Download - Che 201 Hand Out 4 Chapter 10
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Computer Aided Balance
Calculations
Dr M. A. A. Shoukat Choudhury
Department o hemical EngineeringBUET, Dhaka 1000
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Motivation
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= . .
DOF = 0 A Unique Solution
,
solutions
< , , ,
made some mistake and wrote more equations
than that you are entitled to. However, in some
other areas, you may find DOF>0 where there isno unique solution
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should be independently specified todefine the roblem com letel . Theseexternally specified variables are called
design variables Once design variables are specified, the
other variables can be calculated from the
re a ons equa ons, w c are ca e s a evariables.
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-.
Mixer
n1 g 2
40 oCn4 kg O2n k N
n2 g 2n3 kg N2
25o
C
Q, kJ
50 oC
1 ,- 3 relations ( 2 MB, 1 EB)
DOF = 3
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-A liquid mixture of n-hexane (HX) and n-heptane
HP at a hi h ressure is abru tl ex osed to a
lower pressure. A portion of the mixture evaporates,yielding a vapor mixture relatively rich in hexane
rich in heptane. The two product streams are in
e uilibrium at tem erature T and ressure P; theircompositions are related by Raoults Law. PerformDOF analysis. Specify variables so that you get a
s ra g - orwar so u on2) trial-error solution
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Example 10.1-1 (contd)
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Example 10.1-1 (contd)
10 variables - n1, n2, n3, x1, x2, x3, T, P, p*HX , p
*HP
2 Raoults Law
2 Antoine Equation
6 E uations
x2 P = x3 p*HX(1 - x2 ) P = (1 - x3 ) p
*HP
DOF = 4
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1. Straight-Forward Solution:
Specify Design Variables - n1, x1, x3, T
- * * ,
calculated from Antoine Equation
- 2
Raoults Law
- a cu a e n2 an n3 rom componen
balance
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1. Straight-Forward Solution (contd):
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2. Trial and Error Solution
3. Impossible Solution - n1, n2, n3 and T
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A process that contains two or more interconnected unitshas fewer degrees of freedom than the sum of thedegrees of freedom of the individual units
1. Draw and completely label the flow-chart
2. Determine the local degrees of freedom for eachprocess un , m x ng po n an s ream sp ng po n s
3. Calculate number of tie variables
4. Determine the overall de rees of freedom. This isequal to the sum of all local dofs minus number of tievariables.
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Example 10.1-2 DOF Analysis of a Multiple-Unit Process
reaction
CO+2H2CH3OH
T e res ee , w c conta ns CO an H2 n sto c ometr c proport on,
enters the process at a rate of 2.2 m3/s at 250C and 6.0 MPa and combinesadiabatically with a recycle stream. The combined stream is heated to 2500C
and fed to the reactor. The reactor effluent emerges at the same temperature
and is cooled to 00C at P= 6.0 MPa, partially condensing the methanol
product. The gas leaving the condenser is saturated with methanol: 1% istaken off for process monitoring purposes and the remainder is recycled. An
overall CO conversion of 98% is achieved. The ratio of H2 to CO is 2 mol
H2/1 mol CO everywhere in the process system. Ideal gas behavior may be
assumed.
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the given information is sufficient to allow the calculation of the component
flow rates for all streams, the required heat duties for all process units, and
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Example 10.1-2 (contd)
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Purge point:
,
0 balance
2 dof
Overall Process DOF: 12 ( Sum of Local DOF)
11 tie variables
1 additional relation
0
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Two Approaches of Computer Aided Simulation
Sequential Modular
- break-down flow chart in terms of modules- write the algorithm/subroutine for the module
- use the modules as needed to solve the whole problemsequentially
- Commercial softwares: ASPEN Plus, HYSIS, CHEMCAD, ICAS,Design II
Equation Based- Equations of all units are collected and solved simultaneously
- simultaneous solution of a large number of equations (some ofthem may be nonlinear) can be cumbersome and time consuming
- powerful equation solving commercial packages Maple, Matlab,Mathcad, E-Z solve
Recently, a combination of the above two approaches are also being used.
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The following two reactions occur in an ethylene oxide
2 C2H4 + O2 = 2 C2H4OC2H4 + 3 O2 = 2 CO2 + 2 H2O
A stream containing equimolar amounts of ethylene and oxygen isjoined by a recycle stream containing pure ethylene, and the
combined stream is fed to the reactor. The reactor effluent goes to a.
first stream, which is sold, is pure ethylene oxide; and the second,which is discarded, contains all the carbon dioxide, oxygen, waterand 5% of the unreacted ethylene leaving the reactor; and the third
, ,unreacted ethylene. Perform a degrees of freedom analysis for theprocess and specify the design variables that must be known tosolve the problem completely.