Tier III Open-ended problem

Module 5 – Controllability Analysis 11

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Tier IIIOpen-ended problem


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Tier III Statement of intentTier III Statement of intent

The goal of this tier is to The goal of this tier is to solve few real-life applications of solve few real-life applications of Controllability Analysis, in which the student must interpret Controllability Analysis, in which the student must interpret the results obtained from a range of Controllability the results obtained from a range of Controllability Analysis tools. At the end of Tier III, the student should be Analysis tools. At the end of Tier III, the student should be able to identify the following:able to identify the following:

Benefits of the use of Controllability Analysis toolsBenefits of the use of Controllability Analysis toolsPotential cost saving opportunities from the use of Potential cost saving opportunities from the use of Controllability Analysis toolsControllability Analysis toolsEnvironmental impact reduction resulting from the Environmental impact reduction resulting from the application of Controllability Analysis toolsapplication of Controllability Analysis toolsHow the application of Controllability Analysis tools How the application of Controllability Analysis tools can be used to obtain an operable processcan be used to obtain an operable process


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3.13.1 Doukas and Luyben reported the transfer function model Doukas and Luyben reported the transfer function model for the distillation column with a side stream product. The for the distillation column with a side stream product. The feed contains benzene (B), toluene (T) and xylene (X), feed contains benzene (B), toluene (T) and xylene (X), with the benzene in the side stream of much less with the benzene in the side stream of much less importance than the other controlled variables. importance than the other controlled variables.

The linearized transfer function model is:The linearized transfer function model is:

-0.7s -60s -2.24s

-0.6s -0.7s -0.42s

T 2 2 2

B-0.5s -0.5s -1.9s

X2

T

-1.986e 5.24e 5.984e

66.7s+1 400s+1 14.3s+1

0.002e -0.33e 2.38eXD ( )7.14s+1 2.4s+1 1.43s+1XS ( )

=-0.176 4.48e -11.7eXD ( )

11.1s+1 12.2s+16.9s+1XB ( )

0

s

s

s

s

1

-7.75s -3.8s -1.6s

2

( )

LSu(s)

(s)

.374e -11.3e -9.81e

22.2s+1 11.4s+121.7s+1

RR s

QB

-0.7s -60s -2.24s

-0.6s -0.7s -0.42s

T 2 2 2

B-0.5s -0.5s -1.9s

X2

T

-1.986e 5.24e 5.984e

66.7s+1 400s+1 14.3s+1

0.002e -0.33e 2.38eXD ( )7.14s+1 2.4s+1 1.43s+1XS ( )

=-0.176 4.48e -11.7eXD ( )

11.1s+1 12.2s+16.9s+1XB ( )

0

s

s

s

s

1

-7.75s -3.8s -1.6s

2

( )

LSu(s)

(s)

.374e -11.3e -9.81e

22.2s+1 11.4s+121.7s+1

RR s

QB

The process is shown on the next slide.The process is shown on the next slide.


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Feed flow Feed flow raterate

XDXDT (mole fraction)

XBXBT

RR (Ratio)RR (Ratio)

XSXSB B (mole fraction)(mole fraction)

Distillation column with a side stream product.Distillation column with a side stream product.

LS (lb mol/ hr)LS (lb mol/ hr)

QB (BTU/ hr)QB (BTU/ hr)

XSXSX X (mole fraction)(mole fraction)

Determine the best loop pairing and calculate the Niederlinski Index Determine the best loop pairing and calculate the Niederlinski Index for each subsystem considered.for each subsystem considered.


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3.23.2 The transfer function model for a pilot scale binary The transfer function model for a pilot scale binary distillation column used to separate ethanol and water distillation column used to separate ethanol and water was given in TIER 2, The process variables are (in terms of was given in TIER 2, The process variables are (in terms of deviations from their respective steady state values):deviations from their respective steady state values):

-2.6s -3.5s -s

1 -6.5s -3s -1.2s

2

-s3 -9.2s -9.4s

0.66e -0.61e -0.0049e

6.7s+1 8.64s+1 9.06s+1y u1.11e -2.3e -0.012e

y =3.5s+1 5s+1 7.09s+1

y0.87 11.61s+1 e-33.68e 46.2e

8.15s+1 10.9s+1 3.89s+1 18.8s+

1

2

3

u

u

-2.6s -3.5s -s

1 -6.5s -3s -1.2s

2

-s3 -9.2s -9.4s

0.66e -0.61e -0.0049e

6.7s+1 8.64s+1 9.06s+1y u1.11e -2.3e -0.012e

y =3.5s+1 5s+1 7.09s+1

y0.87 11.61s+1 e-33.68e 46.2e

8.15s+1 10.9s+1 3.89s+1 18.8s+

1

2

3

u

u

1 1

2 2

3 3

= overhead mole fraction ethanol = overhead reflux flowrate

= side stream ethanol mole fraction = side stream draw-off rate

= Temperature on Tray #19

y u

y u

y u = reboiler steam pressure


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Feed flow rate Feed flow rate (d)(d)

Overhead mole Overhead mole fraction ethanol fraction ethanol

(y1)

Reboiler steam Reboiler steam pressure pressure (u2)

Overhead reflux Overhead reflux flow rate (uflow rate (u11))

Distillation column used in separating ethanol and Distillation column used in separating ethanol and waterwater

Mole fraction of ethanol Mole fraction of ethanol in the side stream in the side stream (y2)

Temperature on tray #19 Temperature on tray #19 (y3)

DesignDesign a steadya steady statestate decouplerdecoupler using the generalizedusing the generalized approachapproach, , withwith GGRR((00) ) chosenchosen asas DiagDiag[[G(0)G(0)]]..


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HE 1HE 1QQ11 A A11 TD TD11




HE 2HE 2QQ22 A A2 2 TDTD22

HE 2HE 2QQ22 A A2 2 TDTD22



ff11 mm11

f5f5

ff44 mm44

mm55

ff77

mm88

mm77

HH11

TTHH11

575 K

718 KHH22

TTHH22

CC11

300 K

TTCC11

CC1A1A

CC1B1B

CC1A11A1

CC1B11B1

400 KTT55

395 K

TT66

TT77

TT33

365 K CC

22

TT22

TT44

TT11

398 K

358 K

CC

33

ff88

3.33.3 S.G.Oliveira and F.S.Liporace [3] have obtained the Gain Array S.G.Oliveira and F.S.Liporace [3] have obtained the Gain Array for the for the HENHEN showed below, where the manipulated variables showed below, where the manipulated variables

are fare f11, f, f44, f, f55 , , ff77 and fand f88 should be used to control the outlets should be used to control the outlets

temperature temperature TTC1C1,T,TH1H1,T,TH2H2. .


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17.483 4.733 6.267 11.652 8.088

= 45.778 5.133 6.867 0 0

25.39 0 0 90.851 63.143

K

17.483 4.733 6.267 11.652 8.088

= 45.778 5.133 6.867 0 0

25.39 0 0 90.851 63.143

K

ff11 ff44 ff88

TTC1C1

TTH1H1

TTH2H2

ff77

The gain array obtained for the system is:

ff55

ChooseChoose thethe bestbest pairingpairing, , usingusing thethe RGARGA andand SVDSVD..


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ReferencesReferences[1][1] Wood, R,K. and M.W. Berry, “Terminal Composition Wood, R,K. and M.W. Berry, “Terminal Composition

Control of a binary distillation column,” Control of a binary distillation column,” Chem. Eng. Chem. Eng. SciSci., 29, 1808 (1973).., 29, 1808 (1973).

[2] Ogunnaike, B. A., J.P. Lemaire, M. Morari, and W.H. [2] Ogunnaike, B. A., J.P. Lemaire, M. Morari, and W.H. Ray, “Advanced multivariable control of a pilot Ray, “Advanced multivariable control of a pilot plant distillation column”, plant distillation column”, AICHEAICHE, 29, 632 (1983)., 29, 632 (1983).

[3][3] Oliveira, S.G., Lopirace, F.S., Araujo, O.Q.F. et al. Oliveira, S.G., Lopirace, F.S., Araujo, O.Q.F. et al. The importance of control considerations for heat The importance of control considerations for heat exchanger network synthesis: a case study. Braz. J. exchanger network synthesis: a case study. Braz. J. Chem. Eng., June 2001, vol.18, no.2, p.195-210. Chem. Eng., June 2001, vol.18, no.2, p.195-210. ISSN 0104-6632. ISSN 0104-6632.

[4][4] Ogunnaike, B. A. and Ray, W. H., Process Dynamics, Ogunnaike, B. A. and Ray, W. H., Process Dynamics, Modeling and Control, Oxford University Press, New Modeling and Control, Oxford University Press, New York (1994).York (1994).

[5][5] Marlin, T. M., Process Control Designing Processes Marlin, T. M., Process Control Designing Processes and Control Systems for Dynamic performance, and Control Systems for Dynamic performance, McGraw-Hill, United States of America (1995).McGraw-Hill, United States of America (1995).

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Tier III Open-ended problem