Robust Life-Cycle Production Optimization With a Support-Vector-Regression Proxy

Abstract

Summary We design a new and general work flow for efficient estimation of the optimal well controls for the robust production-optimization problem using support-vector regression (SVR), where the cost function is the net present value (NPV). Given a set of simulation results, an SVR model is built as a proxy to approximate a reservoir-simulation model, and then the estimated optimal controls are found by maximizing NPV using the SVR proxy as the forward model. The gradient of the SVR model can be computed analytically so the steepest-ascent algorithm can easily and efficiently be applied to maximize NPV. Then, the well-control optimization is performed using an SVR model as the forward model with a steepest-ascent algorithm. To the best of our knowledge, this is the first SVR application to the optimal well-control problem. We provide insight and information on proper training of the SVR proxy for life-cycle production optimization. In particular, we develop and implement a new iterative-sampling-refinement algorithm that is designed specifically to promote the accuracy of the SVR model for robust production optimization. One key observation that is important for reservoir optimization is that SVR produces a high-fidelity model near an optimal point, but at points far away, we only need SVR to produce reasonable approximations of the predicting output from the reservoir-simulation model. Because running an SVR model is computationally more efficient than running a full-scale reservoir-simulation model, the large computational cost spent on multiple forward-reservoir-simulation runs for robust optimization is significantly reduced by applying the proposed method. We compare the performance of the proposed method using the SVR runs with the popular stochastic simplex approximate gradient (StoSAG) and reservoir-simulations runs for three synthetic examples, including one field-scale example. We also compare the optimization performance of our proposed method with that obtained from a linear-response-surface model and multiple SVR proxies that are built for each of the geological models.

Application of nature-inspired algorithms and artificial neural network in waterflooding well control optimization

“…Hence, these models were built to yield the results of a predefined variable, such as NPV and total oil production at a particular time (normally at the end of simulation). In this context, Guo and Reynolds (2018) applied support vector regression (SVR) to build a static proxy model that predicted the NPV as a function of control sets by considering different geological realizations. Then, the static proxy was maneuvered to perform robust production optimization.…”

Improved CRM Model for Inter-Well Connectivity Estimation and Production Optimization: Case Study for Karst Reservoirs

“…The StoSAG deals with reservoir simulator as a black box and approximates gradient through the inputs and outputs of all the ensemble runs. Various theoretical analyses [35][36][37][38][39] showed that StoSAG can yield a significantly higher NPV than that obtained with the standard EnOpt. However, there are few proposals using the newly developed StoSAG for estimation of inter-well connectivity.…”

Multi-solution well placement optimization using ensemble learning of surrogate models

“…Surrogate models (SMs, also known as proxy models) are employed as an approximation method in the optimization process to reduce the cost of objective function evaluations when the underlying fullphysics model is expensive to simulate. Three main types of surrogate modeling approaches are commonly employed in the field development and control optimization problems: (1) physics-based approaches such as reduced order modeling (Van Doren et al, 2006;Cardoso and Durlofsky, 2010;Durlofsky, 2010;He and Durlofsky, 2014;Trehan and Durlofsky, 2016) or streamline-based simulation methods (Thiele and Batycky, 2003;Park and Datta-Gupta, 2011;Salehian and Çınar, 2019;Ushmaev et al, 2019), (2) Machine Learning (ML) techniques such as support vector machine (SVM) (Drucker et al, 1997;Guo and Reynolds, 2018;Panja et al, 2018;Zhang et al, 2021), Artificial Neural Network (ANN) (Jain et al, 1996;Güyagüler et al, 2002;Yeten et al, 2003;Golzari et al, 2015;Rahmanifard and Plaksina, 2019;Sabah et al, 2019;Sun and Ertekin, 2020;Enab and Ertekin, 2021;Gouda et al, 2021), Gaussian Process Regression (GPR) (Knowles, 2006;Zhang et al, 2009;Horowitz et al, 2013) methods, and (3) Deep Learning (DL) methods such as Convolutional Neural Network (CNN) (LeCun et al, 1998;Glorot et al, 2011;Hinton et al, 2012;Chu et al, 2020;Kim et al, 2020;Kim et al, 2021). Physics-based approaches can approximate the original reservoir behavior with lower-order equations to reduce the computational cost.…”

“…However, they have been so far tested on synthetic, box-shaped models only (de Brito and Durlofsky, 2020a;de Brito and Durlofsky, 2020b) and can become unrepresentative in real fields with often complex structures. ML techniques are widely applied within the context of well control optimization (Ahmadi and Bahadori, 2015;Golzari et al, 2015;Chugh et al, 2016;Guo and Reynolds, 2018;Chen et al, 2020;Zhao et al, 2020) and are shown to provide a reasonably accurate, data-driven SM while considering the reservoir simulator as a black box. The accuracy of ML techniques reduces significantly when the control variables become categorical or integer (Junior et al, 2021).…”