Non-equilibrium effect modeling and particle velocity estimation for particulate flow in porous media - Jin, Yi; Zhang, Zenghua; Moghanloo, Rouzbeh Ghanbarnezhad (Frontiers in Earth Science, 2023)
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 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. The velocity equations for particle transport in different flow path geometries are derived with the proposed NE equation, offering a quick estimation of particle velocity in particulate flow. 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 problem in the large-scale problems.