1.2.6-7 Graphical determination min reboil ratio

Points: 13 No answer

This task will familiarize you with the graphical determination of the minimum reboil ratio $$R^G$$ for a binary mixture from the yx-diagram (McCabe Thiele diagram).

The sketch shows in a McCabe Thiele diagram the VLE-data for four different binary zeotropic mixtures, each with a different separation factor "alpha". The "alpha=1" line is just given as the bisectrix (not as a mixture). The operational line of the feed and the operational curve of the stripper are also given. Recall that the operational curve of the stripper is a straight line ONLY for certain circumstances, which we assume to be fulfilled here. Right next to the yx-diagram the here relevant operational equations are given.

You can extract from the McCabe Thiele diagram that the composition of the bottom product is $$x^B=$$ and that the global composition of the feed is $$x^F=$$ .

zF1=

Feed operation line and equation:

You can extract from the diagram that the slope of the feed operation line is . Considering the feed operation equation (for constant $$𝐿 ̇/𝐺 ̇$$), you can compute the caloric state of the feed from this slope . Consequently, the caloric state of the feed is $$q^F=$$ .

Alternatively, you could have determined $$q^F$$ from the axis intercept of the feed operation line. According to the sketch, the feed operation line intersects the "y-axis" at   and according to the feed operation equation then the caloric feed state is $$q^F=$$ .

qF=

Stripper operation curve and equation:

Once again it has to be underlined that this operation equation can be represented by a straight line only, if the ratio $$𝐿 ̇/𝐺 ̇=const$$ all over the stripping section. We assume this to be true here! Again you have two options for the graphical determination of the external reboil ratio $$R^G$$ or the internal reboil ratio $$𝐿 ̇/𝐺 ̇$$. One option is via the slope of the operation line and the other option is via the the axis intercept.

The slope of the operation line is . The y-axis intercept cannot be read from the given diagram, because it only covers positive y-values. But as you already know the slope and with this the internal reboil ratio $$𝐿 ̇/𝐺 ̇$$, you can easily compute the y-axis intercept when considering again the stripper operation curve. The y-axis intercept is (consider the sign!) . So, considering the slope, the external reboil ratio is $$R^G=$$ (two digits precision) and when considering the axis intercept the external reboil ratio is also $$R^G=$$ (two digits precision). This value implies that the reboiled molar stream is 1/3 of the bottom product molar stream.

You already know from the lecture or from previous opal tasks that the minimum reboil ratio follows, when the feed operation line and the stripper operation line intersect at the equilibrium curve. This is the case in the sketch above for the separation coefficient of alpha= . Let us now assume the same caloric state of the feed and the same overall feed composition (the feed operation line remains constant), but a binary mixture with a smaller separation factor alpha=2. The composition of the bottom product also remains constant. As a consequence, the operation line of the stripper can be sketched with a smaller slope. I approximate the slope of the stripper operation line for this new condition as 7/4. Therefore, the external reboil ratio is $$R^G=$$ (two digits precision), which implies that now the molar bottom product stream is smaller than the reboiled molar stream.

Recall from the lecture that the minimum energy demand of the reboiler (heating utility) is a linear function of the minimum reboil ratio. This Opal task has shown that for the binary mixture with the alpha =4 the min external reboil ratio was 1/3, and that for the binary mixture with the alpha=2 the minimum external reboil ratio was 4/3. We thus conclude that the binary mixture with the alpha=4 demands for only  % of the energy the mixture with the alpha=2 demands for.

1.2.7 Graphical determination min reflux ratio

Points: 11 No answer

This task will familiarize you with the graphical determination of the minimum reflux ratio $$R^L$$ for a binary mixture from the yx-diagram (McCabe Thiele diagram).

The sketch shows in a McCabe Thiele diagram the VLE-data for four different binary zeotropic mixtures, each with a different separation factor "alpha". The "alpha=1" line is just given as the bisectrix (not as a mixture). The operational line of the feed and the operational curve of the enricher are also given. Recall that the operational curve of the enricher is a straight line ONLY for certain circumstances, which we assume to be fulfilled here. Right next to the yx-diagram the here relevant operational equations are given.

You can extract from the McCabe Thiele diagram that the composition of the distillate is $$x_1^D=$$ and that the global composition of the feed is $$z_1^F=$$ .

Feed operation line and equation:

You can extract from the diagram that the slope of the feed operation line is (consider the sign!). The slope of the feed operational line is described by $$-(q^F/(1-q^F)$$  (compare the feed operation equation). Consequently, the caloric state of the feed can be computed. $$q^F=$$
Alternatively, you could have determined $$q^F$$ from the axis intercept of the feed operation line. According to the sketch, the feed operation line intersects the "y-axis" at $$y_1=$$ and according to the feed operation equation the axis intercept is $$(z^F/(1-q^F)$$. Thus, you also can compute the caloric feed state as $$q^F=$$

Enricher operation curve and equation:

Once again it has to be underlined that this operation equation can be represented by a straight line only, if the ratio $$L ̇/G ̇=const$$ all over the enriching section. We assume this to be true here! Again you have two options for the graphical determination of the external reflux ratio $$R^L$$ or the internal reflux ratio  $$L ̇/G ̇$$. One option is via the slope of the operation line and the other option is via the the axis intercept. Let the slope be $$2/3$$ and let the axis intercept be (approximately) $$0.3$$. So, considering the slope, the external reflux ratio is $$R^L=$$ and when considering the axis intercept the external reflux ratio is also $$R^L=$$ . This value implies that the reflux molar stream is twice the top product stream.

You already know from the lecture or from previous opal tasks that the minimum reflux ratio follows, when the feed operation line and the enricher operation line intersect at the equilibrium curve. This is the case in the sketch above for the separation coefficient of alpha= . Let us now assume the same caloric state of the feed and the same overall feed composition (the feed operation line remains constant), but a binary mixture with a larger separation factor alpha=5. The composition of the distillate also remains constant. As a consequence, the operation line of the enricher can be sketched with a smaller slope and also  with a larger axis intersept. I approximate the slope of the enricher operation line for this new condition as 1/3. Therefore the external reflux ratio is  $$R^L=$$ , which implies that now the molar product stream is twice the molar reflux stream.

Recall from the lecture that the minimum energy demand of the condenser (cooling utility) is a linear function of the minimum reflux ratio. This Opal task has shown that for the binary mixture with the alpha =2 the min external reflux ratio was 2, and that for the binary mixture with the alpha=5 the minimum external reflux ratio was 1/2. We thus conclude that the binary mixture with the alpha=5 demands for only  % of the energy the mixture with the alpha=2 demands for.