Double-Gaussian Distributed Activation Energy Model for Coal

Sep 17, 2012 - The Distributed Activation Energy Model (DAEM) was used to fit experimental data obtained with a ... Waste Management 2016 58, 230-240 ...
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Double-Gaussian Distributed Activation Energy Model for Coal Devolatilization Benedetta de Caprariis,*,† Paolo De Filippis,† Carlos Herce,‡ and Nicola Verdone† †

Dipartimento di Ingegneria Chimica Materiali Ambiente, Sapienza University of Rome, via Eudossiana 18, 00184 Rome, Italy CIRCE, Research Center on Energy Resources and Consumptions, Mariano Esquillor, 15, 50018 Zaragoza, Spain

‡

ABSTRACT: Understanding and modeling of coal pyrolysis assume particular importance, since it is the first step of combustion and gasification processes. The complex reactions occurring during pyrolysis lead to difficulties in the process modeling. The aim of this work is to find a global kinetic model that well represents the pyrolysis of two different coals with opposite rank, a sub-bituminous and an anthracite coal, in order to carry out the kinetic parameters of the process. The Distributed Activation Energy Model (DAEM) was used to fit experimental data obtained with a thermogravimetric analysis. The model assumes that a series of first order parallel reactions occurs sharing the same pre-exponential factor, k0, and having a continuous distribution of the activation energy. One of the limits of the standard Gaussian DAEM is that with this model is not possible to distinguish the primary from the secondary pyrolysis. A two Gaussians DAEM was developed considering that two classes of reactions take place having the same k0 and different distribution of activation energy. Since in the model k0 is highly correlated with the mean activation energies, it was fixed at characteristic values taken from literature.

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can be schematized as a two steps process:6 a primary pyrolysis occurring at lower temperature where the light gas and tar are released and a secondary pyrolysis, at higher temperature, where the repolymerization of coal molecules takes place to produce char. The global kinetic models can be divided into two classes, depending on whether a single or a two steps mechanism is considered.7 The global kinetic mechanisms are less detailed but very effective when implemented in computational fluid dynamics model, allowing saving computational time.8,9 In this work, the distributed activation energy model (DAEM), originally developed by Pitt,10 is used to model coal pyrolysis. The model assumes that a series of first-order parallel reactions occurs. All the reactions share the same preexponential factor, and the reactivity distribution is represented by a continuous distribution of activation energies. The model equation that represents the change of total volatile yield is

INTRODUCTION The study of coal pyrolysis becomes more and more important, since it affects the coal conversion in combustion and gasification processes. Pyrolysis influences char reactivity in terms of particle porosity and surface morphology, and carbon burnout in terms of amount of char remaining. During the pyrolysis process, weight losses range from 10% to 50%, depending on the coal type and on the operative conditions as heating rate, maximum temperature achieved, and residence time at the maximum temperature. A great number of different species is produced, with the two main product classes being light gas and tar, which is the condensable part of the volatiles. The knowledge of the composition of the produced species is needed to evaluate the energy released by their combustion. Moreover, the volatile pyrolysis products control ignition, flame stability, and temperature. The tar, which can account for up to 50% of the total volatile, is a problem in combustion processes, since it is a soot precursor that affects the radiative heat transfer in boilers; in gasification plants, tar can be a great source of problems because it condensates in cold spots, thus causing filter and pipe obstruction and reduction of the heat transfer efficiency.1,2 It is then clear that an accurate knowledge of the pyrolysis process is necessary, since all the models of coal combustion and gasification involve pyrolysis modeling. However pyrolysis is a complex process, the kinetic parameters of which are difficult to obtain. The high number of pyrolysis products leads to difficulties in the process modeling because distinguishing all the species is a very complex task. A large number of kinetic models were proposed in the literature.3−5 Pyrolysis can be modeled with a detailed kinetic model that takes into account the evolution of a selected number of species or, as in this work, with a global kinetic mechanism that considers the evolution of a unique species, such as CxHyOz, representing all the volatiles. Pyrolysis © 2012 American Chemical Society

1−

v = v*

∫0

∞

⎛ exp⎜ −k 0 ⎝

∫0

t

⎛ E ⎞ ⎞ ⎟ d t ⎟f ( E ) d E exp⎜ − ⎝ RT ⎠ ⎠

(1)

where v and v* are the volatile yield as a function of time and the total amount of volatiles, respectively, k0 is the preexponential factor, t is the time, and T the temperature. f(E) is the distribution curve of the activation energy E, which satisfies the condition:

∫0

∞

f (E ) d E = 1

(2)

In the literature, different forms of f(E) can be found: Gaussian,11 Weibull,12 or Gamma13,14 distributions. In this work, the Gaussian distribution was investigated: Received: June 28, 2012 Revised: August 24, 2012 Published: September 17, 2012 6153

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1 σE

Article

⎛ −(E − E )2 ⎞ 0 ⎟ exp⎜ 2π 2σE2 ⎝ ⎠

were selected. Small samples were used to ensure uniform heating and to avoid problems of transport phenomena through the sample bed in the crucible. The tests were conducted in a N2 inert atmosphere. The Sulcis samples were heated to 1223 K, while the Russian samples were heated to a higher temperature, 1350 K, necessary to release all the volatiles. The samples were maintained at the maximum temperature for 10 min. The experimental tests were carried out varying the heating rate from 5 K/min to 100 K/min. The weight loss plot obtained with a heating rate of 100 K/min is reported in Figure 1. The difference between the two coals in terms of volatile amount is evident.

(3)

where E 0 is the mean activation energy and σ E the corresponding standard deviation. The kinetic parameters that we want to estimate from the data are k0, E0, and σE. However, as already noticed by many authors,15,16 k0 and E0 are highly correlated, and therefore, k0 has to be fixed in some way. Miura17 presented an effective method to estimate both k0 and f(E) using three sets of experimental data at different heating rates without assuming any functional form for f(E). The problem of this method is that pyrolysis is considered to be a one step process rather than a two stages process as it is. This assumption is an approximation that can give good results for coals or biomasses for which the primary and secondary pyrolysis have comparable activation energies and begin at the same time. In a great number of studies, attempts are made on how to solve the DAEM equation without using an approximated model. Gunes and Gunes18 determined the kinetic parameters of the DAEM fixing k0 to a constant value, and by using a direct search method, they obtained good agreement with experimental data. Cai and Li19 adopted a pattern search method to model biomass pyrolysis, obtaining good results in interpreting the available experimental data. Both these works assume one step kinetic global mechanism. In this work, a numerical method to estimate the kinetic parameters of f(E) is presented, assuming a literature value for k0. The model was tested on experimental data obtained from the pyrolysis of an Italian sub-bituminous coal (Sulcis) and an anthracite from Russia. A single Gaussian model (1-DAEM) did not reproduce satisfactory the data. We found that instead a double-Gaussian model (2-DAEM) is very suitable to represent the experimental data, as already suggested by Burnham and Braun.20

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Figure 1. Volatile yields for the two coals obtained at a heating rate of 100 K/min.

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RESULTS AND DISCUSSION 1-DAEM Approach. The DAE model was selected to fit the experimental data and to obtain the mean activation energy and the standard deviation values of the corresponding Gaussian distribution. Since coal was heated at a constant heating rate, α, starting from a low temperature T0, eq 1 was rewritten considering the temperature a linear function of time, t:

EXPERIMENTAL SECTION

The two coals studied in this work were an anthracite from Russia and an Italian sub-bituminous coal (Sulcis), having different ranks. During pyrolysis, the anthracite releases an amount of volatiles equal to 10% of its initial weight, while Sulcis shows a loss of weight of about 45%. The proximate analyses were performed following the ASTM D5142/02 method with a thermogravimetric analyzer (TGA). The elemental coal composition was carried out using a EA3000 (Eurovector) elemental analyzer (Table 1). The experimental tests were performed with a TGA SDT Q600 (TA Instruments). Before the pyrolysis experiments, coals were grounded and the finer particle fractions in a size range 50−80 μm

T = αt + T0

Therefore, the resulting DAEM equation is 1−

Proximate Analysis (% wt) moisture 4.1 volatiles (% dry) 8.9 fixed carbon (% dry) 77.8 ashes (% dry) 13.3 Ultimate Analysis (%wt) C 86.6 H 4.1 N 0.7 S 0.4 O (diff) 8.2

v = v*

∫0

∞

⎛ k exp⎜ − 0 ⎝ α

∫0

T

⎛ E ⎞ ⎞ ⎟dT ⎟f (E)dE exp⎜ − ⎝ RT ⎠ ⎠ (5)

The experimental data in the form 1 − v/v* are reported in Figure 2 for a heating rate of 100 K/min. It can be noticed that the curves present two different slopes, indicating that two different mechanisms occur. To fit experimental data, a C++ program was written and run into the ROOT environment,21 an object-oriented data analysis program, using the routine MINUIT for the minimization of the function selected for the fitting:

Table 1. Coal Proximate and Ultimate Analysis Russian coal

(4)

Sulcis coal 5.1 42.7 41.9 15.4

N

χ2 =

∑ (yis − y(Ti))2

(6)

i=1

yis

where N is the number of data points and and y(Ti) are the experimental and the calculated data, respectively. In each step of the minimization, the DAE equation (eq 5) is integrated numerically with the method of Gaussian quadrature. The computation power of present computers allows to perform the minimization algorithm in less than one minute, avoiding the

74.7 5.5 1.3 8.3 10.2 6154

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macromolecule is composed by functional groups and aromatic and hydroaromatic clusters linked by aliphatic bridges. During the pyrolysis, the functional groups are decomposed to form light gas, and the aliphatic bridges, which are weaker than the aromatic ones, are broken producing lighter fragments (tar).24 These fragments extract hydrogen from the hydroaromatic and aliphatic groups increasing the aromatic carbon content of the initial coal. Since we are considering a global kinetics that includes the transport phenomena, in the Sulcis coal, the light gas are facilitated in the transition to the gas phase as the particle becomes more and more porous. The Russian coal is composed by almost only aromatic and hydroaromatic clusters and some functional groups that contain oxygen. The energy required to decompose hydroaromatic groups and to extract hydrogen from them is much higher than that required to break aliphatic bonds and to extract hydrogen from the aliphatic chains. 2-DAEM Approach. A double-Gaussian model was developed assuming that the pyrolysis process occurs in two steps with different kinetic behaviors. The pyrolysis process is divided into two steps: the tar and light hydrocarbon gas formation during the primary pyrolysis and the char condensation, cross-linking reactions, and a further gas production during the secondary pyrolysis. Serio et al.25 proposed a model that is an extension of a model originally developed by Chermin and van Krevelen,26 in which the pyrolysis is divided into three steps. The first corresponds to the breakage of light bonds and the release of some guest molecules by breakage of very weak bonds, the second is the primary pyrolysis, and the third is the secondary pyrolysis. In this work, only two stages are taken into account, considering the first and the second steps described by Serio et al.25 have the same activation energy. Two sets of parallel reactions occur, sharing the same pre-exponential factor but not the same distributed activation energy. The 2-DAEM equation can be written as

Figure 2. Inverse of volatiles production curve for the Russian and the Sulcis coal obtained with a heating rate of 100 K/min.

use of functional approximations of the DAE equation, as reported in several works in the literature.16,22 In the model adopted, the pre-exponential factor, k0, is shared by all the reactions. From the literature,16 it is known that it is difficult to obtain from the fit a trustworthy value of k0, since it is highly correlated with the mean activation energy E0. Using our experimental data, the fit correlation coefficient between the two parameters assumes, as expected, a high value (0.971). This means that when the value of the pre-exponential factor is fitted together with the other parameters, the solution is not unique. Multiple and interrelated values of the kinetic parameters are allowed by the fitting algorithm: the higher the k0, the higher the E0. Thus, the activation energy or the preexponential factor must be fixed. In most of the literature works,5,11,19 k0 is fixed; however, some authors4 choose to estimate it from the fit by fixing the activation energy to literature values. We choose to fix k0 and to estimate the rest of the parameters from the fit. From the minimization point of view, the choice of k0 is arbitrary: we saw that data are well reproduced by values of k0 ranging between 1010 and 1022. However, to obtain kinetic parameters comparable with other works, we fixed them to literature23 values referred to coals similar to those here investigated. The value of a sub-bitouminous coal (Wandoan coal) was chosen for the Sulcis, k0 = 8 × 1012 (s−1), and the value of an anthracite (Keystone coal), k0 = 5 × 1011 (s−1), was chosen for the Russian coal.

1−

Russian coal

Sulcis coal

5 × 1011 246 62.3

8 × 1012 212 30.8

∫0

∞

⎛ k exp⎜ − 0 ⎝ α

∫0

T

⎛ E ⎞ ⎞ ⎟dT ⎟ exp⎜ − ⎝ RT ⎠ ⎠

(wf1(E) + (1 − w)f2 (E))dE

(7)

where f i(E) is a Gaussian function of the form: fi (E) =

1 σEi

⎛ −(E − E )2 ⎞ 0i ⎟ exp⎜ 2π 2σEi2 ⎝ ⎠

(8)

and w is a parameter that weighs the two reaction classes, varying from 0 to 1. This parameter describes how many volatiles are released during the primary or during the secondary pyrolysis. The value of w would be 0 if all the volatiles were produced during the secondary pyrolysis and 1 if they were released during the primary one. In this case, there are five parameters to be estimated: two mean activation energies E01 and E02, two standard deviations σE1 and σE2, and w. The results of the fitting procedure are reported in Figure 4, where it can be noticed that the model reproduces very well the experimental data. In Table 3 the kinetic parameters obtained from the fit are reported. It can be noticed that for the Sulcis coal the mean activation energy values are quite similar. Instead, the two mean activation energies obtained for the Russian coal are quite different. This behavior is more evident looking at the plots

Table 2. Kinetic Parameters of the 1-DAEM for a Heating Rate of 100 K/min k0 (1/s) fixed E0 (kJ/mol) σE (kJ/mol)

v = v*

The fit results are reported in the Table 2. From Figure 3, it can be seen that the agreement between the model and the experimental data is poor, showing that the model is not able to catch the two different slopes of the volatiles production curves. As expected, the value of Sulcis coal mean activation energy is lower than that of Russian coal; this is due to the much more consistent amount of volatiles in the sub-bituminous coal. This behavior can be explained by considering that the Sulcis coal 6155

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Figure 3. Comparison between the experimental data (red points) and 1-DAEM fit (black line) for the Russian (a) and the Sulcis (b) coals, obtained with a heating rate of 100 K/min.

Figure 4. Comparison between the experimental data (red points) and 2-DAEM fitting (black line) for the Russian (a) and the Sulcis (b) coals, for a heating rate of 100 K/min.

low value of activation energy, which does not correspond to the literature values for the pyrolysis and which gives a small contribution to the total amount of volatiles released due to the low value of the w parameter, 0.23. This behavior is explained by the fact that the anthracite has a very high density, so the release of water and guest molecules does not have time to end before 383 K, which is the drying coal temperature, but continues up to 650 K. This is also the reason that explains the weight loss beginning at 400 K; in fact, the real pyrolysis initial temperature is 800 K, which, as expected, is higher than that of the Sulcis, which is 650 K. This hypothesis is confirmed by the w parameter value: for the Russian coal, almost all the volatiles are produced during the second phase, which means no real primary pyrolysis occurs, since the coal does not contain weak

Table 3. Kinetic Parameters of the 2-DAEM for a Heating Rate of 100 K/min k0 (1/s) fixed E01 (kJ/mol) σE1(kJ/mol) E02 (kJ/mol) σE2(kJ/mol) w

Russian coal

Sulcis coal

5 × 1011 139 29.16 266.44 31.67 0.23

8 × 1012 200 7.33 233 49 0.442

showed in Figure 5 where the f(E) function vs activation energy for 1-DAEM and 2-DAEM are reported. The Russian coal presents two separate Gaussian distributions; the first one has a

Figure 5. Distribution activation energy curves as a function of activation energy, in red the curve for 1-DAEM in black for 2-DAEM. (a) Russian coal; (b) Sulcis coal. 6156

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Figure 6. Comparison between experimental reaction rates and reaction rates obtained with the 2-DAEM kinetic parameters for the Russian (a) and the Sulcis (b) coal for a heating rate of 100 K/min.

bridges to be broken at low activation energy. Instead, for the Sulcis coal the volatile production can be attributed to primary and secondary pyrolysis for the same amount. From Figure 5b, it can be noticed that Sulcis primary pyrolysis occurs in a small interval of activation energy (σE1 = 7.33 kJ/mol) and therefore is confined in a narrow temperature range (650−750 K); this process is fast, and the energy required to break both functional group and aliphatic bonds is similar. The secondary pyrolysis stage, where the dehydrogenation of the hydroaromatic clusters and aliphatic groups, the char condensation, and cross-linking take place, is slower and requires more energy to be accomplished. The two Gaussians are partly superimposed as the cross-linking reactions and char condensation begin at the same time of the primary pyrolysis. The high amount of volatiles released instantaneously makes the particle very porous and the coal very reactive, and the char condensation mechanism begins in the particle zone where the first volatiles are released. However, the first Gaussian is predominant in the primary pyrolysis and the second, peaking at 950 K, in the secondary pyrolysis. The behavior of the secondary pyrolysis showed by the Russian coal is the same of that of the Sulcis. The activation energies of the process are higher, since the coal is less reactive. The hydrogen extraction from the hydroaromatic clusters occurring during the char condensation takes place with higher activation energy than that needed for Sulcis coal where hydrogen is extracted from the aliphatic less energy bonds either. In Figure 6, the reaction rates obtained from experimental data are compared with the reaction rate due to the two Gaussians. Each curve represents the contribution of one of the two Gaussians distributions in the whole process. The fast primary pyrolysis reactions for the Sulcis coal and the superimposition of the two steps can be noticed. One problem of the 2-DAEM is the correlation between the kinetics parameters. The correlation coefficients have a mean value of 0.42 and 0.46 for the Sulcis and Russian coal, respectively. Above all, the w parameter presents a correlation with the mean activation energy as high as 0.67. To decorrelate the parameters, it was tried to fit simultaneously sets of data taken at different heating rates.16,27 The experimental data obtained at heating rates ranging from 5 to 100 K/min are reported in Figure 7 for the Sulcis coal. In the analysis code, a function such as that reported in eq 6 was created for each set of data, fixing the heating rate to the proper value. The minimization algorithm was then configured to find the model

Figure 7. 1 − v/v* for Sulcis coal varying the heating rate from 5 to 100 K/min.

parameters which, at the same time, better reproduced the different sets of data. With the simultaneous fit, the correlation between the parameters is lowered to a mean value of 0.34 and 0.36 for the Sulcis and the Russian coal, respectively. The improvement is not impressive, but it seems that performing a simultaneous fit with data taken at different heating rates makes the solution more independent. Therefore, spanning the heating rate over a wider range would make it possible to further decorrelate the parameters. Unfortunately our experimental apparatus does not permit increasing the heating rate by more than 100 K/min. As an example, the results of the simultaneous fit are reported in Figure 8 for the Sulcis coal, showing a good agreement with all the experimental curves. As it can be seen from Table 4, the kinetics parameters calculated with the simultaneous fit do not vary significantly from the values of the single fit reported in Table 3. The improvement in the representation of the pyrolysis process using the 2-DAEM is evident. Table 5 gives the residual sum of squares for the two models and the relative improvement of the 2-DAEM. For Sulcis coal, the benefit given by the 2-DAEM is higher, since the two Gaussians model fit better the experimental data that for the Russian coal.

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CONCLUSIONS In this work, the pyrolysis of two coals with different rank, a sub-bituminous and an anthracite, was studied by means of thermogravimetric tests. The DAE model was applied to reproduce the weight losses curve in order to obtain the kinetic 6157

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Figure 8. Comparison between experimental data taken at different heating rate (red points) and 2-DAEM simultaneous fit for the Sulcis coal.

parameters of the process. The model assumes that the process occurs with a series of parallel first-order reactions sharing the same pre-exponential factor and having a Gaussian distribution of activation energies. First, the standard DAE model was used to fit the experimental data, showing that it was not able two catch the two different slopes of the weight loss curves. A double-Gaussian DAE model was then developed assuming a two steps mechanism for the pyrolysis, a primary and a secondary pyrolysis. The 2-DAEM well represents the behavior of the studied coals, reproducing the two different steps of the pyrolysis in accordance with the experimental data. The kinetics parameters obtained are consistent with the literature values for coal pyrolysis. The results for the anthracite show that it is not possible to individuate a primary and a secondary pyrolysis for this kind of coal because it seems that only a secondary pyrolysis takes place, due to the small volatile content and the high coal density structure.

Table 4. Kinetic Parameters of the 2-DAEM Obtained Using the Simultaneous Fit k0 (1/s) fixed E01 (kJ/mol) σE1(kJ/mol) E02 (kJ/mol) σE2(kJ/mol) w

Russian coal

Sulcis coal

5 × 1011 143 9.42 267.35 33.05 0.23

8 × 1012 202 7.33 237 52 0.442

Table 5. Summary for the Residual Sums of Squares for the Two Models 1-DAEM 2-DAEM χ2(1-DAEM)/χ2(2-DAEM)

Russian coal

Sulcis coal

3.4 × 10−3 3.7 × 10−5 92

3.16 × 10−3 1.41 × 10−5 244

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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