  The lattice Boltzmann (LB) method is used to study the kinetics of domain
growth of a binary fluid in a number of geometries modeling porous media.
Unlike the traditional methods which solve the Cahn-Hilliard equation, the LB
method correctly simulates fluid properties, phase segregation, interface
dynamics and wetting. Our results, based on lattice sizes of up to $4096\times
4096$, do not show evidence to indicate the breakdown of late stage dynamical
scaling, and suggest that confinement of the fluid is the key to the slow
kinetics observed. Randomness of the pore structure appears unnecessary.
