Modeling of Non-Equilibrium Effects in Particulate Flow Through Porous Media

Abstract

Abstract The complex dynamics of fluid and particles flowing through pore space demands some relaxation time for particles to catch up with fluid velocity which manifest themselves as non-equilibrium (NE) effect. Previous studies have shown that NE effect in particulate transport can have significant consequences when relaxation time is comparable to the characteristic time associated with the fluid flow field. However, the existing models are lacking to account for this complicated relation between particles and fluid. In this paper, we adapt the general form of harmonic oscillation equation to describe NE effects in particulate flow system. The NE parameter is defined as a function of local particle velocity (vp) and fluid velocity (vf)[1-vp/vf]. The NE effect is evaluated by solving coupled mass balance equations with computational fluid dynamic (CFD) techniques within COMSOL Multiphysics®. Simplified straight tube model, periodic converging-diverging tube model and SEM image of a real pore network are applied in the NE analyses. The results indicate that the time variation of the NE effect complies with the theory of stability. Two key parameters of oscillator equation are amplitude (A) and damping ratio (ζ), where the former represents the magnitude of NE and the latter is an indication of flow path geometry. NE parameter in a diverging flow path illustrates that the ζ value is between 0 and 1. Reducing fluid viscosity yields an increased value of A indicating a larger magnitude of NE effect. For converging flow path, the ζ value is between 0 and −1. The NE effect increases exponentially as a function of time implying that particle velocity always remains less than the fluid velocity. The flow simulation of SEM image shows consistent results with diverging and converging flow results as particles travel along pore network. By conducting simulation on the SEM image of a real pore structure, the equivalent radii of the pores that particles move through were obtained. The outcome of this work can shed light upon explaining the complex NE effects in porous media. The generalized equation to model NE can help temporarily decouple particle transport equation from fluid equations facilitating much advanced particulate flow modeling in the large-scale problems.