CO2 mixtures

Journal Pre-proof On the evolution of pore microstructure during coal char activation with steam/CO2 mixtures

Juan C. Maya, Robert Macías, Carlos A. Gómez, Farid Chejne PII:

S0008-6223(19)31221-7

DOI:

https://doi.org/10.1016/j.carbon.2019.11.088

Reference:

CARBON 14845

To appear in:

Carbon

Received Date:

11 October 2019

Accepted Date:

26 November 2019

Please cite this article as: Juan C. Maya, Robert Macías, Carlos A. Gómez, Farid Chejne, On the evolution of pore microstructure during coal char activation with steam/CO2 mixtures, Carbon (2019), https://doi.org/10.1016/j.carbon.2019.11.088

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Journal Pre-proof 1 On the evolution of pore microstructure during coal char activation with steam/CO2 mixtures Juan C. Maya1, Robert Macías1, Carlos A. Gómez1 and Farid Chejne*1 1

Universidad Nacional de Colombia – Sede Medellín, Facultad de Minas –

Departamento de Procesos y Energía – TAYEA – Cr 80 No 65-223, Medellín, 050034 – Colombia Abstract- Abstract- The present work develops a novel mathematical model for coal char activation with CO2, steam, and a CO2/steam mixture. The main assumption is that CO2 and steam react with distinct active sites, considered by attributing a unique char structure effect to each gasifying agent; the CO2-char reaction increases the pore length, whereas the steamchar reaction increases the pore radius. Additionally, pore overlapping effect was taken into account and the radial pore growth was computed by means of a population balance equation. Model predictions of both the pore size distribution and specific surface area changes were compared with experimental data, resulting in an outstanding fit. This supports the model main assumption, which reconciles discrepancies between various authors regarding the overall reaction rate during activation of coal chars with CO2/steam mixtures. Finally, the maximum specific surface area occurs under chemically-controlled conditions, where all particle zones reach their maximum surface areas simultaneously, while for activation with diffusional limitations each particle zone attains its maximum specific surface area at a different time. Keywords: Mathematical modelling, activation, gasification, coal char, carbon dioxide.

1.

Introduction

Activation of carbonaceous materials by partial gasification has been widely examined for its applications in wastewater treatment processes [1], the removal of undesirable tastes, colors and odors, solvent recovery, and recently in the pharmaceutical industry for toxin

Journal Pre-proof 2 removal [2]. In this process, a gas penetrates through the pores of the char and reacts with the carbon at the pore surface, which produces a change in the microstructure. During the initial stage of activation, there is an increase in both pore volume and specific surface area; however, at some point, a maximum specific surface area is reached. This maximum value is mainly determined by the char’s initial microstructure and the gasifying agent. Therefore, understanding the development of the microstructure during the activation process is fundamental to producing high quality activated carbon. Two of the most commonly used gasifying agents are steam and CO2, which is why a large number of experimental and theoretical studies on gasification with these molecules can be found in the scientific literature. Most of these works examine gasification with either steam or CO2, while few examine gasification with steam/CO2 mixtures. Roberts and Harris [3] found that for gasification with a steam/CO2 mixture at high pressures, the char-CO2 and char-steam reactions take place on common active sites. Similarly, Umemoto et al. [4] proposed a reaction model assuming that CO2 and steam share active sites, obtaining good agreement with experimental data. However, several authors [5–10] found that for gasification with steam/CO2 mixtures at atmospheric pressure, the char-CO2 and char-steam reactions occur at distinct active sites, such that the overall reaction rate can be expressed as the sum of the reaction rate of each gas. Furthermore, Arenas and Chejne [11] found that CO2 elongates pores whereas steam widens pores. That is, CO2 increases the average pore length while steam increases the average pore radius. Similar observations were made by Coetzee et al. [12,13], who used an interesting approach to follow the evolution of the gasification process based on Small Angle X-ray Scattering (SAXS), which can be used to evaluate pore sizes. They found that, for the steam gasification, smaller pores increase their size as the conversion increases and, in contrast, during the CO2 gasification, there is an increase in the number of pores (or pore length) with an insignificant change in pore size. To better predict the behavior of the microstructure during the activation process, it is necessary to develop particle models that adequately predict structural variables such as specific surface area, porosity, and Pore Size Distribution (PSD). Essentially, a particle model starts with a geometric description of the particle and its internal structure, i.e. the

Journal Pre-proof 3 porous structure. Probably the simplest model is the Shrinking Core Model (SCM), in which the solid particle reacts, generating a layer of solid product through which gases diffuse. Although the SCM can appropriately describe the overall activation kinetics [14], this model does not describe the internal structure of the particle, which defines the quality of the activated carbon. Another model simulating char gasification kinetics is the Single Pore Model [15], in which the particle is described by a set of pores of uniform size that grow due to the chemical reaction. The so-called grain model describes the particle as a population of uniform grains that react following an SCM mechanism. The latter two models adequately describe the evolution of conversion over time and also consider the existence of concentration gradients in the particle. However, they predict a monotonic variation of the specific surface area, which is not in accordance with the experimental observations. The pore growth in the early stage of activation causes an increase in the specific surface area. However, as the activation progresses, the growing pores intersect with adjacent pores. Therefore, the specific surface area increases due to the growth of the pores, and decreases due to the intersection of adjacent pores. Eventually the specific surface area reaches a maximum, after which the pore intersection dominates, leading to a monotonic decrease of the surface area until the char is completely consumed. To simulate the phenomenon described above, some authors proposed models based on population balances that predict the Pore Size Distribution [16–18]. These models assume that the reactant solid is formed of a population of cylindrical pores that grow and coalesce due to the gasification reaction. Nonetheless, these models require the adjustment of a parameter known as aggregation frequency, which lacks a physical meaning within the activation process. In addition, pore coalescence does not adequately represent the real phenomenon, which is pore intersection; that is, although the pores intersect, they do not lose their identity at medium and low conversions, which is the case of the activation process. To represent the effect of pore intersection, the so-called pore overlapping models [19] were developed, of which the most widely used is the Random Pore Model (RPM) [20] and its derivatives [21–23]. These models assume that the particle is formed of cylindrical pores that grow and overlap randomly as the gasification reaction proceeds. Nevertheless, the overlapping models consider that the pores

Journal Pre-proof 4 grow only radially, which may not be the case, as experimental data show that pore growth during gasification may be longitudinal [16,24–26], especially for the CO2-char reaction. The most commonly used models to describe the gasification reaction with steam/CO2 mixtures are the Random Pore Model [27], the Shrinking Core Model, and the volumetric model [28], which does not take into account the microstructure of the reactant particle. Thus, although these models have been able to properly describe the overall kinetics of the reaction with steam/CO2 mixtures, the evolution of the microstructure, or PSD, of the solid has not been predicted. Furthermore, at present, the models for gasification only consider radial pore growth. Consequently, this work presents a mathematical model that elucidates the effect of steam/CO2 mixtures on the microstructure (PSD) evolution of coal char during activation by partial gasification. This model takes into account the pore overlap phenomenon and both radial and longitudinal pore growth, and is validated with experimental data taken by both porosimetry and thermogravimetry. The proposed model prioritizes involving the minimum number of parameters necessary to fit. Lastly, the effect of intraparticle concentration gradients on the evolution of the specific surface area is also considered.

2. Experimental Three samples of Colombian coals were used, designated as C1-3. The proximate analysis of these three parent coals (reported in as-received basis (ar)), and the initial specific surface area of their respective chars are shown in Table 1.

Table 1. Proximate analysis of parent coal samples and initial specific surface area of chars. Coal

C1

C2

C3

Journal Pre-proof 5 Ash (wt% ar)

2.2

4.1

3.7

Moisture (wt% ar)

11.1

8.6

7.9

Volatile matter (wt% ar)

42.3

40.7

38.6

Fixed carbon (wt% ar)

44.4

46.6

49.8

Initial specific surface area of chars

(

𝑚2𝑜𝑓 𝑝𝑜𝑟𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 3

𝑚 𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

)

3.4E+08 3.1E+08 2.8E+08

2.1. Determination of Chemical Control conditions. The present paper studies the evolution of the PSD and specific surface area during activation, under both chemical control conditions and with intraparticle gradients. Therefore, it was initially necessary to determine under which particle size and gas flow conditions chemical control is achieved. Several experiments (at T=850 °C) varying the particle size and gas flow were carried out in a LINSEIS STA PT1600 thermogravimetric balance. Intraparticle gradients were found to disappear for average particle sizes smaller than or equal to 0.07 mm. Additionally, the external mass transfer resistance was negligible for gas flows larger than 100 mL STP/min. 2.2. Evolution of the PSD and specific surface area. The coals were both devolatilized and activated using a heating muffle. The sample was spread on a ceramic plate inside the heating muffle at room temperature in a pure N2 atmosphere. Subsequently, the muffle was heated up to a temperature of 850 °C, which was held for 90 min to ensure complete devolatilization. The muffle was then turned off, maintaining the pure N2 atmosphere until returning to room temperature. The sample was withdrawn from the heating muffle to measure its weight and the initial pore size distribution. Each coal char sample was then reheated to a temperature of 850 °C in a N2 atmosphere. The gasifying agent was injected up to the desired concentration in the gasification atmosphere (90% CO2 and 10% N2 for the CO2 activation; 10% steam and 90 % N2 for the steam

Journal Pre-proof 6 activation; and 10% steam and 90% CO2 for the steam/CO2 activation). After a specific time, the atmosphere was returned to pure N2 and the muffle was turned off. Upon reaching room temperature, the sample was weighed, sieved, and carried for the specific surface area and porosimetry measurements. The specific surface area and porosimetry measurements were performed by means of CO2 adsorption using a Micrometrics TriStar II Plus surface and porosity analyzer. The Pore Size Distribution (PSD) was calculated using the NonLocal Density Functional Theory (NLDFT) method, and the specific surface area was calculated using the Dubinin-Radushkevich equation (each measurement of specific surface area was performed three times and an average was taken). A previous work [29] reports that the activated carbon produced from the coals of this work are microporous, signifying that characterization by CO2 adsorption should properly describe the solid microstructure. Table 2 shows the sampling times, conversions, and specific surface areas associated with the experiments developed under both chemical control and diffusional limitations.

Table 2. Sampling times, conversions and specific surface areas of each experiment. Chemical control conditions Samp le

C1 (CO2)

C1 (steam )

C1 (steam/C O2)

C2 (CO2)

Sampling time (min) 11 53 8 32 84 13 -

t1 t2 t3 t4

12 21 40 60

38 60 100 150

6 9 15 20

t5

80

200

25

-

C2 (steam )

C2 (steam/C O2)

-

-

Conversion 0.13 0.22 0.23 0.34

C3 (CO2)

C3 (steam)

C3 (steam/CO2)

14 43

71 114

11 17

-

-

-

-

-

-

0.22 0.53

0.11 0.20

X1 X2

0.32 0.49

0.15 0.26

0.23 0.36

0.2 0.5

X3

0.72

0.5

0.62

-

-

-

-

-

-

X4

0.84

0.7

0.79

-

-

-

-

-

-

X5

0.92

0.87

0.9

-

-

-

-

-

-

(m2/m3)

S1 S2 S3

1.5E+ 09 1.9E+ 09 2.0E+ 09

5.3E+0 8 6.7E+0 8 6.8E+0 8

Specific surface area 1.2E+ 5.0E+0 1.3E+09 09 8 1.2E+09 2.0E+ 6.0E+0 1.4E+09 09 8 1.4E+09

0.23 0.35

1.7E+09

-

-

-

1.1E+ 09 1.8E+ 09 -

4.3E+08

1.1E+09

4.9E+08

1.3E+09

-

-

Journal Pre-proof 7 1.8E+ 09 1.1E+ 09

S4 S5

3.7E+0 8 5.7E+0 7

1.2E+09 5.7E+08

-

-

-

-

-

-

-

-

-

-

-

Reaction with diffusive limitations C1 (CO2)

Sample t1 t2 t3 t4

25 50 75 100

40 80 120 160

t5

-

200

C1 (steam/ CO2)

C1 (steam)

C2 (CO2)

C2 (steam/ CO2)

C2 (steam)

Sampling time (min) -

20 30 40 50 -

C3 (stea m)

C3 (CO2)

C3 (steam/CO2 )

-

-

-

-

-

-

-

-

-

Conversion -

-

-

-

-

X1

0.14

0.12

0.21

-

X2 X3 X4

0.3 0.44 0.58

0.26 0.41 0.56

0.35 0.47 0.56

-

-

-

-

-

-

-

-

-

-

-

-

X5

-

0.71

-

-

-

-

-

-

-

Specific surface area (m2/m3)

S4

7.4E+ 08 1.2E+ 09 1.2E+ 09 1.1E+ 09

S5

-

S1 S2 S3

5.2E+0 8 6.2E+0 8 6.8E+0 8 5.7E+0 8 3.9E+0 8

8.9E+08 6.8E+08 5.6E+08 4.5E+08 -

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

3.

3.1.

The model

Model Assumptions

The following assumptions were made in the development of this model:



The reactions to be modelled are 𝐶 + 𝐶𝑂2(𝑔)→2𝐶𝑂(𝑔)

Journal Pre-proof 8 𝐶 + 𝐻2𝑂(𝑔)→𝐶𝑂(𝑔) + 𝐻2(𝑔) 

The reactant particle is spherical and formed by cylindrical pores that grow axially when reacting with steam and longitudinally when reacting with CO2.



The particle maintains its spherical shape and initial radius throughout the reaction.



Two resistances to activation are considered: diffusion within pores, and surface chemical reactions.



At the beginning of the reaction, pore radii are distributed non-uniformly.



The process is considered isothermal in the model proposed herein. Intraparticle temperature gradients have been reported to be negligible for experimental conditions similar to those used in this work [30].



A non-steady state is considered.



Pore overlapping is considered.

3.2.

Model Development

In the present work’s model, the reacting particle is described by a population of cylindrical pores with non-uniform initial radii that grow lengthwise due to the CO2-char reaction and radially due to the steam-char reaction. Consequently, the intrinsic reaction rates for the CO2char and steam-char reactions may be expressed in terms of the change in mean pore length and pore radius, respectively:

𝑑𝑙 𝑑𝑡

=

𝑑𝑟𝑝 𝑑𝑡

𝑘1(𝐶𝐶𝑂2)

=

(1)

𝜌𝑚

𝑘2(𝐶𝐻2𝑂)

(2)

𝜌𝑚

where 𝜌𝑚 is the molar density of the reactant solid, 𝑙 is the mean pore length, 𝑟𝑝 is the pore radius, 𝐶𝐶𝑂2 is the CO2 concentration, 𝐶𝐻2𝑂 is the steam concentration, and 𝑘1 and 𝑘2 are the reaction kinetic constants for the CO2-char and the steam-char reactions, respectively. The

Journal Pre-proof 9 mass balances for the particle, taking into account the mass transfer by diffusion and the chemical reaction, are given by: ∂𝐶𝑖

1 ∂

∂𝐶𝑖

(

)

𝜀 ∂𝑡 = 𝑅2∂𝑅 𝐷𝑒,𝑖𝑅2 ∂𝑅 ― 𝑟𝑖

(3)

where 𝜀 is the porosity, 𝑅 is the radial coordinate within the particle, 𝐶𝑖, 𝐷𝑒,𝑖, and 𝑟𝑖 are the concentration, the effective diffusivity, and the volumetric reaction rate, respectively, which are associated with each component 𝑖 = 𝐶𝑂2, 𝐻2𝑂. For the sake of simplicity, the sub-index 𝑖 always refers to variables related to both the CO2 and steam. Equation (3) is subject to the following boundary conditions ∂𝐶𝑖 ∂𝑅

=0

at R=0

𝐶𝑖 = 𝐶𝑖,𝑏 at R=Rp where 𝐶𝑖,𝑏 is the concentration in the bulk phase. The volumetric reaction rates for both CO2 and steam are functions of their intrinsic reaction rates and their specific surface areas: 𝑑𝑙

(4)

𝑑𝑟𝑝

(5)

𝑟𝐶𝑂2 = 𝑣𝐶 𝜌𝑚𝑑𝑡𝑆𝐶𝑂2

𝑟𝐻2𝑂 = 𝑣𝐶 𝜌𝑚 𝑑𝑡 𝑆𝐻2𝑂

where 𝑣𝐶 is the volumetric fraction of carbon in the particle, and 𝑆𝐶𝑂2 and 𝑆𝐻2𝑂 are the specific surface area of the CO2-char and steam-char reactions, respectively. However, since it is assumed that the steam-char reaction increases the pore size, the surface reaction must take place at the pore walls; therefore, 𝑆𝐻2𝑂 gives the pore wall surface area per unit volume. On the other hand, because it is assumed that the CO2-char reaction increases the pore length, the CO2 must react with the bottom surfaces (approximately equal to the cross-sectional area of the pore) of the dead-end pores; therefore, 𝑆𝐶𝑂2 is the area of the pore ends per unit volume. The effective diffusivity is expressed as follows [31]

Journal Pre-proof 10

𝐷𝑒,𝐶𝑂2 = 𝜀2𝐷𝑔,𝐶𝑂2

(6)

where 𝐷𝑔,𝐶𝑂2 is the pore diffusivity of CO2, which is calculated from the combination of molecular diffusivity and Knudsen diffusivity [32]. The local conversion is expressed as a function of initial and current porosities

𝑋(𝑅,𝑡) = 1 ―

(1 ― 𝜀) ― 𝑣𝑎𝑠ℎ

(7)

(1 ― 𝜀0) ― 𝑣𝑎𝑠ℎ

where 𝑣𝑎𝑠ℎ is the volumetric fraction of ash. The average conversion is computed by integrating local conversion over the entire particle radius as follows 𝑅

𝑋(𝑡) =

∫0 𝑃4𝜋𝑅2𝑋(𝑅,𝑡)𝑑𝑅 4

(8)

3 3𝜋𝑅𝑃

3.3. Pore overlapping As pore length and radius grow due to the CO2/steam activation reaction, the pores begin to overlap. For a non-overlapped pore system, the cumulative pore volume distribution function is defined as follows 𝑟

𝐹𝑒 = ∫0𝑝𝑓𝜀,𝑒(𝑟𝑝')𝑑𝑟𝑝'

(9)

where 𝑓𝜀,𝑒(𝑟𝑝) and 𝐹𝑒 are the porosity density distribution function and the cumulative pore distribution, respectively, for the non-overlapped pore population. Avrami [33] found that the differential change of a population of objects randomly overlapped in space is

Journal Pre-proof 11 proportional to the fractional differential change of the correspondent non-overlapped system: (10)

𝑑𝐹 = (1 ― 𝐹)𝑑𝐹𝑒

where 𝐹 and 𝐹𝑒 are the cumulative fraction of pore volume occupied by the overlapped and non-overlapped pore systems, respectively. Similar expressions were used in the development of RPM, which assumes radial pore growth [20]. However, the concept of pore overlapping is also valid for longitudinally varying pore systems. Thus, Eq. (10) is solved by the expression 𝑟

𝐹 = 1 ― exp ( ― ∫0𝑝𝑓𝜀,𝑒(𝑟𝑝')𝑑𝑟𝑝')

(11)

The porosity density distribution function of the non-overlapped porous system 𝑓𝜀,𝑒(𝑟𝑝) is computed as 𝑓𝜀,𝑒(𝑟𝑝) = 𝜋𝑟2𝑓(𝑟𝑝)𝑙

(12)

where 𝑓(𝑟𝑝) is the pore radius density distribution function. For instance, 𝑓(𝑟𝑝) 𝑑𝑟𝑝 gives the number of pores per unit volume belonging to the radius range [𝑟𝑝, 𝑟𝑝 + 𝑑𝑟𝑝]. From Eq. (11), it is possible to derive an equation for the porosity density distribution function of the overlapped porous system. By definition, the density and cumulative distributions are related by 𝑑𝐹 𝑑𝑟𝑝

(13)

= 𝑓𝜀(𝑟𝑝)

where 𝑓𝜀(𝑟𝑝) is the porosity density distribution function of the non-overlapped porous system. Hence, by differentiating Eq. (11) with respect to 𝑟𝑝, we obtain 𝑟

𝑓𝜀(𝑟𝑝) = 𝑓𝜀,𝑒(𝑟𝑝) × exp ( ― ∫0𝑝𝑓𝜀,𝑒(𝑟𝑝')𝑑𝑟𝑝')

(14)

Journal Pre-proof 12 From Eq. (11), the total porosity of the sample can be readily calculated as follows ∞

lim 𝐹 = ∫0 𝑓𝜀(𝑟𝑝)𝑑𝑟𝑝 = 𝜀 = 1 ― exp( ― 𝜀𝑒)

(15)

𝑟𝑝→∞

where 𝜀𝑒 is the porosity of the non-overlapped system, which is given by ∞

𝜀𝑒 = ∫0 𝑓𝜀,𝑒(𝑟𝑝)𝑑𝑟𝑝

(16)

To derive expressions for 𝑆𝐶𝑂2 and 𝑆𝐻2𝑂, the cylindrical pores of the non-overlapped system are taken to grow radially by a differential amount 𝑑𝑟𝑝, leading to the following expression 𝑑𝜀𝑒 = 𝑆𝑒,𝐻2𝑂 𝑑𝑟𝑝

(17)

where 𝑆𝑒,𝐻2𝑂 is the specific surface area of the pore walls for the non-overlapped system. Similarly, for an overlapped system with radial pore growth, we have 𝑑𝜀 = 𝑆𝐻2𝑂 𝑑𝑟𝑝

(18)

Deriving Eq. (15) with respect to 𝜀𝑒 and combining with Eqs. (17) and (18) gives 𝑆𝐻2𝑂 = 𝑆𝑒,𝐻2𝑂 (1 ― 𝜀)

(19)

If the cylindrical pores grow in the axial direction a differential amount 𝑑𝑙, the following relations must be satisfied for the non-overlapped, Eq. (20), and the overlapped, Eq. (21), systems 𝑑𝜀𝑒 = 𝑆𝑒,𝐶𝑂2𝑑𝑙

(20)

𝑑𝜀 = 𝑆𝐶𝑂2 𝑑𝑙

(21)

Journal Pre-proof 13

where 𝑆𝑒,𝐶𝑂2 is the specific surface area of pore ends for the non-overlapped system. Following a similar procedure to that for deriving 𝑆𝐻2𝑂 leads to 𝑆𝐶𝑂2 = 𝑆𝑒,

𝐶𝑂2(1

― 𝜀)

(22)

The total specific surface area 𝑆 is given by the sum of 𝑆𝐻2𝑂 and 𝑆𝐶𝑂2 as 𝑆 = 𝑆𝐶𝑂2 + 𝑆𝐻2𝑂

(23)

The specific surface area of the pore walls for the non-overlapped system is given by

𝑆𝑒,𝐻2𝑂 =

∫

∞

2𝜋𝑙𝑟𝑝𝑓(𝑟𝑝)𝑑𝑟𝑝

(24)

0

while the specific surface area of the pore ends for the non-overlapped system is given by

𝑆𝑒,

𝐶𝑂2 =

∫

∞

𝜋𝑟𝑝2𝑓(𝑟𝑝)𝑑𝑟𝑝

(25)

0

Finally, 𝑓(𝑟𝑝) is calculated from the following population balance

[( ) ]

∂𝑓 ∂ 𝑑𝑟𝑝 =― 𝑓 ∂𝑡 ∂𝑟𝑝 𝑑𝑡

(26)

The model described above was solved using the ordinary differential equations solver ode15s from Matlab (R2017a), and the population balance Eq. (26) was computed using a variation of the Extended Method of Moments (EMOM), which is described elsewhere [31]. The reaction kinetic constants were fitted from the experiments under chemical control carried out in the thermogravimetric balance. Both the initial mean pore length and the pore

Journal Pre-proof 14 radius density distribution functions were obtained by following the procedure described by Gavals (1980) [19].

4.

4.1.

Analysis and results

Chemically-controlled conditions

The predictions of the model proposed herein were analyzed and compared with experimental data on the evolution of the PSD under chemically-controlled conditions for various atmospheres and char samples. Figures 1a-c show the PSD at different conversion degrees during activation with CO2 for C1-3, respectively. In these figures, the model predictions properly fit the experimental data and the PSD tends to grow in the y-axis direction. The latter indicates that the cylindrical pores increase in length with CO2gasification, without a significant variation in radius, which supports the main assumption of this work.

Journal Pre-proof 15

Figure 1a. Evolution of PSD during activation with CO2 for C1.

Figure 1b. Evolution of PSD during activation with CO2 for C2.

Journal Pre-proof 16

Figure 1c. Evolution of PSD during activation with CO2 for C3. Despite the agreement, the model proposed here fails to predict the evolution of the smallest microspores (𝑟𝑝=1.5-2.5 Å) of the PSD for C3. This behavior can be explained by experimental observations showing that CO2 opens the closed micropores initially present in some coal-chars [34]. This behavior could be modeled mathematically in a similar way to a nucleation phenomenon [17]. However, this requires additional parameters describing the kinetics of the appearance of pores, which is not compatible with this work’s goal of modeling coal char microstructure development with the minimum number of parameters.

Journal Pre-proof 17

Figure 2a. Evolution of PSD during activation with steam for C1.

Journal Pre-proof 18

Figure 2b. Evolution of PSD during activation with steam for C2.

Figure 2c. Evolution of PSD during activation with steam for C3.

Journal Pre-proof 19

Figures 2a-c show the evolution of PSD during steam activation for C1-3, respectively. The model predictions agree with experimental data. Moreover, the PSD tends to move toward the right side of the x-axis as the reaction takes place. This confirms past observations [11,34] and the model’s assumption that steam’s main effect on the coal-char microstructure during activation is the increase in pore radius. However, the model overpredicts the PSD at X=0.13 for C2. This may be due to three reasons. Firstly, it is likely that the kinetic constant of the reaction varies during steam-C2 activation as steam gasification is an endothermic reaction (+131 kJ/mol [35]), which can result in a transient reduction of the kinetic constant during early stages of the process where the reaction rate is faster [36]. Secondly, thermal annealing decreases the reaction rates during gasification due to a reduction in reactive sites [11,37]. Finally, the model developed herein does not consider the occurrence of homogeneous reactions (e.g., water-gas shift reaction), which can also affect the fit between the model predictions and experimental data.

Journal Pre-proof 20 Figure 3a. Evolution of PSD during activation with a CO2/steam mixture for C1.

Figure 3b. Evolution of PSD during activation with a CO2/steam mixture for C2.

Figure 3c. Evolution of PSD during activation with a CO2/steam mixture for C3.

Journal Pre-proof 21 Figures 3a-c show the evolution of PSD during CO2/steam activation for C1-3, respectively. In these figures, the PSD moves to the right on the x-axis due to the effect of steam and up on the y-axis due to the pore growth. Thus, the model predicts the tendency of all distributions, confirming the assumption that during coal-char activation with steam/CO2 mixtures, each gasifying agent reacts on different active sites, such that the overall reaction rate is the sum of the reaction rates of each agent. Nevertheless, it must be said that this conclusion is only valid for the experimental conditions of this work. These results show that pore size may be controlled during char activation by using CO2/steam mixtures. For instance, it is common for the adsorption process to require the existence of large pores that facilitate transport within the char particle and micropores that provide sufficient surface area for adsorption to occur [38]. In this case, the appropriate concentration of steam in the mixture allows the pore size to be increased to the desired value so that the final activated carbon contains both mesopores and micropores for transport and adsorption, respectively. It is important to analyze why other authors [3,4] found that CO2 and steam share active sites during coal char activation. First, Roberts & Harris [3] conducted their experiments under high pressures, while those carried out in this work were conducted under atmospheric pressure. Secondly, the work of Umemoto et al. [4] presents two significant sources of error: (1) the specific surface area used for the reaction rate calculations was taken from the RPM, which only considers radial pore growth; and (2), the authors used different values of the RPM parameter 𝛹 for the CO2-char and the steam-char reactions. However, this parameter only depends on the initial pore structure of the char (it is only function of the initial total pore length, the initial specific surface area, and the initial porosity), which implies that it should have the same value regardless of the reaction taking place.

4.2.

Intraparticle gradients

The effect of the concentration gradients within the particle on the development of the specific surface area during coal char activation with CO2, steam, and a CO2/steam mixture was analyzed. An average particle size of 2 mm was used during the activation test at 850 °C. Figures 4a-c show the evolution of the normalized specific surface area (defined as the ratio

Journal Pre-proof 22 of the current specific surface area 𝑆 to the initial specific surface area 𝑆0) with respect to the conversion of C1 for activation with CO2, steam, and CO2/steam, respectively. Each figure presents the model predictions and the experimental data under both chemical control and diffusional limitations. The so-called percolation threshold, defined as the critical porosity at which the porous matrix can no longer maintain its structure and fragments into smaller particles, is an important characteristic. For reactions with diffusive limitations, the particle size decreases as gasification occurs due to peripheral fragmentation. However, to take this phenomenon into account, two parameters are required [39]: the critical porosity 𝜀𝑐 at which fragmentation occurs, and the critical porosity gradient ∇𝜀𝑐. Critical porosity may vary over a wide range (𝜀𝑐 ≈ 0.2 ― 0.99 [40]), whereas the critical porosity gradient must be determined using experimental data for each coal char sample. However, due to the objective of modeling coal char activation using the least number of parameters, the percolation threshold was not taken into account. Consequently, only experimental data exhibiting no significant sample fragmentation were considered. The percolation threshold does not affect the chemically-controlled reactions due to negligible porosity gradients; therefore, the fragmentation phenomenon does not occur [39].

Journal Pre-proof 23

Figure 4a. Evolution of normalized specific surface area for the activation of C1 with CO2.

Journal Pre-proof 24

Figure 4b. Evolution of normalized specific surface area for the activation of C1 with steam.

Figure 4c. Evolution of normalized specific surface area for the activation of C1 with a CO2/steam mixture.

Journal Pre-proof 25 Figure 4a shows that chemical control conditions lead to a specific surface area larger than that for the CO2-char reaction with intraparticle gradients. The latter is better understood by defining the following dimensionless variable 𝜏𝐷

𝜃 = 𝜏𝐶

(27)

where 𝜏𝐶 and 𝜏𝐷 are the complete conversion times (𝑋=99.9 %) for chemical control conditions and intraparticle gradients, respectively. The parameter 𝜃 quantifies the relative effect of diffusive limitations on the overall reaction kinetics. Thus, as 𝜃 tends to one, the intraparticle pore diffusional resistance becomes negligible. Conversely, as 𝜃 becomes larger than one, the relative importance of pore diffusion on the overall kinetics increases. The present work found θ to be 1.77, meaning that pore diffusion resistance causes the gasification with intraparticle gradients to take almost twice as long to complete as the chemically controlled reaction. In other words, the particle center takes about two times longer to complete the reaction than the periphery. This signifies that when the particle center reaches its maximum specific surface area, the overlap effect has already reduced the specific surface area of the outermost layer of the particle to below its maximum. Consequently, for the experimental conditions of this work, the maximum specific surface area obtained by CO2 activation with diffusional limitations cannot be as large as that achieved with chemical control conditions. Figure 4b shows that the maximum specific surface areas for steam activation with chemical control conditions and with intraparticle gradients are very similar. In this case, 𝜃 was found to be 1.1, indicating that diffusive limitations are smaller than those of the CO2-char reaction, Figure 4a. This behavior can be explained by the steam increasing the radius of the pores as the reaction progresses, whereas for the CO2-char reaction the pores maintain an almost constant radius. Therefore, the fluid-pore wall interactions [32,41] of CO2 are stronger than those of steam, with an effective CO2 diffusivity significantly smaller than that of steam. This is illustrated by defining the mean effective diffusivity 𝐷𝑒𝑓𝑓,𝑖, which is calculated by averaging the effective diffusivity over time and space as follows

Journal Pre-proof 26 𝐷𝑒𝑓𝑓,𝑖 = 4

1 3𝜋

𝑅𝑝3

𝑡

𝑅

∫0𝑓∫0 𝑝𝐷𝑒𝑓𝑓,𝑖(𝑡,𝑅) 4𝜋𝑅2𝑑𝑅 𝑑𝑡

(28)

× 𝑡𝑓

where 𝑡𝑓 is the simulation time. The calculated mean effective diffusivity for steam activation was 1.3*10-5 m2/s, whereas for CO2 activation it was 3.2*10-7 m2/s. It is observed that the model fails to fit the experimental specific surface area for the steam-char reaction with intraparticle gradients at later stages. This is due to the fact that CO2 is only capable of measuring microporosity under typical adsorption conditions (T=273 K). The specific surface area predictions for the CO2-char reactions are in agreement with experimental data over the whole conversion range; the CO2 does not significantly increase the pore radius, leaving the char microporous during all reaction stages. Conversely, steam-char activation increases the pore radius as the reaction progresses, leading to wide pores at late reaction stages which cannot be measured by CO2 adsorption. Figure 4c shows that the maximum specific surface area for the reactions with intraparticle gradients is much smaller than that of the chemically-controlled reactions. This difference is the most pronounced with the mixed agents, followed by the case of CO2 activation, Figure 4a. This is expected since the gas mixture produces a higher reactivity than that obtained using each gas separately. For steam/CO2 mixture activation with chemical control, the calculated initial reactivity

𝑑𝑋 𝑑𝑡

is 0.029 min-1, while for steam and CO2 activation,

𝑑𝑋 𝑑𝑡

is

0.009 min-1 and 0.019 min-1, respectively. This increase in reactivity causes diffusive phenomena to gain importance, leading to a 𝜃 of 2, implying that diffusive limitations are more significant for activation with CO2/steam mixtures than for activation with either gas separately.

Conclusions The present work develops a new mathematical model for coal char activation with CO2/steam mixtures. It considers the pore overlapping phenomenon that strongly affects the development of both porosity and specific surface area during the physical activation process.

Journal Pre-proof 27 Radial pore growth associated with the steam-char reaction was taken into account using a population balance equation. Additionally, the longitudinal pore growth associated with the CO2-char reaction was also considered, which had not been done so far. The model predictions were compared with experimental data of both PSD and specific surface area development. Even though the model only requires the fitting of two parameters (the reaction kinetic constants for booth CO2-char and steam-char reactions), a remarkable agreement between experimental data and simulations was observed. This indicates that, for the experimental conditions of this work, the two main assumptions of this model are correct: (1) the effect of CO2 on the char microstructure during activation is the increase in pore length; and (2) the main effect of steam is the increase in pore radius. Therefore, pore size may be controlled during char activation by using the proper concentration of steam in the CO2/steam mixture. This can be applied when designing activated carbons since it is known that the adsorption process requires both micropores and mesopores for adsorption and transport, respectively. The experimental data for char activation with the CO2/steam mixture were suitably predicted by taking the overall reaction rate to be the sum of the reaction rates of the CO2-char and steam-char reactions. This supports the idea that steam and CO2 react on different active sites for the experimental conditions of this work. Similarly, no inhibition or synergy effects were observed. Intraparticle concentration gradients during activation reactions reduce the maximum obtainable specific surface area to less than that achievable under chemical control conditions due to a mismatch in timing. By the time the inner zone of the particle reaches its maximum specific surface area, the specific surface area of the periphery has already begun to decrease below its maximum value due to the overlapping effect.

Nomenclature 𝐶𝑖

concentration of gas 𝑖 (𝑖=CO2, steam),

[ ] 𝑚𝑜𝑙 𝑚3

Journal Pre-proof 28 𝐶𝑖,𝑏

concentration in the bulk phase of gas 𝑖 (𝑖=CO2, steam),

[ ] 𝑚𝑜𝑙 𝑚3

𝑚2 𝑠

[ ]

𝐷𝑒,𝑖

effective diffusivity of gas 𝑖 (𝑖=CO2, steam),

𝐷𝑒𝑓𝑓,𝑖

mean effective diffusivity of gas 𝑖 (𝑖=CO2, steam),

𝑚2 𝑠

[ ]

𝑚2 𝑠

[ ]

𝐷𝑔,𝑖

pore diffusivity of gas 𝑖 (𝑖=CO2, steam),

𝐹

cumulative fraction of pore volume occupied by the overlapped pore system

[

𝑚3𝑜𝑓 𝑝𝑜𝑟𝑒 𝑚3𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

]

𝑓(𝑟𝑝)

pore radius density distribution function

𝐹𝑒

cumulative fraction of pore volume occupied by the non-overlapped pore system

𝑓𝜀(𝑟𝑝) 𝑓𝜀,𝑒(𝑟𝑝)

[

[

]

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑟𝑒𝑠

𝑚3𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 × 𝑚 𝑜𝑓 𝑝𝑜𝑟𝑒 𝑟𝑎𝑑𝑖𝑢𝑠

𝑚3𝑜𝑓 𝑝𝑜𝑟𝑒 𝑚3𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

]

porosity density distribution function of the overlapped pore system

[

]

𝑚3𝑜𝑓 𝑝𝑜𝑟𝑒

𝑚3𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 × 𝑚 𝑜𝑓 𝑝𝑜𝑟𝑒 𝑟𝑎𝑑𝑖𝑢𝑠

porosity density distribution function of the non-overlapped pore population

[

]

𝑚3𝑜𝑓 𝑝𝑜𝑟𝑒

𝑚3𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 × 𝑚 𝑜𝑓 𝑝𝑜𝑟𝑒 𝑟𝑎𝑑𝑖𝑢𝑠 𝑚 (n=1,2), 𝑠

[]

𝑘𝑛

Reaction kinetic constant

𝑙 𝑅 𝑟𝑖

mean pore length, [𝑚] radial coordinate within the particle, [𝑚] 𝑚𝑜𝑙 volumetric reaction rate, 𝑠 𝑚3

𝑟𝑝 𝑆

pore radius, [𝑚]

[ ]

total specific surface area,

[

𝑚2𝑜𝑓 𝑝𝑜𝑟𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑚3𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

] [

𝑆𝑒,𝐶𝑂2

specific surface area of pore ends for the non-overlapped system,

𝑆𝑒,𝐻2𝑂

specific surface area of the pore walls for the non-overlapped system,

[

𝑚2𝑜𝑓 𝑝𝑜𝑟𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑚3𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

[

specific surface area of pore ends for the overlapped system,

𝑆𝐻2𝑂

specific surface area of the pore walls for the overlapped system,

𝑆0 𝑇 𝑡𝑓 𝑣𝑎𝑠ℎ 𝑣𝐶

initial specific surface area, temperature, [𝐾] simulation time, [𝑠] volumetric fraction of ash,

[

[

𝑚 𝑜𝑓 𝑝𝑜𝑟𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑚3𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

𝑚3𝑜𝑓 𝑎𝑠ℎ 𝑚3𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

]

]

volumetric fraction of carbon in the particle,

[

𝑚3𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

]

]

𝑆𝐶𝑂2

2

𝑚2𝑜𝑓 𝑝𝑜𝑟𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒

𝑚3𝑜𝑓 𝑐𝑎𝑟𝑏𝑜𝑛 𝑚3𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

]

𝑚2𝑜𝑓 𝑝𝑜𝑟𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒

]

𝑚3𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑚2𝑜𝑓 𝑝𝑜𝑟𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒

[

𝑚3𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

]

Journal Pre-proof 29 𝑋 𝑋

Conversion, [ ― ] average conversion, [ ― ]

Greek letters symbols 𝜀 𝜀𝑒 𝜀𝑐

porosity of particle,

[

𝑚3𝑜𝑓 𝑝𝑜𝑟𝑒 𝑚3𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

]

porosity of the non-overlapped system, critical porosity,

[

3

𝑚 𝑜𝑓 𝑝𝑜𝑟𝑒 𝑚3𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

[

𝑚3𝑜𝑓 𝑝𝑜𝑟𝑒 𝑚3𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

]

]

𝜃 𝜌𝑚

Parameter defined in equation (27), [ ― ] 𝑚𝑜𝑙 molar density of the reactant solid, 𝑚3

𝜏𝐶 𝜏𝐷 𝛹

conversion time for chemical control conditions, [𝑠] conversion time for control intraparticle gradients, [𝑠] Parameter from the random pore model, [ ― ]

Acknowledgments The authors wish to thank to the project "Strategy of transformation of the Colombian energy sector in the horizon 2030" funded by the call 788 of Colciencias Scientific Ecosystem, Contract number FP44842-210-2018. Finally, the second author thanks call 785 of Colciencias “Convocatoria de Doctorados Nacionales 2017”.

Journal Pre-proof 30 References [1]

A. Bhatnagar, W. Hogland, M. Marques, M. Sillanpää, An overview of the modification methods of activated carbon for its water treatment applications, Chem. Eng. J. 219 (2013) 499–511. https://doi.org/10.1016/j.cej.2012.12.038.

[2]

M. Danish, T. Ahmad, A review on utilization of wood biomass as a sustainable precursor for activated carbon production and application, Renew. Sustain. Energy Rev. 87 (2018) 1–21. https://doi.org/10.1016/J.RSER.2018.02.003.

[3]

D.G. Roberts, D.J. Harris, Char gasification in mixtures of CO2 and H2O: Competition

and

inhibition,

Fuel.

86

(2007)

2672–2678.

https://doi.org/https://doi.org/10.1016/j.fuel.2007.03.019. [4]

S. Umemoto, S. Kajitani, S. Hara, Modeling of coal char gasification in coexistence of CO2 and H2O considering sharing of active sites, Fuel. 103 (2013) 14–21. https://doi.org/https://doi.org/10.1016/j.fuel.2011.11.030.

[5]

S. Nilsson, A. Gómez-Barea, P. Ollero, Gasification of char from dried sewage sludge in fluidized bed: Reaction rate in mixtures of CO2 and H2O, Fuel. 105 (2013) 764– 768. https://doi.org/10.1016/J.FUEL.2012.09.008.

[6]

Z. Huang, J. Zhang, Y. Zhao, H. Zhang, G. Yue, T. Suda, M. Narukawa, Kinetic studies of char gasification by steam and CO2 in the presence of H2 and CO, Fuel Process.

Technol.

91

(2010)

843–847.

https://doi.org/https://doi.org/10.1016/j.fuproc.2009.12.020. [7]

R.C. Everson, H.W.J.P. Neomagus, H. Kasaini, D. Njapha, Reaction kinetics of pulverized coal-chars derived from inertinite-rich coal discards: Gasification with carbon

dioxide

and

steam,

Fuel.

85

(2006)

1076–1082.

https://doi.org/10.1016/J.FUEL.2005.10.016. [8]

H.-L. Tay, S. Kajitani, S. Zhang, C.-Z. Li, Effects of gasifying agent on the evolution of char structure during the gasification of Victorian brown coal, Fuel. 103 (2013) 22– 28. https://doi.org/10.1016/J.FUEL.2011.02.044.

Journal Pre-proof 31 [9]

C. Guizani, F.J. Escudero Sanz, S. Salvador, The gasification reactivity of highheating-rate chars in single and mixed atmospheres of H2O and CO2, Fuel. 108 (2013) 812–823. https://doi.org/https://doi.org/10.1016/j.fuel.2013.02.027.

[10]

K. Jayaraman, I. Gokalp, Effect of char generation method on steam, CO2 and blended mixture gasification of high ash Turkish coals, Fuel. 153 (2015) 320–327. https://doi.org/https://doi.org/10.1016/j.fuel.2015.01.065.

[11]

E. Arenas, F. Chejne, The effect of the activating agent and temperature on the porosity development of physically activated coal chars, Carbon N. Y. 42 (2004) 2451–2455. https://doi.org/http://dx.doi.org/10.1016/j.carbon.2004.04.041.

[12]

G.H. Coetzee, R. Sakurovs, H.W.J.P. Neomagus, L. Morpeth, R.C. Everson, J.P. Mathews, J.R. Bunt, Pore development during gasification of South African inertiniterich chars evaluated using small angle X-ray scattering, Carbon N. Y. 95 (2015) 250– 260. https://doi.org/10.1016/J.CARBON.2015.08.030.

[13]

G.H. Coetzee, R. Sakurovs, H.W.J.P. Neomagus, R.C. Everson, J.P. Mathews, J.R. Bunt, Particle size influence on the pore development of nanopores in coal gasification chars: From micron to millimeter particles, Carbon N. Y. 112 (2017) 37–46. https://doi.org/10.1016/J.CARBON.2016.10.088.

[14]

Q. Liu, H. He, H. Li, J. Jia, G. Huang, B. Xing, C. Zhang, Y. Cao, Characteristics and kinetics of coal char steam gasification under microwave heating, Fuel. 256 (2019) 115899. https://doi.org/https://doi.org/10.1016/j.fuel.2019.115899.

[15]

H. Fatehi, X.-S. Bai, Structural evolution of biomass char and its effect on the gasification

rate,

Appl.

Energy.

185

(2017)

998–1006.

https://doi.org/https://doi.org/10.1016/j.apenergy.2015.12.093. [16]

M. Navarro, N. A. Seaton, A. M. Mastral, R. Murillo, Assessment of the development of the pore size distribution during carbon activation: A population balance approach, Stud. Surf. Sci. Catal. 160 (2007) 551–558. https://doi.org/10.1016/S01672991(07)80071-1.

[17]

K. Hashimoto, P.L. Silveston, Gasification: Part I. Isothermal, kinetic control model

Journal Pre-proof 32 for a solid with a pore size distribution, AIChE J. 19 (1973) 259–268. https://doi.org/10.1002/aic.690190209. [18]

G.A. SIMONS, The Structure of Coal Char: Part II.— Pore Combination, Combust. Sci. Technol. 19 (1979) 227–235. https://doi.org/10.1080/00102207908946883.

[19]

G.R. Gavals, A random capillary model with application to char gasification at chemically

controlled

rates,

AIChE

J.

26

(1980)

577–585.

https://doi.org/10.1002/aic.690260408. [20]

S.K. Bhatia, D.D. Perlmutter, A random pore model for fluid-solid reactions: I. Isothermal,

kinetic

control,

AIChE

J.

26

(1980)

379–386.

https://doi.org/10.1002/aic.690260308. [21]

J.S. Gupta, S.K. Bhatia, A modified discrete random pore model allowing for different initial

surface

reactivity,

Carbon

N.

Y.

38

(2000)

47–58.

https://doi.org/https://doi.org/10.1016/S0008-6223(99)00095-0. [22]

S.L. Singer, A.F. Ghoniem, An adaptive random pore model for multimodal pore structure evolution with application to char gasification, Energy & Fuels. 25 (2011) 1423–1437. https://doi.org/10.1021/ef101532u.

[23]

J. Cai, S. Wang, C. Kuang, A modified random pore model for carbonation reaction of CaO-based limestone with CO2 in different calcination-carbonation cycles, Energy Procedia.

105

(2017)

1924–1931.

https://doi.org/https://doi.org/10.1016/j.egypro.2017.03.561. [24]

M.V. Navarro, N.A. Seaton, A.M. Mastral, R. Murillo, Analysis of the evolution of the pore size distribution and the pore network connectivity of a porous carbon during activation,

Carbon

N.

Y.

44

(2006)

2281–2288.

https://doi.org/10.1016/J.CARBON.2006.02.029. [25]

I. Karaman, E. Yagmur, A. Banford, Z. Aktas, The effect of process parameters on the carbon dioxide based production of activated carbon from lignite in a rotary reactor, Fuel

Process.

Technol.

https://doi.org/10.1016/j.fuproc.2013.07.021.

118

(2014)

34–41.

Journal Pre-proof 33 [26]

C. Guizani, M. Jeguirim, R. Gadiou, F.J. Escudero Sanz, S. Salvador, Biomass char gasification by H2O, CO2 and their mixture: Evolution of chemical, textural and structural

properties

of

the

chars,

Energy.

112

(2016)

133–145.

https://doi.org/https://doi.org/10.1016/j.energy.2016.06.065. [27]

J. Li, Y. Qiao, X. Chen, P. Zong, S. Qin, Y. Wu, S. Wang, H. Zhang, Y. Tian, Steam gasification of land, coastal zone and marine biomass by thermal gravimetric analyzer and a free-fall tubular gasifier: Biochars reactivity and hydrogen-rich syngas production,

Bioresour.

Technol.

289

(2019)

121495.

https://doi.org/https://doi.org/10.1016/j.biortech.2019.121495. [28]

J. Preciado-Hernandez, J. Zhang, M. Zhu, Z. Zhang, D. Zhang, An experimental study of CO2 gasification kinetics during activation of a spent tyre pyrolysis char, Chem. Eng.

Res.

Des.

149

(2019)

129–137.

https://doi.org/https://doi.org/10.1016/j.cherd.2019.07.007. [29]

F. Chejne, Z. Zapata, D.A. Rojas, E. Arenas, C. Londoño, J.D. Pérez, Obtención de carbones activados a partir de carbones colombianos. Final Technical report, Minercol, Medellín, Colombia, 2001.

[30]

S. Lee, J.C. Angus, R. V. Edwards, N.C. Gardner, Noncatalytic coal char gasification, AIChE J. 30 (1984) 583–593. https://doi.org/10.1002/aic.690300409.

[31]

J.C. Maya, F. Chejne, Novel model for non catalytic solid–gas reactions with structural changes by chemical reaction and sintering, Chem. Eng. Sci. 142 (2016) 258–268. https://doi.org/10.1016/j.ces.2015.11.036.

[32]

J. Yuan, B. Sundén, On mechanisms and models of multi-component gas diffusion in porous structures of fuel cell electrodes, Int. J. Heat Mass Transf. 69 (2014) 358–374. https://doi.org/http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.10.032.

[33]

M. Avrami, Kinetics of phase change. II Transformation-time relations for random distribution

of

nuclei,

J.

Chem.

Phys.

8

(1940)

212.

https://doi.org/10.1063/1.1750631. [34]

F. Rodríguez-Reinoso, M. Molina-Sabio, M.T. González, The use of steam and CO2

Journal Pre-proof 34 as activating agents in the preparation of activated carbons, Carbon N. Y. 33 (1995) 15–23. https://doi.org/10.1016/0008-6223(94)00100-E. [35]

R. Slezak, L. Krzystek, S. Ledakowicz, Steam gasification of pyrolysis char from spent mushroom substrate, Biomass and Bioenergy. 122 (2019) 336–342. https://doi.org/https://doi.org/10.1016/j.biombioe.2019.02.007.

[36]

G.H. Fong, S. Jorgensen, S.L. Singer, Pore-resolving simulation of char particle gasification

using

micro-CT,

Fuel.

224

(2018)

752–763.

https://doi.org/10.1016/J.FUEL.2018.03.117. [37]

A. Zolin, A.D. Jensen, P.A. Jensen, K. Dam-Johansen, Experimental study of char thermal deactivation, Fuel. 81 (2002) 1065–1075. https://doi.org/10.1016/S00162361(02)00009-1.

[38]

L.P. Ding, S.K. Bhatia, F. Liu, Kinetics of adsorption on activated carbon: Application of heterogeneous vacancy solution theory, Chem. Eng. Sci. 57 (2002) 3909–3928. https://doi.org/10.1016/S0009-2509(02)00306-8.

[39]

F. Golfier, L. Van de steene, S. Salvador, F. Mermoud, C. Oltean, M.A. Bues, Impact of peripheral fragmentation on the steam gasification of an isolated wood charcoal particle

in

a

diffusion-controlled

regime,

Fuel.

88

(2009)

1498–1503.

https://doi.org/10.1016/J.FUEL.2009.02.043. [40]

B. Feng, S.K. Bhatia, B.F. and, S.K. Bhatia*, B. Feng, S.K. Bhatia, Percolative fragmentation of char particles during gasification, Energy & Fuels. 14 (2000) 297– 307. https://doi.org/10.1021/ef990090x.

[41]

X. Gao, J.C. Diniz da Costa, S.K. Bhatia, Understanding the diffusional tortuosity of porous materials: An effective medium theory perspective, Chem. Eng. Sci. 110 (2014) 55–71. https://doi.org/10.1016/j.ces.2013.09.050.

Journal Pre-proof

CRediT author statement Juan C. Maya: Investigation, Methodology, Software, Writing - Original Draft, Validation. Robert Macías: Investigation, Writing - Review & Editing. Carlos A. Gómez: Investigation, Writing - Review & Editing. Farid Chejne: Conceptualization, Methodology, Writing - Review & Editing, Investigation.

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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

None.