## 1 Introduction
Water vapor adsorption studies at low pressures of 500-7000 Pa of A and RD types of silica gel showed the results at the level of 0.4 and 0.45 wt.%, respectively [25]. In the literature, there are also attempts to increase the adsorption of vapor by modifying the adsorbent, e.g., modifying the CaCl\({}_{2}\) silica gel increases the contact surface of the sorbent with water vapor, thus allowing the maximum sorption capacity to be reached at the level of 0.75 wt.%. [26]. Since the discovery of carbon nanotubes (CNT) more than two decades ago [27], they have been widely used as adsorbents for gases [28; 29], heavy metals [30], organic compounds [31], and pollution prevention reagents [32; 33], among others. They have also been successfully used as part of high-performance composite materials [34; 35]. From a mechanical point of view, a noteworthy advantage of nanocomposites over conventional materials is the extremely high surface-to-volume ratio of the reinforcing phase. The reinforcing material can consist of particles, sheets, or fibers. Such a large surface area enhancement can have a huge impact on composite properties at the macroscale, even in the presence of relatively less enhancement at the nanoscale. The addition of CNTs improves the electrical and thermal conductivity of the material. Since CNT also exhibit hydrophobic properties, this enables their use in a wide range of industries. As well as other types of nanoparticles can give better optical properties, dielectric properties, heat resistance, or mechanical properties such as stiffness, strength, and resistance to wear and damage [20; 36; 37]. The work on creating or modeling the performance of efficient silica gel composites and CNTs is still relevant and applicable in many application pathways. In work [37], composites of single-walled and multi-walled carbon nanotubes were created for functionalization with silica composite materials. The use of such composite was aimed to show the way for various novel applications including effective earth element adsorption performance. The addition of a small amount of double-walled carbon nanotubes (2.06%) to silica gel-based aerogel produced significant improvements in tensile strength and elastic modulus [38]. The application of CNT in adsorption is limited by their characteristics: hydrophobicity/hydrophilicity, presence of functional groups, size of specific surface area, or surface charge. While the removal of contaminants from water by nanotubes is a successful method, the use of CNTs in the adsorption of inorganic compounds, including vapors and gases, may result in a reduction in sorption efficiency. This is due to the selectivity of CNTs and their unique properties. CNTs are often added to silica aerogels [39; 40; 41] to use as adsorbents for organic contaminants [42] or specific adsorption applications [43]. Model application studies are underway to improve the cooling performance of a solar-powered adsorption unit using a novel composite adsorbent with multilayer carbon nanotubes [44; 45]. There are works on silica coatings reinforced with carbon nanotubes, which improve their strength and provide higher wear resistance [46]. Thermodynamically, the adsorption phenomenon is a spontaneous process during which the free energy of the system decreases. The adsorbed phase has fewer degrees of freedom than the gas phase, and therefore the entropy decreases during adsorption [47]. In consequence, the adsorption process is exothermic--the heat is produced. In contrast, desorption is an endothermic process characterized by the consumption of heat. The isosteric preheating is the heating and pressurization stage when both the sorption bed condenser and bed evaporator valves are closed. The sorption bed operates as a closed system subjected to heating. The increase in bed temperature induces the vapor pressure inside the bed to increase, with the total amount of adsorbate in the adsorbed phase constant at the maximum concentration.