CHE656 2012 Homework6 Solutions

7/29/2019 CHE656 2012 Homework6 Solutions

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CHE656

Computer Applications for Chemical Engineering Practice

Homework Set #6 Solutions

Class-16

Prepared by

Dr. Hong-ming Ku

King Mongkuts University of Technology Thonburi

Chemical Engineering Department

Chemical Engineering Practice School

May 2012 Use with Permission of the Author Only


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FLASH-1

FLASH-2

MIXER

SPLITTER

1

2

3

4

5

6

7

8

45. Flowsheet Convergence, II

Consider the flowsheet below which consists of two flashes, one splitter, and one mixer. The

feed enters the process at 70 F and 14.7 psia with the following composition: 10 lbmol/hr n-

butane, 10 lbmol/hr n-pentane, 10 lbmol/hr n-hexane, and 10 lbmol/hr benzene. When you

create your flowsheet, you must use the same stream IDs and block IDs as shown in the figure.

The two flashes have the following operating conditions:

FLASH-1: Vfrac = 0.3, P = 0 FLASH-2: Vfrac = 0.7, P = 0

The splitter has the following split fraction: Stream 5 = 5%

(a)Using PENG-ROB, propose two convergence schemes to converge the given flowsheet.You may use any tear stream convergence algorithm in A+ and select your own tear

streams (or use the A+ default), but in doing so you must:(i) reinitialize your run.

(ii) not provide any guesses for the tear streams.

(iii)not increase the default maximum number of iterations (30) in the algorithm orchange its default parameter settings.

Note that the two convergence schemes you propose must involve two different

algorithms, i.e. you cannot use the same algorithm and just change the tear streams in the

two schemes.

Answer the following questions:

Scheme 1: Tear streams: ___Stream 3 and Stream 4______


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Your convergence algorithm: ____Broyden_____

Note that Streams 3 and 4 are the only tear stream set that Broyden will converge in 25

iterations. Broyden will need more than 25 iterations if one uses other tear stream sets suchas Streams 6 and 7.

Scheme 2: Tear streams: ____Stream 6 and Stream 7_____

Your convergence algorithm: ___Newton_____

Total flow rate of Stream 6 = ____760.212_____ lbmol/hr

Mole fraction of benzene in Stream 4 = ____0.315_____

Mole fraction ofn-butane in Stream 7 = ____0.141____

Note that the other two algorithms, namely Wegstein and Direct, will not converge thisflowsheet.

(b)Now, we want to add two composition constraints to the flowsheet such that the molefraction of benzene in Stream 4 is equal to 0.35 (0.0001) and the mole fraction ofn-

butane in Stream 7 is 0.15 (0.0001). These two constraints or design-specs are achieved

by varying the vapor fraction in FLASH-1 and FLASH-2, respectively. Propose two

different convergence schemes in ASPEN PLUS to solve this constrained problem.

Note that this is an extremely difficult problem to converge. You have to be creative and

try many different convergence schemes, including examining the bounds of your

manipulated variables (to make them narrow enough) and/or changing their initial guesses.

Once again, you must reinitialize each run and may not provide initial guesses for the tearstreams. But in this part, you are allowed to increase the maximum number of iterations in

the convergence algorithm.


Your convergence scheme 1: (Be very specific with your answer, e.g. what algorithms

were used to converge tear streams and design-specs and whether the convergence wassimultaneous or nesting, and if nesting what was the order of nesting.)

Converge tear streams 3 and 4 simultaneously using Broyden and converge the twodesign-specs without changing the given Vfrac initial guesses in Part (a) using Newton.The flowsheet will converge in both cases in which we nest the design-specs loop either

inside or outside the tear stream loop. The maximum number of iterations in Broyden was

increased from 30 to 100.


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Your convergence scheme 2: (Be very specific with your answer, e.g. what algorithms

were used to converge tear streams and design-specs and whether the convergence wassimultaneous or nesting, and if nesting what was the order of nesting.)

Converge tear streams 3 and 4 simultaneously using Broyden and converge the two

design-specs separately without changing the given Vfrac initial guesses in Part (a) using

Secant. Then nest the two design-spec loops inside the tear stream loop. The maximum

number of iterations in Broyden was increased from 30 to 100.

Vapor fraction in FLASH-1 = __0.4627__ Vapor fraction in FLASH-2 = __0.5179__

(c)Solve the constrained problem in Part (b) using only one Broyden loop to converge thetear streams and the two design-specs simultaneously with re-initialization and without

entering any initial guesses for the tear streams.

How did you converge the flowsheet? In order to converge the two tear streams (Streams 3

and 4) and the two design-specs, you need to change the initial guess of Vfrac in FLASH-2from 0.7 to 0.5. Then increase the maximum number of iterations in Broyden from 30 to

100. Broyden will converge the flowsheet in 98 iterations.

Input Summary:

;

;Input Summary created by Aspen Plus Rel. 23.0 at 01:36:08 Fri Jun 17, 2011

;Directory I:\HMKu\ChEPS\ChEPS Courses\ChE656-15thYear\Final FilenameC:\DOCUME~1\USER\LOCALS~1\Temp\~ap603.tmp

;

DYNAMICS

DYNAMICS RESULTS=ON

IN-UNITS ENG

DEF-STREAMS CONVEN ALL

SIM-OPTIONS OLD-DATABANK=NO

DESCRIPTION "

General Simulation with English Units :

F, psi, lb/hr, lbmol/hr, Btu/hr, cuft/hr.

Property Method: None

Flow basis for input: Mole


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Stream report composition: Mole flow"

DATABANKS 'APV71 PURE22' / 'APV71 AQUEOUS' / 'APV71 SOLIDS' / &

'APV71 INORGANIC' / NOASPENPCD

PROP-SOURCES 'APV71 PURE22' / 'APV71 AQUEOUS' / 'APV71 SOLIDS' &

/ 'APV71 INORGANIC'

COMPONENTS

N-BUTANE C4H10-1 /N-PENTAN C5H12-1 /

N-HEXANE C6H14-1 /

BENZENE C6H6

FLOWSHEETBLOCK FLASH-1 IN=2 7 OUT=3 4

BLOCK FLASH-2 IN=4 OUT=7 8

BLOCK MIXER IN=1 6 OUT=2

BLOCK SPLITTER IN=3 8 OUT=5 6

PROPERTIES PENG-ROB

PROP-DATA PRKBV-1

IN-UNITS ENGPROP-LIST PRKBV

BPVAL N-BUTANE N-PENTAN .0174000000 0.0 0.0 -459.6699923 &

1340.329993BPVAL N-PENTAN N-BUTANE .0174000000 0.0 0.0 -459.6699923 &

1340.329993

BPVAL N-BUTANE N-HEXANE -5.6000000E-3 0.0 0.0 -459.6699923 &1340.329993

BPVAL N-HEXANE N-BUTANE -5.6000000E-3 0.0 0.0 -459.6699923 &

1340.329993

BPVAL N-PENTAN BENZENE .0174000000 0.0 0.0 -459.6699923 &

1340.329993BPVAL BENZENE N-PENTAN .0174000000 0.0 0.0 -459.6699923 &

1340.329993

BPVAL N-HEXANE BENZENE 9.30000000E-3 0.0 0.0 -459.6699923 &

1340.329993

BPVAL BENZENE N-HEXANE 9.30000000E-3 0.0 0.0 -459.6699923 &

1340.329993

STREAM 1SUBSTREAM MIXED TEMP=70. PRES=14.7


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MOLE-FLOW N-BUTANE 10. / N-PENTAN 10. / N-HEXANE 10. / &

BENZENE 10.

BLOCK MIXER MIXER

BLOCK SPLITTER FSPLIT

FRAC 5 0.05

BLOCK FLASH-1 FLASH2

PARAM PRES=0. VFRAC=0.3

BLOCK FLASH-2 FLASH2PARAM PRES=0. VFRAC=0.5

DESIGN-SPEC DS-1DEFINE XBZ MOLE-FRAC STREAM=4 SUBSTREAM=MIXED &

COMPONENT=BENZENESPEC "XBZ" TO "0.35"

TOL-SPEC "0.0001"

VARY BLOCK-VAR BLOCK=FLASH-1 VARIABLE=VFRAC SENTENCE=PARAM

LIMITS "0.1" "0.9"

DESIGN-SPEC DS-2

DEFINE XNC4 MOLE-FRAC STREAM=7 SUBSTREAM=MIXED &

COMPONENT=N-BUTANE

SPEC "XNC4" TO "0.15"TOL-SPEC "0.0001"

VARY BLOCK-VAR BLOCK=FLASH-2 VARIABLE=VFRAC SENTENCE=PARAM

LIMITS "0.4" "0.7"

EO-CONV-OPTI

CONV-OPTIONS

PARAM TEAR-METHOD=NEWTON

CONVERGENCE C-2 BROYDEN

TEAR 3 / 4SPEC DS-1 / DS-2

PARAM MAXIT=100

CONV-ORDER C-2

STREAM-REPOR MOLEFLOW MOLEFRAC

;

;;


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1

8

3

147

2

6

109

13

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15

4

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48.Flowsheet Convergence, IIIConsider the complex flowsheet from Problem 4 shown below, but this time with a process

feed and two process output streams also included. We wish to use ASPEN PLUS to studythe convergence behavior of this flowsheet by replacing each block with either a mixer or a

splitter. For simplicity, we will assume that the process fresh feed contains pure water at 70

F and 14.7 psia (flowrate is unknown). Except for splitter Block B whose split fraction isunknown, all other splitter blocks split the total inlet feed into outlet streams with equal flow

rates. The two unknowns can be determined from the following two constraints:

a. The total molar flow rate of the product stream (Product-1) from Block D is equal to40 lbmol/hr (0.01 lbmol/hr).

b. The ratio of the molar flow rate of Stream 2 to the molar flow rate of Stream 3 ismaintained at 2.0 (0.001).

(a) Using A+ and automatic convergence and sequencing (Level 1), determine the water feedflow in Stream Feed and the split fraction in Block B going to Stream 2.

Water flow rate in Stream Feed = _______________ lbmol/hr

Split fraction in Block B going to Stream 2 = _______________

Also, write down the CPU seconds required by your computer to converge this flowsheet.

Simulation time in CPU seconds: ________________

A B C D

E F G

Feed

Product-1

Product-2


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(b) You undoubtedly noticed that, because of the nesting of various loops, this problem took

some time to converge (on my laptop, this CPU time was nearly 50 seconds before ReportWriter is entered). Propose two different Level 3 convergence schemes and use them to

converge the flowsheet in Part (a) again. Your aim is to cut down the CPU time by half orless. In both cases, you are not allowed to initialize the tear streams and each run must

start with a re-initialization, i.e. purge all the results first before running the model.

Briefly write down your two schemes:

Scheme 1: _____________________________________________________________

_____________________________________________________________

CPU seconds of Scheme 1: ________________

Scheme 2: _____________________________________________________________

_____________________________________________________________

CPU seconds of Scheme 2: ________________

Solution:

(a)Using A+ and automatic convergence and sequencing (Level 1), determine the water feedflow in Stream Feed and the split fraction of Stream 2 in Block B.

Water feed flow in Stream Feed = ____120.024____ lbmol/hr

Split fraction of Stream 2 in Block B = ___0.8570____

Also, write down the CPU seconds required by your computer to converge this flowsheet.

Simulation time in CPU seconds: ___49.11 seconds___

(b)You undoubtedly noticed that, because of the nesting of various loops, this problem tooksome time to converge (on my laptop, this CPU time was nearly 50 seconds before Report

Writer is entered). Propose two different Level 3 convergence schemes and use them to

converge the flowsheet in Part (a) again. Your aim is to cut down the CPU time by half or

less. In both cases, you are not required to initialize the tear streams and each run must

start with a re-initialization, i.e. purge all the results first before running the model.

Briefly write down your two schemes:


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Scheme 1: Converge DS-2 (flow ratio design-spec) and Tear Streams 1, 5, and 11

together using Broyden, and then converge DS-1 (Product-1 flow design-spec)in the outside loop using Secant.

CPU seconds of Scheme 1: ___19.72 seconds___

Scheme 2: Converge all 3 loops (2 design-specs and one tear-stream set) using Newton.

Note that trying to converge all 3 loops together using Broyden will result in a

FORTRAN error.

CPU seconds of Scheme 2: ___18.65 seconds____

A+ Input Summary File:

;

;Input Summary created by Aspen Plus Rel. 13.2 at 16:42:20 Tue Jun 12, 2007

;Directory C:\ChEPS\ChEPS Courses\ChE656-11thYear\Final Filename

C:\DOCUME~1\Samsung\LOCALS~1\Temp\~apb8.tmp

;

DYNAMICS

DYNAMICS RESULTS=ON


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IN-UNITS ENG


DESCRIPTION "





Stream report composition: Mole flow

"

DATABANKS PURE13 / AQUEOUS / SOLIDS / INORGANIC / &NOASPENPCD

PROP-SOURCES PURE13 / AQUEOUS / SOLIDS / INORGANIC

COMPONENTS

H2O H2O

FLOWSHEET

BLOCK A IN=3 8 FEED OUT=1BLOCK B IN=1 OUT=2 7

BLOCK C IN=2 6 14 OUT=3 4 13

BLOCK D IN=4 OUT=5 15 PROD-1BLOCK E IN=7 12 OUT=6 8 9

BLOCK G IN=5 11 OUT=10 12 14 PROD-2

BLOCK B1 IN=9 13 10 15 OUT=11

PROPERTIES STEAMNBS

STREAM FEED

SUBSTREAM MIXED TEMP=70. PRES=14.7MOLE-FLOW H2O 100.

BLOCK A MIXER

BLOCK B1 MIXER

BLOCK B FSPLIT

FRAC 2 0.5


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BLOCK C FSPLIT

FRAC 3 0.3333 / 4 0.3333

BLOCK D FSPLITFRAC 5 0.33333 / 15 0.33333

BLOCK E FSPLIT

FRAC 6 0.33333 / 8 0.33333

BLOCK G FSPLIT

FRAC 10 0.25 / 12 0.25 / 14 0.25

DESIGN-SPEC DS-1

DEFINE PROD1 STREAM-VAR STREAM=PROD-1 SUBSTREAM=MIXED &

VARIABLE=MOLE-FLOWSPEC "PROD1" TO "40"

TOL-SPEC "0.01"VARY STREAM-VAR STREAM=FEED SUBSTREAM=MIXED &

VARIABLE=MOLE-FLOW

LIMITS "50" "150"

DESIGN-SPEC DS-2

DEFINE F2 STREAM-VAR STREAM=2 SUBSTREAM=MIXED &

VARIABLE=MOLE-FLOW

DEFINE F3 STREAM-VAR STREAM=3 SUBSTREAM=MIXED &

VARIABLE=MOLE-FLOWSPEC "F2/F3" TO "2.0"

TOL-SPEC "0.001"

VARY BLOCK-VAR BLOCK=B SENTENCE=FRAC VARIABLE=FRAC ID1=2LIMITS "0.1" "0.9"

EO-CONV-OPTI

STREAM-REPOR MOLEFLOW

;

;

;;

;


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Flash-1

Flash-2

Flash-3

Flash-4

Feed

Light product

Heavy product

R1

R2

R3

P1

P2

Z1

Z2

S1

S2

S3

P (Flash-1) = 200 psia




49.Flowsheet Convergence, VI

Consider the following flowsheet by Cavett (1963) which has been used repeatedly in theliterature to study tear stream convergence. The flowsheet consists of two mixers and four

flashes which are used to separate the feed into light and heavy hydrocarbon products.

The feed is a saturated liquid at 50 psia and has a flowrate of 100 lbmol/hr with the following

composition (mole basis): 20% methane, 20% ethane, 20% propane, 20% n-butane, and 20%

n-pentane. All flashes were designed to vaporize 30% of the feed entering the blocks at the

pressures given in the flowsheet.

(a)Converge this flowsheet which contains tear streams with ASPEN PLUS using PENG-ROB. Specify exactly how you manage to converge the flowsheet. You may use any

convergence scheme, i.e. any user convergence level including the default Level 1.However, in converging the flowsheet, you:

(i) must reinitialize your run every time.

(ii) must not provide any guesses for the tear streams.

(iii)must not increase the default maximum number of iterations in the convergencealgorithm or change its default settings. If you do, 5 points will be automatically

deducted.

i) Your convergence scheme:

Mixer-1

Mixer-2


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Tear streams: ___________________

Convergence algorithm: ________________

ii) Ratio of the total molar flow of stream R2 to that of stream R3 = ___________

(b)Now, we want to add a constraint to the flowsheet such that the ratio of the total molarflow of stream R2 to that of stream R3 is exactly 2.00 (0.001). This constraint or design-spec is achieved by varying the vapor fraction in Flash-3. Use ASPEN PLUS to converge

this constrained problem.



manipulated variable. Once again, you must reinitialize each run, may not provide initialguesses for the tear streams, and may not increase the maximum number of iterations orchange the default settings of the convergence algorithm. Points will be deducted if you

do any of the above (unless you are running out of time and like to see a converged

solution).


Tear streams: __________________

Convergence algorithm for tear streams: ________________

Convergence algorithm for design-spec: ________________

Nesting or simultaneous convergence? _________________

If nesting, the nesting order: __________________________

ii) Vapor fraction in Flash-3 = _____________

Solution:

(a)Converge this flowsheet which contains tear streams with ASPEN PLUS using PENG-ROB. Specify exactly how you manage to converge the flowsheet. You may use any

convergence scheme, i.e. any user convergence level including the default Level 1.

However, in converging the flowsheet, you:

(i) must reinitialize your run every time.

(ii) must not provide any guesses for the tear streams.(iv)must not increase the default maximum number of iterations in the convergence

algorithm or change its default settings. If you do, 5 points will be automatically

deducted.


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Tear streams: ___S1 and Z2______

Convergence algorithm: ___Broyden_____

ii) Ratio of the total molar flow of stream R2 to that of stream R3 = ___ 1.4285____

Note that the default convergence Level 1 of using Wegstein will not converge this

flowsheet in 30 iterations.

(b)Now, we want to add a constraint to the flowsheet such that the ratio of the total molarflow of stream R2 to that of stream R3 is exactly 2.00 (0.001). This constraint or design-spec is achieved by varying the vapor fraction in Flash-3. Use ASPEN PLUS to convergethis constrained problem.



manipulated variable. Once again, you must reinitialize each run, may not provide initial

guesses for the tear streams, and may not increase the maximum number of iterations or

change the default settings of the convergence algorithm. Points will be deducted if you

do any of the above (unless you are running out of time and like to see a converged

solution).


Tear streams: ____S1 and Z2______

Convergence algorithm for tear streams: ____Broyden_____

Convergence algorithm for design-spec: ____Secant_______

Nesting or simultaneous convergence? ___Nesting___

If nesting, the nesting order: ___Design-spec loop is outside the tear stream loop_____

ii) Vapor fraction in Flash-3 = ___0.3749____

It appears that this flowsheet will only converge when the tear-stream loop is nested insidethe design-spec loop. Simultaneous convergence does not work, and changing

convergence methods does not work either.


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Part (a) Input Summary:;


;Directory D:\A+ Runs Filename D:\A+ Runs\problem_3a_convergence.inp;

IN-UNITS ENG


DESCRIPTION "






"

DATABANKS PURE13 / AQUEOUS / SOLIDS / INORGANIC / &

NOASPENPCD

MIXER-1

MIXER-2

FLASH-2

FLASH-1

FLASH-3

FLASH-4

FEED

Z1

S1

P1

R1

S2

Z2

R2

S3

P2

R3


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COMPONENTS

METHANE CH4 /ETHANE C2H6 /

PROPANE C3H8 /

N-BUTANE C4H10-1 /

N-PENTAN C5H12-1

FLOWSHEET

BLOCK MIXER-1 IN=FEED R1 R2 OUT=Z1

BLOCK MIXER-2 IN=S2 R3 OUT=Z2BLOCK FLASH-2 IN=Z1 OUT=S1 S2

BLOCK FLASH-1 IN=S1 OUT=P1 R1

BLOCK FLASH-3 IN=Z2 OUT=R2 S3BLOCK FLASH-4 IN=S3 OUT=R3 P2

PROPERTIES PENG-ROB

PROP-DATA PRKBV-1


BPVAL METHANE ETHANE -2.6000000E-3 0.0 0.0 -459.6699923 &

1340.329993

BPVAL METHANE PROPANE .0140000000 0.0 0.0 -459.6699923 &

1340.329993BPVAL METHANE N-BUTANE .0133000000 0.0 0.0 -459.6699923 &

1340.329993

BPVAL METHANE N-PENTAN .0230000000 0.0 0.0 -459.6699923 &1340.329993

BPVAL ETHANE PROPANE 1.10000000E-3 0.0 0.0 -459.6699923 &

1340.329993BPVAL ETHANE N-BUTANE 9.60000000E-3 0.0 0.0 -459.6699923 &

1340.329993

BPVAL ETHANE N-PENTAN 7.80000000E-3 0.0 0.0 -459.6699923 &

1340.329993

BPVAL PROPANE N-BUTANE 3.30000000E-3 0.0 0.0 -459.6699923 &1340.329993

BPVAL PROPANE N-PENTAN .0267000000 0.0 0.0 -459.6699923 &

1340.329993


1340.329993

STREAM FEED

SUBSTREAM MIXED PRES=50. VFRAC=0. MOLE-FLOW=100.MOLE-FRAC METHANE 0.2 / ETHANE 0.2 / PROPANE 0.2 / &


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N-BUTANE 0.2 / N-PENTAN 0.2

BLOCK MIXER-1 MIXER

BLOCK MIXER-2 MIXER









EO-CONV-OPTI

CONVERGENCE C-1 BROYDENTEAR Z2 / S1

STREAM-REPOR MOLEFLOW MOLEFRAC

;

;;

;

;

Part (b) Input Summary:

;


;Directory D:\A+ Runs Filename D:\A+ Runs\problem_3b_convergence.inp

;

IN-UNITS ENG


DESCRIPTION "

General Simulation with English Units :F, psi, lb/hr, lbmol/hr, Btu/hr, cuft/hr.


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"

DATABANKS PURE13 / AQUEOUS / SOLIDS / INORGANIC / &

NOASPENPCD


COMPONENTS

METHANE CH4 /ETHANE C2H6 /

PROPANE C3H8 /N-BUTANE C4H10-1 /

N-PENTAN C5H12-1

FLOWSHEETBLOCK MIXER-1 IN=FEED R1 R2 OUT=Z1

BLOCK MIXER-2 IN=S2 R3 OUT=Z2

BLOCK FLASH-2 IN=Z1 OUT=S1 S2

BLOCK FLASH-1 IN=S1 OUT=P1 R1

BLOCK FLASH-3 IN=Z2 OUT=R2 S3BLOCK FLASH-4 IN=S3 OUT=R3 P2

PROPERTIES PENG-ROB

PROP-DATA PRKBV-1


BPVAL METHANE ETHANE -2.6000000E-3 0.0 0.0 -459.6699923 &

1340.329993

BPVAL METHANE PROPANE .0140000000 0.0 0.0 -459.6699923 &

1340.329993BPVAL METHANE N-BUTANE .0133000000 0.0 0.0 -459.6699923 &

1340.329993

BPVAL METHANE N-PENTAN .0230000000 0.0 0.0 -459.6699923 &

1340.329993

BPVAL ETHANE PROPANE 1.10000000E-3 0.0 0.0 -459.6699923 &

1340.329993

BPVAL ETHANE N-BUTANE 9.60000000E-3 0.0 0.0 -459.6699923 &

1340.329993BPVAL ETHANE N-PENTAN 7.80000000E-3 0.0 0.0 -459.6699923 &


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1340.329993

BPVAL PROPANE N-BUTANE 3.30000000E-3 0.0 0.0 -459.6699923 &1340.329993

BPVAL PROPANE N-PENTAN .0267000000 0.0 0.0 -459.6699923 &1340.329993


1340.329993

STREAM FEED

SUBSTREAM MIXED PRES=50. VFRAC=0. MOLE-FLOW=100.

MOLE-FRAC METHANE 0.2 / ETHANE 0.2 / PROPANE 0.2 / &

N-BUTANE 0.2 / N-PENTAN 0.2

BLOCK MIXER-1 MIXER

BLOCK MIXER-2 MIXER








DESIGN-SPEC DS-1

DEFINE R2 STREAM-VAR STREAM=R2 SUBSTREAM=MIXED &

VARIABLE=MOLE-FLOWDEFINE R3 STREAM-VAR STREAM=R3 SUBSTREAM=MIXED &

VARIABLE=MOLE-FLOW

SPEC "R2/R3" TO "2.0"

TOL-SPEC "0.001"

VARY BLOCK-VAR BLOCK=FLASH-3 VARIABLE=VFRAC SENTENCE=PARAMLIMITS "0.3" "0.4"

EO-CONV-OPTI

CONV-OPTIONS

PARAM SPEC-LOOP=OUTSIDE

CONVERGENCE C-1 BROYDENTEAR S1 / Z2


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STREAM-REPOR MOLEFLOW MOLEFRAC;

;;

;

;


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FLASH-1

FLASH-2

FLASH-3

MIXER

SEP-1

SEP-2

1

2

3

4

5

6

7

8

9

10

11

12

SPLITTER

13

14

15

50.Flowsheet Convergence, VII

Consider the flowsheet below which consists of three flashes, two separators, one mixer, and

one splitter. The feed enters the process at 100 F and 30 psia and has a flowrate of 100lbmol/hr with the following composition (mole basis): 20% n-butane, 20% n-pentane, 20% n-

hexane, 20% n-heptane, and 20% n-octane. When you create your flowsheet, you must use

the same stream IDs and block IDs as shown in the figure.

The three flashes have the following operating conditions:

FLASH-1: Vfrac = 0.05, P = 20 psia FLASH-2: Vfrac = 0.95, P = 20 psia

FLASH-3: Vfrac = 0.50, P = 10 psia

The splitter splits the inlet flow evenly, i.e. 50%-50%. The following component split

fractions occur in the two separators (no need to specify the outlet flash):

SEP-1: Stream 12, n-butane 0%, n-pentane 20%, n-hexane 40%, n-heptane 60%, and n-octane

80%SEP-2: Stream 5, n-butane 80%, n-pentane 60%, n-hexane 40%, n-heptane 20%, and n-octane

0%

Stream 6, n-butane 10%, n-pentane 20%, n-hexane 30%, n-heptane 40%, and n-octane

50%

(a)Using PENG-ROB, converge the given flowsheet using all four tear stream algorithms,namely Wegstein, Broyden, Newton, and Direct. Based on what you learned about tear


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stream convergence, which method is the best for this problem and why (give reasons why

the other three methods are not as good as your choice). Note that in converging theflowsheet with each algorithm, you must:

(i) reinitialize your run.(ii) not provide any guesses for the tear streams.

(iii) not increase the default maximum number of iterations in the algorithm or change

its default setting.


Tear streams: ___________________

The best convergence algorithm: ________________

Your reasons: __________________________________________________________

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

(b)Now, we want to add two constraints to the flowsheet such that the ratio of the molar flowofn-hexane in Stream 10 to that in Stream 13 is equal to 1.42 (0.0001) and the total flow

of Stream 14 is 60 lbmol/hr ((0.001). These two constraints or design-specs are achieved

by varying the split fraction ofn-hexane going to Stream 12 in SEP-1 and the total molar

flow of the process feed Stream 1, respectively. Use ASPEN PLUS to converge this

constrained problem.


try many different convergence schemes, including examining the bounds of yourmanipulated variables (to make them narrow enough). Once again, you must reinitialize

each run, may not provide initial guesses for the tear streams, and may not increase the

maximum number of iterations or change the default settings of the convergencealgorithm. Points will be deducted if you do any of the above (unless you are running out

of time and like to see a converged solution).

Your convergence scheme: (Be very specific with your answer, e.g. what algorithmswere used to converge tear stream and design-specs and whether the convergence was

simultaneous or nesting, and if nesting what was the order of nesting.)

______________________________________________________________________


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______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

Split fraction ofn-hexane in SEP-1 going to Stream 12 = _____________

Total molar flow of Stream 1 = ____________ lbmol/hr

(c) Propose a second convergence scheme that will converge this flowsheet. Note that using

different values of limits for the two manipulated variables does not count as a different

scheme.

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

Solution:

(a) Tear streams: __Streams 10, 13, and 11___

The best convergence algorithm: ___Broyden____

Your reasons: Both Wegstein and Direct algorithms did not converge in 30 iterations.

Newton did converge but it took a long time to do so (about 19 CPU seconds on my

laptop). Broyden also converged and is the best algorithm because it took only about 3

CPU seconds to find the solution which is a lot faster than Newton. However, it did take

Broyden 25 iterations to converge and almost hit the maximum of 30 iterations.

(b) Now, we want to add two constraints to the flowsheet such that the ratio of the molar flow

ofn-hexane in Stream 10 to that in Stream 13 is equal to 1.42 (0.0001) and the total flow

of Stream 14 is 60 lbmol/hr ((0.001). These two constraints or design-specs are

achieved by varying the split fraction ofn-hexane going to Stream 12 in SEP-1 and the

total molar flow of the process feed Stream 1, respectively. Use ASPEN PLUS toconverge this constrained problem.


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try many different convergence schemes, including examining the bounds of yourmanipulated variables (to make them narrow enough). Once again, you must reinitialize

each run, may not provide initial guesses for the tear streams, and may not increase themaximum number of iterations or change the default settings of the convergence

algorithm. Points will be deducted if you do any of the above (unless you are running out

of time and like to see a converged solution).

Your convergence scheme: (Be very specific with your answer, e.g. what algorithms

were used to converge tear stream and design-specs and whether the convergence was

simultaneous or nesting, and if nesting what was the order of nesting.)

The default convergence scheme will not converge, which uses Wegstein to converge

Streams 10, 11, and 15 simultaneously and Secant to converge the two design-specs. Also,

the default scheme created 3 nested loops with Design-Spec 2 as the outermost loop andDesign-Spec 1 as the innermost loop. The tear stream loop is the middle loop.

Ive found the following schemes to converge this complex problem:

1. Specify a convergence block using Broyden to converge Streams 10, 11, and 15simultaneously, but let A+ create its own two convergence blocks to converge the twodesign-specs using Secant. A+ will create three nested loops. This scheme will only

converge if the limits of the two manipulated variables are set as follows: 0.25 0.35

for split fraction and 80 300 for Stream 1 flow rate. Any attempts to use different

values, even those limits that are more narrow, would fail to converge the problem.

2. Specify three convergence blocks all using Broyden to converge the three tear streamsand the two design-specs. We let A+ do the nesting which consists of three nested

loops. The following limits are used for the manipulated variables: 0.25 0.35 for splitfraction and 50 350 for Stream 1 flow rate. Using Newton for the design-specs will

not converge the problem.

3. Converge the three tear streams (Streams 10, 11, and 15) and the two design-specssimultaneously in one single loop using Newton. The limits for the design-specs are

the same as in Scheme 2.

Note that converging the tear streams together with the two design-specs using one singleloop with Broyden does not work either.

Split fraction ofn-hexane in SEP-1 going to Stream 12 = __0.2949__

Total molar flow of Stream 1 = ___201.681____ lbmol/hr

(c) Propose a second convergence scheme that will converge this flowsheet. Note that using

different values of limits for the two manipulated variables does not count as a differentscheme.


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________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

Part (a) Input Summary Using Broyden:

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;Input Summary created by Aspen Plus Rel. 26.0 at 13:30:47 Mon Jul 30, 2012

;Directory F:\HMKu\ChEPS\ChEPS Courses\CHE656-16thYear FilenameC:\Users\NBPC\AppData\Local\Temp\~ap66c1.txt

;

TITLE 'Complex Flowsheet Convergence'

IN-UNITS ENG


DESCRIPTION "






"

DATABANKS 'APV732 PURE26' / 'APV732 AQUEOUS' / 'APV732 SOLIDS' &

/ 'APV732 INORGANIC' / NOASPENPCD

PROP-SOURCES 'APV732 PURE26' / 'APV732 AQUEOUS' / &

'APV732 SOLIDS' / 'APV732 INORGANIC'

COMPONENTS

N-C4 C4H10-1 /N-C5 C5H12-1 /


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N-C6 C6H14-1 /

N-C7 C7H16-1 /N-C8 C8H18-1

FLOWSHEET

BLOCK FLASH-1 IN=1 15 OUT=2 3




BLOCK SEP-1 IN=3 8 OUT=11 12

BLOCK SEP-2 IN=10 OUT=5 6 9

BLOCK SPLITTER IN=13 OUT=14 15

PROPERTIES PENG-ROB

PROP-DATA PRKBV-1


BPVAL N-C4 N-C5 .0174000000 0.0 0.0 -459.6700000 &

1340.330000

BPVAL N-C5 N-C4 .0174000000 0.0 0.0 -459.6700000 &1340.330000

BPVAL N-C4 N-C6 -5.6000000E-3 0.0 0.0 -459.6700000 &

1340.330000

BPVAL N-C6 N-C4 -5.6000000E-3 0.0 0.0 -459.6700000 &

1340.330000BPVAL N-C4 N-C7 3.30000000E-3 0.0 0.0 -459.6700000 &

1340.330000

BPVAL N-C7 N-C4 3.30000000E-3 0.0 0.0 -459.6700000 &1340.330000

BPVAL N-C5 N-C7 7.40000000E-3 0.0 0.0 -459.6700000 &

1340.330000BPVAL N-C7 N-C5 7.40000000E-3 0.0 0.0 -459.6700000 &

1340.330000

BPVAL N-C5 N-C8 0.0 0.0 0.0 -459.6700000 1340.330000

BPVAL N-C8 N-C5 0.0 0.0 0.0 -459.6700000 1340.330000

BPVAL N-C6 N-C7 -7.8000000E-3 0.0 0.0 -459.6700000 &1340.330000

BPVAL N-C7 N-C6 -7.8000000E-3 0.0 0.0 -459.6700000 &

1340.330000

STREAM 1

SUBSTREAM MIXED TEMP=100. PRES=30.

MOLE-FLOW N-C4 20. / N-C5 20. / N-C6 20. / N-C7 20. / &

N-C8 20.


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BLOCK MIXER MIXER

PARAM

BLOCK SPLITTER FSPLITFRAC 14 0.5

BLOCK SEP-1 SEP

FRAC STREAM=12 SUBSTREAM=MIXED COMPS=N-C4 N-C5 N-C6 N-C7 &

N-C8 FRACS=0. 0.2 0.4 0.6 0.8

BLOCK SEP-2 SEP

PARAMFRAC STREAM=5 SUBSTREAM=MIXED COMPS=N-C4 N-C5 N-C6 N-C7 &

N-C8 FRACS=0.8 0.6 0.4 0.2 0.

FRAC STREAM=6 SUBSTREAM=MIXED COMPS=N-C4 N-C5 N-C6 N-C7 &N-C8 FRACS=0.1 0.2 0.3 0.4 0.5






EO-CONV-OPTI

CONVERGENCE C-1 BROYDENTEAR 10 / 13 / 11

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Part (b) Input Summary:

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;Input Summary created by Aspen Plus Rel. 26.0 at 13:34:58 Mon Jul 30, 2012

;Directory F:\HMKu\ChEPS\ChEPS Courses\ChE656-13thYear\Final Filename

C:\Users\NBPC\AppData\Local\Temp\~ap3def.txt

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TITLE 'Complex Flowsheet Convergence'

IN-UNITS ENG


DESCRIPTION "





Stream report composition: Mole flow"

DATABANKS 'APV732 PURE26' / 'APV732 AQUEOUS' / 'APV732 SOLIDS' &

/ 'APV732 INORGANIC' / NOASPENPCD

PROP-SOURCES 'APV732 PURE26' / 'APV732 AQUEOUS' / &'APV732 SOLIDS' / 'APV732 INORGANIC'

COMPONENTS

N-C4 C4H10-1 /

N-C5 C5H12-1 /N-C6 C6H14-1 /

N-C7 C7H16-1 /

N-C8 C8H18-1

FLOWSHEET

BLOCK FLASH-1 IN=1 15 OUT=2 3BLOCK FLASH-2 IN=4 11 OUT=8 7



BLOCK SEP-1 IN=3 8 OUT=11 12

BLOCK SEP-2 IN=10 OUT=5 6 9BLOCK SPLITTER IN=13 OUT=14 15

PROPERTIES PENG-ROB

PROP-DATA PRKBV-1

IN-UNITS ENG

PROP-LIST PRKBV

BPVAL N-C4 N-C5 .0174000000 0.0 0.0 -459.6700000 &1340.330000


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BPVAL N-C5 N-C4 .0174000000 0.0 0.0 -459.6700000 &

1340.330000BPVAL N-C4 N-C6 -5.6000000E-3 0.0 0.0 -459.6700000 &

1340.330000BPVAL N-C6 N-C4 -5.6000000E-3 0.0 0.0 -459.6700000 &

1340.330000

BPVAL N-C4 N-C7 3.30000000E-3 0.0 0.0 -459.6700000 &

1340.330000

BPVAL N-C7 N-C4 3.30000000E-3 0.0 0.0 -459.6700000 &

1340.330000

BPVAL N-C5 N-C7 7.40000000E-3 0.0 0.0 -459.6700000 &

1340.330000BPVAL N-C7 N-C5 7.40000000E-3 0.0 0.0 -459.6700000 &

1340.330000

BPVAL N-C5 N-C8 0.0 0.0 0.0 -459.6700000 1340.330000BPVAL N-C8 N-C5 0.0 0.0 0.0 -459.6700000 1340.330000

BPVAL N-C6 N-C7 -7.8000000E-3 0.0 0.0 -459.6700000 &1340.330000

BPVAL N-C7 N-C6 -7.8000000E-3 0.0 0.0 -459.6700000 &

1340.330000

STREAM 1

SUBSTREAM MIXED TEMP=100. PRES=30.

MOLE-FLOW N-C4 20. / N-C5 20. / N-C6 20. / N-C7 20. / &

N-C8 20.

BLOCK MIXER MIXER

PARAM

BLOCK SPLITTER FSPLIT

FRAC 14 0.5

BLOCK SEP-1 SEP


N-C8 FRACS=0. 0.2 0.4 0.6 0.8

BLOCK SEP-2 SEPPARAM


N-C8 FRACS=0.8 0.6 0.4 0.2 0.


N-C8 FRACS=0.1 0.2 0.3 0.4 0.5




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DESIGN-SPEC DS-1

DEFINE C6GAS MOLE-FLOW STREAM=10 SUBSTREAM=MIXED &

COMPONENT=N-C6

DEFINE C6LIQ MOLE-FLOW STREAM=13 SUBSTREAM=MIXED &

COMPONENT=N-C6

SPEC "C6GAS/C6LIQ" TO "1.42"TOL-SPEC "0.0001"

VARY BLOCK-VAR BLOCK=SEP-1 SENTENCE=FRAC VARIABLE=FRACS &

ID1=MIXED ID2=12 ELEMENT=3LIMITS "0.25" "0.35"

DESIGN-SPEC DS-2

DEFINE S14FLO STREAM-VAR STREAM=14 SUBSTREAM=MIXED &

VARIABLE=MOLE-FLOW

SPEC "S14FLO" TO "60.0"TOL-SPEC "0.001"

VARY STREAM-VAR STREAM=1 SUBSTREAM=MIXED VARIABLE=MOLE-FLOW

LIMITS "50" "350"

EO-CONV-OPTI

CONV-OPTIONS

PARAM CHECKSEQ=YES


TEAR 10 / 11 / 15


SPEC DS-1

CONVERGENCE C-3 BROYDENSPEC DS-2

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CHE656 2012 Homework6 Solutions

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