Automatic History Matching in Petroleum Reservoirs Using the TSVD Method

History matching is an important inverse problem extensively used to estimate petrophysical properties of an oil reservoir by matching a numerical simulation to the reservoir's history of oil production. In this work, we present a method for the resolution of a history matching problem that aims to estimate the permeability field of a reservoir using the pressure and the flow rate observed in the wells. The reservoir simulation is based on a two-phase incompressible flow model. The method combines the truncated singular value decomposition (TSVD) and the Gauss-Newton algorithms. The number of parameters to estimate depends on how many gridblocks are used to discretize the reservoir. In general, this number is large and the inverse problem is ill-posed. The TSVD method regularizes the problem and decreases considerably the computational effort necessary to solve it. To compute the TSVD we used the Lanczos method combined with numerical implementations of the derivative and of the adjoint formulation of the problem.