Transfer unit

The overall mass transfer coefficients KG and Kl can be related through Henry s Law, which states that 

Classical treatment of mass transfer is to consider a unit, of mass transfer as a measure of the interphase equilibrium changes needed to produce a desired degree of diffusion [13], This concept is best applied to the concept of a theoretical plate in distillation [4], Defining Gm as the gas superficial molar velocity (mole/hr/ft2 of tower cross section) and dy as the change of concentration of the diffusing species, then 

The molar flux expression (Equation 3.58) can thus be rewritten as follows  

Let a signify the surface area per cubic foot of tower (ft2/ft3). Then the total area is  

We will apply these definitions in Chapter 5 to analyzing cooling tower operations. At this point the reader should examine some of the problems at the end of this chapter to review some of the concepts discussed thus far. 

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 correspond to the process requirement  

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

Equation 1 is normally integrated by graphical or numerical means utilizing the overall material balance and the saturated air enthalpy curve. 

Khodaparast has provided an equation for Hs, that allows simpler evaluation of Equation 1  

The concept of a transfer unit is useful in the design of heat exchangers and in assessing their performance, since its magnitude is less dependent on the flowrate of the fluids than the heat transfer coefficient which has been used so far. The number of transfer units N is defined by  

Transfer units are also used extensively in the calculation of mass transfer rates in countercurrent columns and reference should be made to Chapter 10. 

For the case where G]C, = G2Cp2, it is necessary to expand the exponential terms to 

Effectiveness factors 37 are plotted against number of transfer units N with (Gi Cpj /GaCpj ) as parameter for a number of different configurations by Kays and London Examples 

A process requires a flow of 4 kg/s of purified water at 340 K to be heated from 320 K by 8 kg/s of untreated water which can be available at 380, 370, 360 or 350 K. Estimate the heat transfer surfaces of one shell pass, two tube pass heat exchangers suitable for these duties. In all cases, the mean heat capacity of the water streams is 4.18 kJ/kgK and the overall coefficient of heat transfer is 1.5 kW/m K. 

Consider a differential height of a packed distillation column of unit cross section as shown in Fig. 5.6 1, For component i. 

For equimolar countenKffusion (approximately the case for distillation). dV = dL, and for ent transfer of i from bulk vapor to the liquid interface. 

Note that this expression applies to the vapor phase only (transfer to the For overall transfer from the bulk vapor to fhe bulk liquid. interface from the bulk vapor). 

The tight sides of Eqs. (5.6-5) and (S.6-6) define the number of vapor-phase transfer units and the number of overall vapor-phase transfer units (vapor concentration basis), respectively. Thus, the required height 

FIGURE 5.6-f Flows in a differential section of a countercurrent contactor. 

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Transfer units Transformation Transformer oils Transformers... 

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... 

Hq and aie called the overall gas-phase height of a transfer unit and the number of overall gas-phase transfer units, respectively. In the case of a straight equiUbrium line, is often neady concentration-independent as explained earher. In such cases, use of equation 47 is especially convenient... 

To use all of these equations, the heights of the transfer units or the mass transfer coefficients and must be known. Transfer data for packed columns are often measured and reported direcdy in terms of and and correlated in this form against and... 

In these cases, a quantitative significance can be given to the concept of a transfer unit. Because Hqq = aP, it follows from equations 52 and 47... 

Therefore, in this case, one transfer unit corresponds to the height of packing required to effect a composition change just equal to the average driving force. 

I umber of Transfer Units. Eor relatively dilute systems the ratios involvingjgj, jy gj, and 1 — y approach unity so that the computation of from equation 50 and -Nq from equation 49 may be simplified to... 

Equation 55 is a tigoious expression for the number of overall transfer units for equimolar counterdiffusion, in distillation columns, for instance. 

NTU p is the "exterior apparent" overall gas-phase number of transfer units calculated neglecting axial dispersion simply on the basis of equation 56, whereas NTU stands for the higher real number of transfer units (Nq ) which is actually required under the influence of axial dispersion. The correction factor ratio can be represented as a function of those parameters that are actually known at the outset of the calculation... 

In these equations S denotes the stripping factor, Equation 77 is only vaUd for a sufftciendy high number of transfer units so that the correction... 

Rate of Mass Transfer in Bubble Plates. The Murphree vapor efficiency, much like the height of a transfer unit in packed absorbers, characterizes the rate of mass transfer in the equipment. The value of the efficiency depends on a large number of parameters not normally known, and its prediction is therefore difficult and involved. Correlations have led to widely used empirical relationships, which can be used for rough estimates (109,110). The most fundamental approach for tray efficiency estimation, however, summarizing intensive research on this topic, may be found in reference 111. 

To estimate the number of transfer units for design, the following empirical correlations which were derived from efficiency measurements employing a variety of trays and operating conditions under the aforementioned assumptions are recommended (111) ... 

The heights of a transfer unit ia each phase thus contribute to the overall heights of a transfer unit. Data on values of HTU for various types of countercurrent equipment have been reviewed (1,10). In normal operating practice, the extraction factor is chosen to be not greatiy different from unity, within the range of 0.5—2. 

This term is a measure of the unit s length. Sometimes it is referred to as the number of transfer units. This simply says that the optimum pressure drop increases as the heat exchanger gets longer, ie, has more transfer units. The forms of F, and F both foUow from the fact that in turbulent flow the... 

The Separation Stage. A fundamental quantity, a, exists in all stochastic separation processes, and is an index of the steady-state separation that can be attained in an element of the process equipment. The numerical value of a is developed for each process under consideration in the subsequent sections. The separation stage, which in a continuous separation process is called the transfer unit or equivalent theoretical plate, may be considered as a device separating a feed stream, or streams, into two product streams, often called heads and tails, or product and waste, such that the concentrations of the components in the two effluent streams are related by the quantity, d. For the case of the separation of a binary mixture this relationship is... 

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