History matching provides to the 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 non-uniqueness 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). In this manuscript the ill-conditioned character of this history matching inverse problem is attenuated by reducing the model complexity using the Spatial Principal Component base and by combining as observables flow production measurements and time lapse seismic cross-well tomographic images. Additionally the inverse problem is solved in a stochastic framework. For this purpose we use a family of Particle Swarm Optimizers that have been deduced from a physical analogy of the swarm system. For the synthetic Stanford VI sand-and-shale reservoir we analyze 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. We show that PSO optimizers have a very good convergence rate and provide in addition, approximate measures of uncertainty around the optimum facies model. Uncertainty estimation makes our algorithms more robust in presence of noise which is always the case for real data. This is an important achievement since in cases where the reservoir exhibits small scale features local methods get trapped and clearly fail to find a good solution. Finally we briefly introduce differential evolution and we show some preliminary results of its performance on the Stanford VI reservoir, showing that we are able to achieve similar results.
Time-lapse seismic modeling is an important step in joint inversion of time-lapse seismic and production data of a field. Rock-physics analysis is the basis for modeling the time-lapse seismic data. However, joint inversion of both types of data for estimation of reservoir parameters is highly nonlinear and complex with uncertainties at each step of the process. So it is essential, before proceeding with large-scale history matching, to investigate sensitive rock-physics parameters in modeling the time-lapse seismic response of a field. We used the data set of the Norne field to investigate sensitive parameters in time-lapse seismic modeling. We first investigated sensitive parameters in the Gassmann’s equation. The investigated parameters include mineral properties, water salinity, pore pressure, and gas-oil ratio. Next, we investigated parameter sensitivity for time-lapse seismic modeling of the Norne field. The investigated rock-physics parameters are clay content, cement fraction, average number of contact grains per sand, pore pressure, and fluid mixing. We observed that the average number of contact grains per sand had the most impact on time-lapse seismic modeling of the Norne field. The clay content was the most sensitive parameter in fluid substitution for calculating seismic velocities of the Norne field. Salinity and pore pressure had minimal impact on fluid substitution for this case. This sensitivity analysis helps to select important parameters for time-lapse (4D) seismic history matching, which is an important aspect of joint inversion of production and time-lapse seismic modeling of a field.
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