27 replies to this topic

[chemical_teo]

Hi all, 

 

I am a new chemical engineering student and I've got an exercise that I don't really understand because it's very different from what I'm used to (no graphic is provided).

 

Butyl acetate (BA) is produced in the liquid phase of Acetic Acid (A) and Butanol (. The extent of reaction is limited by the equilibrium constant since it's an esterification. 

 

An equimolar mixture of reactants (no products) at a flow rate of 100 kmol/h is fed to the flash at T = 389 K (constant) and p = 1 bar. The equilibrium constant is given to be K = 2.77 .  

 

 

I need to find the liquid composition, the butanol conversion at equilibrium and the dew point pressure of the mixture. All of this assuming no vapor phase (so a simple reactor). 

 

Concerning the butanol conversion, I think it's quite simple: K = x^2 / (0.5-x)^2 => x = 0.31 . Thus, there is still 0.18 of butanol  (31% has been converted). 

 

Concerning the liquid composition, I don't get the question. I know at this temperature water will be in the vapor phase but I don't have the boiling temperature of the rest. 

 

All the other informations I have are Antoine's parameters, enthalpies of formation (liq), enthalpies of vaporisation and heat capacities at constant pressure. 

 

 

Many thanks in advance for your kind help.

 

[MrShorty]

Your assumption that water will be in the vapor phase is only partially correct. Yes some of the water produced will go into the vapor phase, some of the water will remain in the liquid phase. The vapor phase will also contain some of each of the other compounds.

 

I am not certain exactly what is expected by "find the dew point pressure of the mixture", but it does not look like you have all of the information needed to find that solution. I would expect that you also need to find out "what am I going to use for my thermodynamic/phase equilibrium model?" (an NRTL based gamma-phi model would be common) and then find out "what are the appropriate interaction parameters for my chosen model?". Can we assume that you have seen gamma-phi vapor-liquid equilibrium (VLE) problems before?

[chemical_teo]

Thank you for your reply!

 

 

 Can we assume that you have seen gamma-phi vapor-liquid equilibrium (VLE) problems before?

 

Yes! I've seen them. However, in most cases I was given a graph of the mixture with the partial fraction. Here, I don't have anything Antoine's parameters, temperature, pressure, Cps and enthalpies. 

 

 

Nonetheless, I was thinking yesterday that we might assume ideal behaviour and therefore find the K-parameter (Raoult) for each component since K = P_sat / P (P_sat found using Antoine's equation). I also found in literature that 1/p(dew) = y1 / p1 + y2/p2 . 

 

However, for the first question which is asking the liquid composition... I really don't see how to solve the problem. They precise "Assuming no vapor phase" so intuitively one would say 100% liquid, no? 

[MrShorty]

I am guessing as much as you are. I cannot say for sure exactly what the homework question is asking.

However, for the first question which is asking the liquid composition... I really don't see how to solve the problem. They precise "Assuming no vapor phase" so intuitively one would say 100% liquid, no?

  I would guess that you are correct -- for this part of the problem assume that the solution is 100% liquid. I would guess that this part of the problem is testing to see if you can solve the chemical equilibrium part of the problem without the complications of solving the phase equilibrium part of the problem. From the OP, I got the impression that you had already done some work on solving the chemical equilibrium problem (% conversion). In the process, were you able to solve for how much of each reactant was made from the products? Can you express that as an overall liquid composition.

 

I would guess that the dew point part of the problem would be visualized as "what then happens if you instantly drop the pressure so that all of that liquid instantly vaporizes with no time for further reaction." Can you solve the phase equilibrium problem and identify a maximum pressure in the drum (assuming no temperature change) so it is all vapor. Can you solve the phase equilibrium problem without worrying about the chemical equilibrium problem.

 

You could assume Raoult's law. I expect that a big part of this depends on whether you instructor is testing for "can the student recognize a VLE problem and apply any VLE model to the problem?" and how much is testing for "can the student choose a good model for a VLE problem?" Assuming ideal is the simplest mathematically, but, considering differing molecular sizes and polarities etc., it is also going to give poor quantitative results. It would be between you and the instructor to decide how much of this is about how well you can choose a VLE model.

 

Those are my guesses at what the instructor wants to see in this overall problem. You are in a better position to clarify with the instructor/assistant what he/she wants to see from you.

[chemical_teo]

Thank you for your help. So, if I consider 100% liquid, I obtain 31.25% of water (W), the same amount of BA (31.25%) and there is still 18.75% of A and B remaining. Concerning the butanol conversion, we see that there is still 18.75/50 = 37.5% of butanol remaining at equilibrium. Thus, the conversion is (100-37.5) = 62.5% . 

 

My tutor told me I could use Raoult's law in the exercise for the second part because we haven't seen how to treat real / non-ideal cases yet. Do you think the way I could do this is by first calculating all the four Ks (Raoults coefficients) and then apply the equation y = K x to obtain the fraction of vapour ? This would allow me to apply the following equation: 

 

 

1/p_dew = y1/p_sat1 + ... + y4/p_sat4

 

(1, ... 4 are the four component)

 

And therefore to find the dew pressure point ? Could also do this with the bubble point I guess...

 

 

Edit: By the way, is there a tool to write LaTex on this forum? Wanted to write $\frac{1}{{{p_{dew}}}} = \frac{{{y_1}}}{{{p_{sat,1}}}} + \frac{{{y_2}}}{{{p_{sat,2}}}} + \frac{{{y_3}}}{{{p_{sat,3}}}} + \frac{{{y_4}}}{{{p_{sat,4}}}}$

Edited by chemical_teo, 26 September 2018 - 01:05 PM.

[MrShorty]

Yes, that should work -- though I think you might not be clear on exactly what you want to do for dew point (hint: which comes first -- calculate Pdew or K? if you decide to do a bubble point calculation as well, which comes first -- Pbub or K?) (hint2: think very carefully about what "bubble point" and "dew point" mean).

 

With that, it looks like you should have everything you need to solve the problem. Any questions about what to do next?

[chemical_teo]

From what I know the bubble point is the pressure (or temperature) where bubbles start to appear in the liquid phase and the dew point is the pressure where dew appear in the saturated vapour phase. 

 

From the equations I would have say to calculate first K since I will use K to find y (fraction of the component in the vapour phase) for the dew point. Concerning the bubble point, I don't think I will need K since we look at the liquid phase. Please correct me if I'm wrong...

 

Thanks!

[MrShorty]

From what I know the bubble point is the pressure (or temperature) where bubbles start to appear in the liquid phase and the dew point is the pressure where dew appear in the saturated vapour phase.

Those are the standard textbook definitions I would expect. Sometimes the challenge is in making sure we really understand (if you've done Heinlein, I want to use "grok" here instead*) what those definitions mean and how they intersect with the problem at hand. In this case in particular, the real question is "exactly what gas is the problem asking you to compute dew point of?"

 

 

Since I am not an educator, I never quite know how best to handle these kinds of questions to best effect. I don't want to give the answers to you, because you need to see them for yourself. I also hope that I am reading and understanding the problem statement correctly, because I will be very embarrassed if I have misunderstood something. Maybe I will answer this way:

 

Concerning the bubble point, I don't think I will need K since we look at the liquid phase.

I think this is correct. Try it and see what you get. What does your result tell you about the "assume everything stays in the liquid" assumption? How far do you need to drop the pressure before a vapor phase will form or how far do you need to increase the pressure to keep all of the products and reactants in the liquid phase?

 

 

 

I would have say to calculate first K since I will use K to find y (fraction of the component in the vapour phase) for the dew point.

I think this is incorrect, but I am going to encourage you to try the calculation this way (it's not a long or difficult calculation, so you should lose little time/effort). I expect one of two things will happen -- 1) you will get part way through the calculation and find yourself stuck and be unable to continue because you encounter a quantity that you don't know. That should help you see why you cannot calculate K first. OR 2) you will get all they way to the end of the calculation with a new dew point pressure, look back at where you started, and become confused. Some thought at this point should help you understand why you get this "trivial" answer which should help you see why you should calculate Pdew first.

 

* -- Wikipedia is probably as good as any for trying to understand what grok means: https://en.wikipedia.org/wiki/Grok

[chemical_teo]

Thanks! 

 

I actually thought about the problem the whole day but I still don't really understand it. For me, the dew point / bubble point we need to find is the one of the mixture and not the one of a specific species. 

 

Nonetheless, I did the calculations with what I had in mind. Here are the K-values I used (calculated them using Antoine's equation): K_A = 1.04997 , K_B = 1.05985 , K_BA = 1.34205 and K_W = 0.648135.

 

I calculated the bubble point as explained in my previous post: P_bubble = x1*p_sat1+...+ x4*p_sat4 (p_sat = K-value * 1bar) => P_bubble = 0.1875*1.04997+...+0.648135*0.3125 = 1.018 Bar approximately.

 

Also did the calculation for the dew point but by using K first... I clearly don't see how I could calculate it without have K since I need to know the amount I have in the vapour phase. Used y = K x to find y for each and then 1/p_dew = y1/p_sat1 + ... (as explained in the previous post). I obtain p_dew = 1.008 Bar. 

 

It is indeed weird that my dew pressure is lower than my bubble pressure but I don't know what is wrong and how I should do it... 

 

 

However, maybe the answer would simply be to tell that there is no vapor-liquid equilibrium existing at the given flash conditions ?

[MrShorty]

However, maybe the answer would simply be to tell that there is no vapor-liquid equilibrium existing at the given flash conditions ?

But is that what your results are saying? Both your calculated bubble point and dew point are above the stated pressure in the problem 1.000 bar. What happens when the set pressure is below the liquid's bubble point? What happens if the set pressure is also below the estimated dew point?

 

I might also ask, when you calculated the K values for the dew point, what pressure did you use? You indicate that you used the Antoine equation for each compound to get P*, but K is also dependent on the system pressure? Did you use the bubble point pressure? The system set pressure? Something else?

[Art Montemayor]

In all the engineering classes, seminars, text books, and lectures that I’ve attended and have had at my disposal and study through the years, I have never heard of a “dew point pressure” of a mixture.  Like Shorty, I’m at a loss in trying to understand what your project or assignment is.  As moderator I’m trying to identify the title of this thread so I can accept it into our Search Machine where it can be documented.  The classical definitions of a dew point and a bubble point that I have lived under are as follows:

 

The dew point is the temperature at which a gas or gaseous mixture starts to form the initial drop of moisture of a condensable component it contains.  That component may be water vapor or possibly a hydrocarbon vapor.  To be specific, the dew point should be defined as to which condensable is involved and at what pressure (usually atmospheric) it is referred to.  Otherwise the information is useless.

 

In phase equilibria, the bubble point is the temperature (at a stated pressure) where the first bubble of vapor is formed when heating a liquid consisting of two or more components.

 

For a pure, single component liquid fluid the bubble point and the dew point are one and the same and are conventionally referred to as the "boiling point" at a stated pressure.

 

Perhaps Chemical Engineering in India is now being taught with the dew point being referred to a pressure rather than a temperature.  I don’t know.  And I can’t imagine what for; but if that’s the case, so be it.

 

Please let us know just what a “Flash Drum” has to do with a Dew Point.  The thread title makes no sense.

[chemical_teo]

Thanks for your replies. 

 

 

I might also ask, when you calculated the K values for the dew point, what pressure did you use? You indicate that you used the Antoine equation for each compound to get P*, but K is also dependent on the system pressure? Did you use the bubble point pressure? The system set pressure? Something else?

 

 

I used the pressure of the system which is equal to 1 bar. 

 

What happens if the set pressure is also below the estimated dew point?

 

 

 

Would mean we're purely liquid and the assumption would make sense, no?

 

 

 

 

Please let us know just what a “Flash Drum” has to do with a Dew Point.  The thread title makes no sense.

 

 

Nothing I guess.. It's simply that this is done in a flash drum... May I change the title ? 

 

Also, the question of the problem is exactly "Determine the bubble and dew point pressure of the mixture at chemical equilibrium". I understand we need a pressure and not a temperature but I may be wrong.

 

 

By the way, I know the definitions but I don't see how to put it into equations to obtain the temperature / pressure... 

[MrShorty]

Would mean we're purely liquid and the assumption would make sense, no?

Are you sure? Let's simplify to a pure component (how about water) where the dew point and bubble point are the same and think through this. Let's say we feed water into this flash drum at 389 K and 1.000 bar (dew point pressure=bubble point pressure=vapor pressure=1.74 bar). If your answer is anything except "the water all evaporates and becomes steam at 389 K and 1.000 bar (assuming pressure and temperature do not change during the process)," then I suggest you think more carefully about what dew point and bubble point really mean (as I said, it can be easy to recite the textbook definitions without really understanding what they mean for the problem at hand).

 

 

 

I used the pressure of the system which is equal to 1 bar.

So, you calculated K at 389 K and 1 bar. It should be obvious that K will vary with system pressure (you would get a different K if you used a system pressure of 0.9 bar or 1.1 bar). As I understand the question, it is stating, "if we could vary the pressure as much as we want (keeping T fixed at 389 K), at what pressure would the liquid disappear?" Because pressure is a variable in this part of the problem, we cannot know K of each component until we know P. Then, however, you assert that you cannot know P, because you don't know y, and you cannot know y without knowing K (and we get into circular logic and we begin to wonder if we can know anything). Hopefully, the key to breaking out of the circular logic is to answer this question -- what will y be at the point when all of the liquid is gone (assuming no further reaction occurs)?

 

@Art: I agree that dew point pressure is less common than dew point temperature, but I encounter dew point pressure often enough that I am not surprised by it. I think that, in most processes, it is easier to fix pressure and let temperature float. In these situations, like meteorologists, we may want to know at what temperature the liquid phase will appear/disappear at a fixed pressure. Though less common, I do encounter situations (maybe because I work on a lab scale rather than process scale) where I fix the temperature and allow the pressure to float, at which point I may want to know at what pressure the liquid phase will appear/disappear. Certainly the problem could have been stated as find Tdew at fixed P of 1 bar (and the OP will almost certainly encounter those problems). At this point, I think the question is trying to help the student grapple with the concepts of bubble and dew point and hopefully begin to understand them before moving on to applying those concepts to non-ideal solutions.

Edited by MrShorty, 28 September 2018 - 10:07 AM.

[Art Montemayor]

Shorty:

 

Thanks for your detailed comments and recommendations.  I totally agree with your ideas on how to best handle this important subject and facilitate the learning experience for Chem_teo.   Your comments and recommendations are valuable not only because they are correct, but they also should be of important input to all students and young engineers possibly reading this thread.

 

I have edited the thread title to what I think best describes the discussed topic.

[chemical_teo]

Let's say we feed water into this flash drum at 389 K and 1.000 bar (dew point pressure=bubble point pressure=vapor pressure=1.74 bar). If your answer is anything except "the water all evaporates and becomes steam at 389 K and 1.000 bar (assuming pressure and temperature do not change during the process)," then I suggest you think more carefully about what dew point and bubble point really mean (as I said, it can be easy to recite the textbook definitions without really understanding what they mean for the problem at hand).

 

 

Before saying that, I think I would have used the Clausius-Clapeyron Equation in order to see the boiling point of water at this pressure to see if we are liquid or not. 

 

As I understand the question, it is stating, "if we could vary the pressure as much as we want (keeping T fixed at 389 K), at what pressure would the liquid disappear?" Because pressure is a variable in this part of the problem, we cannot know K of each component until we know P. Then, however, you assert that you cannot know P, because you don't know y, and you cannot know y without knowing K (and we get into circular logic and we begin to wonder if we can know anything). Hopefully, the key to breaking out of the circular logic is to answer this question -- what will y be at the point when all of the liquid is gone (assuming no further reaction occurs)?

 

 

Said like that, I suppose at this point (the dew point, right?) y_H2O = 1 (H2O because it's the one we look from what I got from the previous discussions with @Art I think). So, this would mean that 1/p_dew = y_H2O / p_satH2O ? So, it will basically be equal to the saturation pressure of water at this temperature given by Antoine's equation? This doesn't make much sense to me since this would mean that the bubble point will be the same as the dew point. True in the case of simple water as you said but not in my case right? (I cannot say y_A = 1 y_B = 1 and y_BA = 1 right?)

 

 

Anyways, it's not a graded exercise or what so I can just wait for the correction. Simply wanted to understand well the problem :-) 

Edited by chemical_teo, 29 September 2018 - 08:37 AM.

[IllusionistXY]

Dear all,
I have been struggling with the calculation of dew and bubble points of a water/non-condensable gases mixture. I hope it is ok  to discuss the problem using this thread.
 

So, I have a mixture of H2O/H2: yH2=0.6 and p=10 bars. Assume ideal gas for simplicity and that H2 is non-condensable (xH2=0).

 

To calculate the bubble point:
sum(yi)=1.

sum (yi)=sum(xi*ps,i/p)=1.
Knowing that xH2=0,  xH2O=1

p=ps,H2O---> bubble point temperature can be calculated using for instance Antoine equation to calculate ps,H2O.
 
Likewise for dew point calculation:
sum(xi)=1, xH2O=1
p*yH2O=ps,H2O.

 

My problem is that, in this case, the dew point temperature would be lower than the bubble point.

Thanks in advance..

Best Regards

just a thought, should I include yH2=0.6 in the calculations of the bubble point?
yH2+xH2O*ps,H2O/p=1 ?!!

Edited by IllusionistXY, 20 November 2018 - 04:48 PM.

[PingPong]

The bubble point of your H₂/H₂O mixture would be extremely low as it would require a temperature at which the H₂ is no longer in gas phase but in liquid or probably solid phase.

 

It is useless to know such theoretical bubble point temperature, so why do you want to determine it?

[IllusionistXY]

PingPong:

 

Thanks for your reply.

 

Originally I have a gas/steam mixture. I want to get rid of the water by condensation.  Therefore, I thought I needed to calculate the dew and bubble point in order to operate the condenser at a temperature below the bubble point.  In this case, I can ensure that all the H₂O is in the liquid phase.  The bubble point could be just the boiling Temperature of pure water?!

 

Thanks in advance.

[MrShorty]

How much water in the liquid phase is "all" of the water. I have heard it said that the difference between a scientist/chemist and an engineer is: The scientist/chemist will point out that the water content of the vapor phase in a problem like this is never exactly 0. The engineer, while conceding the point, will say, "I can't make the water content of the vapor phase exactly 0, but I can make it small enough that it is, for my practical purposes, essentially 0." The key step for the engineer is to specify exactly what vapor content of water is small enough, then find out what temperature/condition that corresponds to. This really isn't a "bubble point calculation". This is more of a generic VLE calculation.

 

Using your assumptions that the gas is non-condensable (so we assume that the liquid is 100% water), we can assume that the partial pressure of water in a H2 atmosphere is simply a function of the vapor pressure curve of water (or ice, if we decide to go below the freezing point of water). The important to realize is that you are not really calculating a bubble point, so don't get distracted by bubble point specific algorithms.

[IllusionistXY]

MrShorty:

 

Well, I do acknowledge the fact that not ALL the water will be condensed.  What I meant earlier is I want a subcooled liquid.  Anyhow, the amount of water in the liquid phase will be a decision variable (I am running an optimization problem).  I need the bubble point/ dew point in order to calculate the heat of condensation.  So, say I want to find these two temperatures, how can I do it?  I know the pressure and the gas/vapor mixture composition entering the condenser.  What have I done wrong that the dew point is lower than the bubble point?

 

Let me rephrase: assuming you have liquid water and non-condensable gas, are we talking here about bubble point or simply boiling point?  Since this problem seems to me like boiling water in an open pot - i.e boiling temperature is reached when ps H₂O is equal to the atmospheric pressure.

 

Likewise, a mixture of non-condensable gas and steam: will we talk here about dew point at which the first drop of water condenses or a condensation temperature that should be the same as boiling point of water?

Thanks in advance

[PingPong]

What you are looking for is not the bubble point or the boiling point.

 

You have to decide how much water vapor is allowed to remain in your non-condensable gas after cooling.

 

Once you set that number it is easy to calculate with what water partial pressure in the gas that corresponds. Assuming ideal behavior you can simply use a steam table to determine the corresponding temperature.

[IllusionistXY]

PingPong:

 

As I said in my previous reply to Mr. Shorty, the water content in the gas mixture is a decision variable that will be optimized.  I will then perform flash calculation to determine the temperature of the Flash unit and the composition in the different phases.  However, I also need to calculate the Latent heat!  The enthalpy of vaporization (here condensation) is temperature dependent.  So, at which temperature should I calculate that?  the dew point temperature?  
I am not performing only the mass balance but also the energy balance of the condenser. 

[PingPong]

I don't really see what there is to optimize here.

Either there is a requirement for water content of gas,

or there is a requirement for outlet temperature.

If there would be no requirement you could chose condenser outlet temperature based on available cooling medium (cooling water, aircooling, .... whatever).

 

In any case you need to set the condition at the condenser outlet.

Set a water content in the gas and calculate the corresponding temperature,

or set a condenser outlet temperature and calculate the corresponding water content in the gas.

Both calculations can easily be done by hand using a steam table, assuming system at only 10 bar behaves nearly ideal.

 

Duty of condenser is enthalpy difference between gas mixture in and gas plus liquid water out.

Enthalpy of water vapor in and out, and liquid water out can be read from steam table.

Edited by PingPong, 24 November 2018 - 05:09 AM.

[IllusionistXY]

PingPong:

 

I don't wanna go into too much details in describing my problem. so, let's forget about my aim of these calculations for a moment and try to solve the main question here: 

I have the aforementioned system with steam and non-condensable gas. How can I calculate the bubble and dew points? did I do anything wrong there? 

[PingPong]

In this case the water dew point can easily be calculated manually using a steam table.

 

In this case the bubble point does not exist !

 

If water comes out of the condenser that water will always have a bubble point equal to the outlet temperature of the condenser. So it can be anything equal to or below the dew point.

It has no meaning so it is about time you stop fussing about it.

 

Now take a steam table and start calculating!

Edited by PingPong, 24 November 2018 - 02:27 PM.