Actual Number of Theoretical Trays

An early observation by Underwood (Trans. Inst. Chem. Eng. 10, pp. 112-152, 1932) of the plate-reflux relation was 

The Gilliland correlation appears to be conservative for feeds with low values of 7 (the thermal condition of the feed), and can be in error when there is a large difference in tray requirements above and below the feed. The principal value of the correlation appears to be for preliminary exploration of design variables which can be refined by computer calculations. Although it is often used for final design, that should be done with caution. Other possibly superior but more difficult to use correlations have been proposed and are described in standard textbooks for example, Hines and Maddox (1985). 

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Underwood-GUliland Method) 395 Minimum Trays 395 Distribution of Nonkeys 395 Minimum Reflux 397 Operating Reflux 397 Actual Number of Theoretical Trays 397 Feed Tray Location 397... 

UK. = Light key component in volatile mixture L/V = Internal reflux ratio L/D = Actual external reflux ratio (L/D) ,in = Minimum external reflux ratio M = Molecular weight of compound Mg = Total mols steam required m = Number of sidestreams above feed, n N = Number of theoretical trays in distillation tower (not including reboiler) at operating finite reflux. For partial condenser system N includes condenser or number theoretical trays or transfer units for a packed tower (VOC calculations) Nb = Number of trays from tray, m, to bottom tray, but not including still or reboiler Nrain = Minimum number of theoretical trays in distillation tower (not including reboiler) at total or infinite reflux. For partial condenser system,... 

The most commonly used definition of efficiency is the overall efficiency, defined as the number of theoretical trays required for a separation divided by the number of actual trays. A theoretical tray is defined as a contacting stage for which the vapor and the liquid streams leaving would be in thermodynamic equilibrium. The overall efficiency is inexact because separation... 

Overall tray efficiency is defined as the number of theoretical trays required for a service divided by the number of actual trays. 

Cp specific heat F feed rate Hs tray spacing M mass flow Ni total number of trays Neq number of theoretical trays Nact number of actual trays AP pressure drop q latent heat Q heat content R tower reflux ratio... 

The number of theoretical trays is determined by stepping off the steps to give 2.4 theoretical trays. The actual number of trays is 2.4/0.25 = 9.6 trays. 

The number of theoretical trays required is obtained as before by stepping off the trays from the distillate to the bottoms. This gives the minimum number of trays that can possibly be used to obtain the given separation. In actual practice, this condition can be realized by returning all the overhead condensed vapor K, from the top of the tower back to the tower as reflux, i.e., total reflux. Also, all the liquid in the bottoms is reboiled. Hence, all the products distillate and bottoms are reduced to zero flow, as is the fresh feed to the tower. 

The system [Eq. (2.1) (2.4)] may have a large number of equations. First, the number of theoretical trays N may be enormous. Second, number of components n may also be very large. For example, petroleum contains thousands of components, which actually, for practical reasons, will be combined into tens of pseudocomponents (or fractions). 

We now repeat the second step, but this time draw the line through the new intercept, i.e., Xd/(R + 1) = 0.92/(0.9 + 1) = 0.48. This is the actual operating line to be used in stepping off the number of theoretical trays. 

The rich benzolized wash oil is stripped of its light oil content by fractional distillation—most commonly in a tray column operated at substantially atmospheric pressure with direct-steam addition to the bottom. The number of theoretical trays required for the separation can be calculated by conventional techniques and the actual requirement estimated on the basis of an assumed tray-efficiency. Overall efficiencies of 45 to 70% have been reported as typical for light oil stripper stills (Silver and Hopton, 1942 Glawacki, 1945), and 10 to 15 actual trays are commonly employed below the feed. 

In Table 9-4 the actual number of trays are included. This is because complete equilibrium between vapor and liquid is normally not reached on each tray. For calculation purposes the number of theoretical flashes may be quite a bit less than the number of trays. For smaller diameter... 

Because a column cannot operate at total reflux and produce net product from the column, a reflux ratio of about 1.1 to 1.5 times the mmmMm reflux will usually give practical results. Be aware that as the reflux ratio comes down approaching the minimum, the number of theoretical and then corresponding actual trays must increase. 

For a constant reflux ratio, the value can be almost any ratio however, this ratio affects the number of theoretical plates and, consequently, actual trays installed in the rectification section to achieve the desired separation. Control of batch distillation is examined in Reference 134. 

Determining the number of theoretical and actual trays in a distillation column is only part of the design necessary to ensure system performance. The interpretation of distillation, absorption, or stripping requirements into a mechanical vessel with internal components (trays or packing, see Chapter 9) to carry out the function requires use of theoretical and empirical data. The costs of this equipment are markedly influenced by the column diameter and the intricacies of the trays, such as caps, risers, weirs, downcomers, perforations, etc. Calcvdated tray efficiencies for determination of actual trays can be lost by any unbalanced and improperly designed tray. 

The foregoing define the number of theoretical states. Actual stages depend upon the tray efficiency, which will probably be the weakest number in the design. Using operating data from a similar system is certainly best where possible. Table 8-1 gives some shortcut correlations. 

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... 

Theoretical Plate In a distillation column, it is a plate onto which perfect liquid-vapor contact occurs so that the two streams leaving are in equilibrium. It is used to measure and rate the efficiency of a column at separating compounds. The ratio of the number of theoretical plates to the actual number of plates required to perform a separation is used to rate the efficiency of a distillation column. Actual separation trays in refinery distillation units are usually less effective than theoretical plates. 

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

The number of actual trays required in a column can be determined from the calculated number of theoretical stages by invoking an efficiency. Various definitions of efficiency... 

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