## 2 Materials and Methods  
### Description and Operation of the Adsorption Storage System  
The main purpose of the thermal energy storage system with an adsorption module is to take advantage of the adsorption process to store part of the thermal energy obtained from solar collectors in an effective and compact way. The thermal energy is firstly used to regenerate the adsorbent material (desorption) and retrieved later to heat up the water in the storage tank, when the previously desorbed working fluid is adsorbed by the adsorbent (adsorption). Additionally, the adsorption module works like a heat pump, capturing low-temperature heat from the surrounding ambient air and releasing it at higher temperatures to heat up the water in the storage tank. The considered system with the adsorption module has the following specificities: (i) the adsorber is immersed in the DHW tank; (ii) during the desorption phase, the cold intake water is preheated by the recovered condensation heat of the desorbed vapor; and (iii) during the evaporation phase, heat is captured from the surrounding ambient air. The system's main objective is to reduce the backup heating needs (usually electric heating) and likewise to reduce the nonrenewable energy consumption. The system, presented in Figure 1, consists of a conventional hot water storage reservoir with an adsorber unit immersed inside. The adsorber is filled with an adsorbent material and is connected to a condenser. This heat exchanger is immersed in a secondary water tank to preheat the intake of cold mains water and is connected to an evaporator exposed to the ambient air. These main components (adsorber, condenser, and evaporator) form a closed airtight circuit operating under moderate vacuum conditions. A first valve (V1 in Figure 1) separates the adsorber unit from the condenser, a second valve (V2 in Figure 1) separates the condenser from the evaporator, and a third valve (V3 in Figure 1) separates the evaporator from the adsorber. A backup electric heater is used at the DHW reservoir outlet to heat up the water, when the temperature setpoint for hot water consumption is not reached in the storage tank. The adsorption working pair in the system is silica gel/water. The adsorber, filled with silica gel, is horizontally immersed in the top section of the DHW tank, to take advantage of the thermal stratification effect. The desorbed water vapor is condensed in the condenser during the desorption phase. The condenser is immersed in the secondary water reservoir, where the cold mains water is preheated before entering the main storage tank. The evaporator receives and stores the condensed water coming from the condenser. This water is later vaporized at low pressure, during the adsorption phase, extracting low-temperature heat from the surrounding ambient air (similarly to what happens in a heat pump). The detailed description and operation of the system can be found in Reference [16], while a study regarding its optimization is presented in Reference [18]. The three phases of the system's operation are briefly described as follows:  
1. Charging At the beginning of the charging phase, all valves remain closed, and heat (solar energy) enters the storage tank. Afterward, when the water temperature in the main tank surpasses a specified value, V1 opens (this setpoint prevents the solar heat input to be used for desorption, while the water in the main reservoir is still not warm enough). The adsorber receives the thermal energy from the hot water in the main tank, and the water vapor is released from the silica gel bed (desorption). The desorbed vapor is subsequently condensed in the condenser, and the resultant condensation heat is recovered to preheat the cold water in the secondary tank. When the charging phase ends, V1 closes, while V2 allows, before it closes, the drainage of the condensate water to the evaporator, where it is stored until the discharge phase starts. 1.