# Dehumidifier and Regenerator Mathematical Model

The aim of the modelling work is to investigate the performance of the dehumidifier and regenerator membrane heat and mass exchangers. This is to (1) enhance the knowledge of the performance of liquid desiccant air conditioning technology, (2) to offer specific considerations for the integration of liquid desiccant and SOFC technology in a tri-generation system set-up and (3) to facilitate the modelling of a SOFC tri-generation system in Chap. 4.

## Mathematical Model Description

This section will describe the development of the mathematical model used to evaluate the dehumidifier and regenerator membrane heat and mass exchangers. The primary role of the dehumidifier and regenerator is to bring the desiccant solution into contact with an airstream without desiccant entrainment. The dehumidification and regeneration process involves the transfer of heat and mass, and are essentially the same but in reverse. Figure 3.7a shows a schematic diagram of the modelled heat and mass exchanger, whilst Fig. 3.7b shows a schematic diagram of a single air channel with the desiccant solution flowing either side of the air channel.

The modelled heat and mass exchanger shown in Fig. 3.7a consists of a series of channels that allow air and desiccant solution to flow in parallel, separated by a fibre membrane. The solution channels consist of polyethylene sheet, with fibre membranes attached on either side. The gap between the two solution channels provides the space for the air to flow. The modelling work assumes that during the dehumidification and regeneration process the desiccant solution completely wets the fibre membrane, and is in direct contact with the airstream. As a result, the membrane poses no resistances to heat and mass transfer, an assumption adopted by previous researchers (Jradi and Riffat 2014a). The model validation presented in Sects. 3.4 and 6.3 demonstrates good agreement with experimental data for a membrane based liquid desiccant heat and mass exchanger.

**Fig. 3.7 a **Schematic diagram of the membrane dehumidification heat and mass exchanger and **b **single channel heat and mass exchanger contacting design

In the dehumidifier, strong cool desiccant solution enters the top of the exchanger and flows downwards, wetting the membrane. The humid air stream passes across the wetted membrane in the adjacent air channel. At the membrane surface, differences in the vapour pressure of the desiccant solution and the humid air causes water vapour absorption from the humid airstream to the desiccant solution, resulting in a reduction in the absolute humidity of the airstream, and an increase or decrease in the air stream temperature depending on the desiccant solution temperature. The desiccant solution absorbs moisture, which reduces its concentration and increases its temperature due to the exothermic nature of the absorption process and heat transfer from the humid air stream.

Absorption of water vapour in the dehumidifier weakens the desiccant solution, therefore reducing its dehumidification potential. The regenerator is used to remove this added water vapour in the desiccant solution. Desorption is usually achieved by heating the desiccant solution to create a higher desiccant side vapour pressure and drive the moisture from the desiccant solution to a scavenger airstream, thus increasing the desiccant solution concentration. The scavenger air stream may be fresh or return room air depending on the application. The regeneration process increases the absolute humidity and temperature of the scavenger air stream.

The dehumidification and regeneration processes are very similar, relying on differences in vapour pressure between the desiccant solution and airstream to drive mass transfer. Therefore, the equations used to evaluate the heat and mass transfer processes in the dehumidifier are the same as those used for the regenerator, and are described together, the driving pressures are simply reversed.

In this modelling work, it is assumed that the heat and mass transfer processes are carried out in the laminar flow regime only. Table 3.3 shows the

**Table 3.3 **Reynolds number calculations for a single air channel

Air condition |
Ta (°C) |
RHa (%) |
Rea |

Hot and humid air |
35 |
80 |
1107 |

Warm and dry air |
25 |
50 |
1205 |

Reynolds (Re) number calculated for a single air channel, with dimensions of 0.21 m X 0.41 m x 0.01 m, at an air velocity of 1 m s ^{1}. Two air conditions are shown. The results show the air flow to be in the laminar regime i.e. <2300 for both cases, and thus the heat and mass transfer equations presented in Sects. 3.2.1 and 3.2.2 can be used with confidence.

The dehumidification process involves both heat and mass transfer; therefore the mathematical model developed needs to solve these sets of equations simultaneously.