Monte Carlo and molecular dynamics computer simulation has been used to study the microscopic properties of aqueous fluids and methane in smectite clays, at the elevated temperatures and pressures that are encountered in sedimentary basins. Methane particles are solvated by approximately 12-13 water molecules, with six oxygen atoms from the clay surface completing the coordination shell. The tendency for hydrophobic methane-methane contacts reaches a maximum at 1 km (310 K and 150 bar), in close agreement with the behaviour observed in the bulk solutions. The self-diffusion coefficients are in excellent agreement with the experimental values for methane diffusion through near-surface shales.