Structural basin

Inversion (geology)

Uncertainty quantification

Mathematics

Biology

Algorithm

Mathematical optimization

Machine learning

Optimization problem

Paleontology

Estimation of covariance matrices

Covariance matrix

CMA-ES

Computer science

Differential evolution

SPE Journal

Summary History matching is a typical inverse problem that adjusts the uncertainty parameters of the reservoir numerical model with limited dynamic response data. In most situations, various parameter combinations can result in the same data fit, termed as nonuniqueness of inversion. It is desirable to find as many global or local optima as possible in a single optimization run, which may help to reveal the distribution of the uncertainty parameters in the posterior space, which is particularly important for robust optimization, risk analysis, and decision making in reservoir management. However, many factors, such as the nonlinearity of inversion problems and the time-consuming numerical simulation, limit the performance of most existing inverse algorithms. In this paper, we propose a novel data-driven niching differential evolution algorithm with adaptive parameter control for nonuniqueness of inversion, called DNDE-APC. On the basis of a differential evolution (DE) framework, the proposed algorithm integrates a clustering approach, niching technique, and local surrogate assistant method, which is designed to balance exploration and convergence in solving the multimodal inverse problems. Empirical studies on three benchmark problems demonstrate that the proposed algorithm is able to locate multiple solutions for complex multimodal problems on a limited computational budget. Integrated with convolutional variational autoencoder (CVAE) for parameterization of the high-dimensional uncertainty parameters, a history matching workflow is developed. The effectiveness of the proposed workflow is validated with heterogeneous waterflooding reservoir case studies. By analyzing the fitting and prediction of production data, history-matched realizations, the distribution of inversion parameters, and uncertainty quantization of forecasts, the results indicate that the new method can effectively tackle the nonuniqueness of inversion, and the prediction result is more robust.

Data-Driven Niching Differential Evolution with Adaptive Parameters Control for History Matching and Uncertainty Quantification