An Iteratively Reweighted Algorithm for History Matching of Oil Reservoirs Is Sparse Domains

Identification of spatially variable hydraulic rock properties such as permeability and porosity is essential for accurate prediction of reservoir performance and planning future development activities. Estimation of these properties from production data usually involves solving a highly underdetermined nonlinear inverse problem. The overwhelming number of unknowns, relative to available data, leads to many parameter combinations that explain the data equally well, but provide different future predictions. To improve non-uniqueness and numerical instability, additional information is typically incorporated into the solution procedure. Reservoir properties often have large-scale spatially correlated features that are amenable to sparse (or compact) representations in compressive bases such as the Fourier or wavelet domains. In this paper, we exploit the inherently sparse representation of correlated reservoir properties to formulate an effective history matching algorithm using sparsity regularization. We show that by minimizing a data misfit cost function augmented with an additive or multiplicative sparsity-promoting regularization term in a sparse domain the reconstruction results are significantly improved. The effectiveness of the proposed implementation is related to adaptive identification of the sparsity pattern through iterative reweighting of the sparse basis components, which we illustrate through several history matching examples in oil reservoirs.