A New Algorithm for Estimating Relative Permeabilities From Displacement Experiments

Abstract

Summary The process of estimating relative permeability curves from two-phase displacement experiments is considered. A parameter estimation approach overcomes significant limitations of the classic calculation procedure. In this approach, functional representations are chosen for the relative permeability curves. Adjustable coefficients (or parameters) in the functional representations are then chosen to minimize a least-squares objective function. Previous applications of this approach have used exponential functional representations with a single adjustable coefficient (the exponent) for each curve. However, significant errors in the relative permeability estimates may be encountered when this function is used. It has been determined, in principle, that cubic spline functional representations may be used to obtain accurate estimates of relative permeability curves. The process of obtaining the least-squares estimates for the parameters is more difficult, however, because a significantly greater number of parameters are to be determined. No algorithm has been reported for this purpose. We present an algorithm for estimating relative permeability curves that uses cubic spline functional representations. A unique and essential feature of the algorithm is that it incorporates inequality constraints that ensure that physically realistic relative permeability curves are maintained throughout the iterative minimization process. The performance of the algorithm is demonstrated with data from hypothetical and laboratory coreflood displacement experiments.