Che 201 Hand Out 4 Chapter 10

8/10/2019 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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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.

- -

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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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.

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Che 201 Hand Out 4 Chapter 10