DYNAMIC MODELING AND PARAMETER ESTIMATION FOR AN ETHYLENEPROPYLENEDIENE POLYMERIZATION PROCESS

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DYNAMIC MODELING AND PARAMETERESTIMATION FOR
ANETHYLENE-PROPYLENE-DIENEPOLYMERIZATION
PROCESS
LOUISIANA STATE UNIVERSITY AND AGRICULTURAL AND
MECHANICAL COLLEGE

• Rujun Li
• Major Professors Dr. Kerry Dooley
• Dr. Armando Corripio
• Gordon A. and Mary Cain
• Department of Chemical Engineering
• June 23, 2003

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OUTLINE

• Introduction
• EPDM Background
• Research Objectives
• Dynamic Modeling
• Broad MWD and Crosslinking
• Off-line Parameter Estimation
• Parameter Selection Procedure
• Steady-State Detection
• Offline Parameter Estimation
• On-line State Estimation

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INTRODUCTION

• EPDM
• Properties chemical, oil and ozone resistance
• Applications tires, seals, hoses, roofing
• Manufacturing
• Cat Ziegler-Natta V(Ti) halide/aluminum alkyl
• Process solution/slurry, CSTR/PFR
• Diene ENB

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• BASIC MECHANISM (Cozewith, AIChE J, 1988)
• Activation C1?C2 ka
• Deactivation C1?D kx, C1M2(M3)?D kx2, kx3
• Initiation C2M1(M2)?P100(Q010) ki1, ki2
• Propagation PijkM1(M2, M3)?Pi1jk(Qij1k,
  Rijk1) k11, k12, k13
• QijkM1(M2)?Pi1jk(Qij1k) k21, k22
• RijkM1?Pijk1 k31
• Termination Pijk(Qijk, Rijk)? Uijk(Vijk, Wijk)
  kt
• Pijk(Qijk, Rijk)M2? Uijk(Vijk, Wijk)
  kt2
• Pijk(Qijk, Rijk)M3? Uijk(Vijk, Wijk)
  kt3
• Chain Transfer Pijk(Qijk, Rijk)H2? Uijk(Vijk,
  Wijk)C2 ktr1
• Pijk(Qijk, Rijk)Al? Uijk(Vijk, Wijk)P100
  ktr
• Pijk(Qijk, Rijk)M2? Uijk(Vijk, Wijk)Q010
  ktrm2

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RESEARCH OBJECTIVES

• Dynamic Modeling
• Basic predict Rx T, polyrate, contents, etc.
• Model broad MWD
• Offline Parameter Estimation
• Determine parameters to be estimated
• Extract reliable steady-state info from plant
  data
• Obtain parameter estimates
• On-Line State Estimation
• Different measurement frequencies and time delays
• Parametric/structural mismatch

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DYNAMIC MODELING OF CROSSLINKING

• Mechanism Pendant double bond (PDB)

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• Gelation
• Physical polymer network, insoluble in typical
  solvents.
• Mathematical infinite second moments,
• Modeling Gelation
• Typical moment method fails
• Florys statistical method only works for batch
• Monte Carlo difficult to apply to online
• Numerical fractionation potential for success

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Numerical Fractionation

• Chains are partitioned into generations
• Zeroth linear
• First two 0-th crosslink
• i-th crosslinks with jth
• Each generation has finite second moments
• Use finite number of generations
• Apply moment method for each generation

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Numerical Fractionation for EPDM

• Fails at gel point because of large difference in
  order of magnitude of moments within and across
  generations
• Alternative pseudo-homopolymer
• Pseudo-Kinetic Constant Approach
• Quasi-Steady State Assumption
• Long Chain Assumption

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Pseudo-Kinetic Constant Approach

• Pseudo-monomer and pseudo-homopolymer
• Reactions
• NF moment equations m-th generation
• g moment, PDB PDB concentration, ?PDBPDB mole
  fraction

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• Non-Closure problem Saidel Katz approximation
• Number of generations
• Steady-state 5
• Dynamic 11

kc3.12kc,c
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Sol fraction vs. t
Gel appears earlier and in larger amount if kc is
larger
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Steady-State Sol Fraction vs. kc
xsol decreases with kc in a linear fashion
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Steady-State Polydispersity vs. kc
Max Pd is obtained when kc is just over kc,c
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MWD Reconstruction
At gel point, lowest peak value
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MWD Reconstruction
At gel point, longest tail
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Offline Parameter Estimation

• Challenges
• Lack of measurements
• Monomer, polymer concentrations cannot be
  measured
• Indirect measurements, no reliable correlations
• Mooney viscosity, Mooney relaxation
• Limited data
• Operation within a limited range
• All parameters cannot be estimated
• Must select subset of parameters for estimation
• FIM-based procedures cannot give consistent
  selections

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Parameter Identifiability Measures

• Relative sensitivity matrix K
• Overall effect Principal Component Analysis
  (PCA)
• Collinearity

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Parameter Selection Procedure

• Select
• Compute
• Select the N1-th highest ranked parameter
• Repeat steps 2 and 3 until stop criteria meet

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Effect of Perturbation
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Nonlinear Extension

• Multiple perturbations
• Uniform distribution in pmin 1? and 1 pmax ?
• Average K matrix
• Parameter selection procedure on

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Steady State Detection Tool

• Determine Potential Steady State Intervals
• Setpoint data
• Determine Raw Steady States
• PV data determine candidates
• Lab data eliminate candidates if samples too few
• Automatic window sliding and expansion
• Collapse Raw Steady States
• Reduce redundant information

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Steady-State Parameter Estimation

• Objective function
• Measurements Rx T, poly rate, M1, M3 contents
• Standard deviations average values from plant
• Durations weighting factor
• Optimization algorithm Simulated Annealing
• Global
• May accept a uphill point with a certain
  probability

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Steady-State Parameter Estimation

• Parameter bounds
• k11 and k22 bounds obtained from literature
• Other propagation parameters
• Reactivity ratios obtained from literature
• Other parameters 0.1 10 initially, subject to
  adjustment

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Steady-State Parameter Estimation Results
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NONLINEAR ONLINE STATE ESTIMATION

• Model-based controller requires
• State estimator estimates states from model and
  measured outputs
• Extended Kalman filter (EKF) is an optimal
  nonlinear state estimator
• Challenges
• Measurements different frequencies with time
  delays
• Parametric/structural Model Mismatch cause bias
• Design
• Model decoupling, hierarchical EKF structure
• Introducing parameters/disturbances as additional
  states

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Model and Measurement Structure

• Measurements 2 different frequencies
• On-line, every 6 min
• related to 0-th moments
• Lab, every 2h w/ 1h delay
• related to 0-th/1st moments
• System triangle
• Zeroth moments
• First moments
• Second moments

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Model Decoupling and EKF Construction

• First subsystem
• where
• An EKF can be constructed
• Prediction from model
• Correction by current measurements

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Model Decoupling and EKF Construction

• Second subsystem
• where
• The EKF handles the time delay
• Prediction to the time measurements taken
• Correction by the measurements
• Integration forward to current time

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Perfect Model w/ Noise (1st System)
Noises are rejected
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Perfect Model w/ Noise (2nd System)
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Parametric Mismatch w/ Noise (1st System)
Noises and biases are reduced
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Parametric Mismatch w/ Noise (2nd System)
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Structural Mismatch w/ Noise (1st System)
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Structural Mismatch w/ Noise (2nd System)
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CONCLUDING REMARKS

• Dynamic Modeling
• Crosslinkng Mechanism Model broad MWD and
  gelation
• Numerical Fractionation/Pseudo Kinetic Constant
• Can compute properties at gel point and in
  post-gel region
• Stable
• Track evolution of MWD
• Offline Parameter Estimation
• Parameter Selection Procedure
• Based on steady-state perturbation test
• Better than FIM-based procedures
• Can be extended to account for nonlinearity and
  dynamics
• Steady-State Detection Tool
• Automatic sliding and expansion
• On-line State Estimation
• Hierarchical EKF structure
• Stable, can reduce noises and biases

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ACKNOWLEDGMENTS

• Advisors Drs. Kerry M. Dooley Armando. B.
  Corripio
• Former advisor Dr. Michael A. Henson (UMass)
• Dr. Michael J. Kurtz Mr. Norman I. Silverman
• Former group members
• Drs. Guang-Yan Zhu (UTC) and Yungchun Zhang
  (UCSB)
• Prashant Mhaskar (UCLA) and Shoujun Bian (UMass)
• Others
• Profs. Teymour (IIT) and Gossage (Lamar)
• Funding
• Department of Chemical
  Engineering
• ex