Determining values of reaction parameters of a reaction model for a pyrolysis process

Abstract

The invention relates to a computer-implemented method for determining values of reaction parameters of a reaction model for a process of pyrolyzing a plastic starting material into plastic products, said method having the following steps: - providing experimental data comprising a plurality of boiling point distributions of plastic products, wherein each boiling point distribution is paired with a pyrolysis temperature and a pyrolysis duration, and each of the boiling point distributions is binned into a number N of lumps L1 to LN, each lump being paired with a boiling point temperature range; and - determining a respective value of the reaction parameter by fitting the reaction parameter of the reaction model to the experimental data. For each lump Li from L1 to LN-1, the reaction model has a partial reaction, which is determined by at least one reaction parameter, in order to describe the conversion of plastic products of said lump into plastic products of an adjacent lump Li+1 lying therebelow with respect to the boiling point temperature range, said reaction model having less than N*(N-1) / 2 partial reactions.

Description

[0001]Determination of reaction parameter values ​​of a reaction model for pyrolysis. The invention relates to a computer-implemented method for determining reaction parameter values ​​of a reaction model for pyrolysis of a plastic starting material into plastic products, a method for carrying out pyrolysis of a plastic starting material into plastic products, a data processing system for executing the computer-implemented method, and a corresponding computer program product. Europe alone generates several million tons of plastic waste annually, of which only a relatively small proportion is collected for recycling. Therefore, large quantities of plastic waste are incinerated, landfilled, or shipped.To increase recycling rates, a deposit return system can be introduced, for example. Plastic waste can be mechanically recycled or chemically reprocessed, for example through depolymerization and repolymerization. A major challenge associated with plastic waste is the sorting of the different types of plastic and the contamination of the waste. Pyrolysis offers a relatively simple way to process plastic waste that is mixed or even contaminated with other waste. In pyrolytic processes, valuable resources are generated from organic substances at high temperatures and in the absence of oxygen. These valuable resources can be used as starting materials for reusing the plastic waste. During pyrolysis, long-chain hydrocarbons in the plastic waste are split into molecules with a lower molecular weight using thermal energy.The products of pyrolysis are liquid or gaseous and can be further processed in existing infrastructure, such as a conventional oil refinery. Due to their high complexity, the chemical processes that take place during pyrolysis are difficult to describe in detail theoretically. To determine suitable parameters, such as the pyrolysis duration and pyrolysis temperature, for a planned pyrolysis, pyrolysis can be modeled in a simplified form using a so-called lump model. The pyrolysis products are typically classified into so-called lumps according to their boiling point. A lump contains pyrolysis products within a specific boiling point temperature range. In known lump models, the individual lumps are typically linked to one another via monomolecular, irreversible first-order reactions.Within the framework of lump models, pyrolysis products of a lump with a high boiling point temperature range can decompose into pyrolysis products of any lump with a lower boiling point temperature range. The reverse process, i.e., polymerization, is negligible within the context of pyrolysis and is typically not modeled in lump models. Each of the reactions is modeled in such a way that a rate or velocity of the respective reaction from one lump to another lump can be specified. Experimental data from a test reactor are typically used to determine the parameters of the individual reactions. For example, Lechleitner, AE; Schubert, T.; Hofer, W.; Lehner, M. Lumped Kinetic Modeling of Polypropylene and Polyethylene Co-Pyrolysis in Tubular Reactors. Processes 2021, 9, 34, https: / / doi.org / 10.3390 / pr9010034, a lump model for the pyrolysis of polypropylene and polyethylene in a tubular reactor.To describe pyrolysis, a model with four lumps is used to classify the products resulting from the pyrolysis of plastic. All lumps are linked together by a monomolecular, irreversible first-order reaction. In addition, an initial process step is provided in which the starting material ("plastic"), which is not assigned to a boiling point temperature range, is converted into products of the lump with the highest boiling point temperature range ("wax 420°C+"). According to the publication, this initial process step could not be evaluated (see Chapter 2.2.1, last paragraph). The total of six reactions k. i are modeled using the Arrhenius equation to capture the temperature dependence of the reactions. Per reaction k i are each an Arrhenius constant A i and an activation energy E A,i, a total of twelve parameters, were determined using experimental data. Another model for the pyrolysis of LDPE (“low-density polyethylene”) is known from Schubert, Teresa, et al., "4-Lump kinetic model of the co-pyrolysis of LDPE and a heavy petroleum fraction." Fuel 262 (2020): 116597. The model features four lumps, each of which is linked to each other by monomolecular, irreversible first-order reactions. According to Naik, Desavath V., et al., "Kinetic modeling for catalytic cracking of pyrolysis oils with VGO in a FCC unit." Chemical Engineering Science 170 (2017): 790-798, two problems typically arise when calculating kinetic parameters. On the one hand, there are convergence problems with an excessive number of parameters. On the other hand, the initialization of the parameters can cause the optimization to reach a local minimum (which would result in incorrect parameters being calculated).The publication presents a 5-lump model for the catalytic cracking of pyrolysis oils. The parameters of the 5-lump model were determined sequentially using a 3-lump and a 4-lump model to minimize the number of parameters to be determined simultaneously. The object of the invention is to mitigate or eliminate the disadvantages of the prior art. In particular, the object of the invention is to provide a computer-implemented method, a data processing system, and a computer program product for determining reaction parameter values ​​of a reaction model for the pyrolysis of a plastic starting material into plastic products, which allows for simple, robust, and efficient modeling of the pyrolysis without significantly impairing the modeling accuracy.The object is achieved by a computer-implemented method for determining values ​​of reaction parameters of a reaction model for a pyrolysis of a plastic starting material into plastic products, the method comprising the following steps: - Providing test data comprising a plurality of boiling point distributions of plastic products, wherein each boiling point distribution is assigned to a pyrolysis temperature and a pyrolysis time, wherein the boiling point distributions are each divided into a number N of lumps L1 to L. N binned, each lump being assigned a boiling point temperature range; - determining a value of the reaction parameters by fitting the reaction parameters of the reaction model to the experimental data; the reaction model for each lump L i from L1 to L N-1a partial reaction determined by at least one reaction parameter to describe a conversion of plastic products of this lump into plastic products of a lump L lying below and adjacent to it in terms of the boiling point temperature range i+1, whereby the reaction model has fewer than N*(N-1) / 2 partial reactions. The reaction models known to date from the state of the art, as described, for example, in the above-mentioned publication by Lechleitner et al. (Processes 2021, 9, 34), include the partial reactions of each individual lump in all lumps below it in the boiling point temperature range. This means that the complexity of the model increases rapidly with the number of lumps, since N*(N-1) / 2 partial reactions must be taken into account. Therefore, the state of the art also strives to get by with as few lumps as possible. Lechleitner et al. originally started with a 6-lump model, which was subsequently simplified to a 4-lump model (cf. Lechleitner et al., Chapter 2.2.1).In the course of the present invention, it has now surprisingly been found that some partial reactions can be neglected without significantly impairing the accuracy of the reaction model. Compared to the prior art, the number of partial reactions is therefore reduced to less than N*(N-1) / 2. By reducing the number of partial reactions, the convergence of the fitting can be improved and, in general, the model complexity can be reduced with the same number of lumps – or, with the same model complexity, the number of lumps considered can be increased. The key here is to understand which partial reactions can be neglected and which cannot be neglected under any circumstances without significantly impairing the accuracy of the reaction model. The most crucial partial reactions for the accurate description of pyrolysis are those between lumps that are adjacent in terms of the boiling point temperature range.It has been found that partial reactions between lumps that are spaced apart in terms of the boiling point temperature range occur less frequently in pyrolysis and are less critical for the accuracy of the reaction model. Conversely, the reaction parameters of these less crucial partial reactions are more difficult to determine because the experimental data only include these partial reactions to a subordinate extent, and therefore the determination of the values ​​of the relevant reaction parameters is subject to greater experimental and statistical uncertainties. Modeling such infrequent partial reactions can negatively influence the overall convergence of the fit. Therefore, it has proven crucial that the reaction model for each lump L. i from L1 to L N-1a partial reaction to describe a conversion of plastic products of this lump into plastic products of a lump L lying below and adjacent to it in terms of the boiling point temperature range i+1as these reactions are the most critical for describing pyrolysis. During the pyrolysis of a plastic starting material into plastic products, thermal energy is supplied to the plastic starting material, whereby long-chain molecules of the plastic starting material are split and plastic products are formed. Any type of plastic waste can be used as the plastic starting material. For example, the plastic starting material can contain polypropylene or polyethylene. The plastic products can, for example, contain (relatively shorter-chain and / or lighter) hydrocarbons such as heavy oils, spindle oils, gas oils, kerosene, naphtha, liquefied petroleum gas (LPG) or hydrocarbons that are gaseous under normal conditions. The pyrolysis can be carried out in a pyrolysis reactor. For example, Lechleitner, AE; Schubert, T.; Hofer, W.; Lehner, M.Lumped Kinetic Modeling of Polypropylene and Polyethylene Co-Pyrolysis in Tubular Reactors. Processes 2021, 9, 34, https: / / doi.org / 10.3390 / pr9010034 a pyrolysis reactor designed as a tubular reactor. Key parameters of pyrolysis are the pyrolysis temperature, i.e., the temperature to which the plastic starting material is heated, and the pyrolysis time, which specifies how long the pyrolysis temperature is maintained. In general, both a higher pyrolysis temperature and a longer pyrolysis time lead to increased conversion to shorter-chain plastic products. One step of the process involves providing experimental data comprising a variety of boiling point distributions of plastic products.The experimental data can be obtained, for example, using a plurality of pyrolysis runs, in which pyrolysis is carried out at a pyrolysis temperature and a pyrolysis time using the same plastic starting material in the same pyrolysis reactor. Each pyrolysis run results in plastic products that can be classified according to their boiling point. Each experimentally determined boiling point distribution is assigned a pyrolysis temperature and a pyrolysis time. Preferably, the experimental data comprise boiling point distributions of a plurality of different pyrolysis temperatures and / or a plurality of different pyrolysis times. The boiling point distributions are each divided into a number N of lumps L1 to L. Nbinned, with each lump being assigned a boiling point temperature range. A measured boiling point distribution can, for example, originally be present continuously as a function of the boiling point temperature, into which lumps are binned and thus be present in the form of a histogram. For example, nine lumps L1 to L9 can be provided, into which the individual boiling point distributions are each binned. The first lump L1 can, for example, contain the plastic starting material and a boiling point temperature range above 600°C. The second lump L2 can, for example, have a boiling point temperature range between 450°C and 600°C and can be referred to as the bottom product or heavy product. The third lump L3 can contain heavy oil and can have a boiling point temperature range between 400°C and less than 450°C. The fourth lump L4 may comprise spindle oil and may have a boiling point temperature range between 350°C and less than 400°C.The fifth lump L5 may comprise gas oil and may have a boiling point temperature range between 225°C and less than 350°C. The sixth lump L6 may, for example, comprise kerosene and have a boiling point temperature range between 165°C and less than 225°C. The seventh lump L7 may, for example, comprise naphtha and have a boiling point temperature range between 20°C and less than 165°C. The eighth lump L8 may, for example, comprise LPG (“Liquefied Petroleum Gas”) and have a boiling point temperature range between -120°C and less than 20°C. In this example, the eighth lump L8 may predominantly comprise hydrocarbons with a number of hydrocarbon atoms between two and four (for example ethene, ethane, propane, propene, butane and / or butene). The ninth lump L9, for example, can contain gaseous hydrocarbons with a boiling point of less than -120°C under normal conditions.The ninth lump L9 can in this case contain predominantly methane. Alternatively, more or fewer lumps can be provided. For example, two or more of the lumps listed above as examples can be combined. For example, other lumps with different boiling point temperature ranges can be provided. In the next step, a value for each reaction parameter is determined by fitting the reaction parameters of the reaction model to the test data. The reaction model describes the conversion of the plastic products and the plastic starting material of the respective lumps into plastic products of other lumps. According to the model, the lumps are preferably linked by monomolecular, irreversible first-order partial reactions. For example, lump L1 is linked to lump L2 with a partial reaction r. 12 connected, where the following relation applies: r 12 = k 12 *X Lump1 . k 12 is a reaction rate between Lump L1 and Lump L2. XLump1 is the mass fraction of plastic products in lump L1 (relative to the total mass of all lumps). The individual partial reactions can be described using the Arrhenius equation to account for the dependence on the pyrolysis temperature T: ^^1 ∗ 2 is an Arrhenius constant (also known as pre-exponential factor or frequency factor). ^^ ^^12 describes the activation energy of the respective transformation, in this case the activation energy for a conversion of plastic products from lump L1 to lump L2. R is the universal gas constant, and T is the (absolute) pyrolysis temperature. In the case where each partial reaction is modeled using an Arrhenius equation, each partial reaction is described by two reaction parameters. The reaction parameters per partial reaction from a lump Li to a lump Lj in this case are ^^ ^ ∗ ^ ^^ and ^^ ^^ ^^ ^^. The reaction model shows for each lump L i from L1 to L N-1 a partial reaction determined by at least one reaction parameter to describe a conversion of plastic products of this lump into plastic products of a lump L lying below and adjacent to it in terms of the boiling point temperature range i+1 i is an index that can take integer positive values ​​between one and the number of lumps N. The reaction model refers to pyrolysis in a pyrolysis reactor. The test data are experimental data obtained using the pyrolysis reactor. The reaction model is a function of the pyrolysis temperature and the pyrolysis duration. A pyrolysis model with three lumps L1, L2, and L3, in which a partial reaction from lump L1 to lump L2 and a partial reaction from lump L2 to lump L3 is considered, can, for example, have the following form. ^^ ^^3= ^^2× ^^ ^^ ^^ 3 2X1, X2, and X3 denote the respective mass fraction in Lump L1, Lump L2, and Lump L3, respectively. t denotes the pyrolysis time. The reaction rates k 12 and k 23 can be described using the Arrhenius equation, which also includes the pyrolysis temperature T. In this case, X1, X2, and X3 are functions of the pyrolysis time t and the pyrolysis temperature T, so, for example, X1 = X1(t,T). In this simplified case, the pyrolysis model has a total of four reaction parameters: ^^1 ∗ 2 and ^^ ^^12 , as well as ^^2 ∗ 3 and ^^ ^^23, the values ​​of which can be determined using the method according to the invention. The test data represent experimental data from pyrolysis runs for a single pair of values ​​consisting of pyrolysis temperature and pyrolysis time. Using the reaction model, interpolation can be carried out between the experimental data and these pairs of values, or extrapolation can be carried out beyond them. Using the reaction model, the boiling point distribution of plastic products from pyrolysis with any pyrolysis temperature and any pyrolysis time can be estimated. Typically, the pyrolysis temperature is between 300°C and 650°C. The pyrolysis time is typically between a few minutes and up to a few hours. For example, the pyrolysis time can have a value between 3 minutes and 100 minutes. The values ​​of the reaction parameters are determined by fitting the reaction parameters of the reaction model to the test data.Fitting in this case means that the values ​​of the reaction parameters are chosen so that the reaction model reproduces the test data as accurately as possible. For example, a sum of the squared distances between the reaction model and the test data can take on the smallest possible value (also known as the “least squares” method). Fitting can, for example, involve minimizing the distance from the test data to the reaction model. The distance can, for example, be calculated using an objective function. For example, the reaction parameters can be varied during fitting so that a minimal distance between the test data and the reaction model is found. The values ​​of the reaction parameters determined in this way lead to the minimal distance between the reaction model and the test data. State of the art reaction models with N*(N-1) / 2 partial reactions are known, i.e. partial reactions between all lumps are taken into account.Compared to the state of the art, the number of partial reactions has been reduced to less than N*(N-1) / 2. By reducing the number of partial reactions, the convergence of the fitting can be improved and the model complexity can be generally reduced. The decisive factor here is which partial reactions can be neglected and which cannot be neglected without significantly degrading the accuracy of the reaction model. As described in more detail above, it is crucial that the reaction model is L for each lump. i from L1 to L N-1 a partial reaction to describe a conversion of plastic products of this lump into plastic products of a lump L lying below and adjacent to it in terms of the boiling point temperature range i+1 because these reactions are the most critical for describing pyrolysis. For example, the reaction model cannot include partial reaction r 1Nfor a reaction between the first lump L1 and the last lump L N This partial reaction has the greatest difference in the boiling point temperature range of the two lumps involved and is therefore particularly irrelevant for the description of pyrolysis. Conversely, the reaction parameters of this partial reaction r 1Nnot be easy to initialize during fitting and also negatively influence the convergence of the fit. In general, the reaction model can have N lumps and fewer than N*(N-1) / M partial reactions, where M is a natural number greater than two that is smaller than the number of lumps N (i.e. N > M). For example, the reaction model can have a number N of at least 4 lumps and fewer than N*(N-1) / 3 partial reactions. The number N of lumps is preferably at least three, more preferably at least four, more preferably at least five, more preferably at least six, more preferably at least seven, more preferably at least eight, more preferably at least nine, more preferably at least ten, more preferably at least eleven, more preferably at least twelve. The number N of lumps can, for example, be at least seven. For example, the number of lumps can be at least twenty.Because the reaction model has a smaller ratio of partial reactions or reaction parameters to the number of lumps compared to the state of the art, it is possible to use a relatively large number of lumps without compromising the convergence of the fit. This makes it possible to increase the granularity of the prediction without significantly degrading the prediction quality. For example, the reaction model can have exactly (N-1) partial reactions. In this case, the reaction model only considers partial reactions between lumps that are adjacent in terms of the boiling point temperature range. In this case, the reaction model can be referred to as a sequential reaction model and features only sequential partial reactions. In this case, the reaction model maps a single reaction path from the first lump L1 to the last lump LN.For example, a conversion from a first lump L1 to a third lump L3 can only occur via a conversion of lump L1 to a second lump L2 and a further conversion of lump L2 to lump L3, where lump 2 lies between lump L1 and lump L3 in terms of the boiling point temperature range and is adjacent to both lump L1 and lump L3. Alternative pathways, such as a direct conversion from lump L1 to lump L3 (which are not adjacent to each other in terms of the boiling point temperature range), are not provided for in the sequential reaction model and are therefore not possible within the reaction model. The sequential partial reactions are the most crucial partial reactions between the lumps with regard to an accurate description of pyrolysis.By restricting the reaction model to (N-1) sequential partial reactions, convergence problems can be largely avoided. Furthermore, the fit and thus the values ​​of the reaction parameters do not depend on initial starting values ​​of the reaction parameters for the fitting. Despite the simplification, the reaction model accurately represents pyrolysis compared to known and more complex reaction models. Furthermore, restricting the reaction model to (N-1) sequential partial reactions allows for a significantly larger number of lumps to be considered without increasing the overall model complexity.The invention further relates to a method for determining reaction parameter values ​​of a reaction model for pyrolysis of a plastic starting material into plastic products, using a computer-implemented method according to the invention for determining reaction parameter values ​​of a reaction model for pyrolysis of a plastic starting material into plastic products, wherein the provision of test data comprises the following steps: - carrying out a plurality of pyrolysis runs with different pyrolysis temperatures and / or pyrolysis times in a pyrolysis reactor; - measuring a boiling point distribution of plastic products per pyrolysis run, wherein each boiling point distribution is assigned to a pyrolysis temperature and a pyrolysis time; - binning the individual boiling point distributions into the N lumps L1 to L. N, where each lump is assigned a boiling point temperature range to obtain test data. The test data were obtained using a number of pyrolysis runs, each of which was carried out with the same plastic starting material in the same pyrolysis reactor at a specific pyrolysis temperature and pyrolysis time. Each pyrolysis run produces plastic products that can be classified according to their boiling point. For each pyrolysis run, the boiling point distribution of the plastic products is measured, and the plastic products are thus classified according to their boiling point. Lechleitner, AE; Schubert, T.; Hofer, W.; Lehner, M. Lumped Kinetic Modeling of Polypropylene and Polyethylene Co-Pyrolysis in Tubular Reactors. Processes 2021, 9, 34. https: / / doi.org / 10.3390 / pr9010034 shows, for example, a pilot plant that is located after the pyrolysis reactor (iedownstream of the pyrolysis reactor) has a flash vessel (can also be called an evaporator). With the help of the flash vessel, plastic products that are in a gaseous state can be separated. For this purpose, a temperature and pressure in the flash vessel can be set in order to influence the separation (the so-called separation cut). Plastic products that are gaseous under the respective conditions (i.e. pressure and temperature) in the flash vessel can leave the evaporator and can be led to one or more cold traps. The plastic products removed in this way can be weighed, cooled and mixed, for example, with a bottom product from the flash vessel to form a liquid end product that can then be analyzed. Plastic products that are gaseous below 0°C can, for example, be collected using a gas balloon and then further analyzed.The analysis of gaseous plastic products can be carried out, for example, using gas chromatography according to DIN 51666:2007-01. This allows, for example, the calorific value, the specific gravity, and / or a detailed molecular composition of the plastic products to be determined. The boiling point distribution of the collected liquid plastic products and any carrier medium can be analyzed, for example, according to ASTM D7169-20e1 using simulated distillation. The boiling point distribution is weighted according to mass. Each experimentally determined boiling point distribution is assigned a pyrolysis temperature and a pyrolysis duration for the respective pyrolysis run. The boiling point distributions are each divided into a number N of lumps L1 to L. Nbinned, with each lump being assigned a boiling point temperature range in order to obtain the test data. Bind means a division or subdivision of the boiling point distribution into classes, the classes in this case being the lumps. Furthermore, the invention relates to a method for carrying out a pyrolysis of a plastic starting material into plastic products, comprising the following steps: - determining values ​​of reaction parameters of a pyrolysis reaction model using the computer-implemented method according to the invention; - specifying an intended boiling point distribution; - setting a pyrolysis temperature and a pyrolysis time by minimizing a distance between a boiling point distribution calculated using the reaction model and the previously determined values ​​of the reaction parameters and the intended boiling point distribution; and - carrying out the pyrolysis with the specified pyrolysis temperature and the specified pyrolysis time.The pyrolysis model is a function of the pyrolysis duration and the pyrolysis temperature. Using the pyrolysis model with the previously determined reaction parameters of the partial reactions, a (theoretical) boiling point distribution of the plastic products can be calculated for each pair of values ​​representing pyrolysis duration and pyrolysis temperature. The calculated boiling point distribution exhibits the same lumps that the pyrolysis model also predicts. In a subsequent step, a desired boiling point distribution is specified. The specified boiling point distribution can be continuous or as a histogram. The specified boiling point distribution can, for example, exhibit the same lumps as the reaction model. The specified boiling point distribution indicates the ideal boiling point distribution that the plastic products should exhibit after pyrolysis of a plastic starting material.The intended boiling point distribution can indicate which lumps the plastic products should preferentially be converted into through pyrolysis. In the next step, the pyrolysis temperature and pyrolysis duration are determined by minimizing the distance between a boiling point distribution calculated using the reaction model and the previously determined values ​​of the reaction parameters and the intended boiling point distribution. For example, the specified boiling point distribution and the calculated boiling point distribution can each be presented as a histogram and have the same lumps. In this example, the distance can be a sum of the differences between a specified cluster value of a lump in the specified boiling point distribution and a corresponding calculated cluster value of a lump in the calculated boiling point distribution.The distance can be weighted; for example, one lump can be weighted more heavily than the other lumps, so that the model represents the more heavily weighted lump most accurately. The pyrolysis temperature and the pyrolysis duration are each variables of the reaction model (and also of the pyrolysis). The specified pyrolysis temperature and the specified pyrolysis duration are the values ​​of these variables that result in the minimum distance between the specified boiling point distribution and the calculated boiling point distribution. In the final step, pyrolysis is carried out with the specified pyrolysis temperature and the specified pyrolysis duration. For this purpose, the pyrolysis reactor is operated such that the specified pyrolysis temperature and the specified pyrolysis duration are reached and maintained.For example, the same plastic starting material can be used as in the pyrolysis runs previously conducted to determine the reaction parameters of the partial reactions. For example, the same pyrolysis reactor can be used for the pyrolysis as was used in the pyrolysis runs previously conducted to determine the reaction parameters.Another method for performing pyrolysis of a plastic starting material into plastic products comprises the following steps: – determining values ​​of reaction parameters of a pyrolysis reaction model using the computer-implemented method according to the invention; – calculating a plurality of boiling point distributions using the reaction model and the previously determined values ​​of the reaction parameters, each calculated boiling point distribution being assigned a pyrolysis temperature and a pyrolysis duration; – selecting one of the calculated boiling point distributions to determine the pyrolysis temperature and the pyrolysis duration; and – performing the pyrolysis with the specified pyrolysis temperature and the specified pyrolysis duration. The selection of the calculated boiling point distribution can be based on predefined criteria, for example. For example, a boiling point distribution can be selected that has a maximum in a predefined lump.Pyrolysis at the specified pyrolysis temperature and the specified pyrolysis duration can lead to a boiling point distribution of the plastic products that essentially corresponds to the selected boiling point distribution. The invention further relates to a data processing system comprising means for executing the steps of the computer-implemented method according to the invention. For example, the data processing system can be a computer, such as a laptop. For example, the data processing system can comprise a processor and a hard disk.The means of the system for data processing can further be set up to carry out the following step: - calculating a pyrolysis temperature and a pyrolysis duration using the reaction model and the previously determined values ​​of the reaction parameters, wherein the pyrolysis temperature and the pyrolysis duration are set such that a distance between a boiling point distribution calculated using the reaction model and a predetermined boiling point distribution is minimized. The invention further relates to a computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the computer-implemented method according to the invention. The present invention is further explained with reference to exemplary embodiments shown in the figures, to which, however, it is not intended to be limited. Fig. 1 shows a schematic diagram of the structure of a pyrolysis reactor.2 shows a schematic representation of a reaction scheme between two lumps as part of the kinetic reaction modeling of lumps. Fig. 3 shows a schematic representation of a reaction model for pyrolysis with nine lumps. Fig. 4 shows a comparison of the kinetic decomposition rates of different plastic starting materials. Figs. 5A-5I show the deviations of the individual lumps of the reaction model as a function of the average pyrolysis temperature. Fig. 6 shows a measured boiling point distribution (dotted line) in comparison to a boiling point distribution calculated using the reaction model (solid line). Figs. 7A-7I show a parameter study of different pyrolysis temperatures and mass flows in the pyrolysis reactor. Example 1 Example 1 relates to a sequential reaction model with nine lumps for the co-pyrolysis of plastic mixtures with a heavy oil fraction and the determination of the reaction parameters of the sequential reaction model.In this case, the plastic feedstock is a plastic mixture with the heavy oil fraction. In this example, a kinetic reaction model based on nine lumps was used. The reaction model features exclusively sequential partial reactions without alternative reaction pathways. This circumstance enabled straightforward implementation of the reaction model. The reaction model was defined based on experimental data collected in a laboratory-sized tubular pyrolysis reactor with a maximum throughput of 2500 g / h. To determine the reaction model, three different types of plastics, mixed with a heavy oil fraction of varying composition, were used as the plastic feedstock for the pyrolysis reactor. The plastics were untreated polypropylene (PP), low-density polyethylene (LDPE), and high-density polyethylene (HDPE) in powder form (see Table 1).Due to the physical dimensions of the reactor, particularly the narrow inner diameter of the pipes, the maximum particle size of the plastic had to be less than 500 µm. For this reason, the plastic was ground under cryogenic conditions before use in the experiments. The maximum plastic-to-carrier medium ratio achievable by the plant design was 30 wt.%. Higher plastic contents would have led to blockages in the reactor feed system. The organic carrier medium used was a readily available byproduct from the petroleum refinery process. It is a predominantly aliphatic medium with an aromatics content of approximately 25%, a density of 880 kg / m³, and a calorific value of 45 MJ / kg. Since the carrier medium is also cracked under the conditions prevailing in the reactor, the (kinetic) reaction parameters were determined only for the carrier medium in preliminary tests. Table 1.Specifications of the plastic types used for the pyrolysis experiments (ie plastic starting materials) Molecular mass Heating value Calorific value TGA (Mw) Inflection point (g / mol) (kJ / kg) (kJ / kg) (°C) Polypropylene 3.624∙10 44.510 47.343 484 LD-Polyethylene 2.3834∙10 43.409 46.159 500 HD-Polyethylene 2.0275∙10 43.525 46.409 509 Experimental setup and procedure The experiments were carried out in a pyrolysis reactor 1 (also called laboratory reactor), which was specially built for this process and is shown schematically in Fig. 1. Pyrolysis reactor 1 essentially corresponds to the reactor described in Schubert T, Lehner M, Hofer W (2018) Experimental and modeling approach of LDPE thermal cracking for feedstock recycling, 14th MINISYMPOSIUM CHEMICAL & PROCESS ENGINEERING and 5th PARTICLE FORUM Book of Abstracts with some adaptations of the experimental procedure.The liquid carrier medium and the plastic powder were mixed manually prior to the test runs in predefined mass ratios between 0 and 30 wt% plastic. The mixture (i.e. the plastic starting material) was then filled into a storage container 2 and continuously stirred there. The plastic starting material is conveyed from the storage container 2 by means of a pump 3 (in this case an eccentric screw pump). Two reactors 4 and 5 were arranged downstream of the pump 3. The reactors 4, 5 were pipe coils 6, which were heated in sand baths 7 to the required temperature range of 400 °C to 550 °C. The length of each reactor coil 6 could be varied between 8 m and 24 m in order to further adjust the residence time (i.e. the pyrolysis time) without changing the flow pattern. The actual pyrolysis took place in reactors 4 and 5. After the medium (i.e.After the pyrolysis product (the plastic products after pyrolysis) had passed through reactors 4, 5, it was cooled to approximately 90 °C by an air cooler 8 and an oil cooler 9. The pressure in the system could be regulated with a valve 10 (either a manual valve or an automatic diaphragm valve) to release the products to atmospheric pressure. For all experiments, the pressure in the system was regulated to 15 bar. A flash vessel 11 was arranged downstream of the oil cooler 9 and the valves 10. The plastic products, which were gaseous under the conditions in the flash vessel 11, left it through a header and were directed to a first cold trap 12 and a second cold trap 13. The first cold trap 12 was set to a temperature of 15 °C, while the second cold trap 13 was set to a temperature of 0 °C.Plastic products present at the bottom of the flash vessel 11 are referred to as bottom products and have left the flash vessel through a bottom line 14. Plastic products collected by the first cold trap 12 are referred to as top products and have left the first cold trap 12 through a top line 15. Plastic products collected by the second cold trap 13 are referred to as light products and have left the second cold trap 13 through a light products line 16. The pyrolysis products (i.e. the plastic products), which were gaseous below 0 °C after the second cold trap 13, were sampled with a gas balloon (not shown). After product removal, all liquids were weighed, cooled in a freezer and mixed to form the final liquid product, which was analyzed. The test conditions, i.e.The pyrolysis temperature and the pyrolysis time were varied mainly by the temperature of the sand baths 6, the length of the reactors 4, 5 and the power of the pump 3. The pump power regulated the mass flow in the reactors 4, 5 and has a minimum flow of 300 g / h and a maximum flow of 2500 g / h. This results in residence times (i.e. pyrolysis times) in a range from 3 min to 60 min, depending on the operating conditions. ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ The residence time can be calculated differentially for each reactor volume element and summed up. A major influence on the residence time (which corresponds to the pyrolysis time) is the reactor temperature, as the vapor content of the medium and thus its average density depend heavily on it. Regarding chemical reactions, the residence time and temperature are independent parameters for the reaction rate.However, physical phenomena also occur in a flow tube that can lead to a correlation between the two parameters. For example, rising temperatures could cause the boiling point to be partially exceeded, which could lead to the formation of vapors. In addition, reactions could occur to form lighter products (or low-boiling lumps), which would increase the vapor content. This could reduce the average density. This would increase the volume flow, which could lead to a shorter residence time at a constant reactor volume. The gaseous plastic product collected using the gas balloon was analyzed using gas chromatography according to DIN 51666:2007-01. The results are the calorific value, specific gravity, and molecular composition of the gas phase.The true boiling point curve of the liquid products and the carrier medium was analyzed according to ASTM D7169-20e1 using simulated distillation (SIM-Dist). Reaction model with 9 lumps Kinetic modeling using lumps is a standard approach for modeling the kinetics of hydrocarbon decomposition. This approach is necessary because the typical starting material for hydrocarbon pyrolysis is a mixture of many different molecules, and considering every single real reaction between each molecule is not feasible. In this method, each individual component of the plastic products is assigned to a specific lump in a reaction network. The lumps were divided according to their boiling point. Alternatively, the division can also be based on other material properties such as molecular structure or density.Each lump acts as a pseudo-component with representative material properties derived from the molecules it contains. The cleavage reactions between the lumps were modeled as irreversible, one-step, monomolecular reactions, as schematically shown in Fig. 2, where the reaction rate r (cf. Eq. (1)) follows the Arrhenius law (cf. Eq. (2)). ^^. 12 = ^^ 12 ∙ ^^^^ ^^ ^^ ^^1 (1) ^^ 12 = ^^1 ∗ 2 ∙ ^^ − ^^ ^^12 ^ ^∙ ^^(2) In the reaction model in this example, the lumps were separated according to their boiling point. First, the boiling point temperature ranges of interest to the refinery were defined, resulting in the classification shown in Table 2, from gas to bottom products. Plastic / wax lumps were defined as all components with a boiling point above 600 °C, which represents the end of the boiling point temperature range of the organic carrier medium. A complete reaction network with nine lumps (i.e., the number N of lumps is nine), in which each heavier lump (i.e., each of the lumps with a higher boiling point temperature range) reacts with each lighter lump (i.e., each of the lumps with a lower boiling point temperature range), would consist of N*(N-1) / 2, i.e., 36 different reactions, each with two kinetic reaction parameters for each reaction.The sequential reaction model only considers one reaction for each heavier lump on the next lighter lump that directly follows it in terms of boiling point. This significantly reduces the number of reactions to eight unknown reactions with 16 kinetic parameters. The resulting reaction model is shown schematically in Fig. 3. The sequential reaction model considers the decomposition of mixtures of plastics and carrier medium in such a way that there is no interaction between the materials. The reaction model can be solved independently for the carrier medium and each plastic in the plastic feedstock. The final mass fraction of lump j is the sum of all lumps with the same boiling point-temperature range from n separate components (Eq. (3)). Table 2. Boiling point-temperature range and number of carbon atoms for the nine lumps of the reaction model Lump Name Lump Boiling point Number of No.Temperature range Carbon atoms (°C) (-) Plastic / Wax 1 >600 >55 (P) Bottom products 2 450 – 600 30-55 (Res) Heavy oil (HO) 3 400 – < 450 23-30 Spindle oil 4 350 – < 400 18-22 (SO) Gas oil (GO) 5 225 – < 350 13-17 Kerosene 6 165 – < 225 10-12 (Kero) Naphtha 7 20 – < 165 5-9 LPG 8 -120 – < 20 2-4 Gas 9 < - 120 1. Simulation and Fitting of Reaction Parameters The reactor was programmed in PetroSim 7.2 as a custom operating unit in Visual Basic. For the simulation, the laboratory plant was divided into nine parts according to its geometry. Each part was simulated as a tubular plug-flow reactor and differs from the others in its geometry, ambient temperature, and pipe insulation. For example, the first part is a horizontal pipe, the second part is a vertical pipe, and the third is a downward-flowing coil. All of these geometries have different formulas for the heat transfer coefficient and different ambient temperatures. The initial conditions for the integration of the first reactor part are the measured mass flow rate, the measured feed temperature, and the feed concentration in lumps. The initial conditions for the subsequent part are the solution of the differential equations of the previous part.In this model, the mass balance with the lump reaction, the energy balance for the fluid temperature required for the reaction rates, and the pressure drop equation for a two-phase fluid were solved. The differential equations were discretized as a one-dimensional grid along the length of the reactor tube (cf. Eqs. (4), (5), (6)). The Darcy friction coefficient for the pressure drop calculation is calculated using the Beggs-Brill correlation for two-phase flows (cf. (1996) Standard handbook of petroleum & [and] natural gas engineering. Gulf Publ, Houston, TX). (. 4) (5) (6) Δ ^^ ^^ ∙ ^^ ∙ ^^ 2 = Δ ^^ ^^ ^^∙ 2 The kinetic parameters of the model were fitted using Matlab and the surrogate optimization solver of the global optimization toolbox. Surrogate optimization is generally used for the global optimization of expensive cost functions for which no derivatives are available. For the fitting, PetroSim was accessed as a Matlab COM server to write the experimental parameters and measurements into the suitcase and obtain the post-computation results. The simulation results are the lump composition of the simulated products compared to the measured real lump composition. The model itself is treated as a black box by the surrogate solver, which does not require a gradient for fitting. The objective function Obj used in this study is the sum of the squared errors between the experimental and calculated lump compositions according to Equation (7). Since it is assumed that there are no interactions between the components, the kinetic reaction parameters can be fitted first for the support medium and then for each plastic individually by conducting experiments with only the support medium and only with the individual plastic (i.e., a plastic feedstock with only one plastic). The parameter ranges and the number of experiments for each plastic composition are listed in Table 3. Two to three experiments from each plastic feedstock were randomly selected for the evaluation of the kinetic parameters. These selected experiments and all experiments with mixed plastics were used only for the evaluation of the model parameters and not for model training. Table 3: Data for the fitting of the kinetic reaction parameters.Mixed plastic runs were used to evaluate the results. Number of runs for testing Temperature Mass Reactor Length Plastics Flow Range Range Range Proportion of Fit Evaluate (-) (-) (°C) (g / h) (m) (wt.%) Carrier 21 3 410-520 600-2500 32-48 0 medium Polypro- 10 2 440-520 600-2500 32-48 10-30 pylene LD-Poly- 20 3 450-530 600-2500 48 10-30 ethylene HD-Poly- 20 3 450-540 600-2500 48 10-30 ethylene Plastics 0 32 440-530 600-2500 32-48 30 Mixture Simulation and Fitting of Reaction Parameters The experimental results showed a significant influence of the process parameters and the composition of the plastic feedstock on the boiling point distribution of the plastic products after the pyrolysis runs. An overview of the experimental process data is provided in Table 4. Table 4. Experimental parameters for the figures. No. Outflow Plas- Tempera- Temperature Mass Flow Material ture Reactor 5 effluent residence time material Reactor 4 (-) (-) (wt.%) (°C) (°C) (g / h) (min) 257 Carrier 0 450 450 1050 ~17 (C) C+PP C+LDPE C+HDPE 275 C+MIX 30 460 470 880 19.9 Decomposition kinetics of the different plastic types Since the heaviest lump (i.e. the lump with the highest boiling point-temperature range and the longest hydrocarbons) consists of plastic and its heaviest wax products, the k1 partial reactions from the respective kinetic nets can be regarded as the decomposition rates of the plastics. Figure 4 shows that polypropylene broke down much faster than low density polyethylene and high density polyethylene over most of the temperature range studied. The reaction rate of low density polyethylene is twice that of high density polyethylene over the temperature range studied. At 500 °C, the reaction rates of all plastics approach a similar value and the differences become smaller.The activation energies and frequency factors of the reactions are shown in Table 5. Table 5. Activation energy and frequency factor of the k12 decomposition reactions of PP, LDPE, and HDPE. Reaction Frequency Factor Activation Energy (1 / s) (kj / mol) k – PP 1.84E+09 167.318 k – LDPE 3.21E+19 316.124 k – HDPE 7.16E+20 338.287 Accuracy of the reaction model The calculated kinetic parameters (i.e., the reaction parameters) were evaluated using experimental data that were not used for fitting the reaction parameters. The criterion for a good model fit was that the maximum deviation of the simulated data from the experimental values ​​was less than 0.05 kg / kg (cf. Eq. (8)) and no obvious systematic error was observed. Figures 5A to 5I show the deviation between the simulated and measured mass fraction for each evaluation experiment plotted against the average temperature in the reactor.No systematic error is evident across all lumps and the entire temperature range. It can also be seen that the accuracy for most lumps lies within the accuracy criterion defined above. The least accurately represented lump is the plastic / bottom products lump. For this lump, two of the experiments show a slightly higher deviation than the threshold, with a maximum deviation of 0.07 kg / kg. Despite the higher deviation, no systematic error is evident, so the kinetic parameters are a good fit despite these two outliers. The higher deviation for the heaviest lump can be explained by the measurement inaccuracy of SimDist, which is less accurate at higher boiling points. Figure 6 shows that the boiling point distributions of the simulation (solid line) are in good agreement with the measured boiling point distribution (dotted line). Test series with a laboratory reactor The kinetic model was used in a case study to find optimal test parameters for the laboratory reactor (which in this case is the pyrolysis reactor). The case study was carried out with a plastic feedstock consisting of 20 wt% LDPE, 10 wt% PP and 70% carrier medium. A separate reaction model was determined for each of the different plastic feedstocks. The individual models can be summed (weighted according to the respective proportion of plastic feedstock). Figures 7A to I show the yield of the lumps from the reactor over the entire temperature and mass flow range. It can be clearly seen that temperatures above 470 °C have a positive influence on the yield of plastic products from more valuable lumps with intersection points below 350 °C. Above this temperature, almost all of the plastic decomposes into the lighter fractions (orLumps) kerosene and gas oil, which exhibit a clearly recognizable maximum yield of 0.14 wt.% and 0.25 wt.%, respectively. Summary of Example 1 Pyrolysis processes for the chemical recycling of plastics are a necessary technology for a fully circular economy. In this example, it was shown that a simple lump-based kinetic reaction model, which has nine lumps and exclusively sequential partial reactions, can model the decomposition of polyolefins in a carrier medium with very good accuracy. The resolution of the boiling points of the plastic products is more precise than with other reaction models with fewer lumps, while the number of unknown reaction parameters for fitting is limited.The maximum deviation of the modeled mass fraction from the experimental results is less than 0.05 kg / kg for most lumps, with the exception of the plastics residue lump which has a maximum deviation of 0.07 kg / kg. This accuracy was demonstrated in the relevant temperature range for slow pyrolysis above 400 °C and below 500 °C. A case study for the laboratory plant showed that there was a clear temperature window between 470 °C and 520 °C for maximum yield of kerosene or gas oil. List of abbreviations C Carrier medium Cal Calculated value Exp Experimentally measured value GO Gas oil HDPE High-density polyethylene HO Heavy fuel oil HTC Heat transfer coefficient IBP Initial boiling point Kero.Kerosene LDPE Low-density polyethylene LKM Reaction model with lumps LPG Liquefied petroleum gas Obj Objective function P Plastic PP Polypropylene Res Bottom products SO Spindle oil TBP Actual boiling point Glossary of symbols C Number of carbon atoms c Heat capacity d Diameter of the reactor Ea Activation energy for the conversion of lump i to lump jk Arrhenius constant (frequency factor) for the partial reaction from lump i to lump jk Rate constant for the partial reaction from lump i to lump jp Pressure R Gas constant (J / molK) r Partial reaction from lump i to lump j T Temperature v Flow velocity X Mass fraction of lump j X Mass fraction of lump j of component iz Length of the reactor α Heat transfer coefficient ΔH Reaction enthalpy λ Darcy friction factor ρ Density.

Claims

Claims:

1. Computer-implemented method for determining values ​​of reaction parameters of a reaction model for a pyrolysis of a plastic starting material into plastic products, the method comprising the following steps: - Providing test data comprising a plurality of boiling point distributions of plastic products, each boiling point distribution being assigned a pyrolysis temperature and a pyrolysis time, the boiling point distributions each being divided into a number N of lumps L1 to L N binned, each lump being assigned a boiling point temperature range; - determining a value of the reaction parameters by fitting the reaction parameters of the reaction model to the experimental data; the reaction model for each lump L i from L1 to L N-1a partial reaction determined by at least one reaction parameter to describe a conversion of plastic products of this lump into plastic products of a lump L lying below and adjacent to it in terms of the boiling point temperature range i+1wherein the reaction model has fewer than N*(N-1) / 2 partial reactions.

2. Computer-implemented method according to claim 1, characterized in that the number N of lumps is at least seven.

3. Computer-implemented method according to one of claims 1 or 2, characterized in that the reaction model has exactly (N-1) partial reactions.

4. Method for determining values ​​of reaction parameters of a reaction model for a pyrolysis of a plastic starting material into plastic products using a computer-implemented method according to one of the preceding claims, characterized in that the provision of test data comprises the following steps: - Carrying out a plurality of pyrolysis runs with different pyrolysis temperatures and / or pyrolysis durations in a pyrolysis reactor - measurement of a boiling point distribution of plastic products per pyrolysis run, with each boiling point distribution being assigned to a pyrolysis temperature and a pyrolysis duration; - binning of the individual boiling point distributions into the N lumps L1 to L N, wherein each lump is assigned a boiling point temperature range in order to obtain test data.

5. A method for carrying out pyrolysis of a plastic starting material into plastic products, comprising the following steps: - determining values ​​of reaction parameters of a pyrolysis reaction model using the computer-implemented method according to one of claims 1 to 3 or the method according to claim 4; - specifying a desired boiling point distribution; - establishing a pyrolysis temperature and a pyrolysis duration by minimizing a distance between a boiling point distribution calculated using the reaction model and the previously determined values ​​of the reaction parameters and the desired boiling point distribution; and - carrying out the pyrolysis at the specified pyrolysis temperature and the specified pyrolysis duration. 6.A data processing system, characterized by means for carrying out the steps of the computer-implemented method according to one of claims 1 to 3.

7. A data processing system according to claim 6, characterized in that the means are further configured to carry out the following step: - calculating a pyrolysis temperature and a pyrolysis duration using the reaction model and the previously determined values ​​of the reaction parameters, wherein the pyrolysis temperature and the pyrolysis duration are set such that a distance between a boiling point distribution calculated using the reaction model and a provided boiling point distribution is minimized.

8. A computer program product, comprising instructions which are used in the. Execution of the program by a computer causes the computer to carry out the steps of the computer-implemented method according to one of claims 1 to 3.

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