Surrogate modeling-based optimization for the integration of static and dynamic data into a reservoir description

Abstract

This paper presents a solution methodology for the inverse problem of estimating the distributions of permeability and porosity in heterogeneous and multiphase petroleum reservoirs by matching the static and dynamic data available. The solution methodology includes, the construction of a “fast surrogate” of an objective function whose evaluation involves the execution of a time-consuming mathematical model (i.e., reservoir numerical simulator) based on neural networks, DACE (design and analysis of computer experiment) modeling, and adaptive sampling. Using adaptive sampling, promising areas are searched considering the information provided by the surrogate model and the expected value of the errors. The proposed methodology provides a global optimization method, hence avoiding the potential problem of convergence to a local minimum in the objective function exhibited by the commonly Gauss–Newton methods. Furthermore, it exhibits an affordable computational cost, is amenable to parallel processing, and is expected to outperform other general-purpose global optimization methods such as, simulated annealing, and genetic algorithms. The methodology is evaluated using two case studies of increasing complexity (from 6 to 23 independent parameters). From the results, it is concluded that the methodology can be used effectively and efficiently for reservoir characterization purposes. In addition, the optimization approach holds promise to be useful in the optimization of objective functions involving the execution of computationally expensive reservoir numerical simulators, such as those found, not only in reservoir characterization, but also in other areas of petroleum engineering (e.g., EOR optimization).