# Comparing different reaction models for combustion kinetics of solid recovered fuel

- 50 Downloads

## Abstract

Possible utilization of SRF (solid recovered fuel) in the energy industry is a widely investigated topic, because even though it is economically feasible, its complex reactions make a steady operation hard to maintain. SRF is prepared as a mixture of the well-combustible (but not recyclable) parts of municipal and industrial waste, which consists of mainly various papers, plastics and textiles with very different combustion characteristics. To describe the kinetics of a complex sample like this, the utilization of more advanced methods is recommended. In this work, genetic algorithm was used to fit four different reaction models to thermogravimetric data measured in oxidative atmosphere, and the results were compared. It was concluded that the tested distributed activation energy model and the simple and expanded *n*th-order models offer only a slightly better fitting value for this special sample, which promotes the usage of the simpler first-order model.

## Keywords

SRF Reaction kinetics Genetic algorithm DAEM## Introduction

Solid recovered fuel (SRF) is a waste-derived fuel produced from various groups of non-hazardous municipal, industrial and commercial wastes that are not recyclable but still have good combustion characteristics. Its classification is determined by the EU standard EN 15359:2011, which helps the producers and the consumers to find a common language when specifying the needs and hopefully maximizing the utilization. With the proper methods, it is possible to create fuels with properties comparable to classical biomasses and coals, creating the possibility of efficient co-combustion without the need of complex boiler reconstruction. It is important to mention that only the non-recyclable part of the waste should be the source of SRF. Albeit both recycling and combustion directly reduce the amount of unprocessed landfilled waste, recycling is an economically and environmentally more feasible process. Regarding the most recent related directive [the Circular Economy Package (January 2018)], EU members should aim to reduce landfill to a maximum of 10% of municipal solid waste by 2030. In an ambitious environment like this, every opportunity to reduce landfill is welcomed. A very similar type of fuel is the refuse-derived fuel (RDF), which shows no major technological differences; the distinction is mostly legal.

To achieve efficient boiler operations with this fuel, it is essential to have reliable knowledge about the nature of the relevant reactions. Thermogravimetric analysis (TGA) is a powerful tool for this, but because of its very heterogeneous composition, the combustion characteristics of SRF are challenging to determine. The main problem is that TGA commonly works with very small samples (a few milligrams), which assumes a very precise sampling, measuring and evaluation process, and to create a representative sample from a suboptimal material like this, sometimes requires compromises.

The decomposition of solid waste-derived fuels was investigated quite thoroughly in the past few years [1, 2, 3, 4, 5, 6, 7], but the reaction kinetics were covered only a few times. To acquire the parameters describing the kinetic behavior, different methods are available, which could be categorized as model-free and model-fitting methods. For similar fuels, the most widely used ones were collected and compared by Cepeliogullar et al. [1]. Acceptable results were achieved by all methods with some limitations, which shows that there is no obviously best way to handle mixed solid fuels; every case needs special attention and thorough investigation. The three most commonly used model-free methods were applied for two kind of solid wastes by Radojevic et al. [2] in nitrogen atmosphere. A more advanced model-fitting method was applied by Conesa et al. [3]. Three parallel *n*th-order reactions were considered in inert and air atmospheres, and the kinetic parameters were calculated using the least squares optimum seeking method. Satisfactory results were presented in all cases, although only the pre-exponential factors were considered different in case of the different atmospheres. One of the most widely investigated fuels is the sewage sludge. In the work of Niu et al. [8, 9], pure sewage sludge with different moisture contents and its blend with coal were evaluated using the model-free Flynn–Wall–Ozawa (FWO) method. Another special recovered fuel type is the automotive shredder residue (ASR), investigated by Conesa et al. [10]. In the study, distributed activation energy method (DAEM) was applied with least squares optimization technique. To describe the complex reactions of the sample, three pseudo-components were defined: 5, 15 and 30 °C min^{−1} heating rate, three different atmospheres (0, 10 and 20% oxygen) were measured, and the DAEM results were compared to the simple first-order ones. The difference in inert atmosphere was small, but in the presence of oxygen the DAEM become more reliable. DAEM was used successfully multiple times to determine the kinetic parameters of other complex solid fuels as well [11, 12, 13, 14]. The principles of the DAEM were originally presented by Anthony et al. [15].

Thus, in most cases, either nitrogen or other inert gas was used as the atmosphere for the TGA measurements. It is feasible, if the aim of the work is identifying the various gases released or using as an input in a model for pyrolysis technology. However, the combustion kinetics of solid (not just waste-derived) fuels are more rarely investigated, which is understandable, as during combustion the reactions are much complex and harder to distinguish. Also, it is much harder to taken a proper TGA measurement, because in combustible atmosphere the pyrolytic and combustion reactions occur simultaneously, and the samples tend to self-ignite resulting in unrealistic behavior in the measured graphs, which makes most kinetic evaluation method unreliable [10]. But there are cases, for example if the determined kinetic parameters supposed to be used as an input for a physical model with combustion, where it is necessary to consider combustion in the kinetics as well.

Instead of distinguishing every possible reaction, it is common to substitute them with only a few pseudo-reaction groups. Identifying the origin of these is quite challenging for these complex samples. In the literature, it is common to relate them to the major waste components, which are cellulosic materials like paper, textiles and sometimes biomasses, and plastics [1, 2, 3, 4, 5, 6, 7]. For combustion, this means three main reaction groups, two of which are responsible for the volatile releases at around 300 °C and 470 °C. The first one describes the pyrolysis of all cellulosic materials, and the second shows the decomposition of the plastics. The third reaction takes place between 600 and 700 °C; it is related to the combustion of all remaining char, mostly from the cellulosic components [1, 2, 3, 4, 5, 6, 7].

The aim of this work is to simultaneously evaluate the combustion kinetics of a complex SRF sample with the most commonly used reaction kinetics models. The results of the models will be compared and rated in regard to precision and usability as an input of more complex combustion models. Sensitivity analysis will be also performed for every optimizable parameter.

## Experimental

Proximate and ultimate analysis of the sample (dry basis)

Ash/mass% | 21.7 |

Volatile/mass% | 66.9 |

Char/mass% (by difference) | 11.4 |

S/mass% | 0.145 |

C/mass% | 45.40 |

H/mass% | 6.12 |

N/mass% | 1.322 |

O/mass% (by difference) | 47.013 |

LHV/kJ kg | 17.830 |

A TA Instruments SDT 2960 simultaneous TG/DTA device was used for the thermal analysis in air atmosphere (130 mL min^{−1}) as described in Bakos et al. [16]. The measurements were taken at 5, 10 and 15 °C min^{−1}. These rates are relatively small compared to what generally used, but on higher rates the self-ignition of sample was too significant to get reliable results. Because of this, and to minimize the impact of the mass and heat transfer phenomena, the sample size was decided to be around 2 mg, as it was suggested by Várhegyi et al. [14].

### Kinetic models

To describe the combustion of the sample, a model-fitting method was selected. With the increase in numerical possibilities in the past years, the model-fitting methods tend to became more and more powerful tools in reaction kinetics. However, it is advisable to consider the basic drawbacks of these kinds of calculations. These were highlighted numerous times in the past, most recently by Várhegyi et al. [17]. The most important is that albeit it is really tempting to use only one measured data with one heating rate (as it is numerically possible), the result from that is only usable for that exact heating rate. The reason is that in that case the system is very ill-defined, and a conversion graph could be described with more sets of parameters. Evaluating more conversion curves with different heating rates simultaneously, however, obligates the optimization process to find parameters that can fit measurements with different heating programs at the same time.

*A*is the pre-exponential factor,

*E*is the activation energy,

*R*is the universal gas coefficient and

*T*is the absolute temperature of the sample.

List of the tested reaction models

Reaction model | Applied equation | |
---|---|---|

First order | \(\frac{{{\text{d}}x}}{{{\text{d}}t}} = \sum A_{\text{i}} \exp \left( {\frac{{E_{\text{i}} }}{RT}} \right)\left( {1 - x} \right)\) | (5) |

| \(\frac{{{\text{d}}x}}{{{\text{d}}t}} = \sum A_{\text{i}} \exp \left( { - \frac{{E_{\text{i}} }}{RT}} \right)\left( {1 - x} \right)^{\text{n}}\) | (6) |

Expanded | \(\frac{{{\text{d}}x}}{{{\text{d}}t}} = \sum A_{\text{i}} \exp \left( { - \frac{{E_{\text{i}} }}{RT}} \right)\left( {x + z} \right)^{\text{m}} \left( {1 - x} \right)^{\text{n}}\) | (7) |

Distributed activation energy model (DAEM) | \(\begin{aligned} \frac{{{\text{d}}x\left( t \right)}}{{{\text{d}}t}} & = \mathop \sum \limits_{j} \mathop \smallint \limits_{{E_{\text{j}} - \sigma }}^{{E_{\text{j}} + \sigma }} D_{\text{j}} \left( E \right){\text{d}}E\frac{{{\text{d}}x_{\text{j}} \left( {t,E_{\text{j}} } \right)}}{{{\text{d}}t}} \\ & = \mathop \sum \limits_{j} \mathop \smallint \limits_{{E_{\text{j}} - \sigma }}^{{E_{\text{j}} + \sigma }} D_{\text{j}} \left( E \right){\text{d}}EA_{\text{j}} \exp \left( { - \frac{{E_{\text{j}} }}{RT\left( t \right)}} \right)\left( {1 - x_{\text{j}} \left( {t,E} \right)} \right) \\ \end{aligned}\) | (8) |

The first one is a simple first-order conversion function (*n *= 1, Eq. 5), the second one is a more general *n*th-order reaction (\(n \ne 1,\) Eq. 6), and the third one is expanded with \(\left( {x + z} \right)^{\text{m}}\) (Eq. 7) as it was suggested in the earlier work of Várhegyi et al. [18].

The third model has the most parameters, and some of them could be neglected in some cases, as it was already suggested [18], because more parameters to optimize demand more computation capacity, and in most cases, the precision of the results could not be increased above a limit. However, it was not investigated for this kind of samples, so in current work it was decided to let it in the original form. The influence of the different parameters and their potential neglecting will be evaluated by sensitivity analysis later in this work.

*k*) with the corresponding activation energies and with the share defined by the distribution function. In summary, it results in the real conversion of

*j*pseudo-component (Eq. 10).

### Parameter fitting

Because of the high number of optimizable parameters, the fitting was performed numerically with genetic algorithm (GA). It is a commonly used optimum seeking method, which is based on the Darwinian evolution theory. The basic principles and the mathematic background are summarized by McCall [19]. It works by producing generations of species as the solutions of the same problem with different parameters. Every generation is evaluated by comparing the results to a desired value, for example measured data, based on which the parameters (species) resulting in the best fits are selected and used to create the new generation. This method ensures that the difference between the benchmark data and the results of the best parameters converges to zero in every generation. The result of the function generating the species should be one number at any time, which is called the fitness value (*F*), and the function that provides it is called the fitness function.

A serious drawback is that the method is very computation heavy, as the same problem is solved multiple times with different parameters without any further simplification, as every generation should have an exact number of independent species that needs to be compared. However, this independency has some benefits as well, and they can be computed simultaneously using multi-core workstations, which significantly decreases the necessary computation time.

Least squares method as the central element of the process has another benefit, as its structure is quite robust, and the actual reaction models can be changed easily while letting most of the code intact.

### Sensitivity analysis

^{2}at both ends, and for high, it should be above 10

^{2}at least at one end.

## Results and discussion

### Experimental results

Three reaction groups (cellulosic materials, plastics and the remaining char) were considered based on the common method in other papers, as it was detailed earlier. These reaction groups are very general; they could be divided to smaller parts, but without special measurements [3] that would be only speculation, as the composition of the sample is very diverse. Moreover, more reaction groups would not lead to more precise results, so it would not have any practical benefits.

*n*th-order and the expanded

*n*th-order models and the DAEM as continuous lines, respectively.

An interesting observation on the experimental (dashed) curves in Fig. 2 is that an elevated heating rate systematically results in a decreasing amount of char remaining after the second step. This may show a certain capability of char for further gasification if more time (slower temperature increase) is available. Also note that none of the investigated models handle this behavior (Figs. 2–5) as char fractions are considered constant in all cases.

### Kinetic parameters

Kinetic parameters in case of three parallel first-order reactions, *FV*: \(2.51 \times 10^{ - 4}\)

Reaction | 1 | 2 | 3 |
---|---|---|---|

| \(4.02 \times 10^{5}\) | \(4.34 \times 10^{5}\) | \(2.83 \times 10^{5}\) |

| 86,829 | 108,348 | 135,578 |

| 0.47 | 0.38 | 0.13 |

To increase the quality of the fitting, the applied reaction model should be improved. Three upgraded methods, a basic and an expanded *n*th-order reaction model and a DAEM were used for that as described earlier. Also, it was decided to let the mass fractions of the reaction groups slightly vary as well, which means that the exact amount of the various components is part of the model, not defined or measured in any other independent way.

*n*th-order reactions, Table 5 for the expanded

*n*th-order model and Table 6 for the DAEM. The distribution of activation energies is shown in Fig. 6.

Kinetic parameters in case of three parallel *n*th-order reactions, *F*: \(2.31 \times 10^{ - 4}\)

Reaction | 1 | 2 | 3 |
---|---|---|---|

| \(9.13 \times 10^{4}\) | \(1.86 \times 10^{5}\) | \(8.42 \times 10^{4}\) |

| 79,304 | 104,081 | 126,336 |

| 0.53 | 0.35 | 0.12 |

| 1.52 | 1.38 | 1.43 |

Kinetic parameters in case of three parallel expanded *n*th-order reactions, *F*: \(2.28 \times 10^{ - 4}\)

Reaction | 1 | 2 | 3 |
---|---|---|---|

| \(8.19 \times 10^{4}\) | \(1.86 \times 10^{5}\) | \(9.55 \times 10^{4}\) |

| 77,560 | 103,154 | 124,488 |

| 0.52 | 0.36 | 0.12 |

| 0.25 | 0.14 | 0.47 |

| 1.61 | 1.49 | 1.13 |

| 0.0165 | 0.0788 | 0.01 |

Kinetic parameters in case of DAEM with three parallel first-order reactions, *F*: \(2.07 \times 10^{ - 4}\)

Reaction | 1 | 2 | 3 |
---|---|---|---|

| \(2.82 \times 10^{5}\) | \(2.01 \times 10^{5}\) | \(4.99 \times 10^{4}\) |

| 85,134 | 104,020 | 122,770 |

| 0.49 | 0.38 | 0.13 |

\(\sigma\)/J mol | 2462 | 3550 | 2040 |

*n*differ from unity led to an improved fitness value, which was only slightly increased in case of the expanded model. The lowest fitness value came from the DAEM, which resulted in approximately 20% decrease compared to the first-order model as Fig. 7 shows.

The pre-exponential factors and activation energies are similar for the first three models and slightly different for the DAEM. These values are hard to be compared to the results of other works with similar samples, as those tend to highly scatter. Conesa et al. [3] with a similar method calculated much higher pre-exponential factors (with magnitudes of 10^{6}, 10^{19} and 10^{21}) with also higher activation energies between 98 and 325 kJ mol^{−1}. However, in case of the *n*th-order model, the reaction orders were below unity, or almost 3 in one case.

Cepeliogullar et al. [1] showed pre-exponential factor with the same magnitude and similar activation energies, with a different model-fitting method (Coats–Redfern) and only for pyrolysis. For the reaction order, five values were tested as parameters between 0 and 2, and it was shown that *A* and *E* were increasing linearly with that. The best fit was found at *n *= 1.5, which is close to the reaction orders of this work’s models.

Luo et al. [22] investigated separately the major components of solid wastes with macro-TGA and FWO method. Here the activation energies of the biomass components were between 23 and 51 kJ mol^{−1}, and for the plastics, they were between 33 and 76 kJ mol^{−1}. These values are a slightly smaller than the ones reported here.

It is clear that with the freedom of the model-fitting methods, it is possible to create infinite number of equally correct models with very different parameters, but it is clear that these values are not comparable without clarifying the measurement technique, the applied model and the used method.

### Sensitivity analysis

Sensitivity levels of parameters

| |||

E | High | High | Medium |

A | Medium | Medium | Poor |

| |||

| High | High | Medium |

| Medium | Medium | Poor |

| Medium | Medium | Poor |

| |||

| High | High | Medium |

| Medium | Medium | Poor |

| None | None | None |

| Poor | Poor | None |

| Medium | Medium | None |

| |||

| High | High | Medium |

\(\sigma\) | None | None | None |

| Medium | Medium | Poor |

It is also clear for the more complex models that the sole effect of the new parameters is quite poor, and the increment rather comes from the modified model structure. In case of the two *n*th-order models, the reaction order has medium impact, which is a little higher for the expanded model. Given the expanded model, the parameter *m* has quite low, and *z* almost non-existent relevance, so those parameters could be neglected, as it was suggested earlier [18].

## Conclusions

In case of complex solid fuels, choosing the correct reaction function could increase the fitness of a kinetic model. However, this complexity could lead to precision problems, especially if oxidative atmosphere is used during the measurements. This should be avoided at all cost, for which detailed suggestions are available in the literature, but if the future application demands suboptimal operation conditions, the already slightly flawed measured data could not be improved by choosing a more precise reaction model.

To investigate this problem, four different reaction models were applied to the thermal decomposition of a quite heterogeneous sample, which is also inclined to self-ignite. For the numerical optimization, genetic algorithm was used, and it was observed that although there is clear improvement in the fitness value in case of more complex models, that difference is not significant. The impact of the additional parameters was also investigated using sensitivity analysis, and as it was expected, their relevance is close to negligible compared to the activation energy.

## Notes

### Acknowledgements

Open access funding provided by Budapest University of Technology and Economics (BME). This work was supported by the National Research, Development and Innovation Fund of Hungary in the frame of FIEK 16-1-2016-0007 (Higher Education and Industrial Cooperation Center) Project. I. M. Szilágyi thanks for a János Bolyai Research Fellowship of the Hungarian Academy of Sciences and an ÚNKP-18-4-BME-238 New National Excellence Program of the Ministry of Human Capacities, Hungary. A GINOP-2.2.1-15-2017-00084, an NRDI K 124212 and an NRDI TNN_16 123631 Grant are acknowledged. The research with Project No. VEKOP-2.3.2-16-2017-00013 was supported by the European Union and the State of Hungary and co-financed by the European Regional Development Fund. The research reported in this paper was supported by the Higher Education Excellence Program of the Ministry of Human Capacities in the frame of Nanotechnology and Materials Science research area of Budapest University of Technology (BME FIKP-NAT).

## References

- 1.Cepeliogullar Ö, Haykiri-Acma H, Yaman S. Kinetic modelling of RDF pyrolysis: model-fitting and model-free approaches. Waste Manag. 2016;48:275–84.CrossRefGoogle Scholar
- 2.Radojevic M, Balac M, Javonovic V, Stojiljkovic D, Manic N. Thermogravimetric kinetic study of solid recovered fuels pyrolysis. Hem Ind. 2018;72(2):99–106.CrossRefGoogle Scholar
- 3.Conesa JA, Rey L. Thermogravimetric and kinetic analysis of the decomposition of solid recovered fuel from municipal solid waste. J Therm Anal Calorim. 2015;120:1233–40.CrossRefGoogle Scholar
- 4.Medic-Pejic L, Fernandez-Anez N, Rubio-Arrieta L, Garcia-Torrent J. Thermal behaviour of organic solid recovered fuels (SRF). Int J Hydrog Energy. 2016;41:16556–65.CrossRefGoogle Scholar
- 5.Danias P, Liodakis S. Characterization of refuse derived fuel using thermogravimetric analysis and chemometric techniques. J Anal Chem. 2018;73(4):351–7.CrossRefGoogle Scholar
- 6.Aluri S, Syed A, Flick DW, Muzzy JD, Sievers C. Pyrolysis and gasification studies of model refuse derived fuel (RDF) using thermogravimetric analysis. Fuel Process Technol. 2018;179:154–66.CrossRefGoogle Scholar
- 7.Chhabra V, Shastri Y, Bhattacharya S. Kinetics of pyrolysis of mixed municipal solid waste: a review. Procedia Environ Sci. 2016;35:513–27.CrossRefGoogle Scholar
- 8.Niu S, Chen M, Li Y, Lu T. Combustion characteristics of municipal sewage sludge with different initial moisture contents. J Therm Anal Calorim. 2017;129:1189–99.CrossRefGoogle Scholar
- 9.Niu S, Chen M, Li Y, Song J. Co-combustion characteristics of municipal sewage sludge and bituminous coal. J Therm Anal Calorim. 2018;131:1821–34.CrossRefGoogle Scholar
- 10.Conesa JA, Rey L, Aracil I. Modeling the thermal decomposition of automotive shredder residue. J Therm Anal Calorim. 2016;124:317–27.CrossRefGoogle Scholar
- 11.Cai J, Wu W, Liu R. An overview of distributed activation energy model and its application in the pyrolysis of lignocellulosic biomass. Renew Sustain Energy Rev. 2014;36:236–46.CrossRefGoogle Scholar
- 12.Lin Y, Chen Z, Dai M, Fang S, Liao Y, Yu Z, Ma X. Co-pyrolysis kinetics of sewage sludge and bagasse using Multiple normal distributed activation energy model (M-DAEM). Bioresour Technol. 2018;259:173–80.CrossRefGoogle Scholar
- 13.Cai J, Wu W, Liu R, Hubert GW. A distributed activation energy model for the pyrolysis of lignocellulosic biomass. Green Chem. 2013;15:1331–40.CrossRefGoogle Scholar
- 14.Várhegyi G, Bobály B, Jakab E, Chen H. Thermogravimetric study of biomass pyrolysis kinetics. A distributed activation energy model with prediction tests. Energy Fuels. 2011;25:24–32.CrossRefGoogle Scholar
- 15.Anthony DB, Howard JB, Hottel HC, Meissner HP. Rapid devolatilization of pulverized coal. Symp (Int) Combust. 1975;15(1):1303–17.CrossRefGoogle Scholar
- 16.Bakos LP, Mensah J, László K, Ignicz T, Szilágyi IM. Preparation and characterization of a nitrogen-doped mesoporous carbon aerogel and its polymer precursor. J Therm Anal Calorim. 2018;134(2):933–9.CrossRefGoogle Scholar
- 17.Várhegyi G, Wang L, Skreiberg Ø. Towards a meaningful non-isothermal kinetics for biomass materials and other complex organic samples. J Therm Anal Calorim. 2017;133(1):703–12.CrossRefGoogle Scholar
- 18.Várhegyi G, Szabó P, Jakab E, Till F. Mathematical modelling of char reactivity in Ar–O
_{2}and CO_{2}–O_{2}mixtures. Energy Fuels. 1996;10:1208–14.CrossRefGoogle Scholar - 19.McCall J. Genetic algorithms for modelling and optimisation. J Comput Appl Math. 2005;184:205–22.CrossRefGoogle Scholar
- 20.The MathWorks, Inc. Optimization toolbox user’s Guide. 2018. Retrieved from https://www.mathworks.com/help/pdf_doc/optim/optim_tb.pdf.
- 21.Cai J, Wu W, Liu R. Sensitivity analysis of three-parallel-DAEM-reaction model for describing rice straw pyrolysis. Bioresour Technol. 2013;132:423–6.CrossRefGoogle Scholar
- 22.Luo J, Li Q, Meng A, Long Y, Zhang Y. Combustion characteristics of typical model components in solid waste on macro-TGA. J Therm Anal Calorim. 2018;132(1):553–62.CrossRefGoogle Scholar

## Copyright information

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.