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Simultaneous Determination of Mass Transfer Coefficient and of Gas and Liquid Axial Dispersions and Holdups in a Packed Absorption Column by Dynamic Response Method V. Llnek," P. Bene& J. Slnkule, and 2. Kilvskq Institute of Chemical Technology, Department of Chemlcal Engineering, 16628 Prague 6, Czechoslovakia
Oxygen was desorbed from air-saturated water into a nitrogen stream at various water and gas flow rates in a countercurrent 0.139-m diameter absorption column packed with 15-mm ceramic Raschig rings. Oxygen concentrations in the two phases at the column outlet were monitored by oxygen probes to determine the response to a sudden oxygen concentration change in the inlet gas. A model of axial dispersive flow in both phases has been used. Values of fie empirical parameters (two give residence times of the two phases, two others characterize longitudinal mixing in the two phases, and the fifth expresses the intensity of interfacial mass transfer) were determined by the least-squares technique. The extent of axial dispersion was greater in the liquid phase than in the gas phase. Longitudinal mixing of the liquid phase has a significant effect on the mass transfer coefficient. The difference between apparent and true liquid phase mass transfer coefficients approached 50% of the apparent values.
Introduction Axial mixing of phases in packed absorption columns decreases the local values of the concentration driving force of interfacial mass transfer in comparison with those driving force values attained during plug flow of the phases through the apparatus (i.e., in the absence of longitudinal mixing). Hence, axial mixing also decreases the overall efficiency of absorption columns. In current practice of packed absorption column designing, it is commonly assumed that the two phases are passing through the apparatus by piston flow, and axial dispersion is ignored. Theoretical studies (Danckwerts, 1953; Miyauchi and Vermeulen, 1963) show that this can lead to unsafe design, since the design height of the apparatus may be calculated too low. Experimental data on the effect of longitudinal mixing on the mass transfer in packed absorption columns are scarcely represented in the literature (Brittan and Woodburn, 1966; Brittan, 1967; Woodburn, 1974; M a t h u and Wellek, 1976; Dunn et al., 1977). Only the effect of axial mixing of the gas phase on COBabsorption into water was studied. This effect appeared to be especially strong at high liquid/gas ratios. However, the experimental techniques used did not permit a simultaneous examination of the effect of longitudinal mixing of the liquid phase, even though this, as has recently been demonstrated, e.g., by Dunn et al. (1977), is much more intensive than is longitudinal mixing of the gas phase. Nevertheless, even this modest amount of available experimental data makes it clear that reliable values of the interfacial mass transfer coefficient cannot be obtained unless the effect of simultaneous longitudinal mixing of both phases is taken into account in the evaluation. A number of models have been postulated to describe the mixing characteristics observed in continuous flow equipment, but the axial diffusion model appears to be a satisfactory representation of the process (Brittan and Woodburn, 1966). This model has been employed in our study. This approach assumes that the various factors causing axial mixing can be described by a diffusion-type process superimposed on plug flow. This is an idealized situation, and thus correspondence between the data and the theoretical equation with suitable values of parameters involved does not necessarily prove that the model truly 00 19-7874/78/ 10 17-0298$01.OO/O
represents the physical situation. Methods were described (Brittan, 1967; Rod, 1965) of the simultaneous determination of gas axial dispersion coefficient and interphase mass transfer coefficients from a steady-state axial gas concentration profile. However, these methods disregard axial mixing of the liquid phase. Their application in simultaneously determining the interfacial mass transfer coefficient and the axial dispersion coefficients in both phases would be very demanding experimentally. It would in fact be necessary to obtain average values of the concentration of the component in each phase for several column cross sections. This is why our attention has been directed toward dynamic methods, based on studying the system response to a well-defined input disturbance. A sudden concentration change of the transferable component in the gas stream at the column inlet has been used here. The concentrations of this component in the two phases at the column outlet were the responses studied. In comparison with the static method, the dynamic measurements thus performed have the advantage of establishing, in addition, the holdups of both phases in the apparatus from the responses. The dynamic method also avoids the difficulties involved in determining the average concentration of the component in the streams, and there is no hampering with the column packing because of inserted concentration probes. The aim of this work is to apply the dynamic method for determining gas and liquid axial dispersion coefficients and holdups as well as the interfacial mass transfer coefficient in the absorption of a sparingly soluble gas (oxygen in water) in a packed absorption column. Theoretical The following assumptions were made in deriving the relationships shown below: (i) the flow pattern is represented by a superimposition of an axial diffusion mechanism on plug flow of the fluids through the packed column; (ii) the interfacial mass transfer coefficient is time independent and is constant along the column; (iii) radial distribution of concentration is uniform in both phases; (iv) absorption is isothermal and isobaric; (v) the flow rates of both phases are constant along the column; and (vi) the 0 1978 American Chemical Society
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continuity is observed in contrast to the situation at the inlets. For purposes of numerical solution of the set of eq 3-8, it is expedient to introduce identical dimensionless time for the gas and the liquid phases and to introduce dimensionless concentrations x g = cg/cg(l+);
XI
= cl/(mcg(l+))
Then the set of equations will assume the form
‘ Figure 1. Schematic axial concentration profiles. The coordinate system.
axg -- -1- a2xg axg _ +-
aTg
Pg 8 2 2
aZ
equilibrium relation is linear. Then the following mass balance can be written for an infinitesimal column section
The coordinate system used is shown in Figure 1. The balance (1)and (2) can be further simplified for absorption of poorly soluble gas. Here the absorption-due component concentration change in gas is negligible and the last term of eq 1 can be omitted. The resistance to interfacial mass transfer of poorly soluble gases is usually concentrated in the liquid phase, and therefore the mass transfer coefficient Kl is equal to the liquid phase mass transfer coefficient kl. Hence, from eq 1 and 2 we obtain (3)
Assume that streams having zero concentration of the transferable component were being introduced into the column a t times t < 0. This concentration is changed suddenly in the gas stream at column inlet at t = 0. Assume further that there exists only a convective mass transfer with the environment. The boundary conditions for such systems vvere the subject of discussions (Danckwerts, 1953; Wehner and Wilhelm, 1956; Bischoff, 1961), and usually a simple form of Danckwerts’ boundary conditions for closed systems is used. Then the appropriate boundary and initial conditions are
cg(1+,TgI O ) = cg(l+)
(7)
= c,(Z,O)
(8)
Cl(2,O)
=0
The physical meaning of the boundary conditions used is illustrated in Figure 1, which shows the concentration distributions for individual streams in the column. The concentration of each entering stream (directions of flow indicated by arrows) will abruptly rise (liquid) or drop (gas) on entry into the column, owing to axial dispersion taking place only inside the clolumn. The concentration patterns become flat as they approach the outlets, and no dis-
The parameter values Pg,P,, rg,A , and K of the model must be found so that the responses xg(O,Tg)and xl(l,Tg) (obtained by numerical integration of the set of eq 10-14) would fit onto the experimentally determined probe responses. Of course, the probes used have their inherent dynamics. Therefore, the concentrations x (O,Tg) and xl(l,Tg),as calculated from the model, have been recalculated to involve the effect of probe dynamics. An oxygen probe of the polarographic type with a membrane-covered solid electrode system as described elsewhere (Cerkasov, 1974; Linek and Benes, 1977) operates on the basis of reducing oxygen at the cathode and measuring the resulting current. Mass transfer is obviously important to the operation of such an analyzer since the instrument reading shows the proportionality of the oxygen flux to the cathode. A resistance to oxygen transfer may occur in any of the following regions: the stagnant liquid film at the outer side of the membrane, the membrane, and the electrolyte layer before the cathode. It was shown (Linek and Vacek, 1977) that the instrument’s response speed is described satisfactorily by a linear equation of nonsteady-state oxygen diffusion across the probe membrane with appropriate boundary and initial conditions. Hence, the probe response Y ( t )to an arbitrary change in oxygen concentration X ( t ) taking place in the bulk of liquid before the probe membrane can be calculated, according to the superimposition principle of solutions of the linear equations, from the probe response G’ to the sudden concentration change by the formula
Appropriate relationships for the probe responses G’ as derived for various operating conditions and oxygen probe designs can be found in the literature. A survey of these relationships is presented in Table I. They always contain AO, kl, k2. some of the following parameters: H , HI, H2, The parameters Hicharacterize the effect on probe dynamics of the liquid film resistance before the probe membrane. They are defined as the ratio of the membrane resistance against oxygen transfer and the resistance of the liquid film before the membrane. For a one-region model, its value (H)can be calculated from the probe readings in air, M:, in nitrogen, Mgn,and in the air-saturated liquid
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Table I. Normalized Responses G1 of Oxygen Probes to Step Concentration Change
Detail A
I
l
l
.-Ll-c'
One-Region Model (Linek and Vacek, 1976, 1977) 00
G 1= 1 - C z, Qn exp(-Ynklt) n=i
Two-Region Model (Linek and Bene;, 1977) m
GI = 1 - AOC, I: Q I nexp(-Ylnklt) n=i
(1 - Ao)Cz
n= 1
Qzn exP(-Yznkzt)
roots of equation: p cot 0 = Hi
pin are positive
Values of Constants Ci, &in, and Yin Hi-+ C:
-2
2 t 2H;
Thermostot8ng
Hi= 0
O
