## 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. ## Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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