**5.1 Brief introduction of technics of PVC polymerization process**

As a thermoplastic resin, when its vinyl chloride molecules are associated, the production of PVC is forming chains of macromolecules, whose process is called polymerization. The vinyl chloride (VC) monomer, dipped in aqueous suspension, is polymerized in a rector shown as Fig.6.

Fig. 6. Flow diagram of PVC polymerization progress

The polymerization process reaction changes violently because the container in the rector goes through water phase, liquid VC phase and solid PVC phase on different stage of reaction. At the start of reaction, water, VC, suspension of stabilizers and initiator are on request loaded into the reactor through respective inlets, and then they are stirred adequately to create a kind of milky solution, suspension of VC droplets.

It is noticed that several indices should be monitored and controlled on each stages of the reaction, especially temperatures. Nine important variables of all the batches depicted on Table 1, are shown in Fig.7 from one batch. At the beginning of the reaction, the hot water is pumped into the jacket of reactor to heat the reactor content to the set temperature (57℃). The indirect heating does not continue until the sufficient reaction heat has been generated 252 Principal Component Analysis

Then one of trajectories, **N***i*(*Kn*×*m*) , that have the largest GCC with **V** (*k* ×*m*) is chosen. If *k*<*K*n, extend **V** (*k* ×*m*) by copying from *k*+1 to *Kn* part of **N***i*(*Kn*×*m*) to follow **V** (*k* ×*m*), otherwise maintain **V** (*k* ×*m*). Although *k* is far less than *Kn* sometimes, the result of Eq.22 reveals the homologous relationship like covariance between the two matrices. Hence, the insufficiency of data of online batch run can be solved by filling the assumptive values in

The second step is pre-treatment of data. Before synchronization, all the measurements of

The third step is synchronization; one can choose DTW or OFA to deal with the asynchronous running trajectory. After that, the new test batch is similar to offline batch so

As a thermoplastic resin, when its vinyl chloride molecules are associated, the production of PVC is forming chains of macromolecules, whose process is called polymerization. The vinyl chloride (VC) monomer, dipped in aqueous suspension, is polymerized in a rector

The polymerization process reaction changes violently because the container in the rector goes through water phase, liquid VC phase and solid PVC phase on different stage of reaction. At the start of reaction, water, VC, suspension of stabilizers and initiator are on request loaded into the reactor through respective inlets, and then they are stirred

It is noticed that several indices should be monitored and controlled on each stages of the reaction, especially temperatures. Nine important variables of all the batches depicted on Table 1, are shown in Fig.7 from one batch. At the beginning of the reaction, the hot water is pumped into the jacket of reactor to heat the reactor content to the set temperature (57℃). The indirect heating does not continue until the sufficient reaction heat has been generated

adequately to create a kind of milky solution, suspension of VC droplets.

different ways.

**5. Case study** 

shown as Fig.6.

new batch should be scaled.

as to be projected onto MPCA/MICA model.

Fig. 6. Flow diagram of PVC polymerization progress

**5.1 Brief introduction of technics of PVC polymerization process** 

from the reaction. PVC in the solution will precipitate quickly to form solid phase PVC granules inside almost each VC monomer droplets on the polymerization, because it is not soluble in water, but little dissolved in the VC.

Fig. 7. Typical batch profiles of nine variable of PVC form one batch


Table 1. Polymerization reactor variables

Due to the exothermic reaction, the temperature of the reactor will rise gradually so that the redundant reaction heat should be removed at once to keep constant temperate. In order to cool down the reactor, a flow of cooling water is pumped into the jacket surrounding the reactor. The condenser on the top the reactor also concentrates VC monomer from vapor to liquid. If temperature of reactor is lower than the set point temperature, the hot water is commanded to be injected in the jacket again, which is the automatic control of process by the parameters of the important variables. At the end of the polymerization, there is a little monomer of remained gaseous VC. With the VC being absorbed from the byproduct of exhaust gas, the polymerization does not continue until the action of terminator.

On-Line Monitoring of Batch Process with Multiway PCA/ICA 255

For those asynchronous batches modeling and monitoring, without intelligent synchronization of DTW or OFA, the rough method of synchrozation, to prune so-called redundant data over the specified terminal or to extend the short trajectories with the last values, is experimented. All the durations of reference batches and test batches should be

Then the reference data set is arranged as a three-way **X** (*I*×*J*×*K*), where *I* corresponds to 50 batches, *J* corresponds to 9 process variables, and *K* corresponds to 3200 *th* time intervals. With the reference batch data **X**, the MPCA and MICA models are constructed initially. Offline analysis of ten test batches is executed to show if this kind of rough construction of data for MPCA or MICA is appropriate or not. After batch-wise unfolding, 8 principal components of the MPCA model are determined by the cross-validation method (Nomikos and MacGregor, 1994), which explain 82.61% of the variability in the data. 8ICs are selected for the MICA for 77.54% variation of the whole data. Fig.9 shows the results of SPE based on MPCA and MICA under 99% control limit. It is clear that neither of MPCA nor MICA does well on the incorrect asynchronous multivariate statistic model: MPCA misses the detection of the batch #2, and MICA reports false alarm batches

2 4 6 8 10

Batch Number

Offline SPE of simple MICA method

off-line 99% limits

0

2000

4000

SPE

On synchronization of DTW operation, all durations of the batches should be 3200. The weight matrix **W**= [1.1527, 1.8648, 0.2390, 1.4778, 0.1742, 0.2118, 0.8186, 0.2760, 0.4592, 3.3258] from Eq.8, 9 for twice iterations. The MPCA model is built and its retained principal number is 8 to show 88.44%the variation of the batch process, whereas MICA retains 3 IC to explain the 93.85% of variation of data. All three solutions of of Nomikos and MacGregor (1995) and GCC are simulated compared with the offline analysis to find which one is the

6000

8000

10000

**5.3 The offline monitoring of batches without intelligent synchronization** 

3200 measurements.

#4,#5, and misses #1,#2.

SPE

2 4 6 8 10

Batch Number

**5.4 Online monitoring of PVC batch process** 

most appropriate in the batch process.

Offline SPE of simple MPCA method

99% limits off line

Fig. 9. Offline analysis for ten test batches of PVC, left: MPCA, right: MICA

**5.4.1 Online monitoring of PVC with DTW-MPCA and DTW-MICA** 
