Transfer units towers

Equation 39 can often be simplified by adopting the concept of a mass transfer unit. As explained in the film theory discussion eadier, the purpose of selecting equation 27 as a rate equation is that is independent of concentration. This is also tme for the Gj /k aP term in equation 39. In many practical instances, this expression is fairly independent of both pressure and Gj as increases through the tower, increases also, nearly compensating for the variations in Gj. Thus this term is often effectively constant and can be removed from the integral ... 

Gj /k aPh.3.s the dimension of length or height and is thus designated the gas-phase height of one transfer unit, The integral is dimensionless and indicates how many of these transfer units it takes to make up the whole tower. Consequently, it is called the number of gas-phase transfer units, N. Equation 40 may therefore be written as... 

Computation of Tower Height The required height of a gas-absorption or stripping tower depends on (1) the phase equilibria involved, (2) the specified degree of removal of the solute from the gas, and (3) the mass-transfer efficiency of the apparatus. These same considerations apply both to plate towers and to packed towers. Items 1 and 2 dictate the required number of theoretic stages (plate tower) or transfer units (packed tower). Item 3 is derived from the tray efficiency and spacing (plate tower) or from the height of one transfer unit (packed tower). Solute-removal specifications normally are derived from economic considerations. 

FIG. 14-5 Nnmher of overall gas-phase mass-transfer units in a packed absorption tower for constant mGf /LM solution of Eq. (14-23). (From Sherwood and Pigford, Absorption and Extraction, McGraw-Hill, New York, 1952. )... 

The HETP of a packed-tower section, valid for either distillation or dilute-gas absorption and stripping svstems in which constant molal overflow can be assumed and in which no chemical reactions occur, is related to the height of one overall gas-phase mass-transfer unit Hqc by the equation... 

Likewise, the height of a transfer unit based on raffinate-phase compositions is the height of tower divided by the number of transfer units [Eq. (15-30)]. 

Spray Towers These are simple gravity extractors, consisting of empty towers with provisions for introducing and removing liquids at the ends (see Fig. 15-32). The interface can be run above the top distributor, below the bottom distributor, or in the middle, depending on where the best performance is achieved. Because of severe axial back mixing, it is difficult to achieve the equivalent of more than one or two theoretical stages or transfer units on one side of the interface. For this reason they have only rarely been applied in extraction applications. 

Two dimensionless variables play key roles in the analysis of single transition systems (and some multiple transition systems). These are the throughput parameter [see Eq. (16-129)] and the number of transfer units (see Table 16-13). The former is time made dimensionless so that it is equal to unity at the stoichiometric center of a breakthrough cui ve. The latter is, as in packed tower calculations, a measure of mass-transfer resistance. 

The section on Performance provides a handy nomograph for quick cooling tower evaluation. More detailed analysis requires the use of transfer units. The performance analysis then asks two questions ... 

How many transfer units can the actual cooling tower or proposed new cooling tower actually perform ... 

Equation 3 Is quite accurate for calculating the number of transfer units for the example cooling tower... 

Calculate N,og and Table 1, from Predict the number of Transfer Units for Cooling Towers, by Kamal Adham Khodaparast, Chemical Engineering Progress, Vol. 88, No. 4, pp. 67-68 (1992). Reproduced by permission of the American Institute of Chemical Engineers. 1992 AlChE. ... 

N = number of trays (theoretical) or transfer units for a packed tower... 

UK. = Light key component in volatile mixture L/V = Internal reflux ratio L/D = Actual external reflux ratio (L/D) ,in = Minimum external reflux ratio M = Molecular weight of compound Mg = Total mols steam required m = Number of sidestreams above feed, n N = Number of theoretical trays in distillation tower (not including reboiler) at operating finite reflux. For partial condenser system N includes condenser or number theoretical trays or transfer units for a packed tower (VOC calculations) Nb = Number of trays from tray, m, to bottom tray, but not including still or reboiler Nrain = Minimum number of theoretical trays in distillation tower (not including reboiler) at total or infinite reflux. For partial condenser system,... 

The HETP (Height Equivalent to a Theoretical Plate (stage or plate)) is the tray spacing divided by the fractional overall tray efficiency [82]. The transfer unit concept has been useful for generalized correlations [89]. Because packed towers operate with continuously changing compositions through the packed height, the concept... 

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. 

Determine the number of transfer units, and the packed tower height. 

Pave = average total pressure in tower, atmospheres Hl = height of liquid film transfer unit, ft Hg = height of gas film transfer unit, ft a = effective interfacial area for contacting gas and liquid phases, ft /ft. Because this is very difficult to evaluate, it is usually retained as a part of the coefficient such as Kca, Ki a, kca, and k.La. 

The transfer unit concept is also applicable to distillation in packed towers. Height of the packing required is ... 

The height of the transfer unit has not been satisfactorily correlated for application to a wide variety of systems. If pilot plant or other acceptable data are available to represent the system, then the height of packing can be safely scaled-up to commercial units. If such data are not available, rough approximations may be made by determining Hg and Hl as for absorption and combining to obtain an Hqg (Ref. 74, pg. 330). This is only very approximate. In fact it is because of the lack of any volume of data on commercial units that many potential applications of packed towers are designed as tray towers. 

A benzene-toluene mixture is to be separated in a tower packed with 1-in. fieri saddles. The feed is 55.2 mol% (liquid feed, saturated), and an overhead of 90 mol% benzene, and bottoms of not more than 24 mol% benzene is desired. Using the data of Ref. 51 plotted in Figure 9-98, determine the number of transfer units in the rectifying and stripping sections using a reflux ratio (reflux to product, L/B) = 1.35. 

The number of transfer units or tower characteristic is based on overall heat and mass transfer ... 

Because the heat load, L, Ga and temperatures are known for an operating tower, its performance as represented by the number of transfer units, or tower characteristics can be determined. Solve Equation 9-129 for Ka V/L, or use the modified Merkel diagram, Figure 9-127. This is the number of transfer units operating in the tower. For relative comparison of Ka values see Figure 9-128. 

N = Number of transfer units N = Number of deck levels in cooling tower Nog = Number of transfer units, based on overall gas film coefficients... 

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