LBM for separation processes

Separation processes find extensive applications in many chemical process industries. Efficient and accurate simulation of separation processes can play a key role in process design, optimization of resource usage, and advanced control strategies which are vital to chemical process industries in an increasingly competitive environment. In this chapter, the lattice Boltzmann method (LBM), extensively used in computational fluid dynamics (CFD) simulations, is presented for efficient and accurate simulation of two widely used separation processes—crystallization and chromatography. The governing equations for these processes resemble advection equation with source terms. The principle of LBM is first discussed for advection equation, and subsequently adaptation of LBM for separation processes is presented. For crystallization process, such adaptation includes handling of nucleation as boundary condition, size-dependent growth rate, as well as aggregation and breakage rate as source terms. Coordinate transformation technique is used for efficient simulation of the size-dependent growth rate, and an accurate implementation of source term is also shown. In contrast, adaptation of LBM for chromatography requires inclusion of rate term accounting for mass transfer between the mobile and stationary phases, and consideration of more than one set of distribution functions when more than one solute species are present in the mobile phase. In order to validate and analyze the performance of LBM, advection equation in one and two dimensions is considered for which analytical solution is available. The results are compared with the well-established finite volume high resolution (FVHR) method in terms of accuracy and computation time. Simulation results are then presented for batch cooling crystallization modeled using population balances and liquid chromatography processes modeled using advection–diffusion type equation with a source term. It is found that LBM provides at least as accurate solution as finite volume schemes considered, while requiring lower computation time.