Integrating production data under uncertainty by parallel interacting Markov chains on a reduced dimensional space

Abstract

In oil industry and subsurface hydrology, geostatistical models are often used to represent the porosity or the permeability field. In history matching of a geostatistical reservoir model, we attempt to find multiple realizations that are conditional to dynamic data and representative of the model uncertainty space. A relevant way to simulate the conditioned realizations is by generating Monte Carlo Markov chains (MCMC). The huge dimensions (number of parameters) of the model and the computational cost of each iteration are two important pitfalls for the use of MCMC. In practice, we have to stop the chain far before it has browsed the whole support of the posterior probability density function. Furthermore, as the relationship between the production data and the random field is highly nonlinear, the posterior can be strongly multimodal and the chain may stay stuck in one of the modes. In this work, we propose a methodology to enhance the sampling properties of classical single MCMC in history matching. We first show how to reduce the dimension of the problem by using a truncated Karhunen–Loève expansion of the random field of interest and assess the number of components to be kept. Then, we show how we can improve the mixing properties of MCMC, without increasing the global computational cost, by using parallel interacting Markov Chains. Finally, we show the encouraging results obtained when applying the method to a synthetic history matching case.