## Nt Nb

xf xB

ln a

where yF and xF at the feed stage are obtained as explained above. The optimal feed-stage location counted from the bottom is then:

corresponding to xHD = xLB = 0.0057. The error may seem large, but it is actually quite good for such a simple formula.

### Optimal Feed Location

The optimal feed-stage location is at the intersection of the two operating lines in the McCabe-Thiele diagram. The corresponding optimal feed-stage composition (xF, yF) can be obtained by solving the following two equations: z = qxF + (1 — q)yF and yF = axF/(1 + (a — 1)xF). For q = 1 (liquid feed) we find Xf — Z and for q = 0 (vapour feed) we find yF = Z (in the other cases we must solve a second-order equation).

There exists several simple short-cut formulas to estimate the feed point location. One may be derived from the Kremser equations given above. Divide the Kremser equation for the top by the one for the bottom and assume that the feed is optimally located to derive:

where N is the total number of stages in the column. Summary for Continuous Binary Columns

With the help of a few of the above formulas it is possible to perform a column design in a matter of minutes by hand calculations. We will illustrate this with a simple example.

We want to design a column for seperating a saturated vapour mixture of 80% nitrogen (L) and 20% oxygen (H) into a distillate product with 99% nitrogen and a bottoms product with 99.998% oxygen (mole fractions).

Component data Normal boiling points (at 1 atm): TbL = 77.4 K, TbH = 90.2 K, heat of vaporization at normal boiling points: 5.57kJmol~1 (L) and 6.82kJmor1 (H).

The calculation procedure when applying the simple methods presented in this article can be done as shown in the following steps:

1. Relative volatility: The mixture is relatively ideal and we will assume constant relative volatility. The estimated relative volatility at 1 atm based on the boiling points is ln a + (AH-7RTb) [(TbH - TbL)/Tb] where AHp =

83.6 K and Th — Tl = 90.2 - 77.7 = 18.8. This gives (AHvap)/(RTb) = 8.87 and we find a + 3.89 (however, it is generally recommended to obtain a from experimental VLE data).

2. Product split: From the overall material balance we get D/F = (z - Xb)/(xd - Xb) = (0.8 - 0.00002)/ (0.99 - 0.00002) = 0.808.

3. Number of stages: The separation factor is S = (0.99 x0.99998)/(0.01x 0.00002) = 4 950 000, i.e. ln S = 15.4. The minimum number of stages required for the separation is Nmin = ln S/ln a = 11.35 and we select the actual number of stages as N = 23 ( + 2Nmin).

4. Feed-stage location: With an optimal feed location we have at the feed stage (q = 0) that yF = zF = 0.8 and xF = yF/(a — (a — 1)yF) = 0.507. Skoges-tad's approximate formula for the feed-stage location gives:

## 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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