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Rate of Gas Absorption
Stage-equilibrium Gas Absorption
Gas-absorption Equipment

Gas absorption/desorption is a process in which a gaseous mixture is brought into contact with a liquid and during this contact a component is transferred between the gas stream and the liquid stream. The gas may be bubbled through the liquid, or it may pass over streams of the liquid, arranged to provide a large surface through which the mass transfer can occur. The liquid film in this latter case can flow down the sides of columns or over packing, or it can cascade from one tray to another with the liquid falling and the gas rising in the counter flow.
The gas, or components of it, either dissolves in the liquid (absorption) or extracts a volatile component from the liquid (desorption).

An example of the first type is found in hydrogenation of oils, in which the hydrogen gas is bubbled through the oil with which it reacts. Generally, there is a catalyst present also to promote the reaction. The hydrogen is absorbed into the oil, reacting with the unsaturated bonds in the oil to harden it. Another example of gas absorption is in the carbonation of beverages. Carbon dioxide under pressure is dissolved in the liquid beverage, so that when the pressure is subsequently released on opening the container, effervescence occurs.

An example of desorption is found in the steam stripping of fats and oils in which steam is brought into contact with the liquid fat or oil, and undesired components of the fat or oil pass out with the steam. This is used in the deodorizing of natural oils before blending them into food products such as margarine, and in the stripping of unwanted flavours from cream before it is made into butter. The equilibrium conditions arise from the balance of concentrations of the gas or the volatile flavour, between the gas and the liquid streams.
In the gas absorption process, sufficient time must be allowed for equilibrium to be attained so that the greatest possible transfer can occur and, also, opportunity must be provided for contacts between the streams to occur under favourable conditions.

Rate of Gas Absorption

The rates of mass transfer in gas absorption are controlled by the extent of the departure of the system from the equilibrium concentrations and by the resistance offered to the mass transfer by the streams of liquid and gas. Thus, we have the familiar expression:

rate of absorption = driving force/resistance,

The driving force is the extent of the difference between the actual concentrations and the equilibrium concentrations. This is represented in terms of concentration differences.

For the resistance, the situation is complicated, but for practical purposes it is adequate to consider the whole of the resistance to be concentrated at the interface between the two streams. At the interface, two films are postulated, one in the liquid and one in the gas. The two-film theory of Lewis and Whitman defines these resistances separately, a gas film resistance and a liquid film resistance. They are treated very similarly to surface heat coefficients and the resistances of the two films can be combined in an overall resistance similar to an overall heat transfer coefficient.

The driving forces through each of the films are considered to be the concentration differences between the material in the bulk liquid or gas and the material in the liquid or gas at the interface. In practice, it is seldom possible to measure interfacial conditions and overall coefficients are used giving the equation

dw/dt = KlA (x* - x) = KgA(y - y*)                                                                              (9.7)

where dw/dt is the quantity of gas passing across the interface in unit time, K1 is the overall liquid mass-transfer coefficient, Kg is the overall gas mass-transfer coefficient, A is the interfacial area and x, y are the concentrations of the gas being transferred, in the liquid and gas streams respectively. The quantities of x* and y* are introduced into the equation because it is usual to express concentrations in the liquid and in the gas in different units. With these, x* represents the concentration in the liquid which would be in equilibrium with a concentration y in the gas and y* the concentration in the gas stream which would be in equilibrium with a concentration x in the liquid.

Equation (9.7) can be integrated and used to calculate overall rates of gas absorption or desorption. For details of the procedure, reference should be made to works such as Perry (1997), Charm (1971), Coulson and Richardson (1978) or McCabe and Smith (1975).

Stage Equilibrium Gas Absorption

The performance of counter current stage contact gas absorption equipment can be calculated if the operating and equilibrium conditions are known. The liquid stream and the gas stream are brought into contact in each stage and it is assumed that sufficient time is allowed for equilibrium to be reached. In cases where sufficient time is not available for equilibration, the rate equations have to be introduced and this complicates the analysis. However, in many cases of practical importance in the food industry, either the time is sufficient to reach equilibrium, or else the calculation can be carried out on the assumption that it is and a stage efficiency term, a fractional attainment of equilibrium, introduced to allow for the conditions actually attained. Appropriate efficiency values can sometimes be found from published information, or sought experimentally.

After the streams in a contact stage have come to equilibrium, they are separated and then pass in opposite directions to the adjacent stages. The separation of the gas and the liquid does not generally present great difficulty and some form of cyclone separator is often used.

In order to calculate the equipment performance, operating conditions must be known or found from the mass balances. Very often the known factors are:
gas and liquid rates of flow,
inlet conditions of gas and liquid,
one of the outlet conditions, and
equilibrium relationships.

The processing problem is to find how many contact stages are necessary to achieve the concentration change that is required. An overall mass balance will give the remaining outlet condition and then the operating line can be drawn. The equilibrium line is then plotted on the same diagram, and the McCabe-Thiele construction applied to solve the problem.

EXAMPLE 9.5. Multiple stage steam stripping of taints from cream
In Example 9.4, a calculation was made for a single-stage steam-stripping process to remove a taint from cream. The conditions were that stage-contact desorption was to be used to remove a taint that was present at a concentration of 10 ppm in the cream, by contact with a counter flow current of steam. Consider, now, the case of a rather more difficult taint to remove in which the equilibrium concentration of the taint in the steam is only 7.5 times as great as that in the cream. If the relative flow rates of cream and steam are given in the ratio 1: 0.75, how many contact stages would be required to reduce the taint concentration in the cream to 0.3 ppm assuming (a) 100% stage efficiency and (b) 70% stage efficiency? The initial concentration of the taint is 10 ppm.

Mass balance

Inlet cream taint concentration    = 10 ppm
                                                = xa
Outlet cream taint concentration  = 0.3 ppm
                                                = xn
Inlet steam taint concentration    = 0 ppm
                                                = yn+1

Assume a cream flow rate of 100 arbitrary units = L
so steam flow rate                          V = 75
If y1 is the outlet steam taint concentration,
                  Total taint into equipment = total taint out of equipment.
                                            100(10) = 75y1 + 100(0.3)
                                     100(10 - 0.3) = 75y1

Therefore                                      y1  = 12.9 ppm = ya

From eqn. (9.6)
                                         yn+1 = xnL/V + ya - xaL/V

                                         yn+1 = xn (100/75) + 12.9 - 10(100/75)
                                                 = 1.33 xn - 0.43
Equilibrium condition:             yn  = 7.5xn

The operating and equilibrium lines have been plotted on Fig. 9.4 and it can be seen that two contact stages are sufficient to effect the required separation. The construction assumes 100% efficiency so that, with a stage efficiency of 70%, the number of stages required would be 2(100/70) and this equals approximately three stages.

So the number of contact stages required assuming:
        (a) 100% efficiency = 2, and
        (b) 70% efficiency   = 3.

Notice that only a small number of stages is required for this operation, as the equilibrium condition is quite well removed from unity and the steam flow is of the same order as that of the cream. A smaller equilibrium constant, or a smaller relative steam flow rate, would increase the required number of contact stages.

Gas Absorption Equipment

Gas absorption equipment is designed to achieve the greatest practicable interfacial area between the gas and the liquid streams, so that liquid sprays and gas-bubbling devices are often employed. In many cases, a vertical array of trays is so arranged that the liquid descends over a series of perforated trays, or flows down over ceramic packing that fills a tower.

For the hydrogenation of oils, absorption is followed by reaction of the hydrogen with the oil, and a nickel catalyst is used to speed up the reactions. Also, pressure is applied to increase gas concentrations and therefore speed up the reaction rates. Practical problems are concerned with arranging distribution of the catalyst, as well as of oil and hydrogen. Some designs spray oil and catalyst into hydrogen, others bubble hydrogen through a continuous oil phase in which catalyst particles are suspended.

For the stripping of volatile flavours and taints in deodorizing equipment, the steam phase is in general the continuous one and the liquid is sprayed into this and then separated. In one design of cream deodorizing plant, cream is sprayed into an atmosphere of steam and the two streams then pass on to the next stages, or the steam may be condensed and fresh steam used in the next stage.

Contact-Equilibrium Processes - Part 2: APPLICATIONS > EXTRACTION AND WASHING

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Unit Operations in Food Processing. Copyright © 1983, R. L. Earle. :: Published by NZIFST (Inc.)
NZIFST - The New Zealand Institute of Food Science & Technology