Applying Machine Learning Algorithms to Oil Reservoir Production Optimization

In well control optimization for an oil reservoir described by a set of geological models, the expectation of net present value (NPV) is optimized. This approach called robust optimization, entails running the reservoir simulator for all the reservoir models at each iteration of the optimization algorithm. Hence, robust optimization can be computationally demanding. One way to reduce the computational burden, is to select a subset of models and perform the optimization on the reduced set. Another popular technique, is using fast proxy models, rather than full-physics simulators. In this work, a kernel clustering technique is used to select a subset of reservoir models that capture the range of uncertainty in the response of the entire set. In this work an adaptive strategy is used to build fast proxy models for the NPV, and then optimizing the proxy model using a pattern search algorithm. The proxy model is generated by training an artificial neural network (ANN) or support vector regression model (SVR) using some training examples. The challenge in building a proxy model is using finding good training examples. In this work, after optimizing the proxy model, new training examples are generated around the current optimal point, and a new proxy model is built and the procedure is repeated. An example is presented that shows the efficiency of kernel k-medoids clustering and building proxy models for production optimization. Introduction Wang et al. (2012) applied retrospective optimization to well placement problem. They applied k-means clustering for selecting the realizations at each subproblem. The focus of this work is on well control optimization. A response vector is introduced to well characterizes the dissimilarity between the response of realizations. Here, kernel k-medoids clustering is applied for choosing a small set of statistically representative realizations. Our objective is to find an optimal well control vector that maximizes the expectation of the lifecycle NPV over the ensemble of reservoir models. The well control vector u, can be shown by u = [ u1, u 2 1, · · · , uc 1 , · · · , u 1 Nw , u 2 Nw , · · · , u Nc Nw ]T , (1) where, each subscript denotes the well index and each superscript denotes the control index; Nw denotes the number of wells and Nc denotes the number of control steps for each well. uj can be either well pressure (BHP) or oil rate or total liquid rate of the jth well at the nth simulation time step. In this work, the well controls are the BHP’s. We only consider simple bound constraints. In robust production optimization, we want to maximize E[J(u,m)], where E[J(u,m)] = 1 Ne Ne ∑