Optimization of Subsurface Flow Operations Using a Dynamic Proxy Strategy

• Published in: Mathematical geosciences 2022-11, Vol.54 (8), p.1261-1287
• Main Authors: Ma, Zhiwei, Kim, Yong Do, Volkov, Oleg, Durlofsky, Louis J.
• Format: Article
• Language: English
• Subjects: Artificial neural networks; Chemistry and Earth Sciences; Computer Science; Computer simulation; Earth and Environmental Science; Earth Sciences; Flow simulation; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Hypercubes; Iterative methods; Latin hypercube sampling; Machine learning; Mathematical models; Net present value; Neural networks; Numerical simulations; Oil production; Optimization; Physics; Procedures; Simulation; Statistics for Engineering; Subsurface flow; Three dimensional models; Water injection; Water wells
• ISSN: 1874-8961; 1874-8953
• DOI: 10.1007/s11004-022-10020-2

Machine-learning-based proxy models are often used to replace many of the flow simulations required in optimizations of subsurface flow processes. Because the optimizer continuously shifts the solution toward promising regions of search space, the proxy must provide predictions outside its original training range. This requires retraining, as proxy models typically have limited extrapolation capabilities. In this work, detailed procedures for continuous proxy retraining are presented and evaluated. The basic proxy is an artificial neural network, and it is implemented in an iterative Latin hypercube sampling optimization procedure. At many optimization iterations, a fraction of the required function evaluations are performed using the proxy, and a fraction are via flow simulation. These simulation results are used to update the proxy, resulting in a dynamic strategy. The procedure is applied to two-dimensional and three-dimensional models of oil production via water injection, with wells operating under bottom-hole pressure control. Results demonstrate the advantages of the dynamic proxy strategy relative to a standard (fully simulation-based) approach. For the three-dimensional case, for example, with about the same number of numerical simulations, the proxy-based method gives a net present value (NPV) that exceeds that of the standard approach by 3.25%. In addition, the proxy strategy requires less than a third of the numerical simulations to achieve the same NPV as the standard procedure. The general strategy should be applicable with different optimizers for a range of optimization problems.