Improved and More-Rapid History Matching With a Nonlinear Proxy and Global Optimization

Abstract

This article, written by Technology Editor Dennis Denney, contains highlights of paper SPE 101933, "Improved and More- Rapid History Matching With a Nonlinear Proxy and Global Optimization," by A.S. Cullick, SPE, W.D. Johnson, SPE, and G. Shi, Landmark Graphics, prepared for the 2006 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 24–27 September. Generating reservoir-simulation models that match field production data has been a long-time industry challenge. Two workflows are presented for assisting history match. One workflow minimizes the misfit between simulated and historical data with a global optimizer. Another workflow trains a comprehensive nonlinear-proxy model with a small set of numerical simulations from experimental design to reduce the number of numerical simulations. Introduction History matching is, by its nature, an ill-posed optimization problem with many unknown reservoir parameters that could be adjusted to achieve a match against a relatively small amount of measured data at wells. The most common method of history match is to execute many simulations one at a time, changing a few parameters in a trial-and-error fashion. Often, a reservoir-simulation history match might require months of effort and many simulations to achieve a single model that neglects model nonuniqueness and often may not be a good predictor of future field performance. Many automated history-match algorithms have been investigated. Early assisted history matching emphasized deterministic gradient-optimization algorithms that require complete derivatives of the production response with respect to reservoir parameters. Subsequently, the emphasis evolved to faster methods to compute the sensitivity coefficients, such as streamline simulation, with emphasis on preserving uncertainty through the integration of geostatistics. Recent developments with adjoint models have renewed interest in sensitivity-based algorithms. However, none of these methods have been taken up widely by practitioners. With black-box optimization, the number of required simulations to achieve a match can be very large, numbered in the hundreds of simulations. If a single simulation model takes many hours to execute, there is good incentive to reduce the number of simulations for the optimization, even with the use of a distributed-computing system. This study used a global optimizer, while seeking to reduce the number of simulations with a fast proxy model. The use of proxy-regression models has been suggested to reduce the number of required simulations, but analytical-response models may not be sufficiently robust to represent the nonlinear reservoir production and pressure vs. time profile data. The use of neural networks as nonlinear-proxy models also has been suggested. In this paper, a history-match workflow is presented that has a robust, nonlinear neural-network proxy model to improve a history match and reduce the number of finite-difference simulations required.