A Simulation of Core Displacement Experiments for the Determination of the Relative Permeability

الملخص

Computations of the relative permeability curves were made through their representation by two functions for wetting and nonwetting phases. Each function contains one parameter that controls the shape of the relative permeability curves. The values of these parameters are chosen to minimize an objective function, that is represented as a weighted sum of the squared differences between experimentally measured data and the corresponding data calculated by a mathematical model simulating the experiment. These data comprise the pressure drop across core samples and the recovery response of the displacing phase. Two mathematical models are constructed in this study to simulate incompressible, one-dimensional, two-phase flow. The first model describes the imbibition process and the other describes the drainage process. The values of the relative permeability parameters are calculated by employing Rosenbrock optimization procedure. The reliability of this procedure has been confirmed by applying it to four displacement cases. The optimum values of the relative permeability parameters, which reflect the final shape of the relative permeability curves, are achieved at the minimum value of the objective function. All the above processes are be embodied in relative permeability package RPP which is constructed in this study using FORTRAN language.