Any textbook on vapor/liquid behavior will go through the steps. Basically, you need the y/x ratios (which are typically in graphs) for the components in your gas stream.
The y fraction are the mol fractions for your gas composition.
You then estimate a temperature, read off the y/x ratios for each component and then calculate x (the mol fraction for each component in the liquid phase) for each component. At the dewpoint, the sum of your x fractions will add up to 1.0 (or sufficiently close). If the sum of x doesn't add up to 1.0, you pick a new temperature and repeat.
The heaviest components have the biggest effect on dew-point and are the most difficult to accurately measure. I'm always suspicious of calculated dewpoints unless I can translate them back to another point in the process and verify that the calculated dewpoint is reasonable.
If you would like to know more about calculating dew points, refer to "The Properties of Gases & Liquids" by Reid, etal. There is a chapter on fluid phase equilibtia in multicomponet systems.
You did not indicate the operating pressure. Generally the higher operating pressures require more difficult calculations.
I agree with TD2K about the accuracy of dew point calculations.
Alternatively, you may want to run a flash in Provision or a similar package to determine the dew point, and check sensitivity by running lightest and heaviest expected feed composition besides expected average.
Nowadays, almost every engineering company,(petro)chemical company, oil refinery, Gas plant, you name it, use some sort of simulation program. If you are working for a company working in these areas, certainly for gas industry, your company must have at least one license of such a simulation program! The most used simulation programs are Pro/II and Hysys. If you have access to these softwares, then it takes 5 minutes to determine the dew point at your operating pressure!
Otherwise you have to look into books like perry and/or other useful books like other poeple have suggested
I have just given you last posting a well-deserved star. I agree with you 100 percent and I applaud you for having said what you did about using spreadsheets or simulators without understanding the theory!!
I will be 83 next week ... do you think that may have some correlation with my applauding your statement??
Seasons greetings to all!
Milton Beychok
(Visit me at www.air-dispersion.com)
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I salute the comments on "looking under the hood" on dew point calcs, and I thought I'd expand a bit on TD2K's remark about the heavies having most effect on dew point. As you sum up the X values, as y/K, you can see which components contribute most to the summation of X. The danger in using software to do dew point calculations is that, even if the method for predicting K values is appropriate for the system, they will just give what I would call a "theoretical" dew point, at which temperature the smallest amount of liquid would start to form. If the gas composition in question is itself generated by computer model and has 1 ppm of a very low-volatile heavy, then the y/K for that component could be calculated as being in the vicinity of 1 at the calculated DP. Yet the real gas, if cooled to that temperature might not show any real amount of condensation until some considerable cooler temperature, what you might call the "measurable" dew point. If a simulator is being used, you could observe this by having it do a condensing curve on the gas. The curve of liquid fraction vs. temperature would be essentially flat until the measurable dew point is reached.
You might contact the AGA in Washington. They have been part of a major (recent) effort to improve the ability to calculate the dewpoint of natural gas. Meetings and conferences on the subject have been on-going for two years now. There are some very good technical people on that committee. There are some simulation programs, but if the gas composition in the pipeline is not the same as in the program, someone will be in for a real shock. Even after predicting the dewpoint, it would be highly recommended to ensure compliance with measurement.
In the gas industry, the "dew point" generally denotes the cricondentherm temperature. On the phase envelope, this corresponds to the highest temperature at which any liquid will ever form, irrespective of pressure. Stated another way, above the cricondentherm temperature, you will never condense liquids out of a vapor mixture of the given composition, as you will be in the supercritical region no matter what the pressure.
Calculating the cricondentherm temperature requires doing phase equilibrium calculations (bubble pressures at gradually increasing temperatures) until you reach the cricondentherm temperature. At this point, the curve swings back toward the critical point. Then you are in the liquid region, following the curve further will take you to the cricondenbar pressure, and so on.
Unfortunately, bubble pressure calculations become progressively harder to converge as the system approaches the cricondentherm temperature. I can personally attest to this fact, having spent considerable effort on the problem myself many years ago.
This has been an area of considerable research (Heidemann and Khalil, Michelsen). Their algorithms are both very reliable and fast, and have been encoded in the major process simulators, as mentioned by Homayun in this thread. That is why the most practical solution is to use a commercial package - most engineers do not have the required chemical engineering knowledge, mathematical training, and programming skill to implement, for example, Michelsen's algorithm themselves on a computer. Also, it is virtually impossible to do this calculation by hand, as a horrendous amount of iteration is involved, no matter which equation of state you use to describe the underlying thermodynamics.
Finally, I would also say the "answer" is by no means unique: it depends on the chosen equation of state and, further, on the binary interaction parameters chosen. In addition, the accuracy of the measurement for the heavy ends is crucial. Very small amounts of heavy ends (1 mole percent or even less) can affect the cricondentherm temperature by 10 deg. F or more. Equally unfortunately, the accurate analysis of the C6+ fraction requires very careful chromatographic analysis by skilled analysts using well-calibrated gas chromatographs.
These are some of the reasons why this is a continuing area of concern in the gas industry. Each gas mixture has its own (very difficult to measure, as Dick Russell has stated) unique dew point. The computerized calculation methods should be regarded only as an approximation to the truth. For this reason, most gas supply contracts specify the calculation method to be used (e.g., Peng-Robinson equation of state with specified interaction parameters for all binary pairs).
The fundamentals of these calculations are described by Daubert in "Chemical Engineering Thermodynamics" (McGraw-Hill, 1985). For the best numerical techniques, you'll have to consult Michelsen's papers in the journal Fluid Phase Equilibria (circa 1985).
The reason I started this thread was to gain an understanding of the methods of calculating HCDs. It is simple for me to obtain HCDs from our own chemical engineers who simply run the Hysys program, but that adds nothing to my understanding.
From the responses above there appears to be a relatively simple method as described by TD2K (and I intend to order the book "The Properties of Gases & Liquids" by Reid, etal as sugested by srfish) and more complicated methods that involves equations of state and the convergence problems mentioned by UmesMathur.
I expect that the more complicated methods are most accurate and hence most appropriate in a professional chemical environment. My concern is that the complexity could hinder my understanding.
At the moment, I am struggling to understand why I need to get involved with equations of state (and fugacities and fugacity coefficients, mentioned on the internet) if equilibrium valves y/x are available for components from C1 to C6+ for thr ranges of pressure and temperatures I need.
I have searched the internet for equilibrium valves y/x but so far without success. I, however, have found a software package ALLPROPS that will give me fugacity coefficients
which appear to be the values of y/x divided by the total system pressure.
I will continue my search for equilibrium valves y/x for components from C1 to C6+. If unsuccesful, I will probably derive them from the ALLPROP fugacity coefficients and then make calculations as suggested by TD2K.
If anyone can see flaws in this approach I would welcome any comments.
Is your goal just to understand the calcs done for you by the engineers using HYSYS, to verify validity of those results, or is it to do your own calcs so as to be independent of others? If the latter, you can pick up a fairly inexpensive flash program that will do more than just provide fugacity coefficients for doing your own spreadsheet flash calcs.
The "K" values (y/x) for such systems are the ratios of liquid to vapor fugacity coefficients, which are generally returned from a routine calculating them as a function of temperature, pressure, and composition as f/py or f/px. Especially at high pressures, there is some composition-dependency. Since at equilibrium the vapor and liquid fugacities are equal, and the pressure is the same of course, then the K value = y/x = (f/px)/(f/py). Clearly, some iteration is in order. A dew point calculation procedure in a flash program will start out with some estimate of temperature and either phase compositions or K values, make two calls for the sets of fugacity coefficients, divide for the K values, and get the summation of x=y/K. If the sum is not essentially 1.0, iteration is in order. Temperature must be found so as to satisfy the sum of x=1.0, and the calculated x must be plugged back into the fugacity calculation to refine the K values used in the summation of x. That is a double iteration, and the techniques for doing it efficiently and robustly vary from one package to another; it's a whole different subject by itself. If you are doing this by hand, you may get a decent approximation of the DP temperature by assuming that the composition-dependency is not too great. That reduces the problem to finding just the temperature that gives the sum of x=1.
Many of the common quations of state for hydrocarbons, such as Soave, Peng-Robinson, and over 100 other derivatives of the original Redlich-Kwong EOS, use cubic or other expressions for phase density, and multiple roots exist. The appropriate root is selected according to phase. If the system is above the cricondenbar, you can't have distinct phases, and the calculations collapse toward fugacity coefficients being the same for "both phases," the K values go to 1.0, and there really isn't an answer. Sometimes a valid answer exists, but the starting point in the calculations ends in failure and perhaps the wrong conclusion about whether there is an answer. This is where the better flash routines do a decent job of finding answers in the troublesome areas.
I haven't meant to scare you off from delving further into doing your own DP calcs, but it does help to be aware that there are some areas where simplifying assumptions can give misleading results. HTH
Please pay great attention to Dick Russell's comments: they come from a respected authority on process simulation who knows ALL the ropes.
I would seriously question the accuracy of fugacity coefficients that are not derived from a respectable (and field-proven) equation of state. It is one thing to do a simple hand calculation (using gross approximations for K-values) just to "get the hang of it", quite another to develop a stand-alone, reliable procedure that is both generic and computationally efficient. You don't sound keen to program a rigorous procedure yourself. This is wise because doing rigorous hand calculations with a cubic EOS for even one complete iteration would take you a month of Sundays.
Also, remember that cubic equations of state are among the simplest of the options available. There are far more complex (and accurate) EOS alternatives that one cannot even begin to contemplate applying in a hand calculation.
Lest my comments are misconstrued, I - like Milton Beychok - applaud your basic position: complex computer calculations should NOT be used without any understanding of the fundamentals. Unfortunately, this is not a common sentiment these days. Many employers create a work environment that values "productivity" at the expense of even the most basic understanding. Even chemical engineers often do not get an in-depth exposure in under-graduate school to such calculations as we have discussed here.
Gentlemen,
I am suprised that no explicit mention has been made of the De Priester nomographs, which were the standard hand VLE calculation method taught for Flash, DEWT, DEWP, etc calcs when I was in school (and most likely never used by us again after graduation). Many texts include these nomographs. Easy to understand and as these were developed circa 1950, they may be well worth a check out for an "old timer" who wants to understand the calcs by actually trying them out.
best wishes, sshep
Good point about the DePriester nomographs ... which are still available in the 6th Edition of "Perry's Chemical Engineers' Handbook".
Perhaps the reason they weren't mentioned before is that they simply provide the equilibrium k=y/x values used in the VLE calculation methods ... and this thread has concentrated more on the calculation methods rather than the k values.
Milton Beychok
(Visit me at www.air-dispersion.com)
.
I think it is time for a recap of what I am trying to do, which to calculate (and understand the methods of such calculations) the hydro carbon dewpoints of natural gases of differing compositions up to pressures of 70bar.
If it at all possible I do not want to use proprietary programs or get involved complex equations of state or flash calculations.
It is for this reason that I described my proposed calculation method in my post of 29 December 2005 which is based on the method first suggested by TD2K. With my proposed method the only information I am missing is the equilibrium values of k=y/x. If these values can be obtained from fugacity coeffs determined by software by ALLPROPS then this will satisfy I think. If not then I will use available graphs and turn them into look-up tables.
So why do I want to determine HCDP for natural gases. Well for combined cycle power plant, the gas turbine suppliers want the fuel gas delivered to the GT at a temperature that is above the HCDP by some margin. As a consultant, I want to estimate the HCDP at a preliminary concept /feasibility /design stage. It will be for the GT contractor to design and supply the fuel system that will deliver fuel gas to the GT at the required conditions based on the analysis of the gas delivered at the plant boundary.
At this moment I am struggling to understand what is wrong with my proposed method. Although I do recognise the pints made above about the impact of small contents of C6+ components on calculated HCDP and the concept of a measurable dew point.
athomas236, in my humble opinion, I don't think there is anything wrong with you doing hand calculations if you are trying to understand and rationalize the determination of hydrocarbon dewpoint for yourself. I agree with previous posters about understanding what the simulator is giving you. I look at my HYSYS software as being one of the coolest calculators there is but I never rely on it to think for me.
However, if I were paying you as a consultant to provide me with engineering services and you had access to superior information or methods and chose not to use them than I would be a bit disappointed. I don't want to sound harsh but sometimes I come off that way before my morning coffee.
Regarding the mention of the DePriester nomographs, a bit of history is in order: The MW Kellogg company originated the Benedict-Webb-Rubin (BWR) equation of state - Manson Benedict was the first author of the two original publications in J. Chem. Phys., Vol. 8, p334 (1940) and Vol. 10, p747 (1942). This is an eight constant EOS, far more complex and accurate than the modern cubic equations such as Soave or Peng-Robinson. It is even today considered highly successful in capturing the composition dependence of K-values over a wide range of T, P when binary interaction parameters are used, a modification suggested many years later by Prausnitz at UC Berkeley.
However, in the 1940s, it was impossible to do fugacity coefficient calculations by hand using such a complex EOS, as there were few computers around. Therefore, Kellogg came up with a large collection of charts called “the Kellogg charts”, which graphed the numerical solutions of the BWR EOS for a wide range of cases. This was an attempt to introduce the composition dependence of the K-values in an approximate and graphical way, since the actual solution of the BWR equation was not required at all. However, much trial and error was still required to use these charts, and the results were NOT as accurate as what would be obtained through rigorous solution of BWR.
Later, the so-called “MIT K charts” were developed at MIT, that were based on the Kellogg K charts, but were far less voluminous and therefore simpler to use. However, these too required trial and error, but were a lot less laborious to use than the Kellogg charts, and also not as accurate. They were certainly much less accurate than the original BWR equation of state.
Next, DePriester developed two nomograms, based on the MIT K charts, that eliminated composition dependence altogether in favor of real simplicity. There is one nomogram for “high temperature” (-5 to 200 C) and another for “low temperature” (-70 to 20 C), and there is an area of overlap where the K-values values do not quite agree. These K-values may be used by the brave of heart for pure hydrocarbon systems at moderate T&P only. One must also decide which one to use when there is an overlap. No guidance is available of what to do when, for example, N2, CO2, H2S, and other important non-hydrocarbon components are also present. DePriester’s nomograms have survived to this day in many textbooks and Perry, I think for historical reasons, but certainly not because they are known to be in any way competitive with a modern EOS for accuracy. Often DePriester’s nomograms charts are replicated with absolutely no commentary as to their historical origin and especially their many limitations with respect to accuracy. The fact remains that it is dangerous, if not foolhardy, in most situations simply to assume that K-values are independent of composition. This is why phase equilibrium remains a pervasively important area for chemical engineering research.
Therefore, I would again urge anyone reading this thread to be aware that computational simplicity for K-values generally comes at an intolerable sacrifice in accuracy. There simply is no way to get quick and dirty K-value answers to a given problem, such as a high-pressure natural gas dew point calculation, that is also likely to be accurate except by pure chance. That is why everyone uses a standard process simulator for such work.
Note for the most intrepid ChEs out there: if a dew point calculation is bad enough to do by hand, imagine how laborious a fully rigorous multicomponent distillation column calculation would be, using any of the most common convergence methods, since many thousands of composition-dependent K-value sets would be required before column convergence is achieved. (Dick Russell will excuse my not elaborating on his “inside-out” method which greatly reduces the number of K-value computations required in distillation).
