CHE656 2012 Homework6 Solutions

CHE656

Computer Applications for Chemical Engineering Practice

Homework Set #6 Solutions Class-16

Prepared by Dr. Hong-ming Ku King Mongkut’s University of Technology Thonburi Chemical Engineering Department Chemical Engineering Practice School  May 2012 – Use with Permission of the Author Only

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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 nbutane, 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% 6

3

5 FLASH-1

SPLITTER 8

2 MIXER 7

1 4

FLASH-2

(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 or change 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 such as 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 of n-butane in Stream 7 = ____0.141____ Note that the other two algorithms, namely Wegstein and Direct, will not converge this flowsheet. (b) Now, we want to add two composition constraints to the flowsheet such that the mole fraction of benzene in Stream 4 is equal to 0.35 (±0.0001) and the mole fraction of nbutane 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 tear streams. But in this part, you are allowed to increase the maximum number of iterations in the convergence algorithm. Answer the following questions: 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 was simultaneous 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 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 was simultaneous 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 the tear 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-2 from 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 Filename C:\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 FLOWSHEET BLOCK 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 ENG PROP-LIST PRKBV BPVAL N-BUTANE N-PENTAN .0174000000 0.0 0.0 -459.6699923 & 1340.329993 BPVAL 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 & 1340.329993 BPVAL 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 1 SUBSTREAM 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 FLASH2 PARAM PRES=0. VFRAC=0.5 DESIGN-SPEC DS-1 DEFINE XBZ MOLE-FRAC STREAM=4 SUBSTREAM=MIXED & COMPONENT=BENZENE SPEC "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 / 4 SPEC DS-1 / DS-2 PARAM MAXIT=100 CONV-ORDER C-2 STREAM-REPOR MOLEFLOW MOLEFRAC ; ; ;

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48. Flowsheet Convergence, III Consider 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 study the 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 is unknown, 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 to 40 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 is maintained at 2.0 (±0.001). Product-1

3

Feed

A

1

8

2

B

6

7

E

C 13

4

14

D 5

10

9

F

15

G 11

12 Product-2

(a) Using A+ and automatic convergence and sequencing (Level 1), determine the water feed flow 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: ________________

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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 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 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 feed flow 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 took some 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 DEF-STREAMS CONVEN ALL DESCRIPTION " General Simulation with English Units : F, psi, lb/hr, lbmol/hr, Btu/hr, cuft/hr. Property Method: None Flow basis for input: Mole 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=1 BLOCK B IN=1 OUT=2 7 BLOCK C IN=2 6 14 OUT=3 4 13 BLOCK D IN=4 OUT=5 15 PROD-1 BLOCK 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=14.7 MOLE-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 FSPLIT FRAC 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-FLOW SPEC "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-FLOW SPEC "F2/F3" TO "2.0" TOL-SPEC "0.001" VARY BLOCK-VAR BLOCK=B SENTENCE=FRAC VARIABLE=FRAC ID1=2 LIMITS "0.1" "0.9" EO-CONV-OPTI STREAM-REPOR MOLEFLOW ; ; ; ; ;

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49. Flowsheet Convergence, VI Consider the following flowsheet by Cavett (1963) which has been used repeatedly in the literature 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. Light product

P (Flash-1) = 200 psia P (Flash-2) = 30 psia P (Flash-3) = 20 psia P (Flash-4) = 10 psia

P1 R1

Flash-1 R2 S1 Z1

Feed

Mixer-1

Flash-2

R3

S2

Z2

Mixer-2

Flash-3 S3

Flash-4 P2 Heavy product

(a) Converge this flowsheet which contains tear streams with ASPEN PLUS using PENGROB. 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 convergence algorithm or change its default settings. If you do, 5 points will be automatically deducted. i) Your convergence scheme:

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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 molar flow of stream R2 to that of stream R3 is exactly 2.00 (±0.001). This constraint or designspec is achieved by varying the vapor fraction in Flash-3. Use ASPEN PLUS to converge 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 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). i) Your convergence scheme: 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 PENGROB. 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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i) Your convergence scheme: 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 molar flow of stream R2 to that of stream R3 is exactly 2.00 (±0.001). This constraint or designspec is achieved by varying the vapor fraction in Flash-3. Use ASPEN PLUS to converge 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 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). i) Your convergence scheme: 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 inside the design-spec loop. Simultaneous convergence does not work, and changing convergence methods does not work either.

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P1

FLASH-1

R2 S1 R1

FLASH-2 R3

Z1

FLASH-3 MIXER-1 FEED

Z2 S2

MIXER-2

FLASH-4 S3

P2

Part (a) Input Summary: ; ;Input Summary created by Aspen Plus Rel. 13.2 at 22:52:25 Tue Jun 10, 2008 ;Directory D:\A+ Runs Filename D:\A+ Runs\problem_3a_convergence.inp ;

IN-UNITS ENG DEF-STREAMS CONVEN ALL DESCRIPTION " General Simulation with English Units : F, psi, lb/hr, lbmol/hr, Btu/hr, cuft/hr. Property Method: None Flow basis for input: Mole Stream report composition: Mole flow " DATABANKS PURE13 / AQUEOUS / SOLIDS / INORGANIC / & NOASPENPCD

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PROP-SOURCES PURE13 / AQUEOUS / SOLIDS / INORGANIC 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=Z2 BLOCK FLASH-2 IN=Z1 OUT=S1 S2 BLOCK FLASH-1 IN=S1 OUT=P1 R1 BLOCK FLASH-3 IN=Z2 OUT=R2 S3 BLOCK FLASH-4 IN=S3 OUT=R3 P2 PROPERTIES PENG-ROB PROP-DATA PRKBV-1 IN-UNITS ENG PROP-LIST PRKBV BPVAL METHANE ETHANE -2.6000000E-3 0.0 0.0 -459.6699923 & 1340.329993 BPVAL METHANE PROPANE .0140000000 0.0 0.0 -459.6699923 & 1340.329993 BPVAL 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 & 1340.329993 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 BPVAL N-BUTANE N-PENTAN .0174000000 0.0 0.0 -459.6699923 & 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 BLOCK FLASH-1 FLASH2 PARAM PRES=200. VFRAC=0.3 BLOCK FLASH-2 FLASH2 PARAM PRES=30. VFRAC=0.3 BLOCK FLASH-3 FLASH2 PARAM PRES=20. VFRAC=0.3 BLOCK FLASH-4 FLASH2 PARAM PRES=10. VFRAC=0.3 EO-CONV-OPTI CONVERGENCE C-1 BROYDEN TEAR Z2 / S1 STREAM-REPOR MOLEFLOW MOLEFRAC ; ; ; ; ; Part (b) Input Summary: ; ;Input Summary created by Aspen Plus Rel. 13.2 at 23:16:24 Tue Jun 10, 2008 ;Directory D:\A+ Runs Filename D:\A+ Runs\problem_3b_convergence.inp ;

IN-UNITS ENG DEF-STREAMS CONVEN ALL DESCRIPTION " General Simulation with English Units : F, psi, lb/hr, lbmol/hr, Btu/hr, cuft/hr.

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Property Method: None Flow basis for input: Mole Stream report composition: Mole flow " DATABANKS PURE13 / AQUEOUS / SOLIDS / INORGANIC / & NOASPENPCD PROP-SOURCES PURE13 / AQUEOUS / SOLIDS / INORGANIC 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=Z2 BLOCK FLASH-2 IN=Z1 OUT=S1 S2 BLOCK FLASH-1 IN=S1 OUT=P1 R1 BLOCK FLASH-3 IN=Z2 OUT=R2 S3 BLOCK FLASH-4 IN=S3 OUT=R3 P2 PROPERTIES PENG-ROB PROP-DATA PRKBV-1 IN-UNITS ENG PROP-LIST PRKBV BPVAL METHANE ETHANE -2.6000000E-3 0.0 0.0 -459.6699923 & 1340.329993 BPVAL METHANE PROPANE .0140000000 0.0 0.0 -459.6699923 & 1340.329993 BPVAL 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 & 1340.329993 BPVAL 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 BPVAL N-BUTANE N-PENTAN .0174000000 0.0 0.0 -459.6699923 & 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 BLOCK FLASH-1 FLASH2 PARAM PRES=200. VFRAC=0.3 BLOCK FLASH-2 FLASH2 PARAM PRES=30. VFRAC=0.3 BLOCK FLASH-3 FLASH2 PARAM PRES=20. VFRAC=0.3 BLOCK FLASH-4 FLASH2 PARAM PRES=10. VFRAC=0.3 DESIGN-SPEC DS-1 DEFINE R2 STREAM-VAR STREAM=R2 SUBSTREAM=MIXED & VARIABLE=MOLE-FLOW DEFINE 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=PARAM LIMITS "0.3" "0.4" EO-CONV-OPTI CONV-OPTIONS PARAM SPEC-LOOP=OUTSIDE CONVERGENCE C-1 BROYDEN TEAR S1 / Z2

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STREAM-REPOR MOLEFLOW MOLEFRAC ; ; ; ; ;

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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 100 lbmol/hr with the following composition (mole basis): 20% n-butane, 20% n-pentane, 20% nhexane, 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% 15 5 SEP-2

9

MIXER

10 2 4 6

FLA SH-3

8 1

FLA SH-1

SEP-1

FLA SH-2

13

11

7

SPLITTER 14

3

12

(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 the flowsheet 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. Answer the following questions: 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 flow of n-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 of n-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. 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). 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). 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.) ______________________________________________________________________

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______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ Split fraction of n-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 of n-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 of n-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.

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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). 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). 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 and Design-Spec 1 as the innermost loop. The tear stream loop is the middle loop. I’ve found the following schemes to converge this complex problem: 1. Specify a convergence block using Broyden to converge Streams 10, 11, and 15 simultaneously, but let A+ create its own two convergence blocks to converge the two design-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 streams and 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 split fraction 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-specs simultaneously 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 single loop with Broyden does not work either. Split fraction of n-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 different scheme.

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________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________

Part (a) Input Summary Using Broyden: ; ;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 Filename C:\Users\NBPC\AppData\Local\Temp\~ap66c1.txt ;

TITLE 'Complex Flowsheet Convergence' IN-UNITS ENG DEF-STREAMS CONVEN ALL DESCRIPTION " General Simulation with English Units : F, psi, lb/hr, lbmol/hr, Btu/hr, cuft/hr. Property Method: None Flow basis for input: Mole 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 /

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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 FLASH-2 IN=4 11 OUT=8 7 BLOCK FLASH-3 IN=6 12 OUT=10 13 BLOCK MIXER IN=2 5 OUT=4 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 IN-UNITS ENG PROP-LIST PRKBV 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 & 1340.330000 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 & 1340.330000 BPVAL 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 FSPLIT FRAC 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 PARAM FRAC 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 BLOCK FLASH-1 FLASH2 PARAM PRES=20. VFRAC=0.05 BLOCK FLASH-2 FLASH2 PARAM PRES=20. VFRAC=0.95 BLOCK FLASH-3 FLASH2 PARAM PRES=10. VFRAC=0.5 EO-CONV-OPTI CONVERGENCE C-1 BROYDEN TEAR 10 / 13 / 11 ; ; ; ; ; Part (b) Input Summary: ; ;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 DEF-STREAMS CONVEN ALL DESCRIPTION " General Simulation with English Units : F, psi, lb/hr, lbmol/hr, Btu/hr, cuft/hr. Property Method: None Flow basis for input: Mole 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 3 BLOCK FLASH-2 IN=4 11 OUT=8 7 BLOCK FLASH-3 IN=6 12 OUT=10 13 BLOCK MIXER IN=2 5 OUT=4 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 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 & 1340.330000 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 & 1340.330000 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 & 1340.330000 BPVAL 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. BLOCK MIXER MIXER PARAM BLOCK SPLITTER FSPLIT FRAC 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 PARAM FRAC 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 BLOCK FLASH-1 FLASH2 PARAM PRES=20. VFRAC=0.05

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BLOCK FLASH-2 FLASH2 PARAM PRES=20. VFRAC=0.95 BLOCK FLASH-3 FLASH2 PARAM PRES=10. VFRAC=0.5 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=3 LIMITS "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 CONVERGENCE C-1 BROYDEN TEAR 10 / 11 / 15 CONVERGENCE C-2 BROYDEN SPEC DS-1 CONVERGENCE C-3 BROYDEN SPEC DS-2 ; ; ; ; ;

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