On the Use of Extents Material Balance Equations Energy Balance - - PowerPoint PPT Presentation

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On the Use of Extents Material Balance Equations Energy Balance - - PowerPoint PPT Presentation

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Extents for Process Monitoring Motivation Problem Statement System Description On the Use of Extents Material Balance Equations Energy Balance for Process Monitoring and Fault Diagnosis Equations Transformation to Vessel Extents

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SLIDE 1

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

On the Use of Extents for Process Monitoring and Fault Diagnosis Sriniketh Srinivasan, Julien Billeter and Dominique Bonvin Laboratoire d’Automatique EPFL, Lausanne, Switzerland

Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 1 / 19

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SLIDE 2

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Outline

1

Motivation Problem Statement

2

System Description Material Balance Equations Energy Balance Equations

3

Transformation to Vessel Extents

4

Fault Detection

5

Conclusion

Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 2 / 19

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SLIDE 3

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Problem Statement

Measurements of numbers of moles n(t), mass m(t) and reactor temperature T(t) are available

20 40 60 80 100 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 Time (min) n(t) (kmol) 20 40 60 80 100 20 22 24 26 28 30 Time (min) T (t) (C) 20 40 60 80 100 60 65 70 75 80 85 90 95 Time (min) m(t) (kg)

Assumption: Stoichiometry, inlet composition and initial conditions are known but no information is available on the reaction kinetics Can we detect faults using only data from the current batch? The answer is Yes, using the extent-based approach...

Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 3 / 19

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SLIDE 4

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Material Balance Equations

For a reaction system with S species, R reactions, p inlets and one outlet, Mole balances for S species

˙ n(t) = NT V (t) r(t) + Win uin(t) − uout(t)

m(t) n(t), n(0) = n0 (S) (S × R) (R) (S × p) (p)

where, ˙ m(t) = 1T

puin(t) − uout(t),

m(0) = m0, ω(t) = −uout(t) m(t)

Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 4 / 19

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SLIDE 5

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Energy Balance Equations

The energy balance equation can be written as: Heat balance

˙ Q(t) = (−∆ H)T rv(t) + qex(t) + ˇ TT

in uin(t) − ω(t) Q(t)

Q(0) = Q0

where Q(t) = m(t)cpT(t) is the heat power ˇ TT

in contains the specific heats of the inlet streams

Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 5 / 19

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SLIDE 6

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Balance Equations

Combining both equations Combined material and energy balance

˙ z(t) = A rv(t) + b qex(t) + C uin(t) − ω(t) z(t)

z =

  • n

Q

  • and z0 =
  • n0

Q0

  • .

A =

  • NT

(−∆ H)T

  • , b =
  • 0S

1

  • , C =
  • Win

ˇ TT

in

  • Laboratoire d’Automatique – EPFL

Extents for Process Monitoring 19th November, 2014 6 / 19

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SLIDE 7

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Linear Transformation

The linear transformation T =

  • A b C z0 P

−1 gives,       xr(t) xex(t) xin(t) xic(t) xiv(t)       = T z(t) The matrix P describes the q-dimensional null space of the matrix

  • A b C z0
  • , with q = S − R − p − 1 .

Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 7 / 19

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SLIDE 8

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Linear Transformation

The transformed system reads ˙ xr(t) = rv(t) − ω(t) xr(t) xr(0) = 0R ˙ xex(t) = qex(t) − ω(t) xex(t) xex(0) = 0 ˙ xin(t) = uin(t) − ω(t) xin(t) xin(0) = 0p ˙ xic(t) = −ω(t) xic(t) xic(0) = 1 xiv(t) = 0q , The numbers of moles n(t) and the heat Q(t) can be reconstructed from the transformed variables:

  • n(t)

Q(t)

  • =
  • NT

(−∆ H)T

  • xr(t) +
  • 0S

1

  • xex(t) +

Win ˇ TT

in

  • xin(t) +
  • n0

Q0

  • xic(t).

Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 8 / 19

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SLIDE 9

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Fault Detection

Objective Use extents to identify faults in:

1

Outlet flowrates uout(t)

2

Inlet flowrates uin(t)

3

Heat exchange qex(t)

Note: In order to identify faults in reactions, we need either historical data or a kinetic model

Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 9 / 19

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SLIDE 10

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Fault Detection - Fault in Flowrates

Compute the reference mass mref (t) ˙ mref (t) = 1T

p uin,ref (t) − uout,ref (t)

mref (0) = mref ,0 Compare mref (t) with the measured mass m(t) using either z-test or t-test If an error is detected, fault either in uin(t) and/or uout(t)

Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 10 / 19

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SLIDE 11

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Fault Detection - Fault in Flowrates

Compute the extents by applying the linear transformation Compute xic,ref (t) xic,ref (t) = −uout,ref (t) mref (t) xic,ref (t) Compare xic,ref (t) with xic(t) - Error in outlet flowrate? Compute xin,ref (t) xin,ref (t) = uin,ref (t) − uout,ref (t) mref (t) xin,ref (t) Compare xin,ref (t) with xin(t) - Error in inlet flowrates?

Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 11 / 19

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SLIDE 12

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Fault Detection - Fault in Heat transfer

Compute xex,ref (t) xex,ref (t) = qex,ref (t) − uout,ref (t) mref (t) xex,ref (t) Compare xex,ref (t) with xex(t) - Error in heat transfer?

Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 12 / 19

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SLIDE 13

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Simulated Example

Consider the hydrodealkylation reaction system C7H8 + H2 → C6H6 + CH4 2 C6H6 → C12H10 + H2 Both reactions are exothermic Simplification: Hydrogen is considered as a dissolved species fed directly into the liquid phase

Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 13 / 19

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SLIDE 14

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Fault Detection - Simulated Example

For the hydrodealkylation example, under normal

  • perating conditions (NOC), n and T vary with time

The measurements are corrupted with 1% zero-mean gaussian white noise

20 40 60 80 100 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 Time (min) n(t) (kmol) 20 40 60 80 100 20 22 24 26 28 30 Time (min) T (t) (C)

Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 14 / 19

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SLIDE 15

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Fault Detection - Fault in uout

NOC: uout(t) = 0.5 kg min−1 AOC: uout(t) = 0 kg min−1 Fault introduced at time t = 30 min.

20 40 60 80 100 60 70 80 90 Time (min) m(t) (kg) 20 40 60 80 100

  • 0.6
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.1 0.2 Time (min) x ic(t) (-)

Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 15 / 19

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SLIDE 16

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Fault Detection - Fault in uin

NOC: uin(t) = 0.2 kg min−1 AOC: uin(t) = 0 kg min−1 Fault introduced at time t = 30 min.

20 40 60 80 100

  • 5

5 10 15 Time (min) x in(t) (kg) Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 16 / 19

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SLIDE 17

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Fault Detection - Fault in qex(t)

The wrong heat transfer coefficient (UA) was used NOC: UA = 500 W K −1 AOC: UA = 5 W K −1

20 40 60 80 100 −10 −8 −6 −4 −2 Time (min) x e x(t) (kJ ) Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 17 / 19

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SLIDE 18

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

Conclusion

The transformation to extents gives variables that depend

  • n a single rate process → easier to detect a fault

associated with that rate This allows isolation of faults without knowledge of kinetics The method requires a proper statistical framework - Generalized Likelihood Ratio (GLR) tests GLR also helps detect sensor faults Thank you for your attention!

Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 18 / 19

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SLIDE 19

Extents for Process Monitoring Motivation

Problem Statement

System Description

Material Balance Equations Energy Balance Equations

Transformation to Vessel Extents Fault Detection Conclusion

References

  • M. Amrhein, N. Bhatt , B.Srinivasan and D. Bonvin, Extents of Reaction and Flow for Homogeneous

Reaction Systems with Inlet and Outlet Streams, AIChE Journal, 56(11), 2873 - 2866 (2010)

  • N. Bhatt, M. Amrhein and D. Bonvin, Incremental Identification of Reaction and Mass - Transfer

Kinetics Using the Concept of Extents, Industrial & Engineering Chemistry Research, 50(23), 12960

  • 12974 (2011)
  • S. Srinivasan, J. Billeter and D. Bonvin, Variant and invariant states for reaction systems, 1st IFAC

Workshop on Thermodynamic Foundations of Mathematical Systems Theory, Lyon, 2013.

  • S. Narasmihan and R. S. H. Mah, Generalized likelihood ratios for gross error identification in

dynamic processes, AIChE Journal, 34(8), 1321 - 1331 (1988) Laboratoire d’Automatique – EPFL Extents for Process Monitoring 19th November, 2014 19 / 19