Correcting the result of Erbar and Maddox with Eq. (3.18) is not performed here.
For the same problem, the Hengstebeck diagram (Sec. 2.3.4) gave 16 theoretical stages, while a rigorous computer simulation (for a reflux ratio of 1.5, as specified in Example 2.4) gave 20 theoretical stages. Figure 3.5 compares results from a Fenske-Underwood-Gilliland (step 1 in Ex ample 3.4 above) hand calculation with a rigorous simulation and a shortcut commercial simulation. The comparison is based on the depropanizer, but extends from minimum to total reflux. Figure 3.5 shows that the shortcut methods approximate the depropanizer reason ably well.
The most popular shortcut relationships for best feed location are the Fenske equation (25) and the Kirkbridge equation (56). The former is recommended by Refs. 11 and 33, and the latter is recommended by Refs. 11, 28, and 37. Both methods are only approximations. Additional feed location criteria are in Sec. 2.3.7.
Fenske equation (25)
2hk jcs.lk where as is the average relative volatility of the light key in the bottom section. The number of actual trays in the bottom section is estimated from
Kirkbridge equation (56) Nx =
Akashah et al. (57) presented a modified version of Eq. (3.22), which gives
Nft = Nr [calculated from Eq. (3.22)] - 0.5 logN (3.23)
Example 3.5 Calculate the ideal feed plate location for the depropanizer in Example 3.4.
c . 10.26 0.417\ ,10 Using the relative volatility values in Example 3.1,
Assuming 20 theoretical stages (Example 3.4), and 12.4 to be the minimum number of stages (Example 3.1),
2. Using Kirkbridge's equation, Eq. (3.22)
Assuming 20 theoretical stages,
3. Applying Akashah et al.'s correction, Eq. (3.23),
4. From the Hengstebeck diagram (Sec. 2.3.4), prorating to 20 stages
5. A rigorous computer calculation gave Ns = 11, Nr = 9.
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