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Mathematical Simulation and Design of Three-Phase Bubble Column Reactor for Direct Synthesis of Dimethyl Ether from Syngas
Journal of Natural Gas Chemistry 16(2007)193–199
Article
Mathematical Simulation and Design of Three-Phase Bubble Column Reactor for Direct Synthesis of Dimethyl Ether from Syngas Dianhua Liu,
Xing Hua,
Dingye Fang*
College of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China [ Manuscript received October 10, 2006; revised December 15, 2006 ]
Abstract: A three-phase reactor mathematical model was set up to simulate and design a three-phase bubble column reactor for direct synthesis of dimethyl ether (DME) from syngas, considering both the influence of part inert carrier backmixing on transfer and the influence of catalyst grain sedimentation on reaction. On the basis of this model, the influences of the size and reaction conditions of a 100000 t/a DME reactor on capacity were investigated. The optimized size of the 10000 t/a DME synthesis reactor was proposed as follows: diameter 3.2 m, height 20 m, built-in 400 tube heat exchanger (φ 38×2 mm), and inert heat carrier paraffin oil 68 t and catalyst 34.46 t. Reaction temperature and pressure were important factors influencing the reaction conversion for different size reactors. Under the condition of uniform catalyst concentration distribution, higher pressure and temperature were proposed to achieve a higher production capacity of DME. The best ratio of fresh syngas for DME synthesis was 2.04. Key words: dimethyl ether; syngas; three-phase reactor; DME synthesis; slurry bed; mathematical simulation model
1. Introduction Dimthyl ether (DME) is regarded as a multisource, multi-purpose clean fuel and a chemical feedstock of the twenty-first century [1]. It can be used as a cleaning fuel for diesel engines, gas turbines in power generation, fuel cells, and liquefied petroleum gas (LPG) alternative for heating and cooking, and a chemical feedstock for higher ethers and oxygenates [2]. DME can be manufactured in large quantities from natural gas, coal, biomass, and municipal solid waste. The single-stage, liquid phase DME synthesis process, incorporates the sequential reaction of methanol synthesis and methanol dehydration in a slurry phase reactor system. The reaction network involved in single-stage synthesis dimethyl ether from ∗
syngas can be shown as follows [3]: CO + 2H2 ⇋ CH3 OH 0 ∆H298K = −90.56 kJ/mol
(1)
CO2 + 3H2 ⇋ CH3 OH + H2 O 0 ∆H298K = −49.43 kJ/mol
(2)
2CH3 OH ⇋ CH3 OCH3 + H2 O 0 ∆H298K = −23.56 kJ/mol
(3)
Dimethyl ether synthesis from syngas is highly exothermic. The catalyst, whose highest reaction temperature is around 270 ℃ for methanol synthesis, will be deactivated over 270 ℃. Therefore, the problem of gas-solid single-stage synthesis for dimethyl ether is how to transfer the exothermic heat and keep the catalyst bed under the overtemperature limit. In
Corresponding author. Tel: (021)64251002; E-mail: [email protected] This work was supported by the National Basic Research Program of China (2005CB221205)
194
Dianhua Liu et al./ Journal of Natural Gas Chemistry Vol. 16 No. 2 2007
under the support of the Japanese government and a 100 t/d pilot plant was built in Hokkaido Japan [7]. But no industrial DME direct synthesis reactor is running up to now. Literature on the simulation and design of the industrial DME synthesis reactor is very scarce. In this article, a mathematical model is proposed, for direct synthesis of dimethyl ether with syngas in a three-phase slurry reactor with a capacity of 100, 000t/a, aiming to provide data for industrial reactor design, to directly synthesize DME from syngas.
a three-phase bed, the inert carrier of the liquid phase with high thermal conductivity and heat capacity, brings about a gas-liquid-solid three phases in high turbulence, which can rapidly disperse the reaction heat and transfer it to the cool medium, thus making the bed close to an isothermal condition and solving the problem of overheating. In addition to the superior heat management allowed by the liquid phase operation, the synergistic effect of these reactions yields more DME than the two-stage sequential processing [4]. The advantages of the three phase reactor are [5]: (1) high efficiency, using a fine particle catalyst to promote the utilization ratio of the catalyst’s inner surface area and get high conversion; (2) multi-source of the raw material, the content of CO can vary in a wide range because of the high heat capacity inert carrier in the reactor; (3) flexibility in operation, gas velocity can be varied in a wide range. Air Products and Chemicals Inc.(APCI) developed a process technology for converting coal-derived syngas to liquid fuel using DOE’s Alternative Fuels Development Unit (AFDU), located at LaPorte, Texas. A single-stage slurry phase process for coproduction of dimethyl ether and methanol was demonstrated at the AFDU in 1991. Substantial increase in the syngas conversion perpass was demonstrated by mixing a fine particle dehydration catalyst with a methanol synthesis catalyst [6]. A pilot scale plant (5t/d) ran successfully in 1999,
rCO
A2 = A1 exp − RT
rCO2
A6 = A5 exp − RT
rD = A9 exp −
2. Mathematical model The three-phase reactor model, considering both the influence of part inert carrier backmixing on transfer and the influence of catalyst grain sedimentation on reaction, was set up to simulate and design a three-phase bubble column reactor. The effect of the catalyst concentration distribution along the bed height on reaction was calculated. The effect of the backmixing of liquid phase heat carrier on the reaction was investigated. The mathematical model for the reactor was envisaged as: (1) gas phase being plug flow, (2) gas phase volume being reduced during the reaction process, (3) mass transfer resistance was ignored in the liquid-solid phase with a result that mass transfer coefficient and mass transfer area in the liquid-solid phase were much greater than those in the gas-liquid phase. The following patterns were chosen as the intrinsic kinetics model for the reaction:
A3 A4 fCO fH2
A7 fCO f A8 2 H2
A10 RT
The parameters in this model are: A1 =0.01733, A2 =2.130×104 J/mol, A3 =0.4079, A4 =0.3372, A5 =0.4029, A6 =4.321×104 J/mol, A7 =0.006034, A8 =3.161, A9 =0.09163, A10 =3.128×104 J/mol, A11 =0.3099 The model of catalyst concentration distribution along the bed height is shown below as: [8] Z Z 0 Ccat = Ccat exp(A) exp L L Z = i · ; i = 1, 2, · · · N N
A11 fM
fM 1− Kf1 fCO fH2 2
!
fM fW 1− Kf2 fCO2 fH3 2
1−
fW fD 2 Kf3 fM
(4)
! (5)
(6)
where L A = −ψl Up ; ψl = Ds
0.026
Up = 1.10U g
Ccat 1− ; ρp
3.5
0 Ut0.80 ψ l ; Ccat =
(7) Ut =
gc Dp2 (ρp − ρl ) ; 18µl
Ccat A ; exp(A) − 1.0
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Journal of Natural Gas Chemistry Vol. 16 No. 2 2007
Ug DR
Ds = 9.6
F r6 Reg
0.1114
Ug ; Fr = ; 0.5 (g D c R) 1.1
+ 0.019Rep
Ut dp ρl U g D R ρl ; Rep = Reg = µl µl The mathematical model of dimethyl ether synthesis in the three-phase slurry bed is set up as follows, taking into consideration the influence of both liquid phase backmixing and grain sedimentation: dCg,j Cg,j −ug = kl,j al − Cl,j dZ Hj (8) j = H2 , CO, CO2 , CH3 OH, H2 O Cg,j d2 Cl,j Z = Ccat rj Cl,j − kl,j al − Cl,j Dl εl dZ 2 Hj j = H2 , CO2 , CO (9)
2 66 66 66 64
−2 1
d2 Cl,j Z Dl εl = −Ccat rj Cl,j − kl,j al dZ 2 j = CH3 OH, H2 O
1 −2 ·
1 · ·
32 77 66 77 66 77 66 75 66 4
Cg,j − Cl,j Hj
(10) Equation set (9) and (10) is a group of the second order differential equations and its boundary conditions are [9,10]: dCl,j =0 dZ Z=L (11)
0 0 Cg,j |Z=0 = Cg,j ; Cl,j |Z=0 = Cl,j ;
where
1.4 Dl = 2.7Ug0.30 DR
The determination of parameter kl,j , al , Hj can be found in references [11−13]. The model Equations (9) and (10) and boundary condition (11) are deduced by discretion to a group of algebraic equations, with a tridiagonal coefficient matrix.
3 2 77 66 77 66 77 = 66 77 66 5 64
0 h2 G1j − Cl,j 2 2 h Gj · · · · · 2 (N−2) h Gj (N−2) Cl,j 1 −2 1 (N−1) (N−2) 4Cl,j − Cl,j (N−1) (N−1) 1 −2 Cl,j h2 Gj − 3 j = H2 , CO, CO2 , H2 O, CH3 OH, CH3 OCH3 0 Cl,j 1 Cl,j · ·
3 77 77 77 77 75
(12)
where i i Ccat Rj Cl,j
Gij
=h
=h
− kl,j al
2
i Cg,j i − Cl,j Hj
Dl εl
i The liquid phase concentration distribution, Cl,j (i=1,2· · · N), on every dispersing reaction crosssection is solved by iterating chasing method. Next,
i−1 (Cl,j
−
i 2Cl,j
!
Dl εl
i i −Ccat Rj Cl,j
Gij
− kl,j al
2
i Cg,j i − Cl,j Hj
+
i+1 k+1 Cl,j )
!
(13) ; j = H2 , CO, CO2
(14) ; j = H2 O, CH3 OH, CH3 OCH3
i the gas phase concentration distribution, Cg,j (i=1, 2· · · N), is solved by Equation (8). The iteration keeps running according to the iterate form
i i ±Ccat Rj Cl,j − kl,j al = Dl εl
k = 0, 1, 2, · · · N ;
i Cg,j i − Cl,j Hj
! k
(positive j=H2 , CO, CO2 , whereas, negative j=H2 O, CH3 OH, CH3 OCH3 ) till satisfying
(15)
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Dianhua Liu et al./ Journal of Natural Gas Chemistry Vol. 16 No. 2 2007
3 X N i k+1 i k X − (Cl,j ) (Cl,j ) 6 ε = 10−4 i )k (Cl,j
(16)
j=1 i=1
3. Simulation and design for the dimethyl ether reactor
The mathematical model of the bubble column slurry reactor has been proved to be reasonable through the pilot test of methanol synthesis [14,15]. Using the above analog calculation of this three-phase slurry dimethyl ether reactor mathematical model, and taking into consideration the influence of grain sedimentation, as well as part of the liquid-phase backmixing, the size and reaction conditions of 100, 000t/a DME reactor are discussed in detail. 3.1. Size of dimethyl ether reactor 3.1.1. The ef fect of superf icial gas velocity on catalyst concentration Figure 1 shows the effect of superficial gas velocity on the catalyst concentration distribution along the bed height.
be improved and the conversion of CO decreases with an increasing superficial gas velocity, but the catalyst concentration distribution along the bed height is not uniform. The results indicate that a small diameter reactor is not suitable as an industrial three-phase bubble column reactor. Table 1. Ef fect of superf icial gas velocity on the conversion of CO Gas flow to
Superficial gas
Conversion
reactor (Nm3 /h)
velocity (m/s)
of CO(%)
1
67000
0.1928
0.7023
2
73000
0.2101
0.6574
3
77000
0.2216
0.6301
No.
3.1.2. The ef fect of reactor diameter on catalyst concentration distribution along the bed height Figure 2 shows the effect of catalyst concentration distribution along bed height with different reactor diameters at a superficial gas velocity of 0.1153 m/s. The results demonstrate that the catalyst concentration distribution along the bed height becomes well-distributed when the reactor diameter increases. The catalyst concentration distribution along the bed height is uniform when the reactor diameter is 3.2 m. The difference of catalyst concentration distribution is less than 9% from the top to the bottom of the catalyst bed.
Figure 1. Ef fect of superf icial gas velocity on catalyst concentration distribution along bed height
The structure of the reactor is: diameter 2.0 m, height 55 m, built-in 300 tube heat exchanger (φ 38×2 mm), inert heat carrier paraffin oil 68 t and catalyst 34.46 t. Gas composition: yCO =0.2816, yCO2 =0.0335, yH2 =0.6787, yN2 =0.0049, yCH4 =0.0013, and superficial gas velocity from 0.1928 to 0.2216 m/s. The reaction is carried out under the condition of 240 ℃ and 5 MPa. Figure 1 and Table 1 clearly demonstrate that the grain sedimentation can
Figure 2. Ef fect of reactor diameter on catalyst concentration distribution along bed height
Journal of Natural Gas Chemistry Vol. 16 No. 2 2007
3.1.3. Brief summary From the above discussion, it may be concluded that slightly increased superficial gas velocity can improve the effect of the catalyst concentration distribution along the bed height. A small diameter reactor is not suitable as an industrial three-phase reactor. Therefore, the 10, 000t/a DME reactor is suggested to be with: diameter 3.2 m, height 20 m, built-in 400 tube heat exchanger φ 38×2 mm, inert heat carrier paraffin oil 68 t, and catalyst 34.46 t. 3.2. Ef fect of reaction conditions and feed gas composition 3.2.1. Ef fects of reaction conditions on conversion of CO and production capacity of DME Using the reactor mentioned above, the effects of reaction temperature and pressure on the conversion of CO, and production capacity of DME were investigated. Gas compositions were yCO =0.2816, yCO2 =0.0335, yH2 =0.6787, yN2 =0.0049, yCH4 = 0.0013. Gas flow to reactor was 75000 Nm3 /h. Figur-
Figure 3. Ef fect of reaction temperature on conversion of CO and production capacity of DME
Figure 4. Ef fect of reaction pressure on conversion of CO and production capacity of DME
197
es 3 and 4 clearly show that both the conversion of CO and production capacity of DME increase when reaction temperature and pressure become higher. The synergistic effect of the reaction of methanol synthesis and methanol dehydration yields more products. 3.2.2. Ef fects of reaction conditions on catalyst concentration distribution along bed height Figure 5 shows that the catalyst concentration distribution along the bed height becomes welldistributed when the reaction pressure decreases. The reason is that the superficial gas velocity increases with a decrease in reaction pressure, with the same gas flow to reactor. To decrease the reaction temperature, the superficial gas velocity accordingly decreases. But this results in good distribution of the catalyst concentration along the bed height (Figure 6). It means that the slurry phase operational height influences the catalyst concentration distribution along the bed height. The reaction temperature and the slurry phase operational height have different effects on the
Figure 5. Ef fect of reaction pressure on catalyst concentration distribution along the bed height
Figure 6. Ef fect of reaction temperature on catalyst concentration distribution along the bed height
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catalyst concentration distribution along the bed height. The latter has a stronger effect than the former. 3.2.3. Ef fect of dif ferent feed gas composition on the reaction For the same reactor with a feed gas flow of 75000 Nm3 /h, reaction pressure of 6.0 MPa, and reaction
temperature of 260 ℃, three groups of gases were investigated (Table 2). It can be seen in Figure 7 that conversion of DME increases when the molar ratio of (H2 -CO2 )/(CO+CO2 ) increases. The best ratio range of fresh syngas of methanol synthesis is from 2.00 to 2.15 [16]. Therefore, the synergistic effect of methanol synthesis reaction and methanol dehydration yields a higher conversion of DME.
Table 2. Feed gas composition No.
H2
CO
CO2
CH4
N2
Molar ratio of (H2 -CO2 ) to (CO+CO2 )
1
0.5856
0.2712
0.0231
0.0531
0.0670
1.91
2
0.5470
0.3890
0.0070
0.0000
0.0560
1.36
3
0.6787
0.2816
0.0335
0.0013
0.0049
2.04
Figure 7. Ef fect of dif ferent feed gas composition on reaction
4. Conclusions The mathematical model is set up for direct synthesis of dimethyl ether from syngas in a three-phase slurry reactor and can be used for the design of an industrial DME synthesis reactor. The results of this simulation show that a small diameter reactor is not suitable for an industrial reactor. The best size for a reactor is not the biggest, but it should be designed by considering the fixed investment and transportation condition. The proposed 10, 000 t/a reactor of DME synthesis is with: diameter 3.2 m, height 20 m, built-in 400 tube heat exchanger (φ 38×2 mm), inert heat carrier paraffin oil 68 t, and catalyst 34.46 t. Reaction temperature and pressure are important factors, which influence the reaction conversion for different size reactors. The conversion of CO and production capacity of DME increase with the pressure increasing, because the moles in the products are less than the moles in the reactants, in the reaction sys-
tem. The reason is that the superficial gas velocity increases with the reaction pressure decreasing, with the same gas flow to the reactor. The conversion of CO and production capacity of DME increases with temperature increase, because the reaction is controlled by the reaction dynamics. But the catalyst concentration distribution along the bed height has a reverse trend. The operational height of the slurry phase influences the trend. The choice of pressure and temperature should take into consideration both the conversion of CO and the catalyst concentration distribution. Under the condition of uniform catalyst concentration distribution, higher pressure and temperature are proposed, to achieve a higher production capacity of DME. The best ratio of fresh syngas of methanol synthesis is 2.04, under the reaction conditions considered in this article. The synergistic effect of methanol synthesis reaction and methanol dehydration yields high conversion of DME. Acknowledgements The authors are very grateful to Prof. Cao Fahai and Prof. Guo Xuhong for their help. Nomenclature rCO , rCO2 , rD intrinsic kinetics rate of carbon monoxide, carbon dioxide, dimehtyl ether, mol/(h·g(cat) ) 0 Ccat catalyst concentration at the gas inlet, kg·m−3 ψl content of liquid in liquid-solid slurry phase L operational slurry height, m w mass of catalyst, kg T temperature, K Rg gas constant, J/(mol·K)
Journal of Natural Gas Chemistry Vol. 16 No. 2 2007
UP Ds Ccat ρp ρl µg µt Z Ccat dp µl gc DR A Fr Reg Rep Cg,j Cl,j H Dl al kl h Ccat
hindered sedimentation velocity of particles, m·s−1 axial dispersion coefficient of particle, m2 ·s−1 average catalyst concentration, kg·m−3 density of catalyst, kg·m−3 density of liquid, kg·m−3 superficial gas velocity, m·s−1 sedimentation velocity of terminal particle, m·s−1 catalyst concentration distribution along the bed height, kg·m−3 particle diameter, m viscosity of liquid, kg/(m·s) acceleration of gravity, 9.81 m·s−2 inner diameter of reactor, m Brodenstein’s number Froude’s number Reynold’s number Reynold’s number of particle jth gas concentration, kmol·m−3 ith liquid concentraion, kmol·m−3 solubility, kg(g)/kg(l) axial dispersion coefficient of liquid, m2 ·s gas-liquid specific surface area, m2 /m3 gas-liquid transfer coefficient at liquid side, m·s−1 L difference discrete step length, m N catalyst concentration in slurry phase, kg·m−3
References [1] Lunsford J H. Catal Today, 2000, 63(2-4): 165 [2] Makarand G. [PhD Dissertation]. Akron: University of Akron, 1992
199
[3] Liu D H, Xu J, Zhang H T, Fang D Y. Huagong Xuebao (J Chem Ind Eng), 2002, 53(1): 103 [4] Lee S, Sardesai A. Topics in Catalysis, 2005, 32(3-4): 197 [5] Fang D Y, Ding B Q. Huagong Jinzhan (Chem Ind Eng Prog), 2003, 22(3): 233 [6] Bhatt B L, Schaub E S, Heydorn E C. 18th Proc. Int. Tech. Conf. Coal Util. Fuel Syst, Pittsburgh, 1993, 197 [7] Ogawa T, Ono M, Okuyama K, Aoki S, Tomura K, Shikada T, Inoue N, Ohno Y. NKK Tech Rev, 1999, 81: 13 [8] Smith D N, Ruether J A. Chem Eng Sc, 1985, 40(5): 741 [9] Zhao Y L, Zhang B J. Huaxue Gongcheng (Chemical Engineering), 1984, 12(2): 45 [10] Deckwer W D, Louisi Y, Zaidi A, Ralek M. Ind Eng Chem Process Des Dev, 1980, 19(4): 699 [11] Song H J, Zhang H T, Ying W Y. Gaoxiao Huaxue Gongcheng Xuebao (J Chem Eng Chin Univ), 2005, 19(2): 253 [12] Song H J, Zhang H T, Ying W Y. Huadong Ligong Daxue Xuebao (J East China Univ Sci Technol), 2004, 30(5): 498 [13] Song H J. [PhD Dissertation]. Shanghai: East China University of Science and Technology, 2005 [14] Wang C W, Zhu B C, Ding B Q, Fang D Y. Huagong Xuebao (J Chem Ind Eng), 2001, 52(1): 1006 [15] Wang C W, Ding B Q, Zhu, B C, Fang D Y. Huagong Xuebao (J Chem Ind Eng), 2001, 52(12): 1090 [16] Fang D Y, Yao P F, Zhu B C. The technology and development of methanol. Shanghai: Huadong Ligong Daxue press, 1990. 210
Article
Mathematical Simulation and Design of Three-Phase Bubble Column Reactor for Direct Synthesis of Dimethyl Ether from Syngas Dianhua Liu,
Xing Hua,
Dingye Fang*
College of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China [ Manuscript received October 10, 2006; revised December 15, 2006 ]
Abstract: A three-phase reactor mathematical model was set up to simulate and design a three-phase bubble column reactor for direct synthesis of dimethyl ether (DME) from syngas, considering both the influence of part inert carrier backmixing on transfer and the influence of catalyst grain sedimentation on reaction. On the basis of this model, the influences of the size and reaction conditions of a 100000 t/a DME reactor on capacity were investigated. The optimized size of the 10000 t/a DME synthesis reactor was proposed as follows: diameter 3.2 m, height 20 m, built-in 400 tube heat exchanger (φ 38×2 mm), and inert heat carrier paraffin oil 68 t and catalyst 34.46 t. Reaction temperature and pressure were important factors influencing the reaction conversion for different size reactors. Under the condition of uniform catalyst concentration distribution, higher pressure and temperature were proposed to achieve a higher production capacity of DME. The best ratio of fresh syngas for DME synthesis was 2.04. Key words: dimethyl ether; syngas; three-phase reactor; DME synthesis; slurry bed; mathematical simulation model
1. Introduction Dimthyl ether (DME) is regarded as a multisource, multi-purpose clean fuel and a chemical feedstock of the twenty-first century [1]. It can be used as a cleaning fuel for diesel engines, gas turbines in power generation, fuel cells, and liquefied petroleum gas (LPG) alternative for heating and cooking, and a chemical feedstock for higher ethers and oxygenates [2]. DME can be manufactured in large quantities from natural gas, coal, biomass, and municipal solid waste. The single-stage, liquid phase DME synthesis process, incorporates the sequential reaction of methanol synthesis and methanol dehydration in a slurry phase reactor system. The reaction network involved in single-stage synthesis dimethyl ether from ∗
syngas can be shown as follows [3]: CO + 2H2 ⇋ CH3 OH 0 ∆H298K = −90.56 kJ/mol
(1)
CO2 + 3H2 ⇋ CH3 OH + H2 O 0 ∆H298K = −49.43 kJ/mol
(2)
2CH3 OH ⇋ CH3 OCH3 + H2 O 0 ∆H298K = −23.56 kJ/mol
(3)
Dimethyl ether synthesis from syngas is highly exothermic. The catalyst, whose highest reaction temperature is around 270 ℃ for methanol synthesis, will be deactivated over 270 ℃. Therefore, the problem of gas-solid single-stage synthesis for dimethyl ether is how to transfer the exothermic heat and keep the catalyst bed under the overtemperature limit. In
Corresponding author. Tel: (021)64251002; E-mail: [email protected] This work was supported by the National Basic Research Program of China (2005CB221205)
194
Dianhua Liu et al./ Journal of Natural Gas Chemistry Vol. 16 No. 2 2007
under the support of the Japanese government and a 100 t/d pilot plant was built in Hokkaido Japan [7]. But no industrial DME direct synthesis reactor is running up to now. Literature on the simulation and design of the industrial DME synthesis reactor is very scarce. In this article, a mathematical model is proposed, for direct synthesis of dimethyl ether with syngas in a three-phase slurry reactor with a capacity of 100, 000t/a, aiming to provide data for industrial reactor design, to directly synthesize DME from syngas.
a three-phase bed, the inert carrier of the liquid phase with high thermal conductivity and heat capacity, brings about a gas-liquid-solid three phases in high turbulence, which can rapidly disperse the reaction heat and transfer it to the cool medium, thus making the bed close to an isothermal condition and solving the problem of overheating. In addition to the superior heat management allowed by the liquid phase operation, the synergistic effect of these reactions yields more DME than the two-stage sequential processing [4]. The advantages of the three phase reactor are [5]: (1) high efficiency, using a fine particle catalyst to promote the utilization ratio of the catalyst’s inner surface area and get high conversion; (2) multi-source of the raw material, the content of CO can vary in a wide range because of the high heat capacity inert carrier in the reactor; (3) flexibility in operation, gas velocity can be varied in a wide range. Air Products and Chemicals Inc.(APCI) developed a process technology for converting coal-derived syngas to liquid fuel using DOE’s Alternative Fuels Development Unit (AFDU), located at LaPorte, Texas. A single-stage slurry phase process for coproduction of dimethyl ether and methanol was demonstrated at the AFDU in 1991. Substantial increase in the syngas conversion perpass was demonstrated by mixing a fine particle dehydration catalyst with a methanol synthesis catalyst [6]. A pilot scale plant (5t/d) ran successfully in 1999,
rCO
A2 = A1 exp − RT
rCO2
A6 = A5 exp − RT
rD = A9 exp −
2. Mathematical model The three-phase reactor model, considering both the influence of part inert carrier backmixing on transfer and the influence of catalyst grain sedimentation on reaction, was set up to simulate and design a three-phase bubble column reactor. The effect of the catalyst concentration distribution along the bed height on reaction was calculated. The effect of the backmixing of liquid phase heat carrier on the reaction was investigated. The mathematical model for the reactor was envisaged as: (1) gas phase being plug flow, (2) gas phase volume being reduced during the reaction process, (3) mass transfer resistance was ignored in the liquid-solid phase with a result that mass transfer coefficient and mass transfer area in the liquid-solid phase were much greater than those in the gas-liquid phase. The following patterns were chosen as the intrinsic kinetics model for the reaction:
A3 A4 fCO fH2
A7 fCO f A8 2 H2
A10 RT
The parameters in this model are: A1 =0.01733, A2 =2.130×104 J/mol, A3 =0.4079, A4 =0.3372, A5 =0.4029, A6 =4.321×104 J/mol, A7 =0.006034, A8 =3.161, A9 =0.09163, A10 =3.128×104 J/mol, A11 =0.3099 The model of catalyst concentration distribution along the bed height is shown below as: [8] Z Z 0 Ccat = Ccat exp(A) exp L L Z = i · ; i = 1, 2, · · · N N
A11 fM
fM 1− Kf1 fCO fH2 2
!
fM fW 1− Kf2 fCO2 fH3 2
1−
fW fD 2 Kf3 fM
(4)
! (5)
(6)
where L A = −ψl Up ; ψl = Ds
0.026
Up = 1.10U g
Ccat 1− ; ρp
3.5
0 Ut0.80 ψ l ; Ccat =
(7) Ut =
gc Dp2 (ρp − ρl ) ; 18µl
Ccat A ; exp(A) − 1.0
195
Journal of Natural Gas Chemistry Vol. 16 No. 2 2007
Ug DR
Ds = 9.6
F r6 Reg
0.1114
Ug ; Fr = ; 0.5 (g D c R) 1.1
+ 0.019Rep
Ut dp ρl U g D R ρl ; Rep = Reg = µl µl The mathematical model of dimethyl ether synthesis in the three-phase slurry bed is set up as follows, taking into consideration the influence of both liquid phase backmixing and grain sedimentation: dCg,j Cg,j −ug = kl,j al − Cl,j dZ Hj (8) j = H2 , CO, CO2 , CH3 OH, H2 O Cg,j d2 Cl,j Z = Ccat rj Cl,j − kl,j al − Cl,j Dl εl dZ 2 Hj j = H2 , CO2 , CO (9)
2 66 66 66 64
−2 1
d2 Cl,j Z Dl εl = −Ccat rj Cl,j − kl,j al dZ 2 j = CH3 OH, H2 O
1 −2 ·
1 · ·
32 77 66 77 66 77 66 75 66 4
Cg,j − Cl,j Hj
(10) Equation set (9) and (10) is a group of the second order differential equations and its boundary conditions are [9,10]: dCl,j =0 dZ Z=L (11)
0 0 Cg,j |Z=0 = Cg,j ; Cl,j |Z=0 = Cl,j ;
where
1.4 Dl = 2.7Ug0.30 DR
The determination of parameter kl,j , al , Hj can be found in references [11−13]. The model Equations (9) and (10) and boundary condition (11) are deduced by discretion to a group of algebraic equations, with a tridiagonal coefficient matrix.
3 2 77 66 77 66 77 = 66 77 66 5 64
0 h2 G1j − Cl,j 2 2 h Gj · · · · · 2 (N−2) h Gj (N−2) Cl,j 1 −2 1 (N−1) (N−2) 4Cl,j − Cl,j (N−1) (N−1) 1 −2 Cl,j h2 Gj − 3 j = H2 , CO, CO2 , H2 O, CH3 OH, CH3 OCH3 0 Cl,j 1 Cl,j · ·
3 77 77 77 77 75
(12)
where i i Ccat Rj Cl,j
Gij
=h
=h
− kl,j al
2
i Cg,j i − Cl,j Hj
Dl εl
i The liquid phase concentration distribution, Cl,j (i=1,2· · · N), on every dispersing reaction crosssection is solved by iterating chasing method. Next,
i−1 (Cl,j
−
i 2Cl,j
!
Dl εl
i i −Ccat Rj Cl,j
Gij
− kl,j al
2
i Cg,j i − Cl,j Hj
+
i+1 k+1 Cl,j )
!
(13) ; j = H2 , CO, CO2
(14) ; j = H2 O, CH3 OH, CH3 OCH3
i the gas phase concentration distribution, Cg,j (i=1, 2· · · N), is solved by Equation (8). The iteration keeps running according to the iterate form
i i ±Ccat Rj Cl,j − kl,j al = Dl εl
k = 0, 1, 2, · · · N ;
i Cg,j i − Cl,j Hj
! k
(positive j=H2 , CO, CO2 , whereas, negative j=H2 O, CH3 OH, CH3 OCH3 ) till satisfying
(15)
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3 X N i k+1 i k X − (Cl,j ) (Cl,j ) 6 ε = 10−4 i )k (Cl,j
(16)
j=1 i=1
3. Simulation and design for the dimethyl ether reactor
The mathematical model of the bubble column slurry reactor has been proved to be reasonable through the pilot test of methanol synthesis [14,15]. Using the above analog calculation of this three-phase slurry dimethyl ether reactor mathematical model, and taking into consideration the influence of grain sedimentation, as well as part of the liquid-phase backmixing, the size and reaction conditions of 100, 000t/a DME reactor are discussed in detail. 3.1. Size of dimethyl ether reactor 3.1.1. The ef fect of superf icial gas velocity on catalyst concentration Figure 1 shows the effect of superficial gas velocity on the catalyst concentration distribution along the bed height.
be improved and the conversion of CO decreases with an increasing superficial gas velocity, but the catalyst concentration distribution along the bed height is not uniform. The results indicate that a small diameter reactor is not suitable as an industrial three-phase bubble column reactor. Table 1. Ef fect of superf icial gas velocity on the conversion of CO Gas flow to
Superficial gas
Conversion
reactor (Nm3 /h)
velocity (m/s)
of CO(%)
1
67000
0.1928
0.7023
2
73000
0.2101
0.6574
3
77000
0.2216
0.6301
No.
3.1.2. The ef fect of reactor diameter on catalyst concentration distribution along the bed height Figure 2 shows the effect of catalyst concentration distribution along bed height with different reactor diameters at a superficial gas velocity of 0.1153 m/s. The results demonstrate that the catalyst concentration distribution along the bed height becomes well-distributed when the reactor diameter increases. The catalyst concentration distribution along the bed height is uniform when the reactor diameter is 3.2 m. The difference of catalyst concentration distribution is less than 9% from the top to the bottom of the catalyst bed.
Figure 1. Ef fect of superf icial gas velocity on catalyst concentration distribution along bed height
The structure of the reactor is: diameter 2.0 m, height 55 m, built-in 300 tube heat exchanger (φ 38×2 mm), inert heat carrier paraffin oil 68 t and catalyst 34.46 t. Gas composition: yCO =0.2816, yCO2 =0.0335, yH2 =0.6787, yN2 =0.0049, yCH4 =0.0013, and superficial gas velocity from 0.1928 to 0.2216 m/s. The reaction is carried out under the condition of 240 ℃ and 5 MPa. Figure 1 and Table 1 clearly demonstrate that the grain sedimentation can
Figure 2. Ef fect of reactor diameter on catalyst concentration distribution along bed height
Journal of Natural Gas Chemistry Vol. 16 No. 2 2007
3.1.3. Brief summary From the above discussion, it may be concluded that slightly increased superficial gas velocity can improve the effect of the catalyst concentration distribution along the bed height. A small diameter reactor is not suitable as an industrial three-phase reactor. Therefore, the 10, 000t/a DME reactor is suggested to be with: diameter 3.2 m, height 20 m, built-in 400 tube heat exchanger φ 38×2 mm, inert heat carrier paraffin oil 68 t, and catalyst 34.46 t. 3.2. Ef fect of reaction conditions and feed gas composition 3.2.1. Ef fects of reaction conditions on conversion of CO and production capacity of DME Using the reactor mentioned above, the effects of reaction temperature and pressure on the conversion of CO, and production capacity of DME were investigated. Gas compositions were yCO =0.2816, yCO2 =0.0335, yH2 =0.6787, yN2 =0.0049, yCH4 = 0.0013. Gas flow to reactor was 75000 Nm3 /h. Figur-
Figure 3. Ef fect of reaction temperature on conversion of CO and production capacity of DME
Figure 4. Ef fect of reaction pressure on conversion of CO and production capacity of DME
197
es 3 and 4 clearly show that both the conversion of CO and production capacity of DME increase when reaction temperature and pressure become higher. The synergistic effect of the reaction of methanol synthesis and methanol dehydration yields more products. 3.2.2. Ef fects of reaction conditions on catalyst concentration distribution along bed height Figure 5 shows that the catalyst concentration distribution along the bed height becomes welldistributed when the reaction pressure decreases. The reason is that the superficial gas velocity increases with a decrease in reaction pressure, with the same gas flow to reactor. To decrease the reaction temperature, the superficial gas velocity accordingly decreases. But this results in good distribution of the catalyst concentration along the bed height (Figure 6). It means that the slurry phase operational height influences the catalyst concentration distribution along the bed height. The reaction temperature and the slurry phase operational height have different effects on the
Figure 5. Ef fect of reaction pressure on catalyst concentration distribution along the bed height
Figure 6. Ef fect of reaction temperature on catalyst concentration distribution along the bed height
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catalyst concentration distribution along the bed height. The latter has a stronger effect than the former. 3.2.3. Ef fect of dif ferent feed gas composition on the reaction For the same reactor with a feed gas flow of 75000 Nm3 /h, reaction pressure of 6.0 MPa, and reaction
temperature of 260 ℃, three groups of gases were investigated (Table 2). It can be seen in Figure 7 that conversion of DME increases when the molar ratio of (H2 -CO2 )/(CO+CO2 ) increases. The best ratio range of fresh syngas of methanol synthesis is from 2.00 to 2.15 [16]. Therefore, the synergistic effect of methanol synthesis reaction and methanol dehydration yields a higher conversion of DME.
Table 2. Feed gas composition No.
H2
CO
CO2
CH4
N2
Molar ratio of (H2 -CO2 ) to (CO+CO2 )
1
0.5856
0.2712
0.0231
0.0531
0.0670
1.91
2
0.5470
0.3890
0.0070
0.0000
0.0560
1.36
3
0.6787
0.2816
0.0335
0.0013
0.0049
2.04
Figure 7. Ef fect of dif ferent feed gas composition on reaction
4. Conclusions The mathematical model is set up for direct synthesis of dimethyl ether from syngas in a three-phase slurry reactor and can be used for the design of an industrial DME synthesis reactor. The results of this simulation show that a small diameter reactor is not suitable for an industrial reactor. The best size for a reactor is not the biggest, but it should be designed by considering the fixed investment and transportation condition. The proposed 10, 000 t/a reactor of DME synthesis is with: diameter 3.2 m, height 20 m, built-in 400 tube heat exchanger (φ 38×2 mm), inert heat carrier paraffin oil 68 t, and catalyst 34.46 t. Reaction temperature and pressure are important factors, which influence the reaction conversion for different size reactors. The conversion of CO and production capacity of DME increase with the pressure increasing, because the moles in the products are less than the moles in the reactants, in the reaction sys-
tem. The reason is that the superficial gas velocity increases with the reaction pressure decreasing, with the same gas flow to the reactor. The conversion of CO and production capacity of DME increases with temperature increase, because the reaction is controlled by the reaction dynamics. But the catalyst concentration distribution along the bed height has a reverse trend. The operational height of the slurry phase influences the trend. The choice of pressure and temperature should take into consideration both the conversion of CO and the catalyst concentration distribution. Under the condition of uniform catalyst concentration distribution, higher pressure and temperature are proposed, to achieve a higher production capacity of DME. The best ratio of fresh syngas of methanol synthesis is 2.04, under the reaction conditions considered in this article. The synergistic effect of methanol synthesis reaction and methanol dehydration yields high conversion of DME. Acknowledgements The authors are very grateful to Prof. Cao Fahai and Prof. Guo Xuhong for their help. Nomenclature rCO , rCO2 , rD intrinsic kinetics rate of carbon monoxide, carbon dioxide, dimehtyl ether, mol/(h·g(cat) ) 0 Ccat catalyst concentration at the gas inlet, kg·m−3 ψl content of liquid in liquid-solid slurry phase L operational slurry height, m w mass of catalyst, kg T temperature, K Rg gas constant, J/(mol·K)
Journal of Natural Gas Chemistry Vol. 16 No. 2 2007
UP Ds Ccat ρp ρl µg µt Z Ccat dp µl gc DR A Fr Reg Rep Cg,j Cl,j H Dl al kl h Ccat
hindered sedimentation velocity of particles, m·s−1 axial dispersion coefficient of particle, m2 ·s−1 average catalyst concentration, kg·m−3 density of catalyst, kg·m−3 density of liquid, kg·m−3 superficial gas velocity, m·s−1 sedimentation velocity of terminal particle, m·s−1 catalyst concentration distribution along the bed height, kg·m−3 particle diameter, m viscosity of liquid, kg/(m·s) acceleration of gravity, 9.81 m·s−2 inner diameter of reactor, m Brodenstein’s number Froude’s number Reynold’s number Reynold’s number of particle jth gas concentration, kmol·m−3 ith liquid concentraion, kmol·m−3 solubility, kg(g)/kg(l) axial dispersion coefficient of liquid, m2 ·s gas-liquid specific surface area, m2 /m3 gas-liquid transfer coefficient at liquid side, m·s−1 L difference discrete step length, m N catalyst concentration in slurry phase, kg·m−3
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