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On-line estimation and identification of a nonlinear, distributed-parameter process: The dehydrogenation of ethylbenzene to form styrene in a tubular, fixed-bed, catalytic reactor

  • Control Of Distributed Parameters
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  • First Online:
New Trends in Systems Analysis

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 2))

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Abstract

The industrial production of styrene monomer is achieved via the dehydrogenation of ethylbenzene in the presence of steam over a metal oxide catalyst at a temperature around 600°C. The goal of this investigation was to develop and demonstrate an online scheme for estimation of process variables and identification of the dehydrogenation reaction parameters using a distributed-parameter, Kalman filter. This technique was first tested by computer simulation and accurately estimated the process states. Reaction parameters were identified well also, although they proved to be more sensitive to process noise than the state variables. A pilot plant and digital computer system were constructed in order to investigate experimentally the on-line identification scheme. The filter proved effective in estimating process variables. As the simulation predicted, the experimental identification of dehydrogenation reaction parameters was sensitive to process noise; however, the identified parameters are shown to be of potential use in optimization of the reactor operating conditions.

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Abbreviations

a:

slope of estimation line

b:

intercept of estimation line

El :

activation energy of dehydrogenation reaction

E(·):

expected value operator

Fl :

frequency factor of dehydrogenation reaction

f:

vector of nonlinear, ordinary differential equations forming steady state model

g:

vector of boundary condition function

H:

output transformation constant vector

h:

output transformation vector function

J:

estimation performance criterion

k:

dehydrogenation rate parameter

L:

length of reactor

P:

Kalman filter gain matrix

P:

Kalman filter gain vector

Q:

variance matrix of measurement error

R:

covariance matrix of model error

Rg :

ideal gas law constant

T:

temperature

t:

time

u:

state vector

y:

measurement vector

z:

spatial independent variable

δ(·):

Dirac measure operator

ν :

measurement noise vector

ψ :

model noise vector

θ:

an arbitrary time value

τ:

catalyst decay time constant

hm:

harmonic mean

i:

measurement location i

j:

discrete time point j

m,n:

indices

ss:

steady state

o:

initial condition

T:

transpose

′:

partition excluding elements relating to k

^:

estimated quantity

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Author information

Authors and Affiliations

  1. Department of Chemical Engineering, University of Colorado, 80309, Boulder, Colorado, USA

    W. Fred Ramirez & David E. Clough

Authors
  1. W. Fred Ramirez
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  2. David E. Clough
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Editor information

A. Bensoussan J. L. Lions

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© 1977 Springer-Verlag

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Ramirez, W.F., Clough, D.E. (1977). On-line estimation and identification of a nonlinear, distributed-parameter process: The dehydrogenation of ethylbenzene to form styrene in a tubular, fixed-bed, catalytic reactor. In: Bensoussan, A., Lions, J.L. (eds) New Trends in Systems Analysis. Lecture Notes in Control and Information Sciences, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0041107

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  • DOI: https://doi.org/10.1007/BFb0041107

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08406-8

  • Online ISBN: 978-3-540-37193-9

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