Comparison of Analytical and Numerical Models of Adsorber/desorber of Silica Gel-water Adsorption Heat Pump

Abstract

In the paper, comparison of an analytical and a numerical model of silica gel/water adsorber/desorber is presented. Adsorber/desorber as a part of the two-bed single-stage adsorption heat pump is discussed. The adsorption heat pump under consideration consists of an evaporator, two adsorber/desorber columns and a condenser. Only heat and mass transfer was taken into account during operation of assumed adsorption heat pump. Adsorption equilibrium was described by the Dubinin-Astachov model. The presented mathematical models, both analytical and numerical, were created to describe the temperature, heat and concentration changes in the adsorber/desorber and consequently to describe the performance of the adsorption heat pump. Heat and mass transfer equations of the model were solved analytically and calculation parameters were entered in the common spreadsheet. The numerical model was established comprising of the set of heat and mass balance partial differential equations, together with the initial and boundary conditions and was solved by the numerical method of lines. The developed analytical model is very basic and can be used only for the initial estimates of mean cyclic temperature of the cooling/heating water in the adsorber/desorber bed. Validation of the numerical model shows reasonable agreement between the numerical and experimental averaged bed temperatures and is an indication of the proper mathematical modeling and the accuracy of the numerical analysis.

Gear and Runge–Kutta Numerical Discretization Methods in Differential Equations of Adsorption in Adsorption Heat Pump

“…The main aim of this work was to find the correct method of calculating equations of heat and mass transfer for the adsorption process and to calculate it numerically in a reasonable amount of time and with proper accuracy. The calculation of the coefficient of performance is a secondary effect to the one presented in the article, but it is widely described in previous papers [38,39], where the performance of two-bed as well six-bed single-stage adsorption heat pumps was considered in detail. The obtained results allowed us to calculate the COP for the abovementioned case of parameters.…”

“…Adsorption heat pump applications in cooling refer to useful cooling [4]; chilled water circuits [5,6]; electric vehicle air conditioners [7]; heat rejection systems, such as dry or wet cooling towers or ground coupled heat exchangers [8]; and solar systems as the driving heat source [9,10]. Heating applications of adsorption heat pumps are found in heating systems, waste heat utilization [3,5], low-temperature heat sources (e.g., ground heat exchangers and geothermal water installations [11]) and driving heat sources (e.g., gas furnace) [12]. Adsorptive storage of CO 2 can be an interesting example of another application [13].…”

“…In this article, the authors focused on describing methods for solving the set of partial differential equations and other assumptions. A detailed description of the developed model can be found in articles [38,39], where the performance of two-bed as well as six-bed single-stage adsorption heat pumps were considered. The set of heat and mass balance equations for the adsorber subelement dx (Figure 2) of the considered adsorption heat pump can be described by…”