Mass transfer tray efficiency

Mass transfer. Tray efficiency increases with pressure in the froth regime (118,119), but decreases with increased pressure in the emulsion regime (44,104,105). The efficiency decrease in the emulsion regime is caused by the greater vapor recycle (44,104,105). In general, there is otherwise little difference between mass transfer in the froth and emulsion regimes. 

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. 

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. 

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. 

Tray Efficiencies in Plate Absorbers and Strippers Compn-tations of the nnmber of theoretical plates N assnme that the hqnia on each plate is completely mixed and that the vapor leaving the plate is in eqnihbrinm with the liqnid. In actnal practice a condition of complete eqnihbrinm cannot exist since interphase mass transfer reqnires a finite driving-force difference. This leads to the definition of an overall plate efficiency... 

Mass-transfer theory indicates that for trays of a given design the factors most hkely to inflnence E in absorption and stripping towers are the physical properties of the flnids and the dimensionless ratio Systems in which the mass transfer is gas-film-controlled may be expected to have plate efficiencies as high as 50 to 100 percent, whereas plate efficiencies as low as 1 percent have been reported for the absorption of gases of low sohibility (large m) into solvents of relatively high viscosity. 

Tray efficiency 0 j is supposed to represent a measure of the deviation from equilibrium-stage mass transfer assuming backmixed trays. However, the estimate of tray efficiency requires accurate knowledge of the equihbrium vaporization constant. Any deviations between the actual equihbrium relation and that predicted by the database will be embodied in the tray efficiency estimate. It is a tender trap to accept tray efficiency as a true measure of the mass transfer hmitations when, in fact, it embodies the uncertainties in the database as well. 

Distillation design is based on the theoretical consideration that heat and mass transfer from stage to stage (theoretical) are in equilibrium [225-229]. Actual columns with actual trays are designed by establishing column tray efficiencies, and applying these to the theoretical trays or stages determined by the calculation methods to be presented in later sections. 

Example 8-42 Mass Transfer Efficiency Calculation for Baffle Tray Column (used by permission [211])... 

HETP is another quantity that is used to express the efficiency of a device for carrying out a separation, particularly in which mass is transferred by a stage-wise action rather than a differential contact. For example, in a tray column, the HETP value is the tray spacing divided by the fractional overall tray efficiency. 

As might be expected, the vapour phase may offer the controlling resistance to mass transfer in high pressure distillations. Values for tray efficiencies at elevated pressure are scarce [23, 24]. The prediction of tray efficiency may be approached in several ways. One way is to utilize field performance data taken for the same system in very similar equipment. Unfortunately such data are seldom available. When they are available, and can be judged as accurate and representative, they should be used as a basis for efficiency specification [25], Another way is to utilize laboratory-or pilot-plant efficiency data. For example a small laboratory-Oldershaw tray-column can be used with the same system. Of course, the results must be corrected for vapour-and liquid mixing effects to obtain overall tray efficiencies for large-scale design [26], Another approach is the use of empirical or fundamental mass-transfer models [27-30],... 

In spite of all the effort that has been expended on this topic, the prediction of mass transfer efficiency still is not on a satisfactory basis. The relatively elaborate method of the AIChE Bubble-Tray Manual (AIChE, New York, 1958) is based on the two-film theory but has not had a distinguished career. A number of simpler correlations have been proposed and have some value as general guidance. That literature has been surveyed recently by Vital, Grossel, and Olsen [Hyd. Proc., 55-56 (Oct. 1984) 147-153 (Nov. 1984) 75-78 (Dec. 1984)]. 

Flooding, holdup, and mass transfer rates are highly interdependent and are not simply related. Reissinger and Schroter (1978) state that tray towers in comparison with other types have good efficiencies at 60 nr /m2 hr at frequencies of 60-90/min and amplitudes of 10 mm. Packed towers have about 2/3 the capacities of tray towers. Also in comparison with unagitated towers, which are limited to interfacial tensions below lOdyn/cm, pulsed towers are not limited by interfacial tension up to 30-40 dyn/cm. Some... 

In this chapter we have presented multistage systems with special emphasis on absorption processes. We have studied multitray countercurrent absorption towers with equilibrium trays for both cases when the equilibrium relation is linear and when it is nonlinear. This study was accompanied by MATLAB codes that can solve either of the cases numerically. We have also introduced cases where the trays are not efficient enough to be treated as equilibrium stages. Using the rate of mass transfer RMT in this case, we have shown how the equilibrium case is the limit of the nonequilibrium cases when the rate of mass transfer becomes high. Both the linear and the nonlinear equilibrium relation were used to investigate the nonequi-librium case. We have developed MATLAB programs for the nonequilibrium cases as well. 

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