Accelerated Bayesian inference-based history matching of petroleum reservoirs using polynomial chaos expansions

The forecast for oil production from an oil reservoir is made with the aid of reservoir simulations. The model parameters in reservoir simulations are uncertain whose values are estimated by matching the simulation predictions with production history. Bayesian inference (BI) provides a convenient way of estimating parameters of a mathematical model, starting from a probable distribution of parameter values and knowing the production history. BI techniques for history matching require Markov chain Monte Carlo (MCMC) sampling methods, which involve large number of reservoir simulations. This limits the application of BI for history matching in petroleum reservoir engineering, where each reservoir simulation can be computationally expensive. To overcome this limitation, we use polynomial chaos expansions (PCEs), which represent the uncertainty in production forecasts due to the uncertainty in model parameters, to construct proxy models for model predictions. As an application of the method, we present history matching in simulations based on the black-oil model to estimate model parameters such as porosity, permeability, and exponents of the relative permeability curves. Solutions to these history matching problems show that the PCE-based method enables accurate estimation of model parameters with two orders of magnitude less number of reservoir simulations compared with MCMC method.