A novel multi-objective optimization method for well control parameters based on PSO-LSSVR proxy model and NSGA-II algorithm

Abstract Single-objective well control problems have been studied for many years as one of the most typical optimization problems by researchers worldwide. However, single-objective optimization often could not meet the needs in practical application processes leading to multi-objective optimization problems which have better adaptability in practical applications. In this study, a new method for multi-objective well controls optimization problem using support-vector regression (SVR) proxy model and non-dominated sorting genetic algorithm-II (NSGA-II) was developed. This method was named the multi-objective optimization with proxy model (MOO-PM). In the MOO-PM method, the net present value (NPV) and cumulative oil production (COP) were considered as the objective functions while the bottom hole pressure of production wells and water injection rate of injection wells were chosen as the optimization variables. To the best of our knowledge, this is the first time that SVR proxy model and NSGA-II are applied simultaneously to the optimization of well controls problems. Compared to reservoir simulation model, the SVR proxy model was computationally more efficient. This meant the large calculation time spent on reservoir simulation operation for multi-objective optimization was sharply reduced by using the SVR proxy model. Furthermore, the accuracy of the SVR proxy model was proved by comparing it to the results of simulation of optimized cases and non-optimized cases for a synthetic field as well as a real reservoir. It was concluded that MOO-PM method could obtain better results with higher efficiency.

[1]  D. Maguire.  The raster GIS design model: a profile of ERDAS , 1992 .

[2]  Albert C. Reynolds,et al.  Ensemble-Based Optimization of the Water-Alternating-Gas-Injection Process , 2016 .

[3]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[4]  Johan A. K. Suykens,et al.  Weighted least squares support vector machines: robustness and sparse approximation , 2002, Neurocomputing.

[5]  Xian-Huan Wen,et al.  Uncertainty quantification and value of information assessment using proxies and Markov chain Monte Carlo method for a pilot project , 2017 .

[6]  Louis J. Durlofsky,et al.  Biobjective optimization for general oil field development , 2014 .

[7]  Auref Rostamian,et al.  The development of a novel multi-objective optimization framework for non-vertical well placement based on a modified non-dominated sorting genetic algorithm-II , 2019, Computational Geosciences.

[8]  Jiang Xie,et al.  Improved Proxy For History Matching Using Proxy-for-data Approach And Reduced Order Modeling , 2015 .

[9]  Mohammad Ali Ahmadi,et al.  A robust proxy for production well placement optimization problems , 2017 .

[10]  Mickaele Le Ravalec-Dupin,et al.  Optimizing Well Placement With Quality Maps Derived From Multi-fidelity Meta-models , 2012 .

[11]  P.M.J. Van den Hof,et al.  Improving the ensemble optimization method through covariance matrix adaptation (CMA-EnOpt) , 2013, ANSS 2013.

[12]  Gijs van Essen,et al.  Robust Waterflooding Optimization of Multiple Geological Scenarios , 2009 .

[13]  Gijs van Essen,et al.  Hierarchical Long-Term and Short-Term Production Optimization , 2011 .

[14]  Hanqiao Jiang,et al.  Determining the levels and parameters of thief zone based on automatic history matching and fuzzy method , 2016 .

[15]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[16]  R. J. de Moraes,et al.  An Efficient Robust Optimization Workflow using Multiscale Simulation and Stochastic Gradients , 2019, Journal of Petroleum Science and Engineering.

[17]  P. A. Slotte,et al.  Response Surface Methodology Approach for History Matching and Uncertainty Assessment of Reservoir Simulation Models , 2008 .

[18]  Albert C. Reynolds,et al.  Robust Life-Cycle Production Optimization With a Support-Vector-Regression Proxy , 2018, SPE Journal.

[19]  P.J.P. Egberts,et al.  Optimal waterflood design using the adjoint method , 2007 .

[20]  Burak Yeten,et al.  A Comparison Study on Experimental Design and Response Surface Methodologies , 2005 .

[21]  Sven F. Crone,et al.  The Impact of Preprocessing on Support Vector Regression and Neural Networks in Time Series Prediction , 2006, DMIN.

[22]  Mahmoud Reza Pishvaie,et al.  Multi-criterion based well placement and control in the water-flooding of naturally fractured reservoir , 2017 .

[23]  Akhil Datta-Gupta,et al.  Handling conflicting multiple objectives using Pareto-based evolutionary algorithm during history matching of reservoir performance , 2015 .

[24]  Jiang Xie,et al.  Proxy-Based Work Flow for a Priori Evaluation of Data-Acquisition Programs , 2016 .

[25]  Christodoulos A. Floudas,et al.  Dimensionality reduction for production optimization using polynomial approximations , 2017, Computational Geosciences.

[26]  Ahmed Y. Abukhamsin.  OPTIMIZATION OF WELL DESIGN AND LOCATION IN A REAL FIELD , 2009 .

[27]  D. K. Babu,et al.  Optimal Well Placement in Heterogeneous Reservoirs Via Semi-Analytic Modeling , 2005 .

[28]  Francesca Verga,et al.  Use Of Evolutionary Algorithms In Single And Multi- Objective Optimization Techniques For Assisted History Matching , 2009 .

[29]  Bjarne A. Foss,et al.  Designing shale-well proxy models for field development and production optimization problems , 2015 .

[30]  Gholami Vida,et al.  Smart Proxy Modeling of SACROC CO2-EOR , 2019, Fluids.

[31]  L. Holden,et al.  Automatic History Matching by use of Response Surfaces and Experimental Design , 1994 .

[32]  Albert C. Reynolds,et al.  Robust Constrained Optimization of Short- and Long-Term Net Present Value for Closed-Loop Reservoir Management , 2012 .

[33]  Yasin Hajizadeh,et al.  Towards Multiobjective History Matching: Faster Convergence and Uncertainty Quantification , 2011, ANSS 2011.

[34]  Albert C. Reynolds,et al.  An Adaptive Hierarchical Multiscale Algorithm for Estimation of Optimal Well Controls , 2014 .

[35]  Sen Yang,et al.  Integrated optimization design for horizontal well placement and fracturing in tight oil reservoirs , 2019, Journal of Petroleum Science and Engineering.

[36]  Michael Andrew Christie,et al.  History Matching and Uncertainty Quantification: Multiobjective Particle Swarm Optimisation Approach , 2011 .

[37]  Markus Krosche,et al.  Multiple-Objective Optimization Applied to Well Path Design under Geological Uncertainty , 2011, ANSS 2011.

[38]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[39]  A. Rostamian.  Well Placement Optimization Enhancement by Implementation of Similarity-based Mating Scheme in Non-dominated Sorting Genetic Algorithm-II , 2017 .

[40]  Dongxiao Zhang,et al.  Efficient Ensemble-Based Closed-Loop Production Optimization , 2009 .

[41]  Mahmoud Reza Pishvaie,et al.  Pareto-based robust optimization of water-flooding using multiple realizations , 2015 .

[42]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[43]  Christopher D. White,et al.  Efficient Design of Reservoir Simulation Studies for Development and Optimization , 2007 .

[44]  Alexander J. Smola,et al.  Support Vector Regression Machines , 1996, NIPS.

[45]  L. Durlofsky,et al.  A derivative-free methodology with local and global search for the constrained joint optimization of well locations and controls , 2014, Computational Geosciences.

[46]  Louis J. Durlofsky,et al.  Implementation of Adjoint Solution for Optimal Control of Smart Wells , 2005 .

[47]  Roald Brouwer,et al.  Closed Loop Reservoir Management , 2009 .