CHE 205 Programming Project 1 | Complete Solution

CHE 205 Programming Project 1

Consider a vapor/liquid separation performed by flash vaporization in a drum:
The feed stream has flow rate F and compositions (in mole fraction) zi for n components, giving
compositions z1, z2, …, zn. In the drum, this feed is separated into a liquid phase that leaves the
system with flow rate L and compositions xi and a vapor phase that leaves the system with flow
rate V and compositions yi.

The thermodynamic principles governing this process are described by n vapor-liquid equilibrium
ratios Ki, one for each component. Given these K-values, a feed flow rate, and feed compositions,
it is possible to find the product flow rates and compositions by finding the root of the following
equation in the interval [0,1]:
€
zi(1−Ki)
1+Ψ(Ki −1)
= 0
i=1
nΣ
,

where the independent variable Ψ is defined as Ψ = V/F. In other words, the system can be
solved by finding a value of Ψ that makes the left-hand side of the equation above equal to zero.
Once this value of Ψ is found, L can be found as L = F – V and the compositions in each phase
can be found as:
€
xi =
zi
1+Ψ(Ki −1)
and
€
yi = xiKi .

Write a program that to find the output flow rates and compositions for such a separation system
with an input flow rate (in mol/h), input compositions (in mole fraction) and K-values
(dimensionless). Your program should be able to handle any number of components in the feed.
Consider a 7-component system where the feed compositions are: z1 = 0.16, z2 = 0.09, z3 = 0.21, z4

= 0.13, z5 = 0.06, z6 = 0.15, and z7 = 0.20; the K-values are K1 = 3.52, K2 = 1.92, K3 = 1.22, K4
= 0.84, K5 = 0.43, and K6 = 0.08. The total feed rate is 1500 mol/h. Plot the output
compositions and flow rates in both phases as functions of K7 as K7 varies from 0.05 to 4.00.
Note: While there are several root-finding routines built into MATLAB as functions,
avoid using them in this project. Instead, write your own root-finding routine based
the one of the algorithms we studied in class.