Bayesian history matching using artificial neural network and Markov Chain Monte Carlo

Bayesian inference is a well-established statistical technique used to solve a wide range of inverse problems. For the great majority of practical problems, it is not possible to formulate the posterior distribution analytically and the most practical manner to solve the problem is by using sampling techniques. Metropolis–Hastings algorithm that belongs to the class of Markov Chain Monte Carlo (MCMC) is very suitable to sample the posterior distribution because it is not necessary to know the normalization constant that arise from the Bayes theorem. However, its application in the probabilistic history matching problem can be prohibitive due to the very high computational cost involved because the algorithm requires a high number of samples to reach convergence. The main purpose of this work is to replace the flow simulator by proxy models generated by artificial neural network (ANN) to make feasible the application of the sampling algorithm in the history matching. An iterative procedure combining MCMC sampling and ANN training is proposed. The proposed procedure was successfully applied to a realistic reservoir model with 16 uncertain attributes and promising results were obtained.