Estimating the Pyrolysis Kinetic Parameters of Coal, Biomass, and

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Estimating the Pyrolysis Kinetic Parameters of Coal, Biomass and their Blends: A Comparative Study Abhijit Bhagavatula, Naresh Shah, and Rick Honaker Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.5b00692 • Publication Date (Web): 10 Nov 2016 Downloaded from http://pubs.acs.org on November 14, 2016

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Energy & Fuels

Estimating the Pyrolysis Kinetic Parameters of Coal, Biomass and their Blends: A Comparative Study Abhijit Bhagavatula1, *, Naresh Shah1 and Rick Honaker2

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1. Department of Chemical and Materials Engineering, University of Kentucky, Lexington, KY – 40508, United States 2. Department of Mining Engineering, University of Kentucky, Lexington, KY – 40508, United States

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* Corresponding Author: Tel.: +1 304 9066529

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E-mail Addresses: [email protected], [email protected]

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Abstract

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The pyrolysis kinetic parameters of two coal ranks (DECS-25 Lignite and DECS-38 Sub-

15

Bituminous), two biomass materials (Corn Stover and Switchgrass) and their respective blends

16

were investigated at various heating rates ranging between 5 ºC/min and 40 ºC/min using

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thermogravimetric analysis. Complex models for devolatilization of the feedstocks were solved

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for obtaining and predicting the global kinetic parameters. Distributed activation energy model

19

(Method 1) and matrix inversion algorithm (Method 2) were utilized and compared for this

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purpose. The results indicate that the matrix inversion algorithm predicts the kinetic parameters

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such that the weight loss characteristics can be best represented for both single fuels as well as

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that of blended materials. The algorithm can also be used for determining the number of

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reactions occurring in the devolatilization temperature interval. The number of reactions

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occuring during the devolatilization of blended materials fall between those that occur during the

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devolatilization of single fuels and the number of reactions gradually decrease with increase of

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biomass concentration in the blend. In addition, weight loss characteristics of fuel blends at 1

ACS Paragon Plus Environment

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unknown heating rates can be effectively predicted within 1 % error through the use of this

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algorithm.

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Keywords: Coal, Biomass, Blends, Thermogravimetric Analysis, Pyrolysis, Kinetics Modeling

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Energy & Fuels

1. Introduction

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Global growth in industrialization, economy, population and most importantly, the

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depletion in fossil fuel resources has resulted in the global energy demand to increase

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exponentially [1-3]. This increasing demand will become more rapid in the future. Currently,

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heavy exploitation and extensive use of fossil fuels are the reasons leading towards their

55

foreseeable depletion within the next few decades [2, 4-10]. Substituting fossil fuels and

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alleviating their negative environmental effects is sine qua non and have therefore led to the

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development of alternative sources of energy and promotion of sustainable low quality fuels. Co-

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conversion technologies mainly pertaining to co-pyrolysis, co-gasification and co-combustion of

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coal and biomass blends are among these alternatives for energy generation and production of

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high quality synthetic chemicals [11, 12].

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Pyrolysis or devolatilization (used interchangeably) is the starting point for all

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heterogeneous gasification reactions. Carbonaceous feedstock can be considered as a complex

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polymer network consisting of aromatic clusters and aliphatic bridges. During pyrolysis, the

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complex structure of such feedstock is broken down in to several small fragments whose vapor

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pressure is high enough to form volatile matter. The products include: pyrolysis gases (CO, H2,

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CH4 and H2O), tar, oil, naphtha and residual solid char [11, 13-15]. A complete description of the

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characteristics of pyrolysis is complicated, but for a given carbonaceous feedstock, the pyrolysis

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behavior depends on the rate of heating, decomposition temperature, residence time, the

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environment under which the pyrolysis takes place, pressure and particle size [16].

70

Single-step reaction models are simple, but difficulties arise while simulating complex

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multi-step reactions such as pyrolysis of solid fuels. On the other hand, segmented reaction

72

models divide a complicated reaction into several steps according to temperature range. Several 3


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methods for assessing non-isothermal pyrolysis kinetic parameters using thermogravimetric

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analysis (TGA) have been developed. These methods are generally categorized as either “model-

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fitting” or “model-free” [17, 18]. During devolatilization of carbonaceous feedstocks, several

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mass loss profiles can be observed with increasing temperatures. Each mass loss profile or the

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thermal event having sudden changes in mass loss slope can be modeled using appropriate

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“model-fitting” techniques for estimating the kinetic parameters. Each thermal event may have a

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discrete reaction order, frequency factor and activation energy.

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Prior investigations reveal that co-pyrolysis of coal-biomass blends generally yield three

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or more thermal events. For example, three thermal events with linear kinetics at temperatures

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ranging between 200 °C and 1400 °C were observed by Meesri and Moghtaderi in their work on

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pyrolytic behavior of coal and woody biomass blends [19]. Similar investigations by Vuthaluru

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[20] also revealed that three thermal events were sufficient enough to explain the mass loss

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profiles of coal/biomass mixtures using non-linear reaction kinetics. More importantly, they

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found that the total yield of the major pyrolysis products were linearly proportional to the

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blending ratio, indicating no synergistic effect between coal and biomass. However,

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contradictorily, Bhagavatula et al. [37] observed significant non-linearity in the evolution of

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volatile matter indicating synergistic behavior during their co-pyrolysis investigations using

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blends of corn stover and sub-bituminous coal which were in conjunction with the findings of

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Aboyade et al. [18], Zhou et al. [21], Cai et al. [27] and Haykiri-Acma and Yaman [22].

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Likewise, Zhou et al. [21] and Cai et al. [27] utilized linear reaction kinetics in their research on

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co-pyrolysis of plastic/biomass blends and coal/plastic blends respectively. Zhou et al. [21]

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observed two thermal events for polypropylene and three thermal events for blends of wood saw

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dust and plastics while Cai et al. [27] utilized four thermal events in their evaluation. In another 4


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Energy & Fuels

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work, multi-component distributed activation energy model involving several parallel

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irreversible first order reactions was employed by Jong et al. [23] who carried out co-pyrolysis

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experiments in Helium atmosphere with blends of biomass and high volatile coal in TGA–FTIR.

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They concluded that the pre-exponential factor had no significant deviation for each reaction and

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can be assumed to be constant although the activation energies followed Gaussian distribution.

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Vamvuka et al. [24] developed a kinetic model for the volatile matter released during the

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pyrolysis of several biomass (i.e. olive kernel, forest and cotton residues) blends with lignite

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using thermogravimetric analysis. Their findings revealed that the biomass possess higher

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thermochemical reactivity with shorter devolatilization times in comparison to the lignite.

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However, in multi-thermal event models the changeovers are not often sharp, making

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demarcation of each thermal event difficult. Moreover, the changeover temperatures may vary

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with the type of feedstock and other conditions, thereby, preventing the use of the model with

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generality. In addition, it was presumed that only one reaction occurred within a certain

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temperature range which is not scientifically warranted.

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The model-free approach does not require assumption of specific reaction models, and

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yields unique kinetic parameters as a function of either conversion (iso-conversional analysis) or

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temperature (non-parametric kinetics). Of the two main model-free methods the iso-conversional

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approach is more frequently adopted, and is increasingly being used in coal/biomass

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thermochemical conversion research. Garcia-Perez et al. [25] employed the iso-conversional

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approach for estimating the thermal decomposition parameters of sugar cane bagasse with

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petroleum residue at various heating rates ranging from 10-60 °C/min in an inert nitrogen

117

atmosphere. Similarly, Biagini et al. [26], Cai et al. [27], and Aboyade et al. [18] employed

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various iso-conversional methods in the analysis of the non-isothermal decomposition of 5


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biomass and/or its components. Investigations by Aboyade et al. [18] revealed that the activation

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energies for biomass materials such as sugarcane bagasse and corn stover were in the range of

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165-200 KJ/mol and much lower than the activation energy displayed by coal (> 250 KJ/mol) at

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a conversion less than 0.8.

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An extensive literature review reveals contrasting methods adopted by various

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researchers in evaluating the thermochemical characteristics of blended fuel feedstocks. Kinetic

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modeling of the devolatilization behavior of coal and biomass is, therefore, an important step in

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assessing the contribution of single materials and their interactions during the devolatilization

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stage. The understanding of kinetics of co-pyrolysis of blends of biomass and coals, particularly

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the blends of Montana coals, corn stover and switchgrass used in this study, is far from clear and,

129

hence, it is important to evaluate various kinetic models and demonstrate a robust and versatile

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model which can be used for predicting the kinetic parameters of co-pyrolysis using various

131

feedstocks. Two models, namely, distributed activation energy model and matrix inversion

132

algorithm were utilized and compared for this purpose in the present work. A detailed

133

description of theory behind each of the kinetic models is provided in Section 2.

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2. Theory

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2.1. Method 1: Distributed Activation Energy Model - Gaussian Distribution Function

136

As discussed in Section 1, kinetic parameters obtained using the model-fitting techniques

137

are actually a starting point in the devolatilization modeling. Although simple and used as a

138

starting point for more complex models, a single first order reaction model utilized for estimating

139

the devolatilization kinetics of complex materials is only applicable over a limited range of

140

experimental conditions. The kinetic parameters obtained through such a model may not be used

141

as global parameters. Activation energy and pre-exponential factor change for different heating 6


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rates, i.e, the parameters obtained through one experimental condition may not be extrapolated to

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an unknown heating rate. More accurate and specific models are required to meet the

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experimental results of each material, one model being the distributed activation energy model

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[36, 44].

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Since coal and biomass are complex fuels with a wide variety of chemical groups, the

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distributed activation energy model treats thermal decomposition of these complex fuels as a

148

large number of independent and analogous rate processes characterized uniquely by their

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activation energy. The thermal decomposition of a single organic species can be described as an

150

irreversible first-order reaction. Thus, the rate at which volatiles are produced by a particular

151

reaction can be defined according to the mass balance on the reactant species.

152

153

154 155

∗ = − ∗ − = ∗ − −

Eq. 1

Eq. 2

Where ∗ is the final quantity of volatile matter for the generic species, i, and is the rate constant of the reaction expressed according to the Arrhenius law.

156

This type of kinetic model requires that the amount of volatiles and kinetic parameters

157

known for all the single reactions. To estimate these parameters from experimental data for all

158

the reactions is practically not possible. The problem can be simplified if it is assumed that the

159

rate constants for all the reactions differ only in the activation energy. The number of reactions is

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large enough so that the activation energy can be expressed as a continuous Gaussian distribution

161 162

function and representing the potential loss of volatile fraction with activation energy between the intervals E and E + dE. Thus, 7


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∗ = ∗ = ∗

163

164

Finally, the yield of volatiles can be calculated using Equation 4.

165

! ∗ − ∗ = exp − "

= −

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Eq. 3

Eq. 4

166

Where,

167

And,

168

Where, ∗ is the global volatile quantity of the material, is the mean activation energy

169

= #2%

.' ()

− − + exp * 2# + ,

Eq. 5

Eq. 6

and # is the standard deviation of the activation energy. Using this approach, low values of

170

activation energies resulting from model-fitting first-order reactions as functions of temperature

171

can be negated [28].

172 173 174 175 176 177 178 179 180 181

In this work, Miura’s method was used to estimate and A values [45] for all the

feedstock materials. Both and A were obtained from at least three thermogravimetric experiments using different heating rates without assuming any functional forms for and A [46]. The procedure used is summarized as follows [45, 46]:

(1) Measure V/V* vs. T using at least three different heating rates on a dry and ash-free basis. (2) Calculate the values of ln (β/T2) and 1/ (RT) at the same V/V*, where β is the heating rate. (3) Plot ln (β/T2) and 1/ (RT) at the selected V/V* ratio and then determine the activation energies E from the slopes and A from the intercept as shown in Equation 7.

8


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Energy & Fuels

-. 1 = -. + 0.6075 − /

23

0

182

4

4

30

Eq. 7

183

(4) Plot V/V* and E and differentiate the V/V* vs. E relationship by E to obtain f (E).

184

(5) Pre-exponential factor, A, can be expressed as a function of activation energy using the following expression:

185

= :) :+

186

Where, :) and :+ are constants dependent on the reacting material.

187 188

Eq. 8

(6) The relationship between V/Vf and E is fitted using a logistic distribution curve using Equation 9.

189

;

;
)? 44 B @

Eq. 9

191

where A1 and A2 are the initial and final conversion points, E0 is the mean activation energy and

192

p is a constant. The values of the constants are obtained by fitting the experimental data with

193

Equation 9.

194

2.2. Method 2: Matrix Inversion Method

195

As described in Section 2.1, the devolatilization mass loss of a complex carbonaceous

196

material can be uniquely characterized within an activation energy interval of E and E + dE at

197

any particular time t [47-49]. If the decomposition is considered to be first order, then Equation 4

198

can be re-written in the following form:

C, = C D ,

199

200

And,

D , = − − "

9


Eq. 10

Energy & Fuels

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201

Where, m (E, t) is the mass density function of the volatile material at any time t and m0 (E) is

202

the initial mass of volatile material within the interval E and E + dE.

203

Since m (E, t) cannot be measured quantitatively, integrating Equation 10 over all activation

204

energies enables the calculation of total amount of material decomposed, Mv (t), at any time t. EF EF@

205

=

EF@ (; EF@

G =

= G D , !

J

Eq. 11

H@ 4

@ H@ 4 I4

206

And,

207

Where, Mv (t) is the mass of volatiles at any time t, Mvo is the initial mass of volatile matter, V (t)

208

is the yield of volatiles and g (E) is the underlying initial distribution of activation energies.

209

Since g (E) is unknown, calculation of kinetic parameters for each parallel reaction is

210

more complex. To overcome this complexity, a mathematical inversion method which does not

211

rely on any assumption of the initial distribution of activation energies is utilized in this research

212

for estimating the kinetic parameters. This method was successfully tested by Scott et al. [48, 49]

213

for evaluating the kinetic parameters of pyrolysis of sewage sludge. This method, which is

214

virtually an extension of Miura’s method, is used for determining the number of reactions

215

occurring during the process of devolatilization, in addition to determining the kinetic

216

parameters.

217

Mathematically, Equation 9 can be rearranged as shown in Equation 12 by assuming that

218

a volatile component of the fuel feedstock with an initial mass fraction of fi,0 reacts with an

219

activation energy of Ei and pre-exponential factor of Ai.

220

= , D 10


Eq. 12

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Energy & Fuels

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Where, fi is the fraction of the ith component remaining as the fuel is devolatilized and Ψi is the

222

double exponential term (Eq. 10). For thermal decomposition by means of several analogous

223

first-order reactions, Equation 12 can be expressed as:

224

225

and, W is the fraction of inert material.

E E@

= K + L2MM 3NOPQRS, , D Eq. 13

226

The problem is therefore to estimate fi,0, Ei and Ai. A unique case of this general problem

227

is the distributed activation energy model which can be generated when an infinite number of

228

reactions co-exist with a constraint that each of the reactions is distinctively characterized by its

229

activation energy [49]. During thermal decomposition, only one particular reaction is dominant

230

at a certain temperature and hence, the kinetic parameters of that particular reaction can be

231

directly and accurately evaluated. Only when multiple reactions occur at the same conversion

232

point or temperature interval, will deviations in activation energy be observed. Therefore,

233

Equation 13 can be interpreted in a matrix form as follows:

234

W D D+ V [ V ) U W) Z U D) ) D+ ) Z U ) U W+ Z = U D) + D+ + E@ U U ⋮ Z U ⋮ ⋮ U Z U TW R Y TD) R D+ R

⋯⋯

⋯⋯

⋯⋯

⋯⋯

⋯⋯

DR DR )

DR + ⋮

DR R

1 ), [ V [ 1Z U+, Z Z U Z 1Z × U_, Z U ⋮ Z 1Z U Z Z TKY 1Y

Eq. 14

235

Equation 14 can therefore be termed as a modified form of the distributed activation energy

236

model. For a constant heating rate experiment, i.e. dT/dt = H and initial temperature T0, the

237

double exponential term, Ψ can be expressed as:

11


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D = D = `− ba 0 c 2

238

0

@

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− d e

Eq. 15

= , D

239

And,

240

Thermogravimetric experiments conducted at two different heating rates, H1 and H2, can be used

241

for calculating the values of Ei and Ai. Assuming that the ith reaction is the only reaction

242

occurring at the same conversion in both experiments, then, f) , ) = f+ , +

243

244

And subsequently.

245

Or,

246

Eq. 16

)

b=

D f) , ) = D f+ , +

g − 30a − 4

Eq. 17

@

(4a 3

h

!

l mn@

!

k

o − ) − 30a + 4

=

4a

!

l mn=

!

k

op =

248

Equation 19 is a non-linear equation, which can be solved analytically for estimating unknown

249

activation energies for each reaction. Once the activation energy, Ei, is determined, pre-

250

exponential factor, Ai, can be calculated by assuming that the conversion of the individual

251

component i of the dominating reaction reaches a particular conversion. For this method, it is

252

assumed that the conversion is:

253

1

@

(4a 3

l mn@

4ij (k k

4

1

h 3

4ij (k

b g − 30a − 4

o − + − 30a +

3

h

247

)

h

4ij (k

Eq. 18

4a

l mn1

q = 1 − () => D = () => ln D = −1 12


4ij (k k

op

Eq. 19

Eq. 20

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254

Energy & Fuels

Combining Equations 15 and 20, Ai can then be estimated.

255

The matrix inversion method is thus different from Method 1 in the sense that this method

256

does not require that each reaction be uniquely characterized by its activation energy and does

257

not use a step function approximation, which is central to Method 1 (Miura’s method) for

258

estimating the amount of each reaction occurring. This type of analysis was used earlier for

259

determining the pyrolysis characteristics of dried sewage sludge [48] and high ash, inertinite-

260

rich, medium rank C South African coal [50]. In this work, the modified distributed activated

261

energy model has been extended for determining the kinetic parameters of single fuels as well as

262

blends of coal and biomass.

263

3. Materials and Methods

264

The pyrolysis characteristics of pure coal, biomass which includes corn stover (CS) and

265

switchgrass (SG) and their blends using thermogravimetric analysis will be discussed extensively

266

in this work. 10%, 20% and 30% by weight of individual biomass samples were blended with

267

two different ranks of coals, namely, DECS-38 sub-bituminous coal (SB) and DECS-25 lignite

268

coal (LG) [12, 51]. The samples were crushed and sieved to -100 mesh (< 150 µm) before

269

blending to limit the effects of intra-particle heat transfer [18, 24, 26, and 29].

270

Subsequently, their non-isothermal weight loss profiles were evaluated and co-pyrolysis

271

kinetic parameters were determined. These coals were chosen based on economic considerations,

272

their low sulfur content, and relatively high percentage of carbon present. Also, in view of the

273

overall gasification process, blends of higher percentages of biomass (in excess of 30% by

274

weight) would be uneconomical for large scale operations since biomass is a low density, low

275

heating value fuel and addition of more biomass would make thermochemical conversion less 13


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276

efficient. Therefore, the blends have been limited to a maximum of 30% by weight of biomass in

277

this study. Proximate analysis, elemental analysis and sulfur analysis of the feedstock samples

278

were conducted according to ASTM standards D7582-12 [52], D5373-08 [53] and D4239-12

279

[54], respectively. The proximate and elemental analyses of the single fuels are presented in

280

Table 1.

Page 14 of 33

281

Pyrolysis of the different feedstocks was carried out in non-isothermal mode using a TA-

282

SDT-Q600 thermogravimetric analyzer. Approximately 15 mg of representative coal sample and

283

about 7 mg of representative biomass samples on an as received basis were used for the

284

experiments. Pure nitrogen was used as the purge gas. Flow of pure nitrogen through the system

285

negates sample oxidation and also removes the volatile pyrolysis products, thus ensuring an inert

286

atmosphere during the run. In the non-isothermal mode, once the sample is inserted into the

287

furnace, the temperature of the furnace was increased from room temperature to 127 °C and held

288

at that temperature for 15 minutes to ensure drying. Subsequently, the furnace temperature was

289

raised to 900 °C at constant heating rates ranging between 5 °C/min and 40 °C/min. An inert

290

nitrogen atmosphere was employed throughout the process and the nitrogen flow rate was

291

maintained constant at 100 ml/min. Upon reaching a temperature of 900 °C, air was introduced

292

into the furnace to burn off the remaining char and obtain the percentage of ash in the respective

293

samples. The process was repeated four times to ensure reproducibility of the weight loss

294

profiles for each sample (error < 5 % for all samples).

295

4. Results and Discussion

296

4.1. Method 1

297

For illustration of the distributed activated energy model (DAEM), Figure 1 describes the

298

method for establishing the kinetic parameters during the pyrolysis of DECS-38 sub-bituminous 14


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Energy & Fuels

299

coal for different heating rates ranging from 5 °C/min to 40 °C/min. The idea is that, with

300

increase in heating rates, the temperature required to attain a particular conversion increases and

301

hence, the kinetic parameters can be determined at each conversion point. Once the activation

302

energies at selected conversions are determined, the relationship between conversion (V/Vf) and

303

activation energies needs to be established through a plot of V/Vf vs E.

304

Once the relationship between V/Vf and E is established and the unknown constants

305

obtained, Equation 9 can be differentiated with respect to E to obtain the values for the function f

306

(E). Finally, a plot of the obtained f (E) values with respect to the activation energy can be fitted

307

using a Gaussian distribution function. This implies that the complex devolatilization reaction

308

kinetics of carbonaceous materials may not be represented by only a single first order reaction

309

but, the reaction is made up of several analogous first order reactions occurring simultaneously

310

with increasing temperatures as described in Section 2.1. For example, as seen from Figure 1 and

311

Table 2, for DECS-38 sub-bituminous coal, the peak of f (E) occurs at 0.00575 KJ/mol

312

corresponding to an activation energy of approximately 269 KJ/mol and the distribution of

313

activation energies follows an approximate Gaussian function (R2 = 0.99). The range of

314

activation energies is between 120-578 KJ/mol within the devolatilization conversion interval of

315

5-99% (Table 2). Also, a linear relationship with reasonable correlation coefficient (R2 = 0.97)

316

exists between ln k0 and activation energy. Within the devolatilization interval, the values of k0

317

range between e20 – e53 min-1 for DECS-38 sub-bituminous coal corresponding well to the values

318

available in literature for coals with similar properties [45, 46]. Using the kinetic parameters thus

319

obtained, Equation 4 is then solved using the quadrature function of MATLAB to predict the

320

weight loss or conversion profiles during devolatilization at all heating rates and compared with

321

the experimental data as shown in Figure 2. Similar procedure has been utilized for analyzing the 15


Energy & Fuels

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322

devolatilization kinetic parameters of all the feedstock materials and these values are shown in

323

Table 2. Figures S.1 through S.5 in supplementary information describe Method 1 for all

324

feedstocks used in this work. The standard correlation coefficient for predicting the

325

devolatilization weight loss using this method is reasonably good (R2 > 0.97) for all feedstocks.

326

4.2. Method 2

327

4.2.1. Kinetics of DECS-38 Sub-Bituminous Coal Devolatilization

Page 16 of 33

328

Figures 3 and 4 describe the matrix inversion algorithm results for DECS-38 sub-

329

bituminous coal. The algorithm was applied to the TGA data at various heating rates and kinetic

330

parameters were obtained at various conversions. The obtained kinetic parameters were then

331

used to model the reactions at unknown heating rates that were not used in the algorithm. The

332

obtained weight loss data was then compared with real TGA data for comparison and accuracy

333

of the method.

334

The ability to accurately predict the thermal mass loss curves at unknown heating rates

335

and also significantly lower data processing times make this inversion algorithm advantageous

336

over Miura’s method. For DECS-38 sub-bituminous coal, TGA data for heating rates 10 °C/min

337

and 20 °C/min were used in the inversion algorithm for determining the kinetic parameters and

338

the obtained parameters were then used to predict the weight loss curves at 5 °C/min and 40

339

°C/min.

340

From these mass loss data sets, a total of 50 conversions were chosen where the kinetic

341

parameters were to be calculated. One candidate reaction is generated at each value of

342

conversion and for cases where more than one real reaction occurs at a particular conversion, the

343

values of E and A generated would be incorrect. Therefore, the values of fi,0 of such unrealistic 16


Page 17 of 33

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Energy & Fuels

344

reactions can be set to zero using the method described in Section 2.2, thereby determining the

345

total number of reactions during devolatilization.

346

Figure 3 shows the values of fi,0 for DECS-38 sub-bituminous coal. Upon examination of

347

these values, 35 parallel reactions have been identified which are deemed to be occurring during

348

the devolatilization of DECS-38 sub-bituminous coal. Increasing the number of conversion

349

points to a number greater than 50 would not make a difference because the total number of

350

parallel reactions occurring in this case falls within the number of conversion points chosen. For

351

example, when the number of conversion points was increased from 50 to 100, the number of

352

parallel reactions occurring was still the same and no change in the activation energy range was

353

observed. It should be noted here that only the decomposition reactions, starting with removal of

354

moisture, are taken into consideration during this method and hence, fixed carbon content and

355

ash content are not included in Figures 3 and 4.

356

The values of kinetic parameters increase with increasing weight loss until a maxima is

357

achieved when the mass fraction of the fuel (sub-bituminous coal) remaining is approximately 55

358

% indicating the completion of the devolatilization process. Activation energy values occurring

359

during pyrolysis of DECS-38 sub-bituminous coal have a range between 84 - 683 KJ/mol with a

360

mean activation energy of approximately 338 KJ/mol while the values of pre-exponential factor

361

are not constant for all reactions but have a large range between 9E+5 min-1 and 5E+32 min-1.

362

The kinetic parameters thus obtained were used to model the TGA curves. A comparison of the

363

actual TGA curves and the predicted curves (Figure 4) indicates that for the two heating rates

364

used in the algorithm, the model predicts the weight loss data and derivative weight loss data

365

excellently with standard error of less than 0.5 % between the experimental and predicted values.

17


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Page 18 of 33

366

The kinetic parameters obtained were then used for modeling the devolatilization reaction

367

at two heating rates, 5 °C/min and 40 °C/min, not used in the algorithm to verify if the model

368

could be extrapolated to unknown heating rates. This is important to verify since the process of

369

devolatilization occurs instantaneously at the top of a moving bed reactor during gasification

370

where the heating rates tend to be much higher, in the order of 100 °C/sec. For the

371

thermogravimetric analyzer used in this work (TA SDT Q600), a linear increase in furnace

372

temperature was not possible at heating rates higher than 40 °C/min. Hence, it must be noted

373

here that the maximum heating rates utilized in this work is 40 °C/min.

374

The model can clearly be utilized for predicting weight loss data for unknown heating

375

rates also. As seen from Figure 4, the predicted weight loss values and derivative weight loss

376

values fall within 1 % of the actual experimental curves suggesting that this model can be

377

successfully utilized for predicting the devolatilization reaction even at extremely high heating

378

rates that are achieved in industrial reactors.

379

It is also important to understand if this model can be extended to various feedstocks with

380

different compositions of moisture, volatile matter and fixed carbon content. Therefore, for this

381

purpose and for comparison with other models described earlier, devolatilization of the two

382

biomass materials (CS and SG) and blends of biomass with the two coals are analyzed further

383

using the matrix inversion method in the following sections. The pyrolysis kinetic parameters

384

and number of reactions occurring during the process for all feedstocks are shown in Table 3.

385

4.2.2. Kinetics of CS and SG Devolatilization

386

The kinetics parameters for corn stover and switchgrass devolatilization were obtained

387

via the matrix inversion method by utilizing the TGA data for heating rates 20 °C/min and 40

388

°C/min in the inversion algorithm and the obtained parameters were then used to predict the 18


Page 19 of 33

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Energy & Fuels

389

weight loss curves at a lower heating rate of 5 °C/min. It is evident that there are far fewer

390

reactions occurring during the devolatilization of corn stover when compared to that of sub-

391

bituminous coal. The values of fi,0 (Supplementary Information Figures S.6-S.7) suggest that the

392

devolatilization of corn stover can be represented by a total of 7 reactions which includes

393

removal of moisture. The range of activation energy values obtained, 55 – 225 KJ/mol, are also

394

comparable to the values obtained using Methods 1. It is evident that this method can also be

395

used for predicting the devolatilization kinetics of high volatile biomass materials such as corn

396

stover. From Table 3, an interesting observation that can be made between corn stover and

397

switchgrass is that the total number of reactions occurring during devolatilization of corn stover

398

(7 reactions) is lesser than that of switchgrass (11 reactions). This can be attributed to the lower

399

total volatile matter percentage in corn stover which evolves at lower temperatures when

400

compared to that of switchgrass.

401

4.2.3. Devolatilization Kinetics of Blended Feedstocks

402

Once the devolatilization kinetics of single fuels was analyzed, the matrix inversion

403

algorithm was tested on the blends of those single fuels. For illustration, the analysis of 10% corn

404

stover blended with 90% sub-bituminous coal is discussed in this section. The activation energy

405

curve (Figure S.8 in Supplementary Information) for the blended feedstock follows a slightly

406

different pattern when compared to that of the single fuels, again, indicating the fact that there

407

are certain interactions between the single fuels during devolatilization unlike several previous

408

works [18-20, 29] where synergistic interactions between coal and biomass blends were not

409

observed. A complete analysis of the synergistic interactions between the blended feedstocks has

410

been previously described elsewhere in detail by the authors [12, 36-37]. 19


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Page 20 of 33

411

The kinetic parameters obtained even for the blended feedstocks represent the weight loss

412

data excellently, with errors of less than 1% for all heating rates. This proves the effectiveness

413

and robustness of the matrix inversion method in representing the devolatilization of various

414

materials when compared with other methods discussed previously. It is expected that the

415

number of reactions occuring during the devolatilization of blended materials would be between

416

those that would occur during the devolatilization of single fuels and that the number would

417

gradually decrease with increase of high volatile matter content fuels in the blend, i.e., corn

418

stover and switchgrass in this case. For a 10% corn stover blend with sub-bituminous coal, the

419

number of devolatilization reactions is 29, while only 20 reactions were observed in 30% blend

420

of corn stover with sub-bituminous coal as shown in Table 3.

421

5. Conclusions

422

Distributed activation energy model (Method 1), and matrix inversion algorithm (Method

423

2) were evaluated for estimating pyrolysis kinetic parameters of different feedstocks (DECS-38

424

sub-bituminous coal, DECS-25 lignite coal, corn stover, switchgrass and respective blends).

425

Although, several previous works utilize a first order model for reasonably predicting the

426

pyrolysis kinetic parameters of single fuels, difficulties in the demarcation of each thermal event

427

and approximations while determining the temperature integral make such a method error prone.

428

Additionally, such models can only be used for determining the kinetic parameters at one heating

429

rate, thereby, preventing the use of the model with generality. Therefore the use of distributed

430

activation energy models (Methods 1 and 2) for determining the pyrolysis kinetic parameters of

431

carbonaceous feedstocks is warranted. However, Method 1 is not “model-free” and can only be

432

used for predicting the kinetic parameters at known heating rates apart from it being labor-

433

intensive (the method requires a minimum of three heating rates for validation). On the contrary, 20


Page 21 of 33

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Energy & Fuels

434

the matrix inversion algorithm (Method 2) is a “model-free” iso-conversional technique that

435

predicts the kinetic parameters such that the weight loss characteristics can be best represented

436

for both single fuels as well as that of blended materials apart from determining the number of

437

devolatilization reactions occurring in the devolatilization temperature interval. In addition,

438

weight loss characteristics of fuel blends at unknown heating rates can be effectively predicted

439

within 1 % error through the use of this algorithm. Finally, it can be stated that the data obtained

440

utilizing this unique analytical technique would provide valuable insights not only pertaining to

441

pyrolysis kinetics but also towards synergistic interactions between blended feedstocks, process

442

modeling, optimization and reaction pathways in the field of co-conversion of coal and biomass.

443

Acknowledgements

444

The authors would like to express their gratitude to the Department of Energy for funding

445

this research (DOE Contract No. DE-FC26-05NT42456) and also to the Center for Applied

446

Energy Research at the University of Kentucky for their timely support in providing the biomass

447

samples.

448 449 450 451 452

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Xu, Q., Investigation of Co-Gasification Characteristics of Biomass and Coal in Fluidized Bed Gasifiers, in Chemical and Process Engineering. 2013, University of Canterbury: Christchurch, NZ.

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Feng, Y., et al., Influence of Particle Size and Temperature on Gasification Performance in Externally Heated Gasifier. Smart Grid and Renewable Energy, 2011. 2(2): p. 158164.

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Vuthaluru, H.B., Investigations into the pyrolytic behaviour of coal/biomass blends using thermogravimetric analysis. Bioresource Technology, 2004. 92(2): p. 187-195. 22


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De Jong, W., Nola, G.Di., Venneker, B.C.H., Spliethoff, H., Wojtowicz, M.A., TG–FTIR pyrolysis of coal and secondary biomass fuels: determination of pyrolysis kinetic parameters for main species and NOx precursors. Fuel, 2007. 86: p. 2367-2376.

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Jerez, A., A modification to the Freeman and Carroll method for the analysis of the kinetics of non-isothermal processes. Journal of Thermal Analysis, 1983. 26(2): p. 315318.

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Fermoso, J., et al., Co-gasification of different rank coals with biomass and petroleum coke in a high-pressure reactor for H(2)-rich gas production. Bioresource technology, 2010. 101(9): p. 3230-5.

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Li, Z., et al., Analysis of coals and biomass pyrolysis using the distributed activation energy model. Bioresource technology, 2009. 100(2): p. 948-52.

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Miura, K. and T. Maki, A Simple Method for Estimating f (E) and K0 (E) in the Distributed Activation Energy Model. Energy and Fuels, 1998. 12: p. 864-869.

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Please, C.P., M.J. McGuinness, and D.L.S. McElwain, Approximations to the distributed activation energy model for the pyrolysis of coal. Combustion and Flame, 2003. 133(1– 2): p. 107-117.

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ASTM Standard D7582-12, "Standard Test Methods for Proximate Analysis of Coal and Coke by Macro Thermogravimetric Analysis". 2013: ASTM International, West Conshohocken, PA.

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578 579 580

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581

Sample

Bank

&

Database

in

Table Captions

582 583

Table 1: Proximate and Elemental Analysis of Feedstocks.

584

Table 2: Method 1: Pyrolysis kinetic parameters for single fuels and blended feedstocks using

585

distributed activation energy model (Gaussian distribution of activation energies).

586

Table 3: Method 2: Pyrolysis kinetic parameters and number of devolatilization reactions

587

obtained for various feedstocks using matrix inversion algorithm.

588

Figure Captions

589

Figure 1: Plots for estimating the activation energy and Arrhenius constant for pyrolysis of

590

DECS-38 sub- bituminous coal at various heating rates using DAEM (Method 1).

591

Figure 2: Comparison between experimental and calculated devolatilization weight loss of

592

DECS-38 sub- bituminous coal with increasing temperature using DAEM (Method 1).

25


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

593

Figure 3: Plots for estimating the number of parallel reactions, range of activation energies and

594

Arrhenius constants for pyrolysis of DECS-38 sub- bituminous coal at various heating rates

595

using Matrix Inversion Algorithm (Method 2).

596

Figure 4: Comparison of experimental and predicted values for devolatilization of DECS-38 sub-

597

bituminous coal using the matrix inversion algorithm (Method 2). (a) weight loss vs temperature

598

at known heating rates of 10 °C/min and 20 °C/min, (b) derivative weight loss vs temperature at

599

10 °C/min and 20 °C/min, (c) weight loss vs temperature at unknown heating rates of 5 °C/min

600

and 40 °C/min, (d) derivative weight loss vs temperature at 5 °C/min and 40 °C/min.

601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616

26


Page 26 of 33

Page 27 of 33

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Energy & Fuels

Table 1: Proximate and Elemental Analysis of Feedstocks.

617

Feedstock

DECS-38 SubBituminous Coal DECS-25 Lignite Coal

Proximate Analysis (As Received Basis) % % % Fixed Volatile Moisture Carbon Matter

Elemental Analysis (As Received Basis) % Ash

%C

%H

%N

%S

%O

22.01

39.66

34.58

3.75

56.82

3.95

0.98

0.44

12.36

34.91

27.32

30.05

7.71

42.80

2.99

0.61

0.47

10.50

Corn Stover

5.66

10.32

76.15

7.87

42.33

6.71

0.73

0.30

42.06

Switchgrass

4.87

9.35

83.62

2.16

45.76

8.09

0.32

0.08

42.87

618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634

27


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Page 28 of 33

635

Table 2: Method 1: Pyrolysis kinetic parameters for single fuels and blended feedstocks

636

using distributed activation energy model (Gaussian distribution of activation energies).

Feedstock Materials

Activation Energy Range KJ/mol

Peak f (E), KJ/mol

Peak Activation Energy, KJ/mol

Arrhenius Constant Range, min-1

Correlation Coefficient, R2

DECS-38 Sub-Bituminous Coal (SB)

120-578

0.00575

269

e20- e53

0.991

DECS-25 Lignite Coal (LG)

100-446

0.00936

210

e19-e43

0.985

Corn Stover (CS)

91-256

0.00859

171

e14-e40

0.995

10% CS + 90% SB

118-374

0.0042

220

e23- e46

0.986

30% CS + 70% SB

110-350

0.0061

175

e17- e46

0.987

10% CS + 90% LG

95-396

0.0047

226

e27- e42

0.981

30% CS + 70% LG

92-320

0.00875

154

e17- e26

0.971

637 638 639 640 641 642 643 644 645 646

28


Page 29 of 33

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Energy & Fuels

647

Table 3: Method 2: Pyrolysis kinetic parameters and number of devolatilization reactions

648

obtained for various feedstocks using matrix inversion algorithm

649

(Correlation Coefficient for actual weight loss vs predicted weight loss, R2 > 0.99 for all feedstocks)

Feedstock Materials

Activation Energy Range

Arrhenius Constant Range

KJ/mol

sec-1

No. of Reactions

DECS-38 Sub-Bituminous Coal (SB)

35

84-683

9E+5 – 5E+32

DECS-25 Lignite Coal (LG)

29

93-300

2E+8 – 2E+14

Corn Stover (CS)

7

55-226

7E+4 – 4E+13

Switchgrass (SG)

11

40-175

1E+0 – 2E+13

10% CS + 90% SB

29

75-722

2E+9 – 5E+41

30% CS + 70% SB

20

89-607

2E+7 – 5E+45

10% CS + 90% LG

25

67-356

2E+5 – 6E+15

30% CS + 70% LG

22

78-320

3E+9 – 2E+22

10% SG + 90% SB

28

112-796

2E+8-2E+51

30% SG + 70% SB

24

41-673

1E+3-8E+31

10% SG + 90% LG

28

59-237

1E+3-4E+29

30% SG + 70% LG

24

40-231

1E+0-5E+17

29


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 33

650

651 652

Figure 1: Plots for estimating the activation energy and Arrhenius constant for pyrolysis of

653

DECS-38 sub- bituminous coal at various heating rates using DAEM (Method 1).

654 655 656 657 658 659 660 661 662 663 664

30


Page 31 of 33

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Energy & Fuels

665 666 667

668 669

Figure 2: Comparison between experimental and calculated devolatilization weight loss of

670

DECS-38 sub- bituminous coal with increasing temperature using DAEM (Method 1).

671 672 673 674 675 676 677 678 679 680

31


Energy & Fuels

681 682 683

0.07

684 0.06

1200

35 parallel reactions identified during devolatilization of DECS-38 sub-bituminous coal

1000

685 0.05 800

Ea, KJ/mol

686 0.04

687 688

F0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 33

0.03

Activation energy range: 84 – 683 KJ/mol

600

Mean: 338 KJ/mol

400

689

0.02

690

0.01

691 692

0 0.55

200

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

0 0.55

Mass Fraction Remaining

0.6

0.65

0.7

0.75

0.8

Mass Fraction Remaining

693 694 695 696 697 698 699 700 701 702 703

Figure 3: Plots for estimating the number of parallel reactions, range of activation energies and

704

Arrhenius constants for pyrolysis of DECS-38 sub- bituminous coal at various heating rates

705

using Matrix Inversion Algorithm (Method 2).

706 707 708

32


0.85

Page 33 of 33

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Energy & Fuels

709 710 711 712

713 714

Figure 4: Comparison of experimental and predicted values for devolatilization of DECS-38 sub-

715

bituminous coal using the matrix inversion algorithm. (a) weight loss vs temperature at known

716

heating rates of 10 °C/min and 20 °C/min, (b) derivative weight loss vs temperature at 10 °C/min

717

and 20 °C/min, (c) weight loss vs temperature at unknown heating rates of 5 °C/min and 40

718

°C/min, (d) derivative weight loss vs temperature at 5 °C/min and 40 °C/min.

719

33


Estimating the Pyrolysis Kinetic Parameters of Coal, Biomass, and

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