Insights in Steam Reforming of Glycerol in a Fluidized Bed by

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Insights in steam reforming of glycerol in a fluidized bed by CFD modeling Shuai Wang, Xiaojiao Song, Juhui Chen, Qi Wang, and Huilin Lu Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b01834 • Publication Date (Web): 13 Sep 2016 Downloaded from http://pubs.acs.org on September 16, 2016

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Insights in steam reforming of glycerol in a fluidized bed by CFD modeling Shuai Wang a,*, Xiaojiao Song a, Juhui Chen a, Qi Wang a, Huilin Lu a a

School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, 150001, China

b

School of Mechanical Engineering, Harbin University of Science and Technology, Harbin 150080, China ABSTRACT Glycerol reforming technology provides an efficient means for hydrogen production industry

and the utilization of biodiesel-derived crude glycerol. Fluidized bed reactors have potential in interphase mass/heat transfer and mitigating catalyst deactivation. In this study, computational fluid dynamics (CFD) is used to investigate the performance of glycerol steam reforming in a fluidized bed system. A bubble-structure-dependent drag model is implemented into the two-fluid model (TFM) model to reflect the bubble effect. A three-dimensional simulation is conducted. The model is verified by experimental data. By analyzing the influence of operating conditions and property parameters, it is found that the reaction temperature plays a vital role in the enhancement of hydrogen production.

Keywords: Glycerol; reforming; Computational fluid dynamics; Bubble; Fluidized bed

∗ Corresponding author. Tel.: +0451 8641 2258; fax: +0451 8622 1048. E-mail address: [email protected]

1

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1. INTRODUCTION Hydrogen is regards as an environmental clean renewable energy carrier in the future, which is widely applied to produce electricity via fuel cells. The most dominant source of hydrogen production derives from fossil fuels. During this process, a large amount of carbon dioxide is generated. Therefore, it is necessary to develop a potential feedstock for hydrogen production.1 Over the past few years, more attentions have been paid on the renewable biomass-derived resources owing to its abundance and sustainability.2 With the progressive growth in biodiesel production, more glycerol is supplied as the main by-product.3,4 It has become an attractive way to utilize glycerol as a renewable resource for hydrogen yield.5 Some thermochemical routes are available to valorize the biodiesel-derived crude glycerol to obtain synthesis gas by different types of reforming technologies.6-8 Compared to methane, glycerol shows a better advantage on high hydrogen production with low carbon formation. Besides the glycerol valorization, it can be found that carbon dioxide released into the atmosphere is reduced due to its carbon neutral reaction.9 Among emerging technologies of glycerol valorization, glycerol steam reforming is one of the most promising options as a result of a lower side-reaction rate and a higher hydrogen yield. A great deal of studies have been attempted on the glycerol steam reforming.10,11 A thermodynamic analysis was performed on hydrogen production via glycerol steam reforming and the effects of process variables including water-to-glycerol feed ratio, system pressure and temperature were discussed on the basis of the criterion of Gibbs free energy minimization.12 It was demonstrated that carbon formation can be inhibited at a higher water to glycerin feed ratio. The performance of glycerol steam reforming in the presence of CO2 or H2 was reported.13 It was found that the introduction of H2 can restrict the carbon formation and enhance the exothermicity of the overall system. However, the addition of CO2 can result in the increase of carbon deposition. Besides thermodynamic 2


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assessments, a phenomenological model was established to predict the glycerol steam reforming in a packed bed reactor.14The model agreed well with experimental result. An unsteady-state two-scale model was established to predict the sorption-enhanced reforming performance in a fixed-bed reactor, where steam glycerol reforming and CO2 capture kinetics were taken into consideration.15 Most researches about glycerol steam reforming have focused on fixed packed bed reactors. A fluidized bed reactor can be applied in different flow regimes such as fast fluidization or bubbling fluidization, which has its advantage in interphase external mass/heat transport characteristics and mitigating catalyst deactivation through coking.16 A two-step strategy for valorisation of biodiesel-derived glycerol was proposed to produce H2 and the catalytic steam reforming process of the refined glycerol was studied in a fluidized bed reactor by means of theoretically and experimentally methods.17 Computational fluid dynamics provides an efficient approach to gain a deep insight into complex flow and reaction mechanics.18 CFD simulations of glycerol steam reforming in a fluidized bed were performed using the two-fluid model integrated with chemical reaction kinetics. The hydrodynamics and products distribution in the reactor were obtained. The results revealed that the residence time is a key parameter on the improvement of hydrogen purity and fuel conversion.19,20 In this work, the two-fluid model with a bubble-structure-dependent drag model is employed to take the bubble impact into consideration to evaluate the glycerol steam reforming performance in a fluidized bed reactor. A three-dimensional simulation is carried out and verified by experimental data. Flow behaviors and gas species distribution in a reforming system are predicted. Additionally, the impacts of different operating conditions and property parameters including reaction temperatures, steam to glycerol ratios and particles diameters are evaluated. 2. MATHEMATICAL MODEL 3


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The Eulerian-Eulerian two-fluid model is employed in this simulation. Here, the assumption is made that the solid phase has a uniform density and diameter. The governing equations consist of continuity equations, momentum conservation equations, species transportation equations, and energy conservation equations. Detailed equations are listed in Table 1. To characterize the energy of the fluctuating velocity of particles, the granular temperature is introduced, which is calculated by means of solving the conservation equation of solids fluctuating energy, as shown in (T1-9). For the description of particles phase stress, the kinetic theory of granular flow is used for closure,21 which is derived for smooth, rigid, nearly elastic, spherical particles. The particle normal force owing to particle-particle interaction is described by the particle pressure including the kinetic and the collisional contributions. The shear stress is expressed as a function of shear viscosity. The frictional stress model is introduced to account for the particles contact at a high solid concentration.22 The corresponding relations are listed in Table 2. 2.1 Bubble structure-dependent (BSD) drag model For a reforming system in the form of a bubbling fluidized bed reactor, bubbles play an essential role in the fluidized state of particles, which can influence interphase mass and heat transfer. To characterize the bubble impact in fluidized beds, the BSD drag model was developed.23 In this model, the heterogeneous flow caused by the bubbles is resolved into local homogeneous flow. Hence, the drag force can be expressed as: β BSD =

ε g Fgs εg = [n F +n F ] U slip U slip e de b db

(1)

Through solutions of local structural parameters, the integrated drag with consideration of bubble and emulsion phases can be obtained. In the previous work, the BSD drag model can give a reasonable prediction on bubble behaviors and flow field via investigations of cold fluidized bed systems.23 The corresponding relations in the BSD drag model are described in Table 3.On the basis 4


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of five hydrodynamic equations (eqs. (T3-1),(T3-7)-(T3-10)) and one stability criterion (T3-11), the model can be closed. Detailed procedures can be found in Wang et al.23 2.2 Reaction kinetic model Biodiesel-derived glycerol steam reforming is a very complex process and a series of reactions are involved, which depend on the reaction conditions and catalytic types. It was pointed out that the biodiesel-derived glycerol has a similar form as the pure glycerol. Here, for simplification, the pure glycerol and some related properties are used in this work. At a high temperature above the 600K, there is almost no carbon formation. Hence, the effect of carbon is neglected in the simulation. The main three reactions are employed as follows:20 C3 H8 O3 (g)+H 2 O(g) ↔ CH 4 (g)+2CO 2 (g)+3H 2 (g)

CH 4 (g)+H 2 O(g) ↔ CO(g)+H 2 (g) CO(g)+H 2 O(g) ↔ CO 2 (g)+H 2 (g)

+123KJ/mol （R1） +206KJ/mol （R2） -41KJ/mol （R3）

In this work, the Ni-based catalyst is employed. From the study of Sundari et al.10, the absence of external and internal transport limitations was confirmed and the glycerol steam reforming process belonged to the kinetically controlled reaction regime. The Laminar finite-rate model is used to calculate the reaction rate and the rate constant is assumed to follow an Arrhenius-type dependence with the temperature. The corresponding reaction rates are described as: 20

R1 = 1.838 ×105 exp(−74210 / T )CC3H8O3 CH2O R2 = 1.198 ×1017 exp(−26830 / T )CCH4 CH2O R3 = 0.01767 exp(4400 / T )CCO CH2O 2.3 Model implementation description

5


(2) (3) (4)

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In this work，the reforming system in the form of a fluidized bed reactor is chosen as the research objective following the experimental setup of Dou et al. 20 The sketch of the system is displayed in Figure 1. The reactor has a height of 1.0m and a bed diameter of 0.3m. The solid particles have a mean density of 2650 kg/m3 and an averaged diameter of 0.0875mm. The initial height and temperature of solid particles are 0.2m and 873K respectively. A three-dimensional simulation is performed based on the above mathematics model. The gas velocity and the steam to glycerol ratio are specified at the bottom of the reactor. Here, the uniform velocity inlet boundary condition is employed.24 The impacts of velocity fluctuating caused by the air-blower or pipes and distributors are assumed to be negligible. The outlet is located at the top of the reactor, where the gas pressure is set to be 1atm. For the wall, no slip boundary conditions are selected for gas and solid phases. Detailed operating conditions and simulation parameters are summarized in Table 4. The model is implemented on the platform of the KFIX CFD code, which is an open source program and has been successfully applied to the predictions of fluidized bed systems.25 Here, the BSD drag model is incorporated into the two-fluid model. The total variation diminishing (TVD) scheme is selected. An adjustable time step is adopted in the range of 1×10-4～1×10-6s . The computational time is 30s. The time-averaged variables are calculated from the last 20s after reaching the quasi-steady state. 3. RESULTS AND DISCUSSION To conduct a mesh-independent investigation, three different grids are used. The predicted profiles of gas pressure under three grids are shown in Figure 2. We can recognize that the profiles of gas pressure show a descending trend as the height increases although the discrepancy among them exists. At the low section of the reactor, the predicted gas pressure using coarse grids is greater 6


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than those by the medium and fine grids. The difference between the medium and fine grids is not clear. Considering the accuracy and computational cost, the medium grid is finally employed as the computational size. To verify the model feasibility, the comparison of gas composition obtained by the simulation and experiments is conducted as shown in Figure 3. We can observe that the BSD drag model gives a fair agreement with measured data. The maximum relative error is less than 10% that is in an acceptable range. The prediction by the Gidaspow drag model is also presented in Figure 3. In contrast, the Gidaspow drag model underestimates the hydrogen and carbon monoxide yield. As was pointed out in the previous work (Wang et al.,2016), the model neglecting the bubble effect can over-predict the bed expansion. Even parts of the particles flow out of the reactor, which leads to the reduction of reaction rates. Therefore, it is important to account for the bubble effect on the interphase force, especially for Geldart A particles. The reforming performance and reaction rates in fluidized bed reactors depend on the fluidization state of catalytic particles. The time-averaged distribution of solid volume fraction and solid axial velocity along the lateral direction is illustrated in Figure 4. It can be clearly found that the non-uniformity appears on the profiles of solid volume fraction and solid velocity at different heights. The solid concentration increases towards the wall where the particle velocity is negative, which indicates there is backflow of particles near the wall. This is attributed to the wall friction that hinders the particles upflow. With the height increased, the lateral discrepancy of solid velocity becomes weak. Overall, the internal circulation flow of particles in the bed is formed. Figure 5 displays the instantaneous distribution of gas species concentrations at 15s. It can be observed that the glycerol concentration decreases with the increasing height and reaction in process. According to the reaction(R1), the methane, hydrogen and carbon dioxide are produced as 7


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the glycerol is consumed. A high solid concentration leads to a clear variation of gas species concentration. There is a low concentration of carbon monoxide near the inlet, which is attributed to that the carbon monoxide is indirectly produced by glycerol as shown in the reaction (R2) and reacts with steam to produce the hydrogen and carbon dioxide. We can also find that there is a lower glycerol concentration near the wall compared to the center zones. Consequently, the other products concentrations are higher near the wall. This can be explained that a high solid concentration results in a greater reaction rate. In addition, the gas resident time is relatively longer near the wall owing to a low velocity and particle backflow. Figure 6 illustrates the instantaneous distribution of the three reaction rates of glycerol steam reforming process. It can be found that the reaction rate of (R1) is larger in the bottom inlet zone owing to a high concentration of glycerol and steam. With the height increased and the reactant gas consumed, the reaction rate of (R1) decreases. As the methane is produced, the reaction rate of (R2) gradually becomes clear. Accordingly, the carbon monoxide is generated by (R2), which reacts with steam to produce carbon dioxide. In contrast to (R3), the reaction rates of (R1) and (R2) are more significant. The glycerin reforming performance in fluidized bed reactors depends on reasonable operating conditions and parameters. Here, the simulations are conducted with the following operating ranges: reaction temperature of 773K to 973K. steam to glycerin ratio of 6:1 to 12:1, solid diameter of 0.07mm to 0.12mm and operating pressure of 0.1Mpa to 0.5Mpa. Figure 7(a) and (b) present the effects of different reaction temperatures and steam to glycerin ratios on the outlet gas composition. Accordingly, the effects of solid diameters and operating pressures on gas composition are also shown in Figure 7(c) and (d). From Figure 7(a), it can be found that H2 and CO molar fractions at the outlet of the reactor are 8


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promoted as the reaction temperature increases, which is attributed to that the reactions (R1) and (R2) are endothermic reactions. An increase of temperature enhances these two reactions towards the positive direction. Although the methane is produced following the reaction (R1), it is also reactant of the reaction (R2) and reacts with steam to produce the H2 and CO. The enhancement of reverse direction of the reaction (R3) that is exothermic reaction results in the reduction of CO2 and further increases the CO molar fraction. Overall, the increase of reaction temperature strengthens the syngas production. The predictions are consistent with thermodynamic analysis. In comparisons with the effect of reaction temperature, the steam-to-glycerol ratio has a less significant impact on the gas composition although the tendency is similar and the H2 and CO production can be also enhanced as the steam-to-glycerol ratio increases. An increase of steam promotes the reaction rates (R1), (R2) and (R3) owing to the increase of reactant concentrations, which results in the enhancement of hydrogen yield. An increase of CO molar fraction can be explained that the steam concentration has a greater influence on the reaction (R2) compared to the reaction(R3). The particle size determines the fluidized state in the reactor. As the particle size decreases, the bed height is expanded. On the one hand, the reactant gas can contact with solid particles adequately, which enhances the reaction rates. On the other hand, the gas residence time is increased, which is attributed to that the reactant gas requires longer time to pass through the bed with a higher bed expansion height. Hence, as the particles diameter decreases, the methane is further consumed and the H2 and CO molar fractions are increased. Although a small particle size is beneficial to the reforming reaction, it is easy for finer particles to flow out of reactor. It is necessary to balance the relationship between operation parameters and particle properties. From Figure 7(d), it can be observed that an increase of operating pressure can promote the hydrogen yield and restrict the 9


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methane formation. This is attributed to that increasing the pressure enhances the gas species molar concentrations and the reaction rates are improved. Hence, it is feasible for fluidized bed reforming process to improve the hydrogen production at a high pressure. 4. CONCLUSION A three-dimensional simulation is carried out to investigate the glycerol steam reforming process in fluidized bed reactors. Under the framework of the two-fluid model, a bubble-structuredependent drag model is employed to reflect the bubble effect. The internal circulation flow in reactors is observed. The impacts of operating parameters including the reaction temperatures, steam to glycerol feed ratios, particle diameters and operating pressures are evaluated. The results reveal that increasing reaction temperature can enhance the fuel conversion and hydrogen yield. Reducing particle sizes and increasing steam to glycerol feed ratios and operating pressures are beneficial to the reforming process and hydrogen production. In the future work, some enhancing methods of glycerol steam reforming in fluidized bed reactors including the sorption-enhanced reforming will be further discussed.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interest. Acknowledgments This research is conducted with financial support from the National Natural Science Foundation of China (51606053), China Postdoctoral Science Foundation funded project (2016T90285) and 10


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Chinese Heilongjiang postdoctoral science funding award No. LBH-Z15055.

Nomenclature a

acceleration [m s-2]

d

particle diameter [m]

db

bubble diameter [m]

D

diffusivity [m2 s-1]

e

restitution coefficient

Fde drag force in the emulsion phase per unit volume[N] Fdb

drag force acting on the bubble per unit volume[N]

g

gravity [m s-2]

H

specific enthalpy [J kg-1]

ks conductivity of fluctuating energy [kg m-1 s-1] Ndf energy dissipation [W kg-1] p

fluid pressure [Pa]

P0 operating pressure [Pa] ps particle pressure [Pa] R

universal gas constant [J mol-1K-1]

T

temperature (K)

u

velocity [m s-1]

U

superficial velocity [m s-1]

Uslip superficial slip velocity [m s-1] 11


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Greek letters

β

drag coefficient [kg m-3 s-1]

γ

collisional energy dissipation [kg m-1 s-3]

ε

volume fration

θ

granular temperature [m2 s-2]

λ

thermal conductivity [W m-1 K-1]

µ

viscosity [Pa s]

ξ

bulk viscosity [Pa s]

ρ

density [kg m-3]

τ

stress tensor [Pa]

Subscripts b

bubble phase

e

emulsion phase

g

gas phase

s

solids phase

w

wall

Reference [1] Adhikari, S., Fernando, S.D., Haryanto, A. Energy Convers Manage.2009,50(10),2600-2604 [2] Pereira, E.B., de la Piscina, P.R., Homs, N. Bioresour. Technol.2011,102,3419-3423 [3] Pagliaro, M., Ciriminna, R., Kimura, H., Rossi, M., Pina, C.D. Angew Chem Int Ed. 2007,46(24),4434-4440. [4] Valliyappan, T., Bakhshi, N.N., Dalai. A.K. Bioresour. Technol.2008,99 ,4476-4483 [5] Escapa, A., Manuel, M.F., Morán, A., Gómez, X., Guiot , S.R., Tartakovsky, B. Energ Fuel. 2009,23(9) ,4612–4618 12


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[6] Luo, N.,Zhao, X., Cao, F., Xiao, T., Fang, D. Energ Fuel.2007, 21 (6), 3505-3512 [7] Galera, S.,Ortiz, F.J.G. Fuel.2015,144, 307-316 [8] Guo,Y., Azmat,M.U., Liu, X., Wang, Y., Lu, G. Appl. Energy.2012, 92,218-223 [9] Gustavsson, L., Borjesson,P., Johansson, B., Svenningsson, P. Energy.1995,20,1097-1113 [10] Sundari, R., Vaidya, P.D. Energ Fuel. 2012, 26 (7),4195-4204 [11] Adhikari, S., Fernando, S.D., Filip To, S. D.,

Bricka, R. M., Steele, P.H.,

Haryanto,A.

Energ Fuel. 2008, 22 (2), 1220-1226 [12] Adhikari, S., Fernando, S., Gwaltney, S.R., Filip To, S.D.,

Bricka, R.M., Steele, P.H.,

Haryanto, A. Int J Hydrogen Energ. 2007,32,2875-2880 [13] Cheng,C.K.,Foo,S.Y.,Adesina,A.A. Int J Hydrogen Energ.2012, 37,10101-10110 [14] Silva,J.M., Soria, M.A., Madeira, L.M. Int J Hydrogen Energ. 2016,41,1408-1418 [15] Iliuta, I., Radfarnia, H.R., Iliuta, M.C. AICHE J. 2013,59(6),2105-2118 [16] Rahimpour, M.R., Elekaei, H. Int J Hydrogen Energ.2009,34 (5),2208-2223 [17] Remón, J., Jarauta-Córdoba, C., García , L., Arauzo, J. Fuel Process Technol. 2016, 145, 130-147 [18] Chen, Y., Zhao, Y., Zheng,C. Chem Eng Sci. 2013, 92,67-80 [19] Dou, B., Dupont, V., Williams, P.T. Energ Fuel. 2008, 22(6),4102-4108 [20] Dou, B., Song,Y. Int J Hydrogen Energ. 2010,35,10271-10284 [21] Gidaspow, D. Applied Mechanics Reviews.1986,39,1-23 [22] Srivastava, A. , Sundaresan, S. Powder Technol.2003, 129,72-85 [23] Wang, S., Chen,J., Wang,Q., Liu,G., Lu,H.,Sun,L. Powder Technol.2016,289, 44-51 [24] Asegehegn,T.W., Schreiber,M., Krautz,H.J. Powder Technol. 2012,219,9-19 [25] Wang, S., Lu,H., Zhao, F., Liu, G. Chem. Eng. J.2014,236,121-130 13


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Table Captions: Table 1 Governing equations used in two-fluid model Table 2 Constitutive correlations in two-fluid model Table 3 Balance equations used in the BSD drag model Table 4 Main operating condition and simulation parameters

Figure Captions: Figure 1 Layout of fluidized bed reforming system Figure 2 Axial profiles of gas pressure at different grid sizes Figure 3 Comparisons of simulated outlet gas composition and experimental data Figure 4 Lateral profiles of time-averaged solid volume fraction and velocity Figure 5 Instantaneous distribution of gas species molar concentrations at 15s Figure 6 Contour plots of reaction rates during the glycerol steam reforming process Figure 7 Effects of operating parameters on gas composition at the outlet (a) reaction temperature, (b) steam to glycerol ratio, (c) particle diameter (d) operating pressure

14


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Figure 1 Layout of fluidized bed reforming system 0.0

0.2

0.4

0.6

0.8

1.0 3000

3000

2500

Coarse grid (12mm×12mm×12mm) Medium grid (9.6mm×9.6mm×9.6mm) Fine grid (8.4mm×8.4mm×8.4mm)

2000 1500

2000

1500

Ug=0.5m/s

1000

1000

500

% (?Y)

Pressure (KPa)

2500

500

0

0

0.0

0.2

0.4

0.6

0.8

1.0

Height (m)

Figure 2 Axial profiles of gas pressure at different grid sizes 0.7 0.6

Ug=0.5m/s

Gidaspow model BSD drag model Experiments (Dou et al,2010b)

0.5

Gas composition

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0.4 0.3 0.2 0.1 0.0 CH4

H2

CO2

CO

Figure 3 Comparisons of simulated outlet gas composition and experimental data

15


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Solid volume fraction

0.7 0.6

Solid velocity (m/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.4

Ug=0.5m/s

0.5 0.4

H=0.05m H=0.10m H=0.15m

0.3 0.2 Ug=0.5m/s

0.0

H=0.05m H=0.10m H=0.15m

-0.4 -0.8

-1.0

-0.5

0.0 X/ R

0.5

1.0

Figure 4 Lateral profiles of time-averaged solid volume fraction and velocity

C3H8O3

CH4

H2

CO2

CO

Figure 5 Instantaneous distribution of gas species molar concentrations at 15s

(a) R1

1.6E-07 1.4E-07 1.2E-07 1E-07 8E-08 6E-08 4E-08 2E-08 9E-09 5E-09 1E-09

3E-05 2.8E-05 2.6E-05 2.4E-05 2.2E-05 2E-05 1.8E-05 1.6E-05 1.4E-05 1.2E-05 1E-05 7E-06 3E-06 1E-07

4.5E-05 4.4E-05 4.3E-05 4.2E-05 4.1E-05 4E-05 3.9E-05 3.8E-05 3.7E-05

(b) R2

(c) R3

Figure 6 Contour plots of reaction rates during the glycerol steam reforming process 16


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0.7

0.5

Temperature 773K 873K 973K

0.4

P0=0.1Mpa

0.3

S/G=6:1 ds=0.0875mm

Gas composition

0.6

0.2 0.1 0.0 CH4

H2

CO2

CO

(a) 0.7

Steam to glycerol ratio(S/G) 6:1 9:1 12:1

0.6

Gas composition

0.5 0.4

P0=0.1Mpa

0.3

T=873K ds=0.0875mm

0.2 0.1 0.0 CH4

H2

CO2

CO

(b) 0.7

Particle diameter 0.07mm 0.0875mm 0.12mm

0.6 0.5

Gas composition

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0.4 P0=0.1Mpa S/G=6:1 T=873K

0.3 0.2 0.1 0.0 CH4

H2

CO2

CO

(c)

17


Energy & Fuels

0.7

Pressure 0.1 Mpa 0.3 Mpa 0.5 Mpa

0.6 0.5

Gas composition

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 22

T=873K S/G=6:1 ds=0.0875mm

0.4 0.3 0.2 0.1 0.0 CH4

H2

CO2

CO

(d) Figure 7 Effects of operating parameters on gas composition at the outlet (a) reaction temperature, (b) steam to glycerol ratio, (c) particle diameter, (d) operating pressure

18


Page 19 of 22

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Energy & Fuels

Table 1 Governing equations used in two-fluid model ___________________________________________________________________________________________ 1. Continuity equations

∂ (ε ρ ) + ∇ ⋅ (ε g ρg ug ) = m& g ∂t g g ∂ (ε ρ ) + ∇ ⋅ (ε s ρs us ) = m& s ∂t s s

(T1-1) (T1-2)

2. Momentum conservation equations

∂ (ε ρ u ) + ∇ ⋅ (ε g ρ g ug ug ) = −ε g ∇p + ε g ∇ ⋅ τ g + ε g ρ g g - β (ug − us ) + m& g ug ∂t g g g

∂ (ε ρ u ) + ∇ ⋅ (ε s ρs us us ) = −ε s ∇p − ∇ps + ε s ∇ ⋅ τ s + ε s ρs g + β (ug − us ) + m& s us ∂t s s s

(T1-3) (T1-4)

3. Energy conservation equations

∂ (ε ρ H ) + ∇ ⋅ (ε g ρg ug H g ) = ∇(λg ∇Tg ) − Qgs + m& g H g ∂t g g g ∂ (ε ρ H ) + ∇ ⋅ (ε s ρs us H s ) = ∇(λs ∇Ts ) + Qsg + m& s H s ∂t s s s

(T1-5) (T1-6)

4. Species transportation equations

µ ∂ (ε g ρ gYg, j ) + ∇ ⋅ (ε g ρg ugYg, j ) = ∇ ⋅ [ε g ( ρg D j + t )∇Yg, j ] + m& g, j ∂t Sc ∂ (ε s ρsYs, j ) + ∇ ⋅ (ε s ρs usYs, j ) = m& s, j ∂t

(T1-7) (T1-8)

5. Conservation equation of granular temperature

3 ∂ (T1-9) [ (ε s ρsθ ) + ∇ ⋅ (ε s ρsθ )us ] = (−∇ps I + τ s ) : ∇us + ∇ ⋅ (ks∇θ ) − γ s − 3βθ + Dgs 2 ∂t ___________________________________________________________________________________________

19


Energy & Fuels

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Page 20 of 22

Table 2 Constitutive correlations in two-fluid model ___________________________________________________________________________________________ 1.Solid pressure

ps,k = ε s ρsθ + 2ρs (1 + e ) ε s2 g0θ ps,f

= (1 -

pc

(T2-1)

∇ ⋅ us n 2 sin(ϕ ) S : S + θ / d

2 s

1024 (ε * − ε g )10  ((1 − ε g ) − ε smin )2  pc = 0.05 (ε g − ε * )5   0

)n−1

(T2-2)

εg < ε* ε * ≤ ε g < (1 − ε sfmin )

(T2-3)

ε g > (1 − ε sfmin )

2. Stress tensor

2 τg = µg{[∇ug + (∇ug )T ] − (∇⋅ ug )I} 3 2 τs = µs{[∇us + (∇us )T ] − (∇⋅ us )I} + ξs∇⋅ usI 3 4 5

µs,k = ε s2 ρs d s g 0 (1 + e)

µs,f =

θ π

+

(T2-4) (T2-5)

10 ρ s d s πθ 4 [1 + g 0ε s (1 + e)]2 96(1 + e)ε s g 0 5

2 ps,f sin(ψ ) S : S +θ / d

 3  n =  2sin(ϕ ) 1.03 

{n − (n − 1)(

2 s

ps,f pc

(T2-6)

)1/( n−1) }

(T2-7)

∇us ≥ 0

(T2-8)

∇us < 0 1/ 2

4 θ  ξ s,k = ε s2 ρ s d s g 0 (1 + e )   3 π

(T2-9)

 

2 3

ξ s,f = − µs,f

(T2-10)

3. Thermal conductivity of particles 1/ 2

ks =

25 ρ s d s πθ 6 θ  [1 + (1 + e ) g 0ε s ]2 + 2ε s2 ρ s d s g 0 (1 + e )   64(1 + e ) g 0 5 π

(T2-11)

4. Dissipation of fluctuation kinetic energy

γ s = 3(1 − e 2 )ε s2 ρ s g 0θ (

4 ds

θ π

− ∇ ⋅ us )

(T2-12)

5. Rate of energy dissipation per unit volume D gs =

18 µ ds ρs ( 2 g ) 2 u g − us 4 πθ g 0 d s ρ s 20


2

(T2-13)

Page 21 of 22

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Energy & Fuels

___________________________________________________________________________________________ Table 3 Balance equations used in the BSD drag model ___________________________________________________________________________________________ 1. Solid momentum equation in the emulsion phase along the flow direction

ne Fde + nb Fdb = (1 − δ b )(1 − ε e )∇pg + (1 − δ b )(1 − ε e )( ρs − ρg )( g + as,e ) + ∇ps ∂( as,e =

(1 − δ b )U s,e (1 − δ b )U s,e ) 1− εe 1− εe ∂z

(T3-1)

(T3-2)

2. Gas momentum equations in the emulsion and bubble phase along the flow direction

ne Fde = −(1 − δ b )ε e ∇pg − (1 − δ b )ε e ρ g ( g + ag,e )

(T3-3)

nb Fdb = −δ b∇pg − δ b ρg ( g + ag,b )

(T3-4)

a g,b = ∂( ag,e =

∂ (δ bU b *δ bU b ) ∂z

(1 − δ b )U g,e (1 − δ b )U g,e

εe

εe

(T3-5)

)

∂z

(T3-6)

3. Pressure drop balance equation between gas in the emulsion phase and bubbles

δb ne Fde = nb Fdb − δ b ρ g (ag,e − ag,b ) (1 − δ b )ε e

(T3-7)

4. Mass conservation equation of gas

ug =

[(1 − δ b )U g ,e + δ bU b ]

εg

(T3-8)

5. Mass conservation equation of particles

(1 − δ b ) U s,e (1 − ε g )

(T3-9)

ε g = (1 − δ b )ε e + δ b

(T3-10)

us = 6. Overall gas volume fraction

7. Stability criterion by minimization of the energy dissipation by drag force

N df =

1 [ne FdeU g,e + nb FdbU bδ b ] → minimum (1 − ε g ) ρs

(T3-11)

__________________________________________________________________________________________ 21


Energy & Fuels

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Page 22 of 22

Table 4 Main operating condition and simulation parameters Description

Simulation

Unit

Particle density Gas viscosity Mean particle diameter Reactor height Reactor diameter Initial solid height Initial solid volume fraction Initial temperature Inlet gas velocity Inlet gas composition (C3H8O3: H2O: N2) Pressure outlet Inlet temperature

2650 1.72×10-5 8.75×10-5 1.0 0.3 0.2 0.53 873 0.5

kg/m3 Pa·s m m m m K m/s

0.028:0.168:0.804

-

1.013×105 873

Pa K

22


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