Lattice Boltzmann simulation of gas–solid adsorption processes at pore scale level

Abstract

A two-dimensional lattice Boltzmann (LB) approach was established to implement kinetic concentration boundary conditions in interfacial mass-transfer processes and to simulate the adsorption process in porous media at pore scale and mesoscopic levels. A general treatment was applied to conduct three types of concentration boundary conditions effectively and accurately. Applicability for adsorption was verified by two benchmark examples, which were representative of the interparticle mass transport and intraparticle mass transport in the adsorption system, respectively. The gas–solid adsorption process in reconstructed porous media at the pore scale level was numerically investigated. Mass-transfer processes of the adsorption reaction were simulated by executing Langmuir adsorption kinetics on surfaces of adsorbent particles. Meanwhile, the homogeneous solid diffusion model (HSDM) was used for mass transport in interior particles. The transient adsorbed amount was obtained in detail, and the impact of flow condition, porosity, and adsorbent particle size on the entire dynamic adsorption performance was investigated. The time needed to approach steady state decreased with increased fluid velocity. Transient adsorption capability and time consumption to equilibrium were nearly independent of porosity, whereas increasing pore size led to a moderating adsorption rate and more time was consumed to approach the saturation adsorption. Benefiting from the advantages of the LB method, both bulk and intraparticle mass transfer performances during adsorption can be obtained using the present pore scale approach. Thus, interparticle mass transfer and intraparticle mass transfer are the two primary segments, and intraparticle diffusion has the dominant role.

Introduction

The lattice Boltzmann method (LBM) is an efficient and emerging numerical method that benefits from its mesoscopic properties [1]. It also has advantages such as the simplicity of programming, inherent parallelism, and ease in dealing with a complex boundary. The LBM has been successfully applied in problems on fluid flow, heat, and mass transfer. These problems include: diffusion process [2], porous media flow [3], turbulence [4], microchannel flow [5], natural convection [6], multiphase and multicomponent flows [7], and chemical reaction [8].

The LBM approach has been further applied on mass transfer in porous media. Introducing a source/sink term to the LB governing equation of mass transport was a prevalent way to incorporate the effect of reactions [9], [10]. Meanwhile, the mass transfer process could be simulated through a multi-scale approach. In this research, the LBM acted as the bridge connecting the macro-scale process with the micro-scale process [11]. Furthermore, the briefness of boundary condition treatments made it even charming for complex morphology in porous media [12], and the porous geometry could thus be fully considered for convenient implementation [13].

Interfacial mass transport exists pervasively in the natural environment and manufacturing fields and is generally regarded as a heterogeneous reaction. The phase interface is the dominating reaction zone at which the constituents in different phases are involved to produce an interfacial mass transfer process. As a consequence, the interface exerts a great influence on the mass transfer performance, and special attention should be paid to the effects of interfacial reaction. Hitherto, great efforts have already been made to conduct kinetic mass transfer treatments for the LBM applications. Wells et al. [14] were the first to adopt the lattice gas automatic (LGA) model to study chemical dissolution and precipitation at mineral surfaces. They did this by allowing wall nodes to serve as sources or sinks for the mass of a dissolved component. However, the intrinsic noise and the difficulty in incorporating the fluid convection with the LGA diffusion–reaction model could not be avoided. Another study was performed by He et al. [15] where they simulated a two-dimensional (2-D) diffusion–convection system that has a first-order boundary reaction through an LBM formula. In the kinetic boundary treatment, it was assumed that the non-equilibrium portion of the distribution function was proportional to the dot product of its microscopic velocity and concentration gradient. Kang et al. [16] rigorously derived the boundary condition of the distribution functions. They did this to successfully overcome the possible mass non-conservation in heterogeneous reactions of He et al. [15]. Chen et al. [17], on the other hand, further extended the work of Kang et al. [16] by treating with the moving boundaries and taking into account the convective effect on boundary nodes. Additionally, they simulated a multiphase reactive transport system that contained static liquid–solid and moving liquid–vapor boundaries. The above-mentioned studies focus on establishing a proper distribution of concentration functions that were affected by interfacial mass transfer processes. Their research promotes the development of the lattice Boltzmann theory in a heterogeneous reaction field from the original and simple LGA scheme to the complex multi-scale LB formula.

Some authors have considered the reaction effect in LBM from the point of reactive mass concentration because the macroscopic concentration is an essential objective. Zhang and Ren [18] addressed the reaction on a straight solid wall surface and simulated 1-D leaching agrochemicals in soil by applying the LB model. The model assigned five directions (stagnant, vertical, and horizontal) to moving chemical particles. Particle concentration was obtained from reactive kinetics. However, the convective velocity should be considerably smaller than the particle velocity in the vertical direction. Sullivan et al. [19] treated the reaction node as a mixed-bed reactor with a production rate term to simulate reactions in porous media. The change in concentration adopted the form of the integration of the production rate to update the mass. Zhang et al. [20] proposed a general halfway bounce-back combined with a finite difference scheme to implement kinetic concentration boundary conditions. Chen et al. [21] observed that in representing the actual smooth boundary geometry, the halfway bounce-back scheme suffered a low resolution. To further improve the spatial resolution, they introduced the velocity and concentration values at the midpoint of a boundary lattice link, which were obtained through an interpolation or an extrapolation along the boundary lattice direction. Machado [22] also simulated the surface reaction in regular porous media by using LBM. They focused on the fuel conversion by the local variation of the flow velocities, reaction zone thickness, and fuel concentration.

The adsorption process is a type of surface-based mass transfer reaction. It has been successfully applied in several industrial systems such as purification, decoloration, deodorization, separation, extraction, and drying [23]. An adsorption interaction usually means the adhesion of atoms, ions, or molecules (adsorbate) from fluid to solid surfaces (adsorbent) [24]. They are generally classified as physisorption and chemisorption depending on the interaction between the adsorbate and the adsorbent. Verma et al. [25], [26] explored the problems of gas–solid adsorption in porous media through the LB scheme. To simulate the adsorption process, they used a sink source per unit volume to incorporate the adsorption effect into the governing equations. The mean porosity was introduced to consider the effect of the porous structure. However, this model was essentially volume-average governing equations. There was only a small amount of information that could be discussed on kinetic adsorption processes, which happened on the interface and the inside of adsorbent particles.

To the best of our knowledge, only a small amount of attention was given to the adsorption processes with porous geometries at the pore scale in the LB approach. Employing the LB method, the current study conducted a dynamic adsorption reaction in porous media. First, concentration boundary conditions were established for the interfacial mass transport process. Then, the model was validated by two benchmark studies, concerning the two mass transfer segments of the adsorption process: interparticle and intraparticle. Finally, the gas–solid adsorption process in porous media at the pore scale level was numerically investigated. The effects of flow conditions and porous properties on adsorption processes were investigated.