The microstructure influence on conductive transport processes is described in terms of volume fraction epsilon, tortuosity tau, and constrictivity beta. Virtual microstructures with different parameter constellations are produced using methods from stochastic geometry. Effective conductivities sigma eff are obtained from solving the diffusion equation in a finite element model. In this way, a large database is generated which is used to test expressions describing different micro-macro relationships such as Archie's law, tortuosity, and constrictivity equations. It turns out that the constrictivity equation has the highest accuracy indicating that all three parameters (epsilon,tau,beta) are necessary to capture the microstructure influence correctly. The predictive capability of the constrictivity equation is improved by introducing modifications of it and using error-minimization, which leads to the following expression: sigma eff =sigma 02.03 epsilon 1.57 beta 0.72/tau 2 with intrinsic conductivity sigma 0. The equation is important for future studies in, for example, batteries, fuel cells, and for transport processes in porous materials. (c) 2014 American Institute of Chemical Engineers AIChE J, 60: 1983-1999, 2014