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 ( B i m ), adsorption Damköhler ( D a a d )} 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 ≲ D a a d B i 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.