Stochastic Inversion for Reservoir Properties Using Parallel Learning-Based VFSA and Pilot Point Parameterization

Abstract

Abstract Joint inversion of flow and seismic data for reservoir parameters is a challenging task in that these disparate datasets are sensitive to different physics and model resolutions for the forward problem. The inverse problem is highly non-linear introducing additional complexity. To overcome some of these challenges, we developed a global optimization method based on very fast simulated annealing (VFSA) and a multi-resolution model parameterization scheme. The choice of proposal distribution for sampling the parameter space and the time consuming of reservoir modeling are two critical issues which need to be resolved. Here, we propose a new parallel learning-based VFSA to address these issues. The key idea behind this method is that at any iteration, the previously sampled models are saved and used as guides in subsequent search resulting in an increased effieciency in our search speed. Parallel computing is used to search a much wider model space without increasing the computing time. Our new method works as follows: (1) the Cauchy distribution is used as the proposal distribution in the beginning; (2) parallel computing is used to sample the parameter space in multiple chains each running at a different temperature; (3) at certain iterations, we collect all the sampled models from the previous parallel runs and compute the binned probability distribution of the model parameters; (4) new proposal distribution is formed by combining the computed probabilityr distribution and Cauchy distribution for every parameter; (5) parallel sampling using the new proposal distribution; (6) collection of all the models and computation of posterior distribution. The results from the synthetic examples reveal that our method is able to obtain reasonable descriptions of the reservoir by combining the global optimization and multi-resolution parameterization. Our new parallel learning-based VFSA shows better performance compared with a conventional method in terms of accuracy.