Mathematical Model for Dynamic Adsorption with Immiscible Multiphase Flows in Three-dimensional Porous Media

In this paper, we present the mathematical model describing the dynamic adsorption processes in three-dimensional porous media. The novelty of this model lies in the ability to study the mass transfer processes with immiscible multiphase flows in porous media. The governing equations describing fluid flow and convective-diffusion of the active component are based on the lattice Boltzmann equations. The phenomena on the interface between two fluids and between fluids and solid phase, including interfacial tension and wetting effects, are described using the most modern version of the color-gradient method. The kinetic of the mass transfer between active component and adsorbent particles is described using the Langmuir adsorption equation. The numerical algorithm has been validated on two benchmarks including the immiscibility of the active component and the displaced fluid, as well as the problem of mass conservation of the active component during its adsorption and transport in porous media. The mathematical model has been adapted for porous media presented by X-ray computed tomography images of natural porous media.