We report preliminary results from simulations of single-phase and two-phase Bow through three-dimensional tomographic reconstructions of Fontainebleau sandstone. The simulations are performed with the lattice-Boltzmann method, a variant of lattice-gas cellular-automation models of fluid mechanics. Simulations of single-phase flow on a sample of linear size 0.2 cm yield a calculated permeability in the range 1.0-1.5 darcys, depending on direction, which compares qualitatively well with a laboratory measurement of 1.3 darcys on a sample approximately an order of magnitude larger. The sensitivity of permeability calculations to sample size, grid resolution, and choice of model parameters is quantified empirically. We also present a qualitative study of immiscible two-phase how in a sample of linear size 0.05 cm; simulations of both drainage and imbibition are presented.