(625d) A Plea for Using Lattice Boltzmann Techniques in Simulating Chemical Reactors

Authors: 
Kamali, M. R., Delft University of Technology


Rather than with the common Finite Volume techniques, the complex interplay of flow and transport phenomena and chemical reactions in single-phase and multi-phase chemical reactors may also be described by means of Lattice Boltzmann (LB) techniques.
In the LB approach, each component or phase is represented by a set of fictitious particles rather than by the usual continuum variables. These fictitious particles, which are allowed to move on a regular lattice with their own discrete velocity distribution functions, carry the macroscopic properties such as density. These particles move and collide with each other as hard spheres resulting in a redistribution in the velocity space such that total mass, momentum and energy in the system are conserved .  In the so-called BGK approximation (on the lattice type D3Q18), this redistribution is conceived as a relaxation to an equilibrium Maxwell distribution with a single relaxation. This relaxation time is an important parameter whose role of responding to spatial or temporal variations is equivalent to that of viscosity in the flow of fluids or of diffusion coefficients in species transport
The method we are developing exploits the pseudo-potential multi-component multi-phase LB model due to Shan and Chen in which the interaction between fictitious particles representing the different components is described in terms of the interaction potential functions ψ of the multiple components and a so-called coupling strength Gij. This coupling strength affects the degree of miscibility and solubility of two components, the sharpness of a phase interface as well as the surface tension (in the case of a gas-liquid system), and the wettability of a solid surface (in the case of a gas/liquid/solid contact: see e.g., (Kamali, Gillissen et al. 2011)).  The Shan-Chen method can be modified to include more realistic equations of state allowing to deal with phase density ratios of practical interest.
In addition, the Shan-Chen method is capable of dealing with multi-component convection-diffusion problems. Realistic mass transport across a phase interface (with the Schmidt number much bigger than unity on the liquid side of the interface) is obtained by allowing the relaxation time to depend on the local density. In order to incorporate a surface reaction (at a catalytic surface), a modified bounce-back rule – the usual LB technique for mimicking the no-slip boundary condition in flow– was applied.
In general, using LB techniques requires a translation from the conventional continuum variables (velocities, concentration, viscosity, diffusivity, ….) into typical LB variables. More specifically, running successful LB simulations depends on selecting proper values for three types of typical LB variables: the potential functions ψ, the coupling strengths Gij, and the relaxation time. This selection process is especially delicate when two-phase flow and multi-component mass transport have to be simulated.
The idea of exploiting LB techniques for CRE applications is illustrated by applying the technique to the case of an isothermal 1-D Fischer-Tropsch reaction involving a multi-component chemical reaction with phase change at a catalytic surface.