1 xD

0.00002" 0.01

1.358

corresponding to the feed stage NF = [N + 1 — (nt — nB)]/2 = (23 # 1 # 5.27)/2 = 14.6. 5. Energy usage: The minimum energy usage for a vapour feed (assuming sharp separation) is Vmin/F" 1/(a — 1) = 1/2.89 = 0.346. With the choice N = 2Nmin, the actual energy usage (V) is then typically about 10% above the minimum (Vmm), i.e. V/F is about 0.38.

This concludes the simple hand calculations. Note again that the number of stages depends directly on the product purity (although only logarithmically), whereas for well-designed columns (with a sufficient number of stages) the energy usage is only weakly dependent on the product purity.

Remark 1 The actual minimum energy usage is slightly lower since we do not have sharp separations. The recovery of the two components in the bottom product is rL = (xL,BB)/(zFLF) = 0.9596 and rH = (xH,BB)/(zFHF) + 0, so from the formulas given earlier the exact value for nonsharp separations is Vmin/F = (0.9596 — 0.0 x 3.89)/(3.89 — 1) = 0.332.

Remark 2 For a liquid feed we would have to use more energy, and for a sharp separation:

Remark 3 We can check the results with exact stage-by-stage calculations. With N = 23, NF = 15 and a = 3.89 (constant), we find V/F = 0.374, which is about 13% higher than Vmin = 0.332.

Remark 4 A simulation with more rigorous VLE computations, using the Soave-Redlich-Kwong (SRK) equation of state, has been carried out using the HYSYS (Hypnotech Ltd.) simulation package.

The result is a slightly lower vapour flow due to a higher relative volatility (a in the range 3.99-4.26 with an average of 4.14). More precisely, a simulation with N = 23, Nf = 15 gave V/F = 0.291, which is about 11% higher than the minimum value V'mm = 0.263 found with a very large number of stages (increasing N > 60 did not give any significant energy reduction below Vmin). The optimal feed stage (with N = 23) was indeed found to be NF = 15.

Thus, the results from HYSYS confirm that a column design based on the very simple short-cut methods is very close to results from much more rigorous computations.

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Solar Panel Basics

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