Interpretation of Pressure Transient Measurements in Realistic Geological Models Using Bayesian Inversion and Surrogate Modeling

Abstract

Abstract Deep transient pressure testing, using a state-of-the-art formation testing platform, allows deeper investigation into a subsurface formation compared to previous wireline-conveyed testing techniques. Given the associated interaction of the pressure with more varied geological features, numerical reservoir models and simulations are generally required to capture the reservoir or formation heterogeneity that may be encountered during a test. However, the long computation time of such numerical simulation poses challenges for some critical interpretation tasks, such as model inversion. We propose a novel method for the parameter estimation in geologically complex reservoirs by conducting Bayesian inversion with surrogate models. To account for the geology complexity, we utilize surrogate models constructed through the polynomial chaos expansion (PCE) method, to substitute for the numerical simulators. It allows simulating the pressure response in a timely manner while at the same time providing global sensitivity analysis for each uncertain parameter in the model. The Markov chain Monte Carlo (MCMC) method is then employed with the surrogate models for conducting the Bayesian inversion with pressure transient measurements. We analyze the properties of PCE surrogate models and demonstrate that, for typical pressure transient interpretation tasks, sufficiently accurate surrogates can be constructed from an ensemble of 200 to 500 numerical model evaluations. These evaluations are performed concurrently in a cloud-based environment thus reducing the time-cost for surrogate model training to less than an hour. We then perform the Bayesian inversion on the pressure measurements and effectively characterize the model parameters with their associated uncertainties via the posterior distributions. The problem of MCMC inversion is solved in a few minutes using the surrogate models. Through our studies, we demonstrate that the adoption of surrogate models considerably reduces the computation time required, allowing the Bayesian inversion to be completed within minutes, which was unachievable with the numerical simulators. Furthermore, this new method offers accurate parameter estimations and provides posterior distributions of uncertain parameters, as well as unveiling correlations among the parameters for the interpretation of measurement. These capabilities were lacking in the current inversion process utilizing numerical simulators. Finally, the new method lends itself well to workflow automation for history matching, thus reducing the workload on petrotechnical experts and addressing today's imperatives of faster and more cost-efficient field development.