What software is important in ChE?
• Numerical Software (focus on Excel and VBA
but Python is becoming more common too)
• Process Simulators (ASPEN/HYSYS,
ChemCad, etc.)
• Professional Applications (Word, Powerpoint,
Visio, etc.)
• Specialized software (MATLAB, Statistics
software, etc).
• Programming Languages (C++, MATLAB,
Mathematica etc.).
MS Excel ! MS Excel ! MS Excel !
This is more
for R&D jobs
Process
Engineering
jobs
This is what is
commonly used
Peng-Robinson EOS (PREOS)
• Cubic Solver
•
• Where Z = compressibility factor Z = PV/RT
• Pure component
• Given T and P
• Use values of Tc, Pc, κ and ω to calculate a(T) and
b (Table 6.6-1, p. 250)
• Use a and b to calculate A, B (Table 6.4-3)
• Use A, B to calculate α, β and γ
• Solve for Z (careful of multiple roots)
Given T, P calculate V, H, S (and G)
What are multiple roots?
• Since it is a cubic equation, you will always
have 3 roots.
• Scenario A – 1 real root, 2 imaginary roots
• Scenario B – 3 real roots
• In A no problem, the 1 root is the answer
• In B use the highest root (gas) and lowest (liquid)
to get two sets of values corresponding to the gas
and liquid conditions.
• Middle root (metastable root) may be ignored.
Once you get Z….
• Can get molar volume (V)
• Use Eqn. 6.4-29 to get
• Use Eqn. 6.4-30 to get
• Solve for H and S (see Illustration 6.4-1)
• Solve for fugacity using Eqn. 7.4-14a (if vapor),
7.4-14b (if liquid)
• Values of a, b, A and B in the equation are the same
as what you calculated
Similar flow chart – Figure 7.5-1
See next slide for better
HR and SR equations
Better approximations than Sandler
one suggestion is to use O2
as a test to
see if your program works. (cross check
against Table 6.4-4). However, O2
is not a
good test for multiple Z roots.
What about mixtures?
• Calculate pure component a and b
• Calculate the mixture a and b (amix and bmix)
• Solve for Z using mixture values (Zmix)
• Use this in Equation 9.4-10 (vapor) or 9.4-11 (liquid)
to get fugacities for each component in the mixture
or
௫
ୀଵ
ୀଵ
௫
ୀଵ
Binary
interaction
parameter
?? and are pure component values e.g. Table 9.4-1
If not available –
use similar or zero
Nested loops
If you have 2 components (c = 2)
amix = y1
y1
a11 + y1
y2
a12 + y2
y1
a21 + y2
y2
a22
If you have 2 components (c =3)
amix = y1
y1
a11 + y1
y2
a12 + y1
y3
a13 + …… + y3
y3
a33
?? and are pure component values
• Natural gas from a fracking facility was estimated to have the
following (molar) composition – 65% methane, 20% ethane and 15%
propane
• In order to design the extraction process, it is important to
understand the properties of the gas mixture. Your bosses ask you to
calculate the fugacity of the components at 100oC. Present your
findings in the form of the table below:
P (bar) Z
???????
??????
???????
5
15
25
Project #2 – FALL 2020
Submit on Blackboard – Excel file titled lastname.xlsx
Answer file (containing only the table): lastname.pdf
Once you get fi….
• You can calculate the activity co-efficient of
component i in the mixture since:
•
• If you know , you can calculate
Pure component fugacity
concentration
Fugacity in the mixture
Why does any of this matter?
Sample Solution