Diffusion-Driven discrepancies in LBM adsorption modeling: A comparative study of active and passive scalar approaches for adsorption processes

Using the Lattice Boltzmann method (LBM) for simulation of fluid dynamics in complex systems such as adsorption with the advection terms of scalar fields (concentration and temperature distribution), different approaches of advection coupling to the fluid motion can be proposed: “Active or Passive Scalers”. In the present study, the usefulness of active or passive scalars in simulation of an adsorption bed using LBM at different operating conditions such as temperature, pressure and feed flow rate were investigated. In the active scalar approach in LBM, the collision operator in the Boltzmann transport equation consists of two terms: the self and cross collision. On the other hand, the collision term for a passive scalar comes from the Chapman relationship. As the cross collision term in active scalar has an inverse relationship with diffusion coefficient, the effect of this term reduces in gas systems such as adsorption with a high diffusion coefficient; thus, the active and passive approaches become similar. It is obvious that in systems with a lower diffusion coefficient (liquid systems), the cross collision term in collision operator in LBM is high; therefore, it is expected that the active approach with more precise results deviates from the passive approach. Results showed that in most cases, the average relative error compared to experimental data was less in active scalar than in passive scalar approach, indicating that the active scalar approach predicts the adsorption behavior with higher accuracy in comparison with the passive approach.