1. Introduction

2. Materials and Methods

2.2. Kinetic model

The mathematical model of the reaction was developed through reaction kinetics using the Langmuir-Hinshelwood mechanism, which involves adsorption of the reactants, catalytic surface reaction, and desorption of the products of the water-gas shift (WGS) reaction, the reverse reaction of dry methane re-forming (RDRM) and the steam reforming reactions of methane (SMR).

2.2.1. Reactions scheme

During the gasification process, the biomass macromolecule is transformed into a series of products, among the main ones are hydrogen $H_2$, carbon monoxide carbon $CO$, carbon dioxide ${CO}_2$, methane ${CH}_4$, water $H_{2}O$, and in smaller amounts coke and tars. To represent the gasification process, the following overall reaction is used [36]:

$$C_x{H}_y{O}_z+{nH}_{2}O\stackrel{∆}{\to }{a}_1{H}_2+a_{2}CO+a_3{CO}_2+a_4{H}_{2}O{+a}_5{CH}_4{+a}_{6}C+ tars$$

(1)

Biomass gasification involves a series of chemical reactions through drying, particle decomposition, oxidation, and reduction (WGS, RDRM, and SRM) In equation $\left(1\right)$ the amounts of each of the products depend on the operating conditions during the reaction, type of biomass, activity and selectivity of the catalyst. Alumina catalysts are characterized by their high surface area, thermal stability and adsorption capacity, so this stage is the determinant for the reaction kinetics [37].

From the general equation for biomass, we work with a solution of 1.5 mL of glucose at a concentration of 15%, taking as a reference the work done by [20] and the following specific equation:

$$C_6{H}_{12}{O}_6+H_{2}O{CH}_4+{3H}_2+{CO}_2+{2H}_{2}O+C$$

(2)

Equation (2) represents the process of transformation of glucose to synthesis gas and other components, with this it is possible to determine the number of moles. Once the number of moles and mass of each of the products were obtained, the molar flux was determined considering a reaction time of 25 seconds.

Provided that appropriate assumptions and approximations are established. Therefore, the following assumptions proposed by [21] are made for the kinetic model:

I.

Biomass is converted to CO, CO₂, H₂ and CH₄, with traces of coke and tar.

I.

II. The CO, CO₂, H₂, CH₄ and H₂O are adsorbed on the catalyst surface, which react until they desorb and form part of the product.

I.

III. The dominant reactions in the reaction are water-gas shift (WGS), dry reforming of methane (DRM) and steam reforming of methane (SRM) reactions.

For assumption (I) to be true during the reaction, the reactor pressure should not exceed 57 psi and the main products generated should be CO, CO₂, H₂, CH₄.

In the case of assumption (III), the value of the activation energies of the Bourdouard reaction and methanation must be greater than the SRM, WGS, and reverse dry reforming of methane (RDRM).

Taking these considerations into account, the following equations are presented.

Table 2. Main reactions of the gasification process.

Table 2. Main reactions of the gasification process.

Reaction	Stoichiometry
The water-gas shift (WGS)	$CO+H_{2}O\leftrightarrow H_2+{CO}_2$	(3)
Steam methane reforming (SMR)	${CH}_4+H_{2}O\leftrightarrow CO+3H_2$	(4)
Reverse dry methane reforming (RDRM)	${CH}_4+{CO}_2\leftrightarrow 2CO+2H_2$	(5)

2.2.1. Steam reforming of methane (SRM)

1. Methane adsorption on the active site of the catalyst:

$${CH}_4+S \begin{array}{c}\stackrel{k1}{\to }\\ \underset{k2}{\leftarrow }\end{array} {CH}_4 -S$$

(6)

2. Vapor adsorption on the active site of the catalyst:

$$H_{2}O+S \begin{array}{c}\stackrel{k3}{\to }\\ \underset{k4}{\leftarrow }\end{array} H_{2}O -S$$

(7)

3. Surface reaction at the active site of the catalyst:

$${CH}_4 -S+H_{2}O -S+2S \begin{array}{c}\stackrel{k5}{\to }\\ \underset{k6}{\leftarrow }\end{array} { CO-S+3H}_2 -S$$

(8)

4. CO desorption on the catalyst surface:

$$CO -S+2S \begin{array}{c}\stackrel{k7}{\to }\\ \underset{k8}{\leftarrow }\end{array} CO+S$$

(9)

5. Desorption of from the catalyst surface:

$$H_2 -S \begin{array}{c}\stackrel{k9}{\to }\\ \underset{k10}{\leftarrow }\end{array} H_2+S$$

(10)

Considering a pseudo-steady state, the following equation is used to describe the adsorption mechanism [36]

$$r_{SRM}=\frac{k_{SRM}{P}_{{CH}_4}{P}_{H_{2}O}}{(1+K_{H_2}{P}_{H_2}+K_{H_{2}O}{P}_{H_{2}O}+K_{CO}{P}_{CO}+K_{{CO}_2}{P}_{{CO}_2}+K_{{CH}_4}{P}_{{CH}_4}{)}^4}\times \left(1-\frac{P_{CO}{P_{H_2}}^3}{K_{SRM}{P}_{{CH}_4}{P}_{H_{2}O}}\right)$$

(11)

where the value of $K_{SRM}$ is the equilibrium rate constant of the SRM, $k_{SRM}$ is the concentrated reaction rate constant for SRM, $K_{H_2 }$is the adsorption rate constant of $H_2$, $K_{H_{2}O }$is the adsorption rate constant of $H_{2}O$, $K_{ CO }$is the adsorption rate constant of $CO$, $K_{{CO}_2 }$is the adsorption rate constant of ${CO}_2$ and $K_{{CH}_4 }$is the adsorption rate constant of ${CH}_4$. $P_{H_2 }$is the pressure of $H_2,$ $P_{H_{2}O }\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{o}\mathrm{f}{H}_{2}O,P_{CO }\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{o}\mathrm{f}CO$, $P_{{CO}_2 }\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{o}\mathrm{f}{CO}_2$ and $P_{{CH}_4 }$is the pressure of ${CH}_4$.

The equilibrium rate constant is:

$$K_{SRM}=\frac{k_6{K}_{CO}{K_{H_2}}^3}{k_5{K}_{{CH}_4}{K}_{H_{2}O}}$$

(12)

2.2.1.2. The water-gas shift

1. Carbone Monoxide adsorption on the active site of the catalyst:

$$CO+S \begin{array}{c}\stackrel{k1}{\to }\\ \underset{k2}{\leftarrow }\end{array} CO -S$$

(13)

2. Vapor adsorption on the active site of the catalyst:

$$H_{2}O+S \begin{array}{c}\stackrel{k3}{\to }\\ \underset{k4}{\leftarrow }\end{array} H_{2}O -S$$

(14)

3. Surface reaction at the active site of the catalyst:

$$CO -S+H_{2}O -S+2S \begin{array}{c}\stackrel{k5}{\to }\\ \underset{k6}{\leftarrow }\end{array} { C{O}_2-S+H}_2 -S$$

(15)

4. CO₂ desorption on the catalyst surface:

$$C{O}_2 -S \begin{array}{c}\stackrel{k7}{\to }\\ \underset{k8}{\leftarrow }\end{array} C{O}_2+S$$

(16)

5. Desorption of H₂ from the catalyst surface:

$$H_2 -S \begin{array}{c}\stackrel{k9}{\to }\\ \underset{k10}{\leftarrow }\end{array} H_2+S$$

(17)

Considering a pseudo-steady-state, the following equation is used to describe the adsorption mechanism [36].

$$r_{WGS}=\frac{k_{WGS}{P}_{CO}{P}_{H_{2}O}}{(1+K_{H_2}{P}_{H_2}+K_{H_{2}O}{P}_{H_{2}O}+K_{CO}{P}_{CO}+K_{{CO}_2}{P}_{{CO}_2}+K_{{CH}_4}{P}_{{CH}_4}{)}^2}\times \left(1-\frac{P_{{CO}_2}{P}_{H_2}}{K_{WGS}{P}_{CO}{P}_{H_{2}O}}\right)$$

(18)

where the value of $K_{WGS}$ is the equilibrium rate constant of the WGS reaction, $k_{WGS}$ is the concentrated reaction rate constant for WGS, $K_{H_2 }$is the adsorption rate constant of $H_2$, $K_{H_{2}O }$is the adsorption rate constant of $H_{2}O$, $K_{ CO }$is the adsorption rate constant of $CO$, $K_{{CO}_2 }$is the adsorption rate constant of ${CO}_2$ and $K_{{CH}_4 }$is the adsorption rate constant of ${CH}_4$. $P_{H_2 }$is the pressure of $H_2,$ $P_{H_{2}O }\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{o}\mathrm{f}{H}_{2}O,P_{CO }\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{o}\mathrm{f}CO,$ $P_{{CO}_2 }\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{o}\mathrm{f}{CO}_2$ and $P_{{CH}_4 }$is the pressure of ${CH}_4$.

The equilibrium rate constant is:

$$K_{WGS}=\frac{k_6{K}_{{CO}_2}{K}_{H_2}}{k_5{K}_{CO}{K}_{H_{2}O}}$$

(19)

2.2.1.3. Reverse dry methane reforming reaction

1. Carbone Monoxide adsorption on the active site of the catalyst:

$$CO+S \begin{array}{c}\stackrel{k1}{\to }\\ \underset{k2}{\leftarrow }\end{array} CO -S$$

(20)

2. Vapor adsorption on the active site of the catalyst:

$$H_2+S \begin{array}{c}\stackrel{k3}{\to }\\ \underset{k4}{\leftarrow }\end{array} H_2-S$$

(21)

3. Surface reaction at the active site of the catalyst:

$$2CO -S+{2H}_2 -S \begin{array}{c}\stackrel{k5}{\to }\\ \underset{k6}{\leftarrow }\end{array} { C{O}_2-S+CH}_4 -S+2S$$

(22)

4. CO₂ desorption on the catalyst surface:

$$C{O}_2 -S \begin{array}{c}\stackrel{k7}{\to }\\ \underset{k8}{\leftarrow }\end{array} C{O}_2+S$$

(23)

5. Desorption of CH₄ from the catalyst surface:

$${CH}_4 -S \begin{array}{c}\stackrel{k9}{\to }\\ \underset{k10}{\leftarrow }\end{array} {CH}_4+S$$

(24)

Considering a pseudo-steady-state, the following equation is used to describe the adsorption mechanism [35].

$$r_{RDRM}=\frac{{k_{RDRM}{P}_{CO}}^2{P_{H_2}}^2}{(1+K_{H_2}{P}_{H_2}+K_{H_{2}O}{P}_{H_{2}O}+K_{CO}{P}_{CO}+K_{{CO}_2}{P}_{{CO}_2}+K_{{CH}_4}{P}_{{CH}_4}{)}^4}\times \left(1-\frac{P_{{CO}_2}{P}_{{CH}_4}}{K_{RDRM}{P_{CO}}^2{P_{H_2}}^2}\right)$$

(25)

where the value of $K_{RDRM}$ is the equilibrium rate constant for the RDRM reaction, $k_{KDRM}$ is the concentrated reaction rate constant for RDRM, $K_{H_2 }$is the adsorption rate constant of $H_2$, $K_{H_{2}O }$is the adsorption rate constant of $H_{2}O$, $K_{ CO }$is the adsorption rate constant of $CO$, $K_{{CO}_2 }$is the adsorption rate constant of ${CO}_2$ and $K_{{CH}_4 }$is the adsorption rate constant of ${CH}_4,$ $P_{H_2}$is the pressure of $H_2,$ $P_{H_{2}O }\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{o}\mathrm{f}{H}_{2}O,P_{CO }\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{o}\mathrm{f}CO,$ $P_{{CO}_2 }\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{o}\mathrm{f}{CO}_2$ and $P_{{CH}_4 }$is the pressure of ${CH}_4$.

The equilibrium rate constant is:

$$K_{RDMR}=\frac{k_5{K_{CO}}^2{K_{H_2}}^2}{k_6{K}_{C{O}_2}{K}_{C{H}_4}}$$

(26)

2.2.2. Reaction rate constants and adsorption rate constant.

The reaction rate constants can be obtained by means of the Arrhenius equation [36].

$$k_j=k_i^0\mathit{exp}\left[-\frac{E_a}{RT}\left(\frac{1}{T}-\frac{1}{T_0}\right)\right]$$

(27)

And for the adsorption rate constant:

$$K_i=K_i^0\mathit{exp}\left[-\frac{{∆H}_i^{ads}}{RT}\left(\frac{1}{T}-\frac{1}{T_0}\right)\right]$$

(28)

where $k_i$ corresponds to the adsorption rate constant of component I, $k_i^0$ corresponds to the pre-exponential factor for component I, ${∆H}_i^{ads}$ is the heat of adsorption for component i-th species, $T$ is the reaction temperature and $T_0$ is the standard Temperature and R is the ideal gas constant.

2.2.3. Dynamic and Steady-State material balance

The additive rate equation was used for component species of the reactions SRM, WGS and RDRM with respect to time [36].

$$R_c=\sum _{j=1}^{Nr}{v}_{i,j}{r}_j$$

(29)

where $v_{i,j}$ is the stoichiometric coefficient of the t i-th species present in the j-th reaction, for j = 1 to Nr (the number of reactions). Accordingly, the material balance for the dynamic model is as follows:

$$\frac{\forall }{RT}\frac{d{P}_{H_2}}{dt}=\frac{d{n}_{H_2}}{dt}=R_{H_2}=\left(r_{WGS}+3r_{SRM}-2r_{RDRM}\right) m_{cat}$$

(30)

$$\frac{\forall }{RT}\frac{d{P}_{CO}}{dt}=\frac{d{n}_{CO}}{dt}=R_{CO}=(-r_{WGS}+r_{SRM}-2r_{RDRM}){ m}_{cat}$$

(31)

$$\frac{\forall }{RT}\frac{d{P}_{{CO}_2}}{dt}=\frac{d{n}_{{CO}_2}}{dt}=R_{{CO}_2}=\left(r_{WGS}+r_{RDRM}\right) m_{cat}$$

(32)

$$\frac{\forall }{RT}\frac{d{P}_{{CH}_4}}{dt}=\frac{d{n}_{{CH}_4}}{dt}=R_{C{H}_4}=(-r_{SRM}+r_{RDRM}){ m}_{cat}$$

(33)

$$\frac{\forall }{RT}\frac{d{P}_{H_{2}O}}{dt}=\frac{d{n}_{H_{2}O}}{dt}=R_{H_{2}O}=\left(-r_{WGS}-r_{RDRM}\right)*m_{cat}$$

(34)

- The steady-state material balance is as follows:

$$\frac{d{\dot{n}}_{H_2}}{d\forall }=R_{H_2}=\left(r_{WGS}+3r_{SRM}-2r_{RDRM}\right)$$

(35)

$$\frac{d{\dot{n}}_{CO}}{d\forall }=R_{CO}=(-r_{WGS}+r_{SRM}-2r_{RDRM})$$

(36)

$$\frac{d{\dot{n}}_{{CO}_2}}{d\forall }=R_{{CO}_2}=(r_{WGS}+r_{RDRM})$$

(37)

$$\frac{d{\dot{n}}_{{CH}_4}}{d\forall }=R_{C{H}_4}=(-r_{SRM}+r_{RDRM})$$

(38)

$$\frac{d{\dot{n}}_{H_{2}O}}{d\forall }=R_{H_{2}O}=\left(-r_{WGS}-r_{RDRM}\right)$$

(39)

The defined equations of the kinetic models of the main products of the gasification reaction with respect to time and longitudinal axis obtained previously were solved using Python with the indicated parameters in [21] which presents the kinetic parameters used in these equations. In addition, a catalytic mass of 3.92 g, a reactor diameter of 0.03 m was considered.

3. Results and Discussion

3.1. Fluid behavior inside the reactor

3.1.1. Velocity through the reactor

The fluid velocity at the reactor inlet was 0.0065 m/s, but as it crossed the biomass and catalyst bed it showed a decrease, where the most central part has a velocity of about 0.00185 m/s, while at the walls the value tends to zero.

Figure 3. a) Behavior of the fluid velocity b) Fluid velocity through the Z-chord.

Figure 3. a) Behavior of the fluid velocity b) Fluid velocity through the Z-chord.

3.1.2. Temperature across the reactor

The temperature distribution inside the reactor considering the flow of the gasifying agent and the gases generated during the reaction was as follows: the gasifying agent entered the reactor at a temperature of 226.85 °C, while the inner walls of the reactor were at 637.2 °C. Therefore, the fluid as it went through the reactor was acquiring a higher temperature, this being around 604.7 °C, this value was used as the gasification reaction temperature.

Figure 4. a) Fluid temperature distribution b) Temperature variation with respect to Z-axis.

Figure 4. a) Fluid temperature distribution b) Temperature variation with respect to Z-axis.

3.1.3. Pressure drop across the reactor

As the fluid passed through the reactor, it presented a resistance, causing a pressure drop, since the steam and gases generated flow through the reactor, so that in the end a negative pressure was obtained, which benefits the exit of the gases by causing them to expand as their density decreases, which facilitates their ascent through the reactor.

Figure 5. a) Pressure variation across the reactor b) Pressure drop with respect to Z-axis.

Figure 5. a) Pressure variation across the reactor b) Pressure drop with respect to Z-axis.

3.2. Simulation of the gasification reaction

3.2.1. Evolution of the number of moles with respect to time

In the gasification reaction, an increase in the production of carbon dioxide and methane was generated, since they are end products in both the WGS and RDRM reaction, as shown in Figure c and d. The Evolution of the hydrogen yield stabilized at approximately 0.16 mol/s, which according to [38] in his work "Hydrogen production through the gasification of glucose using 5% Ni catalysts with 2% La, Ce and Mg and derivation of an intrinsic reaction rate equation"; he reports resulting values approaching 0.3 mol/s for temperatures close to those above 600 °C and catalysts with higher nickel contents. In addition, [39] in their study "Hydrogen production through glucose gasification using γ-Al2O3 catalysts with Ni, Ce and La and interpretation of results using a non-stoichiometric model", using glucose as biomass model reaches the maximum hydrogen vapor using temperatures up to 600 °C with a reaction time of 30 seconds.

Figure 6. Evolution of the behavior of molar fluxes resulting from the glucose gasification reaction over time. a) Hydrogen flux b) Carbon monoxide flux b) Carbon dioxide flux d) Methane flux.

Figure 6. Evolution of the behavior of molar fluxes resulting from the glucose gasification reaction over time. a) Hydrogen flux b) Carbon monoxide flux b) Carbon dioxide flux d) Methane flux.

The constant $H_2:CO$ ratio of approximately 2.2. According to [38] in his work "Heterogeneous Catalysis for the Energetic Use of Biomass", he reports values close to or equal to 2 to achieve an optimal use of hydrogen. Generally, a high $H_2:CO$ ratio occurs when working at high temperatures, exceeding 500 °C, reaching ranges of between 1.7- 2 [40].

Figure 7. a) Evolution of water flux obtained in the simulation b) Hydrogen/Carbon Monoxide ratio with respect to time.

Figure 7. a) Evolution of water flux obtained in the simulation b) Hydrogen/Carbon Monoxide ratio with respect to time.

3.2.2. Evolution of the number of moles with respect to the longitudinal axis

In this case study, the pressure was raised to 2 bar, however, there were no significant changes in obtaining the synthesis gas products compared to the analysis with respect to time. Figure a shows the decrease of hydrogen generated when consumed in the RDRM reaction, this behavior also occurred for figure b, where the trend decreases when consumed in the WGS reaction. For the case of carbon dioxide, an increase was observed, since it is generated only in WGS, this being the predominant reaction. Dry reforming of methane, on the other hand, results in the formation of methane together with carbon dioxide.

In WGS and SRM, one of the reactants is water, this consumption is shown in Figure 8. Finally, the same $H_2:CO$ ratio was obtained with the same resultant as in the study with respect to time.

Figure 8. Evolution of flow behavior along the axial z-axis. a) Hydrogen flow b) Carbon monoxide flow c) Carbon dioxide flow d) Methane flow e) Water flow.

Figure 8. Evolution of flow behavior along the axial z-axis. a) Hydrogen flow b) Carbon monoxide flow c) Carbon dioxide flow d) Methane flow e) Water flow.

Figure 9. a) Evolution of water flux obtained in the simulation b) Hydrogen/Carbon Monoxide ratio with respect to Z-axis.

Figure 9. a) Evolution of water flux obtained in the simulation b) Hydrogen/Carbon Monoxide ratio with respect to Z-axis.

4. Conclusion

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