spreadsheet for mass balance

8/12/2019 Spreadsheet for Mass Balance

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Process flowsheeting withSpreadsheet


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H82CYS - Computer System Intro to Process Simulation 2

Degree of freedom revisitedDegree of freedom (ndf) of a system:

ndf= nvnewhere, nv= variables; ne= independent eq

If ndf= 0 (e.g. 3 unknowns & 3 independenteq), the unknown variables can be

calculated.If ndf> 0 (e.g. 5 unknowns & 3 independent

eqndf= 2), specify the design variables&calculate the state variables.

If ndf< 0 (independent eq > unknowns)process is over-specified.

(Felder & Rousseau, 2000)


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Degree of freedom revisitedUnknown variablesfor a single unit:

Unknown component amounts / flowrate for all inlet &outlet streams

Unknown stream T& P

Unknown rate of energy transfer (as heat & power)

Equationto determine these unknowns:

Material balances for each independent species

Energy balance

Phase & chemical equilibrium relations

Additional specified relationship among process

variables


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Example : A heated mixerHeated mixer

n2(kg O2)

n3(kg N2)

25C

n4(kg O2)

n5(kg N2)

50C

n1(kg O2)

40C

Q (kJ)

ndf analysis:

6 variables (n1, , n5, Q)

3 eq (2 material balances & 1 energy balances)= 3 degrees of freedom

Specify 3 design variables& solve the rest.


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Degree of freedom revisited Given the following equations:

x1+ 2x2x3

2

= 05x1x23+ 4 = 0

i. What is the ndf for this system?ii. Which design variable to be chosen for an easier

solution?


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Tutorial 1: Mass energy balances

Determine the ndffor the system

What are the design variables& state variables?

Mixing

nA3(mol A/s)

nB3(mol B/s)

nC3(mol C/s)

nD3(mol D/s)nE3(mol E/s)

T3(C)

nA2(mol A/s)nB2(mol B/s)

nC2(mol C/s)

nD2(mol D/s)

nE2(mol E/s)

T2

(C)

nA1(mol A/s)

nB1(mol B/s)

nC1(mol C/s)nD1(mol D/s)

nE1(mol E/s)

T1(C)

S1

S2

S3



7/29H82CYS - Computer System Intro to Process Simulation 7

Tutorial 1: Mass energy balancesMass balance equations:

nA3 = nA1+ nA2nB3 = nB1+ nB2nC3 = nC1+ nC2nD3 = nD1+ nD2

nE3 = nE1+ nE2Energy balance equation:

DH = SnoutHoutSninHin

(assumption: P= 1 atm; temp = T1H1= 0; no

phase change; constant Cp)ndf= 18 variables (6 on each streams) 6 equations

= 12 degrees of freedom


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Tutorial 1: Mass energy balances Specify the design variables:

Stream 1:nA1= 23.5 mol A/s

nB1= 16.2 mol B/s

nC1= 8.5 mol C/s

nD1= 5.6 mol D/s

nE1= 2.2 mol E/s

T1= 135.0C

Stream 2:nA2= 0.0 mol A/snB2= 57.0 mol B/snC2= 29.0 mol C/snD2= 15.6 mol D/snE2= 0.0 mol E/s

T2= 23.0

Other info [constant heat capacity inJ/(mol.C)]:CpA= 77.3; CpB= 135.0; CpC= 159.1; CpD= 173.2; CpE=188.7

Determine the component flowrate & Tfor stream 3.


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Tutorial 1: Mass energy balancesEnergy balance equation (cont.):

DH = SnoutHoutSninHin = 00 = [ nA3CpA+ nB3CpB+ + nE3CpE] (T3T1)

[ nA2CpA+ nB2CpB+ + nE2CpE] (T2T1)

[ nA1CpA+ nB1CpB+ + nE1CpE] (T1T1)

(reference temperature taken as T1)

Rearrange the equation, solving for T3:

12

33333

22222

13 TT

CnCnCnCnCn

CnCnCnCnCnTT

pEEpDDpCCpBBpAA

pEEpDDpCCpBBpAA

= 0



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Tutorial 1 in spreadsheet solution


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ime for exercise


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Approaches for processflowsheetingSequential-modular

Equation-oriented


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Tutorial 2 (continue from Tutorial 1)

MixingnA3(mol A/s)

nB3(mol B/s)

nC3(mol C/s)

nD3

(mol D/s)

nE3(mol E/s)

T3(C)

nA2(mol A/s)

nB2(mol B/s)

nC2(mol C/s)

nD2(mol D/s)nE2(mol E/s)

T2(C)

nA1(mol A/s)

nB1(mol B/s)

nC1(mol C/s)

nD1(mol D/s)

nE1(mol E/s)

T1(C)

nA4(mol A/s)

nB4(mol B/s)

nC4(mol C/s)

nD4(mol D/s)

nE4(mol E/s)

T4= ?

S1

S2

S3 S4

Heater, Q =

100,000 J


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Equation-oriented (EO) Solution is obtained by solving simultaneously all

the modelling equations.Advantages:Flexible environment for specifications, which may be

inputs, outputs, or internal unit (block) variables.Better treatment of recycles, and no need for tear streams.

Note that an object oriented modelling approach is wellsuited for the EO architecture.

Disadvantages:More programming effort.Need of substantial computing resources (but this is less

and less a problem with new PCs).Difficulties in handling large differential algebraic

equations systems.Difficult convergence follow-up and debugging.


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Equation solving by matrix Solve matrix equation: A X= B

where,A= a known (ix i) coefficient matrix;B= a know solution vector (ix 1);X= an unknown vector (ix 1)

Example matrix with i= 3:

A(3x3) X(3x1) = B(3x1) X = A-1 B

xyz

a1 b1 c1a2 b2 c2a3 b3 c3

= d1d2

d3

xyz

= d1d2

d3

-1

a1 b1 c1a2 b2 c2a3 b3 c3


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Tutorial 3Solve for the following simultaneous

equations:x + y + z = 1

2x - 2y + 5z = 1

2.5 y + z = 1Set up matrix equation:

A X = B

xyz

1 1 12 -2 50 2.5 1

=111


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Matrix solving by Excel spreadsheet


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Tutorial 4: BTX separation problem

C1 C235 kg B

50 kg T15 kg X

n1(kg)

0.673 kg B/kg

0.306 kg T/kg

0.021 kg X/kg

n2(kg B)n3(kg T)n4(kg X)

n5(kg)

0.059 kg B/kg

0.926 kg T/kg

0.015 kg X/kg

n6(kg B)n7(kg T): 10% of T in feed to C1n8(kg X): 90% of X in feed to C1

C1: 4 variables (n1, , n5)3 material balances

= 1 local ndf

C2: 7 variables (n1, , n5)3 material balances

= 4 local ndf

Process: 5 local ndf3 ties (n2, n3 , n4)2 relations (recovery of T & X in C2 bottoms)= 0 degrees of freedom


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Tutorial 4: BTX separation problem

C1 C235 kg B

50 kg T15 kg X

n1(kg)

0.673 kg B/kg

0.306 kg T/kg

0.021 kg X/kg

n2(kg B)n3(kg T)n4(kg X)

n5(kg)

0.059 kg B/kg

0.926 kg T/kg

0.015 kg X/kg

n6(kg B)n7(kg T): 10% of T in feed to C1n8(kg X): 90% of X in feed to C1

C1 balances:

B: 35 = 0.673n1+ n2T: 50 = 0.306n1+ n3X: 15 = 0.021n1+ n4

C2 balances:

B: n2= 0.059n5+ n6T: n3= 0.926n5+ n7X: n4= 0.015n5+ n810% T recovery: n7= 0.1 (50) = 5.090% X recovery: n8= 0.9 (15) = 13.5


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Tutorial 4: BTX separation problemSolve the mass balance equation using MS

Excel spreadsheet:0.673n1+ n2= 35 (1)

0.306n1+ n3= 50 (2)

0.021n1+ n4= 15 (3)

0.059n5+ n6n2= 0 (4)

0.926n5+ n7n3= 0 (5)

0.015n5+ n8n4= 0 (6)

n7= 5.0 (7)n8= 13.5 (8)


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H82CYS - Computer System Simulation of Recycle Streams 21

The Onion model

Reactor

Separation &

recycle

Heat exchange

network

Utilities (Linnhoff et al., 1982;

Smith 1995, 2005)


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Types of recycle streamsMaterial recycle

Heat recycle


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Simulation of recycling system with SM

A B C D E F

Recycle stream

Unit operation

in simulator

Tearrecycle stream

r1 r2

(Turton et al., 1998)


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Simulation of recycling system with SMBasic algorithms in handling a recycle

stream:Before the Equipment C is solved, some

estimationof stream rmust be madea tearstream occurs.Provided information is supplied about Stream

r2, we can solve the flowsheet all the way toStream r1 by using sequential modular approach.Compare Streams r1 and r2.If r1 & r2 agree within some specified tolerance

we have a converge solutionOr else, r2 is modified & simulation is repeated

until convergence is obtained.


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Tutorial 5 isomerisation process

In an isomerisation process, component Ais converted tocomponent B.

The mixture from the reactor is separated into relativelypureA(which is recycled) & relatively pure product B.

No by-products are formed and the reactor performance canbe characterised by its conversion.

The performance of the separator is characterised by therecovery ofAto the recycled stream (rA) and recovery of Bto the product (rB). (Smith, 2005)


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Mass balance equations Given the following variables: mi ,j= molar flowrate of Component i in Streamj

X = reactor conversion ri= fractional recovery of Component i

Mass balance equationsfor each unit may be written as: Mixer:

Reactor:

Separator:

mA,2

= mA,1

+ mA,5

mB,2= mB,1+ mB,5

mA,3= mA,2(1 X)

mB,3= mB,2+ XmA,2

mA,4= mA,3(1 rA)

mA,5 = rAmA,3

mB,4= rBmB,3

mB,5= mB,3(1 rB)


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Strategy with SM approach

Calculation sequencein SM:. However, problem is encountered at the mixer, as the

flowrate & composition of the recycle are unknown. Strategy using SM approach: Tearthe recycle streams

Add a recycle convergenceunit/solver in the tear stream. Estimate the component molar flowrates of the tear stream. Thisallows the material balance in the reactor and separator to be solved,& provide the molar flowrates for the recycle stream.

The calculated and estimated values of the tear stream are comparedto test whether errors are within a specified tolerance.

(Smith, 2005)


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Data given Given the following values: mA,1= 100 kmol; mB,1= 0 kmol

X = 0.7 rA= 0.95; rB = 0.95

Assume the flowrate of componentAand Bin the recycledstream(stream 5) as follow:

mA,5= 50 kmol mB,5= 5 kmol

Setting at the recycle convergence unit/solveriterationstops when the scaled residueis smaller than a specifiedtolerance (1 x 10-5for this case). Scaled residue is given as:

(Smith, 2005)

valueEstimated

valueestimated-valueCalculatedresidueScaled


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Recycle simulation with spreadsheet

spreadsheet for mass balance

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