C. Pan

Estimating interfacial areas resulting from lattice Boltzmann simulation of two-fluid-phase flow in a porous medium

The relationship among capillary pressure, fluid saturations, and interfacial areas ( psa relationship) has been a subject of significant recent attention in multiphase porous medium dynamics. First, we consider a set of computational approaches for estimating interfacial areas based upon both integer and real number representations of fluid distributions. We quantify the errors associated with such computations for model systems, and we show relatively accurate estimates are possible for the sorts of data that are available for multiphase prous medium systems. Second, we performed a preliminary investigation of the psa relationship using a lattice-Boltzmann (LB) simulation approach, which we have previously shown to agree well with highly resolved laboratory experiments. Preliminary results are presented and compared to other observations of the psa relationship that have appeared in the literature.

An evaluation of lattice Boltzmann equation methods for simulating flow through porous media

We evaluated lattice Boltzmann equation (LBE) methods for modeling flow through porous media. We compared a three-dimensional, 19-velocity, multiple-relaxation-time (MRT) LBE model with a popular single-relaxation-time, Bhatnagar-Gross-Krook (BGK) LBE model. It can be shown that the latter (BGK-LBE) model is a special case of the former (MRT-LBE) model for a certain set of parameter constraints used in the collision operator. We compared the accuracy of the two models for two test cases: (1) Poiseuille flow between parallel plates, and (2) flow past a periodic simple cubic (SC) array of spheres. We also compared two solid-phase, boundary condition approximations: (1) a linearly interpolated bounce-back (LIBB) method, and (2) a standard bounce-back (SBB) method without interpolation. Our results clearly demonstrate advantages of the MRT-LBE model over its BGK counterpart, and the benefits of the LIBB method over the SBB method in terms of numerical accuracy.

Viscous coupling effects for two-phase flow in porous media

Recent studies have revealed that viscous coupling effects in immiscible two-phase flow, caused by momentum transfer between the two fluid phases, are important for a range of cases of porous medium flow. Generalized governing equations for coupled immiscible two-phase flow in porous media have been suggested through a formulation that includes two viscous coupling coefficients, in addition to the two conventional relative permeabilities. However, a quantitative understanding of the coupling effects and their dependence on factors including capillary number, viscosity ratio, and wettability still remains as an open issue. In this work, we use a three-dimensional parallel processing version of a two-fluid-phase lattice Boltzmann (LB) model to investigate this phenomenon. A multiple-relaxation-time (MRT) approximation of the LB equations is used in the simulator, which leads to stable results. We validate our model by verifying the velocity profile for flow through a channel with a square cross-section. We then simulate co-current flow through a sphere-pack porous medium and determine the relative permeabilities. Correlations of the relative permeabilities as a function of the fluid viscosities and wettability are investigated. The results are qualitatively consistent with experimental observations by Avraam and Payatakes [1] and the numerical simulations of Langaas and Papatzacos [12].

Pore-scale modeling of residual nonaqueous phase liquid dissolution

For nonaqueous phase liquids (NAPLs) that are commonly found at contaminted sites, the aqueous/ nonaqueous phase mass transfer is a process of crucial importance for both predicting groundwater contamination and determining the best cleanup methodology. The mass transfer process deserves further study as the constitutive relations derived from the experimental porous medium systems are generally not applicable to other media. In this work, we applied a multi-step pore-scale modeling approach to simulate the dissolution of a residual NAPL in a three-dimensional random sphere-pack medium. The residual NAPL distribution was generated using a morphological approach. With a detailed flow field simulated with a lattice-Boltzmann (LB) approach, we solved the advection-diffusion equation in the pore space using a high-resolution, adaptive-stencil numerical scheme and operator splitting. The mass transfer rate predicted in the approach was compared to experimental observations by Miller et al. [16].