History Matching Using Probabilistic Approach in a Distributed Computing Environment
A novel methodology for delineating multiple reservoir domains for the purpose of history matching in a distributed computing environment has been proposed. A fully probabilistic approach to perturb permeability within the delineated zones is implemented. The combination of robust schemes for identifying reservoir zones and distributed computing significantly increases the accuracy and efficiency of the probabilistic approach. The information pertaining to the permeability variations in the reservoir that is contained in dynamic data is calibrated in terms of a deformation parameter rv. This information is merged with the prior geologic information in order to generate permeability models consistent with the observed dynamic data as well as the prior geology. The relationship between dynamic response data and reservoir attributes may vary in different regions of the reservoir due to spatial variations in reservoir attributes, well configuration, flow constraints etc. The probabilistic approach then has to account for multiple rv values in different regions of the reservoir. In order to delineate reservoir domains that can be characterized with different rn parameters, principal component analysis (PCA) of the Hessian matrix has been done. The Hessian matrix summarizes the sensitivity of the objective function at a given step of the history matching to model parameters. It also measures the interaction between the parameters affecting the objective function. The basic premise of PCA is to isolate the most sensitive and least correlated regions. The eigenvectors obtained during the PCA are suitably scaled and appropriate grid block volume cut-offs are defined such that the resultant domains are neither too large (which increases interactions between domains) nor too small (implying ineffective history matching). The delineation of domains requires calculation of the Hessian, which could be computationally costly and also restricts the current approach to some specific simulators. Therefore a robust technique to evaluate a covariance matrix, which is analogous to the 'Hessian matrix', from a set of equi-probable realizations has also been developed. This technique is easy to implement. It yields the domains, which could be intuitively justified. Since the domain delineation process yields zones that are least correlated with each other, each rn parameter can be optimized independently and simultaneously using individual nodes of a cluster of computers. Further, the least correlation criterion helps in retaining the simplicity of 1-D optimization during the history matching. Upon convergence, the perturbed regions are put together and the history match is verified. The proposed approach results in a set of independent tasks of equal magnitude and thus is particularly suited for distributed computing. The methodology has been successfully tested on various synthetic cases.