Analytical and numerical methods are used to investigate ion transport and storage within the pore network of a porous bed of nanoporous particles. Under simplifying assumptions that electromigration dominates ion transport, that the pore capacitance is constant, and that the electrolyte exhibits ideal behavior, transport within this hierarchical pore network is modeled using a coupled pair of one-dimensional equations describing net charge motion into the bed by way of the interparticle void and subsequently into smaller pores within particles. These diffusion-like equations are solved analytically via Laplace transforms, and the results are used to determine the optimum interparticle porosity yielding the maximum energy deliverable in a specified time. Both step and periodic boundary conditions are considered, and closed-form expressions for the optimum porosity are derived for the periodic case. We find that the optimum porosity is remarkably similar for the periodic and step boundary conditions when the normalized bed thickness is very large or very small. We also find that the optimum porosity increases at least linearly with bed thickness when the thickness is small but is independent of both the thickness and prescribed time for delivery when the bed thickness is large. Sample results are presented and discussed.