Packed towers mass-transfer coefficients

In 1966, in a paper that now is considered a classic, Danckwerts and Gillham [Tmns. Inst. Chem. Eng., 44, T42 (1966)] showed that data taken in a small stirred-ceU laboratoiy apparatus could be used in the design of a packed-tower absorber when chemical reactions are involved. They showed that if the packed-tower mass-transfer coefficient in the absence of reaction (/cf) can be reproduced in the laboratory unit, then the rate of absorption in the l oratoiy apparatus will respond to chemical reactions in the same way as in the packed column even though the means of agitating the hquid in the two systems might be quite different. 

When it is known that Hqg varies appreciably within the tower, this term must be placed inside the integr in Eqs. (5-277) and (5-278) for accurate calculations of hf. For example, the packed-tower design equation in terms of the overall gas-phase mass-transfer coefficient for absorption would be expressed as follows ... 

Traditional Design Method The traditionally employed conventional procedure for designing packed-tower gas-absorption systems involving chemical reactions makes use of overall volumetric mass-transfer coefficients as defined by the equation... 

According to this method, it is not necessaiy to investigate the kinetics of the chemical reactions in detail, nor is it necessary to determine the solubihties or the diffusivities of the various reactants in their unreacted forms. To use the method for scaling up, it is necessaiy independently to obtain data on the values of the interfacial area per unit volume a and the physical mass-transfer coefficient /c for the commercial packed tower. Once these data have been measured and tabulated, they can be used directly for scahng up the experimental laboratory data for any new chemic ly reac ting system. 

Danckwerts and Gillham did not investigate the influence of the gas-phase resistance in their study (for some processes gas-phase resistance may be neglected). However, in 1975 Danckwerts and Alper [Trans. Tn.st. Chem. Eng., 53, 34 (1975)] showed that by placing a stirrer in the gas space of the stirred-cell laboratoiy absorber, the gas-phase mass-transfer coefficient fcc in the laboratoiy unit could be made identical to that in a packed-tower absorber. When this was done, laboratoiy data obtained for chemically reacting systems having a significant gas-side resistance coiild successfully be sc ed up to predict the performance of a commercial packed-tower absorber. 

It would be desirable to reinterpret existing data for commercial tower packings to extract the individual values of the interfacial area a and the mass-transfer coefficients fcc and /c in order to facilitate a more general usage of methods for scaling up from laboratory experiments. Some progress in this direction has afready been made, as discussed later in this section. In the absence of such data, it is necessary to operate a pilot plant or a commercial absorber to obtain kc, /c , and a as described by Ouwerkerk (op. cit.). 

Principles of Rigorous Absorber Design Danckwerts and Alper [Trans. Tn.st. Chem. Eng., 53, 34 (1975)] have shown that when adequate data are available for the Idnetic-reaciion-rate coefficients, the mass-transfer coefficients fcc and /c , the effective interfacial area per unit volume a, the physical solubility or Henry s-law constants, and the effective diffusivities of the various reactants, then the design of a packed tower can be calculated from first principles with considerable precision. 

Inspection of Eqs. (14-71) and (14-78) reveals that for fast chemical reactions which are liquid-phase mass-transfer limited the only unknown quantity is the mass-transfer coefficient /cl. The problem of rigorous absorber design therefore is reduced to one of defining the influence of chemical reactions upon k. Since the physical mass-transfer coefficient /c is already known for many tower packings, it... 

The other major type is gas absorption of inorganic components in aqueous solutions. For this type design one uses mass transfer coefficients. Packed towers are used so often for this type that its discussion is often included under sections on packed towers. However, in this book it is included here. 

Overall Mass Transfer Coefficient C02/Na0H System Metal Tower Packings... 

Because the packed tower is a continuous contacting device as compared to the step-wise plate tower, performance capacity is expressed as the number of transfer units, N, the height of the transfer unit, H.T.U., and mass transfer coefficients K a and Kj a. Figure 9-68 identifies the key symbols and constant flow material balance. 

Water is to be cooled in a small packed column from 330 to 285 K by means of air flowing countercurrently. The rate of flow of liquid is 1400 cm3/m2 s and the flow rate of the air, which enters at a temperature of 295 K and a humidity of 60%, is 3.0 m3/m2 s. Calculate the required height of tower if the whole of the resistance to heat and mass transfer may be considered as being in the gas phase and the product of the mass transfer coefficient and the transfer surface per unit volume of column is 2 s-1. 

Ammonia is to be recovered from a 5 per cent by volume ammonia-air mixture by scrubbing with water in a packed tower. The gas rate is 1.25 m3/m2s measured at 273 K and 101.3 kN/m2 and the liquid rate is 1.95 kg/m2s. The temperature of the inlet gas is 298 K and the temperature of the inlet water 293 K. The mass transfer coefficient is Kaa = 0.113 kmol/m3s (mole ratio difference) and the total pressure is 101.3 kN/m2. What is the required height of the tower to remove 95 per cent of the ammonia. The equilibrium data and the heats of solutions are ... 

For purely physical absorption, the mass transfer coefficients depend on the hydrodynamics and the physical properties of the phases. Many correlations exist, for example that of Dwivedi Upadhyay (IEC Proc Des Dev 16 157, 1977) for packed towers,... 

Mass transfer coefficients have been obtained in a packed tower with 40% K2C03 (6.8 mols/liter of water) (Kohl Riesenfeld, Gas Purification, p 227, 1985). 

Mass transfer coefficients and specific area in packed towers... 

Molstad, M. C., McKinney, J. F. and Abbey, R. G. Trans. Am. Inst. Chem. Eng. 39 (1943) 605. Performance of drip-point grid tower packings, III. Gas-film mass transfer coefficients additional liquid-film mass transfer coefficients. 

To determine the mass-transfer rate, one needs the interfacial area in addition to the mass-transfer coefficients. The literature on tower packings, for example, normally reports kGpa values measured at very low inlet-gas concentrations, so that yBM — 1, and at a total pressure close to 1 atmosphere. Thus, the correct rate coefficient for use in packed-tower design involving the use of the driving force (y-y /yBM is obtained by multiplying the reported kGpa values by the value of Pj employed in the actual test unit (here 1 atm = 101.3 kPa) and not the... 

In another study of gas-side mass transfer-limited absorption involving S02 absorption into a sodium hydroxide solution using a wire screen packing, the overall mass transfer coefficient was found to be lower than reported data for packed towers (16). Replacing the wire screen packing with two parallel rotating plates significantly enhanced the mass transfer performance. 

In a countercurrent packed column, n-butanol flows down at the rate of 0.25 kg/m2 s and is cooled from 330 to 295 K. Air at 290 K, initially free of n-butanol vapour, is passed up the column at the rate of 0.7 m3/m2 s. Calculate the required height of tower and the condition of the exit air. Data Mass transfer coefficient per unit volume, hDa = 0.1 s 1. Psychrometric ratio, (h/hDpAs) = 2.34. Heat transfer coefficients, hL = 3hG. Latent heat of vaporisation of n-butanol, A = 590 kJ/kg. Specific heat capacity of liquid n-butanol, Cl = 2.5 kJ/kg K. Humid heat of gas , s = 1.05 kJ/kg K. 

The mass-transfer coefficients are taken from [14], assuming that they are the same order of magnitude in a packed bed and spray tower ... 

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