Proceedings of the 2011 4th International Symposium on Advanced Control of Industrial Industrial Processes, Thousand Islands Lake, Hangzhou, P.R. China, May 23-26, 2011
WePoPo.1
Research Research on Industrial Modeling of Ethylene Oxide Hydration Reactor Fan. Sun, Na. Luo, Rongbin. Qi and Feng. Qian
Abstract —
Focusing Focusing on ethylene oxide (EO) (EO) hydration hydration reactor reactor industrial equipment, the reaction mechanism model is established. Based on the principle of material balance, energy balance and kinetics of the reactions of ethylene oxide with water, partial least squares regression (PLSR) was used in the model to establish a corresponding relationship between the reaction rate constant and the reaction temperature. With kinetic parameters correction by using field data, the results are more tallies with the actual operation. Influences of water/EO molar ratio and inlet temperature on product quality, outlet temperature and energy consumption are analyzed according to the established model. The results showed that the model can preferably reflect the performance of EO hydration reactor and have certain guidance functions to the further advanced control strategies. NTRODUCTION I. I NTRODUCTION
A
S the simplest glycol, ethylene glycol (EG) is an important raw material for industrial applications with extensive uses. EG is used in the manufacture of polyester resins, antifreezes, and solvents, etc [1-2]. EG is commonly produced by the hydration of ethylene oxide (EO) [3-7]. In this paper, the EG production adopts American SD company technologies by oxidation in pure oxygen and EO is synthesized by reaction of ethylene and oxygen under high temperature and high pressure in the presence of catalyst. Then EG is produced by the hydration of EO under the conditions of 22/1 water/EO molar ratio. Though EO hydration reactor is an important device in EG production, there are very few articles about mechanism of hydration of EO and industrial model. Considering the Manuscript received July 23, 2010. This work was funded by Distinguished Young Scholars Program of the National Natural Science Foundation of China (NSFC) (Grant Number:60625302), Natural Science Foundation of China (60704028), the National High Technology Research and Development Program of China (863 Program, No: 2007AA04Z193). Fan. Sun is with Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai, 200237 China (e-mail: sun.fan-007@ 163.com). Na. Luo is with Automatic Automatic Institute, Key Laboratory of Advanced Advanced Control and Optimization for Chemical Processes, Ministry of Education, State-Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai, 200237 China (e-mail:
[email protected]). Rongbin.Qi is with Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai, 200237 China (e-mail:
[email protected],
[email protected]). Feng. Qian is with Automatic Institute, Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, State-Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai, 200237 China (phone: 86-21-64252060; fax: 86-21-64252056; e-mail:
[email protected]).
differences between laboratory results and practical production conditions, first a kinetic model was put forward by the laboratory data, and then using using field data to correct the kinetic parameters. II. MATHEMATICAL MODEL EO hydration reactor is an adiabatic tubular reactor. During the reaction, diethylene glycol (DEG), triethylene glycol (TEG) and polyethylene glycol (PEG) are produced as byproduct. Both DEG and TEG are also used for the manufacture of many chemicals, especially in the production of various polymers. EO reacts with glycols to make higher order glycols and polyglycols. It is an exothermic and cascade reaction. The reactions of EO with glycols occur based on the following stoichiometry [8-9] : 1 (1) → C2 H6 O2 C2 H 4 O + H 2 O k
→ C2 i H4 i +2 Oi +1 , i = 2, , 6 (2) C2 H 4O + C2 i −2 H4 i−2 Oi ki Due to the reactor axial length is far greater than the radial length, we can assume that there is no temperature gradient and concentration gradient in radial direction. So it can be assumed plug flow in the reactor and there is no back mixing. Axial and radial diffusion can be ignored. According to the material balance, energy balance and reaction kinetics equation, model are as follows: A. Reaction kinetics The reactions of EO with water and EG can be expressed as: 1 EO + H 2O k → EG 2 → DEG EO + EG k
(3)
3 → TEG EO + DEG
k
4 → PEG EO + TEG Where k 1 , k 2 , k 3 and k 4 are the reaction rate constants.
k
Each step given in Eqs(3) can be assumed as an irreversible, bimolecular, and constant density reaction. The rate expressions, with this assumption, can be given by: dC H 2O = − k1C EO C H 2O dt dC EO = − k1C EO CH 2O − k 2C EO CEG dt −k3C EO CDEG − k4 CEO CTEG dC EG dt
= k1C EO CH O − k 2C EO CEG 2
456
dC DEG dt dC TEG dt dC PEG dt
(PLSR) method to establish the relationship between the reaction rate constant and the reaction temperature [10-12]. Reaction temperature is the main influencing factor to determine the reaction rate constants. This process of creating the regression equation, taking reaction temperature T x as
= k2C EOC EG − k3C EOC DEG = k3C EOCDEG − k4C EOCTEG
= k 4C EOC TEG
the independent variable, and calculating the results to forecast the dependent variable k i [13]: ki = α 0i + α1iTx + α 2iTx 2 + α 3iT x 3 , i = 1, 2, 3, 4
B. Material balance equation
(5)
Taking differential section dl , the mass balance equation of EG in l to l + dl is as follows: d ( FC EG ) (4) FC EG − [ FC EG + dl ] = rEGπ R 2 dl dl Where F is feed flow, R is reactor radius, C EG is the
factors of correction. We used the 5 groups of experimental data in literature [9] to get 5 groups of the reaction rate constants in different conditions. Then according to the values of T x , we can get the
concentration of EG in the reaction mixture and r EG is
square of T x and the cube of T x . So there are a
reaction rate of EG. Because of the flow is almost constant, Eqs (4) can be simplified as follows:
5 × 3 dimensional nonlinear independent variable matrix
dC EG
=−
rEGπ R 2
=−
rEOπ R 2
dl Similarly, dC EO dl dC H 2O dl dC DEG dl dCTEG dl dC PEG
F
F
=−
( r1 − r2 )π R 2
=−
(− r1 − r2 − r3 − r4 )π R2
=−
rH 2Oπ R 2
=−
rDEGπ R2
F F 2
=−
rTEGπ R
=−
rPEGπ R 2
F
=
F
F
r1π R 2
=− −
F ( r2 − r3 )π R 2 F
( r3 − r4 )π R
=−
F
2
r4π R 2
dl F F Where r1 ~ r 4 are reaction rates of the reactions in Eqs (3) .
Where T x is absolute temperature in kelvin,
α 0i
~ α 3i are
X 1 and a 5 × 1 dimensional dependent variable matrix Y 1 .
After standardization of X 1 and Y 1 , we can get the new matrixes X and Y .The two matrixes are decomposed as: (6) X = TP + E (7) Y = UQ + F T ( 5 × 3 dimensional) and U ( 5 × 3 dimensional) are latent component matrixes, P ( 3 × 3 dimensional) and Q ( 3 × 1 dimensional) represent loading matrixes, E ( 5 × 3 dimensional) and F ( 5 × 1 dimensional) are residual matrixes. Basic idea of extracting component t is finding the max covariance between the latent component vectors t and u . Cov(t , u ) = r (t , u ) Var (t )Var (u )
(8)
Where t and u are column vectors of T and U , Cov( t, u ) is the covariance between t and u , r (t , u ) is the
correlation coefficient, Var is variance operator. When the correlation coefficient is small, the regression results are not satisfactory. So we applied orthogonal C. Energy balance equation projection theory to improve PLSR which removes the The energy balance equation: irrelevant information in the independent variable matrix. d (Fc pT ) 2 T T − ρ − ( r1∆H1 + r2 ∆H 2 + r3 ∆H3 + r4 ∆H4 )π R = 0 X YY X is a 3 × 3 dimensional symmetric matrix and the dl rank of the matrix is l. So there are 2 orthonormal eigenvectors Where ρ is the density of the reaction mixture, c p is which eigenvalue equals 0. Take these 2 orthonormal specific heat capacity of the reaction mixture, ∆ H is reaction eigenvectors as column vector, we can get a 3 × 2 heat. dimensional matrix B = (b1 , b2 ) . In this way, we get In general, the flow is relatively stable, F is almost biT X T YY T Xbi = 0 , so (b1 , b2 , Y T X ) must be a 3 dimensional constant. The value of c p is dependent upon temperature and orthonormal basis. components. The vector which consists of independent variable matrix X and is perpendicular to dependent variable matrix Y can III. THE REACTION RATE CONSTANT REGRESSION be denoted by H = XA . Then we have Y T XA = 0 . So A The value of the preexponential factor has an uncertainty consists of orthocomplement space of Y T X . Then A can be of ±10% in the literature [8]. According to the experimental expressed by a linear combination about the columns of data in the literature [9], the reaction rate constants can be B that can be denoted by A = BD . Next step we need to find worked out by regression analysis. And thus the the D that can make the variance of XBD reaches the macro-kinetics model can be proposed. maximum, so the useless information between independent We applied improved partial least squares regression variable and dependent variable can be removed as much as
457
k1 ' = a1k 1
possible. The eigenvector corresponding to the largest eigenvalue of BT X T XB is just the vector that makes the variance of XBD reaches the maximum. So we get D and when X is projected to the orthocomplement space of H , the new matrix which removes most of the useless information is obtained: X 0 = X − H ( H T H ) −1 H T X . At last, replacing
k 2 ' = a2 k 2
(10)
k3 ' = a3 k 3 k 4 ' = a4 k 4
1) Input the real-time operation conditions, including the inlet temperature, pressure, flow and components of the reactor. According to the input conditions, we can calculate the outlet components of the reactor when taking the value of k 1 , k 2 , k 3 , k 4 as initial value.
X with X 0 , we get the improved PLSR model.
The cross validation method is used to validate the results [14-15]. It is a procedure for accurately assessing the forecast performance of a model and determining the optimum number of principal components. The main index in the assessment is prediction residual error sum of squares (PRESS) that is defined as follows: n (9) PRESS ( h) = ∑ ( yi − yi' ( h)) 2 i =1 Where yi is the i-th original value, yi' ( h) is the i-th fitting
2) According to the calculating values and the actual values in the factory, we used the sequential quadratic programming (SQP) algorithm to get the correction coefficients a1 , a2 , a3 , a4 . The SQP algorithm has been one of the most successful general methods for solving nonlinear constrained optimization problems [16-22]. The objective function is: 2 2 ( y − z EG ,i ) + ( yDEG,i − z DEG,i ) EG ,i (11) min ∑ 2 2 i =1 + y ( TEG ,i − zTEG,i ) + ( y PEG,i − z PEG,i ) n
value of modeling set up with sample i , PRESS (h) indicates the quality of phase h prediction equation. A model has the best prediction ability when the value of PRESS ( h) reaches minimum, wherein the value of h is the
Boundary conditions: ki > 0, i = 1, 2, 3, 4 , C j ≥ 0 Initial value: ai = 1, i = 1,2,3,4
optimum number of principal components. PRESS ( h)
Where C j is the concentration of the components in the
reached its minimum when the number h of principal components was 4, indicating 4 principal components were adequate to generalize the information of the original samples. When the optimum number of principal components is 4, using nonlinear iterated partial least squares (NIPALS) algorithm to get the regression coefficient α 0 i ~ α 3i in
reaction mixture, y EG ,i is the calculating value of EG, z EG ,i is the actual value of EG. 3) Using the correcting reaction rate constants to calculate the model, we can get the simulation results which are more suitable for the operation conditions.
Eqs(5): k1 = 3.5654 × 106 − 1.5114 ×104 T x + 0.6733Tx 2 + 0.0385Tx3
V. THE CALCULATED RESULTS AND RESULTS A NALYSIS
k 2 = 8.6762 × 106 − 3.6548 × 104 T x + 1.4247Tx 2 + 0.0925Tx 3
A. The calculated results of the model reactions of ethylene oxide with water are irreversible The
k3 = 9.7358 × 10 − 4.0825 × 10 T x + 1.4298Tx + 0.1027Tx 6
4
2
3
k 4 = 1.0795 × 107 − 4.5102 × 104 T x + 1.4350Tx 2 + 0.1129Tx3
Where T x is absolute temperature in Kelvin, k i is in Lmol −1 min −1 . Using the 5 groups of experimental data and another 2 groups of experimental data to verify the reliability of the model, the absolute value of average relative error between the predicting data and the experimental data is 5.92%. Using the same data to calculate the model which established based on the method in literature, the absolute value of average relative error is 8.56%. There was a 30.84% decrease. So this model proved effective. IV. PARAMETER CALIBRATION OF INDUSTRIAL MODEL Due to various reasons (such as heat loss, etc), the laboratory results are different with the actual industrial conditions. On account of kinetic parameters correction by using field data, the results are more tallies with the actual operation. Correction factors a1 , a2 , a3 , a4 are introduced to correct the changes of reaction r ate constants.
and exothermic. The conversion rate of EO can reach to 100% in industry control. The model can preferably reflect the performance of EO hydration reactor after the parameter calibration. Using 10 groups of field data to verify the reliability of the model, the absolute value of average relative error is 4.82%. The model calculating components are compared with the designed conditions in Table I. TABLE I SIMULATION RESULTS OF ETHYLENE OXIDE HYDRATION REACTOR
Mass Fraction
Reactor Inlet (designed)
Reactor Outlet (designed)
Reactor Outlet (calculated)
EO
0.0999
0.0000
0.0000
H2O
0.8985
0.8600
0.8595
EG
0.0016
0.1269
0.1281
DEG TEG
0.0000 0.0000
0.0123 0.0007
0.0117 0.0006
PEG
0.0000
0.0001
0.0001
Total Flow(Kg/hr)
260377.5
260377.5
260377.5
Axial temperature distribution of the reactor is shown in Fig.1. EO’s conversion rate is shown in Fig.2. The flow rates of the components along the reactor length are shown in Fig.3.
458
changes of DEG, TEG and PEG are shown in Fig.4.
460
B. Effect of water/EO molar ratio on the product
450
In the process of EG production, different water/EO molar ratios can lead to different product distributions. When the flow rate of EO is unchanged, adjusting the flow rate of water can get different water/EO molar ratios. Taking the flow rate of EO for constant, the flow rate of water for variable, and then different product distributions at different water/EO molar ratios are shown in Table II.
440 ) K 430 ( T
420 410 400
20
40
60
80 100 l(m)
120
1 40
160
Fig. 1. Axial temperature distribution 1
0.8
0.6 O E x
TABLE II PRODUCT DISTRIBUTIONS AT DIFFERENT WATER /EO MOLAR RATIOS Water/E O Molar Ratios
EG (kg/h)
DEG (kg/h)
TEG (kg/h)
PEG (kg/h)
Outlet Temperat ure (C)
20
32992.4
3305.6
188.9
33.7
179.8
21
33174.9
3174.5
172.9
30.8
177.7
22
33345.5
3051.4
157.8
28.1
175.7
23
33502.5
2936.4
145.1
25.8
173.8
24
33649.2
2829.6
133.1
23.7
172.2
25
33777.1
2730.8
122.4
21.8
170.9
0.4
0.2
0
20
40
60
80 100 l(m)
120
140
160
Fig. 2. The conversion rate of EO 5
x 10
) h / g k (
2
G E P y , G 1.5 E T y , G E D y 1 , G E y , O 2 H y , 0.5 , O E y
0
yEO yH2O yEG yDEG yTEG yPEG
20
40
60
80 l(m)
100
120
140
160
Fig. 3. The flow rates of every component 3500
3000 ) h / g k (
TABLE III
2500
OUTLET COMPONENTS AND TEMPERATURES AT DIFFERENT INLET
yDEG
TEMPERATURES
yTEG
G E 2000 P y , G E T 1500 y , G E D y 1000
yPEG
500
0
From the data above, analysis is as follows: 1) Water/EO molar ratio has great influence on EG production. Increasing water/EO molar ratio can increase the output of EG and decrease by-products DEG, TEG and PEG. But at the same time, the outlet temperature falls sharply which will cause more consumption of subsequent high-pressure steam. And also when the water/EO molar ratio increases, purification of the product needs removing a lot of water by evaporation which will increase the energy consumption. 2) How to adjust the water/EO molar ratio depends on the market price of the product. If the benefits of increasing the output of EG are lower than the costs of increasing the energy consumption, smaller water/EO molar ratio should be taken. On the other hand, if the benefits of increasing the output of EG are higher than the costs of increasing the energy consumption, bigger water/EO molar ratio should be taken. In general, adjusting the water/EO molar ratio bases on comprehensive consideration of product benefit, energy consumption and the market price changes of EO, EG and TEG.
20
40
60
80 l(m)
100
120
140
160
Fig. 4. The flow rates of the by-products
The contents of by-products DEG, TEG and PEG are relatively less. They are not obvious in Fig.3. So the specific
Inlet Temperat ure (C)
EG (kg/h)
DEG (kg/h)
TEG (kg/h)
PEG (kg/h)
Outlet Temperat ure (C)
127
33352.3
3041.2
157.3
28.0
172.9
128
33350.2
3044.6
157.5
28.0
173.8
129
33347.8
3078.0
157.7
28.0
174.8
130
33345.5
3051.4
157.8
28.1
175.7
131
33343.2
3054.7
158.0
28.1
176.6
132
33340.8
3057.9
158.2
28.1
177.7
133
33338.5
3061.3
158.3
28.1
178.6
459
C. Effect of the inlet temperature on the product Under the designed conditions, the inlet temperature of the reactor is 130℃. In order to analyze the effect of the inlet temperature fluctuations on the reaction, taking 3 ℃ of fluctuating range simulated and analyzed. When the inlet temperature ranges from 127℃ to 133℃, the outlet components and temperatures are shown in Table Ⅲ. Increasing inlet temperature had little influence on product distributions. Increasing reaction temperature can slightly promote the reaction degree and it will lead to the outlet temperature increasing which will cause less consumption of subsequent high-pressure steam. So increasing inlet temperature is one of the methods that expand the capacity of EO hydration reactor.
[9]
[10]
[11]
[12]
[13]
[14]
VI.
CONCLUSION
PLSR was used to establish the EO hydration reactor model. Utilizing the PLSR method decreased the error for the reaction rate constants fitting. By using SQP algorithm for dynamic equation calibration, the results are more tallies with the industrial equipment. According to the established model, we analyzed influences of water/EO molar ratio and inlet temperature on product quality. Increasing water/EO molar ratio can increase the output of EG but will increase the energy consumption. Adjusting water/EO molar ratio bases on comprehensive consideration of product benefit, energy consumption and the market price changes of EO, EG and TEG. Appropriately increase of the inlet temperature can reduce energy consumption.
[15]
[16]
[17]
[18]
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