## 2 Heat and Mass Balance Equations for Adsorber of Adsorption Heat Pump  
The ability of a porous solid medium to adsorb volumes of vapor is called adsorption. That process is caused by a mass separation agent (adsorbent) and determined by the quality of the sorbent. At low temperatures, the porous adsorbent adsorbs vapor (adsorbate), while at high temperatures, it desorbs it. This is the basis of the adsorption heat pump with silica gel operation. Vapour molecules (adsorbate) come into contact with adsorbent and are captured by the surfaces' pores. The use of a porous solid is relatively simple and provides high adsorptive capacity (domain of equilibria of the process). Small pores in a porous medium give rise to diffusional resistance (domain of kinetics of the process). Usually, adsorption in a porous solid medium is performed in columns packed with sorbent particles or fixed bed adsorbers; however, it is primarily a surface rather than a bulk process [32; 33]. An adsorption heat pump with silica gel adsorbent and water adsorbate was considered. A silica gel/water pair was used because it is considered suitable for utilizing low-temperature heat sources less than 100 \({}^{\circ}\)C (waste heat, geothermal water) due to silica gel's high capacity at low temperatures and moderate pressures as well as due to temperature for activation and regeneration of this sorbent [32; 33; 34]. The Dubinin-Astakhov (D-A) adsorption equilibria of the selected adsorbent/adsorbate pair were sourced from the available literature [35; 36; 37]. The adsorption heat pump under consideration consists of an evaporator, an adsorber/desorber, and a condenser. The configuration of the single stage adsorption heat pump under consideration is presented in Figure 1.  
The adsorber/desorber column was encapsulated and contained tubes with deposited adsorbent (silica gel). The design of the adsorber/desorber tube arrangement is presented in Figure 2.  
The adsorption heat pump's operation mechanism included a series of cyclic transient processes. These processes ran at different temperatures and pressure levels. The adsorption process was followed by a preheating process to raise the temperature and pressure of the sorption reactor to the condenser pressure. The desorption process began afterwards. Next, the precooling process started, which cooled down the adsorber/desorber so that it would have a low pressure equal to the evaporator pressure. When the refrigerant from the evaporator was transported to the condenser and returned back to the evaporator, one cycle was completed and the circuit was restarted. A one-dimensional numerical model was created to describe the temperature and uptake changes in the adsorber/desorber and consequently to describe the performance of the adsorption heat pump. Only heat and mass transfer were taken into account during operation of the assumed adsorption heat pump. Noting that although the advanced models of these components are more accurate in simulation, they are too time-consuming in the research process, which may reduce the possibility of finding better solutions in a limited time. Thus, the following main simplifying assumptions were made:  
Figure 1: Configuration of the adsorption heat pump under consideration. Figure 2: Design of the adsorber/desorber element (tube with deposited silica gel bed). 1. Pressure losses of vapor at the adsorbate flows both from the evaporator to the silica gel grains and from the grains to the condenser are negligibly small. 2. During the adsorption process, pressure inside the adsorber/desorber equals that inside the evaporator. During the desorption process, pressure inside the adsorber/desorber equals that inside the condenser. 3. The average temperature of reactor's cooling and hot water as well as the average specific heat of the adsorbent and water are constant. 4. Thermal conductivity of the adsorbent is constant. 5. The temperature inside evaporator as well as inside condenser is constant. 6.