The Bruggeman model is routinely employed to determine transport parameters in macro-scale electrochemical models. Yet, it relies on both a simplified representation of the porescale structure and specific hypotheses on the transport dynamics at the pore scale. Furthermore, its inherent scalar nature prevents it from capturing the impact that pore-structure anisotropy has on transport. As a result, the complex topology of electrochemical storage devices, combined with the broad range of conditions in which batteries operate, renders the Bruggeman relationship approximate, at best. We propose a self-consistent multiscale framework, based on homogenization theory, which a priori allows one to calculate effective parameters of battery electrodes for a range of transport regimes while accounting for full topological information at the pore scale. The method is based on the solution of a closure problem on a translationally periodic unit cell and generalized to handle locally non-periodic structures. We compare the Bruggeman and the closure-problem predictions of the effective diffusivity for a set of 18,000 synthetically generated images and propose a data-driven polynomial function correlating porosity and effective diffusivity, as calculated from a solution of the closure problem. We test its predictive capability against measured diffusivity values in a LiCoO2 cathode and a Ni-YSZ anode.