This paper is concerned with two related problems:
the construction of geometrical models of porous media relevant to reservoir sandstones and
the description of transport processes in these model systems.
We will show that a variety of interesting porous media can be generated by the packing and subsequent modification of spherical grains. This modification may involve a change in either the grain's size, shape, or both. Steady state transport processes such as the flow of electrical current or viscous fluids are controlled by the distribution of pore throat sizes and, within the present framework, can be studied efficiently by random walk simulations of diffusion. The techniques developed here are also of interest in connection with dynamic transport processes such as the filtration of fine grained particles into consolidated granular networks. The modeling of such processes will be discussed briefly, as will the interaction of steady state and dynamic transport.