From the summary: We construct a three-dimensional 19 velocity lattice Boltzmann model for immiscible binary fluids with variable viscosities and density ratio. The model is tested for the following binary fluid flow problems: a stationary planar interface among two fluids; channel flow of immiscible binary fluids; Laplace problem; and a rising bubble. The results agree well with semi-analytic results in a range of Eötvös Morton and Reynolds number. We also present preliminary simulation results for two large-scale realistic applications: the flow of air-water mixture in a waste-water batch reactor, and the saturation hysteresis effect in soil flow. We discuss some limitations of lattice Boltzmann method in the simulation of realistic and difficult multiphase problems.