Uncertainty Quantification for History-Matching Problems

Abstract

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 181611, “Uncertainty Quantification for History-Matching Problems With Multiple Best Matches Using a Distributed Gauss-Newton Method,” by Guohua Gao, SPE, Jeroen C. Vink, SPE, Chaohui Chen, SPE, Mohammadali Tarrahi, SPE, and Yaakoub El Khamra, Shell, prepared for the 2016 SPE Annual Technical Conference and Exhibition, Dubai, 26–28 September. The paper has not been peer reviewed. It is critically important for decision making and an extremely challenging task to quantify the uncertainty of model parameters and production forecasts properly after conditioning to production data. This paper presents a novel approach to generate approximate conditional realizations using the distributed Gauss-Newton (DGN) method together with a multiple local Gaussian approximation technique. Results are compared with those obtained from other approaches, such as randomized maximum likelihood (RML), ensemble Kalman filter (EnKF), and Markov-chain Monte Carlo (MCMC). Introduction It is well-known that oil- and gasfield development is a high-risk venture. Uncertainties originating from geological models (e.g., structure, stratigraphy, channels, and geobodies) are coupled with uncertainties of reservoir models (e.g., distribution of permeability and porosity in the reservoir) and uncertainties of economic parameters (e.g., oil and gas prices and costs associated with drilling and other operations). It is critically important to properly quantify the uncertainty of such parameters and their effect on production forecasts and economic evaluations. Recently, multiobjective-optimization techniques have been developed to maximize expectations of some economic indicators (e.g., net present value) and, at the same time, to minimize associated uncertainty or risk. Because of limited access to the subsurface reservoir (e.g., it is impossible to measure the permeability and porosity at the location of each gridblock of a simulation model), reservoir properties have quite large uncertainties. In a greenfield, before starting production, available data are limited to static data or hard data such as core data, well-log data, well-testing data, and sometimes seismic data. Hence, it is necessary to generate multiple realizations of structural and petrophysical models with limited information, on the basis of prior estimates of the relative probability of each realization. Then, uncertainty in reservoir performance or production forecasting can be quantified (e.g., with design of experiment or with other techniques). Generally, production profiles generated by running reservoir-simulation models with these prior realizations or unconditional realizations do not honor production data. Uncertain model parameters, such as permeability and porosity, potentially in each gridblock, have to be tuned so that the modified reservoir models are able to generate production profiles that are compatible with production data (e.g., by use of assisted history matching).