Enhanced Reparameterization and Data-Integration Algorithms for Robust and Efficient History Matching of Geologically Complex Reservoirs
Authors: Gao Guohua , Vink Jeroen C. , Chen Chaohui , Alpak Faruk O. , Du Kuifu 
Published: September 2015

Abstract
It is extremely challenging to design effective assisted history matching (AHM) methods for complex geological models with discrete facies types. History matching then requires minimizing a data mismatch objective, while gradually changing facies types in a way that preserves geological realism.
The recently introduced pluri-principal-component-analysis (pluri-PCA) technique effectively overcomes this challenge and furthermore reduces the number of AHM model parameters from millions to hundreds. This drastic reduction of the number of parameters for AHM makes it possible to apply efficient data-integration methods that employ perturbation-based derivatives or derivative-free techniques.
In this paper, a novel AHM approach is developed that combines pluri-PCA with a highly efficient data mismatch minimization technique. A parallelized direct-pattern-search (DPS) approach with auto-adaptive pattern size updating is developed to guarantee the convergence of the data mismatch minimization, when the objective function becomes non-smooth due to numerical noise. A trust region variant of the Gauss-Newton (GN) or quasi-Newton (QN) method is effectively hybridized with the DPS method to further enhance the performance by taking into account the smoothness features of the de-noised objective function or data when applicable.
The new approach is applied to a synthetic case where the truth is known and a real channelized turbidite reservoir model with three facies types. The model parameters subject to AHM include the PCA-coefficients, which automatically reconstruct the facies indicators and permeability, porosity, and net-to-gross maps. Additional matching parameters include the aquifer strength, fault transmissibility, etc. For the synthetic case, the observed data are obtained by adding Gaussian random noise with zero mean and known variance to the data generated with a truth case simulation. Numerical tests indicate that the hybrid GN-DPS algorithm performs the best among all tested algorithms. The history-matched reservoir models obtained with the new AHM approach (GN-DPS) honor the production measurements with good accuracy. The latter is validated in the synthetic test case by the fact that the normalized objective function converges to a value close to the theoretically expected value of one. For both the synthetic and real cases, the history-matched reservoir models preserve geological realism. Compared to quasi-Newton approaches and the traditional Gauss-Newton (GN) approach using gradient approximated by finite difference with small constant perturbation size, the proposed new AHM approach is more efficient both in terms of the total number of iterations and objective function evaluations (through simulation) required to satisfy a preset convergence criterion. Furthermore, as indicated by the data-mismatch convergence profiles generated from the final history-matched models, the GN-DPS method converges to models with much lower data-mismatch values when compared with traditional methods.