Accounting for correlations in the reaction network

Because we talk about reaction networks, usually we have to estimate the kinetic parameters of a set of correlating reactions, e.g. if more light components are formed in hydrocracking, a lesser amount of heavier components will be produced, meaning that the corresponding reactions are also not independent from each other. There is one thing, though. This issue is seldom addressed in the literature. Therefore, the key idea is to merge the lumped components with the highest correlation in the reaction network, then calculate their concentrations based on this correlation.

While used extensively, the properties of lumped reaction networks are infrequently studied in the literature. In an early work on the lumping of complex reaction networks, it is stated that the core of the lumping process is that the species grouped together into a lump are strongly interacting on a shorter time-scale [185]; i.e. the lumping method is not directly connected to the physical properties of the components; rather, it is related to the reactions themselves. The lumping process is a tradeoff between model prediction and precision (i.e.

explicitly depicting as many components as possible to characterize the reaction mixture (fuel)) and the capabilities of the analytical techniques (i.e. we would want to use uncomplicated and fast methods) [65]. Therefore, it often comes in handy to lump together what we can to arrive at a more elementary model and use algebraic expressions later to express the concentrations of multiple components on the longer time-scale that are all part of the same lump.

With this, we can also target what kind of measurement we need to follow a particular process. This could bear high significance. Even at a laboratory scale, the detailed composition of the reaction mixture is usually not often determined.

There are some works in that the final product is analyzed using different methods, mainly gas chromatography. Calemma et al. applied GC-MS and

13C NMR to analyze hydrocracking products of Fischer-Tropsch waxes [186].

Elordi et al. used both online GC and GC-MS techniques to measure product yields during HDPE pyrolysis [187]. Djokic et al. combined two-dimensional gas chromatography with Fourier Transform-Ion Cyclotron Resonance Mass Spectrometry [188]. On the other hand, detailed interim measurement is much less often carried out. Onwudili et al. investigated the effect of residence time on product composition during polyethylene and polystyrene pyrolysis and observed a significant effect [189]. The longer residence time provided an opportunity for secondary reactions to occur; hence, the average molecular weight of the pyrolysis oil decreased and the amount of pyrolysis gas and char increased. It should be noted that the process was carried out in a pressurized batch reactor and the volatile products have not been withdrawn continuously.

The effect of residence time is more likely investigated in a tube reactor, e.g. in the work of Ying et al. and apparently the shorter the carbon chain gets, the lower

its reactivity becomes [190]. This indicates that if volatiles are continuously purged from the system, the importance of the secondary reactions will diminish.

Zheng et al. also reached this conclusion, stating that the secondary reactions between the product lumps immediately stopped after quenching had been introduced [191]. This is also the reason behind that, in many cases, thermogravimetric analysis is enough to follow the process [192–194].

However, detailed intermediate and end-product analysis, if available, provides an excellent opportunity to identify specific correlations between the formations of different components. Hashimoto et al. identified such correlations in biomass pyrolysis between the rate parameters and solid residue yield and between lignin content and solid residue yield, indicating that these correlations can positively be used in the kinetic parameter estimation [195]. Detailed kinetic models utilize correlations between the reaction rate parameters to avoid the number of model parameters to be identified to be too high [196,197]. In the long run, exploring these correlations makes the parameter estimation of more complex reaction mechanisms from a more elementary set of measurement data possible. Both the correlations between kinetic parameters and the correlations between the amounts of products are worth to be explored. The former represents a direct reduction in the number of parameters to be identified, while the latter contributes to this indirectly as it gives an opportunity to consolidate the number of components that consequently comes with a smaller number of kinetic parameters to be determined. One might not consider this an advantage in itself, but it does give space to expand the reaction network in other dimensions, as shown in Chapter 7.

In most works, the authors deal with one single lumped reaction network. This is perfectly logical as the modeling requirements can be met using that particular network; on the other hand, there can be underlying alternatives and the reasoning behind the final choice is usually fairly implicit. Nevertheless, there are a number of such works available in the literature. Arabiourrutia et al. investigated tire pyrolysis in a conical spouted bed reactor and compared two similar lumped kinetic models, one involving a secondary reaction between the volatiles, the main aim of which was to improve the fit of the model to the experimental results. It is worth noting that the activation energy of the secondary reaction was the highest

that is consistent with the assumption that the reactivity of volatile components during pyrolysis is significantly lower [198]. Puron et al. developed a four-lump kinetic model for vacuum residue hydrocracking and varied the number of reactions between four and nine; the intention of the kinetic modeling here was to obtain the best fit to the experimental data, but also involving the analysis of possible reaction pathways [199]. Santos et al. did a comparative study of kinetic models that can be derived from DTG (differential thermogravimetry) curves for bagasse pyrolysis, showing that the main degradation steps are parallel in nature [200]. Trejo et al. varied also the number of pseudocomponents in the kinetic model for the hydrocracking of asphaltenes by separating the feedstock into easy-to-react asphaltenes and hard-easy-to-react asphaltenes [201]. Félix and Ancheyta compared four lumped reaction networks for crude oil hydrocracking, highlighting that there can be reactions present in the networks that do not actually take place at given operating conditions [202].

Still, the possible correlations between the lumped components are rarely mapped out. And this is what our aim here; to vary the pseudocomponents included in the lumped reaction network and use the correlations identified by analyzing the experimental data to reach an optimal lumped reaction network in sense of capturing as many characteristics of the measurement as possible for a given number of reactions.