A dimensionless framework for adsorber dynamics

Design, optimization, and control of adsorption-based systems are constrained by a fidelity–portability trade-off in dynamic modelling: geometry-specific formulations rarely transfer across adsorber configurations or operating regimes, whereas simplified surrogates can obscure the rate-controlling physics. This work introduces a dimensionless framework for adsorber dynamics that unifies vapour-phase exchange among cycle components, fluid–solid heat transfer, and intraparticle diffusion. Intraparticle kinetics are obtained analytically by solving the Fickian problem with a time-varying boundary concentration via a convolution kernel, replacing the customary heat-affected linear-driving-force approach. Nondimensionalization on characteristic geometric, kinetic, and thermodynamic scales yields a compact set of dimensionless groups that separates design from operation. A stable, memory-lean implicit solver integrates the coupled balances and evaluates the kernel efficiently over long horizons. Capability of the approach is demonstrated on a closed-vessel, near-isothermal step for silica gel–water, constructing a performance map of the dimensionless time to 90% the final uptake (t_90^*) in the {mass transfer Biot (Bi_m), adsorption Damköhler (Da_ad)} plane that delineates surface-barrier- and diffusion-limited regimes and highlights high-gain directions for rapid equilibration. In the baseline simulated case, while the t_90^* map identifies a high-sensitivity band at 10^(-6)≲Da_ad Bi_m≲10^(-3), where modest parameter shifts yield disproportionate reductions in t_90^*, results show that the adsorbent mean temperature increases by only ∼1.4% and the heat-carrier outlet by <0.1%. The framework is portable across scales and operating modes, enabling comparative benchmarking, design–operation co-optimization, and model-based control in adsorption processes.