Here’s what the 22 independent material balances should supposedly
look like:
W1 – W2 -W3=0
H1 – H2 – H3 = 0
S1 – S2 – S3 = 0
H2 – H4- H5 = 0
W2 – W5 = 0
S2-S5 = 0
W5-W7=0
S5-S7 = 0
H5-H7=0
G6-G7=0
W3+W7-W8=0
H3+H7-H8=0
G7-G8=0
S3-S8+S7=0
-0.685H2+H4=0
W1+H1+S1=7500
-0.42H5 + G6=0
0.38W1-0.62H1-0.62S1=0
-0.05W1-0.05H1+0.95S1=0
0.38W2-0.68H2-0.68S2=0
-0.05W2 -0.05H2+0.95S2 =0
0.021W8+0.021H8+0.021S8-0.979G8=0
And here are the answers (composition and flow rates? Which is which?)
x =
1.0e+003 *
4.6500
2.2759
2.3741
2.2759
2.2759
4.6500
2.4750
1.0945
1.3805
0.7497
0.3448
0.3448
1.7253
0.3750
0.1774
0.1976
0.1774
0.1774
0.3750
0.1448
0.1448
0.1448
And here are the variables set up in Excel. Matrix A will be all the
coefficients on the left-hand side of the material balances (columns
W1-G8) and Matrix B will be the right-hand side of the material balances
(the column called ‘Ans’). Then we solve for x by x=inv(a)*(b).
W1 W2 W3 W5 W7 W8 H1 H2 H3 H4 H5 H7 H8 S1 S2 S3 S5 S7 S8 G6 G7 G8 Ans
1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0
0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0
0 0 1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 1 -1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 -1 0 0 0 0
0 0 0 0 0 0 0 -0.685 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 7500
0 0 0 0 0 0 0 0 0 0 -0.42 0 0 0 0 0 0 0 0 1 0 0 0
0.38 0 0 0 0 0 -0.62 0 0 0 0 0 0 -0.62 0 0 0 0 0 0 0 0 0
-0.05 0 0 0 0 0 -0.05 0 0 0 0 0 0 0.95 0 0 0 0 0 0 0 0 0
0 0.38 0 0 0 0 0 -0.68 0 0 0 0 0 0 -0.68 0 0 0 0 0 0 0 0
0 -0.05 0 0 0 0 0 -0.05 0 0 0 0 0 0 0.95 0 0 0 0 0 0 0 0
0 0 0 0 0 0.021 0 0 0 0 0 0 0.021 0 0 0 0 0 0.021 0 0 -0.979 0
The Matlab Program
%Matrix-gotta love it
clear
clc
% variable portion of the matrix
a=[1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0
0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0
0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0
0 0 1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 1 -1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 -1 0 0 0
0 0 0 0 0 0 0 -0.685 0 1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 -0.42 0 0 0 0 0 0 0 0 1 0 0
0.38 0 0 0 0 0 -0.62 0 0 0 0 0 0 -0.62 0 0 0 0 0 0 0 0
-0.05 0 0 0 0 0 -0.05 0 0 0 0 0 0 0.95 0 0 0 0 0 0 0 0
0 0.38 0 0 0 0 0 -0.68 0 0 0 0 0 0 -0.68 0 0 0 0 0 0 0
0 -0.05 0 0 0 0 0 -0.05 0 0 0 0 0 0 0.95 0 0 0 0 0 0 0
0 0 0 0 0 0.021 0 0 0 0 0 0 0.021 0 0 0 0 0 0.021 0 0 -0.979]
% answer portion of the matrix
b=[0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7500
0
0
0
0
0
0
]
x=inv(a)*(b)
Test
a =
Columns 1 through 7
1.0000 -1.0000 -1.0000 0 0 0 0
0 0 0 0 0 0 1.0000
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 1.0000 0 -1.0000 0 0 0
0 0 0 0 0 0 0
0 0 0 1.0000 -1.0000 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 1.0000 0 1.0000 -1.0000 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
1.0000 0 0 0 0 0 1.0000
0 0 0 0 0 0 0
0.3800 0 0 0 0 0 -0.6200
-0.0500 0 0 0 0 0 -0.0500
0 0.3800 0 0 0 0 0
0 -0.0500 0 0 0 0 0
0 0 0 0 0 0.0210 0
Columns 8 through 14
0 0 0 0 0 0 0
-1.0000 -1.0000 0 0 0 0 0
0 0 0 0 0 0 1.0000
1.0000 0 -1.0000 -1.0000 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 1.0000 -1.0000 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 1.0000 0 0 1.0000 -1.0000 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
-0.6850 0 1.0000 0 0 0 0
0 0 0 0 0 0 1.0000
0 0 0 -0.4200 0 0 0
0 0 0 0 0 0 -0.6200
0 0 0 0 0 0 0.9500
-0.6800 0 0 0 0 0 0
-0.0500 0 0 0 0 0 0
0 0 0 0 0 0.0210 0
Columns 15 through 21
0 0 0 0 0 0 0
0 0 0 0 0 0 0
-1.0000 -1.0000 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
1.0000 0 -1.0000 0 0 0 0
0 0 0 0 0 0 0
0 0 1.0000 -1.0000 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 1.0000 -1.0000
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 1.0000
0 1.0000 0 1.0000 -1.0000 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 1.0000 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
-0.6800 0 0 0 0 0 0
0.9500 0 0 0 0 0 0
0 0 0 0 0.0210 0 0
Column 22
0
0
0
0
0
0
0
0
0
0
0
0
-1.0000
0
0
0
0
0
0
0
0
-0.9790
b =
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7500
0
0
0
0
0
0
x =
1.0e+003 *
4.6500
2.2759
2.3741
2.2759
2.2759
4.6500
2.4750
1.0945
1.3805
0.7497
0.3448
0.3448
1.7253
0.3750
0.1774
0.1976
0.1774
0.1774
0.3750
0.1448
0.1448
0.1448
Chemical and Biochemical Engineering Homework Solutions
#9739
Matlab -- Developing 22 independent material balances and solving in Matlab
Please see the attached file for the fully formatted problem(s).
Find composition and flow rates from mass percent data.
The composition and flow rate of a feed stream is calculated using Matlab.
What is this?
By OTA - Overall OTA Rating
Claudiu Giurumescu, PhD (IP) - 5/5
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- Plain text response
- Attached file(s):
- Matlab.htm
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