Theoretical and Experimental Studies of Rate-Dependent Two-Phase Immiscible Flow

Abstract

Summary Theoretical predictions are obtained with both Eulerian and Lagrangian methods for calculating saturation profiles in two-phase immiscible displacements in the presence of capillary pressure effects. The one-dimensional (1D) simulator WFLOOD is described with Lagrangian and Eulerian options for refined calculations of saturation distributions throughout all stages of a linear core flood. WFLOOD calculations are presented to demonstrate typical waterflood performance in a 1-m [3.3-ft] core with two different capillary-pressure functions at high and low flow rates. Steady-state and dynamic brine/tetradecane displacement experiments are described with Clashach sandstone cores that have radioactive ferrocene in the oil phase to measure saturation by a new nucleonic method. Some of the nonuniform character of these cores has been revealed by measurements. The PORES reservoir simulation model is used for a theoretical analysis of the experiments in which the nonuniform initial saturation distributions must be represented. It is shown that PORES, used in conjunction with measured steady-state relative permeabilities and measured static capillary pressure data, reproduces the time-dependent saturation profiles to within the accuracy of the measurements at high and low flow rates. The Lagrangian treatment in WFLOOD provides a theoretical benchmark that defines the levels of numerical dispersion present in the PORES Eulerian finite-difference calculations. A theoretical analysis is used to derive a constraint on the form of krw(dpc/dSw), as a function of Sw, which is valuable when capillary pressure functions Pc = Pc(Sw) are chosen for numerical modeling of immiscible displacements.