A thermodynamic lattice gas (automaton) model is used to simulate disp
ersion in porous media. Simulations are constructed at two distinctly
different scales, the pore scale at which capillary models are constru
cted and large scale or Darcy scale at which probabilistic collision r
ules are introduced. Both models allow for macroscopic (pore scale) ph
ase separation. The pore scale models clearly show the effect of pore
structure on dispersion. The large scale (mega scale) simulations indi
cate that when the pressure difference between the displacing phase an
d displaced phase is properly chosen (representing the average pressur
e gradient between the phases). The simulation results are consistent
with both theoretical predictions and experimental observations.