Reservoir model estimation by simultaneous optimization of multiple objective functions

We present a new approach for estimating reservoir models consistent with multiple data types and constraints, by combining geostatistical simulation with a multi-objective stochastic optimization method. Our approach starts by generating an ensemble of initial reservoir models using geostatistical simulation techniques. We then compute the corresponding model responses (seismic etc.) using the appropriate forward modeling operators, compare the simulated responses with the real data, and iterate to obtain the best match. Since each geological and geophysical data set has its own strengths and weaknesses, realistic models are best obtained by simultaneously matching all of the multiple data constraints. The main advantage of our approach is that we can define multiple objective functions for a variety of data types and constraints, and simultaneously minimize the mismatches. Using our approach, the resulting models converge to a Pareto front, which represents the set of best compromise model solutions for the defined objectives. We test our new approach on a 3D object-oriented reservoir model, where variogram-based simulation techniques typically fail to reproduce realistic models. Our results indicate that improved reservoir property models and flow-unit connectivity can be obtained with this new multi-objective optimization approach.