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A mathematical model and numerical investigation for glycerol gasification in supercritical water with a tubular reactor
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A mathematical model and numerical investigation for glycerol gasification in supercritical water with a tubular reactor Hui Jin a,∗ , Simao Guo a , Liejin Guo a,b , Changqing Cao a a
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China The College of Engineering, Department of Mechanical Thermal Engineering and Chemical & Material Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia b
a r t i c l e
i n f o
Article history: Received 25 January 2015 Received in revised form 27 June 2015 Accepted 27 June 2015 Available online xxx Keywords: Supercritical water gasification Tubular reactor Numerical study Glycerol Hydrogen production
a b s t r a c t This paper developed a three-dimensional computational fluid dynamics model of the supercritical water gasification (SCWG) process of glycerol. The detailed flow field, temperature field and chemical species distributions inside the reactor were revealed, and the effects of the operating parameters on the results in the SCWG of glycerol were investigated. The reasons for incomplete gasification were discussed, and relevant possible improvements were proposed. (1) The residence time is not long enough for the complete gasification; therefore, the optimal length of the tubular reactor was obtained under different operating conditions. (2) A side-reaction region was formed near the feeding inlet and methods to reduce the volume of the side-reaction region were investigated. A high preheated water temperature and a 135◦ feeding angle were proved to obviously avoid side-reaction. A multi-injection feeding method can also suppress the side-reaction, but the carbon gasification efficiency decreased. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Supercritical water (SCW) is defined as water with temperature and pressure beyond the critical point (374 ◦ C, 22.1 MPa), and it has many unique properties, such as low viscosity, high diffusivity and low dielectric constant. These properties make supercritical water a good solvent for both organic matters and gas to provide a homogenous reaction medium for efficient gasification within a short residence time. Supercritical water gasification (SCWG) is a promising technology to convert glycerol and other organic wastes to hydrogen-rich gas products [1–4]. Much research on SCWG has been carried out by various authors in the last two decades. These works have mainly focused on the development of SCWG reactors [5–7], investigation of different feedstocks (such as glucose [8,9], cellulose [10,11], lignin [12–14], real biomass [15–17], coal [18–21] and waste organics [22–24]), investigation of effects of different gasification parameters (such as temperature, pressure and residence time) [25], evaluation of catalysts [26,27] and thermodynamic analysis [28,29]. The research work mentioned above has proven the feasibility of glycerol gasification in SCW and helped uncover more information about the characteristics of SCWG to obtain a method to improve the carbon gasification efficiency.
∗ Corresponding author. Tel.: +86 29 8266 0876; fax: +86 29 8266 9033. E-mail address: [email protected] (H. Jin).
Most published reactors for SCWG are bench-scale reactors or even micro-reactors. It is essential to gain a better understanding of the complex physical process (including flow and heat transfer) and chemical reactions in continuous SCWG reactors from the point of view of chemical reaction engineering for the reactor scaleup and industrial applications. Unfortunately, little information about internal fluid flow, heat transfer, mass transfer and reactions in SCWG reactors has been revealed by experimental measurement methods thus far due to the extreme operating conditions. As a result, computational fluid dynamics (CFD) modeling may be applied to obtain valuable information about the gasification process in an SCWG reactor. It is a good way to understand the detailed gasification process inside the reactor and provide guidance for upgrading reactors. However, little work has been done in modeling the SCWG process, especially taking gasification kinetics into account. The difficulty in modeling the SCWG process may lie in the following aspects: (1) thermodynamic and transport properties of the reaction mixture in the reactor [30], (2) an appropriate turbulent heat-transfer model of supercritical water and (3) reliable gasification kinetics in SCW. Yoshida [31] conducted CFD simulations to investigate the reactant flow and particle participation in his reactor for structural design improvement, but the chemical reactions were not considered. Goodwin [32] proposed a CFD model to simulate xylose gasification in the microchannel reactor and studied the effect of residence time on gasification. Moreover, the kinetics model for xylose in SCW was incorporated in the CFD
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Please cite this article in press as: H. Jin, et al., A mathematical model and numerical investigation for glycerol gasification in supercritical water with a tubular reactor, J. Supercrit. Fluids (2015), http://dx.doi.org/10.1016/j.supflu.2015.06.028
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3. Mathematical model 3.1. Governing equations Mass conservation:
∂ =0 + ∇ · ∂t
(1)
is the velocity vector. where is the fluid density and Momentum conservation: Fig. 1. Geometric construction for tubular reactor of hydrogen production by glycerol gasification in supercritical water.
model, which could predict gas yields. Adaze [33] studied effects of various operating parameters on heating time and heating length of supercritical water reactors with a CFD model and proposed a semi-theoretical model for calculating the heating time constant of a SCW reactor. The objective of this study is to develop a model of the SCWG process, considering flow, heat transfer and gasification reaction. A three-dimensional computational fluid dynamics (CFD) model was established with a kinetics model for supercritical water gasification of glycerol. The combined model was validated by our experimental results regarding the SCWG of glycerol in a tubular reactor. The detailed distributions of velocity, temperature and species in the reactor were revealed by the CFD model. The effects of operating parameters on the SCWG of glycerol were also investigated. Moreover, the CFD model was also used for the optimal design for SCWG tubular reactor including the feeding method.
∂ + ∇ · = −∇ p + ∇ · + f ∂t
where is the viscous stress tensor and f is the mass force vector. Energy conservation:
∂ (h) h = ∇ · + ∇ · ∂t where h =
Yj hj , hi =
∇ T − h0i
conductivity, and h0i Tref,i formation of species i. Species conservation:
hi Ji
+
i
T
Tref,i +
Tref,j
Dp + : ∇ Dt
(3)
cp,i dT , is the thermal
is the standard mole enthalpy of the
∂ Yi = −∇ · Ji + Ri (Yi ) + ∇ · ∂t
(4)
where Yi is the mass fraction of i, Ji is the diffusion flux of specie i, Ri is the total chemical reaction rate, and N
i Qr
(5)
r=1
2. Experimental setup
The experiments were performed in a continuous SCWG system developed in State Key Laboratory of Multiphase Flow in Power Engineering (SKLMFPE) [18,22]. The feedstock (glycerol solution) was first mixed with high-temperature preheated water for fast heating to suppress side reactions. The mixing flow entered the reactor located in the center of three ovens equipped along the reactor length. The reactor was fabricated from Hastelloy C276 tubing and had dimensions of 17.15 mm o.d. × 10.85 mm i.d. × 1.26-m length (Fig. 1). The design temperature and pressure were 800 ◦ C and 30 MPa, respectively. Two type-K thermocouples were inserted into the central line of the inlet and outlet of the reactor, respectively, to measure the fluid temperature.
j
Ri = Mw,i
2.1. Apparatus and procedure
(2)
where Qr is the reaction rate of reaction r, vi is the stoichiometric coefficient of species i in reaction r, and Mw,i is the molar weight of species i. 3.2. Reaction kinetics A kinetic model used for calculating gas yields by glycerol gasification in supercritical water was developed in our previous work [34]. The reactions and rates were as follows: Glycerol pyrolysis I. K1
C3 H8 O3 −→Int + CO2 + 2H2
Q1 = 102.60 exp
−53.3 × 103 (RT)
CC3 H8 O3
(R1)
CC3 H8 O3
(R2)
Glycerol pyrolysis II. 2.2. Data interpretation The GE, CE and gas yield were selected to evaluate the gasification characteristics and are defined as follows [20]: CE =
(total carbon in the gaseous products) × 100 (%) (total carbon in the feedstock)
K2
C3 H8 O3 −→Int + CO + H2 + H2 O
Q2 = 102.76 exp
−59.8 × 103 (RT)
Intermediate steam reforming I. K3
Int + H2 O−→2CO + 3H2 GE =
(mass of the gaseous products) × 100 (%) (mass of the feedstock)
Gas yield =
Q3 =
106.63 exp
(molar amount of a certain component of the gaseous products) (molar amount of glycerol)
−114.1 × 103 (RT)
CInt CH2 O
(R3)
(mol/mol)
Please cite this article in press as: H. Jin, et al., A mathematical model and numerical investigation for glycerol gasification in supercritical water with a tubular reactor, J. Supercrit. Fluids (2015), http://dx.doi.org/10.1016/j.supflu.2015.06.028
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Intermediate steam reforming II. 625
Q4 = 106.15 exp
3
−109.6 × 10 (RT)
CInt CH2 O
Intermediate product pyrolysis. K5
Int−→CO + CH4
Q5 =
4.13
10
exp
−66.7 × 103 (RT)
(R4)
CInt
(R5)
Water-gas shift reaction (WGSR).
Reactor outlet temperature /ºC
K4
Int + 3H2 O−→2CO2 + 5H2
K6
Q6 = 10
exp
−76.5 × 103 (RT)
CCO CH2 O
Q7 = 104.42 exp
−74.3 × 103 (RT)
525 500 475 450
500
550
600
650
700
Reactor wall temperature /ºC Fig. 2. Experimental and simulated temperature of effluent with different wall temperatures (preheated water flow rate: 4 kg/h, preheated water temperature: 426 ◦ C; glycerol concentration: 10 wt%; feedstock flow rate: 1 kg/h; feedstock temperature:
K7
550
(R6)
Methanation reaction. CO + 3H2 −→CH4 + H2 O
575
425
CCO CH2
(R7)
where “Int” represents the lumped liquid intermediate, which was assumed to have an average molecular formula of C2 H4 O. It is worth noting that the kinetics model was a conservative model due to limitations of the experiments [34]. Thus, the kinetics may underestimate the reaction rates at a specific temperature. 3.3. Properties The physical properties (, Cp , and ) of pure water were calculated by IAPWS-IF97 [35]. The properties of gas (H2 , CO2 , CO and CH4 ) at 25 MPa were obtained from the NIST database [36]. The diffusion coefficient of gas in supercritical water was determined by He’s method [37]. The corresponding properties of the fluid mixture were calculated by mass weight average. 3.4. Model validation The numerical study of heat transfer of supercritical water flow has been a hot research topic [38–41] in recent years, but there is still no commonly acknowledged turbulence model for SCW under different experimental conditions thus far. The detailed analysis or modification of turbulence models for heat transfer of SCW is beyond the scope of this paper. In this work, four turbulence models (standard –ε, realizable –ε, RNG –ε and Launder–Sharma) were compared to find which could accurately describe the SCWG process by comparing numerical results with experimental data obtained in SKLMFPE. In addition to the turbulence models, the mesh and the wall function also affect the numerical results [41]. The enhanced wall function was chosen, and the mesh structure was modified to guarantee y+ ≈ 1. Fig. 2 shows the comparison of the experimental temperature with the simulated outlet temperature of the reaction flow with different reactor wall temperatures. It was noted that the results obtained by the RNG –ε model fit best and that the outlet temperature increased linearly with the reactor wall temperature. The literatures [42–44] also recommend RNG –ε for calculation of the heat transfer of SCW in a circle tube. The following simulation in this work was carried out using the RNG –ε model. The comparison of experimental gas yields with simulated gas yields is shown in Fig. 3. It can be observed that the CFD model provided reasonable simulated values of gas yields. The simulated
15 ◦ C). ( ) Standard –ε; ( (䊏) experimental data.
) realizable –ε; (
) RNG –ε; (
) Launder–Sharma;
3.5
-1
2.11
Experimental gas yield/ mol mol glycerol
CO + H2 O−→CO2 + H2
600
3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-1
Simulated gas yield/ mol mol glycerol Fig. 3. Comparison of experimental gas yields with simulated gas yields. (䊏) 600 ◦ C; (䊉) 650 ◦ C; () 700 ◦ C; Gas yield: (black color) H2 ; (green color) CH4 ; (red color) CO; (blue color) CO2 [34]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
results were lower than the experimental data mainly due to the conservative reaction kinetics model mentioned in Section 3.2 [34]. 4. Results and discussion 4.1. Simulation of a typical reaction condition Typical operating conditions of SCWG (reactor wall temperature of 650 ◦ C, preheated water temperature of 426 ◦ C, preheated water flow rate of 4 kg/h, feedstock flow rate of 1 kg/h) were simulated using the CFD model. Fig. 4 displays the detailed flow field, temperature field and feedstock distribution on the symmetry plane of the inlet of the tubular reactor. It can be seen that the preheated water with high velocity and high temperature carried the feedstock flow with low velocity and low temperature into the tubular reactor. When the feedstock was mixed with preheated water, a region was formed near the feeding inlet with the characteristics of low temperature, low flow rate and high feedstock concentration [45 and 46]. Char/tar may be easily generated by the side-reaction
Please cite this article in press as: H. Jin, et al., A mathematical model and numerical investigation for glycerol gasification in supercritical water with a tubular reactor, J. Supercrit. Fluids (2015), http://dx.doi.org/10.1016/j.supflu.2015.06.028
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Fig. 4. Contours on the symmetry plane at the inlet of the tubular reactor. (a) Temperature; (b) velocity magnitude; (c) mass fraction of glycerol.
and aggregated in this region to result in a plugging problem, which was obviously not beneficial for the gasification reaction. The region is referred to as the side-reaction region in this paper. The strategy for reducing the volume of the side-reaction region appeared to be one of the optimization principle. A detailed discussion will be provided in Sections 4.4 and 4.5. The reaction rate distribution of each reaction along the axis of the reactor can be observed in Fig. 5. In the inlet of the reactor and the front end of the reactor, the decomposition rates of glycerol Reactions (R1) and (R2) were high due to the high concentration of glycerol, although the temperature was not high. Side-products were also generated with high risks of generating incomplete gasification products, such as tar. As the concentration of glycerol decreased, the reaction rates of (R1) and (R2) decreased. However, at the terminal end of the reactor, (R1) and (R2) increased due to the high temperature, even when the concentration of
glycerol was relatively low. The reaction rates of the steam reforming of the intermediates (R3) and (R4) and the decomposition reaction of the intermediate (R5) increased first and then decreased due to the consumption and lack of reactants. The reaction rates of the water-gas shift reaction (R6) and methanation reaction (R7) reaction were low, and the reaction rates were rather low in the region with low temperature. As the concentration of the reactant began to accumulate and the temperature increased, the rate of (R7) increased, while the rate of (R6) also increased but only within a small range. The distributions of reaction species along the axial direction of the reactor are presented in Fig. 6. It can be observed that the gas yields accumulated steadily and that the glycerol was gradually consumed. The yield of the intermediate increased first and then decreased. The intermediates contained acid and aldehyde [34], which may provide the design basis for the lining protecting the inner wall from acid corrosion.
1.8
1.0 0.8 0.6 0.4 0.2
2.4 2.1
0.2
1.8 1.5 1.2 0.1 0.9 0.6 0.3
0.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
reactor length / m
-1
1.2
2.7
intermediate yield / mol.mol glycerol
-1 species yields / mol.mol glycerol
-1
1.4
reaction rate / mol (L.s)
0.3
3.0
1.6
0.0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
reactor length / m
Fig. 5. Distribution of chemical reaction rates along the axial direction of the tubular
Fig. 6. Distribution of species along the axial direction of the tubular reactor. (䊏)
reactor. (䊏) R1; ( ) R2; ( ) R3; ( ) R4; ( ) R5; ( ) R6; ( ) R7. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
) H2 ; ( ) CH4 ; ( ) CO; ( ) CO2 ; ( ) C2 H4 O. (For interpretation of glycerol; ( the references to color in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: H. Jin, et al., A mathematical model and numerical investigation for glycerol gasification in supercritical water with a tubular reactor, J. Supercrit. Fluids (2015), http://dx.doi.org/10.1016/j.supflu.2015.06.028
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100
CE / %
90 80 70 60 50 0.0
0.2
0.4
0.6
0.8
1.0
Reaction fluid temperature /ºC
600 550 500 450 400 350 300
Reactor length added / m 0.0
Fig. 7. Effect of reactor length upon the CE (Carbon gasification Efficiency). Reactor wall temperature (䊏) 700 ◦ C; (䊉) 650 ◦ C; () 600 ◦ C.
It is a known fact that the low temperature and low heating rate work against complete supercritical water gasification [45 and 46] because side-reactions occur to generate char and tar. The feedstock flow with ambient temperature can be heated up rapidly to or even above the pseudo-critical parameter by mixing with hightemperature preheated water to avoid the side reaction, thus the stable and continuous operation of the system is guaranteed. The preheated water temperature is a key parameter for the system because it greatly determines the mixing temperature of the fluid in the reactor. A high preheated water temperature may lead to the waste of energy, while a low preheated temperature may result in the production of by-products. The effects of different preheated water temperatures on the SCWG of glycerol were studied via the CFD model. Fig. 8 displays the distributions of reaction fluid temperature along the axial direction of the reactor at different preheated water temperatures (350, 370, 390, 426, 500, 550 and 600 ◦ C). It can be seen that the temperature of the preheated water decreased sharply after mixing with the feedstock. If the temperature of preheated water was below the pseudo-critical temperature (e.g., 350, 370 ◦ C, etc.), the reaction fluid temperature increased slowly along the reactor length and the outlet temperature was low. If the preheated water had a temperature above the pseudo-critical temperature (e.g., 390–600 ◦ C), the reaction fluid temperature after mixing would be near or even above the pseudo-critical point. The reaction fluid temperature increased rapidly, and the outlet temperature was comparatively high. Whether the preheated water temperature was above the pseudo-critical temperature made a significant difference in the
0.8
1.0
1.2
Fig. 8. Effect of preheated water temperature on the temperature profile of the ◦
◦
◦
) 370 ◦ C; (
) 390 ◦ C;
◦
( ) 426 C; ( ) 500 C; ( ) 550 C; ( ) 600 C. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
temperature profile of the reaction fluid due to the large specific heat region near the pseudo-critical point of water. If the reaction fluid temperature after mixing was far below the pseudo-critical temperature, a large amount of heat was needed to increase the water temperature, and the temperature increased very slowly along the reactor length, making the gasification inefficient and even discontinuous. Thus, one of the design principles of the preheater in this type of SCWG system may be that the preheated water temperature needs to be high enough to ensure that the mixture temperature is above the pseudo-critical point. The effect of the preheated water temperature on the gas yield (shown in Fig. 9) also supported this design principle. When the preheated water temperature was below 400 ◦ C, the increase rate in the gas yield with increasing preheated water temperature was not obvious. As the temperature of the preheated water increased further, the gas yield increased sharply. When the preheated water temperature increased from 426 ◦ C to 600 ◦ C, the hydrogen yield increased from 2.6 to 3.2 mol/mol glycerol. Gasification efficiency
100
3.0 2.5
80
2.0 60
1.5
GE and CE / %
4.3. Effect of preheated water temperature
0.6
reaction fluid. Preheated water temperature: (䊏) 350 ◦ C; (
-1
It can be seen in Fig. 6 that the glycerol and intermediates were not completely consumed and that the lengthening of the tubular reactor might be beneficial for complete gasification. One of the main advantages of the tubular reactor is that the structure is simple and the length of the reactor is easily extended. The optimization of the length of the reactor under different operating conditions appears to be worth studying. The gasification results with various lengths with different wall temperatures (600, 650 and 700 ◦ C) were simulated, and the results can be seen in Fig. 7. It can be seen that the carbon gasification efficiency increased with the reactor length, and the increasing rate became slow. If a carbon gasification efficiency of 90% was the target, the reactor length should be extended by 1.03, 0.71 and 0.43 m when the reactor wall temperature is 600, 650 and 700 ◦ C, respectively.
0.4
Reactor length / m
Gas yield/ mol.mol glycerol
4.2. Optimization of tubular reactor length
0.2
1.0 40 0.5 20 350
400
450
500
550
600
Preheated water temperature / ºC Fig. 9. Effect of preheated water temperature on the gas yield based on the CFD model. (䊏) H2 ; (
) CO; (
) CH4 ; (
) CO2 ; (
) GE (gasification efficiency);
( ) CE (carbon gasification efficiency). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: H. Jin, et al., A mathematical model and numerical investigation for glycerol gasification in supercritical water with a tubular reactor, J. Supercrit. Fluids (2015), http://dx.doi.org/10.1016/j.supflu.2015.06.028
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Fig. 10. Distributions of the velocity, temperature and glycerol concentration of different feeding method designs.
and carbon gasification efficiency increased from 76% and 64% to 93% and 79%, respectively. Although the gas yield increased with the preheated water temperature, the optimal choice of preheated water temperature should be determined by comprehensive consideration of the energy and economic analysis of the entire system.
Feedstock
... Preheated water
Tubular reactor
4.4. Optimization of the feeding method
Fig. 11. Schematic diagram of the multi-injection method for the tubular reactor of glycerol gasification in supercritical water.
Increasing the preheated water temperature requires extra supplement of heat while adjusting the feeding method might reduce the volume of the side-reaction region in a certain preheated water temperature. Four types of feeding designs (the initial type with
a feeding angle of 90◦ , type 1 with a feeding angle of 45◦ , type 2 with a feeding angle of 135◦ and type 3 with sudden enlargement structure) were analyzed to reduce the side-reaction region. The velocity distributions, temperature distributions and glycerol
(a)
0.0018
500
0.0015
Mass concentration
550 o
Temperature / C
600
450 400 350 300 250 200 0.0
0.5
1.0 1.5 Reactor length / m
0.0012 0.0009 0.0006 0.0003 0.0000 0.0
2.0 0.05
(b)
0.5
1.0 1.5 Reactor length / m
2.0
(c)
Mass concentration
0.04 0.03 0.02 0.01 0.00 0.0
0.5
1.0 1.5 Reactor length / m
2.0
Fig. 12. Comparison of the one-injection and two-injection feeding methods: (a) fluid temperature (b) glycerol concentration (c) Concentration of “Int” along the axial ) direction of the reactor. (Reactor wall temperature: 650 ◦ C; preheated water flow rate: 4 kg/h; feedstock flow rate: 2 kg/h; glycerol concentration: 10 wt%). ( One-injection method; (—) Two-injection method. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: H. Jin, et al., A mathematical model and numerical investigation for glycerol gasification in supercritical water with a tubular reactor, J. Supercrit. Fluids (2015), http://dx.doi.org/10.1016/j.supflu.2015.06.028
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concentration distributions were compared. Fig. 10 shows the distributions of velocity, temperature and glycerol concentration of different feed inlet designs. It can be seen that the side-reaction region volume of type 1 and type 3 was larger than that of the initial type, indicating that the flow and mixing condition near the feeding inlet was not improved but even worsened, especially in the sudden enlargement design case seen in type 3. In the case of type 2 (with a feeding angle of 135◦ ), the side-reaction region was obviously smaller than that of the initial type, indicating that the cold feedstock can be well mixed with the preheated water flow and carried away from the side-reaction region quickly by the preheated water flow. It is believed that the feed inlet design of type 2 is the optimal design and may have better anti-plugging performance in the SCWG process than the other methods. 4.5. Multi-injection feeding method The multi-injection method might provide another solution to reduce the side-reaction region volume, as seen in Fig. 11. A typical case (a reactor length of 2.16 m and injection inlets located at 0.1 m and 1.1 m; the flow rates of preheated water and feedstock were kept constant) was simulated and compared with the one-injection case. It can be seen from the simulated result that the CE (Carbon gasification Efficiency) values of the two-injection case and the one-injection case were 60% and 69%, respectively. It was proven that the two-injection method decreased the carbon gasification efficiency. However, as seen in Fig. 12, the temperature distribution can be improved in the two-injection case to keep the feedstock away from the side-reaction region. It also can be seen that the concentration of intermediates distributed uniformly along the axial direction of the reactor. This can avoid the side reactions caused by high intermediate concentration and also reduce the local corrosion problem caused by high concentration of acidic intermediates. 5. Conclusions This paper proposed a mathematical model and conducted a numerical simulation to investigate the process of glycerol gasification in supercritical water with a tubular reactor. The validity of the model was well verified by the experimental results. The simulation results revealed the physical and chemical field distribution characteristics in the tubular reactor. Two possible bottlenecks for complete gasification were proposed, and relative solutions were analyzed. (1) The residence time of certain chemical species was not long enough for complete gasification. The optimal length to guarantee a high carbon gasification efficiency under certain operating conditions were obtained by this model. (2) The mixing of feedstock and preheated water forms a side reaction region with low temperature and low velocity but high glycerol concentration. A high preheated water temperature can reduce the volume of the side-reaction region, but extra heat supplement was needed. The feeding angle of 135◦ was simulated to obviously reduce the region volume to avoid sidereactions. The multi-injection feeding method can also reduce the side-reaction region volume, but the carbon gasification efficiency decreased in the case of the two-injection feeding method. Acknowledgments This work was financially supported by the National Natural Science Foundation of China (Contract no. 51306145 and 51236007)
7
and the National Basic Research Program of China (Contract no. 2012CB215303).
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The Journal of Supercritical Fluids journal homepage: www.elsevier.com/locate/supflu
A mathematical model and numerical investigation for glycerol gasification in supercritical water with a tubular reactor Hui Jin a,∗ , Simao Guo a , Liejin Guo a,b , Changqing Cao a a
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China The College of Engineering, Department of Mechanical Thermal Engineering and Chemical & Material Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia b
a r t i c l e
i n f o
Article history: Received 25 January 2015 Received in revised form 27 June 2015 Accepted 27 June 2015 Available online xxx Keywords: Supercritical water gasification Tubular reactor Numerical study Glycerol Hydrogen production
a b s t r a c t This paper developed a three-dimensional computational fluid dynamics model of the supercritical water gasification (SCWG) process of glycerol. The detailed flow field, temperature field and chemical species distributions inside the reactor were revealed, and the effects of the operating parameters on the results in the SCWG of glycerol were investigated. The reasons for incomplete gasification were discussed, and relevant possible improvements were proposed. (1) The residence time is not long enough for the complete gasification; therefore, the optimal length of the tubular reactor was obtained under different operating conditions. (2) A side-reaction region was formed near the feeding inlet and methods to reduce the volume of the side-reaction region were investigated. A high preheated water temperature and a 135◦ feeding angle were proved to obviously avoid side-reaction. A multi-injection feeding method can also suppress the side-reaction, but the carbon gasification efficiency decreased. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Supercritical water (SCW) is defined as water with temperature and pressure beyond the critical point (374 ◦ C, 22.1 MPa), and it has many unique properties, such as low viscosity, high diffusivity and low dielectric constant. These properties make supercritical water a good solvent for both organic matters and gas to provide a homogenous reaction medium for efficient gasification within a short residence time. Supercritical water gasification (SCWG) is a promising technology to convert glycerol and other organic wastes to hydrogen-rich gas products [1–4]. Much research on SCWG has been carried out by various authors in the last two decades. These works have mainly focused on the development of SCWG reactors [5–7], investigation of different feedstocks (such as glucose [8,9], cellulose [10,11], lignin [12–14], real biomass [15–17], coal [18–21] and waste organics [22–24]), investigation of effects of different gasification parameters (such as temperature, pressure and residence time) [25], evaluation of catalysts [26,27] and thermodynamic analysis [28,29]. The research work mentioned above has proven the feasibility of glycerol gasification in SCW and helped uncover more information about the characteristics of SCWG to obtain a method to improve the carbon gasification efficiency.
∗ Corresponding author. Tel.: +86 29 8266 0876; fax: +86 29 8266 9033. E-mail address: [email protected] (H. Jin).
Most published reactors for SCWG are bench-scale reactors or even micro-reactors. It is essential to gain a better understanding of the complex physical process (including flow and heat transfer) and chemical reactions in continuous SCWG reactors from the point of view of chemical reaction engineering for the reactor scaleup and industrial applications. Unfortunately, little information about internal fluid flow, heat transfer, mass transfer and reactions in SCWG reactors has been revealed by experimental measurement methods thus far due to the extreme operating conditions. As a result, computational fluid dynamics (CFD) modeling may be applied to obtain valuable information about the gasification process in an SCWG reactor. It is a good way to understand the detailed gasification process inside the reactor and provide guidance for upgrading reactors. However, little work has been done in modeling the SCWG process, especially taking gasification kinetics into account. The difficulty in modeling the SCWG process may lie in the following aspects: (1) thermodynamic and transport properties of the reaction mixture in the reactor [30], (2) an appropriate turbulent heat-transfer model of supercritical water and (3) reliable gasification kinetics in SCW. Yoshida [31] conducted CFD simulations to investigate the reactant flow and particle participation in his reactor for structural design improvement, but the chemical reactions were not considered. Goodwin [32] proposed a CFD model to simulate xylose gasification in the microchannel reactor and studied the effect of residence time on gasification. Moreover, the kinetics model for xylose in SCW was incorporated in the CFD
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3. Mathematical model 3.1. Governing equations Mass conservation:
∂ =0 + ∇ · ∂t
(1)
is the velocity vector. where is the fluid density and Momentum conservation: Fig. 1. Geometric construction for tubular reactor of hydrogen production by glycerol gasification in supercritical water.
model, which could predict gas yields. Adaze [33] studied effects of various operating parameters on heating time and heating length of supercritical water reactors with a CFD model and proposed a semi-theoretical model for calculating the heating time constant of a SCW reactor. The objective of this study is to develop a model of the SCWG process, considering flow, heat transfer and gasification reaction. A three-dimensional computational fluid dynamics (CFD) model was established with a kinetics model for supercritical water gasification of glycerol. The combined model was validated by our experimental results regarding the SCWG of glycerol in a tubular reactor. The detailed distributions of velocity, temperature and species in the reactor were revealed by the CFD model. The effects of operating parameters on the SCWG of glycerol were also investigated. Moreover, the CFD model was also used for the optimal design for SCWG tubular reactor including the feeding method.
∂ + ∇ · = −∇ p + ∇ · + f ∂t
where is the viscous stress tensor and f is the mass force vector. Energy conservation:
∂ (h) h = ∇ · + ∇ · ∂t where h =
Yj hj , hi =
∇ T − h0i
conductivity, and h0i Tref,i formation of species i. Species conservation:
hi Ji
+
i
T
Tref,i +
Tref,j
Dp + : ∇ Dt
(3)
cp,i dT , is the thermal
is the standard mole enthalpy of the
∂ Yi = −∇ · Ji + Ri (Yi ) + ∇ · ∂t
(4)
where Yi is the mass fraction of i, Ji is the diffusion flux of specie i, Ri is the total chemical reaction rate, and N
i Qr
(5)
r=1
2. Experimental setup
The experiments were performed in a continuous SCWG system developed in State Key Laboratory of Multiphase Flow in Power Engineering (SKLMFPE) [18,22]. The feedstock (glycerol solution) was first mixed with high-temperature preheated water for fast heating to suppress side reactions. The mixing flow entered the reactor located in the center of three ovens equipped along the reactor length. The reactor was fabricated from Hastelloy C276 tubing and had dimensions of 17.15 mm o.d. × 10.85 mm i.d. × 1.26-m length (Fig. 1). The design temperature and pressure were 800 ◦ C and 30 MPa, respectively. Two type-K thermocouples were inserted into the central line of the inlet and outlet of the reactor, respectively, to measure the fluid temperature.
j
Ri = Mw,i
2.1. Apparatus and procedure
(2)
where Qr is the reaction rate of reaction r, vi is the stoichiometric coefficient of species i in reaction r, and Mw,i is the molar weight of species i. 3.2. Reaction kinetics A kinetic model used for calculating gas yields by glycerol gasification in supercritical water was developed in our previous work [34]. The reactions and rates were as follows: Glycerol pyrolysis I. K1
C3 H8 O3 −→Int + CO2 + 2H2
Q1 = 102.60 exp
−53.3 × 103 (RT)
CC3 H8 O3
(R1)
CC3 H8 O3
(R2)
Glycerol pyrolysis II. 2.2. Data interpretation The GE, CE and gas yield were selected to evaluate the gasification characteristics and are defined as follows [20]: CE =
(total carbon in the gaseous products) × 100 (%) (total carbon in the feedstock)
K2
C3 H8 O3 −→Int + CO + H2 + H2 O
Q2 = 102.76 exp
−59.8 × 103 (RT)
Intermediate steam reforming I. K3
Int + H2 O−→2CO + 3H2 GE =
(mass of the gaseous products) × 100 (%) (mass of the feedstock)
Gas yield =
Q3 =
106.63 exp
(molar amount of a certain component of the gaseous products) (molar amount of glycerol)
−114.1 × 103 (RT)
CInt CH2 O
(R3)
(mol/mol)
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Intermediate steam reforming II. 625
Q4 = 106.15 exp
3
−109.6 × 10 (RT)
CInt CH2 O
Intermediate product pyrolysis. K5
Int−→CO + CH4
Q5 =
4.13
10
exp
−66.7 × 103 (RT)
(R4)
CInt
(R5)
Water-gas shift reaction (WGSR).
Reactor outlet temperature /ºC
K4
Int + 3H2 O−→2CO2 + 5H2
K6
Q6 = 10
exp
−76.5 × 103 (RT)
CCO CH2 O
Q7 = 104.42 exp
−74.3 × 103 (RT)
525 500 475 450
500
550
600
650
700
Reactor wall temperature /ºC Fig. 2. Experimental and simulated temperature of effluent with different wall temperatures (preheated water flow rate: 4 kg/h, preheated water temperature: 426 ◦ C; glycerol concentration: 10 wt%; feedstock flow rate: 1 kg/h; feedstock temperature:
K7
550
(R6)
Methanation reaction. CO + 3H2 −→CH4 + H2 O
575
425
CCO CH2
(R7)
where “Int” represents the lumped liquid intermediate, which was assumed to have an average molecular formula of C2 H4 O. It is worth noting that the kinetics model was a conservative model due to limitations of the experiments [34]. Thus, the kinetics may underestimate the reaction rates at a specific temperature. 3.3. Properties The physical properties (, Cp , and ) of pure water were calculated by IAPWS-IF97 [35]. The properties of gas (H2 , CO2 , CO and CH4 ) at 25 MPa were obtained from the NIST database [36]. The diffusion coefficient of gas in supercritical water was determined by He’s method [37]. The corresponding properties of the fluid mixture were calculated by mass weight average. 3.4. Model validation The numerical study of heat transfer of supercritical water flow has been a hot research topic [38–41] in recent years, but there is still no commonly acknowledged turbulence model for SCW under different experimental conditions thus far. The detailed analysis or modification of turbulence models for heat transfer of SCW is beyond the scope of this paper. In this work, four turbulence models (standard –ε, realizable –ε, RNG –ε and Launder–Sharma) were compared to find which could accurately describe the SCWG process by comparing numerical results with experimental data obtained in SKLMFPE. In addition to the turbulence models, the mesh and the wall function also affect the numerical results [41]. The enhanced wall function was chosen, and the mesh structure was modified to guarantee y+ ≈ 1. Fig. 2 shows the comparison of the experimental temperature with the simulated outlet temperature of the reaction flow with different reactor wall temperatures. It was noted that the results obtained by the RNG –ε model fit best and that the outlet temperature increased linearly with the reactor wall temperature. The literatures [42–44] also recommend RNG –ε for calculation of the heat transfer of SCW in a circle tube. The following simulation in this work was carried out using the RNG –ε model. The comparison of experimental gas yields with simulated gas yields is shown in Fig. 3. It can be observed that the CFD model provided reasonable simulated values of gas yields. The simulated
15 ◦ C). ( ) Standard –ε; ( (䊏) experimental data.
) realizable –ε; (
) RNG –ε; (
) Launder–Sharma;
3.5
-1
2.11
Experimental gas yield/ mol mol glycerol
CO + H2 O−→CO2 + H2
600
3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-1
Simulated gas yield/ mol mol glycerol Fig. 3. Comparison of experimental gas yields with simulated gas yields. (䊏) 600 ◦ C; (䊉) 650 ◦ C; () 700 ◦ C; Gas yield: (black color) H2 ; (green color) CH4 ; (red color) CO; (blue color) CO2 [34]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
results were lower than the experimental data mainly due to the conservative reaction kinetics model mentioned in Section 3.2 [34]. 4. Results and discussion 4.1. Simulation of a typical reaction condition Typical operating conditions of SCWG (reactor wall temperature of 650 ◦ C, preheated water temperature of 426 ◦ C, preheated water flow rate of 4 kg/h, feedstock flow rate of 1 kg/h) were simulated using the CFD model. Fig. 4 displays the detailed flow field, temperature field and feedstock distribution on the symmetry plane of the inlet of the tubular reactor. It can be seen that the preheated water with high velocity and high temperature carried the feedstock flow with low velocity and low temperature into the tubular reactor. When the feedstock was mixed with preheated water, a region was formed near the feeding inlet with the characteristics of low temperature, low flow rate and high feedstock concentration [45 and 46]. Char/tar may be easily generated by the side-reaction
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Fig. 4. Contours on the symmetry plane at the inlet of the tubular reactor. (a) Temperature; (b) velocity magnitude; (c) mass fraction of glycerol.
and aggregated in this region to result in a plugging problem, which was obviously not beneficial for the gasification reaction. The region is referred to as the side-reaction region in this paper. The strategy for reducing the volume of the side-reaction region appeared to be one of the optimization principle. A detailed discussion will be provided in Sections 4.4 and 4.5. The reaction rate distribution of each reaction along the axis of the reactor can be observed in Fig. 5. In the inlet of the reactor and the front end of the reactor, the decomposition rates of glycerol Reactions (R1) and (R2) were high due to the high concentration of glycerol, although the temperature was not high. Side-products were also generated with high risks of generating incomplete gasification products, such as tar. As the concentration of glycerol decreased, the reaction rates of (R1) and (R2) decreased. However, at the terminal end of the reactor, (R1) and (R2) increased due to the high temperature, even when the concentration of
glycerol was relatively low. The reaction rates of the steam reforming of the intermediates (R3) and (R4) and the decomposition reaction of the intermediate (R5) increased first and then decreased due to the consumption and lack of reactants. The reaction rates of the water-gas shift reaction (R6) and methanation reaction (R7) reaction were low, and the reaction rates were rather low in the region with low temperature. As the concentration of the reactant began to accumulate and the temperature increased, the rate of (R7) increased, while the rate of (R6) also increased but only within a small range. The distributions of reaction species along the axial direction of the reactor are presented in Fig. 6. It can be observed that the gas yields accumulated steadily and that the glycerol was gradually consumed. The yield of the intermediate increased first and then decreased. The intermediates contained acid and aldehyde [34], which may provide the design basis for the lining protecting the inner wall from acid corrosion.
1.8
1.0 0.8 0.6 0.4 0.2
2.4 2.1
0.2
1.8 1.5 1.2 0.1 0.9 0.6 0.3
0.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
reactor length / m
-1
1.2
2.7
intermediate yield / mol.mol glycerol
-1 species yields / mol.mol glycerol
-1
1.4
reaction rate / mol (L.s)
0.3
3.0
1.6
0.0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
reactor length / m
Fig. 5. Distribution of chemical reaction rates along the axial direction of the tubular
Fig. 6. Distribution of species along the axial direction of the tubular reactor. (䊏)
reactor. (䊏) R1; ( ) R2; ( ) R3; ( ) R4; ( ) R5; ( ) R6; ( ) R7. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
) H2 ; ( ) CH4 ; ( ) CO; ( ) CO2 ; ( ) C2 H4 O. (For interpretation of glycerol; ( the references to color in this figure legend, the reader is referred to the web version of this article.)
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100
CE / %
90 80 70 60 50 0.0
0.2
0.4
0.6
0.8
1.0
Reaction fluid temperature /ºC
600 550 500 450 400 350 300
Reactor length added / m 0.0
Fig. 7. Effect of reactor length upon the CE (Carbon gasification Efficiency). Reactor wall temperature (䊏) 700 ◦ C; (䊉) 650 ◦ C; () 600 ◦ C.
It is a known fact that the low temperature and low heating rate work against complete supercritical water gasification [45 and 46] because side-reactions occur to generate char and tar. The feedstock flow with ambient temperature can be heated up rapidly to or even above the pseudo-critical parameter by mixing with hightemperature preheated water to avoid the side reaction, thus the stable and continuous operation of the system is guaranteed. The preheated water temperature is a key parameter for the system because it greatly determines the mixing temperature of the fluid in the reactor. A high preheated water temperature may lead to the waste of energy, while a low preheated temperature may result in the production of by-products. The effects of different preheated water temperatures on the SCWG of glycerol were studied via the CFD model. Fig. 8 displays the distributions of reaction fluid temperature along the axial direction of the reactor at different preheated water temperatures (350, 370, 390, 426, 500, 550 and 600 ◦ C). It can be seen that the temperature of the preheated water decreased sharply after mixing with the feedstock. If the temperature of preheated water was below the pseudo-critical temperature (e.g., 350, 370 ◦ C, etc.), the reaction fluid temperature increased slowly along the reactor length and the outlet temperature was low. If the preheated water had a temperature above the pseudo-critical temperature (e.g., 390–600 ◦ C), the reaction fluid temperature after mixing would be near or even above the pseudo-critical point. The reaction fluid temperature increased rapidly, and the outlet temperature was comparatively high. Whether the preheated water temperature was above the pseudo-critical temperature made a significant difference in the
0.8
1.0
1.2
Fig. 8. Effect of preheated water temperature on the temperature profile of the ◦
◦
◦
) 370 ◦ C; (
) 390 ◦ C;
◦
( ) 426 C; ( ) 500 C; ( ) 550 C; ( ) 600 C. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
temperature profile of the reaction fluid due to the large specific heat region near the pseudo-critical point of water. If the reaction fluid temperature after mixing was far below the pseudo-critical temperature, a large amount of heat was needed to increase the water temperature, and the temperature increased very slowly along the reactor length, making the gasification inefficient and even discontinuous. Thus, one of the design principles of the preheater in this type of SCWG system may be that the preheated water temperature needs to be high enough to ensure that the mixture temperature is above the pseudo-critical point. The effect of the preheated water temperature on the gas yield (shown in Fig. 9) also supported this design principle. When the preheated water temperature was below 400 ◦ C, the increase rate in the gas yield with increasing preheated water temperature was not obvious. As the temperature of the preheated water increased further, the gas yield increased sharply. When the preheated water temperature increased from 426 ◦ C to 600 ◦ C, the hydrogen yield increased from 2.6 to 3.2 mol/mol glycerol. Gasification efficiency
100
3.0 2.5
80
2.0 60
1.5
GE and CE / %
4.3. Effect of preheated water temperature
0.6
reaction fluid. Preheated water temperature: (䊏) 350 ◦ C; (
-1
It can be seen in Fig. 6 that the glycerol and intermediates were not completely consumed and that the lengthening of the tubular reactor might be beneficial for complete gasification. One of the main advantages of the tubular reactor is that the structure is simple and the length of the reactor is easily extended. The optimization of the length of the reactor under different operating conditions appears to be worth studying. The gasification results with various lengths with different wall temperatures (600, 650 and 700 ◦ C) were simulated, and the results can be seen in Fig. 7. It can be seen that the carbon gasification efficiency increased with the reactor length, and the increasing rate became slow. If a carbon gasification efficiency of 90% was the target, the reactor length should be extended by 1.03, 0.71 and 0.43 m when the reactor wall temperature is 600, 650 and 700 ◦ C, respectively.
0.4
Reactor length / m
Gas yield/ mol.mol glycerol
4.2. Optimization of tubular reactor length
0.2
1.0 40 0.5 20 350
400
450
500
550
600
Preheated water temperature / ºC Fig. 9. Effect of preheated water temperature on the gas yield based on the CFD model. (䊏) H2 ; (
) CO; (
) CH4 ; (
) CO2 ; (
) GE (gasification efficiency);
( ) CE (carbon gasification efficiency). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: H. Jin, et al., A mathematical model and numerical investigation for glycerol gasification in supercritical water with a tubular reactor, J. Supercrit. Fluids (2015), http://dx.doi.org/10.1016/j.supflu.2015.06.028
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ARTICLE IN PRESS
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Fig. 10. Distributions of the velocity, temperature and glycerol concentration of different feeding method designs.
and carbon gasification efficiency increased from 76% and 64% to 93% and 79%, respectively. Although the gas yield increased with the preheated water temperature, the optimal choice of preheated water temperature should be determined by comprehensive consideration of the energy and economic analysis of the entire system.
Feedstock
... Preheated water
Tubular reactor
4.4. Optimization of the feeding method
Fig. 11. Schematic diagram of the multi-injection method for the tubular reactor of glycerol gasification in supercritical water.
Increasing the preheated water temperature requires extra supplement of heat while adjusting the feeding method might reduce the volume of the side-reaction region in a certain preheated water temperature. Four types of feeding designs (the initial type with
a feeding angle of 90◦ , type 1 with a feeding angle of 45◦ , type 2 with a feeding angle of 135◦ and type 3 with sudden enlargement structure) were analyzed to reduce the side-reaction region. The velocity distributions, temperature distributions and glycerol
(a)
0.0018
500
0.0015
Mass concentration
550 o
Temperature / C
600
450 400 350 300 250 200 0.0
0.5
1.0 1.5 Reactor length / m
0.0012 0.0009 0.0006 0.0003 0.0000 0.0
2.0 0.05
(b)
0.5
1.0 1.5 Reactor length / m
2.0
(c)
Mass concentration
0.04 0.03 0.02 0.01 0.00 0.0
0.5
1.0 1.5 Reactor length / m
2.0
Fig. 12. Comparison of the one-injection and two-injection feeding methods: (a) fluid temperature (b) glycerol concentration (c) Concentration of “Int” along the axial ) direction of the reactor. (Reactor wall temperature: 650 ◦ C; preheated water flow rate: 4 kg/h; feedstock flow rate: 2 kg/h; glycerol concentration: 10 wt%). ( One-injection method; (—) Two-injection method. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: H. Jin, et al., A mathematical model and numerical investigation for glycerol gasification in supercritical water with a tubular reactor, J. Supercrit. Fluids (2015), http://dx.doi.org/10.1016/j.supflu.2015.06.028
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concentration distributions were compared. Fig. 10 shows the distributions of velocity, temperature and glycerol concentration of different feed inlet designs. It can be seen that the side-reaction region volume of type 1 and type 3 was larger than that of the initial type, indicating that the flow and mixing condition near the feeding inlet was not improved but even worsened, especially in the sudden enlargement design case seen in type 3. In the case of type 2 (with a feeding angle of 135◦ ), the side-reaction region was obviously smaller than that of the initial type, indicating that the cold feedstock can be well mixed with the preheated water flow and carried away from the side-reaction region quickly by the preheated water flow. It is believed that the feed inlet design of type 2 is the optimal design and may have better anti-plugging performance in the SCWG process than the other methods. 4.5. Multi-injection feeding method The multi-injection method might provide another solution to reduce the side-reaction region volume, as seen in Fig. 11. A typical case (a reactor length of 2.16 m and injection inlets located at 0.1 m and 1.1 m; the flow rates of preheated water and feedstock were kept constant) was simulated and compared with the one-injection case. It can be seen from the simulated result that the CE (Carbon gasification Efficiency) values of the two-injection case and the one-injection case were 60% and 69%, respectively. It was proven that the two-injection method decreased the carbon gasification efficiency. However, as seen in Fig. 12, the temperature distribution can be improved in the two-injection case to keep the feedstock away from the side-reaction region. It also can be seen that the concentration of intermediates distributed uniformly along the axial direction of the reactor. This can avoid the side reactions caused by high intermediate concentration and also reduce the local corrosion problem caused by high concentration of acidic intermediates. 5. Conclusions This paper proposed a mathematical model and conducted a numerical simulation to investigate the process of glycerol gasification in supercritical water with a tubular reactor. The validity of the model was well verified by the experimental results. The simulation results revealed the physical and chemical field distribution characteristics in the tubular reactor. Two possible bottlenecks for complete gasification were proposed, and relative solutions were analyzed. (1) The residence time of certain chemical species was not long enough for complete gasification. The optimal length to guarantee a high carbon gasification efficiency under certain operating conditions were obtained by this model. (2) The mixing of feedstock and preheated water forms a side reaction region with low temperature and low velocity but high glycerol concentration. A high preheated water temperature can reduce the volume of the side-reaction region, but extra heat supplement was needed. The feeding angle of 135◦ was simulated to obviously reduce the region volume to avoid sidereactions. The multi-injection feeding method can also reduce the side-reaction region volume, but the carbon gasification efficiency decreased in the case of the two-injection feeding method. Acknowledgments This work was financially supported by the National Natural Science Foundation of China (Contract no. 51306145 and 51236007)
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and the National Basic Research Program of China (Contract no. 2012CB215303).
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Please cite this article in press as: H. Jin, et al., A mathematical model and numerical investigation for glycerol gasification in supercritical water with a tubular reactor, J. Supercrit. Fluids (2015), http://dx.doi.org/10.1016/j.supflu.2015.06.028