2023 CHE 205 Programming Project 1 Consider a vapor liquid separation performed by flash vaporization | Assignment Collections

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]:
n

zi (1 − K i )
= 0,
i −1)

∑ 1+ Ψ(K
i=1

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.

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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
and y i = x iK i .
1+ Ψ(K i −1)

Write a program that to find the output flow rates and compositions for such a separation system
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with an input flow rate (in mol/h), input compositions (in mole fraction) and K-values
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(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.