A computational fluid dynamics (CFD) model of a sieve tray is developed using the lattice Boltzmann method (LBM), a mesoscale simulation framework where macroscopic properties are determined from moments of particle velocity distributions functions. First a 2D version, and then a 3D, are simulated with commercial software Xflow on an Intel Xeon HPC cluster. To validate the simulation, the clear liquid height calculated is compared with the obtained from the Bennett correlation. The 2D model shows an average error of less than 7 %, similar to the correlation error. In the 3D version, the error is around 30 %, a larger value that is attributed to the short time length of the simulation, not reaching steady state. In both cases, characteristic flow patterns of distillation trays are observed and the visualized results show a realistic appearance of the froth regime.