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\DOI{10.5802/crchim.379}
\datereceived{2024-06-29}
\daterevised{2024-10-31}
\datererevised{2024-12-20}
\dateaccepted{2025-01-16}
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\dateposted{2025-03-12}
\begin{document}

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\title{Kinetic, thermodynamic, and reaction mechanism study of raw
\textit{Phragmites australis} pyrolysis using thermogravimetric analysis}

\alttitle{\'{E}tude cin\'{e}tique, thermodynamique et du m\'{e}canisme
r\'{e}actionnel de la pyrolyse du \textit{Phragmites australis} brut par analyse
thermogravim\'{e}trique (ATG)}

\author{\firstname{Imen} \lastname{Dhifallah}\CDRorcid{0009-0004-1144-910X}\IsCorresp}
\address{Laboratory of Research: Process Engineering and Industrial Systems (LR11ES54), 
National School of Engineers of Gabes, University of Gabes, 6029 Gabes, Tunisia}
\email[I. Dhifallah]{dhifallah.imen8@gmail.com}

\author{\firstname{Wafa} \lastname{Saadi}}
\addressSameAs{1}{Laboratory of Research: Process Engineering and Industrial Systems (LR11ES54), 
National School of Engineers of Gabes, University of Gabes, 6029 Gabes, Tunisia}

\author{\firstname{Souad} \lastname{Souissi-Najar}\CDRorcid{0000-0002-6695-9041}}
\addressSameAs{1}{Laboratory of Research: Process Engineering and Industrial Systems (LR11ES54), 
National School of Engineers of Gabes, University of Gabes, 6029 Gabes, Tunisia}

\shortrunauthors

\keywords{\kwd{Pyrolysis}
\kwd{TGA}
\kwd{Isoconversional models}
\kwd{Activation energy}
\kwd{Pre-exponential factor}
\kwd{Thermodynamic parameters}
\kwd{Coats--Redfern method}}

\altkeywords{\kwd{Pyrolyse}
\kwd{ATG}
\kwd{Mod\`{e}les iso-conversionnels}
\kwd{\'{E}nergie d'activation}
\kwd{Facteur pr\'{e}-exponentiel}
\kwd{Param\`{e}tres thermodynamiques}
\kwd{M\'{e}thode de Coats--Redfern}}

\thanks{Ministry of Higher Education and Scientific Research in
Tunisia}

\begin{abstract}
The  present study aimed at investigating the pyrolysis of \textit{Phragmites
australis} (PA) using non-isothermal thermogravimetric analysis (TGA)
under  nitrogen atmosphere at different heating rates (10, 20, 30,  40,
and  50 \textdegree C/min).  The activation energy values estimated
using two models, Ozawa--Flynn--Wall and Kissinger--Akahira--Sunose,
are approximately equal (156.98 \tralicstex{kJ\textperiodcentered{}mol\textsuperscript{--1}}{$\mathrm{kJ}{\cdot}\mathrm{mol}^{-1}$} and 
158.46 \tralicstex{kJ\textperiodcentered{}mol\textsuperscript{--1}}{$\mathrm{kJ}{\cdot}\mathrm{mol}^{-1}$}, respectively), and the
pre-exponential factor ranges between \tralicstex{2.37\texttimes 10\textsuperscript{11} s\textsuperscript{--1} and 1.13\texttimes 10\textsuperscript{12} s\textsuperscript{--1}}{$2.37\times 10^{11}$ s$^{-1}$ and $1.13\times 10^{12}$ s$^{-1}$}. The reaction mechanism estimated
based on the Coats--Redfern  method indicates that the diffusion model
(D3), as characterized by the Ginstling--Brounshtein equation, is the
most appropriate mechanism in Region 1. However, in Region 2, the
reaction mechanism can be described by two diffusion models: the
Ginstling--Brounshtein (D3) and  Valensi (D2) models.

Thermodynamic parameters, including enthalpy \tralicstex{Î”\textit{H}}{$\Delta H$}, Gibbs free
energy \tralicstex{Î”\textit{G}}{$\Delta G$}, and entropy \tralicstex{Î”\textit{S}}{$\Delta S$}, are calculated
(151.24 kJ/mol, 225.04 kJ/mol, and 
\tralicstex{--94.49 J/(mol\textperiodcentered{}K)}{${-}$94.49 $\mathrm{J}/(\mathrm{mol}{\cdot}\mathrm{K})$}, respectively).
They indicate the endothermic and non-spontaneous nature of the process
and that the conversion of raw PA into bioenergy seems to be
potentially viable and the product formation would be favorable.
Therefore, raw PA appears to be an interesting material for conversion
into bioenergy, activated carbon, and biochar synthesis used for liquid
effluent treatment.
\end{abstract}

\begin{altabstract}
Le pr\'{e}sent travail vise \`{a} \'{e}tudier la pyrolyse du \textit{Phragmites
australis} (PA) en utilisant l'analyse thermogravim\'{e}trique non
isotherme (TGA) sous une atmosph\`{e}re d'azote \`{a} diff\'{e}rentes
vitesses de chauffe (10, 20, 30, 40 et 50 \textdegree C/min). Les
valeurs de l'\'{e}nergie d'activation estim\'{e}es \`{a} l'aide des
deux mod\`{e}les ; Ozawa--Flynn--Wall (OFW) et Kissinger--Akahira--Sunose
(KAS), sont tr\`{e}s proches (156,98
\tralicstex{kJ\textperiodcentered{}mol\textsuperscript{--1}}{$\mathrm{kJ}{\cdot}\mathrm{mol}^{-1}$} et 158,46
\tralicstex{kJ\textperiodcentered{}mol\textsuperscript{--1}}{$\mathrm{kJ}{\cdot}\mathrm{mol}^{-1}$}, respectivement), et le facteur
pr\'{e}-exponentiel se situe entre \tralicstex{2,37\texttimes{}10\textsuperscript{11} s\textsuperscript{--1} et 1,13\texttimes{}10\textsuperscript{12} s\textsuperscript{--1}}{2,37$\times$ 10$^{11}$ s$^{-1}$ et 1,13 $\times$ 10$^{12}$ s$^{-1}$ }. Le m\'{e}canisme de la r\'{e}action de pyrolyse
estim\'{e} sur la base de la m\'{e}thode Coats--Redfern (CR) indique que
le mod\`{e}le de diffusion (D3), caract\'{e}ris\'{e} par l'\'{e}quation
de Ginstling--Brounshtein, est le m\'{e}canisme le plus appropri\'{e}
dans la r\'{e}gion 1. Cependant, dans la r\'{e}gion 2, le m\'{e}canisme
de cette r\'{e}action peut \^{e}tre d\'{e}crit par deux mod\`{e}les de
diffusion : le mod\`{e}le de Ginstling--Brounshtein (D3) et le mod\`{e}le
de Valensi (D2).

Les param\`{e}tres thermodynamiques, y compris l'enthalpie \tralicstex{Î”\textit{H}}{$\Delta H$},
l'\'{e}nergie libre de Gibbs \tralicstex{Î”\textit{G}}{$\Delta G$} et l'entropie \tralicstex{Î”\textit{S}}{$\Delta S$} ont
\'{e}t\'{e} aussi calcul\'{e}s (151,24 kJ/mol, 225,04 kJ/mol et
\tralicstex{--94,49 J/(mol\textperiodcentered{}K)}{${-}$94,49 $\mathrm{J}/(\mathrm{mol}{\cdot}\mathrm{K})$}, respectivement).
Ils indiquent la nature endothermique et non spontan\'{e}e du processus
et que la conversion du PA brut en bio\'{e}nergie semble \^{e}tre
potentiellement viable et que la formation du produit serait favorable.
Par cons\'{e}quent, le PA brut semble \^{e}tre un mat\'{e}riau
int\'{e}ressant pour la conversion en bio\'{e}nergie, en charbon actif
et en biochars utilis\'{e}s pour le traitement des effluents liquides.
\end{altabstract}

\maketitle

\vspace*{-1pt}

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\section{Introduction}\label{sec1}
Biodegradable wastes, particularly lignocellulosic biomass, represent a
promising sustainable energy source due to their abundance and
renewability. This biomass, derived from agricultural residues and
forestry byproducts, has garnered global interest due to its
availability worldwide and its ability to be converted into various
forms of bioenergy with net zero  impact~\cite{1} by reducing
greenhouse gas emissions~\cite{2} and substituting fossil fuels. It
also contributes to waste management by repurposing materials that
would otherwise be  discarded~\cite{3}. Additionally, the processing of
lignocellulosic biomass can promote rural development and  a
circular  bioeconomy~\cite{4}. 

Advanced technologies, such as thermochemical conversion, are being
explored to enhance the efficiency of converting lignocellulosic
materials into bioenergy, making them a viable alternative to
traditional energy  sources~\cite{5}. Among these methods, pyrolysis is
an environmentally friendly process in which the decomposition of
organic material is conducted at temperatures ranging between 
400~\textdegree C and  900~\textdegree C in the absence of 
oxygen~\cite{6}. It leads to the formation of biogases (volatiles),
bio-oil (liquid), and biochar  (solid)~\cite{7}. Bio-oil is a highly
promising biofuel that is used for heating and/or for power generation,
but biochar can be used as soil amendment and soil carbon
sequestration or to remove contaminants from the environment (water or
gas  treatment)~\cite{8}.

Pyrolysis 
is considered a good waste processing method because it uses a wide variety
of residues including agricultural  residues~\cite{9}, municipal solid
waste~\cite{10}, plastic  waste~\cite{11}, sludges~\cite{12}, and so on.
During pyrolysis, lignocellulosic biomass undergoes thermal
degradation, leading to the release of volatile compounds and the
formation of solid char  residues~\cite{13}.

Thermogravimetric analysis (TGA) is a pivotal technique for
investigating the pyrolysis of lignocellulosic biomass, offering
insights into the thermal stability and decomposition behavior of
complex organic  materials~\cite{14}. The TGA quantifies weight loss as a
function of temperature, allowing for the determination of key
parameters such as moisture content, ash yield, volatile matter, and
fixed carbon  contents~\cite{15,16}. By analyzing the thermal
degradation profiles of biomass experimental data and the use of
kinetic models, it is possible to calculate kinetic parameters such as
the activation energy and the pre-exponential  factor~\cite{17,18}; it
is also possible to identify the pyrolysis mechanism and its
thermodynamic  parameters~\cite{19}.

This analysis not only aids in optimizing pyrolysis processes for
energy production but also enhances the understanding of product yields
and the environmental implications of biomass utilization. Overall, TGA
serves as an essential tool in the sustainable development of bioenergy
from lignocellulosic  \mbox{materials~\cite{20}.} 

\textit{Phragmites australis} (PA)
is one of the most widespread wetland plants
globally, with significant biomass production due to its rapid growth
and  invasiveness~\cite{21,22}. Its ability to thrive in diverse
environments has led to ecological concerns, particularly in regions
where it outcompetes native species and disrupts ecosystems, impacting
negatively the  biodiversity~\cite{23,24}, which makes its valorization
in the pyrolysis process a promising approach to energy production and
waste  management~\cite{25,26}.

Zhao et~al. and Barbooti et~al. investigated the thermal degradation of
PA, and~they found that this process occurs in three stages: the
first stage corresponds to moisture evaporation; the second 
\mbox{corresponds}
to the thermal degradation of cellulose, hemicellulose, and lignin; 
the third is characterized by the formation of fixed carbon and
degradation of lignin, resulting in biochar formation and higher
thermal  stability~\cite{25,27}. To the best of our knowledge,
the~pyrolysis reaction mechanism of PA was investigated by some
researchers using the master plot method, and there is no mention of
the~Coats--Redfern (CR) method for PA pyrolysis. This method is
based on the application of heterogeneous reaction models (CR models)
to the experimental data and compares the activation energy values
obtained to those calculated with isoconversional models 
(Kissinger--Akahira--Sunose (KAS) and Ozawa--Flynn--Wall 
(OFW) models) to attain the best-fitted model and to predict the thermal
degradation  mechanism~\cite{28}. This method was used by Dhaundiyal 
and Gangwar~\cite{29} to investigate the pyrolysis mechanism of pine
needles. Moreover, for instance, there is little information about the
thermodynamic properties of the PA pyrolysis mechanism.

The main aim of the current work is to investigate the thermal behavior
of Tunisian PA pyrolysis using experimental TGA data to obtain
more information about kinetic and thermodynamic PA thermal
degradation and the CR method to study this pyrolysis
reaction mechanism. Besides, the climatic conditions in the
Mediterranean basin and North Africa contribute to variations in biomass
resource  composition~\cite{30}, which makes the focus on Tunisian PA
pyrolysis critical to the development of localized biomass-to-energy
conversion strategies.

\section{Material and methods}\label{sec2}

\subsection{Preparation of raw and pyrolyzed biomass}\label{sec2.1}
\textit{Phragmites australis} was collected from Gabes, a region situated in the southern part of
Tunisia. It was initially washed with distilled water several times to
remove any impurities stuck to different plant parts. Then, the plant
was dried in an air oven at 323~K for 48~h, crushed, and sieved to the
desired particle size (ranging from 0.1 to 0.2~mm).

Raw PA pyrolysis was performed in a vertical cylindrical ceramic
reactor with fixed parameters (nitrogen flow of 20~mL/min, heating rate
of 10~\textdegree C/min, and 1~h of pyrolysis time) to evaluate its
morphology and functional groups.

\subsection{Characterization of raw and pyrolyzed
biomass}\label{sec2.2}

\subsubsection{Morphology and composition of raw and\newline pyrolyzed
PA}\label{sec2.2.1}
A scanning electronic microscope (SEM, type Tescan VEGA3 SBH model with
tungsten filament) coupled to Bruker XFlash EDS sensor microanalysis
for energy-dispersive X-ray (EDX) was used to examine the raw PA
surface morphology (under 275${\times}$ magnification) and to determine the
percentage of some chemical elements (C, O, Na, Cl, and K). 

The surface microstructure of the pyrolyzed PA was examined using an SEM
(type FEIQ250/EDAX Thermo Fisher) under 2000${\times}$ magnification.

Volatile matter  $(V_{\mathrm{M}})$ was obtained from the TGA
data,  and fixed carbon $(F_{\mathrm{C}})$ content was calculated using
this expression:
{\begin{equation}\label{eq1}
F_{\mathrm{C}}~(\%) =100- V_{\mathrm{M}}~(\%) -
\mbox{moisture}~(\%)-\mbox{ash}~(\%) 
\end{equation}}\unskip

\subsubsection{Determination of functional groups}\label{sec2.2.2}
Raw and pyrolyzed PA functional group measurements were carried out
with a Bruker ALPHA 
Fourier transform infrared (FTIR) spectrometer with
a~spectrum ranging between 400~cm$^{-1}$ and  4000~cm$^{-1}$. The
samples were prepared using the~KBr method by Gardon 
et~al.~\cite{31}. This technique involves mixing the powdered and dried
samples with potassium bromide (KBr) in a ratio of about 1:100. The
mixture is then placed into a pellet press; then, high pressure is
applied to form a transparent pellet, which is analyzed in
transmission mode.


\subsection{Thermogravimetric analysis}\label{sec2.3}
The thermobalance  SETARAM S60/58B41 was used to evaluate the
weight loss of a definite mass of raw PA. Different heating rates
(ranging from  10~\textdegree C/min to 50~\textdegree C/min) were
applied to the PA samples under a~fixed flow of inert gas
(N$_{2}$) of 20 mL/min, and the results were presented as
weight loss  and derivative or differential thermogravimetric (DTG)
curves for each heating rate.

\subsection{Kinetic modeling}\label{sec2.4}
The TGA data of raw PA was used to study the thermal decomposition
behavior during the pyrolysis process. The PA thermal degradation is
considered a non-linear process composed of different stages, which can
be described with various models. The Arrhenius law is used to analyze the
PA pyrolysis as a~function of  thermal degradation time 
$t$~\cite{14,15,17}:
{\begin{equation}\label{eq2}
\frac{\mathrm{d}\alpha}{\mathrm{d}t}=K(T)f(\alpha)
\end{equation}}\unskip
where  $f(\alpha)$ is the function of the reaction mechanism
determined by the reaction type and $\alpha$ is the conversion rate
described as
{\begin{equation}\label{eq3}
\alpha =\frac{m_{0}-m}{m_{0}-m_{\mathrm{f}}}
\end{equation}}\unskip
where $m_{0}$ and $m_{\mathrm{f}}$ are the initial and the final mass,
respectively, and $m$ is the mass at a given time $t$ (during thermal
degradation). 

$K(T)$ is the reaction rate constant, which can be defined by the Arrhenius
law~\cite{14,15,17}: 
{\begin{equation}\label{eq4}
K(T)=A\exp\left(-\frac{E_{\mathrm{a}}}{RT}\right)
\end{equation}}\unskip
where  $E_{\mathrm{a}}$ is the activation energy (kJ/mol),  $A$ is
the~pre-exponential factor  (min$^{-1}$),  $R$ is the universal gas
constant  $(8.314~\mathrm{J}/\mathrm{mol}{\cdot}\mathrm{K})$, and  $T$
is the reaction temperature (K).

Equation~(\ref{eq2}) combined with  Equation~(\ref{eq4}) gives
{\begin{equation}\label{eq5}
\frac{\mathrm{d}\alpha}{\mathrm{d}t}=
A\exp\left(-\frac{E_{\mathrm{a}}}{RT}\right)f(\alpha)
\end{equation}}\unskip
The integral form $g(\alpha )$ of the reaction model is
{\begin{equation}\label{eq6}
g(\alpha )=
\int_{0}^{\alpha}
\frac{\mathrm{d}\alpha }{f(\alpha )}=
\frac{A}{\beta }
\int_{T_{0}}^{T}
\exp 
\left(-\frac{E_{\mathrm{a}}}{RT}\right)\,\mathrm{d} T
\end{equation}}\unskip
where $\beta$ is the heating rate (\textdegree C/min).

Some methods have been proposed to resolve  Equation~(\ref{eq6}); among
them is the CR method, which is used to estimate the reaction
mechanism.

\subsubsection{Isoconversional models}\label{sec2.4.1}
Isoconversional models are used to evaluate the activation energy
for different values of the conversion rate. These models require that the
kinetics of reactions do not depend on the heating rate, and then
the conversion of raw materials into products takes place in a one-step
process~\cite{7}. The temperature increases from  $T_{0}$ with a
constant heating rate $\beta$ as described by these expressions:
{\begin{eqnarray}
T &amp;=&amp;
\beta t+T_{0}\label{eq7}\Seqnsplit
\mathrm{d}T &amp;=&amp;
\beta \,\mathrm{d}t \label{eq8}
\end{eqnarray}}\unskip

Combining these expressions with  Equation~(\ref{eq6}) gives
{\begin{equation}\label{eq9}
g(\alpha )=
\frac{AE_{\mathrm{a}}}{\beta R}
\int_{x}^{\infty }u^{-2}\mathrm{e}^{-u}\,\mathrm{d} u=
\frac{AE_{\mathrm{a}}}{\beta R}
P(x)
\end{equation}}\unskip
where $P(x)$ is the temperature integral and has no analytical form and
$x=E_{\mathrm{a}}/RT$. 

\paragraph*{The KAS model}%2.4.1.1
The KAS model represents all the chemical and physical reactions that
take place during thermal decomposition. In this model, the temperature
integral $P(x)$ is     
{\begin{equation}\label{eq10}
P(x)=x^{-2}\mathrm{e}^{-x}
\end{equation}}\unskip
Then, Equation~(\ref{eq9}) becomes
{\begin{equation}\label{eq11}
\mathrm{Ln}
\left(\frac{\beta }{T^{2}}\right)=
\mathrm{Ln} \left(\frac{AE_{\mathrm{a}}}{Rg(\alpha)}\right)-
\frac{E_{\mathrm{a}}}{RT}
\end{equation}}\unskip
The activation energy can be calculated using the slope of the curve
$\mathrm{Ln} (\beta /T^{2})$  versus  $(1/T)$ for different conversion
rates.

\paragraph*{The OFW model}%2.4.1.2
The OFW model requires the measurement of temperatures corresponding to
fixed conversion rates at different heating rates. In this case, the
determination of  activation energy does not require prior knowledge
of reaction  mechanisms~\cite{32}. 

This model, developed by Flynn and Wall~\cite{33} and Ozawa~\cite{34},
uses a correlation among the heating rate, the activation energy, and
the temperature of the samples during  pyrolysis~\cite{7}. The
derivation of this correlation is based on Doyle's 
approximation~\cite{35}:
{\begin{equation}\label{eq12}
\log (p(x))\simeq -2.315+0.4567x
\end{equation}}\unskip
Then, the OFW  equation becomes
{\begin{equation}\label{eq13}
\mathrm{Ln} \beta =
\mathrm{Ln} 
\left(\frac{AE_{\mathrm{a}}}{Rg(\alpha )}\right)-
1.0516\frac{E_{\mathrm{a}}}{RT}
\end{equation}}\unskip
$E_{\mathrm{a}}$ is calculated using the slope of the plot $\mathrm{Ln} (\beta)$
versus $(1/T)$. 

\subsubsection{Determination of the pre-exponential
factor}\label{sec2.4.2}
The pre-exponential factor  $(A)$ is an important parameter to obtain
some information about the chemical reaction and then to optimize the
pyrolysis. It can be calculated using this  equation~\cite{36}:
{\begin{equation}\label{eq14}
A=
\frac{\beta E_{\mathrm{a}}}{R{T}_{\mathrm{p}}^{2}}
\mathrm{e}^{{E_{\mathrm{a}}}/R{T_{\mathrm{p}}}}
\end{equation}}\unskip
where  $T_{\mathrm{p}}$ is the maximum peak temperature observed from the
DTG curves.

\subsection{Thermodynamic parameters}\label{sec2.5}
Enthalpy $(\Delta H)$, Gibbs free energy  $(\Delta G)$, and entropy
$(\Delta S)$ were calculated using kinetic data  ($E_{\mathrm{a}}$ and
$A$), TGA data points, and the following equations~\cite{37}:
{\begin{eqnarray}
\Delta H &amp;=&amp;
E_{\mathrm{a}}-RT \label{eq15}\Seqnsplit
\Delta G
&amp;=&amp;
E_{\mathrm{a}}+RT_{\mathrm{m}}\ln 
\left(\frac{K_{\mathrm{B}}T}{h\cdot A}\right)\label{eq16}\Seqnsplit
\Delta S
&amp;=&amp;
\frac{\Delta H-\Delta G}{T_{\mathrm{m}}} 
\label{eq17}
\end{eqnarray}}\unskip
where $T_{\mathrm{m}}$ is the maximum temperature at which maximum decomposition
is achieved, $K_{\mathrm{B}}$ is the  Boltzmann constant 
$(1.381\times10^{-23}~\mathrm{m}^{2}{\cdot}\mathrm{kg}/
\mathrm{s}^{2}{\cdot}\mathrm{K}^{-1})$, and $h$ is the Planck constant 
$(6.626\times10^{-34}~\mathrm{m}^{2}{\cdot}\mathrm{kg}/\mathrm{s})$.

\subsection{Estimation of the reaction mechanism}\label{sec2.6}
The model developed by Coats and Redfern~\cite{28} is used to estimate
the activation energy values by applying  Equation~(\ref{eq15}) for
the kinetic function corresponding to the appropriate pyrolysis
mechanism.
{\begin{equation}\label{eq18}
\mathrm{Ln}
\left[\frac{g(\alpha )}{T^{2}}\right]=
\mathrm{Ln}
\frac{AR}{\beta E_{\mathrm{a}}}
\left(1-\frac{2RT}{E_{\mathrm{a}}}\right)-
\frac{E_{\mathrm{a}}}{RT}
\end{equation}}\unskip
Table~\ref{tab1} presents most of the solid-state degradation reactions
and their functions $f(\alpha)$ and  $g(\alpha)$. The $E_{\mathrm{a}}$-value associated with
each reaction mechanism is determined using the slope of the plot
$\mathrm{Ln}(g(\alpha)/T^{2})$ versus $1/T$. The appropriate reaction
mechanism corresponds to the one that has the nearest $E_{\mathrm{a}}$-value to those
obtained with KAS and OFW models.

\begin{table*}
\caption{\label{tab1}Reaction mechanisms functions, 
model names, and  $f(\alpha)$ and $g(\alpha)$\vspace*{-4pt}}
\begin{tabular}{ccc} 
\thead 
Model name &amp; $f(\alpha)$ &amp; $g(\alpha)$\\
\endthead 
\multicolumn{3}{c}{Chemical reaction order} \\
Chemical reaction order 0 (F0) &amp; 1 &amp; $\alpha$\\ 
Chemical reaction order 1 (F1) &amp; $1-\alpha $ &amp; 
$-\mathrm{Ln}(1-\alpha )$\\
Chemical reaction order 1.5 (F1.5) &amp; 
$(1-\alpha )^{3/2}$ &amp; $2[(1-\alpha )^{-3/2}-1]$\\ 
Chemical reaction order 2 (F2) &amp; 
$(1-\alpha )^{2}$ &amp; $(1-\alpha)^{-1}-1$ \\ 
Chemical reaction order 3 (F3) &amp; 
$(1-\alpha )^{3}$ &amp; $[(1-\alpha )^{-2}-1]/2$\\ 
Chemical reaction order 4 (F4) &amp; 
$(1-\alpha )^{4}$ &amp; $[(1-\alpha )^{-3}-1]/3$\vspace*{5pt}\\
\multicolumn{3}{c}{Diffusion} \\ 
Parabolic law (D1) &amp; $1/(2\alpha )$ &amp; $\alpha ^{2}$ \\ 
Valensi equation (D2) &amp; $-[\mathrm{Ln} (1-\alpha )]^{-1}$ &amp;
$\alpha +(1-\alpha )\mathrm{Ln}(1-\alpha )$\\ 
Ginstling--Brounshtein equation (D3) &amp; 
$(3/2)[(1-\alpha )^{1/3}-1]^{-1}$ &amp; 
$(1-2\alpha /3)-(1-\alpha )^{2/3}$\\ 
Jander equation (D4) &amp; 
$(3/2)(1-\alpha )^{2/3}[1-(1-\alpha )^{1/3}]^{-1}$ &amp; 
$[1-(1-\alpha )^{1/3}]^{2}$\vspace*{5pt}\\ 
\multicolumn{3}{c}{Nucleation and growth}\\ 
Avrami--Erofeev equation (N1.5) &amp; 
$3(1-\alpha )[-\mathrm{Ln} (1-\alpha )]^{2/3}$ &amp; 
$[-\mathrm{Ln} (1-\alpha )]^{2/3}$\\
Avrami--Erofeev equation (N2) &amp; 
$2(1-\alpha )[-\mathrm{Ln} (1-\alpha )]^{1/2}$ &amp; 
$[-\mathrm{Ln} (1-\alpha )]^{1/2}$\vspace*{5pt}\\ 
\multicolumn{3}{c}{Phase interfacial reaction}\\ 
Shrinkage geometrical column (S1) &amp; 
$2(1-\alpha )^{1/2}$ &amp; $1-(1-\alpha )^{1/2}$\\ 
Shrinkage geometrical spherical (S2) &amp; 
$3(1-\alpha )^{2/3}$ &amp; $1-(1-\alpha )^{1/3}$
\botline
\end{tabular}
\vspace*{-3pt}
\end{table*}

\section{Results and discussion}\label{sec3}

\subsection{Characterization of raw and pyrolyzed PA}\label{sec3.1}

\subsubsection{Composition of raw PA}\label{sec3.1.1}
As illustrated in  Figure~\ref{fig1}, EDX analysis was conducted to identify 
some components present in the raw PA. The peaks show the
prevalence of carbon and oxygen along with the presence of other
components in trace amounts (Na, Cl, Si, Cl, and K).  
\mbox{Table~\ref{tab2}}
presents an elemental composition of the raw PA added to ash, volatile
matter, fixed carbon, and moisture content. High carbon and oxygen
contents (47.35\% and 48.58\%, respectively) coupled with  low
moisture and ash contents (3.34\% and 8.73\%,  
\mbox{respectively)} indicate
that this biomass is a highly promising raw material for a range of
applications in energy, activated carbon, and biochar production
processes. The composition of the PA Tunisian variety is close to the
Egyptian PA reported by El \mbox{Shahawy}  
and  Heikal~\cite{38}. Other biomasses
observed in the literature like  pine cones~\cite{13}, olive
stones~\cite{14}, and cocoa shell~\cite{36} have high contents of
volatile matter and fixed carbon  and low ash content, which is
important for gasification and pyrolysis processes. However, there are
differences in composition, which may be due to species, variety,
type of soil, or climatic  conditions~\cite{39}.

\begin{figure}
\includegraphics{fig01}
\caption{\label{fig1}Energy-dispersive X-ray spectra of raw PA.}
\end{figure}

\begin{figure*}
\includegraphics{fig02}
\vspace*{4pt}
\caption{\label{fig2}SEM of raw (a) and pyrolyzed (b) PA.
(a) SE MAG: 275${\times}$, HV: 20 kV, WD: 16.3~mm; (b) SE MAG: 2000${\times}$,
HV: 20 kV, WD: 10.5~mm.}
\end{figure*}

\begin{table*} 
\caption{\label{tab2}Composition of raw PA}
\begin{tabular}{cccccccccc} 
\thead
Moisture (\%) &amp; Ash (\%) &amp; $V_{\mathrm{M}}$ (\%) &amp; $F_{\mathrm{C}}$ (\%) &amp; 
C (\%) &amp; O (\%) &amp; Na (\%) &amp; Si (\%) &amp; Cl (\%) &amp; K (\%)\\
\endthead
3.34 &amp; 8.73 &amp; 45.125 &amp; 42.81 &amp; 47.35 &amp; 48.58 &amp; 0.51 &amp; 0.53 &amp;
1.07 &amp; 1.96
\botline
\end{tabular}
\vspace*{10pt}
\end{table*}

\subsubsection{Morphology of raw and pyrolyzed PA}\label{sec3.1.2}
The SEM analysis of raw PA presented in  
\mbox{Figure~\ref{fig2}a} shows~that
the biomass is rough with a~regular and compact structure with fibers
arranged in  bundles~\cite{38}. The presence of a small number of pores
and a cylindrical fiber structure gives the idea that the biomass has a
typical compact lignocellulosic fibrous  structure~\cite{40,41}. Ponce
et~al.~\cite{39} also revealed this structure for sugarcane bagasse,
corn husk, and rice husk characterized by a cylindrical fiber with a rough
structure. 

After pyrolysis, as shown in  Figure~\ref{fig2}b, the biochar develops
a fairly high porosity, the surface morphology changes, and it becomes
cleaner and fluffier than raw biomass. Many cracks, cavities, and
spherical pores are also visible on the surface, but with different
shades due to the loss of moisture and volatile matter. This
structure is of great importance as it 
\mbox{develops} the PA pore
structure, thereby enhancing the uptake of pollutants from aqueous
solutions and the retention capacities of the  biochar~\cite{8}. This
structure was also observed by Kordoghli  et~al.~\cite{42} after orange
peel pyrolysis and by Bouaik  et~al.~\cite{8} after red alga pyrolysis
in which they have noticed the presence of pores with different forms
(fluffy sponges, balls) and formless particles.

\subsubsection{Functional groups of raw and carbonized
PA}\label{sec3.1.3}
The FTIR analysis of raw and pyrolyzed PA is presented in 
Figure~\ref{fig3}. The raw PA spectrum is similar to those obtained for
other lignocellulosic materials such as olive stones, rice husk,
sugarcane bagasse, and wheat  straw~\cite{14,42}.

\begin{figure}
\includegraphics{fig03}
\vspace*{-2pt}
\caption{\label{fig3}FTIR of raw and pyrolyzed PA before and after
pyrolysis.}
\vspace*{-3pt}
\end{figure}

The peak situated around  $3128~\mathrm{cm}^{-1}$ refers to the --OH
stretching vibration of hydroxyl groups present in cellulose,
hemicellulose, and lignin  structures~\cite{43}. The C${=}$O stretching
vibrations at 1730~cm$^{-1}$ can be assigned to carbonyl groups
(ketones, phenols, carboxylic acids, and aldehydes) and confirm higher
concentrations of lipids and fatty  acids~\cite{44}. The band at
1603~cm$^{-1}$ corresponds to the C--H deformation in methyl,
methylene, and methoxyl groups of  lignin~\cite{45}. The band observed
at 1498~cm$^{-1}$ is associated with lignin aromatic  rings~\cite{40}.
The peak at  1400~cm$^{-1}$ is due to the bending vibration of C--O--C
pyranose ring skeletal vibration of cellulose present in the 
biomass~\cite{40}. The C--C ring breathing bands at 1229~cm$^{-1}$ can
be attributed to the presence of ether, ester, and phenol groups of 
lignin~\cite{45,46}.  The band situated at 1036~cm$^{-1}$ represents
C--H or 
\mbox{C--OH} stretching vibration bonds in cellulose and 
hemicellulose~\cite{38} while the peaks appearing at 622 and
562~cm$^{-1}$ are associated with bending vibrations of CH$_{3}$,
${=}$CH$_{2}$, and ${\equiv}$CH, which are cellulose  components~\cite{14}.
Several biomasses such as pine cones~\cite{13} and olive 
stones~\cite{14} present the same spectrum overall, which is explained
by the primordial presence of cellulose, hemicellulose, and lignin in
their structure, characteristic of lignocellulosic biomasses.

After pyrolysis, as shown in  Figure~\ref{fig3}, the 
\mbox{O--H} stretching
bands located at 3128~cm$^{-1}$ become significantly reduced because of
the destruction of these groups as dehydration occurs and water is
released as most of the organic oxygen-containing groups are 
broken~\cite{47}. It is also clear that the C${=}$O stretching bands
associated with carbonyl groups (at 1730~cm$^{-1}$) disappear because
they are thermally  decomposed~\cite{47}. The band situated at
1400~cm$^{-1}$ presents a significant reduction, reflecting the
destruction of glycosidic  linkages~\cite{47}.

Globally, a significant quantity of lignin, cellulose, and
hemicellulose has been removed from the plant's structure during 
pyrolysis~\cite{48,49}. The same interpretation was developed by Tabal 
et~al.~\cite{44} and Kordoghli et~al.~\cite{41} who noticed that after
the pyrolysis of Ficus wood and orange peels, several band intensities
such as aliphatic remain weak or disappear due to organic decomposition
in the presence\unskip\break 
of heat.

\subsection{Thermogravimetric analysis}\label{sec3.2}
Thermogravimetric analysis is commonly employed to investigate the
thermal composition of~materials. The TG and DTG curves illustrating
respectively the weight loss and derivative  thermogravimetric variation
as a~function of temperature at different heating rates (10, 20,
30, 40, and 50~\textdegree C/min) are presented in  Figure~\ref{fig4}a
and b. The shape of these curves is typical of the~thermal degradation
of lignocellulosic biomasses like olive  stones~\cite{14}, pomegranate
peels~\cite{15}, rice husk~\cite{50}, cardoon  leaves~\cite{51}, and
Typha latifolia~\cite{52}, and they all reveal the presence of three
stages of decomposition.

\begin{figure}
\includegraphics{fig04}
\caption{\label{fig4}Weight loss (TG) (a) and differential
thermogravimetric (DTG) (b) curves for different heating rates.}
\end{figure}

The first stage ranges from 350~K to 475~K for all the heating rates,
and it is characterized by a small drop with a mass loss of about
2.35\%, which corresponds to the evaporation of free physisorbed
water in  micropores and mesopores  (moisture)~\cite{14}. The remaining low
 moisture makes the PA suitable for pyrolysis and 
combustion~\cite{53}.

The second stage in which the most significant weight loss is observed
(58.92\%) and the temperature ranges between 475~K and 675~K indicates
the \mbox{degradation} of hemicellulose and cellulose present in the PA 
structure~\cite{54}.

This stage in which the degradation of PA occurs is divided into two
regions for all the heating rates. Region 1 (R1) characterized by
the presence of a strong peak in the DTG curve situated at
a~temperature between 475~K and 575~K and by a conversion rate
\mbox{$\alpha\leq0.35$}
corresponds to the zone in which the hemicellulose
is mainly pyrolyzed. Region 2 (R2) situated between 575~K and 675~K
corresponds to the zone in which the cellulose is mainly 
pyrolyzed~\cite{14,15}.

The third stage, observed at  $T\geq675$~K, presents a loss of weight
of 8.97\%, and it is associated with lignin  decomposition~\cite{47}.
The constant mass present in this stage is attributed to ash content
representing the inorganic components present in  PA~\cite{55}.

\begin{figure*}
\includegraphics{fig05}
\vspace*{-3pt}
\caption{\label{fig5}Linear fit plots of KAS (a) and OFW (b) models.}
\vspace*{-4pt}
\end{figure*}

Zhao et~al.~\cite{56} revealed that PA pyrolysis occurs in three
stages. The first stage involves the loss of cellular water (the
temperature ranges between 323 and 513~K), and the second stage occurs as
the temperature increases from 513 to 773~K and in which the major part
of the organic material is decomposed (weight loss greater than 50\%).
This stage is divided into two regions: Region 1 in which the
temperature increases from 513 to 591~K and Region 2 where the
temperature increases from 591 to 773 K. The third stage is observed
for a temperature over 773~K where there is a slight continued loss of
weight which corresponds to a slow decomposition of residuals and
carbonaceous matters present in the biomass.

Zhao et~al.~\cite{27}, who studied  PA pyrolysis under different
heating rates, also revealed  the presence of three stages (stage 1:
from 313 to 422~K with 8\% weight loss, stage 2: from 422 to 872~K with
about 60\% weight loss, and stage 3: from 872 to 1153~K with 4.65\%
weight loss).

When comparing these results, the presence of some
similarities and differences attributed to the PA characteristics and
origin, experimental conditions, and sample preparation is observed.

\subsection{Kinetic modeling}\label{sec3.3}

\subsubsection{Evaluation of activation energy}\label{sec3.3.1}
The plots corresponding to OFW and KAS models shown in 
Figure~\ref{fig5} (a and b, respectively) are used to estimate the
activation energy of  raw PA pyrolysis at conversion rates ranging
between 0.1 and 0.6.

The results presented in  Figure~\ref{fig6} show the dependence of 
activation energy on the~conversion rate. The obtained values rise as
the conversion rate values increase from around 133~kJ/mol for a
conversion rate of 0.1 to nearly 193~kJ/mol for a conversion rate of
0.6. The lower $E_{\mathrm{a}}$-value indicates that less energy was
required to initiate a reaction, and then the energy increased as the
reaction  progressed~\cite{57}. This proves that pyrolysis is a
multi-step process with various apparent activation 
energies~\cite{58}. Hemicellulose decomposition dominance in R1
requires less energy than cellulose decomposition, which is dominant in
R2~\cite{59}. In their investigation of olive kernel pyrolysis,
Boukaous  et~al.~\cite{30} observed that the activation energies
$(E_{\mathrm{a}})$ increase with increasing conversion rates from
approximately 170~kJ/mol to around 230~kJ/mol. This trend follows a
similar $E_{\mathrm{a}}\ndash\alpha$ shape to that observed in PA
pyrolysis studies. Besides, the values obtained with the two models 
are approximately equal with a minimal deviation of approximately 1\%,
confirming their validity (average $E_{\mathrm{a}}$-value of 
157.72~kJ/mol).

\begin{figure}
\includegraphics{fig06}
{\vspace*{-2pt}}
\caption{\label{fig6}Variation of $E_{\mathrm{a}}$-values with conversion rate for
KAS and OFW models.}
{\vspace*{-1pt}}
\end{figure}

\begin{table*}
\caption{\label{tab3}Pre-exponential factor for different heating
rates}
\begin{tabular}{ccccccc}
\thead
$\beta$ (\textdegree C/min) &amp; 10 &amp; 20 &amp; 30 &amp; 40 &amp; 50 &amp; Average \\
\endthead 
$A~(\mathrm{s}^{-1})$ &amp; $2.88\times10^{11}$ &amp; $3.03\times10^{11}$ &amp;
$3.89\times10^{11}$ &amp; $6.4\times10^{11}$ &amp; $1.04\times10^{12}$ &amp;
$5.33\times10^{11}$
\botline
\end{tabular}
\end{table*}

\subsubsection{Evaluation of the pre-exponential
factor}\label{sec3.3.2}
The pre-exponential factor is related to the reaction chemistry. In
fact, lower $A$-values $({\leq}10^{9}~\mathrm{s}^{-1})$ indicate a
surface reaction, whereas higher values
$({\geq}10^{9}~\mathrm{s}^{-1})$ indicate a more complex 
reaction~\cite{52}. All the $A$-values calculated with the average
$E_{\mathrm{a}}$-value obtained from KAS and OFW models are presented in 
Table~\ref{tab3}. They are above $10^{9}~\mathrm{s}^{-1}$, which shows
the dominance of cellulose  decomposition~\cite{60}. They also indicate
the complexity of PA, the rotation of the active complex, and that
the reagent remains constant during the monomolecular reactions of PA
\mbox{decomposition~\cite{61}.} Moreover, these values are lower when compared
to the $A$-values of Typha latifolia ($A$-values range from 
$5.53\times10^{10}$ to $3.02\times10^{15}~\mathrm{s}^{-1}$)~\cite{52}
and cocoa shell ($A$-values range from $4.26\times10^{9}$ to 
$1.44\times10^{15}~\mathrm{s}^{-1}$)~\cite{36}.

Table~\ref{tab4} groups together the kinetic parameter values obtained
for various biomasses from the literature and those obtained in this
work. They are well aligned and characteristic of lignocellulosic
materials. When comparing the activation energy of PA
(157.72~kJ/mol) with other biomasses, it falls into a moderate range,
indicating that it requires a reasonable amount of energy for thermal
breakdown. In contrast, materials like cardoon stems and maize cobs
(224.51~kJ/mol and 202.19~kJ/mol, respectively) exhibit significantly
higher activation energies, suggesting that they are more resistant to
decomposition and may necessitate more intensive processing techniques.
Conversely, biomasses such as pomegranate peels and olive stones 
(88.98~kJ/mol and 124~kJ/mol, respectively) have much lower activation
energies, making them easier to convert into energy. This positions
PA as a potentially efficient feedstock, requiring
more energy than softer materials but less than highly fibrous substances,
allowing for versatile application in various conversion processes
while balancing energy requirements and processing costs.

\begin{table*}
\caption{\label{tab4}Activation energies and pre-exponential factors
obtained for different biomasses}
\begin{tabular}{cccc} 
\thead
Biomass &amp; $E_{\mathrm{a}}$~(kJ/mol) &amp; $A~(\mathrm{s}^{-1})$ &amp; References \\
\endthead 
Phoebe zhennan wood  &amp; 170.49       &amp; $3.47\times10^{17}$ &amp; \cite{2}\\
Cardoon stems        &amp; 224.51       &amp; $1.9\times10^{19}$  &amp; \cite{7}\\
Olive stone          &amp; 124          &amp; $8.38\times10^{8}$  &amp; \cite{14}\\
Pomegranate peels    &amp; 88.98        &amp; $3.41\times10^{12}$ &amp; \cite{15}\\
Cocoa shell          &amp; 104.5        &amp; $2.74\times10^{11}$ &amp; \cite{36}\\
Typha latifolia      &amp; 183          &amp; $1.5\times10^{15}$        &amp; \cite{37}\\
Maize cob            &amp; 202.19       &amp; $8.14\times10^{17}$ &amp; \cite{62}\\
Soybean straw        &amp; 154.15       &amp; $8.61\times10^{14}$ &amp; \cite{63}\\
\textit{Phragmites australis} &amp; 163--212.87  &amp; $2.07\times10^{10}$ &amp; \cite{27,56}\\
\textit{Phragmites australis} &amp; 157.72       &amp; $5.33\times10^{11}$ &amp; This work
\botline
\end{tabular}
\vspace*{1pc}
\end{table*}

\subsection{Thermodynamic parameters}\label{sec3.4}
Enthalpy ($\Delta H$), entropy ($\Delta S$), and Gibbs free energy
($\Delta G$) calculated for the different heating rates are presented
in  Table~\ref{tab5}. 

\begin{table*}
\caption{\label{tab5}Thermodynamic parameters of PA pyrolysis}
\begin{tabular}{ccccccc}
\thead
Heating rate (\textdegree C/min) &amp; 10  &amp; 20 &amp; 30 &amp; 40 &amp; 50 &amp; Average\\
\endthead
$\Delta H~(\mathrm{kJ}{\cdot}\mathrm{mol}^{-1})$ &amp;
\mn151.57   &amp; \mn151.4  &amp; \mn151.24  &amp; \mn151.07   &amp; \mn150.9\0     &amp; \mn151.24\\
$\Delta G~(\mathrm{kJ}{\cdot}\mathrm{mol}^{-1})$ &amp;
\mn218.54   &amp; \mn220.57 &amp; \mn224.25  &amp; \mn228.59   &amp; \mn233.29    &amp; \mn225.04\\
$\Delta S~(\mathrm{J}{\cdot}                     
\mathrm{mol}^{-1}{\cdot}\mathrm{K}^{-1})$ &amp; 
\0${-}$90.49 &amp; \0${-}$91  &amp; \0${-}$93.6\0 &amp; \0${-}$96.89 &amp; ${-}$100.46 &amp; \0${-}$94.49
\botline
\end{tabular}
\vspace*{7pt}
\end{table*}

The positive $\Delta H$-values indicate the endothermic nature of 
PA  pyrolysis~\cite{64}. In fact, an external energy source is required
to increase the energy level of the reagent and facilitate its 
transition~\cite{65}. The lower difference between $E_{\mathrm{a}}$- and  
$\Delta H$-values ($E_{\mathrm{a}}-\Delta H\leq6.5$~kJ/mol) indicates that the pyrolytic
conversion of PA into bioenergy seems to be potentially viable and the
product formation would be  favorable~\cite{52,66}. 

Barrier energy is represented by the low activation energy needed to
break the chemical bonds found in organic molecules. Furthermore, it
shows that the activation energy needed to break the chemical bonds in
organic molecules and enable the synthesis of products seems to be low,
indicating that the process might be completed with ease. This proves
that the chemicals produced by pyrolyzing
PA, such as coals, fuel gases, and bio-oils, are created without
requiring a significant amount of extra heat. The efficient conversion
of PA into bioenergy is shown by the preferential production of these
products at lower  enthalpy~\cite{52,67}.

The parameter $\Delta G$ represents the amount of bioenergy that becomes available
when pyrolysis  occurs~\cite{67}. The  $\Delta G$-values of PA
pyrolysis range between 218.54 and 233.29~kJ/mol, indicating the
non-spontaneous nature of raw PA  pyrolysis~\cite{52}. 
These values are higher when 
compared with Typha Latifolia (173--175~kJ/mol)~\cite{52}, rice husk
(143~kJ/mol), coffee husk (143~kJ/mol), groundnut shell (166.11~kJ/mol),
and tea waste  (169.238~kJ/mol)~\cite{4}. This indicates that the
pyrolysis of PA will provide more energy than Typha latifolia, rice
husk, coffee husk, groundnut shell, and tea waste.

The negative $\Delta S$-values obtained in this study reveal that the
decomposition of PA takes place at low  speed~\cite{68}, and it is
also close to its thermodynamic equilibrium with higher thermodynamic
stability~\cite{37}. This is confirmed by the results of the studies
carried out by  Mumbach  et~al.~\cite{36} on cocoa shell pyrolysis 
($\Delta S$-values between ${-}$39.51 and ${-}$72.7~J/mol.K) and Bongomin 
et~al.~\cite{4} on rice husk pyrolysis  ($\Delta S$-value of 
${-}190.3~\mathrm{J}/\mathrm{mol}{\cdot}\mathrm{K})$. 

\subsection{Pyrolysis mechanism}\label{sec3.5}
The CR method was used to estimate the raw PA pyrolysis mechanism. It is
based primarily on tracing the plots of $\mathrm{Ln}(g(\alpha)/T^2)$
versus $1/T$ at all the heating rates (10, 20, 30, 40, and 
50~\textdegree C/min) and for the two regions, R1
$(0.1\leq\alpha\leq0.35)$ and R2  $(0.35\leq\alpha\leq0.6)$.  The
slopes of these curves are used to calculate the activation energies
for different reaction mechanism functions  $g(\alpha)$ presented in 
Table~\ref{tab1}. 

Finally, the comparison between the obtained values and those
calculated with the isoconversional models KAS and OFW helps to
estimate the appropriate model. In fact, the $E_{\mathrm{a}}$-values, which are
nearly equal, show that this mechanism function is the best fit for the
pyrolysis in this region.    Figure~\ref{fig7} shows the plots obtained
with different functions $g(\alpha)$ at a  heating rate of
10~\textdegree C/min, and  Table~\ref{tab6} regroups the $E_{\mathrm{a}}$-values
obtained from the slopes of these curves traced for all the heating
rate values (from 10 to  50~\textdegree C/min).

\begin{table*}[t!]
\caption{\label{tab6}$E_{\mathrm{a}}$- and $R^{2}$-values obtained for
different reaction mechanisms using the CR method}
\fontsize{9.7}{12}\selectfont\tabcolsep=3.2pt
\begin{tabular}{cccccccccccccc} 
\thead
\multicolumn{2}{c}{\morerows{1}{\parbox[t]{1.2cm}{\centering Reaction model}}} &amp; 
\multicolumn{2}{c}{10~\textdegree C/min} &amp; 
\multicolumn{2}{c}{20~\textdegree C/min} &amp; 
\multicolumn{2}{c}{30~\textdegree C/min} &amp; 
\multicolumn{2}{c}{40~\textdegree C/min} &amp; 
\multicolumn{2}{c}{50~\textdegree C/min} &amp; 
\multicolumn{2}{c}{Average values}
\vspace*{2pt}\\
\cline{3-4}\cline{5-6}\cline{7-8}\cline{9-10}\cline{11-12}\cline{13-14}
&amp; &amp;
\parbox[t]{1.1cm}{\centering $E_{\mathrm{a}}$ (kJ/mol)} &amp;  $R^{2}$ &amp; 
\parbox[t]{1.1cm}{\centering $E_{\mathrm{a}}$ (kJ/mol)} &amp;    $R^{2}$ &amp;
\parbox[t]{1.1cm}{\centering $E_{\mathrm{a}}$ (kJ/mol)} &amp;    $R^{2}$ &amp;
\parbox[t]{1.1cm}{\centering $E_{\mathrm{a}}$ (kJ/mol)} &amp;    $R^{2}$ &amp; 
\parbox[t]{1.1cm}{\centering $E_{\mathrm{a}}$ (kJ/mol)} &amp;    $R^{2}$ &amp; 
\parbox[t]{1.1cm}{\centering $E_{\mathrm{a}}$ (kJ/mol)} &amp;    $R^{2}$
\vspace*{2pt}\\
\endthead
\multicolumn{14}{c}{Reaction order}\\
\morerows{5}{R1} 
&amp;F0 &amp; \054.766 &amp; 0.962 &amp; \060.926 &amp; 0.966 &amp; \062.997 &amp; 0.967 &amp; \059.096 &amp; 0.961 &amp; \056.68\0 &amp; 0.979 &amp; \058.893 &amp; 0.967\\
&amp;F1 &amp; \062.83\0 &amp; 0.972 &amp; \069.773 &amp; 0.976 &amp; \072.121 &amp; 0.976 &amp; \067.731 &amp; 0.972 &amp; \069.391 &amp; 0.976 &amp; \068.369 &amp; 0.974 \\
&amp;F1.5 &amp; \076.316 &amp; 0.984 &amp; \084.57 &amp; 0.986 &amp; \087.388 &amp; 0.977 &amp; \082.172 &amp; 0.979 &amp; \084.162 &amp; 0.987 &amp; \082.921 &amp; 0.982 \\
&amp;F2 &amp; \0\00.505 &amp; 0.289 &amp; \0\01.248 &amp; 0.634 &amp; \0\01.48\0 &amp; 0.727 &amp; \0\00.856 &amp; 0.373 &amp; \0\00.939 &amp; 0.489 &amp; \0\01.005 &amp; 0.502 \\
&amp;F3 &amp; \0\06.465 &amp; 0.929 &amp; \0\07.786 &amp; 0.934 &amp; \0\08.225 &amp; 0.943 &amp; \0\07.23\0 &amp; 0.909 &amp; \0\07.463 &amp; 0.926 &amp; \0\07.433 &amp; 0.928 \\
&amp;F4 &amp; \012.505 &amp; 0.941 &amp; \014.413 &amp; 0.942 &amp; \015.062 &amp; 0.947 &amp; \013.686 &amp; 0.927 &amp; \014.072 &amp; 0.937 &amp; \013.947 &amp; 0.938
 \vspace*{6pt}\\
\morerows{5}{R2}
&amp;F0 &amp; \027.355 &amp; 0.998 &amp; \029.652 &amp; 0.991 &amp; \030.869 &amp; 0.988 &amp; \030.294 &amp; 0.991 &amp; \044.997 &amp; 0.957 &amp; \032.633 &amp; 0.985 \\
&amp;F1 &amp; \042.053 &amp; 0.973 &amp; \045.237 &amp; 0.984 &amp; \047.04\0 &amp; 0.985 &amp; \046.264 &amp; 0.988 &amp; \050.292 &amp; 0.985 &amp; \046.177 &amp; 0.983 \\
&amp;F1.5 &amp; \070.823 &amp; 0.986 &amp; \075.722 &amp; 0.973 &amp; \078.696 &amp; 0.977 &amp; \077.523 &amp; 0.979 &amp; \083.722 &amp; 0.973 &amp; \077.297 &amp; 0.977 \\
&amp;F2 &amp; \011.955 &amp; 0.892 &amp; \013.087 &amp; 0.856 &amp; \013.89\0 &amp; 0.883 &amp; \013.528 &amp; 0.885 &amp; \033.863 &amp; 0.824 &amp; \017.264 &amp; 0.868 \\
&amp;F3 &amp; \033.116 &amp; 0.925 &amp; \035.458 &amp; 0.9 &amp; \037.172 &amp; 0.917 &amp; \036.514 &amp; 0.918 &amp; \039.538 &amp; 0.902 &amp; \036.359 &amp; 0.912 \\
&amp;F4 &amp; \059.316 &amp; 0.932 &amp; \063.538 &amp; 0.908 &amp; \044.365 &amp; 0.947 &amp; \065.374 &amp; 0.925 &amp; \070.328 &amp; 0.909 &amp; \060.584 &amp; 0.924 
 \vspace*{6pt}\\
\multicolumn{14}{c}{Diffusion}\\ 
\morerows{3}{R1}
&amp;D1 &amp; 118.57\0 &amp; 0.967 &amp; 131.078 &amp; 0.971 &amp; 135.31\0 &amp; 0.971 &amp; 127.553 &amp; 0.967 &amp; 130.62\0 &amp; 0.972 &amp; 128.626 &amp; 0.969 \\
&amp;D2 &amp; 248.21\0 &amp; 0.971 &amp; 273.597 &amp; 0.974 &amp; 282.243 &amp; 0.974 &amp; 266.638 &amp; 0.971 &amp; 272.99\0 &amp; 0.975 &amp; 268.735 &amp; 0.973 \\
&amp;D3 &amp; 125.52\0 &amp; 0.972 &amp; 138.702 &amp; 0.975 &amp; 143.175 &amp; 0.975 &amp; 134.994 &amp; 0.971 &amp; 138.24\0 &amp; 0.975 &amp; 136.126 &amp; 0.973 \\
&amp;D4 &amp; 250.27\0 &amp; 0.972 &amp; 275.858 &amp; 0.974 &amp; 284.571 &amp; 0.975 &amp; 268.841 &amp; 0.971 &amp; 275.25\0 &amp; 0.975 &amp; 270.958 &amp; 0.973 
\vspace*{6pt}\\
\morerows{3}{R2}
&amp;D1 &amp; \064.501 &amp; 0.999 &amp; \069.251 &amp; 0.993 &amp; \071.777 &amp; 0.991 &amp; \070.687 &amp; 0.993 &amp; \076.637 &amp; 0.994 &amp; \070.57\0 &amp; 0.994 \\
&amp;D2 &amp; 145.245 &amp; 0.998 &amp; 155.28\0 &amp; 0.993 &amp; 160.69\0 &amp; 0.992 &amp; 158.481 &amp; 0.994 &amp; 171.01\0 &amp; 0.993 &amp; 158.141 &amp; 0.994 \\
&amp;D3 &amp; 152.121 &amp; 0.998 &amp; 162.55\0 &amp; 0.992 &amp; 168.25\0 &amp; 0.991 &amp; 165.955 &amp; 0.993 &amp; 178.99\0 &amp; 0.992 &amp; 165.573 &amp; 0.993 \\
&amp;D4 &amp; \076.523 &amp; 0.998 &amp; \082.005 &amp; 0.991 &amp; \085.002 &amp; 0.989 &amp; \083.746 &amp; 0.992 &amp; \090.631 &amp; 0.991 &amp; \083.581 &amp; 0.992 
 \vspace*{6pt}\\
\multicolumn{14}{c}{Nucleation and growth} \\ 
\morerows{1}{R1}
&amp;N1.5 &amp; \038.874 &amp; 0.968 &amp; \043.441 &amp; 0.972 &amp; \044.974 &amp; 0.973 &amp; \042.034 &amp; 0.967 &amp; \043.089 &amp; 0.973 &amp; \042.482 &amp; 0.97 \\
&amp;N2 &amp; \026.896 &amp; 0.962 &amp; \030.276 &amp; 0.968 &amp; \031.401 &amp; 0.968 &amp; \028.185 &amp; 0.961 &amp; \029.938 &amp; 0.968 &amp; \029.339 &amp; 0.965 
\vspace*{6pt}\\
\morerows{1}{R2}
&amp;N1.5 &amp; \024.772 &amp; 0.993 &amp; \026.845 &amp; 0.980 &amp; \028.015 &amp; 0.981 &amp; \027.477 &amp; 0.985 &amp; \030.112 &amp; 0.981 &amp; \027.444 &amp; 0.984 \\
&amp;N2 &amp; \016.131 &amp; 0.991 &amp; \017.647 &amp; 0.975 &amp; \018.502 &amp; 0.976 &amp; \018.083 &amp; 0.983 &amp; \020.022 &amp; 0.977 &amp; \018.077 &amp; 0.98 
\vspace*{6pt}\\
\multicolumn{14}{c}{Phase interfacial reaction} \\
\morerows{1}{R1}
&amp;S1 &amp; \058.705 &amp; 0.967 &amp; \065.248 &amp; 0.971 &amp; \067.453 &amp; 0.972 &amp; \063.315 &amp; 0.967 &amp; \064.872 &amp; 0.972 &amp; \063.918 &amp; 0.969 \\
&amp;S2 &amp; \060.06\0 &amp; 0.969 &amp; \066.733 &amp; 0.973 &amp; \068.986 &amp; 0.973 &amp; \064.765 &amp; 0.968 &amp; \066.356 &amp; 0.973 &amp; \065.38\0 &amp; 0.971
 \vspace*{6pt}\\
\morerows{1}{R2}
&amp;S1 &amp; \034.257 &amp; 0.997 &amp; \036.973 &amp; 0.988 &amp; \038.485 &amp; 0.987 &amp; \037.729 &amp; 0.99 &amp; \041.225 &amp; 0.988 &amp; \037.733 &amp; 0.99 \\
&amp;S2 &amp; \036.755 &amp; 0.996 &amp; \039.622 &amp; 0.987 &amp; \041.21\0 &amp; 0.986 &amp; \040.507 &amp; 0.989 &amp; \044.131 &amp; 0.987 &amp; \040.445 &amp; 0.989
\botline
\end{tabular}
\end{table*}

\begin{figure*}
\includegraphics{fig07}
\caption{\label{fig7}Coats--Redfern plots for pyrolysis of PA 
(for Regions R1 and R2 and
$\beta=10~\text{\textdegree}\mathrm{C}/\mathrm{min}$).}
\end{figure*}

In R1, the average $E_{\mathrm{a}}$-value obtained from the application of the
diffusion model  D3 (about 136~kJ/mol) is the closest value to
that obtained by KAS and OFW models (about 158~kJ/mol), with $R^{2}$
equal to 0.9737, which shows that three-dimensional diffusion is
responsible for the reaction of pyrolysis in Region 1. In R2,
$E_{\mathrm{a}}$-values obtained from the diffusion models  D2 and
D3 are closest to the values obtained from KAS  and OFW
models, with an $R^{2}$-value nearly equal to 1. As a result, the most
appropriate mechanism of raw PA pyrolysis in R2 is two- and
three-dimensional diffusion described by Valensi and
Ginstling--Brounshtein equations. Overall, the results suggest that PA
pyrolysis is governed by diffusion mechanism across all regions. 
This
mechanism is described as a solid-state reaction that often takes place
between crystal lattices or with molecules that must enter 
lattices where motion is limited and may depend on lattice 
defects~\cite{2}. This result is also observed in the investigation
conducted by Bongomin  et~al.~\cite{4} on the thermal behavior of
coffee husk, ground shell, Macadamia nutshell, rice husk, and tea waste.
They conclude that pyrolysis is predominately governed by different
diffusion mechanisms in all regions, which reflect the complex thermal
decomposition of these biomasses. A similar study was also conducted by
Raza and Abu-Jdayil~\cite{69} on date seeds and cashew shells. They found that
the pyrolysis mechanism of these biomasses is described by two
diffusion models: Ginstling--Brounshtein and Jander models.\looseness=-1

However, Mabrouki et~al.~\cite{70} carried out a study on Ziziphus
wood, date palm trunk, date palm leaflets, olive stones, vine stems, and
almond shell. They reported that the pyrolysis of these biomasses could be
described by a first-order chemical reaction model (F1) in R1 and second-
and third-order chemical reaction models (F2, F3) in R2. Ahmad 
et~al.~\cite{52},
though, studied Typha latifolia pyrolysis; they showed
that diffusion played a key role in Region 1, but Region 2 is governed
by second- and third-order reaction models. 

\section{Conclusion}\label{secIV}
In this work, the pyrolysis behavior of \textit{Phragmites australis} was
investigated using TGA carried out at
different heating rates (10, 20, 30, 40, and  50~\textdegree C/min).
This analysis shows that PA pyrolysis occurs in three stages
(the release of water molecules, hemicellulose and cellulose
decomposition, and  lignin decomposition). In
addition, the activation energy values obtained by the OFW and KAS
models are approximately equal, 
with a minimal deviation of approximately 1\%,
indicating high reliability of the results (with an average value of
157.72~kJ/mol). The pre-exponential factors obtained at different
heating rates are in the range of 
$2.88\times10^{11}$--$6.4\times10^{11}~\mathrm{s}^{-1}$, which shows
the dominance of cellulose decomposition and the 
\mbox{complexity} of this
biomass. Thermodynamic analysis shows that this reaction is
endothermic, non-spontaneous, and it takes place at low speed and with
high thermodynamic stability. Moreover, the CR method was
used to estimate the reaction mechanism. It was found that the diffusion
model (D3) characterized by the Ginstling--Brounshtein equation is the most
appropriate mechanism in Region 1. However, in Region 2, the reaction
mechanism can be described by two models: Ginstling--Brounshtein (D3) and
Valensi (D2). All the results obtained from this study show that  PA
is an interesting source of thermal energy production. It is a
promising energy feedstock and is also useful for biochar and activated carbon
production with ecological and economic benefits, especially for 
\mbox{liquid} effluent treatment.

\section*{Greek symbols} 

\begin{inftab}
\begin{tabular}{ll}
\tbody
$\alpha$ &amp; conversion rate $(-)$\\
$\beta$  &amp; heating rate $(\text{\textdegree}\mathrm{C}{\cdot}\mathrm{min}^{-1})$\\
$\Delta H$ &amp; enthalpy variation $(\mathrm{kJ}{\cdot}\mathrm{mol}^{-1})$\\
$\Delta G$ &amp; Gibbs free energy $(\mathrm{kJ}{\cdot}\mathrm{mol}^{-1})$\\
$\Delta S$ &amp; entropy variation $(\mathrm{J}{\cdot}\mathrm{mol}^{-1}{\cdot}\mathrm{K}^{-1})$
\end{tabular}
\end{inftab}

\section*{Nomenclature} 

\begin{inftab}
\begin{tabular}{ll}
\tbody
A &amp; pre-exponential factor $(\mathrm{s}^{-1})$\\ 
CR &amp; Coats--Redfern\\
DTG &amp; \parbox[t]{6.3cm}{\raggedright derivative/differential thermogravimetric curve}\\ 
$E_{\mathrm{a}}$  &amp; activation energy $(\mathrm{kJ}{\cdot}\mathrm{mol}^{-1})$\\
EDS &amp; energy-dispersive X-ray\\
$F_{\mathrm{C}}$ &amp; fixed carbon (\%)\\
FTIR &amp; Fourier transform infrared\\
$f(\alpha)$ &amp; function of reaction mechanism\\
$g(\alpha)$ &amp; complex integral function\\
$h$ &amp; Planck constant $(1.38\times10^{-23}~\mathrm{m}^{2}{\cdot}\mathrm{kg}/\mathrm{s}^{2}{\cdot}\mathrm{K}^{-1})$\\
KAS &amp; Kissinger--Akahira--Sunose\\ 
$K_{\mathrm{B}}$ &amp; \parbox[t]{6.3cm}{\raggedright Boltzmann constant $(6.626\times10^{-34}~\mathrm{m}^{2}{\cdot}\mathrm{kg}{\cdot}\mathrm{s}^{-1})$}\\
$m_{0}$ &amp; initial mass (kg)\\ 
$m_{\mathrm{f}}$ &amp; final mass (kg)\\
$m$ &amp; mass at given time $t$ (kg)\\
OFW &amp; Ozawa--Flynn--Wall\\
PA &amp; \textit{Phragmites australis} \\
$P(x)$ &amp; temperature integral\\
\inftabbreak
$R$ &amp; universal gas constant $(8.314~\mathrm{J}{\cdot}\mathrm{mol}^{-1}{\cdot}\mathrm{K}^{-1})$\\
R1 &amp; Region 1\\
R2 &amp; Region 2\\
SEM &amp; scanning electronic microscope\\
$T$ &amp; temperature (\textdegree C)\\
$T_{0}$ &amp; initial temperature (\textdegree C)\\
$T_{\mathrm{f}}$ &amp; final temperature (\textdegree C) \\
$T_{\mathrm{p}}$ &amp; maximum temperature (\textdegree C)\\
TGA &amp; thermogravimetric analysis\\ 
TG  &amp;  weight loss\\
$t$ &amp; time (s)\\
$V_{\mathrm{M}}$ &amp; volatile matter (\%)
\end{tabular}
\end{inftab}

\section*{Declaration of interests}
The authors do not work for, advise, own shares in, or receive funds
from any organization that could 
\mbox{benefit} from this article, and have
declared no affiliations other than their research organizations.

\section*{Acknowledgment}
This work was supported by the Ministry of Higher Education and
Scientific Research in Tunisia. 

\back{}

\printbibliography
\refinput{crchim20240529-reference.tex}

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