Automatic history matching considering surrogate-based optimization and Karhunen–Loève expansions

Abstract

In oil reservoir engineering one stage of great interest is the production history matching process, in which the numerical model is adjusted to reproduce the observed field production. The objective is to find the model parameters which minimize the difference between calculated and observed fluid production rates. However, the consideration of the rock properties along every cell of the numerical model that represents the reservoir as design variables would lead to an unfeasible large number of variables and consequently, a very difficult problem to be solved. To overcome that, we will assume that the permeability field will be stochastic and represented by a spectral decomposition through the Karhunen–Loeve expansion (KLE). In this work both linear and nonlinear forms for KLE expansions will be investigated. The mathematical formulation of this problems leads to nonsmooth and high-cost objective functions leading to a difficult problem to be tackled. To overcome that, surrogate models are built and incorporated in a sequential optimization strategy. Results are presented and the potential of the developed tool is discussed.