Assisted History Matching Using Three Derivative-Free Optimization Algorithms

Abstract

Abstract Gradient-based optimization algorithms can be very efficient in history matching problems. Since many commercial reservoir simulators do not have an adjoint formulation built in, exploring capability and applicability of derivative-free optimization (DFO) algorithms is crucial. DFO algorithms treat the simulator as a black box and generate new searching points using objective function values only. DFO algorithms usually require more function evaluations, but this obstacle can be overcome by exploiting parallel computing. This paper tests three DFO algorithms, Very Fast Simulated Annealing (VFSA), Simultaneous Perturbation and Multivariate Interpolation (SPMI) and Quadratic Interpolation Model-based (QIM) algorithm. Both SPMI and QIM are model-based methods. The objective function is approximated by a quadratic model interpolating points evaluated in previous iterations, and new search points are obtained by minimizing the quadratic model within a trust region. VFSA is a stochastic search method. These algorithms were tested with two synthetic cases (IC fault model and Brugge model) and one deepwater field case. Principal Component Analysis is applied to the Brugge case to parameterize the reservoir model vector to less than 40 parameters. We obtained good matches with all three derivative-free methods. In terms of number of iterations used for converging and the final converged value of the objective function, SPMI outperforms the others. Since SPMI generates a large number of perturbation and search points simultaneously in one iteration, it requires more computer resources. QIM does not generate as many interpolation points as SPMI, and it converges more slowly in terms of time. VFSA is a sequential method and usually requires hundreds of iterations to converge.