Stochastic pore networks (UC in cnzkngly being used to represent porous media and model uanspcrt processes occurring in them. Most frequeatly. square or cubic rqular grids of pores are employed. It has been shown _vncly that regular and random nehvorks give significantly differentaortuositiesbothwrder~ofdiffusion_onlyanddiffusioawithsimulEaneousreaction. In this study the relationship between random and regular topologies is more formally investigated using percolation and finite-size scaling theories. Critical properties of the random model are determined from Monte Carlo simtdations on large netwo&r andtheSe~COlIlparedWiththf3lWUltS for regular lattices. Percolation thresholds are mr in the random models; it is observed that the greatest difference occurs at low pare umnectivities. The critical exponents wae e by fin& size scaling and found to be independent of topology and connectivity. Further, at low connectivities thcclustersizedistriinis markcdlydiffeRWktWeen~alldrandamtopologies. The random model is also used to represent the hi-disperse porous structures which arise in commonly used catalyst sqports. Itisdemonsuatedthat unreasonabIe results am obtained if macropores and micro-pores are assigned from two distributions in an uncorrelaced manner. Using an appmpriate random model, anomalously high tortuosities obtained by other workers are avoided. This demonstrates the importance of using a model which is a realistic representation of the porous stnuXum.