An improved lattice Boltzmann model for multicomponent reactive transport in porous media at the pore scale

In this paper, we improve the lattice Boltzmann pore-scale model for multicomponent reactive transport in porous media developed in a previous study. Instead of applying a thermal boundary condition to solute transport, we rigorously derive the distribution function boundary condition for the total solute concentration. This is achieved first by correcting an expression of the particle distribution function in terms of the corresponding concentration and its gradient and then by deriving and using the relation that the nonequilibrium portion of the distribution function in opposite directions takes on opposite signs. We implement the new boundary condition in both the two-dimensional nine-speed (D2Q9) and four-speed (D2Q4) lattices. Simulations of reactive transport in various chemical and geometrical systems using different models are carried out, and results are compared to analytic expressions or two-dimensional FLOTRAN simulations. It is found that with this new boundary condition, the solute mass is strictly conserved by heterogeneous reactions, as was not the case using the thermal boundary condition. It is also found that compared with the D2Q9 model, the D2Q4 model has comparable accuracy and better computational efficiency.