A simple steady state model of the TCA has been created in EES (Klein and Alvarado, 2003). The model is built in four parts:

• Heat exchanger for condenser/evaporator

• Pressure drop calculation for mass transport

• Effective AT between vessels

• Heat exchanger for reactor

The heat exchangers are modelled as a simple counter-flow heat exchanger with fixed UA — value, using the effectiveness relationship of Equ. 3 (Incropera and DeWitt, 1996). Cmin is the lower of the two heat capacitance rates, and Thi/Tci are the hot and cold inlet temperatures respectively. The effectiveness is a function of the UA-value and capacitance rates.

Qt є Cmjn (Thi — Tci) Equ. 3

In the tested prototypes, the heat exchangers were spirally wound smooth tubes. On the outside of the tubes there is condensation, evaporation, desorption or absorption depending on the vessel concerned. All of these processes are assumed to take place at essentially constant temperature over the heat exchanger. This is implemented in the model by making the heat capacitance rate on the outside of the tubes 1000 times greater than that on the inside. The heat transfer coefficients used in the model are given in Table

The pressure drop due to mass transport of water vapour is modelled using classical equations: ‘L’. , _ . Equ. 4

APvap = f •

vap

D

2

1.

Table 1. Heat transfer coefficients for the TCA units. Heat Exchanger U-value [W/m2.K] Area [m2] UA [W/K] Condenser 2000 3 6000 Main reactor (desorber) 700 4 2800 Evaporator 750 3 2150 Slave reactor (absorber) 500 4 2000 2 ^ P • vvap

Where:

f Friction factor

L Length between evaporation and condensation

D Hydraulic diameter

p Density of steam

vvap Velocity of the water vapour

For laminar flow, the case here, the friction factor is given by: г л f =

64 — v

V VvaP

D • p

Equ. 5

v Viscosity of the vapour

ДР

vap _ CAP ‘

Equ. 6

The velocity of the vapour is directly proportional to the rate of evaporation or condensation and thus the heat transfer rate, assuming no heat losses. Using this fact and putting all factors relating to the geometry into one coefficient CAP, the pressure drop during discharge becomes:

Properties for the vapour are taken for the temperature in the evaporator (Te), where the mass transport is most critical due to the low pressure.

The effective temperature difference between the reactor and the evaporator (ATeff, sr) is calculated in a number of stages. First the mass fraction of LiCl required for saturated solutions at the theoretical reactor temperature (Tsr*) is calculated (Equ. 7) using the relationship derived for the solubility line (Conde, 2004). Next the vapour pressure for this saturated solution at Tsr* is calculated using another relationship derived by Conde (Equ. 8), as is that for water in the evaporator (Equ. 9). These two pressures are related in Equ. 10 by the pressure drop due to the mass transport (APcooi) as calculated by Equ. 6. The effective temperature in the reactor (Tsr) is different to the theoretical temperature by ATsubcool (Equ. 11), a measure of the imperfection in the absorption process. The effective temperature difference (lift) is then calculated by Equ. 12.

Tsr* — fSat, LiCl(^sr )	Equ. 7
Psr _ fLiCl 0= sr>Tsr* )	Equ. 8
Pe = fwater (Te )	Equ. 9
Psr + Apcooi = pe	Equ. 10
Tsr _ Tsr* _ ^Tsubcool	Equ. 11
^Teff, sr “ Tsr _ Te	Equ. 12
Q e _ Fchem *Q sr	Equ. 13

It is assumed that a certain fraction (Fchem) of the heat transferred to the TCA during is stored chemically in the TCA, and that during discharge this is released (Equ. 13). This implicitly assumes zero losses from the TCA and neglects losses due to the cooling down of the vapour between the reactor and the condenser during charge and of heating the vapour between evaporator and reactor during discharge. Fchem is set to 0.3 in the model. The temperatures for the charging process are calculated in a similar manner.

Comparison with Measured Data

A prototype unit was tested both by the producing company, ClimateWell (then called Solsam), and by Vattenfall AB (Setterwall and Bales, 2003). The tests were carried out for both charging and discharging, using constant inlet temperatures to the condenser (Tcii) and reactor (Tsrii) respectively. Figure 5 shows the temperatures relevant for these measurements.

The required charging temperature (Tmr, i) is plotted against the charging rate (Q’mr) in Figure 6 a), and the chiller supply temperature (Te, o) is plotted against the cooling rate (Q’e) in Figure 6 b). ATsubcooi was adjusted to best fit the measured data, one value each for charging and discharging, whilst CAP was estimated to be 20 based on the geometry of the prototype.

Qmr [kW]

0 1 2 3 4 5 6 Qe [kW]

т

Figure 5. Two TCA units: for charging (left) and discharging (right).

т

a) b)

Figure 6. Comparison of model output (solid lines) with measured data (symbols) for three different boundary conditions, for a) charging, and b) discharging (cooling).

A value of 15°C was required for ATsubcool in order to give good agreement with measured data for discharging. This is higher than can be achieved in low-temperature absorption chillers (Foley et al., 2000), and shows that there is a large potential for improvement in
heat exchanger design and thus available temperature lift. A figure of 3-5°C should be possible, and work is in progress to improve the heat exchanger design. A value of 7.5°C was required for ATsubcooi, in order to fit the measured data for charging. This correction term is not usually required for the generator in absorption chillers and the relatively large value could be due to the fact that crystallisation takes place on the tubes. Alternatively the equations derived by Conde could be inaccurate in this temperature range. Further measurements of vapour pressure above saturated solutions of LiCl are required for temperatures of 60 — 100°C solution temperature. These could not be made at ClimateWell due to limitations of their measurement equipment.

Conclusions

The principles of operation of the TCA have been described in general terms. The process offers some advantages over other heat driven cooling process:

• High energy density storage in the solid crystals, with 180 kWh/m3 based on the volume of the main reactor and condenser vessels. This is of the same order as for prototype thermal stores using adsorption of water with silica gel.

• Good heat and mass transfer, as this occurs with solution. The heat transfer characteristics are similar to those for absorption chillers, but significantly better than for adsorption chillers.

• Constant operating conditions, with constant temperature difference between the reactor and condenser for a given solution temperature.

The TCA has desorption temperatures of below 100°C for ambient temperatures below 40°C, which is relatively low. The temperature lift depends on the cooling rate supplied and varies from 15°C for design cooling rate of 5 kW per TCA unit and 30°C inlet temperature to the reactor, to 20°C for a cooling rate of 2.5 kW.

The TCA has so far been tested only with LiCl as the salt. Theoretically it is possible with other salts, but these have not been tested. Physical properties of LiCl have been found in the literature, including equations for the most important properties including solubility line and vapour pressure. Measurements made by ClimateWell agree well with these relationships for temperatures up to 60°C, but further measurements are required above this point to check whether the relationships from literature are valid for these temperatures, relevant for charging conditions in the TCA.

A simplified steady state model of the TCA has been made based on the physical properties of LiCl as defined in the literature and a heat exchanger model with fixed UA — value. This model needs to be refined as follows:

• Calculation of the fraction of energy stored chemically (Fchem) based on the physical properties of LiCl.

• Calculation of heat losses due to changes in temperature of the vapour between reactor and condenser/evaporator.

• Estimation of losses from the TCA vessels to ambient.

This model has shown that the absorber heat exchanger works significantly worse than absorbers in equivalent low-temperature absorption chillers, and that this is a critical component for future development.