Bubble/Dew point calculation for mixtures of three or more components

[davidemenegazzo]

Hi Ian, I would like to calculate bubble and dew points for mixtures of more than 2 components. For binary mixtures, one can use mix_VLE_Tx. May it be extended to n components?

[ianhbell]

Yes it should be possible. I think I can update the Jacobian and residual functions to allow multiple components and just make the function more general. There is nothing magic about binaries from the VLE standpoint.

[ianhbell]

This will be sorted in concert with #142 in short order. I am writing a generalized multi-phase equilibrium routine and working out the mathematics. You will have to provide guess values for the two phases.

[ianhbell]

I have worked out the math, just need to do the implementation in teqp. It is going to be a very generalized treatment allowing for an arbitrary number of phases in equilibrium; it ends up being a pretty nice formulation that will replace the existing routines completely.

[ianhbell]

The stuff is all working, committed to https://github.com/usnistgov/teqp/tree/genphaseequil branch. Once the docs build, you should be able to see an example here: https://github.com/usnistgov/teqp/actions/runs/10512900351 in the generated docs in the algorithms section

[ianhbell]

@svenpohl1991 I know you were also interested

[ianhbell]

Complete aside from specification equations where a variable is in h,s,u

[ianhbell]

@longemen3000 I think this could be useful for Clapeyron.jl as well since a lot of the same machinery is available

[longemen3000]

i'll have to check this out!, we have a "generalized" algorithm for the bubble/dew pressure/temperatures, but not flashes, and more critically, not multiphase. on

equilibria, our current bubbledew implementations do the following:

• V-T-μres: they do equality of chemical potentials and pressures.
• P-T-ϕ: they solve K and sum(x). they perform volume iterations on each step.

as a first glance, i saw that you are using the first one, right? but there is additional processing related to the specification and the handling of zero compositions, right?

[ianhbell]

Yes @longemen3000, if I understand you correctly, I think my method is like your first one, although more general to permit a wide range of specification equations. We are working on a little paper working out the mathematics for future readers. The derivatives are not too painful when you are living in the isochoric formalism.

I think there are some downsides to the approach I am doing, notably, that you have more independent variables. An upside is that it is very flexible, but a very big upside is that the volume iteration is avoided. Let me know if you have questions. I should be merging into main sometime next week I think after I sort out the h, s, u derivatives which are all similar, and easy relative to some of the other specifications.

[longemen3000]

@ianhbell is the name here alright? https://github.com/usnistgov/teqp/blob/01f5b8a7b16734c70e044b32392c746267037b32/include/teqp/algorithms/phase_equil.hpp#L543-L544C17 i see that you are calling residual derivatives for an ideal term?, shouldn't it be something like gradient_Psiig = R*T*map(log,rhovec) ?

[ianhbell]

You raise two good points. First, the gradient method was named when I didn't have any vision of being able to handle ideal-gas terms, thus the r for residual, but it operates just as well on ideal-gas terms. Second, I think your treatment is not quite correct. See the derivations in the SI of https://dx.doi.org/10.1002/aic.16074, summarized as: