Application of Global Optimization Methods for History Matching and Probabilistic Forecasting - Case Studies

Abstract

Abstract Subsurface uncertainties have a major influence on investment decisions in major capital projects. By understanding and quantifying subsurface uncertainties better, investment risks can be reduced and decision quality can be improved. Quantifying subsurface uncertainties for a mature field involves history matching or solving the inverse problem, which is not only difficult but also non-unique in nature. A suite of acceptable history matched models, which have multiple combinations of model parameters, is required to obtain a probabilistic view of the reservoir performance. Once a suite of models that all match history has been obtained, they are calibrated for predicting the future performance and assessment of uncertainty and risk associated with a particular development plan. In this paper, we demonstrate a structured approach to history matching, uncertainty assessment, and probabilistic forecasting for mature assets through application of global optimization methods. This work involves application of global optimization methods (Evolutionary Strategy and Genetic Algorithm) for history matching, uncertainty assessment, and infill well optimization. Specifically, the process involves re-evaluation of manually history matched models, investigation of the possibility of achieving multiple history matches, and quantification of the impact these results had on the decision process. Furthermore, the study used a workflow to determine P10-P50-P90 outcomes without using response surface (or proxy) methodology. Results from application of our approach to two mature West African reservoirs are presented here. Both these studies explore various subsurface uncertainties to achieve a probabilistic view of multiple history-matched models and optimization of various development scenarios. The case studies also show how a computer assisted approach coupled with a structured workflow can speed up the forecasting and uncertainty assessment process. Introduction Uncertainties in reservoir modeling are mainly due to two factors: data error and modeling error. Data error refers to measurement errors and is often quantified by applying random noises on the data. Modeling error, however, is difficult to quantify as it is a composite error from multiple types and levels of uncertainties (e.g. uncertainties associated with conceptual sedimentological model, parameterization, discretization scheme, boundary conditions, and numerical artifacts). A reservoir model, whether it is a geological model or a history matched engineering model, is a product of integration of sparse noisy data within a framework of imperfect (or uncertain) mathematical or numerical model which contains uncertain model parameters. Based on such a model, therefore, prediction of future performance and reservoir management decisions can be quite risky. Traditionally, a reservoir modeling workflow has been focused on conditioning reservoir models to dynamic data (e.g. production data) as well as static data (e.g. core or well log data), with the belief that reservoir models derived from static data are considered to be further revised by integrating dynamic data to account for flow characteristics of reservoirs. Integration of dynamic data requires a solution of an inverse problem. Gradient based methods have been commonly used to solve the inverse problem and they require either solution of adjoint equations or computation of sensitivity of reservoir performance with respect to reservoir parameters to obtain the gradient search direction (Carter et al., 1974; Chen et al., 1974; Anterion et al., 1989; Wu et al., 1999; Vasco et al., 1999; Landa et al., 2000). Computation of gradients, however, often becomes more expensive than solving flow and transport problems. Some have used fast streamline-based simulation techniques for the data integration (Emanuel and Milliken, 1998; Vasco et al., 1999; Wang and Kovscek, 2000). The idea is to make use of a streamline simulator as an efficient forward model for the inverse problem and its ability to reveal flow paths for identifying reservoir parts attributed to match production history.