INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XIV, Issue II, February 2025
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Mathematical Modelling of Hydrothermal Carbonization of Biomass
Using MATLAB
Rakhman Sarwono
Research Centre for chemistry – National Research and Innovation Agency, Komplek PUSPIPTEK Serpong, Tangsel (15314),
Indonesia
DOI : https://doi.org/10.51583/IJLTEMAS.2025.14020026
Received: 17 February 2025; Accepted: 03 March 2025; Published: 15 March 2025
Abstract: This paper presents an original reaction kinetics model as a tool for estimating the carbon yield in hydrothermal
carbonization (HTC) of biomass. The kinetics model was developed in MATLAB. The reaction pathways described through a model,
in which biomass is converted into solid, liquid and gaseous products. Runge-Kutta method was used to solve the 4 equations derived
from the reaction suggestion, through the estimation of 6 Arrhenius kinetics parameters (k
1
, k
2
, k
3
, k
4
, k
5
, and k
6
). The HTC reaction
pathway was described through a lumped model, in which biomass is converted into three phase, residual solid, liquid and gaseous
products. By choosing the values of k
1
and others k values and modelling predictions are in the good of the figure pattern. The k
values gave good pattern of figure 3 were k
1
= 0.3, k
2
=0.1, k
3
=0.3, k
4
=0.1, k
5
=0.2, and k
6
=0.1. They resulted that the biomass
conversion was very high about of 90%, carbon content of 39%, liquid content of 24, and gaseous content of 30%.
Key words: HTC, model, kinetics, figure pattern
I. Introduction
Biomass mainly consists of lignin, hemi-cellulose and celluloses. Cellulose shows various unique characteristics such as resistance to
chemical or including water, and structural rigidity. It was found that crystalline cellulose underwent transformation to an amorphous
state in hot and compressed water, which was followed by complete dissolution (Deguchi, 2007). Cellulose molecules are bound to
each other by inter- and intra-molecular hydrogen linkages through their hydroxyl groups, and crystalline cellulose is difficult to
decompose. Direct liquefaction of biomass in sub- and super-critical solvents water has proven to be an effective approach to convert
lignocelluloses materials into low molecular weight chemicals (Wang, 2009).
Biomass can be converted into smaller molecules in the grade of fuels using thermo-chemical processes. The basic reaction
mechanisms of biomass liquefaction can be described: (i) The first step is to dissolved the α-cellulose crystalline into liquid phase. (ii)
depolimerization of the α-cellulose (iii) decomposition of the biomass monomers by cleavage, dehydration, decarboxylation and
deamination; (iv) recombination of the reactive fragments through condensation, cyclization, and polymerization to form new
compounds (Huang, 2011). In the first step cellulose is converted into glucose, hemi-cellulose into xylose, and lignin into polyols.
The first step is very important step that influents to the whole reaction. Reaction between α-cellulose crystalline can be derived as a
fluid-solid reaction.
Information about the fundamentals of the hydrothermal carbonization model system have been studied using model carbohydrate
precursors (e.q. D-Xylose and D-Glucose) and their decomposition products (e.q. furfural and HMF) (Baccile, 2008). Degradation of
solid biomass become three fraction namely, residual solid, dissolved liguid and gaseous. Biomass dissolved macrostructures and
monomers, by further reaction time degradation continue intermediate and gas reaction included dehydration, hydrolysis,
aromatization and polymerization (Pedersen, 2016). Lucian (2018) scheme the reaction of degradation in HTC is described that gas
can come from degradation of biomass and liquid. It’s resulted in the different model of kinetic.
It was demonstrated that under hydrothermal conditions all hexose become sugars, regardless of their complexity, degrade to a HMF
intermediate, which finally condenses to a carbon-like materials having similar morphologies and the same chemical and structural
composition, independent of the starting precursor. By contrast, D-xylose dehydrates to furfural, which in turn reacts to provide
carbon structures very similar to those obtained from using a pure furfural precursor, which are importantly different from materials
derived from the hexose (Baccile, 2009). The hydrothermal carbonization reaction essentially proceeds via three important steps:
Dehydration of the carbohydrate to HMF or furfural, Polymerization towards polyfurans, and carbonization via further intermolecular
dehydration.
Hu (2010) reported that in direct hydrothermal carbonization biomass compounds were heated in sealed autoclaves in the presence of
citric acid at 200
o
C for 16 hours. Interestingly they found two types of carbonaceous materials: soft tissues and hard plant tissues.
Soft plant tissues were without extended crystalline cellulose scaffolds of spherical carbonaceous nanoparticles of a very small size
and porosity. Hard plant tissues are with structural crystalline cellulose scaffolds, however, they can preserve the shape and large
scale features on a macro and micro scale; as a result of considerable mass loss, there arises a significant structural change on a nano-
scale resulting in a sponge like continuous carbon network with well-defined meso-porous structures.
II. Materials and Methods
The HTC process was degraded biomass into smaller molecules in the form of residual solid, dissolved liquid, and gaseous. As
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XIV, Issue II, February 2025
www.ijltemas.in Page 237
mention above the biomass crystalline was degraded into smaller molecules through several steps as describe by (Huang, 2011).
Degradation biomass was complex chemical reaction, it’s hard to describe by every singular reaction to define the whole reaction in
the degradation process. Simplified the whole reaction in HTC process, reseachers used simulation methods to solve the complexity
of reaction (Lucian, 2018; Lucian, 2019).
It’s can be imagined that the reaction scheme can be shown in Figure 1.
Figure 1. The Schematic of HTC process reaction.
In HTC processes the reaction run simultaneously, in the certain residence time (τ ) the scheme can be simplified into single step.
Figure 2. In certain residence time (τ) the HTC process can be simplified in single step.
Mathematical model can be drawn as follows:
1.
C
C
2.
3.
4.
– k6C
G
B= Biomass
C= Char
L= Liquid
G= gas
K value:
, i= 1,2,3…..6
The kinetics model, developed using MATLAB software.
I. III. Result and Discussion
The simulation of HTC degradation derive by k value that resulted the figure of degradation products, namely residual solid, liquid
and gaseous products. By different k value resulted different of figure patterns. In Figure 3,4, and 5, k values with k
1
= 0.3, 0.4, and
0.5 values of k
2
= 0.1, k
3
= 0.3, k
4
=0.1, k
5
=0.2. and k
6
=0.1 have different pattern of component distribution. In k
1
= 0.3 with 10
minutes of running resulted the components distribution were relatively good compared with the k
1
values of 0.4 and 0.5. The
component distribution already decreased after 10 minutes run. The carbon component is higher compared to liquid and gas
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
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components. It,s good results of carbon production (Fig. 3). The biomass conversion was very high about of 90%, carbon content of
39%, liquid content of 24%, and gaseous content of 30%There were a good pattern of conversion and degradation of biomass.
Figure 3. Value of k
1
= 0.3, k
2
=0.1, k
3
=0.3, k
4
=0.1, k
5
=0.2, and k
6
=0.1
Figure 4. Value of k
1
= 0.4, k
2
=0.1, k
3
=0.3, k
4
=0.1, k
5
=0.2, and k
6
=0.1
In figure 4 shown that by k
1
= 0.4 and in ten minutes running gave a pattern of biomass degradation was good enough, biomass
degradation was about of 80%, and resulted the carbon content of 50%, liquid content up to 300%, and gaseous content nearly 200%.
It’s out of prediction. According to the reaction scheme in Figure 4. Increase k
1
from 0.3 to 0.4, there were a different pattern of
components distribution in Figure 3 and 4. The liquid and gaseous products rapidly increase, while biomass conversion and carbon
products were slowly increase.
Figure 5. Value of k
1
= 0.5, k
2
=0.1, k
3
=0.3, k
4
=0.1, k
5
=0.2, and k
6
=0.1
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
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ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XIV, Issue II, February 2025
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In figure 5 shown that by k
1
values of 0.5 and 10 minutes of running resulted the components distribution were increased gradually
after 10 minutes. It’s meant that choosing the value of k
1
= 0.5 were resulted liquid and gaseous products increase rapidly. Biomass
degradation was increased after 5 minutes run. The conversion of biomass about of 30%, carbon production was about of 40%, but
liquid and gaseous products were very high, it’s up 100%, it’s out of prediction. While biomass conversion and carbon products were
slowly increase.
Figure 6. Value of k
1
= 0.3, k
2
=0.1, k
3
=0.2, k
4
=0.1, k
5
=0.1, and k
6
=0.1
In Figure 6 shown that k
1
=0.3, k
3
=0.2 and k
5
= 0.1 resulted degradation component composition. Biomass degradation resulted
conversion of 70%, carbon of 40%, gaseous of 50%, and liquid production up to 120% (out of prediction). By the different of k
value , there was different pattern of figure between Figure 3 and Figure 6. The k value in Figure 3 were that k
3
= 0.2, k
5
=0.2 and in
Figure 4 the k value were k
3
=0.2 and k
5
=0.1. There was different pattern of Figure between Figure 3 and Figure 6. In Figure 6
biomass degradation was about 72%, carbon content of 40%, gaseous production was about 48%, while liquid production was about
120% (out of prediction). Reduced the value of k
3
from 0.3 to 0.2 carbon and gaseous production were similar values in Figure 3 and
6. Liquid production completely different, in Figure 3 liquid production was 24% and in Figure 6 was about 120%.
Figure 7. Value of k
1
= 0.3, k
2
=0.1, k
3
=0.3, k
4
=0.1, k
5
=0.1, and k
6
=0.1
In Figure 7 shown that by different value of k
5
in Figure 3 k
5
= 0.2 and Figure 7, k
5
= 0.1, there were different pattern of components
distribution. In Figure 7 resulted biomass conversion of 80%, carbon conversion of 48%, gaseous conversion of 42%, and liquid
conversion of 105%. The liquid result is to high.
V. Conclusions
The simulation can be concluded that after several run resulted different figures of degradation biomass become solid residue, liquid
and gaseous. Each run with different k value gave a typical pattern of figure that presentation of the degradation composition. The
good pattern of the figure is in figure 3, with the value of k
1
= 0.3, k
2
=0.1, k
3
=0.3, k
4
=0.1, k
5
=0.2, and k
6
=0.1. It was resulted biomass
degradation about 80%, carbon content of about 40%, liquid content about of 30% and gaseous content of about 39%. It was a good
results that closed to the real laboratorium works.
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MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XIV, Issue II, February 2025
www.ijltemas.in Page 240
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