The Influence of Capillary Pressure when Determining Relative Permeability from Unsteady-State Corefloods

Abstract

ABSTRACT An automatic history-matching algorithm has been developed to determine relative permeabilities and capillary pressure curves simultaneously from the production history of a displacement test of oil and water through a core. Relative permeability and capillary pressure curves are represented by power functions. Those representations contain some parameters which are found by minimizing an objective function. The objective function is formed by the sum of the square of the differences between experimentally measured and numerically simulated production data. The numerical simulator is an IMPES finite-difference program which models the one dimensional two-phase flow. The minimization is performed by a non-linear regression algorithm: the Quasi-Newton Approximation for the Least-Squares Problem (Broyden-Fletcher-Goldfarb-Shanno formulae). The automatic history Bitching algorithm is applied to analyze the influence of capillary pressure on the determination of relative permeability curves. The algorithm is tested with simulated data and with actual experimental data. Database consisting of simulated experiments with random errors are tested to demonstrate the feasibility of the method. Besides, they provide exact relative permeability curves for comparison purposes. In effect, results obtained by using simulated data show the convergence and uniqueness of the algorithm. But the main observation is that relative permeabilities estimates can be in error when capillary pressure terms are neglected. Several sets of actual experimental data at inlet constant pressure are also tested. Convergent solutions are always found. Three different objective functions are applied. They are formed by oil rates, total fluid rates or a combination of both. The solution is dependent on the chosen objective function. Best adjustments are found by applying a combination of oil and total fluid rates, and including capillary pressure.