A Two-Temperature Model of the Regenerative Solid-Vapor Heat Pump

Abstract

A thermally driven heat pump using a solid/vapor adsorption/desorption compression process is thermodynamically analyzed. Heat regeneration between the two adsorbent beds is accomplished through the use of a circulating heat transfer (HX) fluid. Effective heat regeneration and system performance requires that steep thermal profiles or waves be established in the beds along the path of the HX-fluid flow direction. Previous studies by Shelton, Wepfer, and Miles have used square and ramp profiles to approximate the temperature profiles in the adsorbent beds, which, in turn, enable the thermodynamic performance of the heat pump to be computed. In this study, an integrated heat transfer and thermodynamic model is described. The beds are modeled using a two-temperature approach. A partial differential equation for the lumped adsorbent bed and tube is developed to represent the bed temperature as a function of time and space (along the flow direction), while a second partial differential equation is developed for the heat transfer fluid to represent the fluid temperature as a function of time and space (along the flow direction). The resulting differential equations are nonlinear due to pressure and temperature-dependent coefficients. Energy and mass balances are made at each time step to compute the bed pressure, mass, adsorption level, and energy changes that occur during the adsorption and desorption process. Using these results, the thermodynamic performance of the heat pump is calculated. Results showing the heat pump’s performance and capacity as a function of the four major dimensionless groups, DR, Pe, Bi, and KAr, are presented.