**1. Introduction**

68 Mass Transfer in Chemical Engineering Processes

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columns. II. Wetted and effective-interfacial areas, gas and liquid phase mass

The careful control of ambient air moisture content is of concern in many industrial processes, with diverse applications such as in metallurgical processes or pharmaceutical production. In the air-conditioning field, the increasingly concern with sick building syndrome also brings humidity control into a new perspective. Underestimated ventilation rates might result in poor indoor air quality, with a high concentration of volatile organic compounds, smoke, bacteria and other contaminants. Epidemiological studies indicate a direct connection between inadequate levels of moisture and the incidence of allergies and infectious respiratory diseases. A popular method of lowering the concentration of contaminants is to increase the ventilation rates. In fact, the fresh air requirement per occupant/hour imposed by the current air-quality standard has doubled over the last three decades. Since the fresh air has to be brought to the thermal comfort condition, increased ventilation rates imply increased thermal loads, which in turn will demand chillers with increased cooling capacity. Accordingly, there is a trade-off between indoor air quality and energy consumption, which is also of main concern of private and public sectors.

Figure (1.a) shows an evaporative cooling system. It essentially consists of a chamber through which air is forced through a water shower. It is a sound system from air-quality, energy consumption and ecological viewpoints. The air quality is provided by a continuous air room change, with no air recirculation. Since the cooling effect is provided by evaporation of water into air, the energy consumption is restricted to the pumping power, which is usually low when compared to the energy needs of a compressor. Unlike vaporcompression systems, which usually employ ozone-depleting refrigerants, evaporative cooling systems exclusively employ water as the refrigerant.

Figure (1.b) shows that the evaporative cooling process is isenthalpic, which means that the air stream enthalpy remains unaltered as it flows through the evaporative cooler. Accordingly, the increase in the air stream humidity occurs at the expense of its own sensible energy, and the air stream is cooled and humidified as it crosses the evaporative cooler. Since the heat and mass transfer processes are mutually dependent, the air stream humidity at the inlet of the evaporative cooler has to be significantly low, if an appreciable cooling effect is to be achieved. Unfortunately this is not always the case, and this cooling technique is not as effective as traditional vapour-compression systems, being restricted to applications on low humidity areas (Khuen et al., 1998).

Mathematical Modelling of Air Drying by Adiabatic Adsorption 71

become extremely low, enabling a much more significant temperature drop through the evaporative cooler. Similarly to the evaporative cooling process, the heat and mass transfer in the desiccant cooling process are also intimately connected: Consider the adsorption process, in which the humidity is attracted to the desiccant felt from the air stream. As the air is dehumidified, two factors contribute to increase its temperature, namely the heat of adsorption, which is the heat released as the vapor molecules are adsorbed, and ordinary heat transfer from the micro-channel walls, which have been exposed to the high temperature regeneration stream during the previous period of time. Since each microchannel can be taken as an adiabatic cell, it can be concluded that the decrease in air humidity must exactly match the increase in air sensible energy, with mutually dependent effects as earlier described. Accordingly, the air crosses the desiccant rotor isenthalpically as shown in Figure (2.b), in the opposite direction of the evaporative cooling, which has been supported by numerical and experimental evidence (Nobrega and Brum, 2009a, 2009b).

The purpose of the modeling is to simulate what the process air outlet state would be, for given values of the inlet air state, length of the channel, period of revolution, desiccant

The mathematical modelling of desiccant wheels is of key importance for equipment developers, so as to provide them with guidelines for improved design. It is also of importance to HVAC engineers, in order to access if the thermal comfort condition can be attained for a typical set of atmospheric conditions. The mathematical model relies on a number of simplifying assumptions, aiming at keeping the model (and its solution) as simple as possible, while retaining the physical meaning. An excellent review of the

material, regeneration temperature and other design parameters.

Fig. 2. Active desiccant rotor

**2. Mathematical model** 

Fig. 1. Evaporative cooling system

One possible way to overcome this restriction would be artificially dry the air stream before it is admitted to the evaporative cooler, which can be accomplished by using a solid sorbent air dryer. Adsorption is primarily used for component separation from a gaseous mixture, and is widely employed in the chemical industry. The main advantage is that the adsorptive material pore size can be designed for selective adsorption of a given component, allowing even trace amounts to be removed (Chung and Lee, 2009). However, the removal of moisture from air for comfort cooling has distinguished features from gas separation usually practiced in the chemical industry.

Consider Figure (2.a), which shows an active desiccant rotor. It consists of a cylindrical drum, fitted with a micro-channel mesh, usually made of aluminum or plastic. The structure material is coated with silica-gel, which can be manufactured as a substrate. Silica-gel is a form of silicon dioxide derived from sodium silicate and sulfuric acid, which has good affinity to water vapor and an adsorbing capacity of as much as 40% of its own weight. Regular density silica gel typically offers an adsorptive area 400m2 per cm3, with an average porous radius corresponds to 11Å. The present model relies on the existence of an air layer in close contact with the solid, from which the adsorbed vapor molecules stem. The silicagel affinity to water can be explained by considering that the state of any solid particle is considerably different, depending on its located on the core or on the solid surface. A particle located in the interior of the solid is neutral equilibrium, uniformly surrounded by other particles, and has minimum potential energy. Conversely, a particle on the surface is subjected to a greater potential energy, which is a representation of the required work to move the particle from the interior to the surface, agains the atractive molecules forces. The nearby vapor molecular are attracted form the air layer to the adsoprtive surface, in an effort to restore equilibrium (Masel, 1996). The desiccant wheel operates between two air streams, the process air stream, which is the stream to be dehumidified, and the regeneration stream, which is a high temperature air stream required to purge the humidity from the desiccant felt. At the process stream side, the humidity migrates from the air to the desiccant coated walls of the channel. Conversely, when the regeneration stream is forced through the microchannels, the desiccant coat returns the humidity back to the air stream, which is dumped back to the atmosphere. Accordingly, the humidity at the outlet of the process stream can

One possible way to overcome this restriction would be artificially dry the air stream before it is admitted to the evaporative cooler, which can be accomplished by using a solid sorbent air dryer. Adsorption is primarily used for component separation from a gaseous mixture, and is widely employed in the chemical industry. The main advantage is that the adsorptive material pore size can be designed for selective adsorption of a given component, allowing even trace amounts to be removed (Chung and Lee, 2009). However, the removal of moisture from air for comfort cooling has distinguished features from gas separation

Consider Figure (2.a), which shows an active desiccant rotor. It consists of a cylindrical drum, fitted with a micro-channel mesh, usually made of aluminum or plastic. The structure material is coated with silica-gel, which can be manufactured as a substrate. Silica-gel is a form of silicon dioxide derived from sodium silicate and sulfuric acid, which has good affinity to water vapor and an adsorbing capacity of as much as 40% of its own weight. Regular density silica gel typically offers an adsorptive area 400m2 per cm3, with an average porous radius corresponds to 11Å. The present model relies on the existence of an air layer in close contact with the solid, from which the adsorbed vapor molecules stem. The silicagel affinity to water can be explained by considering that the state of any solid particle is considerably different, depending on its located on the core or on the solid surface. A particle located in the interior of the solid is neutral equilibrium, uniformly surrounded by other particles, and has minimum potential energy. Conversely, a particle on the surface is subjected to a greater potential energy, which is a representation of the required work to move the particle from the interior to the surface, agains the atractive molecules forces. The nearby vapor molecular are attracted form the air layer to the adsoprtive surface, in an effort to restore equilibrium (Masel, 1996). The desiccant wheel operates between two air streams, the process air stream, which is the stream to be dehumidified, and the regeneration stream, which is a high temperature air stream required to purge the humidity from the desiccant felt. At the process stream side, the humidity migrates from the air to the desiccant coated walls of the channel. Conversely, when the regeneration stream is forced through the microchannels, the desiccant coat returns the humidity back to the air stream, which is dumped back to the atmosphere. Accordingly, the humidity at the outlet of the process stream can

Fig. 1. Evaporative cooling system

usually practiced in the chemical industry.

become extremely low, enabling a much more significant temperature drop through the evaporative cooler. Similarly to the evaporative cooling process, the heat and mass transfer in the desiccant cooling process are also intimately connected: Consider the adsorption process, in which the humidity is attracted to the desiccant felt from the air stream. As the air is dehumidified, two factors contribute to increase its temperature, namely the heat of adsorption, which is the heat released as the vapor molecules are adsorbed, and ordinary heat transfer from the micro-channel walls, which have been exposed to the high temperature regeneration stream during the previous period of time. Since each microchannel can be taken as an adiabatic cell, it can be concluded that the decrease in air humidity must exactly match the increase in air sensible energy, with mutually dependent effects as earlier described. Accordingly, the air crosses the desiccant rotor isenthalpically as shown in Figure (2.b), in the opposite direction of the evaporative cooling, which has been supported by numerical and experimental evidence (Nobrega and Brum, 2009a, 2009b).

Fig. 2. Active desiccant rotor

The purpose of the modeling is to simulate what the process air outlet state would be, for given values of the inlet air state, length of the channel, period of revolution, desiccant material, regeneration temperature and other design parameters.
