Transfer units concentrated solutions

Example 11 Number Transfer Units—Concentrated Solutions... 

Determine the controlling resistance for mass transfer. For concentrated solutions, the ratio of the gas-phase driving force to that in the liquid phase in equivalent concentration units is... 

In these equations, the first term is a correction for finite liqiiid-phase concentrations, and the integral term represents the numbers of transfer units required for dilute solutions. It would be very unusual in practice to find an example in which the first (logarithmic) term is of any significance in a stripper design. 

Solution. For TGE in water, the Henry s law coefficient may he taken as 417 atm/mf at 20°G. In this low-concentration region, the coefficient is constant and equal to the slope of the eqnihhrinm hne m. The solnhility of TGE in water, based on H = 417, is 2390 ppm. Because of this low solnhility, the entire resistance to mass transfer resides in the liquid phase. Thus, Eq. (14-25) may he used to obtain Nql, the nnmher of overall hqnid phase transfer units. 

Whenever these conditions on the ratio yjy apply, the design can be based upon the physical rate coefficient /cg or upon the height of one gas-phase mass-transfer unit He- The gas-phase mass-transtor hmited condition is approximately vahd, for instance, in the following systems absorption oi NH3 into water or acidic solutions, vaporization of water into air, absorption of H9O into concentrated sulfuric acid solutions, absorption of SO9 into alkali solutions, absorption of H9S from a dllute-... 

The response of solute concentration in the raffinate to the sol-vent-to-feed ratio S /F can be calculated by Eqs. (15-26) and (15-27) for a constant number of transfer units based on the overall raffinate phase N r-... 

Figure 16-27 compares the various constant pattern solutions for R = 0.5. The curves are of a similar shape. The solution for reaction kinetics is perfectly symmetrical. The cui ves for the axial dispersion fluid-phase concentration profile and the linear driving force approximation are identical except that the latter occurs one transfer unit further down the bed. The cui ve for external mass transfer is exactly that for the linear driving force approximation turned upside down [i.e., rotated 180° about cf= nf = 0.5, N — Ti) = 0]. The hnear driving force approximation provides a good approximation for both pore diffusion and surface diffusion. 

The dominant mechanism of purification for column ciystallization of sohd-solution systems is reciystallization. The rate of mass transfer resulting from reciystallization is related to the concentrations of the solid phase and free hquid which are in intimate contac t. A model based on height-of-transfer-unit (HTU) concepts representing the composition profQe in the purification sec tion for the high-melting component of a binaiy solid-solution system has been reported by Powers et al. (in Zief and Wilcox, op. cit., p. 363) for total-reflux operation. Typical data for the purification of a solid-solution system, azobenzene-stilbene, are shown in Fig. 22-10. The column ciystallizer was operated... 

The above expression indicates that the number of overall mass transfer units, Nqg, is only controlled by the concentrations of the solute in the inlet and outlet gas streams. 

Since 1 is a monomer with low activity, copolymers 2 obtained at any stage of the copolymerization process, irrespective of the monomer ratio in the initial mixture, always contain a smaller amount of monomeric units of 1 than that in the corresponding monomer mixture. 1 being prone to enter the chain-transfer reaction, the increase of its content in the initial monomer mixture reduces substantially the reaction rate and decreases the molecular mass of the copolymers. It was found that copolymers 2 which contain 2—8% of monomeric units of 1 and are suitable for obtaining fibres must have a molecular mass between 45 000 and 50000. Such copolymers can be obtained with a AN 1 ratio in the initial mixture between 95 5 and 85 15. Concentrated solutions of copolymers, especially those with a molecular mass smaller than the above limit, are characterized by a very low stability which is a substantial shortcoming of these copolymers. 

The advantage of using the transfer unit in preference to the transfer coefficient is that the former remains much more nearly constant as flow conditions are altered. This is particularly important in problems of gas absorption where the concentration of the solute gas is high and the flow pattern changes in the column because of the change in the total rate of flow of gas at different sections. In most cases the coefficient is proportional to the flowrate raised to a power slightly less than unity and therefore the HTU is substantially constant. 

Clearly the concept of a stage has no meaning in such a tower. Instead, we deal with differential transfer units, which are a measure of the change in concentration per unit of difference in concentration (recall that the rate of extraction is determined largely by the difference between the actual and the equilibrium concentration of a solute, or driving force ). 

Use of HTU and K a Data In estimating the size of a commercial gas absorber or liquid stripper it is desirable to have data on the overall mass-transfer coefficients (or heights of transfer units) for the system of interest, and at the desired conditions of temperature, pressure, solute concentration, and fluid velocities. Such data should best be obtained in an apparatus of pilot-plant or semiworks size to avoid the abnormalities of scale-up. Within the packing category, there are both random and ordered (structured) packing elements. Physical characteristics of these devices will be described later. 

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