The Flash Operation
Contains Links to scripts and models to solve Flash, Dew- and Bubble Point Calculations using ASCEND IV
Consider a simple phase separation problem. The discussion you see here follows closely the discussion given in Systematic Methods of Chemical Process Design by Lorenz T. Beigler, Ignacia E. Grossman and Arthur W. Westerberg, page 217, a book published by Prentice Hall, ISBN-0-13-492422-3 (TP155.7.B47.1997).

You have a feed stream (molar flow rate, F) with a known composition (z_i). Let there be C components in the feed stream. Assume for a moment that this feed stream phase separates, into a liquid stream (with a molar flow rate, L and a composition x_i) and a vapor stream (with a molar flow rate V and a composition y_i).

Let us write down as many equations as we can to describe this system. Where necessary, I have provided comments on what the equations are and why we are writing them.

F = L + V

(1)

fi = F zi  li = L xi  vi = V yi (2)

F zi = L xi + V yi  or written as  fi = li + vi

(3)

xi = li å li   yi = vi å vi

(4)

Equations 1, 2,  3 are what we call Mass Balance Equations, with equation 4 defining mole fractions in terms of the individual component flows and the total molar flow rates.

gi fio xi = fi P yi

(5)

F Hf + Q = V Hv + L Hl

(6)

In the Equilibrium relationship written as equation 5, the activity coefficient (g_i) will in general be a function of the composition of the liquid phase, Temperature and Pressure, the fugacity coefficient (f_i) will be a function of the composition of the vapor phase, Temperature and Pressure, while f_i^o which is the pure component fugacity can often be approximated as the pure component vapor pressure (P_i^*) which is often approximated as a function of Temperature.

Now let us count the number of equations and the number of variables we have to deal with. Equation 3 is written for each i component (so we have C equations), the equilibrium relationship, equation 5 is written for each i component (we have C more equations) and we have the Enthalpy Equation written as equation 6. This gives us a total of 2C + 1 equations. Number of variables to solve for? We need to determine each of the x_i's, the y_i's (that is 2C variables). The other variables include: Temperature (T), Pressure (P) and Heat (Q, if the flash operation is done adiabatically then Q will be zero, else Q will be have some non-zero value). Thus we have 2C + 3 variables. Thus (2C + 3) - (2C + 1) = 2 or we have two degrees of freedom, meaning we must specify two of the variables to get a solution.

The manner we have written the equations will fail however if one of the phases disappears during the flash operation, for example when you are doing a Bubble-Point or a Dew-Point calculation. So let's try writing the equations in a manner where we will not have trouble no matter what the conditions are expected to be.

Let's keep equations 3 (C equations) and  6 (1 equation) like before and then these equations

yi = Ki xi

(7)

Ki = gi fio fi P

(8)

If we now consider equations 7 and  8 we get additional 2C equations and together with equations 3 and  6 we have a total of 3C + 1 equations. Let's add the number of variables, 3C (x_i, y_i and z_i) add Temperature (T), Pressure (P), F, L and V and you get a grand total of 3C + 5 variables. But since neither the x_i or the y_i's are specified, we can include the overall mass balance equation 1. But we have to be careful here since we have said nothing about the fact that the molefractions x_i and y_i must add upto one. This can lead to strange solutions if we are not careful.

If the temperature and the pressure are specified, we can solve the mass balance equations without using the enthalpy balance equation. We can then write

xi = zi 1.0 + (Ki - 1.0) V F

(9)

yi = Ki zi 1.0 + (Ki - 1.0) V F

(10)

We can require that either åx_i = 1.0 or åy_i = 1.0 to give us a model that we can solve with 2 degrees of freedom (count the number of equations and variables).

å xi = å F zi F + (Ki - 1.0)V = 1.0

(11)

å yi = å F Ki zi F + (Ki - 1.0)V = 1.0

(12)

The problem with equations 11 and  12 is that both of these equations are trivially satisfied for every Flash Problem if you set the x_i's or the y_i's to the feed composition, z_i. The alternative is to write the specification as the difference in the sum of the x_i's and the y_i's and set that to zero

å yi - å xi = å é ë F æ è Ki - 1 ö ø zi F + æ è Ki - 1 ö ø V ù û = 0.0

(13)

The Flash Model can then be given by Equations 3,  7,  8,  1,  13 and  6 with two degrees of freedom.

So How can one solve the equations?

Once you have downloaded both the SCRIPT files (these have the *.a4s extension ... for example the script for a simple PT flash is called ptflash.a4s) and the MODEL files (the model for the PT flash is in the ptflash.a4c file) you are ready.

An ASCEND Script and an ASCEND model that details a simple PT-Flash Calculation for an ideal gas, ideal liquid are given below. You will need to save the script file as say ptflash.a4s and the model file as say ptflash.a4c. If you are using NETSCAPE, click the right mouse button on the link and do a SAVE the LINK AS.

In the ASCEND script window, you will then read in the script file, select ALL the statements and execute the file. In the BROWSER, you will see the results of the calculations. Make a print out of both ptflash.a4s AND ptflash.a4c, read these files. Look for example the variables I have declared to be TRUE (means, we know them, do not solve for them!) and those that are FALSE (means, please find these for me!).

You can easily modify these scripts, models and use them for your own Dew Point, Bubble Point and Flash Calculations. By studying how these simple models are written and solved, perhaps you can/will use them for other calculations you may have to do. Watch these pages for more examples, and models.

Script for the PT Flash
Model for the PT Flash

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File translated from T_EX by T_TH, version 3.70.
On 16 Jan 2006, 21:16.