History Matching of Oil and Gas Production in Heterogeneous Formations

Uncertainty exists naturally in reservoir simulation due to measurement error, interpolation error, modeling error, numerical error and the non-uniqueness of the inverse problems. In the research, our goal is to propose a novel method for rapid quantification of uncertainty in history matching reservoir models using a Markov chain Monte Carlo method via transformed adaptive stochastic collocation method. Bayesian inference provides a convenient framework for history matching and prediction. In this framework, the prior knowledge, the system nonlinearity, and the measurement errors can be directly incorporated into the posterior distribution of the parameters. The Markov chain Monte Carlo method is a powerful tool to generate samples from the posterior distribution. However, the Markov chain Monte Carlo method usually requires a large number of forward simulations. Hence, it can be a computationally intensive task, particularly when dealing with large-scale flow and transport models. To address this issue, we will construct a surrogate system for the model responses in a form of polynomials by the stochastic collocation method. In addition, we employ interpolation based on the nested sparse grids and adaptively take into account the different importance of parameters for high-dimensional problems. Furthermore, we introduce an additional transform process to improve the accuracy of the surrogate model, in case of strong nonlinearities such as discontinuous or unsmooth relation between the input parameters and the output responses. Once the surrogate system is built, we may evaluate the likelihood with little computational cost. We will test the proposed method in 2D water-flooding and 3D black-oil examples to demonstrate its efficiency in estimation of the posterior statistics and providing accurate results for history matching and prediction of the observed data with proper reduction of parameter uncertainty. The proposed method can be extended to sensitivity analysis, decision making and optimization of oil and gas production. It is also expected to be applicable to wide range of physical models, e.g., geothermal, geomechanical, geochemical, etc.