Improved lumped-capacitance model for heat and mass transfer in adsorbed gas discharge operations

An improved lumped-capacitance formulation for heat and mass transfer in adsorbed gas discharge operations has been developed. The formulation is obtained by employing the Coupled Integral Equations Approach (CIEA) for reducing one-dimensional transport equations for adsorbed gas storage in a cylindrical domain to a lumped-capacitance form. The CIEA is based on the traditional Hermite formulas for approximating integrals, which are used for producing relations between average potentials and values at boundaries. This approach is shown to reduce the original spatial-dependent PDEs to two time-dependent ODEs, as similar to the ones obtained using classical lumped-system analyses, the main differences being an additional equation that is required for calculating the reservoir wall temperature, and modified Biot numbers. Two different approximation schemes are tested, and one of them is demonstrated to extend the application range of the classical lumped formulation for Fourier values at least two orders of magnitude smaller than the usual limit seen for this problem.