Determinación de Permeabilidades Relativas y Presión Capilar Mediante un Método Inverso

Abstract

An inverse method is applied to obtain relative permeability and capillary pressure curves from transient flow rate data measured during a laboratory displacement test of oil by water through a core. Those unknown curves are described by power functions, each of them containing, at most, two parameters.
Parameters are found by minimizing an objective function which is the weighted sum of the square of the differences between experimentally measured and numerically simulated flow rate data. The minimi zation is performed by two different algorithms; Levenberg-Marquardt (LM) and Quasi Newton Approximation for the Least Squares Problem (AQN).
The main purpose of this paper is to compare the behavior of both techniques.
AQN is always convergent to the optimal solution, though it takes more computing time. When capillary pressure is neglected LM is also convergent. However, when capillary pressure is included, LMgets sometimes stranded being unable to find the optimum. Moreover, when the capillary pressure curve is included by means of two additional parameters, a better matching to experimental data is observed.