Institute of Statistics and Decision Sciences
Duke University
presents:
Michael Goldstein
University of Durham, England
"Pressure Matching for Hydrocarbon Reservoirs: A Case Study in the Use of Bayes Linear Strategies for Large Computer Experiments"
Abstract: In the oil industry, efficient management and prediction of hydrocarbon production depends crucially on having a good multi-phase fluid flow model of the reservoir. The model is too complex to be solved analytically, and an approximate numerical solution is obtained using a `reservoir simulator'. The aim of history matching is to find settings of the input geology which result in a simulator run with outputs which match as closely as possible to the corresponding reservoir history. Running the simulator with a given input geology may be very time-consuming, so that a large number of runs is therefore impractical, rendering infeasible standard methods of numerical analysis. In practice, this inverse problem, choosing input geology and perhaps making structural changes to the model to match historical time series, is tackled by reservoir engineers on a trial and error basis.
History matching may be viewed as a `design for control' problem in a computer experiment. The natural way to approach the problem is to use the detailed prior knowledge of geologists and reservoir engineers to direct our search. A full Bayesian approach is extremely difficult, as it requires elicitation, analysis and design for very high dimensional distributions. Therefore, we have developed a Bayes linear approach for history matching, which formally incorporates the expert beliefs of the reservoir engineer, but which only requires a limited specification of aspects of second order beliefs. In the case study, we will present an account of our experiences in applying the strategy to match the pressure history of a substantial active reservoir.
While we focus on history matching, the methodology that we develop is appropriate for many general applications involving sequential design of computer experiments to solve high dimensional inverse problems.
Wednesday, October 4, 1995
11:45 - 12:45
116 Old Chemistry Building Any questions concerning the seminar may be addressed to Cheryl McGhee @ (919) 684-8029, e-mail cheryl@isds.duke.edu, or finger seminar@isds.duke.edu.