Li-ion batteries are frequently modeled using variants of the one-dimensional approach that was initially developed by Newman and colleagues (e.g., [2]). Necessarily such an approach is based upon assumptions about the electrode microstructure, and quantitative predictions depend upon empirical parameters such as effective conductivities and diffusion coefficients. The present paper develops a three-dimensional model that can resolve electrode structure at the submicron scale. Although the three-dimensional model is capable of representing arbitrary electrode microstructure, the present paper considers regular arrays of spherical particles. The model is applied to evaluate approximations in one-dimensional models and to assist in establishing empirical relationships that can be used in reduced-dimension models. General relationships for effective particle radius in one-dimensional models are derived from the three-dimensional simulations. The results also provide a basis for estimating the empirical Bruggeman exponents that affect Li-ion transport within electrolyte solutions.