Uncertainty Quantification in Reservoirs with Faults Using a Sequential Approach

Download or read book Uncertainty Quantification in Reservoirs with Faults Using a Sequential Approach written by Samuel Clay Estes and published by . This book was released on 2019 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reservoir simulation is critically important for optimally managing petroleum reservoirs. Often, many of the parameters of the model are unknown and cannot be measured directly. These parameters must then be inferred from production data at the wells. This is an inverse problem which can be formulated within a Bayesian framework to integrate prior knowledge with observational data. Markov Chain Monte Carlo (MCMC) methods are commonly used to solve Bayesian inverse problems by generating a set of samples which can be used to characterize the posterior distribution. In this work, we present a novel MCMC algorithm which uses a sequential transition kernel designed to exploit the redundancy which is often present in time series data from reservoirs. This method can be used to efficiently generate samples from the Bayesian posterior for time-dependent models. While this method is general and could be useful for many different models, we focus here on reservoir models with faults. A fault is a heterogeneity characterized by a sharp change in the permeability of the reservoir over a region with very small width relative to its length and the overall size of the reservoir domain [1]. It is often convenient to model faults as lower dimensional surfaces which act as barriers to the flow. The transmissibility multiplier is a parameter which characterizes the extent to which fluid can flow across a fault. We consider a Bayesian inverse problem in which we wish to infer fault transmissibilities from measurements of pressure at wells using a two-phase flow model. We demonstrate how the sequential MCMC algorithm presented here can be more efficient than a standard Metropolis-Hastings MCMC approach for this inverse problem. We use integrated autocorrelation times along with mean-squared jump distances to determine the performance of each method for the inverse problem