  Understanding the dynamics of electric-double-layer (EDL) charging in porous
media is essential for advancements in next-generation energy storage devices.
Due to the high computational demands of direct numerical simulations and a
lack of interfacial boundary conditions for reduced-order models, the current
understanding of EDL charging is limited to simple geometries. Here, we present
a theoretical framework to predict EDL charging in arbitrary networks of long
pores in the Debye-H\"uckel limit without restrictions on EDL thickness and
pore radii. We demonstrate that electrolyte transport is described by
Kirchhoff's laws in terms of the electrochemical potential of charge (the
valence-weighted average of the ion electrochemical potentials) instead of the
electric potential. By employing this equivalent circuit representation with
modified Kirchhoff's laws, our methodology accurately captures the spatial and
temporal dependencies of charge density and electric potential, matching
results obtained from computationally intensive direct numerical simulations.
Our framework provides results up to five orders of magnitude faster, enabling
the efficient simulation of thousands of pores within a day. We employ the
framework to study the impact of pore connectivity and polydispersity on
electrode charging dynamics for pore networks and discuss how these factors
affect the timescale, energy density, and power density of the capacitive
charging. The scalability and versatility of our methodology make it a rational
tool for designing 3D-printed electrodes and for interpreting geometric effects
on electrode impedance spectroscopy measurements.
