Transfer Coefficient in a Tray Column

Example 11 Mass-Transfer Coefficient in a Tray Column... 

A mixture of ethanol(l)-t-butyl alcohol(2)-water(3) is being distilled in a sieve tray column operating in the froth regime. Estimate the mass transfer coefficients in a dispersion... 

Plate efficiency is a function of the rate of mass transfer between liquid and vapor. The prediction of mass-transfer coefficients in sieve trays and their relationship to plate efficiency are discussed in Chap. 21. Some published values of the plate efficiency of a 1.2-m column are shown in Fig. 18.34. This column had sieve trays with 12.7-mm holes and 8.32 percent open area, a 51-mm weir height, and... 

The nonequilibrium stage in Figure 14.1 may represent either a single tray or a section of packing in a packed column. In the models described in this chapter the same equations are used to model both types of equipment and the only difference between these two simulation problems is that different expressions must be used for estimating the binary mass transfer coefficients and interfacial areas. 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

The numerical case given is fgr a 20-tray column with 10 trays in the stripping section. A constant relative volatility of 2 1 used. The column steadystate profile is given in Table 12.3, together with the values of coefficients and the transfer functions in terms of log modulus (decibels) and phase angle (degrees) at frequencies from 0 to 10 radians per minute. The values at zero frequency are the steadystate gains of the transfer functions. 

Domenech and Enjalbert (1974) carried out a series of experimental tests in a laboratory batch distillation column. A binary mixture of Cyclohexane and Toluene was considered for the purpose. The experimental equipment used was a perforated plate column, with 4 trays and a 60 litre reboiler heated with a heat transfer coefficient of 3 kw. The experimental results obtained by Domenech and Enjalbert together with column input data are presented in Table 4.5. 

The number of equations, M5C + 1), for a large number of trays and components, can be excessive. The global Newton method will suffer from the same problem of requiring initial values near the answer. This problem is aggravated with nonequilibrium models because of difficulties due to nonideal if-values and enthalpies then compounded by the addition of mass transfer coefficients to the thermodynamic properties and by the large number of equations. Taylor et al. (80) found that the number of sections of packing does not have to be great to properly model the column, and so the number of equations can be reduced. Also, since a system is seldom mass-transfer-limited in the vapor phase, the rate equations for the vapor can be eliminated. To force a solution, a combination of this technique with a homotopy method may be required. 

As noted above, a number of equipment parameters must normally be specified so that the mass transfer coefficients can be estimated correctly. For example, the diameter of all columns must be known. For trayed columns, the tray type, weir height, liquid flow path length, and bubbling area must be known for packed columns, the packing type, size, and material must be known. It may also be necessary to allow for different diameters, tray or packing type, or other tray or packing parameters in different parts of the same column. 

The actual process flow rates are important in nonequilibrium model simulations, whereas in most equilibrium stage simulations, a simulation with a feed flow rate of 1 unit is as meaningful as a simulation with a feed flow of 10, 100, or 573 units. In real columns the flow rates influence the mass transfer coefficients as well as the tray hydraulics. An inappropriate flow specification may mean the column will flood or, just as likely, dump all the liquid through the holes in the tray. Thus, it is important to ensure that the specified (or calculated) flows and tray or packing characteristics are consistent with the satisfactory operation of the column. 

A droplet containing a mixture of acetone(l)-benzene(2)-methanol(3) has a diameter of 8 mm and attains a velocity of 0.1 m/s in a sieve tray extraction column when it is dispersed in a continuous hydrocarbon phase. Use the penetration model to estimate the matrix of low flux mass transfer coefficients [A ] inside the droplet. 

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