Intraparticle Mass Transfer in Adsorption Heat Pumps: Limitations of the Linear Driving Force Approximation

Adsorption heat pumps and chillers (ADHPCs) can utilize solar or waste heat to provide space conditioning, process heating or cooling, or energy storage. In these devices, intraparticle diffusion is shown to present a significant mass transfer resistance compared with interparticle permeation. Therefore, accurate modeling of intraparticle adsorbate mass transfer is essential for the accurate prediction of overall ADHPC performance. The linear driving force (LDF) approximation is often used to model intraparticle mass transfer in place of more detailed equations because of its computational simplicity. This paper directly compares the adsorbate contents predicted using the LDF and Fickian diffusion (FD) equations for cylindrical and spherical geometries. These geometries are typical of adsorbents commonly used in adsorption refrigeration such as cylindrical activated carbon fibers (ACFs) and spherical silica gel particles. In addition to the conventional LDF approximation, an empirical LDF approximation proposed by El-Sharkawy (2006, “A Study on the Kinetics of Ethanol-Activated Carbon Fiber: Theory and Experiments,” Int. J. Heat Mass Transfer, 49(17–18), pp. 3104–3110) for ACF-ethanol (cylindrical geometry) is compared with the FD solution. By analyzing the relative error of the LDF approximation compared with the FD solution for an isothermal step-change boundary condition, the conditions under which the LDF approximation agrees with the FD equation are evaluated. It is shown that for a given working pair, agreement between the LDF and FD equations is affected by diffusivity, particle radius, half-cycle time, initial adsorbate content, and equilibrium adsorbate content. A step change in surface adsorbate content for an isothermal particle is shown to be the boundary condition that yields the maximum LDF error, and therefore provides a conservative bound for the LDF error under nonisothermal conditions. The trends exhibited by the ACF-ethanol and silica gel-water working pairs are generalized through dimensionless time and dimensionless driving adsorbate content, and LDF error is mapped using these two variables. This map may be used to determine ranges of applicability of the LDF approximation in an ADHPC model.