1 reply to this topic

[Chellani]

Hi all,
I am very much comfortable with activity coefficient models even group contribution methods as well. I’ve written few programs to estimate BIPs from literature VLE data (isobaric & isothermal) and estimation of VLE using these BIPs as well. My major problem is with the modified equation of state (EOS) models, following are my doubts:

1. Liquid Phase modeling: Do EOS models use BIPs from the simulator’s database similar to activity coefficient models or these BIPs are estimated using properties of pure components? Do EOS models work in similar fashion compared to activity coefficient models i.e. estimate BIPs using actual VLE data by regression and then use them while performing flash in the simulation environment? Here I am talking about liquid phase non-ideality only.

2. Vapor Phase modeling: Even for the vapor phase as well; do EOS models use BIPs which are part of database of a simulator? Is fugacity coefficient estimated using BIPs which have been estimated using actual VLE data. I’ve worked with carboxylic acid-water system which uses NRTL for liquid phase modeling and a parameter (Z) to model dimerization of acids in the vapor phase. Parameter Z is estimated from actual data but I ain’t sure about fugacity coefficient. I am facing this problem as most of the systems I’ve worked in past were at lower pressures so I was never bothered about vapor phase non-ideality however things are different now.
Above two doubts have basically come into picture because of van der Waal’s EOS which doesn’t need any BIP, the constants a and b are basically dependent on pure component property i.e. Pc and Tc. As per my understanding, van der Waal property method should be used for modeling carboxylic-acid system for the vapor phase but I have no clue about what is going in the back-end of simulator.

3. EOS and Hypos: This one is pretty major and tricky doubt. If my Pt 1 holds true; how are BIPs for hypos estimated. When we create an Assay, hypos are automatically created and BIPs page is automatically populated; so where are these BIPs coming from. I’ve thought a lot about this and the things which I can think about are below:
a. When we define an assay (auto or defined cut), hypos are created; and BIPs for these hypo-hypo and hypo-pure component are part of database which are populated on BIPs page which are used to perform flash (that is what I think but is it true?)
b. These BIPs should have been estimated using experimental data. For e.g. if I have an assay in the range of 250-360 degC (TBP / D86 or whatever) and simulator estimated five hypos as Hypo250, Hypo 275, Hypo 290, Hypo 325 and Hypo 360 (just random numbers) and if I have actual VLE data, BIPs between these components can be estimated and they should go in the database of simulator. Similarly if I have VLE data for the above mentioned assay and few pure components (basically light ends), BIPs between these hypos and pure components can be estimated but the problem in this methodology is multiple combinations and solutions. Just imagine how many combinations can we arrive at and it can always have multiple solutions i.e. BIPs estimated between two hypos using Assay 1 and Assay 2 can be very different (provided these two hypos are part of these two Assays).

I know that I’ve taken everyone's lot of time in explaining what the problem statement is. If not the problem is still not clear, please forgive me for wasting everyone’s time. Thanks for going through the problem and thanks in advance for the reply. I’ve already read Peng Robinson’s original paper but it is too confusing mainly because of cfs; I guess it is trying to say that Pt 1 is true. I would really appreciate if someone can provide standard literature which explains these concepts in simple steps; no need to provide whole paper even citation would also serve the purpose.

Edited by Chellani, 01 September 2009 - 10:46 AM.

[MrShorty]

I don't know that I have answers for all your questions. Here are some thoughts:

1. Liquid Phase modeling: Do EOS models use BIPs from the simulator’s database similar to activity coefficient models or these BIPs are estimated using properties of pure components?

Yes -- it depends on the EOS. As you noted below, the usual mixing rule for the Van der Waal EOS uses only pure component information without any kind of empirical BIP. The mixing rule for other EOS's (like the Peng-Robinson) often do include an empirical BIP that is derived/regressed from experimental data.

Do EOS models work in similar fashion compared to activity coefficient models i.e. estimate BIPs using actual VLE data by regression and then use them while performing flash in the simulation environment?

The best one's do. Most of the time, a mixing rule with one BIP is used, but there are other mixing rules that allow for more BIP's (Of interesting note might be in Stryjek and Vera's paper on the Peng-Robinson equation of state, they suggest using, as one possible mixing rule, a variation that uses the Wilson equation)

Here I am talking about liquid phase non-ideality only. 2. Vapor Phase modeling: Even for the vapor phase as well; do EOS models use BIPs which are part of database of a simulator?

In some ways, it is difficult to talk "only" about liquid phase non-ideality. A good EOS will represent both vapor and liquid non-idealities with the same equation/BIP. Perhaps the best way to see this is to consider the cubic EOS's (like Van der Waals and Peng-Robinson). When you solve these equations, you get three real roots: one represents the liquid phase, and one represents the vapor phase, and the third is considered physically meaningless.

Is fugacity coefficient estimated using BIPs which have been estimated using actual VLE data. I’ve worked with carboxylic acid-water system which uses NRTL for liquid phase modeling and a parameter (Z) to model dimerization of acids in the vapor phase. Parameter Z is estimated from actual data but I ain’t sure about fugacity coefficient. I am facing this problem as most of the systems I’ve worked in past were at lower pressures so I was never bothered about vapor phase non-ideality however things are different now.
Above two doubts have basically come into picture because of van der Waal’s EOS which doesn’t need any BIP, the constants a and b are basically dependent on pure component property i.e. Pc and Tc. As per my understanding, van der Waal property method should be used for modeling carboxylic-acid system for the vapor phase but I have no clue about what is going in the back-end of simulator.

3. EOS and Hypos: This one is pretty major and tricky doubt. If my Pt 1 holds true; how are BIPs for hypos estimated. When we create an Assay, hypos are automatically created and BIPs page is automatically populated; so where are these BIPs coming from. I’ve thought a lot about this and the things which I can think about are below:
a. When we define an assay (auto or defined cut), hypos are created; and BIPs for these hypo-hypo and hypo-pure component are part of database which are populated on BIPs page which are used to perform flash (that is what I think but is it true?)
b. These BIPs should have been estimated using experimental data. For e.g. if I have an assay in the range of 250-360 degC (TBP / D86 or whatever) and simulator estimated five hypos as Hypo250, Hypo 275, Hypo 290, Hypo 325 and Hypo 360 (just random numbers) and if I have actual VLE data, BIPs between these components can be estimated and they should go in the database of simulator. Similarly if I have VLE data for the above mentioned assay and few pure components (basically light ends), BIPs between these hypos and pure components can be estimated but the problem in this methodology is multiple combinations and solutions. Just imagine how many combinations can we arrive at and it can always have multiple solutions i.e. BIPs estimated between two hypos using Assay 1 and Assay 2 can be very different (provided these two hypos are part of these two Assays).

I know that I’ve taken everyone's lot of time in explaining what the problem statement is. If not the problem is still not clear, please forgive me for wasting everyone’s time. Thanks for going through the problem and thanks in advance for the reply. I’ve already read Peng Robinson’s original paper but it is too confusing mainly because of cfs; I guess it is trying to say that Pt 1 is true. I would really appreciate if someone can provide standard literature which explains these concepts in simple steps; no need to provide whole paper even citation would also serve the purpose.

A reference that I have found useful for this kind of discussion is the book Phase Equilibria in Chemical Engineering by Stanley M. Walas. It's currently out of print, but he does a pretty good job of describing the basic theory of EOS's in chapter 1. The bibliography for that chapter would also give you some references for further study.