Modeling of Bisphenol A Condensation Reaction based on UKF Algorithm

9th International Symposium on Advanced Control of Chemical Processes June 7-10, 2015. Whistler, British Columbia,Control Canadaof Chemical Processes 9th Available online at www.sciencedirect.com 9th International International Symposium Symposium on on Advanced Advanced Control of Chemical Processes June June 7-10, 7-10, 2015. 2015. Whistler, Whistler, British British Columbia, Columbia, Canada Canada

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Modeling of Bisphenol A Condensation Reaction Modeling Bisphenol A Modeling of ofbased Bisphenol A Condensation Condensation Reaction on UKF Algorithm Reaction based on UKF Algorithm based on UKF Algorithm Wentao Cang, Li Xie, Huizhong Yang  Wentao Wentao Cang, Cang, Li Li Xie, Xie, Huizhong Huizhong Yang Yang Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, PR Key Laboratory of Process Control Light Industry Key Laboratory of Advanced Advanced Process Control for for Light Industry China ([email protected]) (Ministry of Education), Jiangnan University, Wuxi 214122, (Ministry of Education), Jiangnan University, Wuxi 214122, PR PR China China ([email protected]) ([email protected])

Abstract: The Bisphenol A concentration at the reactor outlet is a direct response to the production quality index, online soft concentration is very necessary. on the Abstract: The Bisphenol A concentration at the is response to production Abstract: Theand Bisphenol A measurement concentration of at Bisphenol the reactor reactorA outlet outlet is aa direct direct response to the theBased production mechanism of Bisphenol A condensation process, the mechanism equations describing the dynamic quality index, and online soft measurement of Bisphenol A concentration is very necessary. Based quality index, and online soft measurement of Bisphenol A concentration is very necessary. Based on on the the behavior of reactor are established, and the state equation and observation equation of Bisphenol A are mechanism of Bisphenol A condensation process, the mechanism equations describing the dynamic mechanism of Bisphenol A condensation process, the mechanism equations describing the dynamic derived simplification and and derivation of equation the soft measurement model, and of then an Unscented behavior of are the and equation Bisphenol A behaviorthrough of reactor reactor are established, established, and the state state equation and observation observation equation of Bisphenol A are are Kalman Filteringsimplification is adopted to and estimate the Bisphenol A concentration. that derived derivation of measurement model, then Unscented derived through through simplification and derivation of the the soft soft measurement Simulation model, and and results then an anconfirm Unscented the method is feasible and effective. Kalman Filtering is to Kalman Filtering is adopted adopted to estimate estimate the the Bisphenol Bisphenol A A concentration. concentration. Simulation Simulation results results confirm confirm that that the method is feasible and effective. the method is feasible and effective. © 2015, IFAC (International Federation of Automatic Control)Reaction; Hosting bySoft Elsevier Ltd. All rights reserved. Keywords: Unscented Kalman Filtering; Condensation Sensor; Mechanism Model; Bisphenol A Keywords: Unscented Kalman Filtering; Condensation Reaction; Soft Sensor; Mechanism Model; Keywords: Unscented Kalman Filtering; Condensation Reaction; Soft Sensor; Mechanism Model; Bisphenol A Bisphenol A  nonlinear system filtering by approximating the probability  1. INTRODUCTION distribution of the nonlinear functions andthe theprobability posterior nonlinear system system filtering by approximating approximating the probability nonlinear filtering by 1. INTRODUCTION 1. INTRODUCTION probability density of state based on a series of deterministic of the nonlinear functions and the posterior Bisphenol A (BPA), an important common monomer for distribution distribution [5-9] of the nonlinear functions and the posterior , and the can use directly samples probability density of state on aa series deterministic production of many polymers such as polycarbonate and Bisphenol A (BPA), an important common monomer for probability density of UKF state based based onnonlinear series of ofmodel deterministic Bisphenol A (BPA), an important common monomer for instead of[5-9] [5-9] linearizing. In this paper, UKF is employed in state , and the UKF can use nonlinear model samples epoxy resins,of manufactured by such acid catalyzed condensation production polymers as and , and the UKF can use nonlinear model directly directly production ofis many many polymers such as polycarbonate polycarbonate and samples estimation and the simulation results are provided to instead of linearizing. In this paper, UKF is employed of acetone phenol. Industrial processes for BPA instead of linearizing. In this paper, UKF is employed in epoxy resins, is by condensation in state state epoxy resins, and is manufactured manufactured by acid acid catalyzed catalyzed condensation demonstrate the effectiveness of the proposed method. estimation and the simulation results are provided to production usually use fixed-bed reactors filled with strong of for of acetone acetone and and phenol. phenol. Industrial Industrial processes processes for BPA BPA estimation and the simulation results are provided to [1] demonstrate the effectiveness of the proposed method. . BPA synthesis acid ion exchange resins as catalysts production production usually usually use use fixed-bed fixed-bed reactors reactors[1]filled filled with with strong strong demonstrate the effectiveness of the proposed method. 2. DYNAMIC MODEL OF BPA SYNTHESIS [1]. BPA kinetics been widely studied and reported in recent years. synthesis acid ion exchange resins as . BPA synthesis acid ionhas exchange resins as catalysts catalysts 2. Various BPA synthesis kinetics models have differences kinetics has been widely studied and reported in recent years. 2. DYNAMIC DYNAMIC MODEL MODEL OF OF BPA BPA SYNTHESIS SYNTHESIS kinetics has been widely studied and reported in recent years. because of the complexities of BPA synthesis. For example, Various BPA synthesis kinetics models have differences 2.1 Observation Equation of BPA Concentration Various BPA synthesis kinetics models have differences [2] et al. proposed kinetics of BPA 2.1 Observation Equation of BPA Concentration Chen Liangcheng because of of synthesis. For because of the the complexities complexities of BPA BPAreaction synthesis. For[3]example, example, 2.1 Observation Equation of BPA Concentration [2] [2] studied synthesis with strong acid conditions. Rahimi et al. proposed reaction kinetics of BPA Chen Liangcheng In industrial production, acetone and phenol are continuously of BPA Chen Liangcheng et al. proposed reaction kinetics [3] [3] kinetics of BPA synthesis by condensation reaction. Bao-he studied synthesis with strong acid conditions. Rahimi from theproduction, top of the acetone reactor. and Thephenol phenolare is continuously excessive in studied fed synthesis with strong acid conditions. Rahimi In industrial industrial production, acetone and phenol are continuously proposed reactionby kinetics of BPAreaction. synthesis with In Wang [4]of kinetics BPA synthesis condensation Bao-he order to improve the conversion rate of acetone and kinetics of BPA synthesis by condensation reaction. Bao-he fed from the top of reactor. The phenol is in from the top of the reactor. The phenol is excessive excessive in [4] [10] [4] proposed cyst amine modifiedreaction resin catalyst. This onwith soft fed kinetics of BPA synthesis Wang : reduce side reaction. The main reaction formula is proposed reaction kinetics of paper BPA focuses synthesis with Wang order to improve the conversion rate of acetone and order to improve the conversion rate of acetone and [10] sensor development for catalyst. online This prediction of theon cyst modified paper soft cyst amine amine modified resin resin catalyst. This paper focuses focuses onBPA soft reduce reduce side side reaction. reaction.k0The The main main reaction reaction formula is is [10]:: k1 formula concentration, which has important practical significance. A   B  (  H )   P  (  H ) sensor development for online prediction of the BPA 1 2 sensor development for online prediction of the BPA kk0 kk1 concentration, which has important practical significance. 0  B  (H )  1  P  (H ) A  concentration, which has important practical significance. 1 2 A   B  (  H )   P  (  H where , , denote acetone, BPA and by-product 2A B P 1 2) In a BPA reaction process, the BPA concentration at the 4’BPA, respectively. The dynamic characteristics of the where , , denote acetone, BPA and by-product A B P reactor outlet is theprocess, most important which directly In reaction the concentration at where A , B , P denote acetone,[11]BPA and by-product 22In aa BPA BPA reaction process, the BPA BPAindex, concentration at the the reaction process can be The written as : characteristics 4’BPA, respectively. dynamic of the determines the production efficiency. However, the real-time reactor outlet is the most important index, which directly 4’BPA, respectively. The dynamic characteristics of the reactor outlet is the most important index, which directly [11] process can be BPA concentration cannot efficiency. be measured online inthe majority of reaction determines the However, real-time reaction be written written as as [11]:: determines the production production efficiency. However, the real-time Material process balance can equation: industrial fields. Incannot order to this online problem, this paper BPA be measured in of BPA concentration concentration cannot be solve measured online in majority majority of Material balance equation: Material balance equation: establishes a nonlinear state-space model for the estimation C (t , z ) industrial industrial fields. fields. In In order order to to solve solve this this problem, problem, this this paper paper u A  R1 (1) of BPA concentration by taking the temperature distribution establishes a nonlinear state-space model for the estimation  establishes a nonlinear state-space model for the estimation C C AA((ztt ,, zz ))  R  u (1) uC (t, z )  R11 (1) in the reactor and theby acetone at distribution the reactor of concentration taking the of BPA BPA concentration by taking concentration the temperature temperature distribution B z   u  R  R (2) 2 2 inlet as the observation variables. Hence, the BPA synthesis in the reactor and the acetone concentration at the reactor  in the reactor and the acetone concentration at the reactor C CBB((ztt ,, zz ))  R  R   u (2) can by a nonlinear distributed parameter model. u  R22  R22 (2) inlet the variables. Hence, BPA inletbeas asdescribed the observation observation variables. Hence, the the BPA synthesis synthesis Energy balance equation: zz can be described by a nonlinear distributed parameter model. can described by a nonlinear distributed parameter model. equation: As abe nonlinear estimation method, the extended Kalman filter Energy Energy balance balance Tc T (equation: t, z) T (t , z ) 2 (EKF) is widely used in state estimation. But the EKF has As a nonlinear estimation method, the extended Kalman filter   C   C u  (3) S PS p As a nonlinear estimation method, the extended Kalman filter 22 H i Ri  cC pcuc TT ((tt ,, zz ))  C u TT((ttz,, zz ))  i 1 H R   C u TTzcc some the But requirement of (EKF) widely state the S C (3) (EKF) is isdeficiencies, widely used used in inincluding state estimation. estimation. But the EKF EKF has has  i i c pc c p (3) S CPS PS t  C p u z  1 Hi Ri  cC pcuc Ezz/ RT differentiability of the state dynamics the as wellrequirement as susceptibility some including of CB . z 1 C A , R2  k1e some deficiencies, deficiencies, including the requirement of where R1  k0eEt / RT CA , R2 kz0e E /ii RT to bias and divergence in thedynamics state estimates. the contrary,  E // RT  E // RT differentiability of as as   k1the RT C . z RTof RT Cz  differentiability of the the state state dynamics as well well On as susceptibility susceptibility R e EE // RT C  where ,, R is the axial 0 R22. In CBB . z  k1ee E industrial R11   kklength CAAthe R22reactor  kk00ee Eand C AA ,, LR where 0e the unscented Kalman filter (UKF) can improve the effect of to bias and divergence in the state estimates. On the contrary, to bias and divergence in the state estimates. On the contrary, is the axial length of the reactor and z  L . In the industrial the the unscented unscented Kalman Kalman filter filter (UKF) (UKF) can can improve improve the the effect effect of of is the axial length of the reactor and z  L . In the industrial 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2015, 2015 IFAC 828Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. Copyright © 828 Copyright © 2015 2015 IFAC IFAC 828 10.1016/j.ifacol.2015.09.071

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production process, the radial temperature grade is much smaller to the axial one, and eqn. (3) can be simplified as:

The simplest concentration equation is independent of temperature:

T T (t , z ) 2 = H i Ri 1  cC pcuc c z z i 1

CB2 (k  1)  KCB2 (k )  w(k )

C p u

(4)

In order to solve nonlinear partial differential eqn. (1), (2) and (4), the reactor is divided into two sections according to the distribution of temperature measurement points and the height of each section is z  1m , then disperse eqn. (1), (2) and (4) to:  C A1 (t )  C A0 (t ) u  k0e E / RT1 (t )C A1 (t )   z  u C A2 (t )  C A1 (t )  k e E / RT2 (t )C (t ) 0 A2  z   CB1 (t )  CB 0 (t )  k0e E / RT1 (t )C A1 (t )  k1e E / RT1 (t )CB1 (t ) u z  u CB 2 (t )  CB1 (t )  k e E / RT2 (t )C (t )  k e E / RT1 (t )C (t ) 0 A2 1 B2 z 

where K is the state transfer coefficient of BPA concentration, w(k ) represent the process noise. The state space expression of BPA concentration can be obtained by combining eqn. (11) and (12): CB 2 (k  1)  KCB 2 (k )  w(k )   y (k )  g (CB 2 (k ))  v(k )

(5)

3. UNSCEBTED KALMAN FILTERING Consider the general discrete nonlinear system: a(k  1)  f (a(k ))  w(k )   y (k )  g (a(k ))  v(k )

(7)

k e 0



 E / RT1 (t )

 u k0e E / RT2 (t )  u



 a0  E (a0 )  T   P0  Var (a0 )  E[(a0  a 0 )(a0  a 0 ) ]

(8)

C A0 (t )

  a, i  0  , i  1,2  n i (k k  1)  a   (n   )  Pa  i  a   (n   )  Pa  , i  n  1, 2n  i  

T2 (t )  T1(t ) u2  H1k0e E / RT2 (t )  C A0 (t ) z k0e E / RT1 (t )  u k0e E / RT2 (t )  u





 H 2k1e E / RT2 (t )CB 2 (t )  cC pcuc



Tc 2 (t )  Tc1(t ) z

Tc1 (t )  Tc 0 (t )  T0 (t )  T1(t )  Tc 2 (t )  Tc1 (t )  T1 (t )  T2 (t )

0m   / (n   )  c 2 0   / (n   )  (1     )  m c i  i  1 / 2(n   ), i  1, 2,   2n  2   n(  1)

(10)

y(t )  g (CB2 (t ))  v(k )

g (CB 2 (t ))  

(11)

,

u H1k0e E / RT2 (t )u 2C A0 (t )   k0 k0e E / RT2 (t )  u 1

(17)

where  m is the weight of the first-order statistical property，and  c is the weight of the second-order statistical property, a is the average of a ,  is a free parameter, n is state vector dimension. The constant  is usually set to 104    1 and   2 is optimal for Gaussian distributions. (3) Time update  i (k k  1)  f ( i (k k  1))  wk , i  0,1, 2n (18)

Eqn. (9) can be written in a standard form: where y(t )  e

(16)

The weights of Sigma points sequence accordingly are

(9) Unfortunately, the real-time temperature of cooling water cannot be measured in the actual production. This paper assumes that the thermal performance of the heat exchanger is good and the temperature difference of cooling water in the axial direction can be approximated as:

 E / RT1 (t )

(15)

(2) Sigma points calculation Sigma points sequence is

Take T0 (t ) , T1(t ) , T2 (t ) and C A0 (t ) as the measurement variables, the observation equation of BPA concentration can be expressed as: C p u

(14)

where a(k )  Rn is the state vector, y(k )  Rm is the output vector. According to the additive noise model shown as Eq. (14), the UKF procedure is given as follows. (1) Initialization

When eqn. (5) is introduced into eqn. (6), the latter becomes: C A2 (t ) 

(13)

where w(k ) and v(k ) are the uncorrelated Gaussian white noise and their variance are qk  0.1 and rk  0.05 , respectively.

(6)

T1 (t )  T0 (t )   H1k0e E / RT1 (t )C A1 (t )  H 2k1e  E / RT1 (t )CB1 (t ) C p u z  T (t )  Tc0 (t )   cC pcuc c1  z  T ( t ) T ( t )   E / RT ( t ) 1 C u 2 2 C (t )  H k e  E / RT2 (t )C (t )  H1k0e A2 2 1 B2  p z  T (t )  Tc1(t )   cC pcuc c 2 z  u2

(12)

2n

a(k k  1)  im i (k k  1)

.

(19)

i 0

2n

T

P(k k  1)  i  i (k k  1)  a(k k  1)   i (k k  1)  a(k k  1)     k0 (  C pu  cC pcuc )(T2 (t )  T1 (t ))  H 2k1e  E / RT2 (t )CB 2 (t )  i 0    i (k k  1)  g ( i (k k  1))  vk , i  0,1, 2n (21)

2.2 State Equation of BPA Concentration

829

c

 



(20)

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Table 1. Model parameters

2n

y (k k  1)  im i (k k  1)

(22)

i 0

Symbols

(4) Measurement update 2n

H k0

T

Pyy  ic  i (k k  1)  y(k k  1)    i (k k  1)  y (k k  1)  (23)     i 0 2n

C pc

T

Pay  ic  i (k k  1)  a(k k  1)    i (k k  1)  y(k k  1)  (24)    

Cp

i 0

a(k k )  a(k k  1)  K (k )  [ y(k )  y(k k  1)]

P(k )  P(k k  1)  K (k )  Pyy  K T (k )

K (k )  Pay  Pyy 1

829

(25)

K H 2  k1

(26)

u uc

(27)

Values 410.228 371.7125 4.2 0.541 0.972 29000 2 0.27

Tab.2 Estimation errors of the model

4. INDUSTRIAL CASE STUDY The state estimation of the BPA concentration is based on the dynamic model described by eqn. (13). However, H 2  k1 and K are both unknown parameters in eqn. (13). In order to determine the values of H 2  k1 and K , we recorded 178 historical data from industry site, and the total of 178 cases was split into 3 parts: one set of 50 samples for reverse calculation of H 2  k1 , the other set of 70 samples for fitting K , and the last set of 58 samples for model testing.

Estimation method

MaxRE/%

UKF

3.9248

MeanRE/% 1.5572

5. CONCLUSIONS In this paper we have established the state-space model for the estimation of BPA concentration by taking the temperature distribution and the acetone concentration as the observation variables, and then UKF is adopted in the state estimation. The simulation results show that the state-space model is able to track the trends of BPA concentration accurately, and the accuracy of the model is satisfactory. This method can be used for online estimation of the BPA concentration, which has guiding significance for the industrial production of BPA.

According to chemical principle, heat of reaction H 2 and pre-exponential factor k1 are constants for the known side reaction, and it is obvious that (H 2  k1) can be approximated by a constant and (H 2  k1) is set to (H 2  k1)=2.9 104 by nonlinear regression. In order to calculate K , the least squares fitting is adopted and K is set to K  0.972 .

REFERENCES

In order to verify the effectiveness of the proposed method, UKF algorithm is adopted to estimate BPA concentration. The BPA concentration estimation results of 58 group data are shown in Fig. 1. Parameters in eqn. (13) are specified in Tab. 1.

Lundquist G E. High productivity bisphenol-A-catalyst: US, 20040181100 [P]. 2004-09-16. Chen Liangcheng, Li Yaqin. Online monitoring of catalyst activity for synthesis of bisphenol A [J]. Lecture notes in computer science, 2010, 6328(1): 45-51. Rahimi, A, Farhangzadeh, S. Kinetics study of bisphenol A synthesis by condensation reaction [J]. Iranian polymer journal, 2001, 10(1): 29-32. Bao-He Wang, Jin-Shi Dong, Shuang Chen, Li-Li Wang, Jing Zhu. ZnCl2-modified ion exchange resin as an efficient catalyst for the bisphenol-A production [J]. Chinese Chemical Letters, 2014, 25: 1423-1427. Julier S J Uhlmann J K. A new approach for filtering nonlinear system: Proc. of the 1995 American Control Conference [C]. 1995: 1628-1632. Kyunghoon Junga, Jaeyong Kima, Jungmin Kima, Eunkook Junga, Sungshin Kim. Positioning accuracy improvement of laser navigation using UKF and FIS [J]. Robotics and Autonomous Systems, 2014, 62(9): 12411247. Jianlin Wang, Liqiang Zhao, Tao Yu. On-line Estimation in Fed-batch Fermentation Process Using State Space Model and Unscented Kalman Filter [J]. Chinese Journal of Chemical Engineering, 2010, 18(2): 258-264. Zhang Xinming. Nonlinear Filtering with Applications to Communication and Navigation Systems [D]. Beijing:

Figure. 1 BPA concentration estimation results. The MaxRE (Maximum Relative Error) and MeanRE (Mean Relative Error) are used to quantify the prediction errors and they are shown in Tab. 2.

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NOMENCLATURE

Beijing University of Posts and Telecommunications, 2012. Wang Xiaoxu. Design of UKF with correlative noises based on minimum mean square error estimation [J]. Control and Decision, 2010, 25(9): 1393-1398. Liang Shuxiang. Bisphenol-A [M], Beijing: Chemical Industry Press, 1981. Zhu Kaihong, Yuan Weikang. Chemical reaction engineering analysis [M]. Beijing: High Education Press, 2002, 433441.

C A acetone concentration, wt % CB BPA concentration, wt % C p specific heat of reactant, kJ  (mol  K )1 C pc specific heat of cooling water, kJ  (mol  K )1 CPS specific heat of catalyst, kJ  (mol  K )1 E reaction activation energy, kJ H1 heat of main reaction, kJ  kg 1 H 2 heat of side reaction, kJ  kg 1 k0 reaction rate constant of main reaction k1 reaction rate constant of side reaction L axial length of reactor, m reaction temperature, K T Tc cooling water temperature, K u feed velocity, m / s uc cooling water velocity, m / s  average density of reactant, kg / m3 c density of cooling water, kg / m3

s

831

density of catalyst, kg / m3