Reservoir characterization and inversion uncertainty via a family of particle swarm optimizers

History matching provides to reservoir engineers an improved spatial distribution of physical properties to be used in forecasting the reservoir response for field management. The ill-posed character of the history-matching problem yields nonuniqueness and numerical instabilities that increase with the reservoir complexity. These features might cause local optimization methods to provide unpredictable results not being able to discriminate among the multiple models that fit the observed data (production history). Also, the high dimensionality of the inverse problem impedes estimation of uncertainties using classical Markov-chain Monte Carlo methods. We attenuated the ill-conditioned character of this history-matching inverse problem by reducing the model complexity using a spatial principal component basis and by combining as observables flow production measurements and time-lapse seismic crosswell tomographic images. Additionally the inverse problem was solved in a stochastic framework. For this purpose, we used a family of particle swarm optimization (PSO) optimizers that have been deduced from a physical analogy of the swarm system. For a synthetic sand-and-shale reservoir, we analyzed the performance of the different PSO optimizers, both in terms of exploration and convergence rate for two different reservoir models with different complexity and under the presence of different levels of white Gaussian noise added to the synthetic observed data. We demonstrated that PSO optimizers have a very good convergence rate for this example, and provide in addition, approximate measures of uncertainty around the optimum facies model. The PSO algorithms are robust in presence of noise, which is always the case for real data.