In this screen cast we are going to perform

a flash calculation for a multicomponent system using the Rachford Rice solution. Now a flash

distillation is where we send a liquid through some kind of pre-heater, get it nice and hot

and that is going to get sent through to a lower pressure tank. And if we do this we

can create a vapor phase and have vapor liquid equilibrium (VLE). So then we get our liquid

at the bottom of the tank and a vapor forming at the top of the tank. So now we have two

streams. We have a vapor stream and a liquid stream and we will call F our feed. So we

do this to separate multiple components as they will preferentially separate and have

different compositions in both the vapor and the liquid stream. So lets start with all

the variables that we would have to define for this system. So w would have some feed

F, and it is going to have some composition, we are going to say zi, which will be the

mole fraction of component i in the feed. This is going to have some temperature associated

with it and a pressure associated with is which we will label Tf and Pf. We are also

going to have an enthalpy associated with the feed stream. On the outside we are going

to have composition of vapor mole fraction, yi, we will also have a pressure associated

with the vapor stream, a temperature and and enthalpy. We will do the same thing for the

liquid where xi denotes the lurid mole fraction of component i. So you can see we already

have 16 variables here and if we add multiple components we have a variable for one component

i we would add three more variables for each component. But because we have plenty of relationships

between these variables our degrees of freedom isn’t that high. So let’s work through some

of these relationships. First and foremost at equilibrium within our tank the pressure

of the liquid phase has to equal the pressure of the vapor phase. This is also true for

the temperature. These are variables that must be equal between phases at equilibrium.

Now the other thing that is true at phase equilibrium is that the phase equilibrium

ratio, also known as the k value for VLE systems. k of component i is equal to the mole fraction

of i in the vapor phase over the mole fraction of i in the liquid phase. Now fortunately

one thing that is always true is that the sum of the mole fractions in the liquid phase

equals the sum of the mole fractions in the liquid phase which we know is 1. Now if we

tie in our material and energy balances we do an overall balance and we know that the

feed going in has to equal the liquid plus the vapor streams. We could also do a component

balance meaning F times the mole fraction of i in the stream has to be equal to all

of component i leaving. So it is the liquid mole flow, times the mole fraction of i in

the liquid phase plus the vapor mole flow times the mole fraction of i in the vapor

phase. Lastly we have our energy balance, the enthalpy associated with the feed stream

plus any energy we add to the system has to be equal to the enthalpy leaving. Believe

it or not we have everything we need here.Now we can rearrange all this and work our way

to what is known as the Rachford Rice solution. Now typically we are going to have information

associated with our feed stream. So we might know our feed variable F as well as the temperature

the pressure and hopefully our composition of the feed stream. If we know this information

then we typically need two more variables. And those for a flash calculation might be

the pressure in the tank and the temperature in the tank. Maybe it is the pressure of the

vapor stream, maybe it is the pressure of the liquid stream. The nice thing we know

is that they have to be the same. So we could use our first two equations if we are given

this information which basically is our operating conditions. So if given our operating conditions.

Of course, now the question becomes what is our vapor and our liquid flow rates, what

are the compositions associated with them and what is the energy that needs to go into

the system if anything, and what is the heat associated with being added to the feed stream

if necessary. So we are going to take our two material balance streams and rearrange

them. Now the first thing is to get rid of our L variable. So we set L=F-V flow. And

we plug this into our second equation. So we want y on the left side. So if we set y

over here now we can arrange this equation. We get the following. But a more convenient

form is where we have the fraction V/F which is the percent or fraction of our feed stream

that is vaporized. And we typically have seen this also written as psi. So the final form

of the equation for our operating line is going to be the following. The only thing

differently that I am going to do is I am going to plug in psi variable. So I am going

to start with this main equation which I will label 1 and divide everything by xi because

remember yi divided by xi is our ki. So you should get the following equation which I

have arranged on the right. So now we could group terms and set equal to zero, multiply

both sides by psi. We are going to bring our mole fractions to the left side. And change

this to yi by introducing ki because remember ki is yi over xi. So that is one way to get

rid of our xi. And that is going to be equal to the rest of it. We are almost there, one

last thing, we are going to solve for yi. So you can see if we bring yi to the right

side and bring the right side and bring it to the left then we get zi*ki divided by the

rest. And our xi is just equal to yi over ki so the only thing left to do is apply the

equation above that we set for our mole fractions. But rearrange it such that the sum of the

vapor mole fractions minus the sum of the liquid mole fractions has to be equal to 0.

so if we do that it is going to look like the following. And we could combine these

terms into one summation except you might see this numerator written just a little bit

differently. Just distributing a negative sign on both sides. So what does this mean?

Say we are given a flash separation problem, the first thing we do if we are given the

temperature of the tank and the pressure of the tank then we know we could look up the

k values at a given temperature and pressure for our components. Using our k values and

our composition of the feed, we plug that in and we iteratively solve for psi such that

we equate the rest of the components to zero. the rest of it falls into place. Once we have

psi, we know that psi is equal to V/F. So F times psi gives us our vapor stream. F minus

our vapor stream gives us L. We go back to our y and x mole fractions. We solve those

using the information we have already found and the last thing we do is solve our energy

balance. Find out what is our heat that we are adding to our system in the pre-heater.

Since we know the compositions and our mass flow rates we figure out the enthalpies associated

with each stream and calculate q. So right here is the main method for solving a flash

tank separation for multiple components. Now before we get neck deep in this tedious solution

which, highly recommended, you should use some kind of software/solver to do this kind

of work. It is important to check if there is a valid roof for the equation such that

our psi falls in between 0 and 1. Now our first sanity check is to check all of the

k values for the components. So if we have five components in the system and all k values

are greater than 1 then we have a superheated vapor. And it is just the opposite if we have

all k values less than 1, then we have a sub cooled liquid. So to have phase equilibrium

between the vapor and the liquid phase we have to have some k values above 1 and some

k values below 1. Second sanity check is to check our function at the dew point and the

bubble point. We want to make sure we are above the bubble point and below the dew point

to have VLE. At the bubble point, that is where psi is equal to 0 because remember that

is the same thing as V/F. So if we have very little vapor, we are just forming that first

bubble, that is our bubble point. Now our check is, if the function of 0 is greater

than 0 then our mixture is below the bubble point so we are not in VLE. The second check

is at the dew point. This is going to be where we have very little liquid or a lot of vapor.

So the function of 1, if that is less than 0 then we are above our dew point and again

we are not going to have VLE. So we need to have k values that are both above and below

a value of 1 and then we need to make sure our function of psi falls in between those

two conditions. Now to see an example check our other screen cast on using this technique

to solve for multiple component flash tank separation.

Why does "all k values 1" imply that we have a superheated vapor? All k values 1 makes that implication make sense to me, but if you had a few components at a quality of 75% percent they would each have a k value of 3 and still be within the VLE.

* all k values bigger than one doesnt make sense. all k values much bigger than one does. sorry for the confusion with the comment below. the symbols on my tablet arent working right.

If all K values are larger than 1 for a multicomponent mixture, then the only possible phase is superheated vapor. Not clear on your statement about quality 75% meaning K-values are equal to 3. K-values are dependent on temperature and pressure for the species and in their simplest form give a relationship between vapor and liquid equilibrium (K=y/x). If all k-values are above 1, then the mole fractions cannot sum to 1 and thus there cannot be two phases.

Were can i find the k-values?

Can i assume k_i=p_i_sat/P as a start guess and then iterate k_i=y_i/x_i?

We used them off a DePriester chart. However you can also use vapor equilibria charts like those seen in refining handbooks

are there any books that you would recommend for design and sizing of flash tanks (e.g. residence time, diameter and height, material selection, etc.)

Dennis, you can assume K_i = y_i/x_i=Psat_i/Ptot==Roult's Law Valid. Understand?

great video

needs to be simplivied,for everyone,free from oil babys

its sounds complicated,but its not

Wonderful explanation

Does an isothermal flash drum exist? what is the general mechanical design for it?

Where can i look up K values?

Great video! I was previously stuck because I didn't realize Sum of x – Sum of y = 0.

Congratulations, great video!

What exactly happened algebraically if one pauses the video at 5:00 ?

Algebra way to complicated, For crying out loud page 10 guys! http://staff.sut.ac.ir/haghighi/download/documents/Single_Equilibrium_Stages_and_Flash_Calculations.pdf

Do I have to use the Newton-Raphson method to get a result from the final equation?