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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