u/Upset_Ad_6140

Hello!

I am a student of chemical engineering who is interested in distillation and the theoretical, thermodynamic assumptions that underlie the common machinery.

For instance, a common way to model tray distillation columns is with the MESH equations, that, among other things, assume vapor-liquid-equilibirum (VLE) on each tray. If we were working strictly with equilibrium thermodynamics, this would imply that each tray "isolated enough" from the rest of the column to apply the principle of stationary entropy on each tray (which is what gives e.g. equality of component fugacities in both phases). Considering that each tray actually experiences large fluxes of both energy and mole numbers, I find this assumption a bit dubious. I am sure that given certain operating points, particularly those in which reactions occur on each tray, this assumption would fail entirely.

Therefore, I am wondering if there are some good texts on the modelling of distillation columns that discuss the topic in terms of irreversible thermodynamics or nonequilibrium thermodynamics. Preferably with the accompanying theoretical foundations (I only know equilibrium thermodynamics).

Thanks in advance!

Hello!

Before I get into the post, let us define thermodynamic equilibrium as a stationary state devoid of macroscopic fluxes. I will begin by giving a short motivation for my question, proceed to quote a relevant section from a standard book, and then ask my question by means of a concrete example.

I am a student of chemical engineering, and as such, equilibrium thermodynamics is the backbone of literally everything that we do. Having read basic, classical theory (notably Callen), I often find myself extremely confused about a particular aspect of what we do as engineers: even though our unit operations are inherently open in literally every conceivable way, we still constantly apply equilibrium thermodynamics with great success.

On p. 26 in the second edition of Thermodynamics and an Introduction to Thermostatistics, Callen outlines the "basic problem of thermodynamics":

>The single, all-encompassing problem of thermodynamics is the determination of the equilibrium state that eventually results after the removal of internal constraints in a closed, composite system. [...] The composite system is termed closed if it is surrounded by a wall that is restrictive with respect to the total energy, the total volume, and the total mole numbers of each component of the composite system.

Note the use of the term closed. Here it really means isolated. This is the motivating problem for the entire book, and is the problem that the postulate of entropy maximization is introduced to solve. As I understand it, the extremum principles of classical equilibrium thermodynamics, strictly, only apply to isolated (composite) systems. Even so, we constantly use the theory for non-isolated systems, and get extremely good predictions.

For instance suppose that we carry out a chemical reaction in a sealed container that is in contact with the atmosphere. Then, we might expect to apply minimization of the Gibbs' potential at constant temperature and pressure (with values equal to those of the atmosphere) to determine the final equilibrium state. However, why is that valid? The atmosphere is not some well-defined thermodynamic system that interacts thermally and barically with our container in the way that the derivation of the principle of minimization of the Gibbs' potential demands. Even if we define this 'reservoir' as a sufficiently large control volume around the container, not even its energy is conserved: energy will clearly flow between this control volume and the rest of the atmosphere, whereas the derivation of Gibbs' minimization requires global conservation of all extensive quantities (i.e. isolated composite system consisting of container + reservoir). Nevertheless, minimizing G with respect to the given constraints does yield correct predictions.

How can this be? Has Callen simply imparted onto me an idea of "isolation" that is too strict/narrow?

Hello!

In the basic chemical engineering courses I have taken thus far, we have discussed flash drums and different kinds of flashes conceptually and mathematically, but not practically. For example, if we know the temperature and the pressure of the tank, we can use the Rachford-Rice equation to calculate the vapor split fraction in the tank. Mathematically, there are no constraints on what values of T and P we are allowed to use.

However, in practice, I would imagine that certain combinations of T and P are simply infeasible or even not possible. This leads me to the question: how are these intensive parameters actually controlled and enforced in practice? Suppose someone would like to flash some stream F isothermally at temperature T and pressure P. How would one typically enforce these conditions in practice?

Other than answers here, if you happen to have some resources where I could read about this (that is, the practical aspect of this unit operation), I would greatly appreciate that, too!

In chapter 14 of the second edition of Callen's Thermodynamics and an Introduction to Thermostatistics, Callen presents a formal solution to the issue of defining entropy for nonequilibrium states. On p. 310, he says:

>To any infinitesimal region we assign a local entropy S(X_0,X_1,...) where, by definition, the functional dependence of S on the local extensive parameters X_0,X_1,... is taken to be identical to the dependence in equilibrium. [...] It is because of this convention, incidentally, that we can speak of the temperature varying continuously in a bar, despite the fact that thermostatics implies the existence of temperature only in equilibrium systems.

As far as I can tell, under any reasonable interpretation of "infinitesimal", the part after the "[...]" does not follow from the part before it. If we partition a system into infinitesimal segments, this does not mean that we get continuous variation of any quantity; an infinitesimal partition is still discrete.

I don't have a problem with the idea that we can recast our formalism in order to allow for continuously defined quantities, but even though the rest of the book is excellent, I am not very impressed by the presentation given by Callen in this instance. In fact, much of the literature I have that consistently uses the assumption that Callen is trying to introduce does not bother to define it, so I don't understand what exactly it is.

Therefore, I am wondering how to rigorously/axiomatically introduce the local equilibrium hyptothesis into the theory. Do we need to reformulate any of the theory (i.e. Callen's four postulates) or do we simply need to add something more to it? Any formulation should allow us to prove the typical results, for example that total internal energy is conserved in isolated systems.

Hello!

I am working privately on a chemical engineering library in Python that I made for an assignment at university a few months ago. One of the classes I have is "Stream" which is exactly what it sounds like: components are connected by streams with a specified temperature, pressure and molar flowrates of different species.

Currently, the class only supports single-phase situations: either the stream is liquid or it is vapor, and unless the stream object is created by a component such as flash tank, this phase is specified by the user. The issue is that this means the user can make unphysical specifications, such as having a stream of pure water at 1 atm and 400 K with phase "liquid".

I am thinking of removing this degree of freedom from the class and instead making it so the phase is determined automatically with the Rachford-Rice equation at a specified pressure, temperature and composition. My question is: is it realistic to have multi-phase streams in a real plant?

Hello!

I am writing a MESH-solver in Python for a chemical engineering project and have currently designed my column class in a way where the user specifies both the reflux ratio and the reboiler heat duty. The condenser is a total condenser and the reboiler is a partial reboiler.

These are the particular specifications I have given the column:

• The reflux ratio R
• The column pressure (taken to be constant)
• The number of equilibrium stages N
• The reboiler heat duty Q (in units of power)
• The equilibrium stage at which the feed is injected

Complete information about the feed stream is also known.

I am having some convergence issues so I am wondering if the specifications I have given are really independent or if the issue is due to overconstraining the column.

I added the "modeling" flair but I am not sure if it's correct. I apologize if I chose the wrong flair.

Thanks in advance!