Risk Analysis Speed-up With Surrogate Models

Risk analysis is crucial in investment decisions. A' more accurate risk analysis for a field development study can demand a large number of simulation runs, which can lead to high computational time. Some techniques have been developed to reduce the number of runs, such as experimental design with surface response methodology. One problem usually associated with this technique is the possibility of lower reliability associated with complex problems. Furthermore, they might not properly represent the problem when there are changes in the uncertain parameters, in this case a complete restart in the process may be necessary. An alternative is proposed here through the use of fast surrogate simulation models that generate results similar to the base model, even with changes in the reservoir attributes. The surrogate simulation model has the same data as the base simulation model, but with a much coarser grid. The coarse grid parameters are adjusted automatically with a gradient-based optimization algorithm, minimizing the difference between the responses from the base and the surrogate models. Due to the large number of variables to adjust, several techniques were incorporated in the optimization algorithm: simultaneous perturbation stochastic approximation, response surface methodology and data partition. After mis adjustment, a risk analysis can be conducted with the surrogate model. Simulation models were constructed to test the results generated with the proposed surrogate model methodology. Sensitivity analysis for several factors has shown acceptable adherence of the coarse and base models. A risk analysis was conducted with both coarse and base models, the results generated with the coarse models were close to those with the base models. Overall, the time spent in adjusting the coarse model and generating responses for the risk analysis was smaller than directly using the base model in a risk analysis. The main contribution of this work is to develop a methodology to construct fast surrogate models and to show that they can help to reduce the time needed to build a risk analysis, generating results that are similar to the full simulation model. Copyright 2012, Society of Petroleum Engineers.213141321Ecopetrol,Halliburton,Baker HughesAmorim, T., (2012) Utilização de Modelo de Fluxo Substituto Na Análise de Risco de Reservatórios de Petróleo, , (Master's thesis). Faculdade de Engenharia Mecânica, Universidade Estadual de Campinas, Campinas, BrazilBarton, R.R., Simulation Optimization Using Metamodels (2009) Proceedings of the 2009 Winter Simulation Conference, pp. 230-238. , Austin, TX, 13-16 DecemberCardoso, M.A., Durlofsky, L.J., Use of Reduced-Order Modeling Procedures for Production Optimization (2010) SPE Journal, 15, pp. 426-435De Berg, M., Cheong, O., Van Kreveld, M., Overmars, M., (2008) Computational Geometry - Algorithms and Applications, , third edition. Berlin: Springer-VerlagDing, D.Y., Development of a Data Partition Technique for Gradiente-Base Optimization Methods in History Matching (2010) SPE EUROPEC/EAGE Annual Conference and Exhibition. Barcelona, Spain, 14-17 June, , Paper SPE 130473 presented at theGao, G., Reynolds, A., An Improved Implementation of the LBFGS Algorithm for Automatic History Matching (2004) SPE Annual Technical Conference and Exhibition. Houston, 26-29 September, , Paper SPE 90058 presented at theHeijin, T., Markovinovic, R., Jansen, J.D., Generation of Low-Order Reservoir Models Using System-Theoretical Concepts (2003) SPE Reservoir Simulation Symposium. Houston, 3-5 February, , Paper SPE 79674 presented at theKleijnen, J.P., An Overview of the Design and Analysis of Simulation Experiments for Sensitivity Analysis (2005) European Journal of Operational Research, 164 (2), pp. 287-300Spall, J.C., An Overview of the Simultaneous Perturbation Method for Efficient Optimization (1998) Johns Hopkins APL Technical Digest, 19 (4)Zubarev, D.I., Pros and Cons of Applying Proxy-Models as a Substitute for Full Reservoir Simulations (2009) SPE Annual Technical Conference and Exhibition. New Orleans, 4-7 October, , Paper SPE 124815 presented at th