A Parallelized and Hybrid Data-Integration Algorithm for History Matching of Geologically Complex Reservoirs

Abstract

Summary It is extremely challenging to design effective assisted-history-matching (AHM) methods for complex geological models with discrete-facies types. One of the difficulties is the irregular and nonsmooth nature of the data-mismatch function that needs to be minimized, because of either numerical noise on simulation results or nonsmooth reparameterization. In this paper, a parallelized direct-pattern-search (DPS) approach with auto-adaptive pattern-size updating is developed to guarantee the convergence of the data-mismatch minimization, even when the objective function is nonsmooth because of numerical noise. A trust-region variant of the Gauss-Newton (GN) or quasi-Newton (QN) method is effectively combined with the noise-insensitive DPS method to enhance its performance by exploiting any available smoothness features of the objective function. The new approach is first validated by a linear toy problem and a nonlinear toy problem where artificial numerical noise is introduced. Then, it is applied to a synthetic case and a real field case for history matching of channelized-turbidite reservoirs with three facies types. The model parameters subject to AHM include principal component analysis (PCA) coefficients, which automatically reconstruct the facies indicators and permeability, porosity, and net-to-gross maps. Other matching parameters such as aquifer strength and fault transmissibility are also included. Numerical tests indicate that the hybrid algorithms perform better than the traditional QN line-search algorithms and the original Hooke-Jeeves DPS algorithm (Hooke and Jeeves 1961). The hybrid algorithms either can converge to a satisfactory solution with the same accuracy using lower cost or find a better solution with the same cost, especially for cases where adjoint derivatives are unavailable and numerical noise is unavoidable from reservoir simulation. The GN-DPS algorithm performs the best among all tested algorithms. The history-matched reservoir models obtained with the new AHM approach (GN-DPS combined with pluri-PCA) honor the production measurements with good accuracy. For both the synthetic and real cases, the history-matched reservoir models preserve geological realism.