ABSTRACT: A new optimization formulation for simulating multiphase flow in porous media is inroduced. A locally mass conservative mixed finite element method is employed for the spatial discretization. An unconditionally stable fully implicit time discretization is used and leads to a coupled system of nonlinear equations that must be solved at each time step. We reformulate this sytem as a least squares problem with simple bounds involving only one of the phase saturations. Both a Gauss-Newton method and a BFGS secant method are considered as potential solvers for the optimization problem. Each evaluation of the least squares objective function and gradient requires solving two single-phase self-adjoint, linear, uniformly elliptic partial differential equations for which very efficient solution techniques have been developed.

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