Mass Transfer in Tray Columns

Several different efficiency terms will be used in this section, and the one ultimately needed for design is overall column efficiency  

The efficiency of a distillation columu depends on three sets of design parameters  

The geometry of the contacting device and how it influences the intimate interaction of vapor and liquid. 

It is dear that each of these parameters is not completely independent of the others and that the designer may not have much control over all of them. Still, it is convenient to consider efficiency from these three viewpoints and there are optimum approaches to combining them. 

Since conditions vary throughout the column, it is more fbndamental to deal with a tray efficiency. 

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Fair reports that the data for mass transfer in spray, packed, and tray columns can be used for heat-transfer calculations for these columns. The pressure drop in these types of columns is usually quite low. 

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 fact, through use of matrix models of mass transfer in multicomponent systems (as opposed to effective diffusivity methods) it is possible to develop methods for estimating point and tray efficiencies in multicomponent systems that, when combined with an equilibrium stage model, overcome some of the limitations of conventional design methods. The purpose of this chapter is to develop these methods. We look briefly at ways of solving the set of equations that model an entire distillation column and close with a review of experimental and simulation studies that have been carried out with a view to testing multicomponent efficiency models. 

This fundamental study, which also serves as an excellent example of the analogy between mass and heat transfer, only gives the kt or kc values for the flow conditions in tray columns, i.e. for flow processes, in which the particle size is set in, or in the immediate neighborhood of the sparger. 

The internal flow of liquid and vapor must be re-evaluated from the standpoint of column capacity, both in the design and performance studies of columns. The physical dimensions of a column can handle only limited ranges of vapor and liquid flow rates. The objective of this chapter is to evaluate the hydraulic aspects of fluid flow in trayed columns. The column performance is examined with regard to factors such as flooding, entrainment, pressure drop, mass transfer, and tray efficiency. 

The simplified tray model assumes idealized hydraulic conditions that enhance mass transfer (high tray efficiency) and maintain a low vapor pressure drop. Proper tray design aims at minimizing the effect of factors that tend to diminish good tray hydraulics. Inefficient performance may either be inherent in the tray type or design for a particular situation or may be the result of operating the column outside the design conditions. A look at some of these factors follows. 

The tray hydraulics model may be extended to include mass and heat transfer rates for calculating the liquid and vapor flow rates and compositions in trayed columns on the basis of a rate-based model. The objective is to more realistically represent the actual performance of the column by providing a basis for estimating a tray. For this approach to be practical, methods should be available for reliably predicting the mass and heat transfer rates. General rate-based models are also discussed in Chapter 15 for solving packed columns. 

Bubbles. Mass transfer between gas bubbles and a liquid phase is oF importance in a variety of operations—gas-liquid reactions in agitated vessels, aerobic reimamaiions, aed absorption or distillation in tray columns. As in liquid-liquid transfer, dispersion of a phase into small units greatly increases tha avtalable area for transfer. If the fractional holdup (volume gas/total volume) of the gas in a gas-liquid mixture is Hs, the imerfacial area par unit volume for bubbles of diameter dB is given by... 

Lee and Dudukovic [18] described an NEQ model for homogeneous RD in tray columns. The Maxwell-Stefan equations are used to describe interphase transport, with the AIChE correlations used for the binary (Maxwell-Stefan) mass-transfer coefficients. Newton s method and homotopy continuation are used to solve the model equations. Close agreement between the predictions of EQ and NEQ models were found only when the tray efficiency could correctly be predicted for the EQ model. In a subsequent paper Lee and Dudukovic [19] presented a dynamic NEQ model of RD in tray columns. The DAE equations were solved by use of an implicit Euler method combined with homotopy continuation. Murphree efficiencies calculated from the results of an NEQ simulation of the production of ethyl acetate were not constant with time. 

In tray columns the first mechanism is dominant. This can lead to a large number of different steady state solutions for a given set of operating conditions. If N is the number of steady states (typically an odd number). Then (N + l)/2 of these steady states are stable. This can lead to complex multi-stable dynamic behavior during column startup and set-point or load changes. These phenomena were observed for vanishing as well as for finite intra-particle mass transfer resistance. An example with a total number of six trays (two reactive and two non-reactive trays plus reboiler and condenser) is shown in Fig. 10.16 for the well-known MTBE process. In contrast to the previous section, the column is now operated in the kinetic... 

Liquid maldistribution affects mass transfer efficiency of columns. However, in tray columns maldistribution is restricted to a single tray since the hquid is well mixed in the subsequent downcomer and evenly redistributed to the next tray. In this respect, tray columns are better suited for large diameter columns than packed... 

Lurgi, in collaboration with Siid-Chemie, developed a solid alkylation process based on a reactive distillation reactor (241). The distillation trays are used as reaction steps, with lateral staged olefin feed, and the catalyst pellets are not fixed but slurried within the liquid hydrocarbons. Vaporization of the reactive mixture at the bottom of the column reactor is used to dissipate the heat of reaction while it provides a rising vapor, which favors the required turbulence for a good mass transfer in the multiphase system. Recent sources indicated that the process is not commercially offered at the moment. 

The multiple phase contact inside the column is promoted by internal mass transfer equipment. Three groups of mass transfer equipment are commonly differentiated, which are separation trays, random packings and structured packings. Besides mass transfer equipment, further column internals are required in rectification to ensure the proper operation of the mass transfer equipment. Such internals may include support and hold-down plates, liquid distributors and redistributors, vapour distributor devices, gas-liquid phase separators and liquid collectors that usually do not participate on mass transfer. 

Overall liquid-phase mass transfer coefficient in tray column,... 

In the distillation column tray, the species concentration is decreasing from inlet to the outlet weir, i.e., under negative gradient. The positive u d means that the diffusion of turbulent mass flux u d is consistent with the bulk mass flow and promotes the mass transfer in x direction. 

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. 

As shown in Fig. 13-92, methods of providing column reflux include (a) conventional top-tray reflux, (b) pump-back reflux from side-cut strippers, and (c) pump-around reflux. The latter two methods essentially function as intercondenser schemes that reduce the top-tray-refliix requirement. As shown in Fig. 13-93 for the example being considered, the internal-reflux flow rate decreases rapidly from the top tray to the feed-flash zone for case a. The other two cases, particularly case c, result in better balancing of the column-refliix traffic. Because of this and the opportunity provided to recover energy at a moderate- to high-temperature level, pump-around reflirx is the most commonly used technique. However, not indicated in Fig. 13-93 is the fact that in cases h and c the smaller quantity of reflux present in the upper portion of the column increases the tray requirements. Furthermore, the pump-around circuits, which extend over three trays each, are believed to be equivalent for mass-transfer purposes to only one tray each. Bepresentative tray requirements for the three cases are included in Fig. 13-92. In case c heat-transfer rates associated with the two pump-around circuits account for approximately 40 percent of the total heat removed in the overhead condenser and from the two pump-around circuits combined. 

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