4 replies to this topic

[adw07]

Hi all,

I have a problem - one which probably doesn't need solving very often but would form a very useful part of my application if I can get it to work.

Consider a separator vessel, two-phase, pressure & temperature known, phase compositions known. I wish to iteratively solve for the vapour fraction (Which is locked since the system is fully defined).

I have a P-T Flash routine (inputs are P, T and mole fractions) which gives the vapour fraction as an output.

I am trying to solve iteratively by guessing a value of vapour fraction - the correct answer will be when the vapour fraction output from the P-T Flash equals the guess.

I need to implement some sort of root-finding solver for this problem, however I don't know which to use as the function is not monotonically decreasing - i.e. can't use bisection type solvers, etc. unless I am doing something wrong?

Any other suggestions on how to solve this problem? (Given pressure, temperature and phase compositions - the vapour fraction is locked, so how to find it?)

[Profe]

Hi ADW
Reviewing your concern and also Perry's Chemical Engineers' Handbook, Chapter 3 "Mathematics" on "NUMERICAL SOLUTION OF NONLINEAR EQUATIONS IN ONE VARIABLE" you find several approximation methods. Of these, I seem the "Wegstein method" could be applied here, and in the subject "Numerical Solution of Simultaneous Nonlinear Equations" in "Method of Successive Substitutions" and "Newton-Raphson Method" you could rewiew for this aplication.

Good luck

[MrShorty]

It is an interesting problem, but I'm unclear on one thing. What are you given and what are you trying to solve for? It is clear to me that you are given P, T, and y (vapor fraction). Are you given x (liquid fraction) as well, or are you trying to find x? If you are given x, are you solving for the activity coefficient?

[adw07]

Hi,

Given Conditions are P, T, y and x
Solving for Vapour Fraction (or, alternatively, overall composition z)

Basically, this is on an input screen for my application, where I am looking to find out the overall composition within a vessel.

Often the overall composition won't be known - but both phase compositions will be.

I could ask for phase densities and phase fraction, then ascertain the overall composition that way but the reason I asked is because theoretically the system should be fully defined with just the above conditions.

I would like to keep things simple and not have to deal with densities, etc. and I was interested in how the above problem would be solved, thanks.

[MrShorty]

I think I just figured out why I was having so much trouble with this problem: I don't think there is a unique solution for the problem as given.

Basic material balance Fz=Lx+Vy shows a functional relationship between fraction vaporized and z. It looks to me like you will have to be given z to find V/F (or given V/F to get z).