Calculating time to reduce alcohol in wine using heating method

[Borek]

Equilibrium case is one for which exact calculations are possible, so it gives a good reference point. As in every other practical case (be it in chemistry of physics) real world is more complicated, typically to the point where it is easier to measure than to calculate.

So yes, this is a spherical cow diagram. But it is the best thing we have to analyze the situation, and it will tell us what are limits, what is possible and what is not (just like energy conservation makes discussions about over unity engines a moot).

 

[Chestermiller]

Here is a simple model to begin to work with.

Let m be the total number of moles of ETOH and water in the tank at any time, let x be the mole fraction ETOH, and let $\dot{m}_I$ be the molar flow rate of inert gas (insoluble also) bubbled through the liquid. Assume the liquid is agitated enough and the depth of the liquid is sufficient for the bubbles too reach vapor-liquid equilibrium with the liquid currently in the tank. Assume also that heat is added to the system at such a rate that the liquid remains at constant temperature T throughout the process. Let the total pressure of the system by constant at $P_T$, with the pure inert gas also furnished at this pressure and temperature T.

We will temporarily assume that the liquid solution is ideal such that Raoult's law is obeyed:$$p_{A}=xP^*_A(T)$$$$p_{W}=(1-x)P^*_W(T)$$where the $P^*(T)$'s are the equilibrium vapor pressures of pure water and ETOH at temperature T,, and the p's are the partial pressures iii the vapor.

Based on these considerations, the rate of change of the total number of moles of liquid in the tank any time is. $$\frac{dm}{dt}=-\frac{(p_A+p_W)}{P_T-(p_A+p_W)}\dot{m}_I\tag{1}$$The rate of change of the number of moles of ETOH in the tank is $$\frac{d(mx)}{dt}=m\frac{dx}{dt}+x\frac{dm}{dt}=-\frac{p_A}{P_T-(p_A+p_W)}\dot{m}_I$$or $$\frac{dx}{dt}=x(1-x)\frac{(P^*_W-P^*_A)}{P_T-(p_A+p_W)}\frac{\dot{m}_I}{m}\tag{2}$$Eqns. 1 and 2 can be integrated with respect to time, subject to the imposed initial conditions.

 

[hutchphd]

It ends up a rate problem but be aware that the atoms in the gas move roughly at the speed of sound. As for diffusion rates they are typically $cm^2 /s$ for atmospheric gasses. some small amounts will return, There a various laws of diffusion, but the rate at a rolling boil will not be significant here I believe.

Edit: Of course @Chestermiller knows the answer which would have taken me an hour at least!!. Notice how rate gets very large near the boiling point T of ethanol.

 

[DaveE]

Here is a simple model to begin to work with.

Thanks! I need to think about this some.

So if I were to add a third inert substance can I just extend these equations like this:

$$\frac{dm}{dt}=-\frac{(p_A+p_W+p_C)}{P_T-(p_A+p_W+p_C)}\dot{m}_I\tag{1}$$

 

[Chestermiller]

Thanks! I need to think about this some.

So if I were to add a third inert substance can I just extend these equations like this:

$$\frac{dm}{dt}=-\frac{(p_A+p_W+p_C)}{P_T-(p_A+p_W+p_C)}\dot{m}_I\tag{1}$$

That would apply only if the 3rd component were present in the wine or soluble in the wine. Otherwise, I have already assumed that an insoluble gas, such as N2, is being bubbled through the wine.

I'm wondering what a good temperature would be for the operation. I was thinking of something like 78.5 C, such that, at 1 atm. total pressure, the initial partial pressures of A, W, and N2 in the exit gas would be about 0.15 atm, 0.4 atm., and 0.45 atm. Thoughts?

 

[DaveE]

That would apply only if the 3rd component were present in the wine or soluble in the wine. Otherwise, I have already assumed that an insoluble gas, such as N2, is being bubbled through the wine.

OK, so molecules that won't transition across the liquid-vapor barrier can be ignored, except for their effect on the total pressure. That makes sense.

 

[ArtZ]

Hey folks, seems that by chipping at this, there is possibly a closed form analytical solution in the works. I will still move forward with the experimental approach. I mentioned earlier that I purchased a hydrometer.

The downside to the hydrometer is that it requires a 250mL volume of the wine to determine the ABV. That is disruptive during the heating process and will not provide accurate results since I would like to test for ABV during heating at 10 minute? intervals. Today, I purchased a Digital Refractometer for Wine/Grape Measurements (% Brix & Potential Alcohol). The Brix scale is used to measure sugar content.

https://www.thomassci.com/Instrumen...rape-Measurements-Brix-And-Potential-Alcohol#

This device will allow me to pipette a small quantity (2-3 drops) into the instrument to get the ABV at my desired sampling intervals.

Since the rain is clearing here, and the temperatures outside are starting to be seasonal, I can thinking about setting this experiment up on my patio. (don't want to smell up the house) I have a single burner butane stove that should work fine as the heat source.

The vessel will be a 12" diameter, 4.5 quart stock pot. I'll use my fast response K thermocouples for T measurement. The downside is that the meter resolution for temperature is only 1C. Before I start this, I'll pop over to Lab Pro and purchase appropriate small sample containers for this experiment.

I am still thinking of using a process temperature of ~83C. Any guesses on the time to reduce the Shaoxing wine from a C0 = .15 to a Cf =. 04? Any bets on the time? My guess from my now discredited calculations is ~ 50 minutes.

​

 

[Chestermiller]

Hey folks, seems that by chipping at this, there is possibly a closed form analytical solution in the works. I will still move forward with the experimental approach. I mentioned earlier that I purchased a hydrometer.

The downside to the hydrometer is that it requires a 250mL volume of the wine to determine the ABV. That is disruptive during the heating process and will not provide accurate results since I would like to test for ABV during heating at 10 minute? intervals. Today, I purchased a Digital Refractometer for Wine/Grape Measurements (% Brix & Potential Alcohol). The Brix scale is used to measure sugar content.

https://www.thomassci.com/Instrumen...rape-Measurements-Brix-And-Potential-Alcohol#

This device will allow me to pipette a small quantity (2-3 drops) into the instrument to get the ABV at my desired sampling intervals.

Since the rain is clearing here, and the temperatures outside are starting to be seasonal, I can thinking about setting this experiment up on my patio. (don't want to smell up the house) I have a single burner butane stove that should work fine as the heat source.

The vessel will be a 12" diameter, 4.5 quart stock pot. I'll use my fast response K thermocouples for T measurement. The downside is that the meter resolution for temperature is only 1C. Before I start this, I'll pop over to Lab Pro and purchase appropriate small sample containers for this experiment.

I am still thinking of using a process temperature of ~83C. Any guesses on the time to reduce the Shaoxing wine from a C0 = .15 to a Cf =. 04? Any bets on the time? My guess from my now discredited calculations is ~ 50 minutes.

​

Are you counting the amount of time it takes to heat up a gallon of wine from 20 C to 83 C?

 

[Dullard]

In a former life, I designed, built, and calibrated 'Breath Interlocks' - a device added to vehicles for those convicted of drunk driving (in many U.S. states). The calibration process used a 'wet-bath' simulator - air was bubbled through a defined ethanol/water solution at a controlled temperature. The product gas was used to calibrate the devices.
From that experience, I can say with confidence that Raoult's Law is of limited utility in the case of low concentration ethanol/water solutions. The inter-molecular forces (in solution) make a mess of the 'expected' ethanol fraction in the gas at a given solution concentration and also cause non-linear (WRT ethanol concentration) behavior over a range of ethanol concentrations.

Caveat: This is true for low ethanol/water concentrations - it is entirely possible that elevated ethanol concentrations behave in a more 'ideal' manner.

 

[Chestermiller]

In a former life, I designed, built, and calibrated 'Breath Interlocks' - a device added to vehicles for those convicted of drunk driving (in many U.S. states). The calibration process used a 'wet-bath' simulator - air was bubbled through a defined ethanol/water solution at a controlled temperature. The product gas was used to calibrate the devices.
From that experience, I can say with confidence that Raoult's Law is of limited utility in the case of low concentration ethanol/water solutions. The inter-molecular forces (in solution) make a mess of the 'expected' ethanol fraction in the gas at a given solution concentration and also cause non-linear (WRT ethanol concentration) behavior over a range of ethanol concentrations.

Caveat: This is true for low ethanol/water concentrations - it is entirely possible that elevated ethanol concentrations behave in a more 'ideal' manner.

Does this more ideal behavior include the region of the azeotrope?

 

[Dullard]

I don't know. My (worthless) guess is 'yes.' My (perhaps) more useful guess is that empirical data for ethanol/water is available (CRC, Perry's...)

 

[ArtZ]

Are you counting the amount of time it takes to heat up a gallon of wine from 20 C to 83 C?

I guess that I should. Under more controlled conditions, I could rely on E = m *Cp * T2-T1. Since a Joule = W*s, I could calculate that time. Since I don't have a hotplate with a known output power (a butane burner) I'll have to include the ramp time in the total time.

 

[Chestermiller]

I don't know. My (worthless) guess is 'yes.' My (perhaps) more useful guess is that empirical data for ethanol/water is available (CRC, Perry's...)

The azeotrope is a non-ideal solution effect.

 

[ArtZ]

Aaah... my CRC Handbook. I may have given it away. Good thought. It has tables for binary and ternary mixtures. Maybe I can locate a copy online.

 

[Borek]

Engineering toolbox site has plenty of tables, I will be surprised if they don't have ethanol/water data.

 

[JT Smith]

If it were me I'd look at this from a volume perspective. That is, approximately how much reduction of the wine volume by boiling will result in a reduction of the alcohol concentration to, say, 25% of it's original value. I suspect you'd have to reduce the wine by quite a bit.

Maybe a better tack is to either dilute the wine into 3 parts water or simply use one fourth as much wine in your recipes. It won't be the same, for sure, but wine cooked for however long you'll need to reduce the alcohol by 3/4 isn't going to be the same either.

 

[ArtZ]

Engineering toolbox site has plenty of tables, I will be surprised if they don't have ethanol/water data.

Lots of good info on Engineering re: thermophysical properties, thanks. However nothing about EtOH evaporation from a water mixture during heating.

 

[ArtZ]

If it were me I'd look at this from a volume perspective. That is, approximately how much reduction of the wine volume by boiling will result in a reduction of the alcohol concentration to, say, 25% of it's original value. I suspect you'd have to reduce the wine by quite a bit.

Maybe a better tack is to either dilute the wine into 3 parts water or simply use one fourth as much wine in your recipes. It won't be the same, for sure, but wine cooked for however long you'll need to reduce the alcohol by 3/4 isn't going to be the same either.

The Shaoxing wine that I want to do the EtOH reduction has a very distinctive bouquet. If a recipe that I would use the Shaoxing already calls for a large amount of liquid, your your strategy may work. For a stir fry though, adding a tablespoon of Shaoxing as the stir fry cooks may result in a residual alcohol taste.

 

[Chestermiller]

This is an attempt to map out a math model for the system of liquid wine in a pot open to the atmosphere at 1 bar, with a horizontal liquid surface of area A. The entire wine is assumed to have been brought to the operating temperature T, and the air above in the pot is also at T. So the time to preheat to the operating temperature is not included.

All the wine is assumed to be at constant water and ethanol concentrations spatially, except, possibly, in close proximity to the interface with the air (see below). The overall mass balances for the wine, and the mass balance for the ethanol component are written as follows:
$$\frac{dm}{dt}=-\left(k_W\frac{p_W}{RT}+k_E\frac{p_E}{RT}\right)A\tag{1}$$
$$\frac{d(mx)}{dt}=-k_E\frac{p_E}{RT}A\tag{2}$$where m is the total moles of wine in the tank, x is the mole fraction ethanol, the k's are the mass transfer coefficients of ethanol and water (cm/sec) to the air, the p's are the partial pressures of ethanol and water at the interface. Implicit in these equations is that the partial pressures of ethanol and water in the far-field air are negligible. The mass transfer coefficients are the largest uncertainties in this analysis, since I have not yet found correlations for these as a function of the operating conditions.

If we subtract Eqn. 1 from Eqn. 2, we obtain $$m\frac{dx}{dt}=-k_E\frac{p_E(1-x)}{RT}A+k_W\frac{p_Wx}{RT}A\tag{3}$$Eqns. 1 and 3 are our starting equations.

Let's next next turn to the Vapor-Liquid Equilibrium behavior which applies at the interface between the liquid and vapor. The first thing I wan to call attention to is the relationship between the equilibrium vapor pressure of pure ethanol and pure water. Over the temperature range of interest (60 C to 100 C), the equilibrium vapor pressure is almost exactly equal to 2.2 times the equilibrium vapor pressure of water: $$P^*_{E}(T)=2.2P^*_W(T)\tag{4}$$
@Dullard has pointed out that the VLE behavior of the ethanol-water system does not satisfy Raoult's Law. However, in the present region of system operation, at law mole fractions of ethanol (x < 0.1), the VLE behavior of this non-ideal system will approach: $$p_w=P^*_W(1-x)\tag{5}$$$$p_E=\gamma P^*_Ex\tag{6}$$where #\gamma# is the infinite dilution activity coefficient of ethanol in water. Experimental values of $\gamma$ reported in the literature (http://www.ddbst.com/en/EED/ACT/ACT Ethanol;Water.php) are approximately 3.2. Therefore, combining Eqns. 5 and 6 gives: $$p_E=7.0P^*_Wx\tag{7}$$The figure below shows observed VLE behavior for the binary system ethanol-water at combined pressures ranging from 1/8 bar to 1/2 bar.

Eqns. 4 and 7 describe this behavior very accurately at ethanol mole fractions < 0.1. Therefore, we can confidently use these equations in our model calculation.

If we now substitute Eqns. 4 and 7 into Eqns. 1 and 3, we obtain:
$$\frac{dm}{dt}=-(k_W(1-x)+7k_Ex)A\frac{P^*_W}{RT}\tag{8}
$$$$m\frac{dx}{dt}=-(7k_E-k_W)Ax(1-x)\frac{P^*_W}{RT}\tag{9}$$
In Eqn. 9, if we neglect the value of x compared to 1, and neglect the change in m (as described In Eqn. 8) relative to its initial value $m_0$, the equation reduces to $$\frac{d\ln{x}}{dt}=-\frac{1}{\tau}\tag{10}$$where the characteristic decay time $\tau$ is given by$$\tau=\frac{m_0}{(7k_E-k_W)A\frac{P^*_W}{RT}}\tag{11}$$

Based on this final approximate equation, the only thing left to do now is to estimate values of the mass transfer coefficients and provide an initial value for the initial number of moles $m = m_0$. I will continueue unless there are substantial objections to the development I have presented. @ArtZ, what is the initial volume of wine you intend to put in the 4.5 quart stock pot? Are you sure that stock pot is 12" in diameter?

 

[ArtZ]

Since the Shaoxing comes wine is sold in 750 mL bottles, I was thinking the sample volumes would be two 250mL samples tested at different temperatures with the other third acting as the taste control sample. The third would remain unheated. Alcohol measurement should be easy as the digital refractometer only requires 2-3 drops of test sample.

 

[Chestermiller]

Since the Shaoxing comes wine is sold in 750 mL bottles, I was thinking the sample volumes would be two 250mL samples tested at different temperatures with the other third acting as the taste control sample. The third would remain unheated. Alcohol measurement should be easy as the digital refractometer only requires 2-3 drops of test sample.

You’re using a 12” diameter pot to heat 250 cc wine?

 

[JT Smith]

The Shaoxing wine that I want to do the EtOH reduction has a very distinctive bouquet. If a recipe that I would use the Shaoxing already calls for a large amount of liquid, your your strategy may work. For a stir fry though, adding a tablespoon of Shaoxing as the stir fry cooks may result in a residual alcohol taste.

I am saying use the same amount of liquid, just dilute the wine. Or, alteratively, use less liquid. Either of these has the unfortunate effect of reducing not just the alcohol but also the other flavor components. But cooking the wine for a long period in advance will also affect the flavor, particularly the volatile aromatics that likely make up most of the bouquet.

You're going to be forced to live with some sort of compromise in quality. Aside from the fun of doing the physics I think that ultimately you'll simply have to try it and see if it's acceptable. So compare that to the alternate method I'm suggesting: using less wine. See how it goes. It's an easy test.

 

[ArtZ]

You’re using a 12” diameter pot to heat 250 cc wine?

I was just thinking about that too. The original plan was to use the entire 750mL. Also, I was thinking about surface area figuring that more SA is better. You are right, and will reduce the size and diameter of cooking pan.

Also was thinking about the thermocouple placement. A couple years ago I was working on recipe for a food product and needed a reliable way to hold the thermometer in the pan.

Created a crude fixture that clipped on the side of the pan. Worked fine. In this experiment I think that it's important to keep the thermocouple away from the side of the pan to prevent erroneous temperature measurements.

What I will do is add a short arm to the clip and attach the thermocouple (TC) to the arm and attach the TC to a small float whereby the TC will remain at a constant depth below the wine surface as the wine volume is reduced.

 

[Chestermiller]

I was just thinking about that too. The original plan was to use the entire 750mL. Also, I was thinking about surface area figuring that more SA is better. You are right, and will reduce the size and diameter of cooking pan.

Also was thinking about the thermocouple placement. A couple years ago I was working on recipe for a food product and needed a reliable way to hold the thermometer in the pan.

Created a crude fixture that clipped on the side of the pan. Worked fine. In this experiment I think that it's important to keep the thermocouple away from the side of the pan to prevent erroneous temperature measurements.

What I will do is add a short arm to the clip and attach the thermocouple (TC) to the arm and attach the TC to a small float whereby the TC will remain at a constant depth below the wine surface as the wine volume is reduced.

I’m thinking a 500 ml beaker 3” in diameter.

 

[ArtZ]

I’m thinking a 500 ml beaker 3” in diameter.

Experiment design always requires iterations. I've worked in research labs my entire career that were well equipped both in instrumentation and labware. Now, being retired, I have no labware access and generally have to make do with what I can scrounge around the house. Your suggestion is a good one. I do plan to hobble over to the local Labpro to get some sample retention bottles with caps for later tasting.

I'll have to rethink the thermocouple positioning; I am sure I can find a way to position the TC that will be acceptable.

 

[ArtZ]

Experiment design always requires iterations. I've worked in research labs my entire career that were well equipped both in instrumentation and labware. Now, being retired, I have no labware access and generally have to make do with what I can scrounge around the house. Your suggestion is a good one. I do plan to hobble over to the local Labpro to get some sample retention bottles with caps for later tasting.

I'll have to rethink the thermocouple positioning; I am sure I can find a way to position the TC that will be acceptable.

Several posters remarked that the process that I'm planning to use heat to reduce the alcohol in the wine is distillation. I didn't get it at first, but, yes it is though I have no interest in recovering the alcohol distillate. What I saw online multiple times is a flask with wine where the wine is heated with a Bunsen burner. The vapors are cooled to recover the distillate using a water condenser.

There is apparently no control of the heating of the wine with the Bunsen burner. The process is probably terminated when the recovered alcohol no longer flows from the condenser.

Maybe I can use my sous vide bath to do this with more precision than the butane burner and a thermocouple.

I'm not sure what maximum temperature of my ANOVA sous vide bath but I'm guessing it must be close to 100C. I probably can't use the distillation flask because I'll want pipette out a small quantity of the remaining wine at intervals to measure ABV so that I plot concentration as function of time at a fixed temperature

 

[Chestermiller]

This is follow up to my post # 54.

According to this online calculator https://www.handymath.com/cgi-bin/e...ncv=15&submit=Calculate&volwght=&calcvolwght=, for 15% ethanol by volume, the mass fraction ethanol in the wine is 12.1%. For a molecular weight of 46 g/mole for ethanol and 18 g/mole water, this breaks down to an initial mole fraction ethanol of $x_0=0.051$ for the ethanol and $(1-x_0)=0.946$ for the water. This reduces to a weighted average molecular weight of 17.1 for the wine mixture. So, if we have 250 g of wine initially (assuming a typical initial wine density of 1.0 g/cc), the initial number of moles of wine in the beaker is $m_0=14.6$.

At 80 C (assumed operating temperature), according to the steam tables,, the term $\frac{P^*_W}{RT}$ in the denominator of Eqn. 11 for the characteristic time for ethanol removal is $1.63x10^{-5}\ moles/cc$. Assuming that the 250 ml wine is contained in a 500 ml "beaker" of diameter 3", the area of the heat transfer surface is A = 45.6 cm^2. Substituting these values into Eqn. 11 of post #54 for the characteristic ethanol removal time $\tau\ (sec)$, we obtain $$\tau=\frac{19700}{7k_E-k_w}$$As noted in post #54, the mass transfer coefficients in the denominator are highly uncertain, and, because of the higher diffusion coefficient of water than of ethanol in air, the value of $k_W$ is expected to be a little higher than $k_E$. Individual k values tend tend to range from about 0.1 cm/sec too about 10 cam/sec. My best crude guess for the value of denominator of this equation would be about 4 cm/sec. Substituting this into the above equation yield a value of $$\tau=\frac{19700}{4}=4900\ sec= 80\ min$$So we are probably looking at times of 10's of minutes to hours for the ethanol concentration to be reduced to desired levels in the wine.

 

[JT Smith]

What final volume of wine is predicted by this model?

 

[Chestermiller]

What final volume of wine is predicted by this model?

For what change in the mole fraction of ethanol?

 

[JT Smith]

Wasn't the premise a reduction to about 4% ABV?

From 0.051 to 0.013.

 

[Mayhem]

Yes, that’s what I said. At 202, it is 7.5% in the liquid.

This diagram is for the binary system water and alcohol; no air.

To which degree would you say the introduction of dissolved acids and flavor compounds would change this data?

 

[Chestermiller]

Wasn't the premise a reduction to about 4% ABV?

From 0.051 to 0.013.

If we divide Eqn. 8 by Eqn. 9 of post #54, we obtain (neglecting the value of x compared to 1):
$$\frac{d\ln{m}}{d\ln{x}}=\frac{(k_W+7k_Ex)}{(7k_E-k_W)}$$Dividing numerator and denominator by $k_W$ and assuming that the ratio of the mass transfer coefficients is proportional to the ratio of their diffusion coefficients in air (i.e.. k_E/k_W=0.4), we obtain:$$\frac{d\ln{m}}{d\ln{x}}=\frac{(1+2.8x)}{1.8}$$The value of x is never larger than 0.05, so, at worst, we have $$\frac{d\ln{m}}{d\ln{x}}=\frac{(1.14)}{1.8}=0.63$$So, based on this crude approximation $$\frac{m}{m_0}=\left(\frac{x}{x_0}\right)^{0.63}=(0.25)^{0.63}=0.42$$So, as you correctly point out, to arrive at the desired reduction in the concentration of ethanol in the liquid, over half the liquid would have to be evaporated.

 

[JT Smith]

Thank you for doing the math for me.

I can't speak for the OP but I believe the idea was to remove most of the ethanol while leaving the character of the wine otherwise unchanged. In this case the wine ends up concentrated. Ignoring that aromatics will undoubtedly be lost and some fraction of the remaining flavor compounds will likely be denatured it would seem to make sense to return enough water so that the final mixture is at the same concentration of flavor components. That way a spoonful of wine in a recipe is still a spoonful of wine. Adding water would further reduce the ethanol concentration. So if 4% ABV is the target and adding some water back to return to the original volume is also desired, then the initial reduction target could be set higher. Maybe you only need to heat it until it's at 7% ABV or whatever.

 

[ArtZ]

Thank you for doing the math for me.

I can't speak for the OP but I believe the idea was to remove most of the ethanol while leaving the character of the wine otherwise unchanged. In this case the wine ends up concentrated. Ignoring that aromatics will undoubtedly be lost and some fraction of the remaining flavor compounds will likely be denatured it would seem to make sense to return enough water so that the final mixture is at the same concentration of flavor components. That way a spoonful of wine in a recipe is still a spoonful of wine. Adding water would further reduce the ethanol concentration. So if 4% ABV is the target and adding some water back to return to the original volume is also desired, then the initial reduction target could be set higher. Maybe you only need to heat it until it's at 7% ABV or whatever.

Hmm, good point about increasing the initial reduction ABV if the remaining if the the original volume is restored by adding water.

 

[ArtZ]

I received the digital refractometer on Thurs. Yesterday, I attempted the calibration of the unit. It's a simple procedure requiring only 2-3 drops of distilled water, then press the cal button. Should return 0.0% ABV on the display. Instead the unit returned different error messages on subsequent cal attempts. I'll try again today to cal the unit. If no success, I'll return it for a replacement.

I see a lot of progress on the analytical side. Great work! Keep going.