Constrained Nonlinear Optimization for Extreme Scenarii Evaluation in Reservoir Characterization

Abstract

The goal of reservoir characterization is the estimation of unknown reservoir parameters by integrating available data in order to take decisions for production scheme and to anticipate risks development in the future. In this inverse problem, the associated forward model consist of a fluid flow simulator and a petro-elastic model based on rock physic Gassmann equations. A set of admissible models comprises models that fit up the observed data to a prescribed tolerance. Hence, the probable set of reservoir data forecasts is the response of the forward simulator, up to a future time, to the set of admissible models. Among them, extreme scenarios forecasts are of great interest for reservoir engineers because they outline risks associated with reservoir development. By evaluating the posterior distribution of the reservoir parameters, a standard Bayesian approach can assess future data forecasts and their associated uncertainty. However, this approach is not well suited to explore extreme scenarios which usually correspond to the tails of the posterior distribution. In this work we propose a practical approach to evaluate such extreme scenarios without relying on the Bayesian framework. This approach consists in solving a nonlinear optimization problem subject to nonlinear constraints. The cost function to be minimized or maximised is a nonlinear function depending on reservoir data forecasts. The standard problem is to explore scenarios which give a maximum total oil production up to a future time. Nonlinear inequality constraints further impose an acceptable history match on a given period of time. This optimization problem is solved with the IFP solver SQPAL developed to solve general nonlinear programming problems dealing with nonlinear constraints. The potential of the approach is illustrated on a synthetic reservoir problem. The results are then compared to the ones obtained using SQA : an IFP free derivative optimization solver.