UNIQUAC Parameter Estimation 3

[tipu144]

Hi to All,

Happy New year to All of you..

Can anybody help me for determining the paratmeters of UNIQUAC equation? I want to use this equation for the prediction of experimental Heat of Mixing Data. This thing is new for me, so i want to start it from basic level..

Thanks
tipu

 

[DickRussell]

Your post is not quite clear, in saying "prediction of experimental" data. Are you trying to predict heat of mixing in the absence of measured data or do you want to fit experimentally measured data to a model? Your first step in either case must be to review good technical discussion of the subject from a thermodynamic point of view. One reference for some of this is in the Liquid-Liquid Equilibrium Data Collection published by Dechema. Those volumes also present a lot of experimental data already fit to various liquid activity models.

 

[tipu144]

DickRussell,

I want to fit experimentally measured heat of mixing data.

tipu

 

[DickRussell]

I made a mistake in citing the Dechema LLE Data Collection; I should have cited the Dechema "Heats of Mixing Data Collection." In these volumes the authors use the term "excess enthalpy." They briefly discuss the use of local composition models Wilson, NRTL, and UNIQUAC. Apparently these models have serious trouble modeling large heats of mixing, above 840 J/mol for the first two and above 1000 J/mol for UNIQUAC. Since about a quarter of the data sets they cover in the volumes have maximum heats of mixing above these limits, they decided not to use these models for fitting the data.

For fitting the data to any model, you'll of course need a good regression program, which I suppose you could write yourself if you have the time and expertise. A good regression program ought to give you both the parameters for the model chosen and a measure of consistency of the data.

 

[tipu144]

DickRussell,

Do you have any idea about the models that are used for fitting the heat of mixing data? if you know, please help me abt this thing, and one more thing i would like to share with you is that, i used NRTL equation to fit the data, and i got 2% AAD. (i used the excel solver for that).

Also I would like to inform you that, Solvents that i am using is giving me the exothermic effect, so i want to know, can these models (NRTL, UNIQUAC, Wilson) give me the good fitting for exothermic effect? as i mentioned that with NRTL equation i got 2 % AAD. But after reading your reply i am not sure what to do..

looking forward your response
thanks

 

[DickRussell]

I didn't mean to imply that those local composition models should not be used at all. I was only repeating what the investigators for the Dechema series found with respect to high heats of mixing.

One thing to keep in mind is that almost any equation form, even a polynomial, could be used to fit some data over a given range, as long as the "fit" looks good. However, if the equation form lacks sound thermodynamic basis, then using it with multiple components or extrapolating it to other conditions won't work well.

The Dechema reference used the Redlich-Kister (1948) equation for most of the data sets they cover, because it worked well. It doesn't really apply to multicomponent systems. They did say that the local composition models should in theory be applicable to multicomponent systems. However, the works they cited indicated that fits to these models without temperature dependency in the regression parameters don't give good results. These remarks were made 20 years ago, and more progress may have been made since then.

You ought to find a place (university ?) that has the Dechema volumes and see if the systems of interest to you already have been measured and fit to some form.

Beyond this, I can't suggest what to do other than to investigate more recent work on the subject. I don't make any claim to being an expert on the subject of proper modeling and fitting of heat of mixing data.

 

[UmeshMathur]

It should also be mentioned that additional issues arise when considering industrial process simulation problems where phase equilibria must be considered in addition to heats of mixing.

Unfortunately, all available literature indicates that a single set of binary interaction parameters for these local composition models (Wilson, NRTL, and UNIQUAC) cannot, in general, predict K-values and heats of mixing extremely accurately at the same time. Heat of mixing predictions, when based on VLE fitted models, are generally in the right direction, but may be off quite a bit numerically. Similarly, VLE predictions based on models calibrated using heats of mixing alone are generally quite bad. Therefore, one should regress both VLE and heat of mixing data simultaneously for each binary to get the best compromise.

Also, it is not feasible to predict the multicomponent case from the Redlich-Kister results for the constituent binaries.

The only good news in all this is that, for most organic mixtures, the heats of mixing effects are not very large, and are generally ignored in calculations such as multicomponent distillation without significant loss of accuracy.

 

[siretb]

A practical way to fit the UNIQUAC parameters to experimental data would be to use the ASPEN plus regressionn module, included in ASPEN.
It would directly accept excess enthalpy and yield the UNIQUAC parameters. Of course we assume here that UNIQUAC is a good model. I prefer NRTL.

 

[tipu144]

Anybody please tell me, which aspen package contain a regression module for NRTL, UNIQUAC models. Actually I have "Aspen One" software, and it has Aspen COMThermo: Workbench tool, in which i found fluid phase regression, but there is no any description of NRTL or UNIQUAC models. so please give me the exact information of such tools for UNIQUAC, NRTL...models.

Thanks
tipu

 

[UmeshMathur]

siretb:
I believe we were responding to tipu144's use of Excel (and the built-in solver) for regressing the interaction parameters. Nobody will quarrel with use of a modern simulator to perform this calculation easily, provided of course you have access to it. Also, I cannot see how one can avoid the use of such simulators for serious work.

I believe that UNIQUAC, which was developed many years later than NRTL, also has a sounder theoretical basis (recall that both models were developed under the guidance of Professor Prausnitz at UC Berkeley). Also, UNIQUAC needs only two interaction parameters per binary, v/s three per binary for NRTL. This may seem unimportant, except that for a binary liquid-liquid system, it is theoretically impossible to estimate three interaction parameters for an activity coefficient model from LLE data alone. This issue alone is a huge theoretical disadvantage for NRTL compared to UNIQUAC.

Also, there is no evidence that supports any contention that UNIQUAC is not a "good model" or that NRTL is generally more accurate. NRTL is just simpler algebraically. Of course, in a given system, the accuracy of fitted parameters for one model over another is determined only statistically (least squares fit). For accurate data, differences in fitting accuracy are usually minor. Finally, it must be noted that UNIQUAC provides the theoretical framework for the widely used UNIFAC group contribution method.

In my own professional practice for over 25 years, I have done hundreds of side-by-side regression evaluations between UNIQUAC and NRTL for VLE, LLE, and VLLE systems and have never found any basis to support your preference. There is also the extensive DECHEMA compilation of regressed VLE and LLE parameters using van Laar, Wilson, NRTL, and UNIQUAC - for each of several thousand binary systems - that would illustrate this point. Besides, for LLE regression work with a binary system, one is forced to assume the third NRTL parameter, alpha, arbitrarily. To get around this difficulty, Tassios (at NJIT, circa 1980s) found that even a fixed value of -1 provides acceptable numerical results, although others have questioned the theoretical validity of a negative value for alpha.

Therefore, I would state that there is considerable support in the literature for asserting that UNIQUAC should be preferred over NRTL.

tipu144:
I believe you need to access the Aspen Plus Data Regression System (DRS) to find the desired interaction parameters by regression. Also, as noted in my post of 5 January, please use interaction parameters based solely on excess enthalpy of mixing data with great care for anything other than enthalpy calculations. For example, if your components are compounds for which the UNIFAC group contribution method applies, and you are also interested in VLE predictions, you will likely be much better off using infinite dilution activity coefficients (based on UNIFAC for VLE) than using interaction parameters based on excess enthalpy of mixing data. I assume, of course, that measured VLE data are not available; otherwise, you would do a simultaneous regression of VLE and excess enthalpy of mixing data and use a single set of interaction parameters.

(Besides, note that it is possible to use different models for VLE and excess enthalpy in a given simulation in Aspen Plus. In fact, it is possible even to use one set of UNIQUAC model parameters for VLE and another for enthalpy in a given simulation problem. This requires creating a new thermo SYSOP.)

Please keep us posted on your experiences, as this is a very interesting area even today.

 

[tipu144]

UmeshMathur,

Thank you very much for your help. I need more support from you, In Aspen Plus regression tool, i found four options for each UNIQUAC and NRTL model, like (1) "UNIQUAC or NRTL"/Hayden-O'connell equation of state with Henry's law, (2) /Nothnagel equation of state with Henry's law (3) /Redlich-Kwong equation of state with Henry's law (4) with ideal gas and henry's law. As you know i don't have much knowledge of this field, so if possible then can you please let me know which option will be the better one for my heat of mixing data? and also one more thing, for NRTL equation i only found binary parameters by using aspen plus regression tool, but then what about the alpha value..!! How can i get this value by using aspen.

 

[UmeshMathur]

Hi, tipu144:

First, the NRTL model DEFINITELY requires 3 binary interaction parameters. You need to look harder at the menus, as the alpha may be fixed by default (I am not aware of which version of Aspen Plus you’re using).

The four options in your post refer to the alternative methods to determine the vapor phase fugacity coefficients, relevant only when discussing VLE:

(1) Hayden-O'Connell is generally used when you have a nonideal vapor containing polar, solvating or associating components, at low to moderate pressures (3 atm or so). Such mixtures are loosely referred to as "chemical" systems.
(2) Nothnagel is another method, based on the so-called “chemical” theory for associating vapors (e.g., partial dimerization of organic acids). In the absence of data – i.e., for acids other than the C1-C4 aliphatic acids - Nothnagel’s method cannot be used for calculating K, the dimerization equilibrium constant. However, Hayden-O’Connell do have an alternate method to estimate the K based on the bound, metastable, and chemical contributions to the second virial coefficient which their method can estimate. Refer to Prausnitz, Lichtenthaler, and Gomez de Azevedo, “Molecular Thermodynamics of Fluid Phase Equilibria” (Prentice-Hall, 3rd Edition, 1999) for further guidance.
(3) Redlich-Kwong is a simple cubic equation of state (EOS) that would be considered for a high-pressure system, provided you are dealing with hydrocarbons (not likely when using an activity coefficient equation for the liquid phase such as UNIQUAC or NRTL).
(4) The ideal gas assumption is used obviously only when the vapor phase fugacity coefficients may all taken as unity without sacrificing K-value accuracy.

In all cases above, mention of Henry's law refers to a method to handle fugacity calculations for supercritical components dissolved in the liquid in relatively small concentrations. These would be components above their critical temperature, for which there is no way to calculate the pure component liquid reference fugacity which is the vapor pressure with the Poynting correction for non-ideality. See Prausnitz’s discussion of the “unsymmetric convention” for such cases.

If you have no possibility of doing VLE calculations (bubble / dew points or flashes), the vapor phase fugacity is irrelevant. Then, you can choose option 4 safely.

You need to make an assessment as to which option is best for your system based on these criteria. I can say more only if you provide the details, including the identity of the components and the approximate composition.

 

[tipu144]

UmeshMathur,

Thank you very much

I am using 2004.1 version of aspen plus. Regarding the identity of component, its a alkanolamine, and i don't want to disclose anyother identity of this chemical, hope you understand this thing. If possible to make any comments for alkanolamines, please let me know...

Tipu

 

[UmeshMathur]

Sorry, I cannot proceed in the absence of the information outlined in my previous post of January 12th.

Cheers.

 

[tipu144]

UmeshMathur,

Can you please suggest any basic criteria for initial guess of binary parameters in Aspen Plus Regression tool.. Because all the time I am getting different parameters if my initial guess is different.

Thanks
tipu

 

[UmeshMathur]

It is important that sensible starting values for the UNIQUAC (or any other activity coefficient model's) interaction parameters be used. Really bad guesses often cause failure to converge or produce nonsensical answers.

For VLE work, I would start with parameters that correspond to infinite dilution activity coefficeints equal to 1 (ideal liquid). These can be back calculated by solving two non-linear algebraic equations for the two interaction parameters. If you don't know how to do this, send me the UNIQUAC pure component r and q parameters and I will send back the appropriate guesses for the ideal solution interaction parameters.

For heat of mixing parameters, you can similarly provide initial guesses for an assumed heat of mixing equal to zero. Alternatively, the same parameters for the ideal liquid assumption (above) may be used as the starting guesses.

 

[tipu144]

Thanks,

My component is N-(2-Hydroxyethyl)ethylenediamine. First i want to try all of my calculation with this component, then after i will try on actual one. if possible then please double check these values, because I am not sure whether i calculated it correctly or not.
For N-(2-Hydroxyethyl)ethylenediamine
value of r is 4.925
and value of q is 4.452

tipu

 

[tipu144]

Umeshmathur,

I forgot to mension in my previous post that my system is aqueous, i.e. first component is water and second component is N-(2-Hydroxyethyl)ethylenediamine.

tipu

 

[siretb]

I was out for a while and would like to clarify my position concerning UNIQUAC versus NRTL.
I never said thta UNIQUAC was bad, I just stated that I prefer NRTL to UNIQUAC. I almost always had a better success with NRTL, than with UNIQUAC, for LV and LLV equilibrium.
The fact that NRTL has 3 parameters is, as Umeshmathur stated a theoretical disadvantage, but also for the engineer an additional chance. I never allowed the alpha NRTL parameter to get negative.
It should also be mentioned that UNIQUAC requires the R and Q, that two additional unary parameters.
Now, regardless of wether one uses UNIQUAC or NRTL, it is always much better to use more than one set od equilibrium dat, for instance using TPXY curves with P not constant, or better still have enthalpy dat available.

 

[UmeshMathur]

January 24, 2006
tipu144:
I'll get back to you shortly in more detail.

siretb:
Re. the NRTL v/s UNIQUAC issue, I would respectfully make the following points:
(1) The UNIQUAC r and q parameters are available readily for all significant molecular groups and also are tabulated for almost all the organic compounds you are ever likely to encounter (over 2000) in the DIPPR databank. Every worthwhile process simulator provides these, so the need to specify them is hardly a disadvantage for UNIQUAC.
(2) I wrote a thesis on the subject of Wilson v/s NRTL v/s UNIQUAC over 25 years ago. My conclusions have not changed after studying many hundreds of additional systems. Also, there is plenty of additional support for choosing UNIQUAC in the literature. If you study the DECHEMA data collection (which contains regressions for the major activity coefficient models for the TOTALITY of the world's published VLE and LLE data sets), I believe you will be able to verify this for yourself at any library.
(3) There is absolutely no theoretical or practical basis for your statement that the third NRTL parameter gives an engineer "an additional chance", presumably to improve things over UNIQUAC. A theoretically sounder model can do a lot better than its competitors even if they have a lot more adjustable parameters. (For example, compare the Antoine equation with its three parameters versus a sixth order polynomial for vapor pressure.) There is plenty of evidence that, in VLE work, simultaneous adjustment of alpha with the other two NRTL parameters does NOT improve the quality of the fit noticeably over UNIQUAC, unless you have a statistical quirk caused by inaccurate measurements.
(4) In fact, engineers often end up mis-specifying the third NRTL parameter in LLE work, simply because there is no way theoretically to estimate alpha using LLE data alone: you just have to pick a number for alpha based on some sort of “rule”, hardly an acceptable situation. How would you propose then to overcome discrepancies caused by poor choices of alpha when making VLE predictions for a multicomponent mixture?
(5) With good data, the quality of the fits from both models is equivalent. Therefore, the question that must be answered is: why insist on using a model that requires 50% more regression parameters to be estimated than the other? This can be a pain with a large number of components.
(6) UNIQUAC has been shown to reduce to both the NRTL and Wilson models when you make the appropriate simplifying assumptions. This is very telling, as it explains why the refinements in UNIQUAC are indeed worthwhile from a theoretical and practical point of view.
(7) No one will disagree that all available data should be used to improve modeling of phase equilibria. However, that is not the issue in this discussion.