%ABV Distillate vs %ABV Wash Chart

[Maritimer]

While poking around in the HD calculations page, http://homedistiller.org/calcs/calc" onclick="window.open(this.href);return false;" rel="nofollow , I came across a formula to calculate the Vapour-Liquid Equilibrium. Having recently acquired Mathematica, I graphed the formula, but relabeled it "%ABV Distillate vs. %ABV Wash" just to make it easier to understand what it shows.

Here is a PDF version, which prints out very nicely.

Distillate vs Wash %ABV.pdf

(434.46 KiB) Downloaded 356 times

Sorry for the labelling of the axes and the grid; I haven't figured out yet how to make it look like Hookline's beautiful Ethanol-Water Phase diagram.

Ethanol-Water_Phase_Diagram_liquid-vapour_F_Lands_Ver2.pdf

(140.84 KiB) Downloaded 319 times

M

Edit: New chart with equal axes. New labels. Included Hookline's phase diagram.

[rad14701]

That doesn't look accurate... I have posted the proper relation charts in both F & C... Not sure if I've posted the actual XLS file...

[Maritimer]

Rad,

This chart is the result you get from the Phase Diagram when you go up from the X-axis (%ABV of wash) to the blue line, over to the red line, and back down to the X-axis (%ABV of distillate).

M

[rad14701]

I'm sorry but those numbers don't look right...

[Maritimer]

Hi Rad,

Take 10%ABV on the X-axis of the Ethanol-Water Phase Diagram,
go up to 93*C on the blue line, over to the red line and down to 53.5%ABV on the X-axis.

Go to the new chart, 10% on the X-axis, read 53% on the Y-axis.

Do the same for any other values, the new chart will agree.

This new chart will make explaining distillation to newbies a bit easier. One thing that helps is that there is no mention of temperature.

M

[Jkhippie]

That chart looks like it's only accurate for one distillation, like a pot still? Wouldn't a reflux column, with its multiple distillations before take-off, throw things off?

[Maritimer]

Hi JK,

The chart shows the instantaneous relationship between the %ABV of the wash and the vapour it is producing. During a pot still run, the %ABV of the wash decreases, so the final %ABV of the product is the accumulation of the instantaneous micro-runs of distillation, as the curve is followed down to the origin. My experience is that from a 10%ABV wash, I'll get 30%ABV low wines.

The curve also applies to reflux stills. In the column, there is continual re-distillation as the condensate from the reflux condenser falls back into the column. For example, suppose you start with 30%ABV low wines. Initially, that will produce 75%ABV vapour from the chart. That vapour gets condensed and falls back into the packing, where it now re-vapourizes at 85%, and so on. Of course, this doesn't magically happen, there is a temperature gradient set up in the column, and also a concentration gradient.

M

[Edwin Croissant]

Hi Maritimer, the chart looks OK to me

As exercise you could also produce the graph for the coefficient k, that is the ratio between the ethanol content of the vapor and that in the liquid. This graph makes it easier to understand that at the end it becomes more difficult to get a richer distillate and will also show more clearly the azeotrope of the mixture (the concentration where k is 1).

Regards,

Edwin

[Maritimer]

Hi Edwin,

Here is the k graph:

And here is a pdf version:

k = % ABV vapour to %ABVliquid.pdf

(460.9 KiB) Downloaded 148 times

Now that is interesting. As the alcohol content approaches zero, the ratio of vapour %ABV to liquid %ABV is around 9.7. At 30%ABV, the starting point of my low wines, the ratio is about 2.4. When the liquid %ABV is 90%, the ratio is only 1.01784, so the vapour is only 1.7% more than the liquid. It really is quite amazing that we can reach azeotrope!

M

[Jkhippie]

Okay, I see now. If you take each distillation in the column seperately, the chart shows the percentages for liquid and vapor in each instance. Got it.

[Lester]

Hello Maritimer,

Can you do a log-log or lin-log plot on Mathematica? Just wondering how it would look like.

The K plot is interesting.

[Maritimer]

Hi Lester,

Here are your plots:

The LogLogPlot is reminiscent of a low-pass filter, where the Bode approximation would be straight dashed lines. But concentrations of 0.01% are rather meaningless, and who knows how accurate the equations are at this level.

M

[Edwin Croissant]

The last graph, the LogLogPlot, is intriguing.

Thank you!

Edwin

[Maritimer]

Been trying various combinations. Here is the inverse k plot:

Kind of hard to get your head around that, though. But it is a nice straight line.

Here is a fitted line, with equation

1/k = 0.0895879 + 0.010576 x %ABVliquid

The equation works quite well from 0 to 80%ABV of the liquid.

M

[Lester]

Thank you Maritimer!

That log-log plot is indeed similar to the response of a single-pole low pass filter.

Nature is amazing!!!

[HookLine]

Interesting plots.

Full set of my phase charts here. Celsius and Fahrenheit versions.

[Maritimer]

Let's review this graph:

This is a plot of

1/k = %ABVLiquid / %ABV Vapour vs. %ABVLiquid (1)
If we solve for %ABVVapour, we get

%ABVVapour = %ABVLiquid/(1/k) (2)

1/k is just what you see on the y-axis, the ratio of liquid to vapour %ABV.

This relationship is very linear over a good portion of the graph. So the question is, why?

The equation of the fitted straight line is

1/k = 0.0895879 + 0.010576 x %ABVliquid = %ABVLiquid / %ABVVapour

If we solve for %ABVVapour we get

%ABVVapour = %ABVLiquid/(0.0895879 + 0.010576 x %ABVliquid ) (3)

That means that the straight line in the graph is actually the denominator of the equation that produces %ABVVapour from a %ABVLiquid.

How does this new equation for %ABVVapour compare to the original equation, which is an 8th order polynomial, obviously fitted to the data (from http://homedistiller.org/calcs/calc" onclick="window.open(this.href);return false;" rel="nofollow ):

%vap = -94.7613*x ^ 8 + 450.932 * x ^ 7 - 901.175 * x ^ 6 + 985.803 * x ^ 5 - 644.997 * x ^ 4 + 259.985 * x ^ 3 - 64.5050 * x ^ 2 + 9.71706 * x

where %vap = % of ethanol in vapour if condensed (mL per mL), and x = % of ethanol in liquid (mL per mL).

Here is a graph of the two together:

That looks pretty good over the range of 0 to 80 %ABVLiquid.

Now the question is not, "Why is the relationship linear?" but "Describe the new equation, what does it say?"

Well, nature likes to do things that are proportional, or inversely proportional (and logarithmic, too).

For example, consider that old favourite, F=ma, Newton's 2nd law of motion. The force that you need to accelerate a mass gets bigger if you have more mass, or it gets bigger if you want to accelerate more.

On the other hand, if you solve for a, you get

a=F/mThis says that if you want to increase the acceleration at a certain rate, you can apply a proportioanlly greater force and the acceleration will increase proportionally.

On the other hand, if you have a given force and you want to accelerate more, you have to decrease the mass in inverse proportion to the desired acceleration. If you want 3 times more acceleration, you need to reduce the mass to 1/3 of the mass, m/3.

So, here is the new equation. It is of the form a=F/m.

The amount of vapour %ABV is directly proportional to the amount of liquid %ABV.

But the amount of vapour %ABV is also inversely proportional to the liquid %ABVwith a constant added .

%ABVVapour = %ABVLiquid/(0.0895879 + 0.010576 x %ABVliquid ) (3)

To be continued. Ideas welcome.

M

[Maritimer]

Here is another result from the new %ABV Distillate vs %ABV Wash graph in the OP. This is the answer to the oft-raised question, "What %ABV will the low wines be from a stripping run when I start with blah-blah %ABV wash?" In this case, we start with, say, a 10% BirdWatcher's wash, and we want to know what the %ABV of the low wines will be. Take a look at this graph:

This was derived from the original %ABV Distillate vs %ABV Wash graph. In this case, we start at 10% on the horizontal axis, go up to the graph line, over to the vertical axis and read 29%ABV low wines.

Here is a pdf, ummm good for printing.

abv from stripping run.pdf

(433.37 KiB) Downloaded 151 times

M

[Maritimer]

More delightful graphs:

Most of us are familiar with the Phase Diagram graph showing the effect of reflux (that stair-step journey to azeotrope). Now that we have a graph showing the Stripped %ABV from Wash %ABV, we can do the same sort of thing for repeated pot still distillations:

Here we start with a 10% wash, strip it to 29%, then strip that to 54% and so on.

And here is the whole deal with a new twist:

The new graph at the bottom shows the difference between the stripped wash's %ABV and the original wash's %ABV. Interesting that the maximum difference is around 26%, where the distillate is almost twice the %ABV.

M

[Lester]

Outstanding work Maritimer!

I have been analyzing the rate at which alcohol evaporates out of the wash, with and without a reboiler in place. (See link to the reboiler in my signature below). I can't understand why the depletion rate of alcohol in the wash is a straight line even with the reboiler in there. I need to think this out some more and I'll be using your graphs to find the cause for this unexpected response.

Thank you!

[Maritimer]

Hi Lester,

It's great to meet a fellow experimenter.

Without your re-boiler, the depletion rate of the wash would decease linearly if you were taking product at a constant rate. Since your product is close to azeotrope, very little water leaves the boiler.

%ABVBoiler = ethanol volume/(ethanol volume + water volume) x 100

Here is a plot of the %ABV of the mixture of 0 to 12 units of alcohol added to 88 units of water. Read the graph from right to left to see the %ABV of the wash as the units of alcohol are constantly removed by the still.

12 units alcohol to 88 units water.jpeg (10.32 KiB) Viewed 4867 times

Edit: this should be 16%, sorry.

Looks can be deceiving. Use a straightedge (on a printout if your screen is distorted) and you can see that it is not a line. (Edit: Quite obvious at 16%)

The volume of liquid in the re-boiler is much smaller than the boiler volume, and if this were added to the boiler there would only be a small difference, probably within the error band of your thermometer-to-%ABV conversion, power level, and extraneous influences. Yes, there could be other stuff hiding in that error band, too.

When I built my still, I built it as a scientific apparatus. (I'm retired from doing just that.) It is crazily insulated and my digitally-controlled-power power supply has 1000 levels. To reduce your error band, you need to have precise control over whatever it is you want to control, and you need to keep out extraneous influences.

Mathematica has a beautiful Fit[] function that allows to to set the model of the equation you want to fit. Maybe your spreadsheet can do this too. See if you can fit the equation above to your data.

M

[Lester]

Maybe your spreadsheet can do this too. See if you can fit the equation above to your data.

Yes it is easy enough to do with Excel.

[Maritimer]

Hi Lester,

That's great! Did you use the equation as a model for the fitting, or did you fit it with a polynomial? Is that your data or the calculated values? We are on opposite sides of the world, so communication can take a day.

M

[Lester]

Hi Lester,

That's great! Did you use the equation as a model for the fitting, or did you fit it with a polynomial? Is that your data or the calculated values? We are on opposite sides of the world, so communication can take a day.

M

Hello Maritimer,

Leftmost column is the water content and it is constant amount, 80.

Middle column is the alcohol content and it goes from 20 down to 0.

Rightmost column is computed to come up with the % ABV in the total mix, like this:

% ABV = alcohol / (alcohol + water)

The % ABV is then plotted in the graph. The straight line was just drawn in place to make the curvature of the plot obvious.

I don't think there is anything significant in the curvature. It's just the way the results come up when computed in the manner I have shown above.

[Maritimer]

Hi Lester,

When you first communicated, you were wondering about the nonlinearity of your %ABV wash as the ethanol was evaporated. I'm wondering what your data plot looks like, and how it would fit the equation. You could just plot the data and the equation together to see how well they coincide, but if you had a fitting algorithm, you could see how well the data and the equation correlate. You could just tabulate the data and I'll use the Mathematica Fit[] function if you don't have it in Excel. That would be fun.

But the real fun of communicating with someone else who is exploring distillation by experimenting and analysis, is the ideas that get generated by working together. In a previous post, I found that the %ABVvapour was approximately related to the %ABVwash over the range of 0 to 80%ABV by:

%ABVVapour = %ABVLiquid/(0.0895879 + 0.010576 x %ABVLiquid ) (3)

and I was trying to understand what this could mean. If we remove the % notation so that only ratios are used, the equation becomes:

ABVVapour = ABVLiquid/(0.0895879 + 1.0576 x ABVLiquid ) (4)

Now ABVLiquid = ethanol/(water+ ethanol), where measurements are in volume.

Substituting in (4) , we get
ABVVapour = 0.872 {ethanol/(ethanol + 0.0781 water)} (5) (that's the ethanol and water volumes in the boiler)

And here is your equation with the % removed:

ABVBoiler = 1.000 {ethanol/(ethanol + 1.000 water)} (6)

M

[Lester]