The pore structure of rocks is highly complex, with wide variations in pore size and shape. In this work, pore-scale heterogeneity was simulated by distributing spheres, tubes, and cracks with variable dimensions on a square lattice. The transport properties of 100 such network realizations, covering 11 orders of magnitude in permeability, were calculated. Seeking the appropriate averaging procedure to calculate the permeability and electrical conductivity from the local pore parameters, we computed the energy locally dissipated in each bond during fluid or electric flow and the energy globally dissipated in the whole network. By equating the latter to the sum of the former, we obtained averaging expressions exactly predicting the transport properties of the network realizations. Since these relations hold on a wide variety of heterogeneous networks covering a broad range of permeabilities and electrical conductivities, we propose that they should also be valid on rocks. We can thus gain insights into how pore-scale heterogeneity affects the transport properties of rocks. ¿ American Geophysical Union 1995