A Unifying Numerical Framework for the “Small-Slope” Based Core-Annular Flow Instability Models

Abstract

The snap-off is an instability phenomenon that takes place during the immiscible two-phase flow in porous media due to competing forces acting on the fluid phases and at the interface between them. Different theoretical approaches have been proposed for the development of mathematical models that describe the dynamics of a fluid/fluid interface in order to analyze the snap-off mechanism. The models studied here are based on the “small-slope” approach and were derived from the mass conservation and other governing equations of two-phase flow at pore scale in circular capillaries for pure and complex interfaces. The models consist of evolution equations; highly nonlinear partial differential equations of fourth order in space and first order in time. Although the structure of the models for each type of interface is similar, different numerical techniques have been employed to solve them. Here, we propose a unifying numerical framework to solve the group of such models. Such a framework is based on the Fourier pseudo-spectral differentiation method which uses the Fast Fourier Transform (FFT) and the inverse FFT (IFFT) algorithms. We compared the solutions obtained with this method to the results reported in the literature in order to validate our framework. In general, acceptable agreements were obtained in the dynamics of the snap-off.