Overall Column Tray Efficiency

Tbe best-established theoretical method for predicting E is that of tbe AlCbE [Buhhle-Tray Design Manual, American Institute of Chemical Engineers, New York, 1958). It is based on tbe sequential prediction of point efficiency, Murpbree efficiency, and overall column efficiency ... 

After actual theoretical trays are determined (see Actual reflux and theoretical stages) one needs to estimate the actual physical number of trays required in the distillation column. This is usually done by dividing the actual theoretical trays by the overall average fractional tray efficiency. Then a few extra trays are normally added for offload conditions, such as a change in feed composition. 

Biddulph [90] emphasizes the importance of using point efficiencies rather than tray efficiencies or overall column efficiencies, due to the wide fluctuations that often exist. 

The reboiler is considered 100% efficient, and likewise any partial condenser, if used. Therefore the value Nq represents the theoretical trays or stages in the column proper, excluding the reboiler and partial condenser. Eq represents the overall tray efficiency for the system based upon actual test data of the same or similar systems, or from the plot of Figure 8-29, giving operating information preference (if reliable). 

Mols of distillate or overhead product, lb mols/hr or batch distillation, mols Mols component, i, in distillate Vaporization efficiency of steam distillation Overall column efficiency Overall tray efficiency Eqg = Murphree point efficiency, fraction Murphree plate/tray efficiency, = E ... 

Unfortimately, the efficiencies for tray and overall column operation are incomplete and nullify to a certain extent some very high quality theoretical performance design. Tray efficiencies may be estimated by Figure 8-29 or Table 8-11. 

Stirred tanks are modeled assuming that both phases are well mixed. Tray columns are usually modeled as well mixed on each tray so that the overall column is modeled as a series of two-phase, stirred tanks. (Distillation trays with tray efficiencies greater than 100% have some progressive flow within a tray.) When reaction is confined to a single, well-mixed phase, the flow regime for the other phase makes little difference but when the reacting phase approximates piston flow, the flow regime in the other phase must be considered. The important cases are where both phases approximate piston flow, either countercurrent or cocurrent. 

As with distillation, the correlation for overall tray efficiency for absorbers, given in Equation 10.7, should only be used to derive a first estimate of the actual number of trays. More elaborate and reliable methods are available, but these require much more information on tray type and geometry and physical properties. If the column is to be packed, then the height of the packing is determined from Equation 9.64. As with distillation, the height equivalent of a theoretical plate (HETP) can vary... 

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],... 

Overall column efficiency can be calculated from the Murphree tray efficiency by using the relationship developed by Lewis [Ind. Eng. Chem. 28, 399 (1936)]. 

Efficiency (overall column efficiency) Ratio of the number of theoretical stages required to effect a distillation separation to the number of actual trays. 

Distillation stage calculations are usually performed with ideal stages, The number of ideal stages required for the separation is divided by the overall column efficiency (Sec, 7,1,1) to obtain the required number of trays. In packed towers, the number of stages in the column is multiplied by the HETP (Height Equivalent of a Theoretical Plate, see Sec. 9.1,2) to obtain the packed height. 

Alternative definitions of tray efficiency are sometimes used. Lockett (12) reviewed the pros and cons of several efficiency definitions. He cited the industry s experience that the more rigorous and theoretically correct a definition is, the more difficult it is to use, For instance, the Standart efficiencies are often considered the soundest fundamentally, but apparently have never been used for a design. For the design and operation engineer, the overall column (or section) efficiency is by far the most important. 

The effective slope of the equilibrium curve, m, and therefore A. [Eq. (7.5)1 differs for each component. Therefore, each component has a different ratio of gas-phase resistance to liquid-phase resistance [Eq. (7.13)] and a different ratio of overall column efficiency to Murphree tray efficiency [Eq. (7.4)]. 

Example 2 Estimation of overall column efficiency. A continuous fractionation unit has been designed to operate on a liquid feed containing components, A, B, C, and D. Calculations have shown that 20 theoretical stages are necessary in the column, not including the reboiler. On the basis of the following data, estimate the overall column efficiency and the number of actual trays needed in the column by (a) Fig. 16-9, (b) Eq. (4), and (c) Eq. (6) ... 

Determine the effects of the physical properties of the system on column efficiency. Tray efficiency is a function of (1) physical properties of the system, such as viscosity, surface tension, relative volatility, and diffusivity (2) tray hydraulics, such as liquid height, hole size, fraction of tray area open, length of liquid flow path, and weir configuration and (3) degree of separation of the liquid and vapor streams leaving the tray. Overall column efficiency is based on the same factors, but will ordinarily be less than individual-tray efficiency. 

The actual number of stages is equal to the number of equihbrimn stages divided by the fractionator efficiency(overall column efficiency). Although the tray efficiency will vary, we will use the fractionator efficiency. The fiactionator efficiency is obtained from the O Coimel correlation given in Figure 6.17. Vital et al. [46] have reviewed and tabulated fractionator and absorber efficiencies for many systems. These data may help to arrive at a reasonable fractionator efficiency. 

The calculated point efficiency must be converted to overall column efficiency, which will lower its value and make it closer to the O Connell prediction. The calculated value of Eog is slightly higher than obtained experimentally (Eog = 0.83-0.92) at the University of Delaware for bubblecap trays (Annual Progress Report of Research Committee, Tray Efficiencies in Distillation Columns, AIChE, New York, 1955). 

An efficiency is a measure of how close to the equilibrium separation the real column or tray comes. The simplest and still a widely used approach is to use an overall column or section efficiency defined by... 

Overall column or section efficiencies are complicated functions of tray design, fluid properties, and operating conditions. Some empirical correlations of overall column efficiency have been developed but are capable only of rough estimates of efficiency that may at best be useful in preliminary design studies (Lockett, 1986). 

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