Introduction

About 29% of primary energy demand is still met by coal, and 40% of electricity is also provided by coal. Apart from enhancing the world's population, the demand for environmentally friendly fuel increases every day at an alarming rate [1,2,3]. Besides, fuel production from biomass plays a significant role in energy production. Gasification is an alternative technology in which coal can be processed in a cleaner way. [3, 4]. During the gasification process, a vast majority of biomass, such as agricultural waste, rubberwood and forestry residues, would be effectively used to produce harmless and renewable heat and power [4, 5]. However, biomass gasification can be seen as a complex thermochemical operation by which biomass turns into valuable gases, including hydrogen, carbon dioxide and carbon monoxide. It is noticeable that in the gasification process, the temperature of the experimental setup should be kept above 800 °C to enhance desired reactions (water–gas shift and steam reforming) which results in valuable products [3,4,5]. Recently, some works have been done about the co-gasification of woody biomass and coal; this has several benefits as follows: The addition of woody biomass to coal gasification can reduce not only CO2 emissions but also the problems caused by sulfur contained in coal; this is because the woody biomass has almost no sulfur. However, biomass gasification is expensive and produces a relatively high content of tar. Therefore, co-gasification can reduce the expenditure of the feedstock and decrease the issues that happen in plant operations due to the generation of tar [3,4,5,6,7,8].

Since hydrogen is not naturally present in the environment, it has to be derived from a variety of starting materials from both renewable and nonrenewable sources [6]. Hence, the research on ameliorating generation and applying hydrogen by various methods has been among the most general studies in the modern age [7]. The generation of hydrogen from the gasification of woody biomass is considered a popular and economical approach with a lower carbon footprint than other methods like cracking, liquefaction and so on [8].

Many factors must be considered for a suitable gasifier design, like final gasifier cost, energy consumption, high product efficiency, safety, etc. [9]. Regarding biomass gasification, it seems urgent to provide details of local fluid flow distribution, concentration and temperature gradient through the gasifier, interactions between fluid flow and reaction and other transport phenomena inside the gasifier. These details give a more profound view of the pre-and post-processing design of the gasification process, especially since the scale-up of the bench-scale gasifier to industrial scale is the fundamental matter [10]. Despite the straightforward structure and geometry of the gasifier, the best-suited chemical kinetics for gasification is complex. Thus, determining the hydrogen production pattern, velocity/temperature profiles and hydrodynamic factors might be the main problems.

Computational fluid dynamics (CFD) is recommended as a suitable approach to get rid of these issues. CFD is a proper technique that can be performed to visualize and predict outcomes such as the production rate of gases from biomass gasification, velocity and temperature field, concentration gradient, and other transport phenomena. CFD codes can simulate the complex fluid flow field and couple the hydrodynamic properties and the chemical reactions that may have interactions, so it is a suitable tool for energy and chemical engineers to design and scale up a gasifier [11, 12].

Some studies have been done to modeling the hydrogen production from the gasification of biomass in recent years. In contrast, studies about the three-dimensional CFD modeling of gasification processes are scarce. Most studies are restricted to the modeling of fluid hydrodynamics in one and two dimensions. Zhao et al. [13] studied hydrogen production by biomass gasification in a fluidized bed reactor using the CFD-DEM technique. They concluded that reactions could impact fluidization, and high wall temperature, low flow rate and initial bed height favor the gasification process. Ku et al. [14] investigated biomass gasification in a fluidized bed reactor using the CFD-DEM approach. In this study, the impacts of temperature and steam/biomass ratio have been done on the production of H2 and CO2 and understood that with increasing temperature and steam/biomass ratio as mentioned above, the rate of gas production could go up dramatically. Kumar et al. [15] studied the 2D modeling of biomass gasification using the CFD method with a volatile break-up approach. There has been a good agreement between simulation results and experimental data.

The fundamental objective of this survey was to use the CFD approach to produce a 3D simulation of hydrogen production from co-gasification of Çan lignite and sorghum biomass in a fixed-bed reactor working in the transient performance. The process carried out in the form of a time-dependent state means that the equation of motion and the mass transport equations change with time. The numerical modeling results for the impact of various parameters such as the inlet flow rate of water, coal/biomass ratio and  temperature  on the hydrogen generation from co-gasification of biomass were validated using experimental data in the literature [1].

CFD implementation

The fixed-bed gasifier simulation setup is schematically displayed in Fig. 1, which was created by COMSOL Multiphysics. Gasification experiments were done in a continuous, cross-flow, fixed-bed reactor. Total 1 g of sample, dry and ash free (daf), coal or coal/biomass blends were charged into the middle of a stainless steel tubular reactor, which was  50 cm in length. Then water was fed into the coal/biomass loaded reactor using an HPLC pump. The inner and outer diameters of the fixed-bed reactor were 0.56 and 1.4 in., respectively. At the next step, water was injected into the coal/biomass loaded gasifier by using an HPLC pump at flow rates between 0.5 × 10−8 and 3.3 × 10−8 m3/s. The fixed-bed tubular reactor was put in a temperature-controlled oven and heated to a suitable temperature at a 30 °C/min. In addition, the proximate analysis of Çan lignite and sorghum (biomass) is shown in Table 1 [1]. The configuration was meshed by triangular cell (unstructured mesh) and constructed by COMSOL Multiphysics V5.1, which is displayed in Fig. 2.

Fig. 1
figure 1

Schematic of the simulation set up

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Table 1 Ash, Moisture and elemental analysis results of Çan lignite and sorghum biomass [1]
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Fig. 2
figure 2

generated mesh of the fixed-bed reactor

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Mathematical modeling

An Eulerian–Eulerian two-fluid model was chosen to study 3D flow and gasification characteristics in the fixed-bed reactor. The Euler–Euler Model is based on averaging the Navier–Stokes equations. In the Eulerian–Eulerian method, both fluid phases and particles are treated as interpenetrating continua [16]. It can anticipate the macroscopic features with relatively low computational cost and has dominated the modeling of the multiphase fluid flow process in recent years. The model and all the governing equations used in this work are time-dependent.

The continuity equation for phase q (solid or gas) is written as follows:

$$\frac{\partial }{\partial t}\left( {\rho_{q} \varphi_{q} } \right) + \nabla .\left( {\rho_{q} \varphi_{q} u_{q} } \right) = 0$$
(1)
$$\mathop \sum \limits_{q = 1}^{n} \varphi_{q} = 1$$
(2)

where φ (dimensionless) refers to the phase volume fraction, ρ is the density and u is the gas and solid phase velocity. The flow regime is deemed a turbulent flow of an incompressible fluid, and finally, the k-ɛ turbulence model is considered for showing turbulent effects in the gas phase. The momentum equation can be shown as follows:

$$\rho_{q} \varphi_{q} \left[ {\frac{\partial }{\partial t}\left( {u_{q} } \right) + u_{q} \nabla .\left( {u_{q} } \right)} \right] = \varphi_{q} \nabla p + \nabla .\left( {\varphi_{q} \tau_{q} } \right) + \varphi_{q} \rho_{q} g + \vec{F}_{m.q} + \varphi_{q} F_{q}$$
(3)

In the above equation, the viscous stress tensor for gas and solid phase is mentioned by τ, Fm is the interphase momentum transfer term, and F is any other volume force [17]. The fluid phases in the above equations are assumed to be Newtonian, and the viscous stress tensors are written as:

$$\tau_{q} = \mu_{q} \left( {\nabla u_{q} + \left( {\nabla u_{q} } \right)^{T} - \frac{2}{3}\left( {\nabla .u_{q} } \right)I} \right)$$
(4)

where µ is the dynamic viscosity of each phase and fluid properties were computed as:

$$\mu = \sum \varphi_{q} \mu_{q}$$
(5)
$$\rho = \sum \varphi_{q} \rho_{q}$$
(6)

In all the correlations, \(\vec{F}_{m}\) refers to the interphase momentum transfer that is the force exerted on one phase by the other phase and is shown as [17]:

$$\vec{F}_{m} = \mathop \sum \limits_{q = 1}^{n} M_{ij} \left( {\vec{u}_{i} - \vec{u}_{j} } \right)$$
(7)

In the above correlation, Mij denotes the interphase coupling term that makes multiphase flows basically different from single-phase flows. Based on the Attou and Ferschneide closure correlations, the interphase coupling term is written in terms of phase volume fractions and interstitial velocities for gas–solid momentum exchange form as expressed in Eq. (8) [17]:

$$M_{GS} = \varphi_{G} \left( {\frac{{180\mu_{G} \left( {1 - \varphi_{G} } \right)^{2} }}{{\varphi_{G}^{2} d_{p}^{2} }}\left[ {\frac{{\varphi_{S} }}{{1 - \varphi_{G} }}} \right]^{{{\raise0.7ex\hbox{$2$} \!\mathord{\left/ {\vphantom {2 3}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$3$}}}} + \frac{{1.75\rho_{G} u_{G} \left( {1 - \varphi_{G} } \right)}}{{\varphi_{G} d_{p} }}\left[ {\frac{{\varphi_{S} }}{{1 - \varphi_{G} }}} \right]^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 3}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$3$}}}} } \right)$$
(8)

The mass transport equation prepares a predefined modeling environment for investigating the evolution of chemical species transported by convection and diffusion. However, the default equation node attributed to the transport of diluted species models in COMSOL Multiphysics software computes the mass transport equation for whole chemical species i following the below equation:

$$\frac{{\partial C_{i} }}{{\partial {\text{t}}}} + \nabla .\left( { - D_{i} \nabla C_{i} } \right) + {\text{u}}.\nabla C_{i} = R_{i}$$
(9)

Di represents the diffusion coefficient of component i, Ri refers to the kinetics of all vital reactions, and Ci is the concentration of components i. The heat transfer in the domain is through the conduction (Qcond) between the particles and convection (Qconv). The energy conservation equation for the gasification process is given as:

$$mC_{p} \frac{dT}{{dt}} = Q_{{{\text{conv}}}} + Q_{{{\text{cond}}}} + \Delta H_{r}$$
(10)

The heat source term ∆Hr takes into account the latent heat of evaporation from solid particles. Simulating the process of gasification in fixed-bed gasifiers is highly challenging because of various reactions taking place in parallel and interacting with each other. The reaction of the present study is homogeneous, and main reactions consisting of water–gas shift and steam reforming reactions are considered during the whole process as follows:

$$\begin{gathered} {\text{CO}} + {\text{H}}_{{2}} {\text{O}} \leftrightarrow {\text{CO}}_{{2}} + {\text{H}}_{{2}} \quad {\text{water - gas shift}} \hfill \\ {\text{CH}}_{{4}} + {\text{H}}_{{2}} {\text{O}} \leftrightarrow {\text{CO}} + {\text{3H}}_{{2}} \quad {\text{steam reforming}} \hfill \\ \end{gathered}$$

Boundary conditions

The initial value of coal/biomass at the inlet of the reactor was deemed as the feedstock concentration inlet boundary condition, while the pressure of 0 bar was selected as the outlet boundary condition. The boundary conditions for the walls were defined as a free slip for gas-phase fluid flow and no-slip for solid phase. Also, the initial temperature of the domain is considered at about 700 °C for solving the energy equation, which is coupled with two other governing equations.

Solution procedure

In this work, the COMSOL Multiphysics V5.1 software is used for computing the linear/nonlinear equations, numerical modeling and meshing. The solving of whole governing equations is implemented by the finite element approach. The convergence was acceptable at the criteria of 10–2 for all the variables computed. The step time for unsteady-state correlations was selected 0.1 s, and the average computational time to acquire the results was about 32 h. The simulation was performed on the ASUS system with core i7 and 24 GB RAM.

Results and discussion

Grid independency check

The gasifier used in this study was divided into smaller cells by free triangular and tetrahedral unstructured meshes. The concentration of hydrogen in the outlet of the reactor was deemed as the criteria for grid independency of results, as shown in Table 2. As the number of cells was risen from 15 × 103 to 22 × 103, the simulation results of hydrogen concentration altered from 2 × 10–2 to 1.52 × 10–2 mol/m3. However, the outcomes have a negligible difference when the grid number went up from 22 × 103 to 3 × 104, and it gained 1.51 × 10–2 mol/m3. Thus, as there is a compromise between the mesh refinement and the selection of computing time, case 2 was deemed sufficient to provide meticulous results, and it was chosen to save computational time.

Table 2 Grid independency
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Validation of the model

To validate the simulation results in the present study, the predicted H2 production was compared with the experimental data in the literature [1] at three different concentrations of H2, which is shown in Table 3. The relative error \(\left( {\frac{{\left| {X_{{{\text{exp}}.}} - X_{{{\text{sim}}.}} } \right|}}{{X_{{{\text{exp}}{.}}} }}} \right)\) × 100 and the sum of squared errors of prediction \(\left( {\sum {\left( {X_{{{\text{exp}}.}} - X_{{{\text{sim}}.}} } \right)}^{2} } \right)\) are less than 6% and 0.2 for all the cases, respectively. This error is rooted in probable numerical solutions, the initial assumptions that were made, and other calculation parameters. This amount of discrepancy is acceptable within any standard CFD model prediction precision, and similar results are published in some previous studies. Based on the results displayed in Table 3, there is a good agreement between the experimental and the simulation results of the H2 and the differences between the two methods were negligible, which confirms that the whole numerical solution applied for modeling of the biomass gasification is acceptable, and thus, the CFD outcomes are reliable.

Table 3 Verification of simulation data for concentration of the H2 against experimental data
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Effects of operation parameters on H2 production

Many parameters influence Çan lignite and sorghum biomass co-gasification. In the following parts, we investigate the effect of several essential parameters on the co-gasification of biomass using the CFD technique, a powerful tool for visualizing and analyzing results. The impacts of water flow rate, coal/biomass ratio in fuel blend and temperature on the co-gasification of Çan lignite and sorghum biomass were studied by employing the CFD approach.

Effect of temperature on H2 production

The whole process was done in three temperatures ranging from 700 to 950 °C, which is shown in Fig. 3. According to the energy equation with increasing temperature, the temperature inside the reactor increased that is apparent from Fig. 3. With increasing the temperature, the red area, according to the contours, increased, especially in 950 °C, which directly impacts the reaction temperature. The higher temperature is accompanied by the higher fluid temperature. In addition, reaction temperature has a significant impact on biomass gasification [18, 19]. By comparing the results displayed in Fig. 4, 5 and 6, it is evident that with temperature increasing from 700 to 950 °C, the H2 production (gasification efficiency) significantly increased from 1.125 × 10–3 mol/m3 to 1.5 × 10–3 mol/m3. Temperature is one of the primary process parameters, which impacts the gasification efficiency depending on the thermodynamic performance of the gasification reactions [18]. Char gasification, steam reforming, cracking and pyrolysis of biomass are all improved by high temperatures causing higher carbon reactions. The total gas volume generated from a gasification process is directly dependent on the capability of carbon conversion and the seen values for the total gas volume [20]. So, as carbon conversion increases with an increase in temperature, total gas volume (H2 production) also increases significantly. In the end, the consistent tendency between simulation and experiment shows that the model introduced in this work can reasonably describe the biomass gasification in a fixed-bed reactor.

Fig. 3
figure 3

The temperature profile along the fixed-bed reactor at (a) 700 °C, (b) 825 °C and (c) 950 °C

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Fig. 4
figure 4

The H2 concentration variation contours (inside and outside views of the reactor) at temperature 700 °C for different water flow rate and coal/biomass ratio (a) 3.3 × 10–8 m3/s, 50% (b) 0.5 × 10–8 m3/s, 50% (c) 1.9 × 10–8 m3/s, 100% and (d) 1.9 × 10–8 m3/s, 0%

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Fig. 5
figure 5

The H2 concentration variation contours (inside and outside views of the reactor) at temperature 825 °C for different water flow rate and coal/biomass ratio (a) 1.9 × 10–8 m3/s, 50% (b) 3.3 × 10–8 m3/s, 0% and (c) 0.5 × 10–8 m3/s, 0%

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Fig. 6
figure 6

The H2 concentration variation contours (inside and outside views of the reactor) at temperature 950 °C for different water flow rate and coal/biomass ratio (a) 3.3 × 10–8 m3/s, 50% (b) 0.5 × 10–8 m3/s, 50% (c) 1.9 × 10–8 m3/s, 0% (d) 1.9 × 10–8 m3/s, 100%

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Effect of water flow rate on H2 production

This study investigated the impact of water flow rate (0.5 × 10–8, 1.9 × 10–8 and 3.3 × 10–8 m3/s) on H2 production. Regarding Figs. 4, 5 and 6, it is clear that the effects of water flow rate on H2 yield are less important than the temperature and biomass ratio of the coal/biomass blend. For instance, regarding Fig. 4 with increasing flow rate from 0.5 × 10–8 m3/s to 3.3 × 10–8 m3/s, the H2 production decreased from 6.25 × 10–3 mol/m3 to 1.125 × 10–3 mol/m3. Also, it can be seen from H2 concentration contours that an increase in water flow rate will not have positive impacts on total gas volume, particularly at temperatures less than 850 °C. Furthermore, to gain a higher total gas and hydrogen yield at temperatures further 850 °C, the higher flow rates should be utilized. The amount of water that exists in the gasifier in unit time relates directly to the flow rate of water. At meager flow rates, the rates of reactions fall down because of the lower concentrations of water steam. When the water flow rate is enhanced to provide enough water vapor concentration in the gasifier, the steam reforming reactions are increased, and an enhancement in H2 concentration is observed. But if the flow rate is more increased, the residence time of H2O on the biomass will be decreased, and this will cause reduced interactions between the reacting species and steam in unit time [21,22,23]. Furthermore, further decreases in flow rate will result in a decline in the gasifier temperature because of excessive water steam absorption, which will cause a decrease in rates of gasification reactions, as most gasification reactions are endothermic. According to the concentration snapshots, at further levels of flow rate, the impact of temperature on H2 production is greater than that of lower levels. Therefore, from simulation results, this could be understood that in order to gain a higher amount of H2, particularly at temperatures after 825 °C, a higher amount of flow rate should be utilized. In gasifications operated in the vicinity of 700–825 °C, flow rates should be fixed low to seize higher H2 yield.

Effect of coal/biomass ratio on H2 production

The biomass concentration in coal/biomass mixtures is a vital parameter that impacts the amount and composition of product gases in gasification processes [24, 25]. The ratio of biomass in coal/biomass blend was found to be individually important on H2 production. Furthermore, the concentration contours of H2 (Figs. 4, 5, 6) indicate that since the percentage composition of biomass in biomass/coal blends is enhanced, hydrogen production will decrease. For example, when the percentage composition of biomass in biomass/coal blends is increased at a temperature of 950 °C, the amount of hydrogen production decreased from 1.5 × 10–2 mol/m3 to 1.1 × 10–2 mol/m3. Finally, the optimum ratio of biomass in the biomass/coal blend was found to be 25.9% in the CFD process.

The velocity distribution within the fixed-bed reactor is presented in Fig. 7. The velocity inside the reactor is dramatically higher than in other regions due to the lack of shear stress and high void fraction in this section. Besides, it can be seen that the velocity of the mixture is about zero near the wall, which satisfied the no-slip condition that is defined in the Euler–Euler equation.

Fig. 7
figure 7

Velocity contour in the reactor for the water flow rate of 3.3 × 10–8 m3/s and temperature 950 °C

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As was mentioned in previous sections, the simulation process was considered time-dependent, meaning that the concentration profiles changed with time, and it is shown in Fig. 8. It is evident from Fig. 8 as time goes by, the amount of hydrogen production was increased.

Fig. 8
figure 8

H2 concentration contours at the temperature of 700 °C and at various times

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Conclusions

This study used CFD simulations based on an Eulerian–Eulerian model to simulate the fluid dynamics coupled with a kinetic model in a packed-bed gasifier for hydrogen production. The focus of the research was firstly on the effect of temperature on hydrogen production and secondly on the effect of water flow rate and coal/biomass ratio on gas production efficiency by 3D simulation of the fixed-bed reactor under transient operational conditions. The H2 concentration variations were depicted along the reactor as the validation results, and the dynamic H2 production behavior analysis was performed using experimental data. Based on the simulated outcomes achieved in this study, the following conclusions can be written:

  • An upward trend is seen for the H2 production by increasing the temperature of the reactor from 700 to 950 °C because of going up the carbon conversions and favoring the endothermic hydrogen generation reactions.

  • Increasing the water flow rate has an adverse impact on hydrogen production percentage, and the gas generation capacity was more in low water flow rates, especially at a temperature less than 850 °C. Furthermore, to gain a higher total gas and hydrogen yield at temperatures further 850 °C, the higher flow rates should be utilized.

  • There was a downward trend for hydrogen production since the percentage composition of biomass in biomass/coal blends is enhanced.

  • For maximum hydrogen generation, the optimal conditions were considered as a temperature of 850 °C, a flow rate of 1.8 × 10−8 m3/s and a biomass ratio of about 50%. In these optimal conditions, the predicted hydrogen concentration was 1.5 × 10–2 mol/m3.