Case Study

2.3.2 Case Study

To illustrate the practical benefits of the presented approach, the monitoring of a medium and high-density polyethylene (MDPE, HDPE) plant is considered.

HDPE is versatile plastic used for household goods, packaging, car parts and pipe.

The plant is operated by TVK Ltd., which is the largest polymer production company (www.tvk.hu) in Hungary. A brief explanation of the Phillips license based low-pressure catalytic process is provided in the following section.

Process Description

Figure 2.22 represents the Phillips Petroleum Co. suspension ethylene polymer-ization process.

Figure 2.22: Scheme of the Phillips loop reactor process.

The polymer particles are suspended in an inert hydrocarbon. The melting point of high-density polyethylene is approximately 135^◦Celsius. Therefore, slurry polymerization takes place at a temperature below 135^◦ Celsius; the polymer formed is in the solid state. The Phillips process takes place at a temperature between 85–110^◦ Celsius. The catalyst and the inert solvent are introduced into the loop reactor where ethylene and anα-olefin (hexene) are circulating. The inert

solvent (isobuthane) is used to dissipate heat as the reaction is highly exothermic.

A cooling jacket is also used to dissipate heat. The reactor consists of a folded loop containing four long runs of pipe 1 m in diameter, connected by short horizontal lengths of 5 m. The slurry of HDPE and catalyst particles circulates through the loop at a velocity between 5–12 m/s. The reason for the high velocity is because at lower velocities the slurry will deposit on the walls of the reactor causing fouling.

The concentration of polymer products in the slurry is 25–40% by weight. Ethy-lene,α-olefin comonomer (if used), an inert solvent, and catalyst components are continuously charged into the reactor at a total pressure of 450 psig. The polymer is concentrated in settling legs to about 60–70% by weight slurry and continu-ously removed. The solvent is recovered by hot flashing. The polymer is dried and pelletized. The conversion of ethylene to polyethylene is very high (95%–98%), eliminating ethylene recovery. The molecular weight of high-density polyethylene is controlled by the temperature of catalyst preparation. The main properties of polymer products (Melt Index (MI) and density) are controlled by the reactor temperature, monomer, comonomer and chain-transfer agent concentration.

Problem Description

The process has to produce about ten different product grades according to the market demand. Hence, there is a clear need to minimize the time of changeover be-cause off-specification products may be produced during transition. The difficulty comes from the fact that there are more than ten process variables to consider.

Measurements are available in every 15 seconds on process variablesx_k, which are thexk,1 reactor temperature (T),xk,2 ethylene concentration in the loop reactor (C2), xk,3 hexene concentration (C6), xk,4 the ratio of the hexene and ethylene inlet flowrate (C6/C2in),xk,5 the flowrate of the isobutane solvent (C4),xk,6the hydrogen concentration (H2),xk,7 the density of the slurry in the reactor (roz), xk,8 polymer production intensity (P E), andxk,9 the flowrate of the catalyzator (KAT). The product qualityy_k is only determined later, in another process.

The interval between the product samples is between half an hour and five hours. The yk,1 melt index (M I) and the yk,2 density of the polymer (ro) are monitored by off-line laboratory analysis after drying the polymer that causes one hour time-delay. Since it would be useful to know if the product is good before testing it, the monitoring of the process would help in the early detection of poor-quality product. There are other reasons why monitoring the process is advantageous. Only a few properties of the product are measured and sometimes these are not sufficient to define entirely the product quality. For example, if only rheological properties of polymers are measured (melt index), any variation in end-use application that arises due to variation of the chemical structure (branching, composition, etc.) will not be captured by following only these product properties.

In these cases the process data may contain more information about events with special causes that may effect the product quality.

Application to Process Monitoring

The SOM of the process has been applied to predict polymer properties from mea-sured process variables and to interpret the behavior of the process. The process data analyzed in this book have been collected over three months of operation.

The database contains the production of nine product grades with the distribution given in Table 2.4.

Table 2.4: Sample distribution of the products Number of samples Product grades

2 1

76 2

5 3

1 4

65 5

94 6

103 7

11 8

52 9

First we applied the classical FCM algorithm with 7×7 = 49 clusters. (The cause of this choice is to ease the visualization in a regular grid.) Then the cluster centers can be arranged in a grid along each dimension. These grids can also be called maps. The maps of the coordinates of the clusters are given in Figure 2.23.

From these maps the following relations can be seen:

• The hydrogen concentration and temperature are highly correlated with the melt index (MFI). Since the first two are state variables and they can be controlled, it can also be said that the hydrogen concentration and the reactor temperature determine the melt index.

• The hydrogen, C6-C2 concentrations, C6/C2 ratio, temperature have an ef-fect on the density of polymer

• Production intensity is influenced by the flowrate of C4 and katalysator.

Unfortunately, it is hard to get more information from these images because there are many scattered regions with different colors so we cannot be sure that all available information has been detected.

The regularized FCM algorithm with random initialization shows better re-sults (Figure 2.24). Here we can see the additional information that the C2, C6 concentration influence the melt index. The relations of the images are easier to interpret, because there are only a few regions with different colors.

Last we initialized the code vectors based on the first two principal component of the data and applied the regularized FCM algorithm. The resulting images

MFI ro T

Figure 2.23: Map obtained by the FCM algorithm.

(Figure 2.25) are easier interpretable as before, but additional information was not revealed.

Based on this map the typical operating regions related to different product grades could be determined. With the regularized FCM algorithm it is possible to detect the typical operating regions related to the frequently produced products: 5, 7, 6, 9. Furthermore, the presented clustering algorithm is a good tool for hunting for correlation among the operating variables. For example, it can be easily seen that the melt index of the polymer (MFI) is highly correlated to the reactor temperature (T). Such extracted knowledge has been proven to be extremely useful for the support of the operators, as the extracted information can be used in the supervision of the process.

For comparison, the maps obtained by Kohonen’s SOM algorithm are also pre-sented. On the map (Figure 2.26) the color codes are the inverse of ours. The border of different regions are sharper on the SOM map because we used inter-polated shading for the representation of the fuzziness of our map. The results show that both SOM and the presented regularized clustering algorithm results in similar component maps.

MFI ro T

Figure 2.24: Map of code vectors obtained by randomly initialized regularized FCM.

2.3.3 Conclusions

Clustering is a useful tool to detect the structure of the data. If there are many clusters, it is hard to evaluate the results of the clustering. To avoid this problem, it is useful to arrange the clusters on a low-dimensional grid and visualize them.

The aim was to develop an algorithm for this visualization task. With the intro-duction of a new regularization term into the standard fuzzy clustering algorithm it is possible to arrange the cluster prototypes on a grid. This type of arrangement of the code vectors helps greatly in the visualization of the results, as the regular-ization orders the similar cluster centers closer to each other. The color-coding of the numerical values of the clusters results in regions on the map that shows the relations among the variables. Hence, the presented algorithm can be used as an alternative of SOM.

MFI ro T

Figure 2.25: Map of cluster prototypes obtained by regularized FCM with initial-ization.

Figure 2.26: SOM map of the process data.

Chapter 3

Clustering for Fuzzy Model