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CFD modeling of a modular reactor for the Fischer–Tropsch synthesis: Effectiveness of a micro-scale cross-current cooling channel
Fuel 158 (2015) 826–834
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CFD modeling of a modular reactor for the Fischer–Tropsch synthesis: Effectiveness of a micro-scale cross-current cooling channel Dong-Yoon Shin a,1, Kyoung-Su Ha b,1, Myung-June Park a,c,⇑, Geunjae Kwak d, Yun-Jo Lee d, Ki-Won Jun d,⇑ a
Department of Energy Systems Research, Ajou University, Suwon 443-749, Republic of Korea Department of Chemical and Biomolecular Engineering, Sogang University, Seoul 121-742, Republic of Korea c Department of Chemical Engineering, Ajou University, Suwon 443-749, Republic of Korea d Research Center for Green Catalysis, Korea Research Institute of Chemical Technology (KRICT), Daejeon 305-600, Republic of Korea b
h i g h l i g h t s Co-based Fischer–Tropsch synthesis (FTS) was conducted in a modular reactor. A micro-scale cross-current cooling channel was utilized. Computational fluid dynamics (CFD) modeling was applied. The effect of different numbers of layers in the distributor was evaluated. CFD modeling showed the temperature of the bed was maintained below the allowable limit.
a r t i c l e
i n f o
Article history: Received 18 March 2015 Received in revised form 29 April 2015 Accepted 10 June 2015 Available online 19 June 2015 Keywords: Fischer–Tropsch synthesis Micro-scale cooling channel Cross-current flow Computational fluid dynamics model Distributor design
a b s t r a c t The merits of increasing the width of the catalytic bed in the channel-type Fischer–Tropsch synthesis reactor module were considered in the present study. Computational fluid dynamics (CFD) modeling was applied to evaluate the effect of different numbers of layers in the gas distributor on the distribution of inlet flows; the use of more than four layers could guarantee that the fraction of dead volume was less than 3%. To obviate the use of the distributor in the cooling channel and successfully dissipate the heat released in the highly exothermic Fischer–Tropsch synthesis, a cross-current flow pattern was considered. In addition, the CFD model including the kinetic reaction rate was validated by comparison of the experimental and simulated results. The cooling performance of the cross-current channel was found to be as good as that of the counter-current case. Further analysis also showed that even when the height of the catalytic bed was increased, the temperature of the bed was maintained below the allowable limit. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction With the increasing instability in the price of crude oil and the depletion of natural crude oil resources, the production of synthetic fuels by the gas-to-liquid (GTL) process has continued to receive more attention [1]. The key concept of the GTL process is chemical conversion of natural gas to synthesis gas (syngas; mixture of CO and H2), followed by conversion of syngas to longer chain hydrocarbons, which are typically in the range of hydrocarbons used in liquid transportation fuels, via Fischer–Tropsch
⇑ Corresponding authors at: Department of Chemical Engineering, Ajou University, Suwon 443-749, Republic of Korea. Tel.: +82 31 219 2383; fax: +82 31 219 2395 (M.-J. Park). Tel.: +82 42 860 7671; fax: +82 42 860 7388 (K.-W. Jun). E-mail addresses: [email protected] (M.-J. Park), [email protected] (K.-W. Jun). 1 These authors equally contributed to this work. http://dx.doi.org/10.1016/j.fuel.2015.06.040 0016-2361/Ó 2015 Elsevier Ltd. All rights reserved.
synthesis (FTS) [2]. Fuels produced from the FTS have high quality due to the absence of aromatics, sulfur, and nitrogen compounds [3,4]. However, the octane number of FT gasoline, which mainly consists of n-paraffin, is lower than that of the gasoline obtained from crude oil processing [5]. Cobalt and iron based catalysts have been widely employed for industrial FT synthesis. Although iron is cheap and iron based catalysts are operative over a wide range of temperatures and H2/CO ratios without a significant rise in CH4 selectivity [6], Co-based catalysts are generally more active and more selective to linear long chain hydrocarbons with very low water gas shift activity [7,8]. FTS catalysts have been applied to conventional reactors such as the multi-tubular fixed bed reactor (TFBR), slurry bubble column reactor (SBCR), and fluidized bed reactor (FBR) [9–11]. Furthermore, micro-channel technology has been recently used to minimize heat transfer resistance [1,12–15], ensuring compactness,
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Nomenclature CP Dm i Dik DTi F h ji KCO KH2 k Mi Mn Nexp p PCO PH2
heat capacity at constant pressure (J/(kg K)) mixture-averaged diffusion coefficient multicomponent Maxwell-Stefan diffusivities (m2/s) thermal diffusion coefficients (kg/(m s)) volume force vector (N/m3) heat transfer coefficient (W/(m2 K)) mass flux relative to the mass average velocity (kg/(m2 s)) adsorption equilibrium parameter for CO (MPa1) adsorption equilibrium parameter for H2 (MPa1) reaction kinetic parameter (mol/(kgcat s MPa2)) molar mass of species i (kg/mol) mean molar mass (kg/mol) total number of experiments pressure (Pa) partial pressure of CO (MPa) partial pressure of H2 (MPa)
Q Qbr Ri –RCO T u u wi xi
heat source (W/m3) mass source term in (kg/(m3 s)) reaction rate (kg/(m3 s)) CO consumption rate (mol/(kgcat s)) temperature (K) linear velocity vector (m/s) linear velocity (m/s) mass fraction of species i molar fraction of species i
Greek letters eP porosity j thermal conductivity (W/(m K)) jbr permeability of the porous medium (m2) l dynamic viscosity (kg/(m s)) q density (kg/m3) s viscous stress tensor (Pa)
high productivity, and thermally stable operation of the synthesis reactor. A number of modeling studies of FTS reactors have been reported, including conventional reactors [11,16–21], a milli-structured reactor [15], a micro-structured reactor [22], and a fixed-bed reactor combined with a membrane assisted fluidized-bed reactor [5]. In addition, due to the recent remarkable advances in computational speed, computational fluid dynamics (CFD) can be used for visualizing local variations in the fluid,
thermal, and mass transport properties of the reactor [23,24]; thus, CFD simulation in combination with a selected number of experiments can be used in the design of unique micro-structured systems of complicated geometry, for which there are only a few reported evaluations [25,26]. In order to increase the capacity of a reactor module while guaranteeing efficiency and compactness, the catalytic channel length can be increased or the channels can be stacked either vertically or horizontally. In our previous work [13], a channel-type reactor
PR
(a)
PR: Pressure Regulator BPR: Back Pressure Regulator
oven reactor
PR BPR
H2 CO CO2 Ar
H2 He
GC 1 GC 2
Feed
(b)
(c)
Catalyc bed
Coolant flow channel
Coolant
Product
Catalyst loading/unloading passage
Fig. 1. (a) Experimental setup, (b) catalytic bed and distributor, and (c) coolant channel.
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Table 1 Experimental conditions, catalyst information, and reactor specification. Case
Temperature (K)a
SV (N m3/(kgcat h))
Pressure (MPa)
H2/CO ratio
1 2 3 4 5 6 7 8
493 503 513 523 493 503 513 523
10
2
2
Catalyst
Type
Density (kg/m3)
Pore volume (m3/kg)
Porosity
Co/Al2O3
547
4.25 104
0.2325
Coolant
Length (m)
Diameter (m)
No. of channels
Silicon Oil (Dow corning 550 Fluid)
5.8 102
1 103
6
Coolant channel
a
Conditions
20
The feed temperatures of the reactant channel and coolant channel were the same.
for the Co-based Fischer–Tropsch synthesis reaction was considered and CFD modeling validated by experimental data was used to evaluate the cooling performance of the counter-current coolant channel; this system was designed to achieve increased catalytic channel length as well as an increased number of catalytic channels by vertical stack-up, for the purpose of determining the optimal capacity of a unit module comprising several catalytic and coolant channels. In the case where the number of catalytic channels is increased, coolant channels are located between the catalytic channel layers to ensure that the cooling performance per unit channel is maintained, and it was shown that temperature was satisfactorily controlled in the case of up to five layers [27]. However, in addition to increasing the channel numbers in the vertical direction, a horizontal increase of the catalytic channel, that is, increasing the width, also should be considered to achieve appropriate dimensions of the module. It should be noted that because the counter-current flow may require the use of distributors for the catalytic and coolant channels, in this study, a catalytic bed with large width is considered, with a cross-current flow applied (cf. Fig. 1; distributor for only catalytic bed with cross-current
flow). On the basis of the suggested structure of the module, CFD modeling is utilized to evaluate the adequacy of the design of the gas distributor for the catalytic bed and the flow scheme for scale-up of the module.
2. Experimental The FTS catalyst with 23 wt% cobalt and 0.05 wt% platinum on a Si-coated Al2O3 support (surface area 170 m2/g, PuraloxÒ) was prepared by the impregnation method using cobalt nitrate and platinum nitrate as precursors. Details of the catalyst preparation method are available in our previous work [13]. Fig. 1a shows the scheme of experimental apparatus in the present study. The finished granular catalysts were tested in a channel-type reactor (1.59 105 m3/d with 1 g catalyst). The volume of the catalyst bed of the reactor was 1 106 m3 (cf. Fig. 1b); the catalyst bed was sandwiched with two plate-type microchannel heat exchangers to achieve cross-current flow, as shown in Fig. 1c. The reactor was placed inside an oven with no forced convection and the oven
Table 2 Detailed stationary equations for each module. Module name
Balance equations
Remarks
Transport of Concentrated Species
rji + r(qxiu) = Ri
Mass balance for the reactant flow channel
where m rM n T ji ¼ qDm i rxi þ qxi Di M n þ Di Dm i ¼ ð1 xi Þ
Heat Transfer in Fluids Heat Transfer in Solids Laminar Flow Free and Porous Media Flow
P
Solid boundary condition
1
; Mn ¼
T
P
xi 1
i Mi
(mixture-averaged diffusion model) qC P u rT ¼ r ðjrTÞ þ Q
Energy balance for the reactant flow channel and the coolant channel Energy balance for the channel bodies, made of stainless steel (SUS304) Momentum balance for the coolant channel
0 ¼ r ðjrTÞ þ Q (with heat transfer by radiation negligible) r ðquÞ ¼ 0 qðu rÞu ¼ r ½pI þ s þ F l l 2l q T u eP ððu rÞ eP Þ ¼ F jbr þ Q br u þ r ½PI þ eP ðru þ ðruÞ Þ 3eP ðr uÞI
Momentum balance for the reactant flow channel
(Brinkman equation for porous media region, while ‘‘Laminar Flow’’ equation is used for free media region)
Inlet boundary conditions for catalytic bed
Outlet boundary conditions
xk k–i Dik
rT
SV = 10 N m3/(kgcat h) T (K) 493 u (m/s) 4.02E3 P = 2 MPa m n qDi rw ¼ 0 n ðjrTÞ ¼ 0 n ðjrTÞ ¼ 0
503 4.10E3
SV = 20 N m3/(kgcat h) 513 4.18E3
523 4.26E3
493 8.04E3
503 513 8.20E3 8.37E3 Constant pressure For mass For heat transfer
523 8.53E3
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D.-Y. Shin et al. / Fuel 158 (2015) 826–834 Table 3 Values of parameters for balance equations. Symbol
Unit
493
503
513
523
q l eP jbr j
kg/m3 Pa s – m2 W/(m K) J/(kg K)
5.964 1.90E05 0.25 3.00E11 0.1262 2346
5.845 1.93E05
5.732 1.97E05
5.603 2.00E05
0.1280 2349
0.1298 2351
0.1320 2362
m2/s
9.61E06 1.11E05 3.43E06 9.91E05 3.18E06 8.29E07 2.42E06 1.06E06 3.10E06 7.39E07
9.95E05 1.15E05 3.55E06 1.03E05 3.29E06 8.59E07 2.51E06 1.10E06 3.21E06 7.65E07
1.03E05 1.19E05 3.67E06 1.06E05 3.41E06 8.89E07 2.60E06 1.14E06 3.32E06 7.92E07
1.07E05 1.23E05 3.80E06 1.10E05 3.53E06 9.19E07 2.69E06 1.18E06 3.44E06 8.19E07
CP Dik
CO, H2 H2O, H2 C8H18, H2 Ar, H2 H2O, CO C8H18, CO Ar, CO C8H18, H2O Ar, H2O Ar, C8H18
Temperature (K)
temperature was set to 343 K. Prior to the FTS activity test, the catalyst was activated at 673 K for 12 h under 5% H2/He flow. The activity test was conducted for ca. 75 h under the reaction conditions presented in Table 1. The coolant flow rate was set to 0.36 m3/h. The detailed syngas composition was H2/CO/CO2/Ar = 57.3:28.4:9.3:5.0 (mol%). Ar was used as an internal standard for GC analysis. Effluent gas from the channel-type reactor was analyzed by using an online gas chromatograph (Young Lin Acme 6000 GC) employing a GS-GasPRO capillary column connected to a flame ionization detector (FID) for the analysis of hydrocarbons, and a Porapak Q/molecular sieve packed column connected to a thermal conductivity detector (TCD) for analysis of carbon oxides and the internal standard gas Ar.
3. Mathematical modeling Computational fluid dynamics (CFD) modeling was conducted using the commercial software COMSOL Multiphysics 4.0a (COMSOL, Inc.), which has built-in modules in the simulation package for the mass, energy, and momentum balances of each flow channel. The reactor diagram was directly generated within COMSOL Multiphysics and then, built-in modules in the simulation package were applied to consider the mass, energy, and momentum balances, respectively, of the reactant flow channel (cf. Table 2). Inlet and outlet boundary conditions are also presented in Table 2, while the specified values are presented in Table 3. The diffusion coefficients in the mass balance equation were calculated using the binary
Fig. 2. Velocity profiles in the distributor and catalytic bed for (a) one, (b) two, (c) three, and (d) four distributor layers.
D.-Y. Shin et al. / Fuel 158 (2015) 826–834
0.15
2.0
0.10
1.6
0.05
1.2
0.00
0.8
0
1
2
3
4
5
" # 59:3 103 1 1 k ¼ 2:89 10 exp T 503:15 R " # 26:9 103 1 1 3 K H2 ¼ 1:56 10 exp T 503:15 R " # 24:2 103 1 1 1 K CO ¼ 3:53 10 exp T 503:15 R 3
Distributor volume ratio
Fraction of the dead volume in the catalytic bed
830
Fig. 3. Effects of the number of distributor layers on the dead volume fraction in the catalytic bed and the distributor volume ratio (Vdistributor/Vdistributor,1layer). Solid lines are regression curves (y = 3.76 103x2 5.44 102x + 0.17 and y = 5.07 102 x2 0.53x + 0.52 for the dead volume fraction and the distributor volume ratio, respectively. The value of r2 is 0.999 for both results).
diffusion coefficient of species i and j [28], while the weight-averaged thermal conductivity was used for the gas mixture [29,30]. Other properties such as density, viscosity, conductivity, and heat capacity were determined from a process simulator, UniSim Design Suite (Honeywell Inc.), while the conductivity of the reactor body (SUS 304) was specified using the default value provided in COMSOL Multiphysics. In the mass balance module, the following reaction kinetics was considered for the CO consumption rate:
kP H2 PCO 1 þ K H2 P H2 þ K CO PCO
In the case where the width of the catalytic channel is large, a gas distributor should be considered for uniform distribution of syngas at the inlet of the bed. A tree-like structure with multiple layers was considered in the present study, and the CFD was utilized to determine the appropriate number of layers since the use of too many layers would be at the expense of the compactness of the module despite the uniform distribution. Fig. 2 shows the flow patterns for the different numbers of layers using the rectangular curved channel shape for simplicity. When one layer was considered as shown in Fig. 2a, a large dead volume was present
where the kinetic parameters were specified to have the same values in the counter-current case [13], since the same catalysts were used.
Conversion [%]
(a)
70 60
SV = 20 Nm3/(kgcat·h)
SV = 10 Nm3/(kgcat·h)
50 40 30
exp sim
20 10
490
500
510
520
530
490
Coolant inlet temperature [K]
Tcenter [K]
(b)
ð4Þ
4. Results and discussion
ð1Þ
2
ð3Þ
The units of k, KH2, and KCO are mol/(kgcat s MPa2), MPa1, and MPa1, respectively, and the temperature is in kelvin. The gas constant (R) is 8.314 J/(mol K). It is to be noted that the selectivity of the produced hydrocarbons was not taken into account because temperature control is one of the main objectives of the present study; moreover, if the reaction rate is too complicated with detailed hydrodynamics (including diffusive mass and conductive heat transfers as well as momentum balances in COMSOL Multiphysics (COMSOL, Inc.)), a high computational load results. For grid generation, the ‘‘Free tetrahedral grid’’ method in the software was selected, resulting in ca. one million grids for the entire reaction system; Galerkin’s method [31] was applied with the tolerance of the relative errors specified as 1 103.
Number of layers
RCO ¼
ð2Þ
530
500
510
520
530
Coolant inlet temperature [K] SV = 20 Nm3/(kgcat·h)
SV = 10 Nm3/(kgcat·h)
520 510 500
exp sim
490 490
500
510
520
Coolant inlet temperature [K]
530
490
500
510
520
530
Coolant inlet temperature [K]
Fig. 4. Comparison of (a) CO conversion and (b) temperature at the center of the catalytic bed (Tcenter) for experimental data versus simulated results; space velocities were 10 (left) and 20 (right) N m3/(kgcat h), respectively. Means of absolute relative residuals (MARR) for conversion and temperature were 7.24% and 0.82%, respectively, while relative standard deviations of individual errors were 5.80% and 0.36%, respectively.
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D.-Y. Shin et al. / Fuel 158 (2015) 826–834 53.948 70 60 50 40 30 20 10
3.8669
(b)
502.55
502.4 502.2 502.0 501.8 501.6 501.4 501.24
(c)
501.17
501.1
501.0
than the height of the catalytic bed may lead to dead volume in the upper and lower part of the bed. Therefore, the threshold value for the fraction was arbitrarily chosen to be less than 3% and thus, four layers were selected. The validity of the kinetic model was verified by comparing the simulated results based on the reactor dynamics in the present study to experimental data. For both CO conversion and the temperature at the center of the catalytic bed (cf. Fig. 4), the simulation was in good agreement with the experimental data. The mean of the absolute relP ative residuals (MARR), defined as 100 i jðyi;exp yi;calc Þ=yi;exp j =N exp , where Nexp represents the number of experimental data points, and the relative standard deviation of the errors are also provided in the figure caption. Notably, the experimentally determined temperature at the center of the catalytic bed was slightly lower than the coolant inlet temperature despite the highly exothermic reaction. This feature is attributed to the fact that there was some heat loss from the reactor module to ambient air despite the use of insulation material around the reactor body. Since there was no forced convection inside the oven, natural convection was assumed in the simulation, and the corresponding heat transfer coefficient (hamb) was specified to be 0.1 W/(m2 K) [13]. Similar temperatures were obtained for both space velocities. Although a high space velocity (20 N m3/(kgcat h)) led to lower conversion than achieved with low space velocity (10 N m3/(kgcat h)) due to the reduced residence time, the high flow rate made the reaction rates and the heat generation for both cases similar. In other words, the productivity depends on the conversion as well as the feed flow rate; there is a tradeoff and thus, the optimal space velocity must be determined to achieve maximum productivity. The CFD simulation results obtained under a specific set of conditions (Tcoolant,inlet = 503 K, space velocity = 10 N m3/(kgcat h)) are presented in Fig. 5. Due to the uniform velocity distribution at the inlet of the bed, CO conversion increased uniformly along the axis, except at the right-lower side of the bed (cf. Fig. 5a). To facilitate catalyst loading and unloading, there should be open passage
(a) ΔTmax in the catalytic bed [K]
(a)
500.98
because of the momentum in the axial direction, whereas the increase in the number of layers reduced the dead volume. The fraction of dead volume and the increase in the distributor volume are compared to the one layer case (V/Vone-layer) in Fig. 3 as a function of the number of layers. When the number of layers is increased, the dead volume is significantly decreased (almost in a linear manner), and the use of five layers may eliminate most of dead volume. However, in the case of five layers, each channel in the gas inlet tube (directly connected to the catalytic bed) becomes too narrow (<1 mm), and the diameter of gas inlet tube smaller
3.0 2.5
SV 10 Nm3/kg/h SV 20 Nm3/kg/h
2.0 1.5 1.0 0.5 490
500
510
520
530
Coolant inlet temperature [K]
(b)
0.34
ΔTmax in the coolant channel [K]
Fig. 5. Profiles of (a) CO conversion, (b) temperature in the catalytic bed, and (c) temperature in the coolant channel when feed and coolant inlet temperature = 503 K, space velocity = 10 N m3/(kgcat h). Maximum and minimum values are provided at the top and bottom of the color bar, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
3.5
0.30 0.26 0.22 0.18 0.14 490
500
510
520
530
Coolant inlet temperature [K] Fig. 6. Maximum temperature increase (DTmax) in (a) the catalytic bed and (b) the coolant channel.
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D.-Y. Shin et al. / Fuel 158 (2015) 826–834
Table 4 Comparison between different flow patterns. SV (N m3/(kgcat h))
Temperature at the center of the catalytic bed (K)
Conversion (%)
Counter-current [13]
Cross-current
Difference
Counter-current [13]
Cross-current
Difference
10
493.8 504.3 514.7 525.1
492.1 502.5 512.8 523.0
1.70 1.81 1.96 2.11
32.1 42.2 53.0 63.4
33.2 44.0 53.8 61.8
1.10 1.77 0.86 1.59
20
494.0 504.5 515.3 527.0
492.3 502.9 513.6 524.3
1.66 1.66 1.70 2.73
17.5 23.9 31.8 41.9
18.5 27.0 37.2 48.0
1.03 3.07 5.42 6.15
50
(a) Conversion [%]
48 46 44 42 40 38
0
2
4
6
8
10
8
10
Scale factor (Sf)
Tcenter [K]
(b) 515 510
505
500
0
2
4
6
Scale factor (Sf) Fig. 7. (a) CO conversion and (b) temperature at the center of the catalytic bed (Tcenter) when the height of the catalytic bed is increased by the scale factor (h = href Sf). Feed and coolant inlet temperature = 503 K; space velocity = 10 N m3/ (kgcat h).
1
ln (selectivity)
0
C5+
-1
C1
-2 -3
C2–4
-4 1.88
1.91
1.94
1.97
2.00
2.03
2.06
1000/T Fig. 8. Selectivies of hydrocarbon products under conditions 1–4 in Table 1. Solid lines represent the regression results; ln SC1 = (8251/T) + 14.26, ln SC2–4 = (8951/ T) + 14.39 and ln SC5+ = (1820/T) 3.795, and the R2 for C1, C2–4 and C5+ are 0.974, 0.993 and 0.996, respectively.
instead of an exit for the effluent around the bend (cf. Fig. 1a). During the reaction tests, the open passage was fully plugged. Therefore, the velocity was relatively low due to the lack of an exit
for the effluent around the bend, resulting in increased conversion. However, because the flow rate was very low, the heat generation was lower than at other spots, and thus, the temperature was also low (cf. right-lower side in Fig. 5b). In the case of coolant flow, the temperature in the channel close to the inlet of the catalytic bed was slightly lower than the temperature close to the catalytic bed exit owing to low conversion. However, the maximum temperature increase in the coolant channel was less than 0.2 K, indicating that the coolant channel was maintained under almost isothermal conditions. It is worth noting that, as discussed above, due to natural convection between the reactor body and ambient air in the oven chamber, the temperature of the coolant channel decreased slightly in the flow direction despite the exothermic reaction. Fig. 6 shows the maximum temperature increase (DTmax) in the catalytic and coolant channels. As shown in Fig. 6a, the maximum temperature increase was ca. 3 K, demonstrating the effectiveness of cross-flow. In addition, the maximum temperature change within the coolant channel was 0.3 K, and thus, the cooling capacity of the oil coolant was sufficient for removing the generated heat. It is also notable that, as shown in Table 4, the temperature at the center of the catalytic bed was lower by ca. 2 K than the case of counter-current flow under the same operating conditions [13]. This feature is attributed to the fact that the coolant channel close to the inlet of catalytic bed effectively removed most of heat generated in the early part of the catalytic bed, indicating that the module structure based on the cross-current flow may be an effective alternative for scale-up of the reaction module. However, if the width of the catalytic bed is increased more than the present study, small number of coolant channel near the inlet of the catalytic bed may be insufficient for heat removal, resulting in temperature control failure. In addition, increasing the width of the catalytic bed leads to the increase in the size of the gas distributor. Therefore, the width of the catalytic bed should be carefully increased during scale-up. As for the conversion, cross-current flow pattern led to higher conversion than cross-current case, probably due to the open passage as discussed above. The height of the catalytic bed was increased in order to determine the allowable heat generation, i.e. the limit of temperature control capability. This analysis is critical because increasing the catalytic channel volume reduces the number of channel layers which determines the manufacturing cost of a reactor module. The space velocity was fixed at 10 N m3/(kgcat h) by increasing the feed flow rate according to the increase in the bed height. Since increasing the bed height led to an increase of the bed volume per unit coolant channel, the temperature increased with increasing bed height, resulting in an increase in the conversion, as shown in Fig. 7. Although the increased conversion and feed flow rate corresponded to increased productivity, it should be noted that the increased temperature decreases the selectivity for the middle distillate and increase the selectivity for methane, as shown in Fig. 8. In addition, the increased heat generation results in non-isothermal temperature profile in the reactor, and
D.-Y. Shin et al. / Fuel 158 (2015) 826–834
(a)
56.298 70 60 50 40 30 20 10
0.1142
(b)
516.47 516.0 514.0 512.0 510.0 508.0 506.0
833
increased heat generation. Therefore, the temperature of the catalytic bed increased, especially around the center. In addition, the heat generation rate exceeded the heat loss from the reactor body to ambient air by natural convection, and thus, the temperature of the coolant channel close to the catalytic bed exit increased in the flow direction. However, the temperature increase within the coolant channel was below 0.36 K. 5. Conclusions The CFD modeling approach was applied to the Fischer–Tropsch synthesis reactor model with a cross-current cooling channel. By analyzing the velocity profiles for different numbers of layers in the gas distributor, the effects of the distributor structure on the inlet flow distribution of the catalytic bed were successfully evaluated, and the structure selected for the experimental study was shown to be effective. The benefit of CFD modeling was also demonstrated by taking the kinetic reaction rate into consideration in such a way that the simulated results could satisfactorily describe the experimental data. In addition, the developed model could be used to predict the temperature control capability of the cooling system with an increase in the height of the catalytic bed, indicating that the modeling approach utilized in the present study can be used in determining the optimal design for the structure of the modular reactor for highly exothermic Fischer–Tropsch synthesis. Acknowledgements
504.0 502.0 501.39
(c)
501.29
501.2
501.1
501.0
500.93
Fig. 9. Profiles of (a) CO conversion, (b) temperature in the catalytic bed, and (c) temperature in the coolant channel when the height of the catalytic bed was increased by eight times (Sf = 8) that of the reference case. Feed and coolant inlet temperature = 503 K; space velocity = 10 N m3/(kgcat h).
thus, a kinetic model that treats the selectivity of hydrocarbon products in detail should be applied. However, that is beyond the scope of the present study, since the purpose is to investigate the effects of the channel structure and flow pattern on the temperature control. Fig. 9 shows the conversion and temperature profiles when the height of the catalytic bed was increased up to eight times compared to the reference case. The conversion profile shown in Fig. 9a was similar to that of the reference case and the temperature was well maintained due to satisfactory cooling performance, even when the space velocity and the number of cooling channels was not changed. For the same space velocity, the feed flow rate increased as the catalyst loading increased, leading to
This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) under the ‘‘Energy Efficiency & Resources Programs’’ (Project No. 2010201010008A) of the Ministry of Trade, Industry & Energy (MOTIE), Republic of Korea. M.-J. Park and K.-S. Ha also acknowledge support from the Engineering Development Research Center (EDRC) funded by the Ministry of Trade, Industry & Energy (MOTIE). References [1] Gumuslu G, Avci AK. Parametric analysis of Fischer–Tropsch synthesis in a catalytic microchannel reactor. AlChE J 2012;58:227–35. [2] Schulz H. Short history and present trends of Fischer–Tropsch synthesis. Appl Catal A: Gen 1999;186:3–12. [3] Rahimpour MR, Forghani AA, Mostafazadeh AK, Shariati A. A comparison of cocurrent and counter-current modes of operation for a novel hydrogenpermselective membrane dual-type FTS reactor in GTL technology. Fuel Process Technol 2010;91:33–44. [4] Yang JH, Kim HJ, Chun DH, Lee HT, Hong JC, Jung H, et al. Mass transfer limitations on fixed-bed reactor for Fischer–Tropsch synthesis. Fuel Process Technol 2010;91:285–9. [5] Rahimpour MR, Elekaei H. A comparative study of combination of Fischer– Tropsch synthesis reactors with hydrogen-permselective membrane in GTL technology. Fuel Process Technol 2009;90:747–61. [6] Zhang Q, Kang J, Wang Y. Development of novel catalysts for Fischer–Tropsch synthesis: tuning the product selectivity. ChemCatChem 2010;2:1030–58. [7] Yao Y, Liu X, Hildebrandt D, Glasser D. The effect of CO2 on a cobalt-based catalyst for low temperature Fischer–Tropsch synthesis. Chem Eng J 2012;193–194:318–27. [8] Holmen A, Venvik HJ, Myrstad R, Zhu J, Chen D. Monolithic, microchannel and carbon nanofibers/carbon felt reactors for syngas conversion by Fischer– Tropsch synthesis. Catal Today 2013;216:150–7. [9] Dry ME. The Fischer–Tropsch process: 1950–2000. Catal Today 2002;71:227–41. [10] Kwack SH, Bae JW, Park MJ, Kim SM, Ha KS, Jun KW. Reaction modeling on the phosphorous-treated Ru/Co/Zr/SiO2 Fischer–Tropsch catalyst with the estimation of kinetic parameters and hydrocarbon distribution. Fuel 2011;90:1383–94. [11] Park N, Kim J-R, Yoo Y, Lee J, Park M-J. Modeling of a pilot-scale fixed-bed reactor for iron-based Fischer–Tropsch synthesis: two-dimensional approach for optimal tube diameter. Fuel 2014;122:229–35. [12] Myrstad R, Eri S, Pfeifer P, Rytter E, Holmen A. Fischer–Tropsch synthesis in a microstructured reactor. Catal Today 2009;147:S301–4. [13] Shin M-S, Park N, Park M-J, Cheon J-Y, Kang JK, Jun K-W, et al. Modeling a channel-type reactor with a plate heat exchanger for cobalt-based Fischer– Tropsch synthesis. Fuel Process Technol 2014;118:235–43.
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[14] Chin YH, Hu J, Cao C, Gao Y, Wang Y. Preparation of a novel structured catalyst based on aligned carbon nanotube arrays for a microchannel Fischer–Tropsch synthesis reactor. Catal Today 2005;110:47–52. [15] Knochen J, Güttel R, Knobloch C, Turek T. Fischer–Tropsch synthesis in millistructured fixed-bed reactors: experimental study and scale-up considerations. Chem Eng Process 2010;49:958–64. [16] Atwood HE, Bennett CO. Kinetics of the Fischer–Tropsch reaction over iron. Ind Eng Chem Process Des Dev 1979;18:163–70. [17] Jess A, Popp R, Hedden K. Fischer–Tropsch-synthesis with nitrogen-rich syngas: fundamentals and reactor design aspects. Appl Catal A: Gen 1999;186:321–42. [18] Marvast MA, Sohrabi M, Zarrinpashne S, Baghmisheh G. Fischer–Tropsch synthesis: modeling and performance study for Fe-HZSM5 bifunctional catalyst. Chem Eng Technol 2005;28:78–86. [19] Rafiq MH, Jakobsen HA, Schmid R, Hustad JE. Experimental studies and modeling of a fixed bed reactor for Fischer–Tropsch synthesis using biosyngas. Fuel Process Technol 2011;92:893–907. [20] Wang Y-N, Xu Y-Y, Li Y-W, Zhao Y-L, Zhang B-J. Heterogeneous modeling for fixed-bed Fischer–Tropsch synthesis: reactor model and its applications. Chem Eng Sci 2003;58:867–75. [21] Yang J, Liu Y, Chang J, Wang Y-N, Bai L, Xu Y-Y, et al. Detailed kinetics of FischerTropsch synthesis on an industrial FeMn catalyst. Ind Eng Chem Res 2003;42:5066–90. [22] Almeida LC, Sanz O, Merino D, Arzamendi G, Gandía LM, Montes M. Kinetic analysis and microstructured reactors modeling for the Fischer–Tropsch synthesis over a Co–Re/Al2O3 catalyst. Catal Today 2013;215:103–11.
[23] Byron Smith RJ, Muruganandam L, Murthy Shekhar S. CFD analysis of water gas shift membrane reactor. Chem Eng Res Des 2011;89:2448–56. [24] Irani M, Alizadehdakhel A, Pour AN, Proulx P, Tavassoli A. An investigation on the performance of a FTS fixed-bed reactor using CFD methods. Int Commun Heat Mass Transfer 2011;38:1119–24. [25] Arzamendi G, Diéguez PM, Montes M, Odriozola JA, Sousa-Aguiar EF, Gandía LM. Computational fluid dynamics study of heat transfer in a microchannel reactor for low-temperature Fischer–Tropsch synthesis. Chem Eng J 2010;160:915–22. [26] Rebrov EV, Duinkerke SA, de Croon MHJM, Schouten JC. Optimization of heat transfer characteristics, flow distribution, and reaction processing for a microstructured reactor/heat-exchanger for optimal performance in platinum catalyzed ammonia oxidation. Chem Eng J 2003;93:201–16. [27] Shin M-S, Park N, Park M-J, Jun K-W, Ha K-S. Computational fluid dynamics model of a modular multichannel reactor for Fischer–Tropsch synthesis: maximum utilization of catalytic bed by microchannel heat exchangers. Chem Eng J 2013;234:23–32. [28] Fuller EN, Schettler PD, Giddings JC. New method for prediction of binary gasphase diffusion coefficients. Ind Eng Chem 1966;58:18–27. [29] Green DW, Perry RH. Perry’s Chemical Engineers’ Handbook. 8th ed. New York: McGraw-Hill; 2008. [30] Poling BE, Prausnitz JM, O’Connell JP. The Properties of Gases and Liquids. 5th ed. New York: McGraw-Hill; 2001. [31] Brenner SC, Scott LR. The Mathematical Theory of Finite Element Methods. 2nd ed. New York: Springer-Verlag; 2002.
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CFD modeling of a modular reactor for the Fischer–Tropsch synthesis: Effectiveness of a micro-scale cross-current cooling channel Dong-Yoon Shin a,1, Kyoung-Su Ha b,1, Myung-June Park a,c,⇑, Geunjae Kwak d, Yun-Jo Lee d, Ki-Won Jun d,⇑ a
Department of Energy Systems Research, Ajou University, Suwon 443-749, Republic of Korea Department of Chemical and Biomolecular Engineering, Sogang University, Seoul 121-742, Republic of Korea c Department of Chemical Engineering, Ajou University, Suwon 443-749, Republic of Korea d Research Center for Green Catalysis, Korea Research Institute of Chemical Technology (KRICT), Daejeon 305-600, Republic of Korea b
h i g h l i g h t s Co-based Fischer–Tropsch synthesis (FTS) was conducted in a modular reactor. A micro-scale cross-current cooling channel was utilized. Computational fluid dynamics (CFD) modeling was applied. The effect of different numbers of layers in the distributor was evaluated. CFD modeling showed the temperature of the bed was maintained below the allowable limit.
a r t i c l e
i n f o
Article history: Received 18 March 2015 Received in revised form 29 April 2015 Accepted 10 June 2015 Available online 19 June 2015 Keywords: Fischer–Tropsch synthesis Micro-scale cooling channel Cross-current flow Computational fluid dynamics model Distributor design
a b s t r a c t The merits of increasing the width of the catalytic bed in the channel-type Fischer–Tropsch synthesis reactor module were considered in the present study. Computational fluid dynamics (CFD) modeling was applied to evaluate the effect of different numbers of layers in the gas distributor on the distribution of inlet flows; the use of more than four layers could guarantee that the fraction of dead volume was less than 3%. To obviate the use of the distributor in the cooling channel and successfully dissipate the heat released in the highly exothermic Fischer–Tropsch synthesis, a cross-current flow pattern was considered. In addition, the CFD model including the kinetic reaction rate was validated by comparison of the experimental and simulated results. The cooling performance of the cross-current channel was found to be as good as that of the counter-current case. Further analysis also showed that even when the height of the catalytic bed was increased, the temperature of the bed was maintained below the allowable limit. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction With the increasing instability in the price of crude oil and the depletion of natural crude oil resources, the production of synthetic fuels by the gas-to-liquid (GTL) process has continued to receive more attention [1]. The key concept of the GTL process is chemical conversion of natural gas to synthesis gas (syngas; mixture of CO and H2), followed by conversion of syngas to longer chain hydrocarbons, which are typically in the range of hydrocarbons used in liquid transportation fuels, via Fischer–Tropsch
⇑ Corresponding authors at: Department of Chemical Engineering, Ajou University, Suwon 443-749, Republic of Korea. Tel.: +82 31 219 2383; fax: +82 31 219 2395 (M.-J. Park). Tel.: +82 42 860 7671; fax: +82 42 860 7388 (K.-W. Jun). E-mail addresses: [email protected] (M.-J. Park), [email protected] (K.-W. Jun). 1 These authors equally contributed to this work. http://dx.doi.org/10.1016/j.fuel.2015.06.040 0016-2361/Ó 2015 Elsevier Ltd. All rights reserved.
synthesis (FTS) [2]. Fuels produced from the FTS have high quality due to the absence of aromatics, sulfur, and nitrogen compounds [3,4]. However, the octane number of FT gasoline, which mainly consists of n-paraffin, is lower than that of the gasoline obtained from crude oil processing [5]. Cobalt and iron based catalysts have been widely employed for industrial FT synthesis. Although iron is cheap and iron based catalysts are operative over a wide range of temperatures and H2/CO ratios without a significant rise in CH4 selectivity [6], Co-based catalysts are generally more active and more selective to linear long chain hydrocarbons with very low water gas shift activity [7,8]. FTS catalysts have been applied to conventional reactors such as the multi-tubular fixed bed reactor (TFBR), slurry bubble column reactor (SBCR), and fluidized bed reactor (FBR) [9–11]. Furthermore, micro-channel technology has been recently used to minimize heat transfer resistance [1,12–15], ensuring compactness,
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D.-Y. Shin et al. / Fuel 158 (2015) 826–834
Nomenclature CP Dm i Dik DTi F h ji KCO KH2 k Mi Mn Nexp p PCO PH2
heat capacity at constant pressure (J/(kg K)) mixture-averaged diffusion coefficient multicomponent Maxwell-Stefan diffusivities (m2/s) thermal diffusion coefficients (kg/(m s)) volume force vector (N/m3) heat transfer coefficient (W/(m2 K)) mass flux relative to the mass average velocity (kg/(m2 s)) adsorption equilibrium parameter for CO (MPa1) adsorption equilibrium parameter for H2 (MPa1) reaction kinetic parameter (mol/(kgcat s MPa2)) molar mass of species i (kg/mol) mean molar mass (kg/mol) total number of experiments pressure (Pa) partial pressure of CO (MPa) partial pressure of H2 (MPa)
Q Qbr Ri –RCO T u u wi xi
heat source (W/m3) mass source term in (kg/(m3 s)) reaction rate (kg/(m3 s)) CO consumption rate (mol/(kgcat s)) temperature (K) linear velocity vector (m/s) linear velocity (m/s) mass fraction of species i molar fraction of species i
Greek letters eP porosity j thermal conductivity (W/(m K)) jbr permeability of the porous medium (m2) l dynamic viscosity (kg/(m s)) q density (kg/m3) s viscous stress tensor (Pa)
high productivity, and thermally stable operation of the synthesis reactor. A number of modeling studies of FTS reactors have been reported, including conventional reactors [11,16–21], a milli-structured reactor [15], a micro-structured reactor [22], and a fixed-bed reactor combined with a membrane assisted fluidized-bed reactor [5]. In addition, due to the recent remarkable advances in computational speed, computational fluid dynamics (CFD) can be used for visualizing local variations in the fluid,
thermal, and mass transport properties of the reactor [23,24]; thus, CFD simulation in combination with a selected number of experiments can be used in the design of unique micro-structured systems of complicated geometry, for which there are only a few reported evaluations [25,26]. In order to increase the capacity of a reactor module while guaranteeing efficiency and compactness, the catalytic channel length can be increased or the channels can be stacked either vertically or horizontally. In our previous work [13], a channel-type reactor
PR
(a)
PR: Pressure Regulator BPR: Back Pressure Regulator
oven reactor
PR BPR
H2 CO CO2 Ar
H2 He
GC 1 GC 2
Feed
(b)
(c)
Catalyc bed
Coolant flow channel
Coolant
Product
Catalyst loading/unloading passage
Fig. 1. (a) Experimental setup, (b) catalytic bed and distributor, and (c) coolant channel.
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Table 1 Experimental conditions, catalyst information, and reactor specification. Case
Temperature (K)a
SV (N m3/(kgcat h))
Pressure (MPa)
H2/CO ratio
1 2 3 4 5 6 7 8
493 503 513 523 493 503 513 523
10
2
2
Catalyst
Type
Density (kg/m3)
Pore volume (m3/kg)
Porosity
Co/Al2O3
547
4.25 104
0.2325
Coolant
Length (m)
Diameter (m)
No. of channels
Silicon Oil (Dow corning 550 Fluid)
5.8 102
1 103
6
Coolant channel
a
Conditions
20
The feed temperatures of the reactant channel and coolant channel were the same.
for the Co-based Fischer–Tropsch synthesis reaction was considered and CFD modeling validated by experimental data was used to evaluate the cooling performance of the counter-current coolant channel; this system was designed to achieve increased catalytic channel length as well as an increased number of catalytic channels by vertical stack-up, for the purpose of determining the optimal capacity of a unit module comprising several catalytic and coolant channels. In the case where the number of catalytic channels is increased, coolant channels are located between the catalytic channel layers to ensure that the cooling performance per unit channel is maintained, and it was shown that temperature was satisfactorily controlled in the case of up to five layers [27]. However, in addition to increasing the channel numbers in the vertical direction, a horizontal increase of the catalytic channel, that is, increasing the width, also should be considered to achieve appropriate dimensions of the module. It should be noted that because the counter-current flow may require the use of distributors for the catalytic and coolant channels, in this study, a catalytic bed with large width is considered, with a cross-current flow applied (cf. Fig. 1; distributor for only catalytic bed with cross-current
flow). On the basis of the suggested structure of the module, CFD modeling is utilized to evaluate the adequacy of the design of the gas distributor for the catalytic bed and the flow scheme for scale-up of the module.
2. Experimental The FTS catalyst with 23 wt% cobalt and 0.05 wt% platinum on a Si-coated Al2O3 support (surface area 170 m2/g, PuraloxÒ) was prepared by the impregnation method using cobalt nitrate and platinum nitrate as precursors. Details of the catalyst preparation method are available in our previous work [13]. Fig. 1a shows the scheme of experimental apparatus in the present study. The finished granular catalysts were tested in a channel-type reactor (1.59 105 m3/d with 1 g catalyst). The volume of the catalyst bed of the reactor was 1 106 m3 (cf. Fig. 1b); the catalyst bed was sandwiched with two plate-type microchannel heat exchangers to achieve cross-current flow, as shown in Fig. 1c. The reactor was placed inside an oven with no forced convection and the oven
Table 2 Detailed stationary equations for each module. Module name
Balance equations
Remarks
Transport of Concentrated Species
rji + r(qxiu) = Ri
Mass balance for the reactant flow channel
where m rM n T ji ¼ qDm i rxi þ qxi Di M n þ Di Dm i ¼ ð1 xi Þ
Heat Transfer in Fluids Heat Transfer in Solids Laminar Flow Free and Porous Media Flow
P
Solid boundary condition
1
; Mn ¼
T
P
xi 1
i Mi
(mixture-averaged diffusion model) qC P u rT ¼ r ðjrTÞ þ Q
Energy balance for the reactant flow channel and the coolant channel Energy balance for the channel bodies, made of stainless steel (SUS304) Momentum balance for the coolant channel
0 ¼ r ðjrTÞ þ Q (with heat transfer by radiation negligible) r ðquÞ ¼ 0 qðu rÞu ¼ r ½pI þ s þ F l l 2l q T u eP ððu rÞ eP Þ ¼ F jbr þ Q br u þ r ½PI þ eP ðru þ ðruÞ Þ 3eP ðr uÞI
Momentum balance for the reactant flow channel
(Brinkman equation for porous media region, while ‘‘Laminar Flow’’ equation is used for free media region)
Inlet boundary conditions for catalytic bed
Outlet boundary conditions
xk k–i Dik
rT
SV = 10 N m3/(kgcat h) T (K) 493 u (m/s) 4.02E3 P = 2 MPa m n qDi rw ¼ 0 n ðjrTÞ ¼ 0 n ðjrTÞ ¼ 0
503 4.10E3
SV = 20 N m3/(kgcat h) 513 4.18E3
523 4.26E3
493 8.04E3
503 513 8.20E3 8.37E3 Constant pressure For mass For heat transfer
523 8.53E3
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D.-Y. Shin et al. / Fuel 158 (2015) 826–834 Table 3 Values of parameters for balance equations. Symbol
Unit
493
503
513
523
q l eP jbr j
kg/m3 Pa s – m2 W/(m K) J/(kg K)
5.964 1.90E05 0.25 3.00E11 0.1262 2346
5.845 1.93E05
5.732 1.97E05
5.603 2.00E05
0.1280 2349
0.1298 2351
0.1320 2362
m2/s
9.61E06 1.11E05 3.43E06 9.91E05 3.18E06 8.29E07 2.42E06 1.06E06 3.10E06 7.39E07
9.95E05 1.15E05 3.55E06 1.03E05 3.29E06 8.59E07 2.51E06 1.10E06 3.21E06 7.65E07
1.03E05 1.19E05 3.67E06 1.06E05 3.41E06 8.89E07 2.60E06 1.14E06 3.32E06 7.92E07
1.07E05 1.23E05 3.80E06 1.10E05 3.53E06 9.19E07 2.69E06 1.18E06 3.44E06 8.19E07
CP Dik
CO, H2 H2O, H2 C8H18, H2 Ar, H2 H2O, CO C8H18, CO Ar, CO C8H18, H2O Ar, H2O Ar, C8H18
Temperature (K)
temperature was set to 343 K. Prior to the FTS activity test, the catalyst was activated at 673 K for 12 h under 5% H2/He flow. The activity test was conducted for ca. 75 h under the reaction conditions presented in Table 1. The coolant flow rate was set to 0.36 m3/h. The detailed syngas composition was H2/CO/CO2/Ar = 57.3:28.4:9.3:5.0 (mol%). Ar was used as an internal standard for GC analysis. Effluent gas from the channel-type reactor was analyzed by using an online gas chromatograph (Young Lin Acme 6000 GC) employing a GS-GasPRO capillary column connected to a flame ionization detector (FID) for the analysis of hydrocarbons, and a Porapak Q/molecular sieve packed column connected to a thermal conductivity detector (TCD) for analysis of carbon oxides and the internal standard gas Ar.
3. Mathematical modeling Computational fluid dynamics (CFD) modeling was conducted using the commercial software COMSOL Multiphysics 4.0a (COMSOL, Inc.), which has built-in modules in the simulation package for the mass, energy, and momentum balances of each flow channel. The reactor diagram was directly generated within COMSOL Multiphysics and then, built-in modules in the simulation package were applied to consider the mass, energy, and momentum balances, respectively, of the reactant flow channel (cf. Table 2). Inlet and outlet boundary conditions are also presented in Table 2, while the specified values are presented in Table 3. The diffusion coefficients in the mass balance equation were calculated using the binary
Fig. 2. Velocity profiles in the distributor and catalytic bed for (a) one, (b) two, (c) three, and (d) four distributor layers.
D.-Y. Shin et al. / Fuel 158 (2015) 826–834
0.15
2.0
0.10
1.6
0.05
1.2
0.00
0.8
0
1
2
3
4
5
" # 59:3 103 1 1 k ¼ 2:89 10 exp T 503:15 R " # 26:9 103 1 1 3 K H2 ¼ 1:56 10 exp T 503:15 R " # 24:2 103 1 1 1 K CO ¼ 3:53 10 exp T 503:15 R 3
Distributor volume ratio
Fraction of the dead volume in the catalytic bed
830
Fig. 3. Effects of the number of distributor layers on the dead volume fraction in the catalytic bed and the distributor volume ratio (Vdistributor/Vdistributor,1layer). Solid lines are regression curves (y = 3.76 103x2 5.44 102x + 0.17 and y = 5.07 102 x2 0.53x + 0.52 for the dead volume fraction and the distributor volume ratio, respectively. The value of r2 is 0.999 for both results).
diffusion coefficient of species i and j [28], while the weight-averaged thermal conductivity was used for the gas mixture [29,30]. Other properties such as density, viscosity, conductivity, and heat capacity were determined from a process simulator, UniSim Design Suite (Honeywell Inc.), while the conductivity of the reactor body (SUS 304) was specified using the default value provided in COMSOL Multiphysics. In the mass balance module, the following reaction kinetics was considered for the CO consumption rate:
kP H2 PCO 1 þ K H2 P H2 þ K CO PCO
In the case where the width of the catalytic channel is large, a gas distributor should be considered for uniform distribution of syngas at the inlet of the bed. A tree-like structure with multiple layers was considered in the present study, and the CFD was utilized to determine the appropriate number of layers since the use of too many layers would be at the expense of the compactness of the module despite the uniform distribution. Fig. 2 shows the flow patterns for the different numbers of layers using the rectangular curved channel shape for simplicity. When one layer was considered as shown in Fig. 2a, a large dead volume was present
where the kinetic parameters were specified to have the same values in the counter-current case [13], since the same catalysts were used.
Conversion [%]
(a)
70 60
SV = 20 Nm3/(kgcat·h)
SV = 10 Nm3/(kgcat·h)
50 40 30
exp sim
20 10
490
500
510
520
530
490
Coolant inlet temperature [K]
Tcenter [K]
(b)
ð4Þ
4. Results and discussion
ð1Þ
2
ð3Þ
The units of k, KH2, and KCO are mol/(kgcat s MPa2), MPa1, and MPa1, respectively, and the temperature is in kelvin. The gas constant (R) is 8.314 J/(mol K). It is to be noted that the selectivity of the produced hydrocarbons was not taken into account because temperature control is one of the main objectives of the present study; moreover, if the reaction rate is too complicated with detailed hydrodynamics (including diffusive mass and conductive heat transfers as well as momentum balances in COMSOL Multiphysics (COMSOL, Inc.)), a high computational load results. For grid generation, the ‘‘Free tetrahedral grid’’ method in the software was selected, resulting in ca. one million grids for the entire reaction system; Galerkin’s method [31] was applied with the tolerance of the relative errors specified as 1 103.
Number of layers
RCO ¼
ð2Þ
530
500
510
520
530
Coolant inlet temperature [K] SV = 20 Nm3/(kgcat·h)
SV = 10 Nm3/(kgcat·h)
520 510 500
exp sim
490 490
500
510
520
Coolant inlet temperature [K]
530
490
500
510
520
530
Coolant inlet temperature [K]
Fig. 4. Comparison of (a) CO conversion and (b) temperature at the center of the catalytic bed (Tcenter) for experimental data versus simulated results; space velocities were 10 (left) and 20 (right) N m3/(kgcat h), respectively. Means of absolute relative residuals (MARR) for conversion and temperature were 7.24% and 0.82%, respectively, while relative standard deviations of individual errors were 5.80% and 0.36%, respectively.
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D.-Y. Shin et al. / Fuel 158 (2015) 826–834 53.948 70 60 50 40 30 20 10
3.8669
(b)
502.55
502.4 502.2 502.0 501.8 501.6 501.4 501.24
(c)
501.17
501.1
501.0
than the height of the catalytic bed may lead to dead volume in the upper and lower part of the bed. Therefore, the threshold value for the fraction was arbitrarily chosen to be less than 3% and thus, four layers were selected. The validity of the kinetic model was verified by comparing the simulated results based on the reactor dynamics in the present study to experimental data. For both CO conversion and the temperature at the center of the catalytic bed (cf. Fig. 4), the simulation was in good agreement with the experimental data. The mean of the absolute relP ative residuals (MARR), defined as 100 i jðyi;exp yi;calc Þ=yi;exp j =N exp , where Nexp represents the number of experimental data points, and the relative standard deviation of the errors are also provided in the figure caption. Notably, the experimentally determined temperature at the center of the catalytic bed was slightly lower than the coolant inlet temperature despite the highly exothermic reaction. This feature is attributed to the fact that there was some heat loss from the reactor module to ambient air despite the use of insulation material around the reactor body. Since there was no forced convection inside the oven, natural convection was assumed in the simulation, and the corresponding heat transfer coefficient (hamb) was specified to be 0.1 W/(m2 K) [13]. Similar temperatures were obtained for both space velocities. Although a high space velocity (20 N m3/(kgcat h)) led to lower conversion than achieved with low space velocity (10 N m3/(kgcat h)) due to the reduced residence time, the high flow rate made the reaction rates and the heat generation for both cases similar. In other words, the productivity depends on the conversion as well as the feed flow rate; there is a tradeoff and thus, the optimal space velocity must be determined to achieve maximum productivity. The CFD simulation results obtained under a specific set of conditions (Tcoolant,inlet = 503 K, space velocity = 10 N m3/(kgcat h)) are presented in Fig. 5. Due to the uniform velocity distribution at the inlet of the bed, CO conversion increased uniformly along the axis, except at the right-lower side of the bed (cf. Fig. 5a). To facilitate catalyst loading and unloading, there should be open passage
(a) ΔTmax in the catalytic bed [K]
(a)
500.98
because of the momentum in the axial direction, whereas the increase in the number of layers reduced the dead volume. The fraction of dead volume and the increase in the distributor volume are compared to the one layer case (V/Vone-layer) in Fig. 3 as a function of the number of layers. When the number of layers is increased, the dead volume is significantly decreased (almost in a linear manner), and the use of five layers may eliminate most of dead volume. However, in the case of five layers, each channel in the gas inlet tube (directly connected to the catalytic bed) becomes too narrow (<1 mm), and the diameter of gas inlet tube smaller
3.0 2.5
SV 10 Nm3/kg/h SV 20 Nm3/kg/h
2.0 1.5 1.0 0.5 490
500
510
520
530
Coolant inlet temperature [K]
(b)
0.34
ΔTmax in the coolant channel [K]
Fig. 5. Profiles of (a) CO conversion, (b) temperature in the catalytic bed, and (c) temperature in the coolant channel when feed and coolant inlet temperature = 503 K, space velocity = 10 N m3/(kgcat h). Maximum and minimum values are provided at the top and bottom of the color bar, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
3.5
0.30 0.26 0.22 0.18 0.14 490
500
510
520
530
Coolant inlet temperature [K] Fig. 6. Maximum temperature increase (DTmax) in (a) the catalytic bed and (b) the coolant channel.
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D.-Y. Shin et al. / Fuel 158 (2015) 826–834
Table 4 Comparison between different flow patterns. SV (N m3/(kgcat h))
Temperature at the center of the catalytic bed (K)
Conversion (%)
Counter-current [13]
Cross-current
Difference
Counter-current [13]
Cross-current
Difference
10
493.8 504.3 514.7 525.1
492.1 502.5 512.8 523.0
1.70 1.81 1.96 2.11
32.1 42.2 53.0 63.4
33.2 44.0 53.8 61.8
1.10 1.77 0.86 1.59
20
494.0 504.5 515.3 527.0
492.3 502.9 513.6 524.3
1.66 1.66 1.70 2.73
17.5 23.9 31.8 41.9
18.5 27.0 37.2 48.0
1.03 3.07 5.42 6.15
50
(a) Conversion [%]
48 46 44 42 40 38
0
2
4
6
8
10
8
10
Scale factor (Sf)
Tcenter [K]
(b) 515 510
505
500
0
2
4
6
Scale factor (Sf) Fig. 7. (a) CO conversion and (b) temperature at the center of the catalytic bed (Tcenter) when the height of the catalytic bed is increased by the scale factor (h = href Sf). Feed and coolant inlet temperature = 503 K; space velocity = 10 N m3/ (kgcat h).
1
ln (selectivity)
0
C5+
-1
C1
-2 -3
C2–4
-4 1.88
1.91
1.94
1.97
2.00
2.03
2.06
1000/T Fig. 8. Selectivies of hydrocarbon products under conditions 1–4 in Table 1. Solid lines represent the regression results; ln SC1 = (8251/T) + 14.26, ln SC2–4 = (8951/ T) + 14.39 and ln SC5+ = (1820/T) 3.795, and the R2 for C1, C2–4 and C5+ are 0.974, 0.993 and 0.996, respectively.
instead of an exit for the effluent around the bend (cf. Fig. 1a). During the reaction tests, the open passage was fully plugged. Therefore, the velocity was relatively low due to the lack of an exit
for the effluent around the bend, resulting in increased conversion. However, because the flow rate was very low, the heat generation was lower than at other spots, and thus, the temperature was also low (cf. right-lower side in Fig. 5b). In the case of coolant flow, the temperature in the channel close to the inlet of the catalytic bed was slightly lower than the temperature close to the catalytic bed exit owing to low conversion. However, the maximum temperature increase in the coolant channel was less than 0.2 K, indicating that the coolant channel was maintained under almost isothermal conditions. It is worth noting that, as discussed above, due to natural convection between the reactor body and ambient air in the oven chamber, the temperature of the coolant channel decreased slightly in the flow direction despite the exothermic reaction. Fig. 6 shows the maximum temperature increase (DTmax) in the catalytic and coolant channels. As shown in Fig. 6a, the maximum temperature increase was ca. 3 K, demonstrating the effectiveness of cross-flow. In addition, the maximum temperature change within the coolant channel was 0.3 K, and thus, the cooling capacity of the oil coolant was sufficient for removing the generated heat. It is also notable that, as shown in Table 4, the temperature at the center of the catalytic bed was lower by ca. 2 K than the case of counter-current flow under the same operating conditions [13]. This feature is attributed to the fact that the coolant channel close to the inlet of catalytic bed effectively removed most of heat generated in the early part of the catalytic bed, indicating that the module structure based on the cross-current flow may be an effective alternative for scale-up of the reaction module. However, if the width of the catalytic bed is increased more than the present study, small number of coolant channel near the inlet of the catalytic bed may be insufficient for heat removal, resulting in temperature control failure. In addition, increasing the width of the catalytic bed leads to the increase in the size of the gas distributor. Therefore, the width of the catalytic bed should be carefully increased during scale-up. As for the conversion, cross-current flow pattern led to higher conversion than cross-current case, probably due to the open passage as discussed above. The height of the catalytic bed was increased in order to determine the allowable heat generation, i.e. the limit of temperature control capability. This analysis is critical because increasing the catalytic channel volume reduces the number of channel layers which determines the manufacturing cost of a reactor module. The space velocity was fixed at 10 N m3/(kgcat h) by increasing the feed flow rate according to the increase in the bed height. Since increasing the bed height led to an increase of the bed volume per unit coolant channel, the temperature increased with increasing bed height, resulting in an increase in the conversion, as shown in Fig. 7. Although the increased conversion and feed flow rate corresponded to increased productivity, it should be noted that the increased temperature decreases the selectivity for the middle distillate and increase the selectivity for methane, as shown in Fig. 8. In addition, the increased heat generation results in non-isothermal temperature profile in the reactor, and
D.-Y. Shin et al. / Fuel 158 (2015) 826–834
(a)
56.298 70 60 50 40 30 20 10
0.1142
(b)
516.47 516.0 514.0 512.0 510.0 508.0 506.0
833
increased heat generation. Therefore, the temperature of the catalytic bed increased, especially around the center. In addition, the heat generation rate exceeded the heat loss from the reactor body to ambient air by natural convection, and thus, the temperature of the coolant channel close to the catalytic bed exit increased in the flow direction. However, the temperature increase within the coolant channel was below 0.36 K. 5. Conclusions The CFD modeling approach was applied to the Fischer–Tropsch synthesis reactor model with a cross-current cooling channel. By analyzing the velocity profiles for different numbers of layers in the gas distributor, the effects of the distributor structure on the inlet flow distribution of the catalytic bed were successfully evaluated, and the structure selected for the experimental study was shown to be effective. The benefit of CFD modeling was also demonstrated by taking the kinetic reaction rate into consideration in such a way that the simulated results could satisfactorily describe the experimental data. In addition, the developed model could be used to predict the temperature control capability of the cooling system with an increase in the height of the catalytic bed, indicating that the modeling approach utilized in the present study can be used in determining the optimal design for the structure of the modular reactor for highly exothermic Fischer–Tropsch synthesis. Acknowledgements
504.0 502.0 501.39
(c)
501.29
501.2
501.1
501.0
500.93
Fig. 9. Profiles of (a) CO conversion, (b) temperature in the catalytic bed, and (c) temperature in the coolant channel when the height of the catalytic bed was increased by eight times (Sf = 8) that of the reference case. Feed and coolant inlet temperature = 503 K; space velocity = 10 N m3/(kgcat h).
thus, a kinetic model that treats the selectivity of hydrocarbon products in detail should be applied. However, that is beyond the scope of the present study, since the purpose is to investigate the effects of the channel structure and flow pattern on the temperature control. Fig. 9 shows the conversion and temperature profiles when the height of the catalytic bed was increased up to eight times compared to the reference case. The conversion profile shown in Fig. 9a was similar to that of the reference case and the temperature was well maintained due to satisfactory cooling performance, even when the space velocity and the number of cooling channels was not changed. For the same space velocity, the feed flow rate increased as the catalyst loading increased, leading to
This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) under the ‘‘Energy Efficiency & Resources Programs’’ (Project No. 2010201010008A) of the Ministry of Trade, Industry & Energy (MOTIE), Republic of Korea. M.-J. Park and K.-S. Ha also acknowledge support from the Engineering Development Research Center (EDRC) funded by the Ministry of Trade, Industry & Energy (MOTIE). References [1] Gumuslu G, Avci AK. Parametric analysis of Fischer–Tropsch synthesis in a catalytic microchannel reactor. AlChE J 2012;58:227–35. [2] Schulz H. Short history and present trends of Fischer–Tropsch synthesis. Appl Catal A: Gen 1999;186:3–12. [3] Rahimpour MR, Forghani AA, Mostafazadeh AK, Shariati A. A comparison of cocurrent and counter-current modes of operation for a novel hydrogenpermselective membrane dual-type FTS reactor in GTL technology. Fuel Process Technol 2010;91:33–44. [4] Yang JH, Kim HJ, Chun DH, Lee HT, Hong JC, Jung H, et al. Mass transfer limitations on fixed-bed reactor for Fischer–Tropsch synthesis. Fuel Process Technol 2010;91:285–9. [5] Rahimpour MR, Elekaei H. A comparative study of combination of Fischer– Tropsch synthesis reactors with hydrogen-permselective membrane in GTL technology. Fuel Process Technol 2009;90:747–61. [6] Zhang Q, Kang J, Wang Y. Development of novel catalysts for Fischer–Tropsch synthesis: tuning the product selectivity. ChemCatChem 2010;2:1030–58. [7] Yao Y, Liu X, Hildebrandt D, Glasser D. The effect of CO2 on a cobalt-based catalyst for low temperature Fischer–Tropsch synthesis. Chem Eng J 2012;193–194:318–27. [8] Holmen A, Venvik HJ, Myrstad R, Zhu J, Chen D. Monolithic, microchannel and carbon nanofibers/carbon felt reactors for syngas conversion by Fischer– Tropsch synthesis. Catal Today 2013;216:150–7. [9] Dry ME. The Fischer–Tropsch process: 1950–2000. Catal Today 2002;71:227–41. [10] Kwack SH, Bae JW, Park MJ, Kim SM, Ha KS, Jun KW. Reaction modeling on the phosphorous-treated Ru/Co/Zr/SiO2 Fischer–Tropsch catalyst with the estimation of kinetic parameters and hydrocarbon distribution. Fuel 2011;90:1383–94. [11] Park N, Kim J-R, Yoo Y, Lee J, Park M-J. Modeling of a pilot-scale fixed-bed reactor for iron-based Fischer–Tropsch synthesis: two-dimensional approach for optimal tube diameter. Fuel 2014;122:229–35. [12] Myrstad R, Eri S, Pfeifer P, Rytter E, Holmen A. Fischer–Tropsch synthesis in a microstructured reactor. Catal Today 2009;147:S301–4. [13] Shin M-S, Park N, Park M-J, Cheon J-Y, Kang JK, Jun K-W, et al. Modeling a channel-type reactor with a plate heat exchanger for cobalt-based Fischer– Tropsch synthesis. Fuel Process Technol 2014;118:235–43.
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