Simulated Annealing for Interpreting Gas/Water Laboratory Corefloods

Abstract

This paper presents a new approach for the simultaneous estimation of relative permeability and capillary pressure curves from two-phase laboratory corefloods. The new technique enables us to retrieve a discrete representation of the flow functions by using a discrete optimization method called simulated annealing. The number of discrete points for each flow curve can be very high and yet will not affect the convergence of the algorithm specially designed for multidimensional optimization problems. Moreover, the algorithm is totally independent from the forward model; therefore, changes in the objective function, boundary conditions, or numerical scheme do not affect the formulation of the optimization problem. Simulated annealing as a global optimization method does not require the evaluation of objective function gradients. Hence, costly gradient computations by finite differences or lengthy derivations of adjoint equations for the optimal control theory are not necessary. The flow functions are estimated after minimizing a least-squares objective function containing all available and reliable experimental data obtained from standard drainage or imbibition experiments. The automatic history-matching code is demonstrated with actual and synthetic experiments, and good matching is obtained for various cases tested. Since the convergence of the algorithm is no longer the major concern, other physical problems such as end effect and the dependence of relative permeability curves on the flow rate are addressed.