“…This equation, when coupled with the mass and energy balances, provides the velocity and pressure gradients in the bed modified by the influence of the reaction and the membrane. Moreover, Brinkman equation can model deviations from ideal plug flow in packed beds (important for D R /d P < 10), by using a suitable radial porosity distribution function [36,37] (Table 4). The first term of Brinkman equation contains the pressure and viscous transport terms, whereas the second term accounts for the energy dissipated by friction with the bed solids.…”