Chinese Journal of Chemical Engineering, 16(4) 650 655 (2008) RESEARCH NOTES

Research and Implementation of Decreasing the Acetic Acid Consumption in Purified Terephthalic Acid Solvent System*

XU Yuan ( ) and ZHU Qunxiong ( )**College of Information Science & Technology, Beijing University of Chemical Technology, Beijing 100029, China

Abstract Decreasing the acetic acid consumption in purified terephthalic acid (PTA) solvent system has become a hot issue with common concern. In accordance with the technical features, the electrical conductivity is in direct proportion to the acetic acid content. General regression neural network (GRNN) is used to establish the model of electrical conductivity on the basis of mechanism analysis, and then particle swarm optimization (PSO) algorithm with the improvement of inertia weight and population diversity is proposed to regulate the operating conditions. Thus, the method of decreasing the acid loss is derived and applied to PTA solvent system in a chemical plant. Cases studies show that the precision of modeling and optimization are higher. The results also provide the optimal operating conditions, which decrease the cost and improve the profit. Keywords acetic acid consumption, purified terephthalic acid solvent system, general regression neural network, particle swarm optimization

1 INTRODUCTION

Acetic acid (AcOH) consumption is considered as one of the important indexes to check whether the processing technology of purified terephthalic acid (PTA) solvent system is optimal or not. Its reduction is one of the necessary factors to decrease the production cost, improve the economic profit, and decide the en-terprise competitiveness. Expert experience is gener-ally applied in the regulation of operating conditions to minimize the acid loss in most of the current pro-duction. However, because of fluctuating product process and other changing conditions, several oper-ating conditions are difficult to ascertain. Failure to reasonably regulate the operating conditions can lead to a non-optimal solution in reality. Thus, operating optimization based on theoretical support is taken as one of the most important parts in actual production.

However, to date, few researchers have carried out theoretical researches on the process of solvent system. Most commonly, the techniques to reduce the acid loss in PTA solvent system are to increase the capacity of single reactor, use the distributed control system (DCS) controlling system, and adopt the mid-low temperature oxidation technique and the azeotropic rectifying technique [1 3]. The optimal re-sults are, however, not satisfactory, which may cause consumption of other materials and energy sources.

The article provides an effective method to de-crease the AcOH loss by modeling and optimization for the PTA solvent system. In accordance with the mechanism analysis, the relevant operating conditions influencing the acid loss are extracted. Then, a general regression neural network (GRNN) model is estab-lished for AcOH loss, which has higher precision compared with the fundamental neural network. Sub-sequently, an improved particle swarm optimization (PSO) with the transformation of inertia weight and increase of population diversity is developed to solve

the optimization of the operating conditions, which has better optimization accuracy and stronger ability of global searching. Thereby, further transformation of energy saving is realized.

2 MECHANISM ANALYSIS OF PTA SOLVENT SYSTEM

PTA solvent system is composed of solvent de-hydration tower and N-butyl acetate (NBA) recovery unit. The flow chart is shown in Fig. 1.

Figure 1 Flow chart of PTA solvent system

The mechanism of azeotropic rectification [4 6]is described as follows.

Equation of composition variation at the tower top:

1 1 2 1 1dd i i i iM x Vy Lx D y

t (1)

Equation of composition variation at the rectifi-cation section (k 2,3,···,kF 1):

Received 2007-07-11, accepted 2008-04-27. * Supported by the National Natural Science Foundation of China (60774079), the National High Technology Research and De-

velopment Program of China (2006AA04Z184), and Sinopec Science & Technology Development Project of China (205073). ** To whom correspondence should be addressed. E-mail: zhuqx@mail.buct.edu.cn

Chin. J. Chem. Eng., Vol. 16, No. 4, August 2008 651

1 1dd

k k k k k ki i i i iM x Lx Vy Lx Vy

t (2)

Equation of composition variation at the feeding plate:

1 1dd

F F F F

F F

k k k ki i i

k k Fi i i

M x Lx Vyt

L F x Vy Fx (3) Equation of composition variation at the strip-

ping section (k kF+1,···, 1n ):

1 1dd

k k k k k ki i i i iM x L F x Vy L F x Vy

t (4)

Equation of composition variation at the tower bottom:

1dd

nn n n ni

i i ix

M L F x B x Vyt

(5)

When the condition of the solvent dehydration tower is stable, the liquid holdup of each tray is the same. Namely,

1 2 nM M M M (6) Equation of total material balance:

F D B (7) The relation between quantity of reflux, steam

quantity, logistics quantity and output quantity at the top and the bottom of tower is described as follows:

D L DB V B

(8)

Combining the above eight equations, the for-mula (9) can be acquired.

11d

0d

nki

F nki i i

xM Fx L D y V F D x

t(9)

According to the energy balance and phase equi-librium, the formula (10) and formula (11) can be ac-quired.

F Reb D B CF H Q D H B H Q (10) 0

k kii i

py x

p (11)

The precondition of Eq. (9) and Eq. (10) is that the process is stable. According to thermodynamic principles, each item in Eq. (10) affects the steam quantity, then affects the temperature and pressure within the tower, further affects the phase equilibrium relationships of components in Eq. (11), and ulti-mately affects the AcOH content of top tower.

Reasoning from Eq. (9) to Eq. (11), the AcOH content of top tower depends on feeding flow, output quantity, steam quantity within the tower, quantity of reflux, pressure within the tower, components of feeding flow, enthalpy of feeding flow, enthalpy of top product, enthalpy of bottom product, heat of the re-boiler, and cooling quantity of the condenser. How-

ever, these variables are not all measurable on line. In summary, the on-line measurable variables affecting the AcOH content of top tower are the feed composi-tion (AcOH content), feeding flow, reflux flow of wa-ter, main-reflux flow of NBA, pumpback reflux flow of NBA, liquid level of reflux tank, steam flow, output flow, feed temperature, reflux temperature, tempera-ture at top tower, and temperature of trays.

3 MODELING OF PTA SOLVENT SYSTEM

The target of the research work is the reduction of AcOH content at top tower, which is taken as the output variable of modeling. However, it cannot be measured on-line. The on-line measurable electrical conductivity at the top tower can reflect it. The larger the electrical conductivity, the more is the AcOH con-tent. Hence, it is taken as the output variable for the modeling instead. The on-line measurable variables influencing the AcOH loss that are described in Sec-tion 2 are taken as the input variables for the modeling. Among these variables, the temperature of trays are included by temperature points near the sensitivity tray (TC1503a, TC1503b), temperature point above the 35th tray (TI1515), temperature point between the 35th tray and the 40th tray (TI1516), temperature point between the 44th tray and the 50th tray (TI1517), and the temperature point between the 53rd tray and the 58th tray (TC1501).

3.1 Data-preprocessing

The first step in modeling is data-preprocessing to ensure the quality of data. As the collected data of PTA solvent system is incomplete, fluctuant, and abundant, several data-preprocessing methods are used in order. They are included by data fusion, steady state test, noise filtering, data normalization, and data anti-normalization [7 9]. Data fusion is multi-source data synthesis based on time scale. Steady state test is taken in accordance with the noise margin of each variable. Noise filtering is adopted by the smooth av-erage method. Data normalization is applied to elimi-nate the dimension influence. Data anti-normalization is the reversion of data normalization. Then, the ART2 clustering algorithm [10] is used for the sample selec-tion, which has the capability of self-learning and is effective in classification for arbitrary sequences of input patterns without guidance.

Collecting the data of PTA solvent system from one chemical plant, the data of feeding flow in Sep-tember 2007 is taken as the original data for the ex-ample of data-preprocessing. The data is disposed from 13248 records to 1234 records. The comparison results of data distribution are shown in Fig. 2 and Fig. 3.

Taking the data collected from July to September in 2007 as an example, it is clustered into 2 categories by the ART2 clustering algorithm. Then, several data records are selected from each category stochastically, and ultimately, 6420 sample records are extracted.

Chin. J. Chem. Eng., Vol. 16, No. 4, August 2008 652

Figure 2 Initial data distribution

Figure 3 Final data distribution

3.2 GRNN modeling

Generally, some fundamental neural networks are used in the modeling of industrial process, such as radial basis function (RBF) network and back propa-gation (BP) network. Compared with these, the GRNN network [11, 12] has a strong ability to simulate non-linear functions, which overcomes the disadvantages of low convergence speed and local minimum prob-lem. It can find the implicit relation between the in-dependent variables and the dependent variables from the sample data. Moreover, it is effective with only a few samples and even with sparse data in multi-dimensional space. Thereby, the GRNN network is more suitable to the modeling for complex industry process.

Taking the data from October to November in 2007 as the original data, 7870 training samples are acquired after data-preprocessing, and nearly 4400 groups of data extracting from the original data are considered as the generalization sample. The com-parison of modeling by GRNN and RBF is described in Table 1. The output of the GRNN model and the actual output are shown in Fig. 4. The output of the RBF model and the actual output are shown in Fig. 5.

Table 1 Comparison of modeling by GRNN and RBF Neural

network Average relative error of

training Average relative error

of generalization

GRNN 1.66% 1.98% RBF 2.04% 3.43%

From the comparison, it is seen that the precision of the GRNN model is better. To prove the validity of modeling, the article uses the trend analysis of the crucial variables. When the feeding flow is 19 t·h 1,the change curves of electrical conductivity with main-reflux flow of NBA and reflux temperature are shown in Fig. 6 and Fig. 7. The main-reflux flow of

NBA is changed from 25 t·h 1 to 55 t·h 1. The reflux temperature is changed from 15°C to 38°C.

According to the mechanism analysis, the AcOH content of top tower decreases with the increase of reflux flow, namely, the electrical conductivity is re-duced, and the rising of reflux temperature indicates the reduction of reflux flow, which leads to the in-crease of the AcOH content of top tower and the elec-trical conductivity. Thus, the trend analysis is correct, which verifies the validity of modeling.

Figure 4 Output of GRNN model and actual output

Figure 5 Output of RBF model and actual output

Figure 6 Change curve of electrical conductivity with main reflux flow of NBA

Figure 7 Change curve of electrical conductivity with reflux temperature

Chin. J. Chem. Eng., Vol. 16, No. 4, August 2008 653

4 OPTIMIZATION OF PTA SOLVENT SYSTEM

Based on the GRNN model described in Section 3, the improved PSO algorithm is applied to optimize the operating conditions of the PTA solvent system, so as to decrease the AcOH content of top tower. The PSO [13 15] algorithm is the recent modern evolution-ary algorithm, which is suitable for solving the nonlin-ear optimization problem. However, the standard PSO algorithm includes some problems. On one hand, local optimization may occur during the multi-peak search-ing. On the other hand, all particles tend to be similar and lack in population diversity under the condition of convergence. Considering these two disadvantages, the article presents the improved PSO algorithm.

4.1 Improvement of PSO

The improvement of PSO is proposed from the inertia weight and the moving direction of particles.

(1) Transformation of inertia weight To balance the ability between global search and

local search, the transformation of inertia weight is proposed to ensure the convergence and avoid local optima during the multi-peak searching. The trans-formation is described as follows.

1 2 c 2 1cos2 2

w w t w ww

c (12)

The inertia weight is changed by cosine function with certain frequency. The balance is maintained by regulating the extent of global search and local search. Once the suitable frequency is set, the particle can search for the optimal point.

(2) Increase of population diversity To enhance the searching ability of solution

space, the moving direction of particles is changed to increase the population diversity. The basic idea is the grouping for particles, which are divided into three different parts. The flight rule of the first group re-mains constant. The particles in the second group fly around the area of optimal result in a certain radius. The particles in the third group fly in opposite direc-

tion away from the optimal result. The moving tracks of particles in the second group and the third group are shown in Fig. 8 and Fig. 9.

Figure 8 Moving track of particles in the second group

Figure 9 Moving track of particles in the third group

The updating for the velocity and position of par-ticles in the first group is taken by standard PSO. The method for updating the position of particles in the second group is described by Eq. (13). The velocity of particles in the second group is random.

1g 3 maxrand()k

id d dx P c x (13)

The method for updating the velocity and posi-tion of particles in the third group is described by Eq. (14) and Eq. (15).

1 1k k kid id idx x v (14)

11

2 g

rand()

rand()

k k kid id id id

kd id

v w v c P x

c P x (15)

Table 2 Comparison of optimization by standard PSO and improved PSO

Average optimal value Function Number of particles Dimension Iteration times Search space Maximum speed

Standard PSO Improved PSO

Sphere 50 10 1000 [ 100, 100]n 10.0 0.001 0

Rastrigrin 50 10 3000 [ 5.12, 5.12]n 1.0 2.1184 1.99

Girewank 50 10 2500 [ 600, 600]n 60.0 0.092 0.071

Schaffer f6 40 2 1000 [ 100, 100]n 10.0 0.0068 0.0039

Table 3 Regulated ranges of optimized variables

Regulated variables Reflux flow of water

/t·h 1Main-reflux flow of NBA

/t·h 1Steam flow

/t·h 1Temperature point near the sensitive tray (TC1503b)

/°C

regulated Ranges (0.5, 2) (25, 37) (18, 24) (95, 98)

Chin. J. Chem. Eng., Vol. 16, No. 4, August 2008 654

The Benchmark test function is taken to check the performance of standard PSO and improved PSO, which is included by Sphere function, Rastrigrin func-tion, Girewank function, and Schaffer f6 function. The parameter settings of standard PSO are described as follows: c1 and c2 are both 2, and w is 0.7. In the im-proved PSO, the particles are divided into three groups. The number of particles in the first group is n-20 (n is the total number of particles); the number of particles in the second group is 10; and the number of particles in the third group is 10. The parameter set-tings of improved PSO are described as follows: c1and c2 are both 2, w1 is 0.9, w2 is 0.4, c3 is 0.2, and c is 30. Each optimization algorithm is run 50 times. The average optimal value is taken as the comparison cri-terion between the standard PSO and the improved PSO. The comparison results are described in Table 2.

From Table 2, it is seen that the improved PSO has better optimization precision and stronger ability of global searching than the standard PSO under the same condition.

4.2 Operating optimization of PTA solvent system

The operating optimization in PTA solvent sys-tem is the realization of decreasing the AcOH content at top tower, so that the optimization target is to minimize the electrical conductivity. Based on the GRNN model established in Section 3, the improved PSO algorithm is used to optimize the operating con-ditions. In practical production, not all input variables of the GRNN model can be regulated. The four inde-pendent variables, which are, the reflux flow of water, the main-reflux flow of NBA, steam flow, and the temperature point near the sensitive tray (TC1503b) can be regulated to realize the optimization.

(1) Objective function It is supposed that the electrical conductivity of

top tower is f(t). The objective function is Min f f(t),where, t is the regulated variable.

(2) Constraint conditions Actually, the variables are only regulated in a

narrow range because of production condition limita-tions. The ranges for the regulated variables are listed in Table 3.

(3) Optimization result The parameter settings of improved PSO are the

same as the description in Section 4.1. When the feeding flow is 19 t·h 1, the optimization results and comparison are demonstrated in Table 4.

From Table 4, it can be seen that the electricity conductivity is reduced apparently by regulating the

operating conditions. Through the actual application in a chemical plant, the AcOH content at top tower is reduced from 0.1% to 0.05% during the period of Oc-tober and November in 2007. Thereby, the proposed method provides an efficient way to decrease the AcOH consumption, and results in cost saving and economic benefit to PTA solvent system.

NOMENCLATURE

B output quantity at the tower bottom B logistics quantity at the tower bottom c parameter for regulating the frequency c1 learning factor c2 learning factor D output quantity at the tower top D logistics quantity at the tower top F feeding flow HB enthalpy of bottom product HD enthalpy of top product HF enthalpy of feeding flow L quantity of reflux M liquid holdup of the tray M k liquid holdup of the kth tray

FkM liquid holdup of the kF th tray Mn liquid holdup of the nth tray M1 liquid holdup of the 1st tray M2 liquid holdup of the 2nd tray Pgd the best place found by the global particles Pid the best place found by the ith particle searching p pressure within the tower

0ip saturated vapor pressure of the ith component

QC cooling quantity of the condenser QReb heat of the reboiler tc current iteration times V steam quantity

kidv the current velocity of the ith particle in D-dimensional space

1kidv the next velocity of the ith particle in D-dimensional space

w inertia weight w1 initial value of inertia weight w2 final value of inertia weight xdmax the maximum position of the particles in D-dimensional space xgBest the optimal solution found by the particle searching

Fix concentration of the ith component in the feeding flow kix concentration of the ith component at the kth tray in the liquid phase

Fkix concentration of the ith component at the Fk th tray in the liquid

phase 1Fk

ix concentration of the ith component at the 1Fk th tray in the liq-uid phase

1kix concentration of the ith component at the ( 1k )th tray in the

liquid phasenix concentration of the ith component at the nth tray in the liquid phase

1nix concentration of the ith component at the ( 1n )th tray in the

liquid phase1ix concentration of the ith component at the 1st tray in the liquid phase

Table 4 Optimized results and comparison

Regulated variables Output variable Reflux flow of

water/t·h 1Main-reflux flow of

NBA/t·h 1Steam flow

/t·h 1Temperature point near the

sensitive tray (TC1503b)/°C Electricity conductivity

of top tower/S before the optimization (Mar.2006 Oct.2007) 0.67 34.2 21.6 115 51.9

after the optimization (Oct.2007 Nov.2007) 0.81 29.1 19.7 116 22.7

Chin. J. Chem. Eng., Vol. 16, No. 4, August 2008 655

kidx the current position of the ith particle in D-dimensional space

1kidx the next position of the ith particle in D-dimensional space

xpBest the optimal solution found by the global particles kiy concentration of the ith component at the kth tray in the vapor phase

Fkiy concentration of the ith component at the Fk th tray in the vapor

phase 1Fk

iy concentration of the ith component at the 1Fk th tray in the va-por phase

1kiy concentration of the ith component at the (k+1)th tray in the va-

por phase niy concentration of the ith component at the nth tray in the vapor phase 1iy concentration of the ith component at the 1st tray in the vapor phase 2iy concentration of the ith component at the 2nd tray in the vapor phase

REFERENCES

1 Dorn, C., Morari, M., “Qualitative analysis for homogenous azeotropic distillation. 1. local stability”, Ind. Eng. Chem. Res., 41 (16), 3930 3942 (2002).

2 Chien, I.L., Wang, C.J., Wong, D.S.H., “Dynamics and control of a heterogeneous azeotropic distillation column: Conventional control approach”, Ind. Eng. Chem. Res., 38, 468 478 (1999).

3 Guo, Z., Chin, J., Lee, J.W., “Feasibility of continuous reactive dis-tillation with azeotropic mixtures”, Ind. Eng. Chem. Res., 43,3758 3769 (2004).

4 Feng, G.Y., Fan, L.T., Seib, P.A., Bertok, B., Kalotai, L., Friedler, F., “Graph-theoretic method for the algorithmic synthesis of azeotropic-distillation system”, Ind. Eng. Chem. Res., 42, 3602 3611 (2003).

5 Bonanomi, E., Morari, M., “Phase-plane analysis of homogeneous azeotropic distillation columns”, Ind. Eng. Chem. Rer Technol., 142,48 58 (2004).

6 Mu, S.J., Su, H.Y., Gu, Y., Chu, J., “Multi-objective optimization of industrial purified terephthalic acid oxidation process”, Chin. J.Chem. Eng., 11 (5), 536 541(2003).

7 Filippidis, A., “Data fusion using sensor data and a priori informa-tion”, Control Eng. Practice, 4 (1), 43 53 (1996).

8 Dai, X., Khorram, S., “Data fusion using artificial neural networks: A case study on multitemporal change analysis”, Computers, Envi-ronment and Urban Systems, 23, 19 31 (1999).

9 Cardoso, M.G.M.S., Themido, I.H., Pires, F.M., “Evaluating a clus-tering solution: An application in the tourism market”, Intelligent Data Analysis, 3 (6), 491 510 (1999).

10 Wann, C.D., Thomopoulos, S.C.A., “A comparative study of self-organizing clustering algorithms dignet and ART2”, Neural Networks, 10 (4), 737 753 (1997).

11 Specht, D.F., “A general regression neural network”, IEEE Transac-tions on Neural Networks, 2 (6), 258 276 (1991).

12 Li, Z.W., Sun, J.Z., ZHANG, Z.Q., “Reconstruction of novel view-point image using GRNN”, Transactions of Tianjin University, 2 (9), 136 139 (2003).

13 Cui, G.Z., Niu, Y.Y., Wang, Y.F., Zhang, X.C., Pan, L.Q., “A new ap-proach based on PSO algorithm to find good computational encoding sequences”, Progress in Natural Science, 6 (17), 712 716 (2007).

14 Gaing, Z.L., “Particle swarm optimization to solving the economic dispatch considering the generator constraints”, IEEE Trans. Power Syst., 18 (3), 1187 1195 (2003).

15 Huang, C.M., Huang, C.J., Wang, M.L., “A particle swarm optimiza-tion to identify the ARMAX model for short term load forecasting”, IEEE Trans. Power Syst., 20 (2), 1126 1133 (2005).