Simultaneous optimization of multiple objective functions for reservoir modeling

Abstract

We have developed a new method, a synthetic validity test, and a field data demonstration for constructing reservoir models that simultaneously match available seismic, borehole, and geologic data in an optimal way. We combine geostatistical simulation with simultaneous nonlinear stochastic optimization of multiple objective functions, and we do not require the selection of weighting schemes or multiple optimization computational runs. Because each geologic and geophysical data set has its own strengths and weaknesses, realistic models are best obtained by simultaneously matching all of the multiple data constraints. We define a set of objective functions for each of the multiple data sets that are used to constrain the reservoir-modeling optimization. In the examples, we specify an [Formula: see text]-norm misfit to match inverted seismic attribute volumes, an [Formula: see text]-norm to match lithofacies and porosity logs, and the Hausdorff metric to match image patterns in geologic map-based information. We use a geostatistical technique to initialize a population (ensemble) of starting models and run a nonlinear evolutionary algorithm to drive the ensembles of model solutions toward the Pareto optimal front, along which represents the best-compromise set of model solutions that simultaneously satisfy all of the multiple objectives. We tested our method on a 3D synthetic object-oriented reservoir model for which variogram-based simulation techniques typically fail to reproduce realistic models. We applied our method on a producing reservoir located offshore Western Australia. Our results indicate that the new method is capable of producing optimal models of reservoir properties and flow-unit connectivity that are consistent with known reservoir information, including dynamic production data such as pressure interference tests, and 4D seismic monitoring data.