Fenske’s Equation

From Fenske s equation, the minimum number of equilibrium stages at total reflux is related to their bottoms (B) and distillate or overhead (D) compositions using the average relative volatility, see Equation 8-29. 

Fenske s equation may be used to find the minimum number of plates. 

Hence, substituting into Fenske s equation gives ... 

Determine the minimum reflux ratio using Fenske s equation and Colburn s rigorous method for the following three systems ... 

The number of plates required for a desired separation under conditions of total reflux can be found by applying Fenske s equation, equation 11.59, to the two key components. 

Nmin is again evaluated using the Fenske s equation ... 

The minimum number of stages is given by Fenske s equation (25)... 

The Winn equation reduces to Fenske s equation when 0 = 1.0 and... 

In this approach, Fenske s equation [Ind. Eng. Chem., 24, 482 (1932)] is used to calculate which is the number of plates required to make a specified separation at total reflux, i.e., the minimum value of N. Underwood s equations [/. Inst. Pet., 31, 111 (1945) 32,598 (1946) ... 

The method proposed is the Hengstebeck Method described in Reference 17. The method is quite simple. First, a heavy key component is selected and the relative volatility (a) of all column components to this heavy key are determined. Once this is done for a colunrn, minor operating changes won t affect a much and the same a can therefore often be used for subsequent sets of data. One can use ocfeed or perhaps more accurately, a = VocToD Bott - Then a plot is made of InD/B versus a. A straight line should result. If a fairly straight line does not result, the analyses are probably faulty. Here, D is the mols/hr of each component in the distillate and B is the mols/hr of each component in the bottoms. Actually, from Fenske s equation (Equation 11 and Reference 18), at total reflux it is shown that In D/B versus In a is a straight... 

To calculate Fenske s equation is usually applied to the heavy key and the light keys. So we are interested in... 

So at an absolute minimum, we need 10 ideal steps, or 9 ideal stages plus the reboiler. Knowing the number of trays, we can also use Fenske s equation to check if indeed the octane fraction in the distillate is negligible as we assumed in Example 1. 

Suppose that the purity specifications are taken to be XD l and xB h. In general D and B are not determined by the specification of these two mole fractions except for the case of a binary mixture. To apply Fenske s equation to determine... 

Any number of methods could be used to pick adequate temperature profiles. The following relatively simple procedure was used to select these profiles. The temperatures of all intermediate stages were taken to be linear with stage number between the distillate temperature TD and the bottoms temperature TB. For different numbers of stages, the top and bottom temperatures were estimated as follows. First, the lowest overhead temperature T0 L and the highest bottoms temperature TB v were found by use of a modified form of Fenske s equation which was deduced in the following manner. Since the value of (N)min computed by Eq. (2) on the basis of the specified values of bjdl and bh/dh is less than Nv, a separation better than the specified one can be obtained. Thus, it is desirable to revise Eq. (1) such that each separation is better than the one which was specified. The result may be realized by introducing the factor fi as follows... 

Fenske s equation (9.85) is not limited to binary mixtures and can be applied to the key components to determine the minimum number of trays,... 

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