Vapour Gas Mass Transfer Absorber
It is generally believed that the vapour absorption systems must be “air tight”, especially systems with sub-atmospheric working pressures, e.g. LiBr/H2O systems where air entrainment is a risk and the performance is seriously affected by the inward leakage. The earliest report on the effects of non-absorbable gases on the absorption process is probably that of Haselden and Malaty. They reported that the presence of air in small volumetric concentrations greatly reduced heat and mass transfer rates in the absorber of an aqua/ammonia system. Later, Burdukov et al. conducted experimental work on water vapour absorption by a thin film of an aqueous solution of lithium bromide. They reported that an air content of 0.5% in the vapour reduced the mass transfer coefficient almost by half. Grossman and Ameel et al. both presented analytical methods to estimate the reduction in the absorber’s performance due to non-absorbable gases. Both reports restricted the analysis to the entry region of the absorber, where an analytical solution to the governing partial differential equations was possible. Leibundgut et al. calculated the reduction of the overall coefficient of performance, COP, of an aqua ammonia heat-pump due to the presence of hydrogen. At a partial pressure of 0.4 bar, hydrogen was found to reduce the overall COP by more than half. Lee and Rose noted that vapour velocities, even at small values, helped eliminate the building up of non-condensable gases at the vapour/liquid interface of a condensate film, hence improving the heat transfer rates. Bologa et al. concluded, after studying the condensation of vapours in the presence of several non-condensable gases, that the deciding factor in the determination of heat transfer intensity is the ratio of the molecular mass of the gas to that of the vapour.
In this paper, an analytical method of predicting of the effects of non-absorbable gases on the performance of the absorption system’s absorber is presented. The method is developed by solving the set of governing algebraic equations obtained from energy and mass balances and the equilibrium conditions at the vapour/liquid interface. The paper then discusses the performance of the absorber for various combinations of gas pressures and mass-transfer coefficients. A brief account is also given of the expected reduction of the COP of a LiBr/H2O system resulting from the evolution of hydrogen.
Fig. 1a shows the gas and refrigerant vapour mass-fractions in the bulk of the vapour/gas mixture and at the vapour/liquid interface and the concentration gradient of the liquid refrigerant in the absorbent. Fig. 1b shows the partial pressures of the gas and the vapour at the mixture and interface zones. When no gas is present, we can assume that Pa=0 and Pv is constant throughout the vapour zone. In this case, there is no resistance to absorption in the vapour phase and the only resistance is that of the actual absorbent. However, when a gas is present, Pa will have a finite value and there will be a resistance of the vapour and of the absorbent and the total resistance to absorption will be the sum of these two. Thus, it is expected that the presence of a gas will reduce the transfer rate.
Initially, before any absorption takes place, no mass or partial pressure gradients exist in the bulk of the vapour/gas mixture and the values of the mass fractions and partial pressures in the bulk equal those at the interface. Once the first quantity of vapour is absorbed (at the interface), concentration boundary layers develop in the vapour/gas mixture as well as the absorbent film. The mass fraction of the refrigerant vapour at the interface (Mvi) and its partial pressure (Pvi) drop and mass fractions and pressure gradients develop, and the amount of absorption will depend on these gradients. As the liquid travels down the plate it becomes more concentrated with the refrigerant and its capacity to absorb vapour decreases, so Mvi increases and so does Pvi, provided that the refrigerant vapour is constantly replenished. This continues until the solution reaches the equilibrium state and the values of Mvi and Pvi are restored once again to their initial values. The procedure of calculating the effect of the gas on an absorber’s performance amounts to solving a set of simultaneous equations obtained from the mass and energy balances of an absorbing film and the equilibrium state assumed at the vapour/liquid interface. The following set of assumptions is made to facilitate the solution:
• The absorbent’s film is smooth (i.e. non-wavy) and of constant thickness.
• An equilibrium state exists at the vapour/liquid interface.
• Constant heat of absorption. Negligible drag effects on the vapour/gas mixture. The mixture, therefore, stays stationary.
• Furthermore, this analysis uses LiBr/H2O as the absorbent with a combination of water vapour/air for the vapour/gas mixture.
The above set of equations was incorporated in a simplified computer simulation of a film absorber, which gives the absorbent’s bulk concentration, Ca, and temperature, Ta, and the vapour’s flow rate, 
v. The computer simulation, detailed in, amounts to solving a set of ordinary differential equations, which describes the performance of a film absorber, using the four point Runge-Kutta method. The simplified simulation was found to give a good degree of agreement with a more complicated model which employs a hybrid method of analytical and finite difference methods, and its results are therefore believed to be reliable.
Here, air is used as an example of a non-absorbable gas. The effects of the existence of air, in terms of its partial pressure Pa, and the vapour’s mass transfer coefficient Gv on the performance of the absorber are shown. The performance is characterised by the overall effectiveness Eo, which is the ratio of actual and maximum absorptions, i.e.
An accepted degree of vacuum in refrigeration systems, which provides a typical value for Pa, is about 0.1 mm Hg (0.013 kPa). The mass transfer coefficient Gv, which is representative of average working conditions in LiBr/H2O systems, was calculated at 0.006 m/s. The results shown in this discussion were obtained for typical values of Pa and Gv to cover a realistic range of working conditions.
Fig. 2 shows the variation of Eo with Pa, (the corresponding values of the air’s mass fraction in the vapour/gas mixture are shown in brackets). The effect is immediately evident. The presence of only 2% of air (Ma=0.02) causes a reduction of more than 650% in the overall effectiveness at a NTU of 2. A further increase in Pa results in an even greater reduction in absorption performance. Fig. 2 also shows that the reduction in performance increases with the length of the absorber (NTU being proportional to the length) passing through a maximum at a NTU in the range of 3–4 from where it diminishes again as the equilibrium conditions are approached.
Fig. 3 shows the effect of the vapour mass transfer coefficient Gv on the overall effectiveness, at an air partial pressure of 0.013 kPa. The higher the value of Gv is calculated assuming the vapour/gas mixture was caused to move perpendicularly to the absorbent film at a speed of 10 m/s. As expected, the figure shows a reversed trend to that of the air pressure. Here, the increase in the mass transfer coefficient effects an increase in the overall effectiveness. Again the diminishing effect of increasing Gv, as the equilibrium conditions are approached, is evident. It can be seen that the absorber’s performance can be improved by (a) maintaining higher degrees of vacuum in the absorber’s chamber or (b) increasing the mass transfer coefficient of the vapour by introducing a forced convection device, e.g. a fan, in the vapour/gas region. It follows that a certain value of effectiveness could be achieved by a different Pa–Gv combination. This point is illustrated in Fig. 4 and Fig. 5. In Fig. 4, Eo is plotted against Pa for the three values of Gv and at two different points along the absorber’s length corresponding to NTU=1 and NTU=80 respectively. In Fig. 5, Eo is plotted against Gv for the four values of Pa at the same points along the absorber’s length, i.e. at NTU of 1 and 80. The figures show that the choice of any particular Pa–Gv combination is a question of optimum economy and design. For example, the values of effectiveness obtained in the presence of air at a Pa of 1 kPa and Gv of 0.006 m/s are comparable with those obtained at a Pa–Gv combination of 0.013 kPa-0.002 m/s. Again, the matter is one of choosing between creating and maintaining higher levels of vacuum or mounting and operating a stirring device in the absorber. Fig. 5 also shows that the performance of the absorber becomes less sensitive to the presence of air as its length (area) increases. At a NTU=80, the absorber’s performance changes very little with Pa for a wide range of Gv.
Tags: mass transfer
