*3.3. Low Density Polyethylene (LDPE)*

Figure 10 compares the test runs with LDPE with the model. The "Light Liquids" fraction is uniformly distributed which indicates a good fit, However, the "Spindle oil" fraction is overpredicted, even there is no reaction to produce "Spindle oil" (compare with Table 3). Consequently, the "Spindle Oil" fraction originates from the carrier fluid which indicates that there is a strong interaction between carrier fluid and LDPE. Additionally, the "Gas" lump has a uniform, but a high relative variance.

**Figure 10.** Deviation of the modeled and measured values of the test runs with carrier fluid and LDPE. "MAE" is the mean absolute error of the optimization of 0.17 <sup>×</sup> <sup>10</sup>−<sup>2</sup> kg/kg. The dashed lines show the 10% deviation.

### *3.4. High Density Polyethylene (HDPE)*

The determined kinetic data for HDPE shows irregularities. At low conversions, the "Residue" lump is underpredicted, whereas the "Light Liquid" lump is overpredicted as shown in Figure 11. As well as in the LDPE kinetic the "Spindle oil" lump is

overpredicted without having a "Spindle oil" producing reaction pathway in the plastic decomposition, and the "Gas" lump is slightly underpredicted.

**Figure 11.** Deviation of the modeled and measured values of the test runs with carrier fluid and HDPE. "MAE" is the mean absolute error of the optimization of 0.44 <sup>×</sup> <sup>10</sup>−<sup>2</sup> kg/kg. The dashed lines show the 10% deviation.

### **4. Discussion**

As shown in the previous chapter, the simple lump models provide a good agreement with the measured data from the pilot plant, especially the carrier fluid can be predicted with sufficient accuracy. The carrier fluid has a significant impact on the pyrolysis, although the reaction rates are lower than those of plastics, as shown in Table 4. Furthermore, the expected trends can be well modeled, whereas following order: PP > LDPE > HDPE for the reaction rates are expected from literature [22]. This is confirmed by the reactions rates for a given temperature producing "Light Liquids" via reactions path k2.


**Table 4.** Reaction rates at 460 ◦C of all determined reactions and the used plastic decomposition reactions "kLit." from [15].

The kinetic values for the plastic degradation reaction kLit. (Table 3) are taken from [15]. Also, the kinetic values of the carrier fluid, obtained by the model calculation are in a similar order of magnitude, which is also confirmed by the activation energy of around 200 kJ/mol. The calculated activation energies of the reaction paths involved in the PP pyrolysis fit well to literature, the lowest activation energy is 80 kJ/mol for the reaction from "Wax" to "Spindle oil" [5,8,16,17]. However, the calculated activation energy of 700 kJ/mol for reaction path k2 for LDPE and HDPE exceed the range of literature, even to those in comparison to oils [24]. Activation energies of oil cracking are in a frame of 50 to 500 kJ/mol [23]. The reason for this deviation can be assigned to the comparatively low product yields of "Light Liquids", which can only be confirmed in test runs with higher temperatures. Further, test runs with increased temperatures and higher conversions need to be performed to receive more detailed data.

However, some differences can be seen between the kinetic data of PP and HDPE in Figures 9 and 11, respectively. In the case of PP, the "Light Liquids" lump is underpredicted, although the total plastic feed is depolymerized, and its resulting "Wax" is also converted with the other product lumps completely. This indicates that there is an interaction between the carrier fluid and the plastic pyrolysis, which is not yet considered in the model. Hence, PP increases the outcome of products of the co-pyrolysis.

Contrariwise, the kinetic data of HDPE underpredicts the "Residue" lump at low conversions. Again, the HDPE is fully decomposed, and the produced "Light Liquids" lump is not originating 2 "Residue" lump is underpredicted, what indicates an interaction of the co-pyrolysis, in which the degradation of the carrier fluid is inhibited, or the carrier fluid produces a high boiling (410+ ◦C) product instead of a "Light Liquids" lump together with HDPE.

Additionally, the lump "Spindle oil" remains on the same level in the model, resulting in a horizontal trend in Figures 8 and 9. "Spindle Oil" is also not produced from LDPE and HDPE, but is nevertheless overpredicted. Consequently, the reaction mechanism of producing "Spindle Oil" is not sufficiently considered in the model, but this has just a low effect on the variance.

### **5. Conclusions**

The provided lumping approach reduces the complexity of the chemical reaction system significantly by reducing the interacting components, this drastically lowers the analytical and computational effort for the model calculation. In contrast, in order to the common practice operating mostly with TGA measurements, this model can investigate the decomposition processes in a tubular reactor by adding consecutive reactions. The reactor calculation can describe the effect of evaporation and the resulting flow regimes inside the reactor pipe. Also, the complexity of the reaction model is still low (just four lumps), the kinetic data for a satisfying description of the pyrolysis of PP, LDPE and HDPE are found. Simultaneously to the chemical reactions, the heat transfer is described analogously to flow boiling which results in reasonable temperature trends. Due to the temperatures, evaporation, condensation and chemical reactions the density of the reaction medium changes over the whole reactor length, but the model considers all these mechanisms, and thus, provides a reasonable residence time of reaction mixtures in the reactor. Furthermore, the often-used Arrhenius approach obviously describes the temperature dependency sufficiently.

Under the used mild cracking conditions, polyethylene has imperfect conversion towards the products lumps "Spindle oil", "Light Liquids" and "Gas". In particular, the "Spindle oil" lump seems to have different chemical mechanisms, interacting with the carrier fluid. Also PP shows interactions with the carrier fluid, in which the conversion to "Light Liquids" is enhanced.

To generate a more precise prediction, these interactions of the carrier fluid and the plastics should be introduced. Moreover, the formation of coke should be included, which could be inserted with a C/H balance to the system.

However, this lumped kinetic model achieve a sufficient description of the process and hence it is already used in a plant simulation to provide data for an upscale.

**Author Contributions:** Conceptualization, A.E.L. and T.S.; methodology, A.E.L.; software, A.E.L.; validation, A.E.L. and T.S.; formal analysis, A.E.L.; investigation, A.E.L.; resources, A.E.L. and W.H.; data curation, A.E.L. and T.S.; writing—original draft preparation, A.E.L.; writing—review and editing, A.E.L.; visualization, A.E.L. and T.S.; supervision, M.L. project administration, W.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Restrictions apply to the availability of these data. Data was obtained from OMV Downstream GmbH and are available from the authors with the permission of OMV Downstream GmbH.

**Conflicts of Interest:** The authors declare no conflict of interest.
