Use of the Linear Driving Force Approximation in Adsorption Heat Pump and Chiller Modeling

Abstract

Adsorption heat pumps and chillers can utilize solar or waste heat to provide space conditioning, process heating or cooling, or energy storage. In these devices, accurate modeling of intraparticle adsorbate mass transfer is an important part of predicting overall performance. The linear driving force (LDF) approximation is often used for modeling intraparticle mass transfer in place of the more detailed Fickian diffusion (FD) equation for its computational simplicity. This paper directly compares the adsorbate contents predicted by the conventional LDF approximation, an empirical LDF approximation proposed by El-Sharkawy et al. [1], and the FD equations for cylindrical adsorbent fibers such as activated carbon fiber (ACF). The conditions under which the LDFs agree with the FD equation are then evaluated. It is shown that for a given working pair, agreement between the LDF and FD equations is affected by the diffusivity, particle radius, half-cycle time, initial adsorbate content, and equilibrium adsorbate content. The maximum possible error in adsorbate content predicted by the LDF approximation compared with the FD solution is then calculated for the ACF (A-20)-ethanol working pair. Although the maximum error will be different for other cases, the technique used in this paper can be reproduced to determine the greatest possible LDF error for any working pair.