Introduction Many present-day commercial gas absorption processes involve systems in which chemical reactions take place in the liquid phase; an example of the absorption of CO2 by MEA has been presented earlier in this section. These reactions greatly increase the capacity of the solvent and enhance the rate of absorption when compared to physical absorption systems. In addition, the selectivity of reacting solutes is greatly increased over that of nonreacting solutes. For example, MEA has a strong selectivity for CO2 compared to chemically inert solutes such as CH4, CO, or N2. Note that the design procedures presented here are theoretically and practically related to biofiltration, which is discussed in Sec. 25 (Waste Management).
A necessary prerequisite to understanding the subject of absorption with chemical reaction is the development of a thorough understanding of the principles involved in physical absorption, as discussed earlier in this section and in Sec. 5. Excellent references on the subject of absorption with chemical reactions are the books by Dankwerts (GasLiquid Reactions, McGraw-Hill, New York, 1970) and Astarita et al. (Gas Treating with Chemical Solvents, Wiley, New York, 1983).
Recommended Overall Design Strategy When one is considering the design of a gas absorption system involving chemical reactions, the following procedure is recommended:
1. Consider the possibility that the physical design methods described earlier in this section may be applicable.
2. Determine whether commercial design overall KGa values are available for use in conjunction with the traditional design method, being careful to note whether the conditions under which the KGa data were obtained are essentially the same as for the new design. Contact the various tower-packing vendors for information as to whether KGa data are available for your system and conditions.
3. Consider the possibility of scaling up the design of a new system from experimental data obtained in a laboratory bench-scale or small pilot-plant unit.
4. Consider the possibility of developing for the new system a rigorous, theoretically based design procedure which will be valid over a wide range of design conditions. Note that commercial software is readily available today to develop a rigorous model in a relatively small amount of time. These topics are further discussed in the subsections that follow.
Dominant Effects in Absorption with Chemical Reaction When the solute is absorbing into a solution containing a reagent that chemically reacts with it, diffusion and reaction effects become closely coupled. It is thus important for the design engineer to understand the key effects. Figure 14-12 shows the concentration profiles that occur when solute A undergoes an irreversible second-order reaction with component B, dissolved in the liquid, to give product C.
The rate equation is
Figure 14-12 shows that the fast reaction takes place entirely in the liquid film. In such instances, the dominant mass-transfer mechanism is physical absorption, and physical design methods are applicable but the resistance to mass transfer in the liquid phase is lower due to the reaction. On the other extreme, a slow reaction occurs in the bulk of the liquid, and its rate has little dependence on the resistance to dif-
fusion in either the gas or the liquid films. Here the mass-transfer mechanism is that of chemical reaction, and holdup in the bulk liquid is the determining factor.
The Hatta number is a dimensionless group used to characterize the importance of the speed of reaction relative to the diffusion rate.
As the Hatta number increases, the effective liquid-phase masstransfer coefficient increases. Figure 14-13, which was first developed by Van Krevelen and Hoftyzer [Rec. Trav. Chim., 67, 563 (1948)] and later refined by Perry and Pigford and by Brian et al. [AIChE J., 7,226 (1961)], shows how the enhancement (defined as the ratio of the effective liquid-phase mass-transfer coefficient to its physical equivalent $ = kjkl) increases with NHa for a second-order, irreversible reaction of the kind defined by Eqs. (14-60) and (14-61). The various curves in Fig. 14-13 were developed based upon penetration theory and
depend on the parameter — 1, which is related to the diffusion coefficients and reaction coefficients, as shown below.
depend on the parameter — 1, which is related to the diffusion coefficients and reaction coefficients, as shown below.
For design purposes, the entire set of curves in Fig. 14-13 may be represented by the following two equations: For, Nna > 2:
kL/k0L = 1 + — 1){1 — exp [—— 1)—1]) exp [1 — 2/NnJ (14-64)
Equation (14-64) was originally reported by Porter [Trans. Inst. Chem. Eng., 44, T25 (1966)], and Eq. (14-64) was derived by Edwards and first reported in the 6th edition of this handbook.
The Van Krevelen-Hoftyzer (Fig. 14-13) relationship was tested by Nijsing et al. [Chem. Eng. Sci., 10, 88 (1959)] for the second-order system in which CO2 reacts with either NaOH or KOH solutions. Nijs-ing's results are shown in Fig. 14-14 and can be seen to be in excellent
agreement with the second-order-reaction theory. Indeed, these experimental data are well described by Eqs. (14-62) and (14-63) when values of b = 2 and DA/DB = 0.64 are employed in the equations.
Applicability of Physical Design Methods Physical design models such as the classical isothermal design method or the classical adiabatic design method may be applicable for systems in which chemical reactions are either extremely fast or extremely slow, or when chemical equilibrium is achieved between the gas and liquid phases.
If the chemical reaction is extremely fast and irreversible, the rate of absorption may in some cases be completely governed by gas-phase resistance. For practical design purposes, one may assume, e.g., that this gas-phase mass-transfer-limited condition will exist when the ratio yjy is less than 0.05 everywhere in the apparatus.
From the basic mass-transfer flux relationship for species A (Sec. 5)
one can readily show that this condition on yjy requires that the ratio x/x, be negligibly small (i.e., a fast reaction) and that the ratio mkG/kL = mkdkLfy be less than 0.05 everywhere in the apparatus. The ratio mk^kLfy will be small if the equilibrium backpressure of the solute over the liquid is small (i.e., small m or high reactant solubility), or the reaction enhancement factor ^ = kL/kL is very large, or both. The reaction enhancement factor ^ will be large for all extremely fast pseudo-first-order reactions and will be large for extremely fast second-order irreversible reaction systems in which there is sufficiently large excess of liquid reagent.
Figure 14-12, case (ii), illustrates the gas-film and liquid-film concentration profiles one might find in an extremely fast (gas-phase mass-transfer-limited), second-order irreversible reaction system. The solid curve for reagent B represents the case in which there is a large excess of bulk liquid reagent B0. Figure 14-12, case (iv), represents the case in which the bulk concentration B0 is not sufficiently large to prevent the depletion of B near the liquid interface.
Whenever these conditions on the ratio yjy apply, the design can be based upon the physical rate coefficient kG or upon the height of one gas-phase mass-transfer unit HG. The gas-phase mass-transfer-limited condition is approximately valid for the following systems: absorption of NH3 into water or acidic solutions, absorption of H2O into concentrated sulfuric acid, absorption of SO2 into alkali solutions, absorption of H2S from a gas stream into a strong alkali solution, absorption of HCl into water or alkaline solutions, or absorption of Cl2 into strong alkali solutions.
When the liquid-phase reactions are extremely slow, the gas-phase resistance can be neglected and one can assume that the rate ofreac-tion has a predominant effect upon the rate of absorption. In this case the differential rate of transfer is given by the equation dnA = RAfHS dh = (k<la/pL)(ci — c)S dh
where nA = rate of solute transfer, RA = volumetric reaction rate (function of c and T), fH = fractional liquid volume holdup in tower or apparatus, S = tower cross-sectional area, h = vertical distance, kl = liquid-phase mass-transfer coefficient for pure physical absorption, a = effective interfacial mass-transfer area per unit volume of tower or apparatus, pL = average molar density ofliquid phase, c, = solute concentration in liquid at gas-liquid interface, and c = solute concentration in bulk liquid.
Although the right side of Eq. (14-66) remains valid even when chemical reactions are extremely slow, the mass-transfer driving force may become increasingly small, until finally c ~ c,. For extremely slow first-order irreversible reactions, the following rate expression can be derived from Eq. (14-66):
where k1 = first-order reaction rate coefficient.
For dilute systems in countercurrent absorption towers in which the equilibrium curve is a straight line (i.e., y, = mx,), the differential relation of Eq. (14-66) is formulated as dnA = —GmS dy = kjcfuS dh
where GM = molar gas-phase mass velocity and y = gas-phase solute mole fraction.
Substitution of Eq. (14-67) into Eq. (14-68) and integration lead to the following relation for an extremely slow first-order reaction in an absorption tower:
In Eq. (14-69) subscripts 1 and 2 refer to the bottom and top of the tower, respectively.
As discussed above, the Hatta number NHa usually is employed as the criterion for determining whether a reaction can be considered extremely slow. A reasonable criterion for slow reactions is
where DA = liquid-phase diffusion coefficient of the solute in the solvent. Figure 14-12, cases (vii) and (viii), illustrates the concentration profiles in the gas and liquid films for the case of an extremely slow chemical reaction.
Note that when the second term in the denominator of the exponential in Eq. (14-69) is very small, the liquid holdup in the tower can have a significant influence upon the rate of absorption if an extremely slow chemical reaction is involved.
When chemical equilibrium is achieved quickly throughout the liquid phase, the problem becomes one of properly defining the physical and chemical equilibria for the system. It is sometimes possible to design a tray-type absorber by assuming chemical equilibrium relationships in conjunction with a stage efficiency factor, as is done in distillation calculations. Rivas and Prausnitz [AIChEJ., 25, 975 (1979)] have presented an excellent discussion and example of the correct procedures to be followed for systems involving chemical equilibria.
Traditional Design Method The traditional procedure for designing packed-tower gas absorption systems involving chemical reactions makes use of overall mass-transfer coefficients as defined by the equation
where KGa = overall volumetric mass-transfer coefficient, ua = rate of solute transfer from the gas to the liquid phase, hT = total height of tower packing, S = tower cross-sectional area, pT = total system pressure, and Ay°m is defined by the equation
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