Revista Facultad de Ingeniería, Universidad de Antioquia, No.111, pp. 31-37, Apr-Jun 2024
Heat flow modeling in the alkaline activation
process of fly ash
Modelamiento del flujo de calor en el proceso de activación alcalina de la ceniza volante
Mauled Yesenia Echeverri-Aguirre1*, Juan Sebastián Rudas-Flórez1, Jarol Esneider
Molina-Mosquera1, Ary Alain Hoyos-Montilla2
1Grupo de investigación e innovación en energía -GiiEN-, Facultad de Ingeniería, Institución Educativa Pascual Bravo.
Calle 73 # 73a-226. C. P. 050034. Medellín, Colombia.
2Grupo Investigación del Cemento y Materiales de Construcción -CEMATCO-, Facultad de Minas, Universidad Nacional de
Colombia. Carrera 80 # 65-223. C. P. 050041. Medellín, Colombia.
CITE THIS ARTICLE AS:
M. Echeverri-Aguirre, J. S.
Rudas-Flórez, J. E.
Molina-Mosquera and A. A.
Hoyos-Montilla. ”Heat flow
modeling in the alkaline
activation process of fly ash”,
Revista Facultad de Ingeniería
Universidad de Antioquia, no.
111, pp. 31-37, Apr-Jun 2024.
[Online]. Available: https:
//www.doi.org/10.17533/
udea.redin.20230624
ARTICLE INFO:
Received: February 04, 2022
Accepted: June 22, 2023
Available online: June 22, 2023
KEYWORDS:
Fly ash; alkaline cement;
modelling
Ceniza volante; cemento
alcalino; modelamiento
ABSTRACT: Cement production plays an important role in strengthening the infrastructure
of growing countries such as Colombia. However, the production of this material has a
high energy cost and contributes to the emission of large amounts of CO2. To address
these environmental concerns, it is essential to explore alternative materials that can
partially or completely replace traditional cement. Alkaline activated cement (AAC)
has emerged as a promising candidate in this regard. Due to this, it is necessary
to understand the process of alkaline activation and the variables that influence
it. This research proposes a phenomenological-based semi-physical model, which
predicts the performance of some variables that control alkaline activation: activator
concentration (NaOH), heat flow, and degree of reaction. The model results show
that with the increment of the activator concentration, the degree of reaction also
increases. Furthermore, the model has an accurate response compared with the
Freisleben-Hansen model. The integral square error criterion (ISE) was used in this
comparison.
RESUMEN: La producción de cemento juega un papel importante en el fortalecimiento
de la infraestructura de un país en pleno crecimiento como lo es Colombia. Sin
embargo, la producción de este material tiene un alto costo energético y contribuye
a la emisión de grandes cantidades de CO2. Para abordar estas preocupaciones
ambientales, es esencial explorar materiales alternativos que puedan reemplazar
parcial o completamente al cemento tradicional. El cemento alcalino activado (AAC)
se ha convertido en un candidato prometedor en este sentido. Por ello, es necesario
comprender el proceso de activación alcalina y las variables que influyen en él. En esta
investigación se propone un modelo semifísico de base fenomenológica, el cual predice
el desempeño de algunas variables que controlan la activación alcalina: concentración
del activador (NaOH), el flujo de calor y el grado de reacción. Los resultados del modelo
indican que con el incremento del activador alcalino (NaOH) el grado de reacción también
se incrementa. El modelo presenta resultados precisos comparados con el desempeño
del modelo propuesto por Freisleben-Hansen. En esta comparación se utilizó el criterio
de error cuadrado integral (ISE).
1. Introduction
The production of Ordinary Portland Cement (OPC) has a
significant environmental impact, primarily due to its high
CO2 emissions and energy consumption.
OPC manufacturing is responsible for the emission of large
quantities of CO2 (0.82 to 1.0tCO2/t cement ) [1]. This
carbon emission is related to the high energy consumption
during manufacture: calcination of limestone and the
heating of raw materials to temperatures above 1450
◦C. [1] Recent studies reported that OPC manufacturing
contributes to annual anthropogenic CO2 emissions of
approximately 8 and 10% [2]. On the other hand, the
energy required for OPC production is as high as 3400 MJ/t
31
* Corresponding author: Mauled Yesenia Echeverri-Aguirre
E-mail: mauled.echeverri481@pascualbravo.edu.co
ISSN 0120-6230
e-ISSN 2422-2844
DOI: 10.17533/udea.redin.20230624 31
Heat flow modeling in the alkaline activation
process of fly ash
Modelamiento del flujo de calor en el proceso de activación alcalina de la ceniza volante
Mauled Yesenia Echeverri-Aguirre1*, Juan Sebastián Rudas-Flórez1, Jarol Esneider
Molina-Mosquera1, Ary Alain Hoyos-Montilla2
1Grupo de investigación e innovación en energía -GiiEN-, Facultad de Ingeniería, Institución Educativa Pascual Bravo.
Calle 73 # 73a-226. C. P. 050034. Medellín, Colombia.
2Grupo Investigación del Cemento y Materiales de Construcción -CEMATCO-, Facultad de Minas, Universidad Nacional de
Colombia. Carrera 80 # 65-223. C. P. 050041. Medellín, Colombia.
CITE THIS ARTICLE AS:
M. Echeverri-Aguirre, J. S.
Rudas-Flórez, J. E.
Molina-Mosquera and A. A.
Hoyos-Montilla. ”Heat flow
modeling in the alkaline
activation process of fly ash”,
Revista Facultad de Ingeniería
Universidad de Antioquia, no.
111, pp. 31-37, Apr-Jun 2024.
[Online]. Available: https:
//www.doi.org/10.17533/
udea.redin.20230624
ARTICLE INFO:
Received: February 04, 2022
Accepted: June 22, 2023
Available online: June 22, 2023
KEYWORDS:
Fly ash; alkaline cement;
modelling
Ceniza volante; cemento
alcalino; modelamiento
ABSTRACT: Cement production plays an important role in strengthening the infrastructure
of growing countries such as Colombia. However, the production of this material has a
high energy cost and contributes to the emission of large amounts of CO2. To address
these environmental concerns, it is essential to explore alternative materials that can
partially or completely replace traditional cement. Alkaline activated cement (AAC)
has emerged as a promising candidate in this regard. Due to this, it is necessary
to understand the process of alkaline activation and the variables that influence
it. This research proposes a phenomenological-based semi-physical model, which
predicts the performance of some variables that control alkaline activation: activator
concentration (NaOH), heat flow, and degree of reaction. The model results show
that with the increment of the activator concentration, the degree of reaction also
increases. Furthermore, the model has an accurate response compared with the
Freisleben-Hansen model. The integral square error criterion (ISE) was used in this
comparison.
RESUMEN: La producción de cemento juega un papel importante en el fortalecimiento
de la infraestructura de un país en pleno crecimiento como lo es Colombia. Sin
embargo, la producción de este material tiene un alto costo energético y contribuye
a la emisión de grandes cantidades de CO2. Para abordar estas preocupaciones
ambientales, es esencial explorar materiales alternativos que puedan reemplazar
parcial o completamente al cemento tradicional. El cemento alcalino activado (AAC)
se ha convertido en un candidato prometedor en este sentido. Por ello, es necesario
comprender el proceso de activación alcalina y las variables que influyen en él. En esta
investigación se propone un modelo semifísico de base fenomenológica, el cual predice
el desempeño de algunas variables que controlan la activación alcalina: concentración
del activador (NaOH), el flujo de calor y el grado de reacción. Los resultados del modelo
indican que con el incremento del activador alcalino (NaOH) el grado de reacción también
se incrementa. El modelo presenta resultados precisos comparados con el desempeño
del modelo propuesto por Freisleben-Hansen. En esta comparación se utilizó el criterio
de error cuadrado integral (ISE).
1. Introduction
The production of Ordinary Portland Cement (OPC) has a
significant environmental impact, primarily due to its high
CO2 emissions and energy consumption.
OPC manufacturing is responsible for the emission of large
quantities of CO2 (0.82 to 1.0tCO2/t cement ) [1]. This
carbon emission is related to the high energy consumption
during manufacture: calcination of limestone and the
heating of raw materials to temperatures above 1450
◦C. [1] Recent studies reported that OPC manufacturing
contributes to annual anthropogenic CO2 emissions of
approximately 8 and 10% [2]. On the other hand, the
energy required for OPC production is as high as 3400 MJ/t
31
* Corresponding author: Mauled Yesenia Echeverri-Aguirre
E-mail: mauled.echeverri481@pascualbravo.edu.co
ISSN 0120-6230
e-ISSN 2422-2844
DOI: 10.17533/udea.redin.20230624 31
M. Echeverri-Aguirreet al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 31-37, 2024
cement corresponding to 2.5 % of the energy used in the
world for the manufacture of materials [3].
Many efforts are being made to reduce the environmental
impact of OPC production without requiring significant
technological changes. Alkaline activated cement
(AAC) has emerged as a promising alternative to OPC.
Studies have shown that AAC has better manufacturing
and application conditions and can be produced using
industrial by-products, thus avoiding waste accumulation
[2, 4]. AAC cement only requires approximately 2 MJ/t to
be transformed into cement, and it has a carbon footprint
for concrete production lower than 9% to that of OPC [3].
One of the scientist’s challenges is designing strategies
to control and optimize AAC manufacturing processes,
including a deep understanding of their kinetic behavior.
According to the literature, the correlation between
the heat released in the processes of hydration and
the maturation of cement can help explain the kinetic
behavior of reactions [5]. Some studies have reported
models to predict the behavior of the activation process
in cementitious materials. Termkhajornkit and Barbarulo
proposed a model of the hydration process on OPC
[6]. This model included the effect of the temperature
on the reaction degree. Moreover, the model offers
an understanding of physical and chemical behavior
from a phenomenological approach. In a different
approach, Parka et. developed an empirical model using
artificial neural networks to predict some properties
of OPC considering the hydration kinetics [7]. Finally,
models based on microcalorimetry experiments [3, 5],
phenomenologically based models [8–10] models
considering molecular computational approach [11, 12],
descriptive based models [13], are some of the most
studied models. However, due to the complexity of the
phenomena involved, no model accurately represents the
dynamics of heat flow associated with alkaline activation
in all its stages [4, 14–16].
This research proposes a phenomenological model with
a semiempirical base to predict the performance of key
variables controlling alkaline activation, such as NaOH
concentration (alkaline activator), heat flow, and degree of
reaction.
2. Methodology
The methodology employed in this study consisted of
three stages: theoretical, simulation, and validation. In
the theoretical stage, a systematic literature review was
carried out to find models that represent the process of
alkaline activation and determine the relevant variables
and equations required to structure the model. The
simulation stage involved solving the mathematical model
using commercial software, specifically Matlab®. In
Figure 1 Shrinking Core Model Schematic Representation.
Adapted from [14]
accordance with the differential equation to be solved and
the recommendations found in [17], the ode45 integration
method was used in Matlab ®. Finally, the proposed model
was validated at different operating points by comparing
the simulation results with other models reported in the
literature, particularly with the Freiesleben-Hansen model
[18]. The Freiesleben-Hansen model has been widely
used to relate the maximum heat generated in a hydration
process and activation alkali process and to predict the
degree of reaction. With the validation purpose, an integral
square-error criterion (ISE) under the Freiesleben-Hansen
model and the proposed model was performed. For further
information on the integral square error criterion (ISE),
additional references can be consulted [19].
3. Model of alkaline activation
In this alkaline activation model, the influence of the
activator, properties of fly ash, and curing temperature on
the process are considered. It is assumed that alkaline
activation will start when fly ash and the activator come
into contact, and the product formed by the process
adheres spherically to the fly ash particles. As shown
in Figure 1, the first layer formed is a thin barrier or
intermediate layer (of thickness x), which is composed of
a metastable product formed by ions from the dissolution
of the process at the stage of the latent period. The
barrier layer gradually disappears, which may be because
it dissolves or becomes more permeable over time.
Additionally, the formation of two different layers of
products is considered, the inner product and the outer
product. The reaction is followed by the variation of the
radius ri of the spherical particle. The above corresponds
to Shrinking Core Model: [14, 20].
The Shrinking Core model equation is given by Equation
1, Where ri is the radius of the unreacted fly ash core,
r0 is the outside particle radius, R is the initial radius
of the fly ash particle, a is the number of moles of the
alkaline solution reacting per mole of fly ash consumed,
32
cement corresponding to 2.5 % of the energy used in the
world for the manufacture of materials [3].
Many efforts are being made to reduce the environmental
impact of OPC production without requiring significant
technological changes. Alkaline activated cement
(AAC) has emerged as a promising alternative to OPC.
Studies have shown that AAC has better manufacturing
and application conditions and can be produced using
industrial by-products, thus avoiding waste accumulation
[2, 4]. AAC cement only requires approximately 2 MJ/t to
be transformed into cement, and it has a carbon footprint
for concrete production lower than 9% to that of OPC [3].
One of the scientist’s challenges is designing strategies
to control and optimize AAC manufacturing processes,
including a deep understanding of their kinetic behavior.
According to the literature, the correlation between
the heat released in the processes of hydration and
the maturation of cement can help explain the kinetic
behavior of reactions [5]. Some studies have reported
models to predict the behavior of the activation process
in cementitious materials. Termkhajornkit and Barbarulo
proposed a model of the hydration process on OPC
[6]. This model included the effect of the temperature
on the reaction degree. Moreover, the model offers
an understanding of physical and chemical behavior
from a phenomenological approach. In a different
approach, Parka et. developed an empirical model using
artificial neural networks to predict some properties
of OPC considering the hydration kinetics [7]. Finally,
models based on microcalorimetry experiments [3, 5],
phenomenologically based models [8–10] models
considering molecular computational approach [11, 12],
descriptive based models [13], are some of the most
studied models. However, due to the complexity of the
phenomena involved, no model accurately represents the
dynamics of heat flow associated with alkaline activation
in all its stages [4, 14–16].
This research proposes a phenomenological model with
a semiempirical base to predict the performance of key
variables controlling alkaline activation, such as NaOH
concentration (alkaline activator), heat flow, and degree of
reaction.
2. Methodology
The methodology employed in this study consisted of
three stages: theoretical, simulation, and validation. In
the theoretical stage, a systematic literature review was
carried out to find models that represent the process of
alkaline activation and determine the relevant variables
and equations required to structure the model. The
simulation stage involved solving the mathematical model
using commercial software, specifically Matlab®. In
Figure 1 Shrinking Core Model Schematic Representation.
Adapted from [14]
accordance with the differential equation to be solved and
the recommendations found in [17], the ode45 integration
method was used in Matlab ®. Finally, the proposed model
was validated at different operating points by comparing
the simulation results with other models reported in the
literature, particularly with the Freiesleben-Hansen model
[18]. The Freiesleben-Hansen model has been widely
used to relate the maximum heat generated in a hydration
process and activation alkali process and to predict the
degree of reaction. With the validation purpose, an integral
square-error criterion (ISE) under the Freiesleben-Hansen
model and the proposed model was performed. For further
information on the integral square error criterion (ISE),
additional references can be consulted [19].
3. Model of alkaline activation
In this alkaline activation model, the influence of the
activator, properties of fly ash, and curing temperature on
the process are considered. It is assumed that alkaline
activation will start when fly ash and the activator come
into contact, and the product formed by the process
adheres spherically to the fly ash particles. As shown
in Figure 1, the first layer formed is a thin barrier or
intermediate layer (of thickness x), which is composed of
a metastable product formed by ions from the dissolution
of the process at the stage of the latent period. The
barrier layer gradually disappears, which may be because
it dissolves or becomes more permeable over time.
Additionally, the formation of two different layers of
products is considered, the inner product and the outer
product. The reaction is followed by the variation of the
radius ri of the spherical particle. The above corresponds
to Shrinking Core Model: [14, 20].
The Shrinking Core model equation is given by Equation
1, Where ri is the radius of the unreacted fly ash core,
r0 is the outside particle radius, R is the initial radius
of the fly ash particle, a is the number of moles of the
alkaline solution reacting per mole of fly ash consumed,
32
M. Echeverri-Aguirreet al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 31-37, 2024
the parameters Dx, Di, D0, are the diffusivities through
the barrier layer, inner and outer products, respectively,
and CNaOH is the concentration of the alkaline solution
(NaOH). In addition, k is the first-order reaction rate
constant, ρ is the molar density of fly ash, and x is the
thickness of the barrier formed in the latent period.
dr
dt = −CNaOH/aρ
[ 1
k + r2
i
Di
( 1
ri − 1
R
)]
+ xr2
i
Dy R2 + r2
i
D0
( 1
R − 1
r0
) (1)
Equation 1 considers three important phenomena in
alkaline activation: reaction/diffusion in inner product,
diffusion in the barrier layer, and diffusion in outer product.
The disappearance of the barrier layer is given by Equation
2 [20]:
x = x0e−β(t−t0) (2)
Where x0 is the initial thickness of the barrier layer, β is
the rate constant of the disappearance of the barrier layer
and t0 is the time where the barrier layer is formed.
The degree of reaction of alkaline activation can be
described by the following Equation 3 [14, 20]:
α = 1 −
( ri
R
)3
(3)
Finally, the heat flow accumulated during the alkaline
activation process, in which the reactions that occur are
exothermic, is given by Equation 4: [14, 20]
Q(t) = Qmaxα (4)
Where Qmax, is the maximum heat released in the alkaline
activation. In Table 1, the parameter values are shown.
The following assumptions are made:
• i) Fly ash is made up of spherical particles that are
uniform in size.
• ii) Sodium hydroxide (NaOH) is considered as the
transported (diffusing) reagent during the activation
process.
• iii) The density of compounds involved in the process
is assumed to remain constant over time and with
temperature changes.
• iv) The kinetics of the reactions occurring during
alkaline activation are assumed to follow a first-order
reaction rate.
• v) The thickness of the metastable barrier layer
is modeled as an exponential function basis on
references [14] and [20].
4. Results and analysis
In order to validate the proposed model, the results
were compared with the results from the model by
Freisleben-Hansen reported in the literature [3, 5, 18].
Freisleben-Hansn model is highly accurate in fitting
the experimental data, which makes it well-suited
for comparisons with other models. This is primarily
since the parametric adjustment process filters out the
inherent variations present in the experimental data
resulting from the precision limitations of the equipment
used. As a result, it provides a clean curve that can
be effectively compared with other models, allowing
a more reliable assessment of their performance and
predictive capabilities. Figure 2 shows the accumulated
heat obtained through the Freiesleben-Hansen and the
proposed model. For both models, a NaOH concentration
of 10 M and a temperature of 25° are considered. As
we can see, the two models present the same dynamic
behavior of the accumulated heat during the activation
process. The Freiesleben-Hansen model presents
more accumulated heat (nearly 13%) than the proposed
model. The most significant difference between the
models is that the Freiesleben-Hansen model does not
consider the first stage of alkaline activation; this is the
reason why the Freiesleben-Hansen model begins the
activation dynamic with 20 (J/g). In this first stage or
initial period, the dissolution and breaking of bonds of the
ash components are carried out. The proposed model
considers this initial period (Reaction/Diffusion term on
Equation 1). Nevertheless, because of the mathematical
structure, specifically, due to the model order, the curve of
accumulated heat is not similar to that of the experimental
data in this stage. Using the integral square-error criterion
(ISE) between the two analyzed models, an ISE= 2,040 was
obtained [19]. This value indicates that there is a 97.96%
similarity in the temporal behavior of the two curves.
In the literature, it is reported that the concentration range
of the alkaline activator (NaOH) yielding the best results
in alkaline activation is typically between 6 and 10 M [21].
Therefore, the analysis in this study focused on three
concentration values within this range: 6 M, 8 M, and 10
M. As shown in Figure 3, an increase in the concentration
of NaOH favors alkaline activation. This effect is due to
the fundamental role of the alkaline activator since it is
responsible for dissolving the aluminosilicate (fly ash) and
accelerating the reaction [23]. However, concentrations
above 10 M of NaOH lead to system saturation, which is
unfavorable for the properties of the cementitious material
[21] and thus were not considered in this study.
Upon contact of the fly ash particles with the alkaline
activator, heterogeneous exothermic reactions have
initiated releasing a certain amount of energy [4].
33
the parameters Dx, Di, D0, are the diffusivities through
the barrier layer, inner and outer products, respectively,
and CNaOH is the concentration of the alkaline solution
(NaOH). In addition, k is the first-order reaction rate
constant, ρ is the molar density of fly ash, and x is the
thickness of the barrier formed in the latent period.
dr
dt = −CNaOH/aρ
[ 1
k + r2
i
Di
( 1
ri − 1
R
)]
+ xr2
i
Dy R2 + r2
i
D0
( 1
R − 1
r0
) (1)
Equation 1 considers three important phenomena in
alkaline activation: reaction/diffusion in inner product,
diffusion in the barrier layer, and diffusion in outer product.
The disappearance of the barrier layer is given by Equation
2 [20]:
x = x0e−β(t−t0) (2)
Where x0 is the initial thickness of the barrier layer, β is
the rate constant of the disappearance of the barrier layer
and t0 is the time where the barrier layer is formed.
The degree of reaction of alkaline activation can be
described by the following Equation 3 [14, 20]:
α = 1 −
( ri
R
)3
(3)
Finally, the heat flow accumulated during the alkaline
activation process, in which the reactions that occur are
exothermic, is given by Equation 4: [14, 20]
Q(t) = Qmaxα (4)
Where Qmax, is the maximum heat released in the alkaline
activation. In Table 1, the parameter values are shown.
The following assumptions are made:
• i) Fly ash is made up of spherical particles that are
uniform in size.
• ii) Sodium hydroxide (NaOH) is considered as the
transported (diffusing) reagent during the activation
process.
• iii) The density of compounds involved in the process
is assumed to remain constant over time and with
temperature changes.
• iv) The kinetics of the reactions occurring during
alkaline activation are assumed to follow a first-order
reaction rate.
• v) The thickness of the metastable barrier layer
is modeled as an exponential function basis on
references [14] and [20].
4. Results and analysis
In order to validate the proposed model, the results
were compared with the results from the model by
Freisleben-Hansen reported in the literature [3, 5, 18].
Freisleben-Hansn model is highly accurate in fitting
the experimental data, which makes it well-suited
for comparisons with other models. This is primarily
since the parametric adjustment process filters out the
inherent variations present in the experimental data
resulting from the precision limitations of the equipment
used. As a result, it provides a clean curve that can
be effectively compared with other models, allowing
a more reliable assessment of their performance and
predictive capabilities. Figure 2 shows the accumulated
heat obtained through the Freiesleben-Hansen and the
proposed model. For both models, a NaOH concentration
of 10 M and a temperature of 25° are considered. As
we can see, the two models present the same dynamic
behavior of the accumulated heat during the activation
process. The Freiesleben-Hansen model presents
more accumulated heat (nearly 13%) than the proposed
model. The most significant difference between the
models is that the Freiesleben-Hansen model does not
consider the first stage of alkaline activation; this is the
reason why the Freiesleben-Hansen model begins the
activation dynamic with 20 (J/g). In this first stage or
initial period, the dissolution and breaking of bonds of the
ash components are carried out. The proposed model
considers this initial period (Reaction/Diffusion term on
Equation 1). Nevertheless, because of the mathematical
structure, specifically, due to the model order, the curve of
accumulated heat is not similar to that of the experimental
data in this stage. Using the integral square-error criterion
(ISE) between the two analyzed models, an ISE= 2,040 was
obtained [19]. This value indicates that there is a 97.96%
similarity in the temporal behavior of the two curves.
In the literature, it is reported that the concentration range
of the alkaline activator (NaOH) yielding the best results
in alkaline activation is typically between 6 and 10 M [21].
Therefore, the analysis in this study focused on three
concentration values within this range: 6 M, 8 M, and 10
M. As shown in Figure 3, an increase in the concentration
of NaOH favors alkaline activation. This effect is due to
the fundamental role of the alkaline activator since it is
responsible for dissolving the aluminosilicate (fly ash) and
accelerating the reaction [23]. However, concentrations
above 10 M of NaOH lead to system saturation, which is
unfavorable for the properties of the cementitious material
[21] and thus were not considered in this study.
Upon contact of the fly ash particles with the alkaline
activator, heterogeneous exothermic reactions have
initiated releasing a certain amount of energy [4].
33
M. Echeverri-Aguirreet al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 31-37, 2024
Table 1 Model parameters
Parameter Meaning Value Unit Data taken
from
R Particle size 15.0∗10−4 cm [21]
CNaOH
Concentration of the (6.0 − 10.0)∗10−3 mol/cm3 Experimental
sodium hydroxide data
a
Number of moles NaOH
5 - Experimentalreacting per mole of
datafly ash consumed
ρ Density of 9.7∗10−3 mol/cm3 [21]
fly ash
Dx/x0∗
Ratio of effective
3.4∗10−7 cm/h Fitting process
diffusivity coefficient
of barrier layer
and thickness.
t0
Time where the
1.0 h Experimentalbarrier layer
datais formed.
β
Rate constant of
1.4 - Experimentaldisappearance of
datathe barrier layer.
Di
Effective diffusivity
8.6∗10−8 cm2/h [11, 20]disappearance of
the barrier layer.
D0
Effective diffusivity
4.2∗10−7 cm2/h [22]disappearance of
the barrier layer.
k Kinetic constant 5.4∗10−5 cm/h [3]
at 25◦C
*This parameter was found through a fitting process, in which the output variables and the ranges
reported in the literature for materials like AAC were considered [20, 22].
Figure 2 Comparison of the accumulated heat of the alkaline activation obtained with the proposed model and model by
Freiesleben-Hasen
34
Table 1 Model parameters
Parameter Meaning Value Unit Data taken
from
R Particle size 15.0∗10−4 cm [21]
CNaOH
Concentration of the (6.0 − 10.0)∗10−3 mol/cm3 Experimental
sodium hydroxide data
a
Number of moles NaOH
5 - Experimentalreacting per mole of
datafly ash consumed
ρ Density of 9.7∗10−3 mol/cm3 [21]
fly ash
Dx/x0∗
Ratio of effective
3.4∗10−7 cm/h Fitting process
diffusivity coefficient
of barrier layer
and thickness.
t0
Time where the
1.0 h Experimentalbarrier layer
datais formed.
β
Rate constant of
1.4 - Experimentaldisappearance of
datathe barrier layer.
Di
Effective diffusivity
8.6∗10−8 cm2/h [11, 20]disappearance of
the barrier layer.
D0
Effective diffusivity
4.2∗10−7 cm2/h [22]disappearance of
the barrier layer.
k Kinetic constant 5.4∗10−5 cm/h [3]
at 25◦C
*This parameter was found through a fitting process, in which the output variables and the ranges
reported in the literature for materials like AAC were considered [20, 22].
Figure 2 Comparison of the accumulated heat of the alkaline activation obtained with the proposed model and model by
Freiesleben-Hasen
34
M. Echeverri-Aguirreet al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 31-37, 2024
Figure 3 Effect of activator concentration (NaOH) on the degree of reaction of alkaline activation at 25◦C
(a) a (b) b
Figure 4 a) Heat accumulated during the alkaline activation process at 25◦C and 8M NaOH. b) Degree of reaction of alkaline
activation at 25◦C 8M NaOH
Figure 4a) represents the predicted energy release during
the alkaline activation process at 25◦C with an NaOH
concentration of 8 M, reaching a value of 140 J/g after
a curing time of 500 hours. Understanding this energy
release can help predict the behavior of activated cement
in real-world applications, addressing performance issues
related to mechanical properties, and even facilitating
the design of new cementitious materials [14, 24, 25].
Figure 4 b) shows the evolution of the reactions of the
alkaline activation process through the degree of reaction.
Particularly, when the curing time was 500 h, a degree of
reaction of 0.9 was reached. If we want to improve this
degree of reaction, we must analyze factors such as the
concentration of the activator (NaOH), the chemical and
physical composition of the ash, and the temperature at
which the alkaline activation is being given. These factors
significantly influence the process and could contribute to
optimizing alkaline activation [23].
5. Conclusions
In this study, a phenomenological-based semi-physical
model was proposed for the alkaline activation of fly ash
with sodium hydroxide. The most significant conclusions
are summarized below:
In the proposed model, we can see the kinetics variation
of fly ash, which accounts for the degree of reaction
in the alkaline activation. Additionally, it allows the
correlation between the degree of hydration and the
heat flow observed during the evolution of the process.
Understanding these relationships, makes it possible to
assess the concentration of species involved in alkaline
activation and identify conditions for process improvement.
Diffusive and reaction processes in a fly ash sphere when
contacting NaOH are represented by a phenomenological
model (proposed model). Unlike parametric models such
as Freisleben-Hansen [3, 21], the proposed model takes
into account the initial phase of the process.
35
Figure 3 Effect of activator concentration (NaOH) on the degree of reaction of alkaline activation at 25◦C
(a) a (b) b
Figure 4 a) Heat accumulated during the alkaline activation process at 25◦C and 8M NaOH. b) Degree of reaction of alkaline
activation at 25◦C 8M NaOH
Figure 4a) represents the predicted energy release during
the alkaline activation process at 25◦C with an NaOH
concentration of 8 M, reaching a value of 140 J/g after
a curing time of 500 hours. Understanding this energy
release can help predict the behavior of activated cement
in real-world applications, addressing performance issues
related to mechanical properties, and even facilitating
the design of new cementitious materials [14, 24, 25].
Figure 4 b) shows the evolution of the reactions of the
alkaline activation process through the degree of reaction.
Particularly, when the curing time was 500 h, a degree of
reaction of 0.9 was reached. If we want to improve this
degree of reaction, we must analyze factors such as the
concentration of the activator (NaOH), the chemical and
physical composition of the ash, and the temperature at
which the alkaline activation is being given. These factors
significantly influence the process and could contribute to
optimizing alkaline activation [23].
5. Conclusions
In this study, a phenomenological-based semi-physical
model was proposed for the alkaline activation of fly ash
with sodium hydroxide. The most significant conclusions
are summarized below:
In the proposed model, we can see the kinetics variation
of fly ash, which accounts for the degree of reaction
in the alkaline activation. Additionally, it allows the
correlation between the degree of hydration and the
heat flow observed during the evolution of the process.
Understanding these relationships, makes it possible to
assess the concentration of species involved in alkaline
activation and identify conditions for process improvement.
Diffusive and reaction processes in a fly ash sphere when
contacting NaOH are represented by a phenomenological
model (proposed model). Unlike parametric models such
as Freisleben-Hansen [3, 21], the proposed model takes
into account the initial phase of the process.
35
M. Echeverri-Aguirreet al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 31-37, 2024
This work explores the potential of using a
phenomenological model to represent and predict
the degree of hydration and heat flow, which constitutes
the basis for estimating the evolution of the reaction
kinetics on AAC.
6. Declaration of competing interest
We declare that we have no significant competing interests,
including financial or non-financial, professional, or
personal interests interfering with the full and objective
presentation of the work described in this manuscript.
7. Funding
The article has been published as part of XVI Simposio
Internacional de Energía - Expotecnológica (XVI SIE–2021)
organized by the Institución Universitaria Pascual Bravo.
Additionally, this work was supported by MINCIENCIAS:
Fondo Nacional de Financiamiento para la Ciencia, la
Tecnología y la Innovación “Francisco José de Caldas”
(Convocatoria 848 del 2019 Programa de Estancias
Postdoctorales), Institución Universitaria Pascual Bravo
Grand 614, ”Talento Pascualino” and Royalties Project in
Colombia BPIN 2020000100407.
8. Author contributions
M.E. Adaptation of the model to alkaline activation, analysis
of results and drafting of the article. J.S.R. Contributed
to the adaptation of the model to alkaline activation,
simulation and analysis of results and critical manuscript
revision. J.M and A.H.M. were involved in the analysis of
results and critical manuscript revision.
9. Data availability statement
The authors confirm that the data supporting the findings
of this study are available within the article [and/or] its
supplementary materials.
References
[1] M. M. A. Elahi, M. M. Hossain, M. R. Karim, M. F. Mohd-Zain,
and C. Shearer, “A review on alkali-activated binders: Materials
composition and fresh properties of concrete,” Construction and
Building Materials, vol. 210, Nov. 10, 2020. [Online]. Available:
https://doi.org/10.1016/j.conbuildmat.2020.119788
[2] A. Palomo, O. Maltseva, I. Garcia-Lodeiro, and
A. Fernández-Jiménez, “Portland versus alkaline cement:
Continuity or clean break: “a key decision for global sustainability”,”
Sec. Solid State Chemistry, vol. 9, Oct. 11 2021. [Online]. Available:
https://doi.org/10.3389/fchem.2021.705475
[3] A. A. Hoyos-Montilla, F. Puertas, and J. I. Tobón, “Microcalorimetric
study of the effect of calcium hydroxide and temperature on the
alkaline activation of coal fly ash,” Journal of Thermal Analysis
and Calorimetry, vol. 131, Sep. 13 2017. [Online]. Available:
https://doi.org/10.1007/s10973-017-6715-4
[4] P. Zhang, Z. Gao, J. Wang, J. Guo, S. Hu, and Y. Ling, “Properties
of fresh and hardened fly ash/slag based geopolymer concrete:
A review,” Journal of Cleaner Production, vol. 270, May. 20, 2020.
[Online]. Available: https://doi.org/10.1016/j.jclepro.2020.122389
[5] F. Xie, Z. Liu, D. Zhang, J. Wang, T. Huang, and D. Wang, “Reaction
kinetics and kinetics models of alkali activated phosphorus slag,”
Construction and Building Materials, vol. 237, Nov. 26, 2019. [Online].
Available: https://doi.org/10.1016/j.conbuildmat.2019.117728
[6] P. Termkhajornkit and R. Barbarulo, “Modeling the coupled effects
of temperature and fineness of portland cement on the hydration
kinetics in cement paste,” Cement and Concrete Research, vol. 42,
no. 3, Nov. 22, 2011. [Online]. Available: https://doi.org/10.1016/j.
cemconres.2011.11.016
[7] K. Bong-Park, T. Noguchi, and J. Plawsky, “Modeling of hydration
reactions using neural networks to predict the average properties
of cement paste,” Cement and Concrete Research, vol. 35, no. 9, Aug.
02, 2004. [Online]. Available: https://doi.org/10.1016/j.cemconres.
2004.08.004
[8] A. A. Siyal, K. Azizi-Azizli, Z. Man, L. Ismail, and M. Irfan-Khan,
“Geopolymerization kinetics of fly ash based geopolymers using
jmak model,” Ceramics International, vol. 42, no. 14, Jul. 01, 2016.
[Online]. Available: https://doi.org/10.1016/j.ceramint.2016.07.006
[9] R. Xiao, X. Jiang, M. Zhang, P. Polaczyk, and B. Huang, “Analytical
investigation of phase assemblages of alkali-activated materials in
cao-sio2-al2o3 systems: The management of reaction products and
designing of precursors,” Materials & Design, vol. 194, Jul. 20, 2020.
[Online]. Available: https://doi.org/10.1016/j.matdes.2020.108975
[10] Y. Sun and H. S. L. K. Q Wang and, “Prediction of compressive
strength development for blended cement mortar considering fly
ash fineness and replacement ratio,” Construction and Building
Materials, vol. 271, Oct. 20, 2020. [Online]. Available: https:
//doi.org/10.1016/j.conbuildmat.2020.121532
[11] X. Y. Wang and H. S. Lee, “Modeling the hydration of concrete
incorporating fly ash or slag,” Cement and Concrete Research,
vol. 40, no. 7, Mar. 01, 2010. [Online]. Available: https://doi.org/10.
1016/j.cemconres.2010.03.001
[12] L. Y. Xu, Y. Alrefaei, Y. S. Wang, and J. G. Dai, “Recent advances in
molecular dynamics simulation of the n-a-s-h geopolymer system:
modeling, structural analysis, and dynamics,” Construction and
Building Materials, vol. 276, Dec. 24, 2020. [Online]. Available:
https://doi.org/10.1016/j.conbuildmat.2020.122196
[13] I. García-Lodeiro, S. Donatello, A. Fernandez-Jiménez, and
A. Palomo, “Hydration of hybrid alkaline cement containing
a very large proportion of fly ash: A descriptive model,”
Materials, vol. 9, no. 605, Jul. 18, 2016. [Online]. Available:
https://doi.org/10.3390/ma9070605
[14] J. J. Thomas, J. J. Biernacki, J. W. Bullard, S. Bishnoi, J. S. Dolado,
G. W. Scherer, and et al., “Modeling and simulation of cement
hydration kinetics and microstructure development,” Cement and
Concrete Research, vol. 41, no. 12, Oct. 07, 2010. [Online]. Available:
https://doi.org/10.1016/j.cemconres.2010.10.004
[15] D. Marchon and R. Flatt, “8 - mechanisms of cement hydration,”
Science and Technology of Concrete Admixtures, vol. 131, Nov. 20 2015.
[Online]. Available: https://doi.org/10.1016/B978-0-08-100693-1.
00008-4
[16] B. Sun, G. Ye, and G. de Schutter, “A review: Reaction mechanism
and strength of slag and fly ash-based alkali-activated materials,”
Construction and Building Materials, vol. 326, Feb. 02, 2022. [Online].
Available: https://doi.org/10.1016/j.conbuildmat.2022.126843
[17] T. M. Works. (1994-2023) Elegir un solver de ode.
[Online]. Available: https://es.mathworks.com/help/matlab/math/
choose-an-ode-solver.html
[18] G. M. Idorn and N. Thaulow, “Effectiveness of research on fly ash
36
This work explores the potential of using a
phenomenological model to represent and predict
the degree of hydration and heat flow, which constitutes
the basis for estimating the evolution of the reaction
kinetics on AAC.
6. Declaration of competing interest
We declare that we have no significant competing interests,
including financial or non-financial, professional, or
personal interests interfering with the full and objective
presentation of the work described in this manuscript.
7. Funding
The article has been published as part of XVI Simposio
Internacional de Energía - Expotecnológica (XVI SIE–2021)
organized by the Institución Universitaria Pascual Bravo.
Additionally, this work was supported by MINCIENCIAS:
Fondo Nacional de Financiamiento para la Ciencia, la
Tecnología y la Innovación “Francisco José de Caldas”
(Convocatoria 848 del 2019 Programa de Estancias
Postdoctorales), Institución Universitaria Pascual Bravo
Grand 614, ”Talento Pascualino” and Royalties Project in
Colombia BPIN 2020000100407.
8. Author contributions
M.E. Adaptation of the model to alkaline activation, analysis
of results and drafting of the article. J.S.R. Contributed
to the adaptation of the model to alkaline activation,
simulation and analysis of results and critical manuscript
revision. J.M and A.H.M. were involved in the analysis of
results and critical manuscript revision.
9. Data availability statement
The authors confirm that the data supporting the findings
of this study are available within the article [and/or] its
supplementary materials.
References
[1] M. M. A. Elahi, M. M. Hossain, M. R. Karim, M. F. Mohd-Zain,
and C. Shearer, “A review on alkali-activated binders: Materials
composition and fresh properties of concrete,” Construction and
Building Materials, vol. 210, Nov. 10, 2020. [Online]. Available:
https://doi.org/10.1016/j.conbuildmat.2020.119788
[2] A. Palomo, O. Maltseva, I. Garcia-Lodeiro, and
A. Fernández-Jiménez, “Portland versus alkaline cement:
Continuity or clean break: “a key decision for global sustainability”,”
Sec. Solid State Chemistry, vol. 9, Oct. 11 2021. [Online]. Available:
https://doi.org/10.3389/fchem.2021.705475
[3] A. A. Hoyos-Montilla, F. Puertas, and J. I. Tobón, “Microcalorimetric
study of the effect of calcium hydroxide and temperature on the
alkaline activation of coal fly ash,” Journal of Thermal Analysis
and Calorimetry, vol. 131, Sep. 13 2017. [Online]. Available:
https://doi.org/10.1007/s10973-017-6715-4
[4] P. Zhang, Z. Gao, J. Wang, J. Guo, S. Hu, and Y. Ling, “Properties
of fresh and hardened fly ash/slag based geopolymer concrete:
A review,” Journal of Cleaner Production, vol. 270, May. 20, 2020.
[Online]. Available: https://doi.org/10.1016/j.jclepro.2020.122389
[5] F. Xie, Z. Liu, D. Zhang, J. Wang, T. Huang, and D. Wang, “Reaction
kinetics and kinetics models of alkali activated phosphorus slag,”
Construction and Building Materials, vol. 237, Nov. 26, 2019. [Online].
Available: https://doi.org/10.1016/j.conbuildmat.2019.117728
[6] P. Termkhajornkit and R. Barbarulo, “Modeling the coupled effects
of temperature and fineness of portland cement on the hydration
kinetics in cement paste,” Cement and Concrete Research, vol. 42,
no. 3, Nov. 22, 2011. [Online]. Available: https://doi.org/10.1016/j.
cemconres.2011.11.016
[7] K. Bong-Park, T. Noguchi, and J. Plawsky, “Modeling of hydration
reactions using neural networks to predict the average properties
of cement paste,” Cement and Concrete Research, vol. 35, no. 9, Aug.
02, 2004. [Online]. Available: https://doi.org/10.1016/j.cemconres.
2004.08.004
[8] A. A. Siyal, K. Azizi-Azizli, Z. Man, L. Ismail, and M. Irfan-Khan,
“Geopolymerization kinetics of fly ash based geopolymers using
jmak model,” Ceramics International, vol. 42, no. 14, Jul. 01, 2016.
[Online]. Available: https://doi.org/10.1016/j.ceramint.2016.07.006
[9] R. Xiao, X. Jiang, M. Zhang, P. Polaczyk, and B. Huang, “Analytical
investigation of phase assemblages of alkali-activated materials in
cao-sio2-al2o3 systems: The management of reaction products and
designing of precursors,” Materials & Design, vol. 194, Jul. 20, 2020.
[Online]. Available: https://doi.org/10.1016/j.matdes.2020.108975
[10] Y. Sun and H. S. L. K. Q Wang and, “Prediction of compressive
strength development for blended cement mortar considering fly
ash fineness and replacement ratio,” Construction and Building
Materials, vol. 271, Oct. 20, 2020. [Online]. Available: https:
//doi.org/10.1016/j.conbuildmat.2020.121532
[11] X. Y. Wang and H. S. Lee, “Modeling the hydration of concrete
incorporating fly ash or slag,” Cement and Concrete Research,
vol. 40, no. 7, Mar. 01, 2010. [Online]. Available: https://doi.org/10.
1016/j.cemconres.2010.03.001
[12] L. Y. Xu, Y. Alrefaei, Y. S. Wang, and J. G. Dai, “Recent advances in
molecular dynamics simulation of the n-a-s-h geopolymer system:
modeling, structural analysis, and dynamics,” Construction and
Building Materials, vol. 276, Dec. 24, 2020. [Online]. Available:
https://doi.org/10.1016/j.conbuildmat.2020.122196
[13] I. García-Lodeiro, S. Donatello, A. Fernandez-Jiménez, and
A. Palomo, “Hydration of hybrid alkaline cement containing
a very large proportion of fly ash: A descriptive model,”
Materials, vol. 9, no. 605, Jul. 18, 2016. [Online]. Available:
https://doi.org/10.3390/ma9070605
[14] J. J. Thomas, J. J. Biernacki, J. W. Bullard, S. Bishnoi, J. S. Dolado,
G. W. Scherer, and et al., “Modeling and simulation of cement
hydration kinetics and microstructure development,” Cement and
Concrete Research, vol. 41, no. 12, Oct. 07, 2010. [Online]. Available:
https://doi.org/10.1016/j.cemconres.2010.10.004
[15] D. Marchon and R. Flatt, “8 - mechanisms of cement hydration,”
Science and Technology of Concrete Admixtures, vol. 131, Nov. 20 2015.
[Online]. Available: https://doi.org/10.1016/B978-0-08-100693-1.
00008-4
[16] B. Sun, G. Ye, and G. de Schutter, “A review: Reaction mechanism
and strength of slag and fly ash-based alkali-activated materials,”
Construction and Building Materials, vol. 326, Feb. 02, 2022. [Online].
Available: https://doi.org/10.1016/j.conbuildmat.2022.126843
[17] T. M. Works. (1994-2023) Elegir un solver de ode.
[Online]. Available: https://es.mathworks.com/help/matlab/math/
choose-an-ode-solver.html
[18] G. M. Idorn and N. Thaulow, “Effectiveness of research on fly ash
36
M. Echeverri-Aguirreet al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 31-37, 2024
in concrete,” Cement and Concrete Research, vol. 15, no. 3, Dec.
21, 1984. [Online]. Available: https://doi.org/10.1016/j.conbuildmat.
2020.119788
[19] M. Letizia-Guerra, L. Sorini, and L. Stefanini, “Quantile and expectile
smoothing based on l1-norm and l2-norm fuzzy transforms,”
International Journal of Approximate Reasoning, vol. 107, Jan. 23,
2019. [Online]. Available: https://doi.org/10.1016/j.ijar.2019.01.011
[20] J. M. Pommersheim and J. R. Clifton, “Mathematical modeling of
tricalcium silicate hydration,” Cement and Concrete Research, vol. 9,
no. 6, Sep. 11, 1979. [Online]. Available: https://doi.org/10.1016/
0008-8846(79)90072-3
[21] A. A. Hoyos-Montilla, F. Puertas, and J. I. Tobón, “Study of the
reaction stages of alkali-activated cementitious materials using
microcalorimetry,” Advances in Cement Research, vol. 33, no. 1, Jan.
22 2021. [Online]. Available: https://doi.org/10.1680/jadcr.19.00025
[22] M. Narmluk and T. Nawa, “Effect of fly ash on the kinetics of portland
cement hydration at different curing temperatures,” Cement and
Concrete Research, vol. 41, no. 6, Feb. 24 2011. [Online]. Available:
https://doi.org/10.1016/j.cemconres.2011.02.005
[23] Z. Li, G. Xu, and X. Shi, “Reactivity of coal fly ash used in cementitious
binder systems: A state-of-the-art overview,” Fuel, vol. 301, May. 08
2021. [Online]. Available: https://doi.org/10.1016/j.fuel.2021.121031
[24] O. Heinz and H. Heinz, “Cement interfaces: Current understanding,
challenges, and opportunities,” Langmuir, vol. 37, no. 21, May.
17 2021. [Online]. Available: https://doi.org/10.1021/acs.langmuir.
1c00617
[25] H. Wang, X. Zhao, T. Wang, L. Su, B. Zhou, and Y. Li, “Determination
of gel products in alkali-activated fly ash-based composites
incorporating inorganic calcium additives,” Advances in Materials
Science and Engineering, vol. 2022, Feb. 15, 2022. [Online]. Available:
https://doi.org/10.1155/2022/7476671
37
in concrete,” Cement and Concrete Research, vol. 15, no. 3, Dec.
21, 1984. [Online]. Available: https://doi.org/10.1016/j.conbuildmat.
2020.119788
[19] M. Letizia-Guerra, L. Sorini, and L. Stefanini, “Quantile and expectile
smoothing based on l1-norm and l2-norm fuzzy transforms,”
International Journal of Approximate Reasoning, vol. 107, Jan. 23,
2019. [Online]. Available: https://doi.org/10.1016/j.ijar.2019.01.011
[20] J. M. Pommersheim and J. R. Clifton, “Mathematical modeling of
tricalcium silicate hydration,” Cement and Concrete Research, vol. 9,
no. 6, Sep. 11, 1979. [Online]. Available: https://doi.org/10.1016/
0008-8846(79)90072-3
[21] A. A. Hoyos-Montilla, F. Puertas, and J. I. Tobón, “Study of the
reaction stages of alkali-activated cementitious materials using
microcalorimetry,” Advances in Cement Research, vol. 33, no. 1, Jan.
22 2021. [Online]. Available: https://doi.org/10.1680/jadcr.19.00025
[22] M. Narmluk and T. Nawa, “Effect of fly ash on the kinetics of portland
cement hydration at different curing temperatures,” Cement and
Concrete Research, vol. 41, no. 6, Feb. 24 2011. [Online]. Available:
https://doi.org/10.1016/j.cemconres.2011.02.005
[23] Z. Li, G. Xu, and X. Shi, “Reactivity of coal fly ash used in cementitious
binder systems: A state-of-the-art overview,” Fuel, vol. 301, May. 08
2021. [Online]. Available: https://doi.org/10.1016/j.fuel.2021.121031
[24] O. Heinz and H. Heinz, “Cement interfaces: Current understanding,
challenges, and opportunities,” Langmuir, vol. 37, no. 21, May.
17 2021. [Online]. Available: https://doi.org/10.1021/acs.langmuir.
1c00617
[25] H. Wang, X. Zhao, T. Wang, L. Su, B. Zhou, and Y. Li, “Determination
of gel products in alkali-activated fly ash-based composites
incorporating inorganic calcium additives,” Advances in Materials
Science and Engineering, vol. 2022, Feb. 15, 2022. [Online]. Available:
https://doi.org/10.1155/2022/7476671
37