Abstract
Determination of well locations and their operational settings (controls) such as injection/production rates in heterogeneous subsurface reservoirs poses a challenging optimization problem that has a significant impact on the recovery performance and economic value of subsurface energy resources. The well placement optimization is often formulated as an integer-programming problem that is typically carried out assuming known well control settings. Similarly, identification of the optimal well settings is usually formulated and solved as a control problem in which the well locations are fixed. Solving each of the two problems individually without accounting for the coupling between them leads to suboptimal solutions. Here, we propose to solve the coupled well placement and control optimization problems for improved production performance. We present an alternating iterative solution of the decoupled well placement and control subproblems where each subproblem (e.g., well locations) is resolved after updating the decision variables of the other subproblem (e.g., solving for the control settings) from previous step. This approach allows for application of well-established methods in the literature to solve each subproblem individually. We show that significant improvements can be achieved when the well placement problem is solved by allowing for variable and optimized well controls. We introduce a well-distance constraint into the well placement objective function to avoid solutions containing well clusters in a small region. In addition, we present an efficient gradient-based method for solving the well control optimization problem. We illustrate the effectiveness of the proposed algorithms using several numerical experiments, including the three-dimensional PUNQ reservoir and the top layer of the SPE10 benchmark model.
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Aarnes, J.E., Gimse, T., Lie, K.-A.: An introduction to the numerics of flow in porous media using Matlab. In: Geometric Modelling, Numerical Simulation, and Optimization, part II, pp. 265–306 (2007)
Asheim, H.: Maximization of water sweep efficiency by controlling production and injection rates. In: Proceedings of the SPE European Petroleum Conference, London, United Kingdom, SPE 18365 (1988)
Bangert, W., Klie, H., Wheeler, M., Stoffa, P., Sen, M.: On optimization algorithm for the reservoir oil well placement. Comput. Geosci. 10(3), 303–319 (2006)
Becker, B.L., Song, X.: Field development planning using simulated annealing-optimal economic well scheduling and placement. In: SPE Annual Technical Conference and Exhibition, SPE 30650 (1995)
Boyd, S., Vandenberghe, L.: Convex Optimization, 7th edn. Cambridge University Press (2009)
Brouwer, D.R., Jansen, J.D.: Dynamic optimization of water flooding with smart wells using optimal control theory. SPE Journal 9(4), 391–402 (2004)
Centilmen, A., Ertekin, T., Grader, A.S.: Applications of neural networks in multiwell field development. In: SPE Annual Technical Conference and Exhibition, Dallas, Texas, SPE 56433 (1999)
Emerick, A., Silva, E., Messer, B., Almeida, L., Szwarcman, D., Pacheco, M., Vellasco, M.: Well placement optimization using a genetic algorithm with nonlinear constraints. In: SPE Reservoir Simulation Symposium, SPE118808 (2009)
Forouzanfar, F., Li, G., Reynolds, A.C.: A two-stage well placement optimization method based on adjoint gradient. In: SPE Annual Technical Conference and Exhibition, SPE135304 (2010)
Gerencsér, L., Hill, S.D., Vágó, Z.: Optimization over discrete sets via SPSA. In: Proceedings of the 38th Conference on Decision and Control, pp. 1791–1795. Phoenix, AZ (1999)
Gerencsér, L., Hill, S.D., Vágó, Z.: Discrete optimization via SPSA. In: Proceedings of the American Control Conference, pp. 1503–1504 (2001)
Marino, G., Xu, H.K.: A general iterative method for nonexpansive mappings in Hilbert spaces. J. Math. Anal. Appl. 318(1), 43–52 (2006)
Montes, G., Bartolome, P.: The use of genetic algorithm in well placement optimization. In: SPE Latin American and Caribbean Petroleum Engineering Conference, SPE69439 (2001)
Nesterov, Y.: Efficiency of coordinate descent methods on huge-scale optimization problems, 2010, CORE Discussion Papers 2010002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)
Pan, Y., Horne, R.N.: Improved methods for multivariate optimization of field development scheduling and well placement design. In: SPE Annual Technical Conference and Exhibition SPE 49055, pp. 27–30 (1998)
Roberto, J., Rogrigues, P.: Calculating derivatives for automatic history matching. Comput. Geosci. 10, 119–136 (2006)
Sarma, P., Durlofsky, L.J., Aziz, K.: Implementation of adjoint solution for optimal control of smart wells. In: Paper Presented in Reservoir Simulation Symposium, The Woodland, Texas, SPE92864 (2005)
Sarma, P., Chen, W.H.: Efficient well placement optimization with gradient-based algorithm and adjoint models. In: Proceedings of the 2008 SPE Intelligent Energy Conference and Exhibition, SPE112257 (2008)
Spall, J.C.: Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE T. Automat. Contr. 37(3), 332–341 (1992)
Spall, J.C.: Adaptive stochastic approximation by the simultaneous perturbation method. IEEE T. Automat. Contr. 45(10), 1839–853 (2000)
Yeten, B., Durlofsky, L.J., Aziz, K.: Optimization of nonconventional well type, location, and trajectory. SPE Journal 8(3), 200–210 (2003)
Wang, C., Li, G., Reynolds, A.C.: Optimal well placement for production optimization. In: Proceedings of the 2007 SPE Eastern Regional Meeting, SPE-111154 (2007)
Zandvliet, M.J., Handels, M., Van Essen, G.M., Brouwer, D.R., Jansen, J.D.: Adjoint-based well placement optimization under production constraints. SPE J. 13(4) 392–399 (2008)
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Li, L., Jafarpour, B. A variable-control well placement optimization for improved reservoir development. Comput Geosci 16, 871–889 (2012). https://doi.org/10.1007/s10596-012-9292-4
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DOI: https://doi.org/10.1007/s10596-012-9292-4