynn, H.P. 1989a. Design andAnalysis of Computer Experiments. Statistical Science 4 (4):409-435.
Sacks, J., Schiller, S.B., and Welch, W.J. 1989b. Designs for ComputerExperiments. Technometrics 31 (1): 41-47.
Sandor, Z. and Andras, P. 2004. Alternative Sampling Methods for EstimatingMultivariate Normal Probabilities. J. of Econometrics 120 (2):207-234.
Simpson, W.T., Mauery, M.T., Korte, J.J., and Mistree, F. 1998. Comparisonof Response Surface and Kriging Models for Multidisciplinary DesignOptimization. Paper AIAA-98-4755 presented at the Symposium onMultidisciplinary Analysis and Optimization, St. Louis, Missouri, 2-4September.
Sobol, I.M. 1967. On the Distribution of Points in a Cube and theApproximate Evaluation of Integrals. Computational Mathematics andMathematical Physics 7 (4): 86-112.
Valajak, M., Novakovic, D., and Bassiouni, Z.A. 2001. Physical and Economic Feasibility ofWaterflooding of Low-Pressure Gas Reservoirs. Paper SPE 69651 presented atthe SPE Latin American and Caribbean Petroleum Engineering Conference, BuenosAires, 25-28 March. DOI: 10.2118/69651-MS.
White, C.D. and Royer, S.A. 2003. Experimental Design as a Frameworkfor Reservoir Studies. Paper SPE 79676 presented at the SPE ReservoirSimulation Symposium, Houston, 3-5 February. DOI: 10.2118/79676-MS.
White, C.D., Wills, B.J., Narayanan, K., and Dutton, S.P. 2001. Identifying and EstimatingSignificant Geologic Parameters With Experimental Design. SPEJ6 (3): 311-324. SPE: 74140-PA. DOI: 10.2118/74140-PA.
Xu, H. 2002. An Algorithm for Constructing Orthogonal and Nearly-OrthogonalArrays with Mixed Levels and Small Runs. Technometrics 44 (4): 356-368