Distillation Fenske Equation

To solve Equation 9.51, it is necessary to know the values of not only a ,-j and 9 but also x, d. The values of xitD for each component in the distillate in Equation 9.51 are the values at the minimum reflux and are unknown. Rigorous solution of the Underwood Equations, without assumptions of component distribution, thus requires Equation 9.50 to be solved for (NC — 1) values of 9 lying between the values of atj of the different components. Equation 9.51 is then written (NC -1) times to give a set of equations in which the unknowns are Rmin and (NC -2) values of xi D for the nonkey components. These equations can then be solved simultaneously. In this way, in addition to the calculation of Rmi , the Underwood Equations can also be used to estimate the distribution of nonkey components at minimum reflux conditions from a specification of the key component separation. This is analogous to the use of the Fenske Equation to determine the distribution at total reflux. Although there is often not too much difference between the estimates at total and minimum reflux, the true distribution is more likely to be between the two estimates. 

The second column in the distillation train of an aromatics plant is required to split toluene and ethylbenzene. The recovery of toluene in the overheads must be 95%, and 90% of the ethylbenzene must be recovered in the bottoms. In addition to toluene and ethylbenzene, the feed also contains benzene and xylene. The feed enters the column under saturated conditions at a temperature of 170°C, with component flowrates given in Table 9.10. Estimate the mass balance around the column using the Fenske Equation. Assume that the K-values can be correlated by Equation 9.68 with constants A , 5 and C, given in Table 9.10. 

This measure was based upon the ratio of the minimum necessary number of plates, A min (averaged over the reboiler composition) in a column to the actual number of plates in the given column, Nj. Christensen and Jorgensen assumed that the mixture has a constant relative volatility a and the column operates at total reflux using constant distillate composition (x o) strategy (section 3.3.2) and evaluated Nmin using the Fenske equation ... 

One might then ask how large a temperature difference between boiling points is required in order to obtain an essentially complete separation. The equation (Fenske equation ) relating the compositions of the distillate and the distilland is... 

If one starts with an equimolar mixture of A and B and wishes to obtain about 95 per cent pure A in die distillate, the initial distillate would have to contain about 98 mole per cent A, since the enrichment decreases as the distillation progresses. The value of a would be given by the Fenske equation... 

Use Aspen Plus and model each distillation column using the DSTWU model as shown in Figure 6.9. First, specify the split of key components for the light component you want 99 percent out of the top and for the heavy component you want 1 percent out of the top. The other components will be split according to the Fenske equation [Eq. (6.3)]. 

This is a set of equations applicable to z = 1,..., C, where C is the total number of components. Equation 12.17 is one form of the Fenske equation (Fenske, 1932) for a total reflux distillation column. The number of stages A, is the minimum required to achieve the separation corresponding to component flow rates and and bottoms rate B. In this equation, N, the number of stages, is also known as the fractionation index. 

The stream defined below is sent to a column at a fixed pressure. The column has a partial condenser with a vapor distillate product and a partial reboiler with a liquid bottoms product. Assuming total reflux and constant relative volatilities, calculate by the Fenske equations the minimum number of trays and the product rates and compositions to meet the following specifications ... 

A distillation column separates the feed stream shown below into butanes in the distillate and pentanes in the bottoms. The relative volatilities (assumed constant) and the separation specifications are also given. Use the first Fenske equation to calculate the minimum number of stages that can meet the specs at total reflux. With an average A -valuc of isopentane A 3 = 0.8, use the second Fenske equation to calculate all the component flow rates in both products. Does this value of produce component flow rates consistent with total flow rates ... 

Calculate component rates in the distillate and bottoms using the other form of the Fenske equation. Adjust the column average temperature to match the bottoms flow rate. If the adjusted temperature is considerably different from the temperature in Part 1, repeat that part with the new temperature then repeat Part 2. 

Relative volatility is a useful tool to judge the feasibility and ease of a distillation separation. In general, the larger the relative volatility between two key components, the easier and less costly will be the separation of those keys. If the relative volatility between the keys is unity, then their separation by ordinary distillation is impossible. Such a situation exists with azeotropes. The relationship between relative volatihty and difficulty of separation may be illustrated by application of a simple relationship (the Fenske equation, to be discussed later) ... 

The procedures presented in Secs. 10-1 through 10-3 are useful in the analysis of the column behavior over wide ranges of operating conditions as demonstrated above. Also, the procedures presented may be used in Chap. 9 in the design of distillation columns instead of the approximate method based on the Fenske equation. 4... 

For continuous distillation of a binary mixture of constant relative volatility, Fenske equation (6-62) can be used to estimate the minimum number of equilibrium stages required for the given separation, iVmin. 

Use the Fenske equation to estimate /Vmin for distillation of the benzene-toluene mixture of Example 6.4. Assume that for this system at 1 atm, the relative volatility is constant at a = 2.5. 

Calculate the minimum number of stages. Specifications are formulated as distillate and bottom rates and compositions, denoted by D, B, xp and xb, respectively from which the Fenske equation gives ... 

For the complex distillation operation shown below, use the Fenske equation to determine the minimum number of stages required between ... 

For multicomponent mixtures, all components distribute to some extent between distillate and bottoms at total reflux conditions. However, at minimum reflux conditions none or only a few of the nonkey components distribute. Distribution ratios for these two limiting conditions are shown in Fig. 12.14 for the debutanizer example. For total reflux conditions, results from the Fenske equation in Example 12.3 plot as a straight line for the log-log coordinates. For minimum reflux, results from the Underwood equation in Example 12.5 are shown as a dashed line. 

For the distillation operation indicated below, calculate the minimum number of equilibrium stages and the distribution of the nonkey components by the Fenske equation using Fig. 7.5 for If-values. 

A saturated liquid feed at 125 psia contains 200 IbmoIe/hr of 5 mole% /C4, 20mole% nCj, 35mole% iCs, and 40mole% nCs- This feed is to be distilled at 125 psia with a column equipped with a total condenser and partial reboiler. The distillate is to contain 95% of the nC4 in the feed, and the bottoms is to contain 95% of the iCs in the feed. Use the Naphtali-Sandholm SC method, with the Chao-Seader correlations for thermodynamic properties, to determine a suitable design. Twice the minimum number of equilibrium stages, as estimated by the Fenske equation in Chapter 12, should provide a reasonable number of equilibrium stages. 

By taking logarithms of both sides of this formula, we obtain the Fenske equation [155] for determining the minimum number of separating stages (see section 5.1.4.2) in a batch distillation of an ideal mixture ... 

In (5.6), a CSTR is considered as reactor, and therefore the reaction rate r is calculated at the reactor outlet concentration, x. At infinite reflux ratio, R = < , the distillate (x°) and bottom concentrations (x ) are related to each other by the Fenske equation [2]... 

Figure 6.5 shows the Fenske equation in graphical form. It will be seen that for a feed split to make 99% molar tops and bottoms (F = 9801), any value of a less than 1.5 will require a very large column. In fact, fractional distillation to produce relatively pure products is seldom the correct choice of technique when the system has a relative volatility of less than 1.3. 

Step 2 Estimation by the Fenske equation [Eq. (14.1)] of the distribution, dA>, of the nonkey components between distillate and bottoms at total reflux using the value of computed in Step 1, the b/d ratio for the heavy key, and the relative volatility between the nonkey and the heavy key, aNK,HK- Although this estimate is for total reflux conditions, it is a surprisingly good estimate for the distribution of the nonkey components at finite reflux conditions for nearly ideal mixtures. 

Step 5 Estimation of the feed-stage location by the Fenske equation. The calculation is made with Eq. (14.1) by applying it to the section of stages between the feed composition and the distillate composition to obtain the minimum number of rectification stages, and then to the section of stages between the feed and bottoms product to obtain the minimum number of stripping stages, The ratio of to Ns,mm is assumed to be the same as the ratio of to at finite reflux conditions. Alternatively, the empirical, but often more accurate, Kirkbride equation can be applied. 

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