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# Vapour Pressure for Mixtures

## Vapour Pressure for Mixtures

(OP)
I require to calculate the vapour pressure for a mixture of hydrocarbon gasses. Unfortunatly I am not really sure how to. I was told that partial pressures might be the right way to go but that this may not be the case. Any help would be appreciated.

### RE: Vapour Pressure for Mixtures

do you have access to a process simulation software? no matter which one, they all should be able to calculate vapor pressure.

If not, even in Perry's they calculate mixture vp as sum of partial vp. so that method should be precise enough for most appliances.

### RE: Vapour Pressure for Mixtures

Dear Friesian

Your question to calculate the vapour pressure of hydrocarbon gases is incorrect. Gases have no vapour pressure to the best of my knowledge. It is liquids that have  vapour pressure which represents the equilibrium between the liquid and its vapor phase. This is readily calculated by Antoine' s eqn.
The method to calculate the partial pressure of a component in the vapour phaseof a  muticomponent liquid  mixture is found by raoults and dalton law if assuming ideality.

### RE: Vapour Pressure for Mixtures

Since you are speaking of a mix of gases, their partial pressures are the result of multiplying the total pressure by the individual mol fraction, assuming no association or otherwise intermolecular effects. Dalton's Law would define them as the pressures they would exert if they were alone in the container. And the formula for each "i" hydrocarbon would be :

Pi = niRT/V

This is the formula for ideal gases (low P, high T). Adding up all estimated individual pressures would result in the total system pressure.

### RE: Vapour Pressure for Mixtures

I find none of the answers provided to date to be theoretically correct.  The only reliable way to compute the vapor pressure of a multicomponent mixture is to perform a bubble point calculation.  This is done using the appropriate thermodynamics to model the vapor and liquid phase fugacities.  For high pressure hydrocarbon systems, an equation of state can be used for both phases.  Examples are the Soave, Peng-Robinson, BWR, or Lee-Kesler equations of state.  The Dalton Law approximation for the vapor phase partial pressures must be multiplied by the vapor phase fugacity coefficient obtained from such an equation of state.

For complex chemical mixtures, one must modify the ideal liquid phase fugacity (Raoult's Law).  This is done by multiplying the liquid mole fraction with the activity coefficient and a reference pure component fugacity (close to the vapor pressure only at low pressures).  Such activity coefficient models include the Wilson, NRTL, or UNIQUAC options.

The vapor and liquid phase fugacities must be equal at equilibrium.  However, the bubble point temperature is unknown and the other terms are complex functions of temperature, pressure, and composition for both vapor and liquid phases.

The overall calculation procedure is, therefore, highly iterative and requires use of a computer in most practical cases.  This is best done using a commercial process simulator.  Selection of the thermodynamic models is the key to success - the wrong choices will give you garbage for answers.

(1) "Chemical Engineeering Thermodynamics" by Smith, van Ness, and Abbott (McGraw-Hill)
(2) "Molecular Thermodynamics of Fluid Phase Equilibria", by Prausnitz et al (Prentice-Hall)
(3) "The Properties of Gases and Liquids" by Reid, Prausnitz, and Poling (McGraw-Hill)

### RE: Vapour Pressure for Mixtures

To mirchee, bubble point calculations are carried out on liquid hydrocarbon mixtures. Dew point calcs. on vapours. The more conventional methods using tabulated K (=y/x) values are still quite useful.

In this particular case friesian is asking for the pressure of a mixture of gases at a given temperature. His wording "vapour pressure" may be confusing since it hints at the presence of liquids. Therefore, I still think, the use of published real (or ideal) gas formulas should be applicable within their margins of error.

### RE: Vapour Pressure for Mixtures

It is interesting how a question that is not too specific draws out some firm responses.  Since the "game" here seems to be to interpret the original question, I am guessing that this person meant "gasses" to mean a mixture of things like methane, propane, butane, etc. without regard to the state that they are in.  I would also guess that this is ambient temperature.   I would assume that the activity coefficients are equal to one since they are most likely similar species (differing only by MW).  If the pressure is not too high then the ideal gas law may be assumed.  Therefore, the vapor pressure can be calculated via Raoult's law which is basically a mole average of the individual component pure vapor pressures.

### RE: Vapour Pressure for Mixtures

This response is directed at coments by 25362 and rbcoulter.

Firstly, I agree that what is needed here is a bubble pressure calculation at a fixed temperature.  That too is an iterative procedure that requires solving equations of state (the Soave, if you follow the recommended procedure in the API Technical Data Book).

The trouble with doing the bubble pressure calculation using a "simple" method is that, in general, a hydrocarbon liquid mixture at ambient conditions may easily contain components that are above their critical point.  For example, in a book by the noted thermodynamicist Bruce H. Sage titled "Thermodynamics of Multicomponent Systems" (Reinhold, 1965), the following experimental mole fraction compositions are given on page 224, Table 12.4, for liquid mixtures of methane, ethane, and n-pentane at a bubble point temperature of 100 F:

Mixture #   Pressure (psia)   Methane    Ethane    n-Pentane
1            500                    0.115      0.223     0.662
2            500                    0.055      0.514     0.431
3           1000                    0.224      0.444     0.331
4           2000                    0.599      0.140     0.261

The component critical temperatures (page 292, Sage) are:

Methane     343.19 R  or  -116.48 F
Ethane      550.35 R  or    90.68 F
n-Pentane   847.08 R  or   387.41 F

It is obvious that there cannot be any way to compute vapor pressures for applying Raoult's law at 100 F when two of the three components would be above their critical temperature.  (The  vapor pressure of any component is, of course, utterly meaningless above the critical temperature and anyone who extrapolates needs to go back to ChE school.)

Even at a lower temperature, say 20 F below the critical temperature of methane, the "simple" method will yield a bubble pressure for these mixtures that will be quite wrong.

To make the argument in terms of activity coefficients, we again see an example in Sage's book: On page 183 (Table 10A.1), activity coefficients are listed for methane in a methane - n-butane mixture at 100 F for pressures ranging from 0 to 3000 psia.  For 80 wt% methane, the activity coefficient goes from 1 at 0 psia down to 0.7824 at 3000 psia.  So much for the assertion that activity coefficients for hydrocarbons are unity.

In this day and age, any one doing serious work should have access to a respectable process simulator.  It is quite wrong to assert that all such tools cost hundreds of thousands of dollars.  In fact, I have used PD-Plus (from Deerhaven Technical Sofware in Burlington, MA) for many years now.  This full-fledged simulator can be bought outright for a one-time fee of \$2,000 and has the fastest as well as the most reliable convergence routines for hydrocarbon distillation that I have yet been able to find.  In fact, the method developed by its author was so good that several major vendors purchased the source code and used it to improve their own products.

All respectable engineering design firms today demand, on pain of termination, that their employees perform such design work using the proper simulation and thermodynamic tools.

### RE: Vapour Pressure for Mixtures

To Mirchee, either way, by hand calculation or by the use of computer programmed simulations, one needs to know the mol fraction of the liquid H/C mixture components to estimate the bubble point, or of the vapour components to estimate the dew point. By the way, published K (=Y/X) values are also given for supercritical temperatures. As far as I understood, rbcoulter made assumptions, as we all did, due to the lack of information given by friesian. Not long ago I gave an example of such a calculation for a light naphtha in another thread.

### RE: Vapour Pressure for Mixtures

Re. June 21, 2003 comment by 25362.

Hi:

I have very much enjoyed this set of exchanges and appreciate the issues brought out in prior communications.  I'm sure you know by now that I do a lot of thermodynamic work to make a living and my views are, perhaps, a bit skewed in favor of rigorous methods above all else.

To respond to your last point, K-values, in general, are functions of T, P, and mixture composition even for light hydrocarbon systems.  While the temperature dependence is stronger than than that on composition, it is nevertheless a highly non-trivial matter to establish the composition dependence properly.

Recall that the orignal 8-constant BWR equation was a seminal work, developed in 1940 by Manson Benedict and his co-workers (Webb and Rubin) long before computers had been invented.  M W Kellogg, an engineering company with a long and distinguished tradition, where Benedict worked, made a huge effort to develop a complex series of charts to try to encapsulate the BWR relationships for practical ranges of interest.  Wih numerous simplifying assumptions, these were then converted into the so-called MIT K charts.  Eventually, DePriester converted them into his famous nomograms where all composition dependence was taken out.

In a similar vein, several groups including Hadden and Grayson, Lenoir and Hipkin, NGPSA, etc. developed other series of charts that attempted to encapsulate the composition dependence in a rational way.  The Hadden and Grayson charts survive today in the API Technical Data Book as valid procedures.  However, their use in hand calculations is prohibitively difficult for even relatively elementary problems.  These methods require use of extensive logical checks to decide which procedure or nomogram should be used.  Then, one has to laboriously interpolate among a series of charts to get the K-values before launching the bubble pressure calculation itself.  Each iteration requires revisitng the charts to update the K-values.  Yuk.

Believe me, I did this kind of hand calculation back in the 1960s many times.  Since then, the arrival of mainframe computers made all this manual work unnecessary.  Today, I dare say almost no one uses these methods in hand calculations.

Even use of the simple DePriester charts is mighty inconvenient, since bubble pressure or bubble temperature calculations both require trial and error.  Besides, you have already sacrificed accuracy since all composition dependence has been thrown away.

So that's the reason for my prejudice.

### RE: Vapour Pressure for Mixtures

to Mirchee, I agree in principle with your recommendation of using computer programs, and as I understand there are various to select from, the use of which often is indispensable indeed.
However, for "one-time" VLE estimates of mixtures of light hydrocarbons, I repeat light hydrocarbons, a young engineer can get the "touch" of it by using K values in manually done iterations.
The iterations are neither so many nor so complicated; K values can be obtained, for example, from the Engineering Data Book of the Gas Processors Supply Association or from Sandler's formula.
I was given to understand that the latest published K values are made functions of T,P and composition to adapt them to non-ideality and made to fit experimental data. I must, however, agree, that they give (however useful) only approximate results. David M. Himmelblau in his Basic Principles and Calculations in Chemical Engineering (Prentice Hall) provides a reasonably ample reference bibliography on the subject.

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