Adaptation of the black oil simulator to two-phase and three-phase relative permeability determination using unsteady-state technique. Status report, Project BE1, Task 4

Abstract

The development of an unsteady-state procedure for determining three-phase relative permeability curves requires the characterization of the relative permeability curves by adjustable parameters and the adaption of a nonlinear least-squares procedure to the finite-difference approximation of the Buckley-Leverett three-phase flow equation including capillary pressure. A method was developed to represent three-phase relative permeability data by a functional form based on experimental data. Three-phase relative permeability experimental data reported by previous investigators were represented by relative permeability functions. These functions express the relative permeability of a given phase to all fluid saturations (three saturations in the case of three-phase flow) by a six parameter power law equation. The six parameter equations fit the experimental data within 0.53% error. An automatic method also was developed for representing three-phase relative permeability expeimental data. This procedure eliminates errors due to subjective bias. The developed relative permeability functions were incorporated in a multi-dimensional, three-phase black oil simulator. Also, a finite difference Levenberg-Marquardt routine for solving least-squares problems was adapted to the black oil simulator. These modifications make the estimation of the parameters in the relative premeability functions possible by fitting simulated transient three-phase displacement tests to experimental tests. Preliminary results using two-phase flow displacement showedmore » that the parameters can be estimated within a reasonable amount of computer time. Although preliminary results showed that the program works adequately for two-phase flow, conclusions cannot be stated at the present time since some errors were found in the Fortran code of the optimization function. Appropriate changes have been made, and the new version is being tested.« less