Optimized History Matching with Direct Sequential Image Transforming for Non-Stationary Reservoirs

History matching techniques are usually applied for conditioning static modeling to reservoir production data. One common problem in applying these techniques is the highly non-linear relationship between the distribution of the fluid dynamic production data and the petrophysical parameters, which frequently have a non-stationary character. This paper proposes a multi-scale optimization approach for geostatistical history matching that aims at tackling the problem inherent to the convergence of static models with complex spatial patterns toward the reservoir production observations. The proposed methodology couples adaptive stochastic optimization and direct sequential simulation with local anisotropy correction as the core of image transforming in a twofold procedure: a global optimization stage and a refining optimization stage. The former consists of optimizing the trend model of anisotropy defined over the space of geological parameters. The latter achieves the local refining optimization based on best individual well production matches. Overall, large-scale trend model parameters are tuned with adaptive stochastic optimization followed by the local refining optimization across multiple realizations using a regional image perturbation algorithm. A deltaic reservoir example illustrates the application of the proposed methodology. The deltaic channel pattern is fairly well reproduced and the optimization procedures allow the match of static models’ dynamic responses to historical production observations.