CFD Modeling of a Thermally Efficient Modular Reactor for Fischer

Article pubs.acs.org/IECR

CFD Modeling of a Thermally Efficient Modular Reactor for Fischer− Tropsch Synthesis: Determination of the Optimal Size for Each Module Jun-Soo Park,† Du-Eil Kim,‡ Yun-Jo Lee,‡ Geunjae Kwak,‡ Ki-Won Jun,*,‡ and Myung-June Park*,†,§ †

Department of Energy Systems Research, Ajou University, Suwon 16499, Republic of Korea Research Center for Green Catalysis, Korea Research Institute of Chemical Technology (KRICT), Daejeon 34114, Republic of Korea § Department of Chemical Engineering, Ajou University, Suwon 16499, Republic of Korea ‡

ABSTRACT: A modular multichannel reaction module with microchannel-based coolant channels was considered, and a computational fluid dynamics (CFD) model was developed to describe the hydrodynamic behavior of the module. Reaction rates for the lumped chain length distribution of hydrocarbon products generated by the Fischer−Tropsch synthesis reaction were proposed, and the developed kinetic and CFD models were shown to satisfactorily fit the experimental data under different production rates. High heat transfer rates resulting from the use of microchannelbased cooling channel maintained the temperature peak below 10 °C, and simulation results with increased size of the catalytic bed and absence of inert materials showed that the high heat of reactions could be efficiently removed over entire catalytic beds, preventing the creation of local hot spots, which are usually observed in conventional fixed bed reactors. In addition, the efficient use of thermal energy could guarantee that methane selectivity, which needs to be maintained as low as possible, was close to approximately 10% under all conditions, while the selectivity of the desired hydrocarbons (C5+) slightly increased with increasing feed flow rates.

1. INTRODUCTION In Fischer−Tropsch synthesis (FTS), synthesis gas, which is produced from more abundant resources, such as coal, natural gas, and biomass, is converted to clean transportation fuels. This is possible because FT-liquids are totally free of sulfur and contain very few aromatics as compared to gasoline and diesel, resulting in lower emission levels when used in internal combustion engines.1−4 Recently, the use of natural gas from remote locations has gained interest owing to environmental and economic reasons, and this has led to intense research on FTS technology.5,6 Several metals, such as Ni, Co, Ru, and Fe, have been found to be activated in the FT reaction; of these elements, Fe and Co catalysts are most common commercial FTS catalysts. Cobased catalysts are preferred over Fe-based catalysts owing to the high activity, high selectivity to long chain hydrocarbons, better catalyst stability in hydrogen rich environments, and lower selectivity to oxygenated compounds exhibited by the Co-based catalysts.7−14 At present, various types of reactors for FTS, including the circulating fluidized-bed, fluidized-bed, tubular fixed-bed, and slurry-phase reactors, are used commercially under several operating conditions and with different catalysts.15−21 The gasto-liquid (GTL) production capacities has increased, as evidenced by the construction of the largest plants to date: Pearl GTL, a joint development by Qatar Petroleum and Shell, © XXXX American Chemical Society

and Oryx GTL owned by Qatar Petroleum and Sasol, both located in Qatar. In today’s competitive world market, advanced design and optimization of such large-scale plants requires a more detailed knowledge of reaction chemistry, heat and mass transport, fluid mechanics, and so on.22,23 One of the important tasks in developing an FT process is to maximize the energy efficiency of the reactor. Hence, microchannel technology has been recently used to minimize heat transfer resistance and to ensure compactness, high productivity, and thermally stable operation of the synthesis reactor.24−32 High heat transfer rates allow very robust control of the reaction temperature, which is a key issue for the strongly exothermic FTS, resulting in not only high syngas conversions, but also effective control of reaction selectivity toward the desired product fraction.33 In addition, because this technology enables the reaction to occur at rates up to 1000 times that in conventional systems, the passages in microchannel systems are dramatically smaller than those in conventional systems.34 In our previous work, the effectiveness of a modular reactor with microchannel cooling channels was corroborated by showing negligible temperature gradient along the reactor Received: June 19, 2016 Revised: August 9, 2016 Accepted: August 22, 2016

A

DOI: 10.1021/acs.iecr.6b02359 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

Figure 1. Schematic diagram of (a) the FTS reaction system and (b) a modular reactor with multiple catalytic beds and microchannel-based coolant channels; dimensions for the catalytic bed and cooling channel are 10 mm × 5 mm × 400 mm (width × height × length) and 2 mm × 400 mm (diameter × length), respectively, while the numbers of the catalytic bed and cooling channel are 9 and 42 for each layer, respectively..

Table 1. Experimental Conditions catalytic bed no.

SV [mL/(gcat·h)]

1 2 3 4 5 6

3408 5921 7668 9287 11758 15762

coolant channel

linear velocity [m/s]

temp [°C]

pressure [bar]

H2/CO ratio

temp [°C]

pressure [bar]

flow rate [mL/min]

10−02 10−02 10−02 10−02 10−02 10−02

233 233 234 232 234 231

21.4 21.7 21.9 21 22.4 21.6

2 2 2 2 2 2

229.9 230.1 230.7 229.1 231.5 229.7

27.6 27.7 28 27.2 28.4 27.5

120 120 120 120 120 120

1.12 1.93 2.48 3.12 3.72 5.14

× × × × × ×

axis.29 The reaction module was further improved for applying it to a commercial-scale process: (1) the size of each catalytic bed was increased as too small tube leads to too many catalyticbed channels and consequently too many unit modules, and (2) the cooling oil was replaced with high-pressure water for larger-scale reactors. In the present study, the rate equation for CO consumption developed in the previous work29 was extended to apply it for the production of hydrocarbons with lumped chain lengths, in order to evaluate the effects of operating conditions on the chain length distribution, and the developed rates were incorporated into a computational fluid dynamics (CFD) model to confirm that latent heat of cooling water is sufficient for removing the released heat. Further analyses were conducted to study the effects of inert materials and space velocity on the heat generation and productivity, and the results were used to provide useful data for the design of an

linear velocity [m/s] 3.79 3.79 3.79 3.79 3.79 3.79

× × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03

energy-efficient reaction module of appropriate (highly profitable) size.

2. EXPERIMENTAL SECTION 2.1. Catalyst Preparation. Gamma-alumina (Sasol Puralox SCCA-5/170, SBET = 165 m2 g−1, pore volume of 0.477 cm3 g−1) was used as the support material for Co FTS catalyst. The support was calcined at 673 K before catalyst loading. Aqueous solution of cobalt nitrate and tetraammineplatinum(II) nitrate in the desired amount was impregnated into the alumina support. The catalysts were dried at 383 K for 12 h, followed by calcination at 673 K for 5 h. Co and Pt loaded in the catalyst were 23 and 0.05 wt %, respectively. 2.2. Fischer−Tropsch Synthesis Reaction. A schematic diagram of the FT reaction system is shown in Figure 1a. The FT reaction of the Co catalyst was performed using a fixed bed reactor with 1/4 in. stainless steel tube. The catalyst (0.5 g) was B


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Industrial & Engineering Chemistry Research Table 2. Detailed Stationary Equations Used for Each Part of the Module name transport of concentrated species

balance equations

remarks mass balance for the reactant flow channel (mixture-averaged diffusion model)

∇·ji + ∇·(ρωi u) = R i where

⎛ ∇M n ∇T ⎞ ji = − ⎜ρDim∇ωi + ρωiDim + DiT ⎟ Mn T ⎠ ⎝ Dim

−1 −1 ⎛ ⎛ xk ⎞⎟ ω⎞ ⎜ , M n = ⎜⎜∑ i ⎟⎟ = (1 − ωi)⎜∑ ⎟ ⎝ i Mi ⎠ ⎝ k ≠ 1 Dik ⎠

heat transfer in fluids (energy balance for the reactant flow channel and the coolant channel)

ρCP u·∇T = ∇·(κ ∇T ) + Q heat transfer in solids (energy balance for the channel bodies, made of stainless steel (SUS 316L)) 0 = ∇ · (κ∇T) + Q (with heat transfer by radiation negligible) (ambient temperature =25 °C) free and porous media flow (momentum balance for the reactant flow channel (Brinkman equation for porous media region, while “Laminar flow” equation is used for free media region))

⎞ ⎛ μ ρ⎛ u⎞ + Q br⎟u ⎜(u·∇) ⎟ = F − ⎜ εP ⎝ εP ⎠ ⎠ ⎝ κbr ⎡ ⎤ 2μ μ (∇·u)I⎥ + ∇·⎢− P I + (∇u + ∇uT ) − 3εP εP ⎣ ⎦ inlet boundary conditions for catalytic beds and coolant channels CO/H2/CO2/Ar = 52/7/27/14 (mass fraction at catalytic bed inlet) outlet boundary conditions −n · ρDmi ∇w = 0 for mass −n · (−κ∇T) = 0 for heat transfer in catalytic beds and coolant channels symmetry condition −n · (ρωiu + ji) = 0 for mass −n · (−κ∇T) = 0 for heat transfer solid boundary condition −n · (−κ∇T) = 0 heat flux −n · (−κ∇T) = q0 where q0 = hcat. (Tjacket − Tcat.) catalytic bed to reactor jacket q0 = hcoolant (Tcoolant − Tjacket) reactor jacket to coolant channel q0 = hambient (Tambient − Tjacket) reactor jacket to ambient thermal conductivity of reactor body (SUS316L), a function of temperature, is built in COMSOL Multiphysics; ca. 11−25 W/(m·K) at 135−1220 K

mixed with 2.5 g of α-alumina as an inert diluent and reduced in situ under a flow of 5% H2/Ar (200 cc/min) at 623 K for 10 h. The activity tests were conducted under the various reaction conditions (cf. Table 1) with the feed compositions of H2/CO/ Ar = 63.0/31.5/5.5 mol %.

domain (details are listed in Table 2) by using built-in calculation modules in the COMSOL Multiphysics, and owing to the symmetry of the module, a quarter of the system was simulated. It should be noticed that, the Maxwell−Stefan model has been shown to be more rigorous than the Wilke formulation used in the present study, guaranteeing the consistency between the mass and mole based pellet equations.35,36 However, while the model is the most detailed diffusion model, the CFD simulation is the most computationally expensive, especially when the chemical reaction which also requires large computational burden is included. Therefore, the Wilke formulation was used for computational efficiency. Coolant water flowed in the coolant channel in the saturated state. In other words, water was at the boiling point and the heat released by the reaction was transferred to the cooling channel, resulting in the evaporation of coolant water. As long as the released heat worked as latent heat, the temperature and pressure in the coolant channel were maintained constant while the fraction of steam increased. If the evaporation was complete and only steam existed in the channel, the temperature would increase due to the heat transferred from the catalytic bed.

3. MATHEMATICAL MODELING CFD modeling of the modular FT reaction system was conducted using the COMSOL Multiphysics 5.2 (COMSOL, Inc.), and the scheme of the module is shown in Figure 1b. The module is composed of catalytic beds, microchannel-based coolant channels, and the reactor body. Note that, in our previous work,29 the reactor consisted of three catalytic beds (layered vertically) with microchannel-based cooling channels inserted between them. In the present study, the reactor had three layers with nine catalytic beds in each layer so that each reactor module had the maximum possible capacity as possible while maintaining its cooling performance so that the capital cost per unit productivity is minimized. Therefore, the aim of this work was to investigate if the cooling performance of the scaled-up reactor was as good as that of the smaller reactor in our previous work. Balance equations were applied to each C


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Industrial & Engineering Chemistry Research Table 3. Values of Parameters for Physical Properties space velocity [mL/gcat/h] symbol μ εP κbr κ CP Dik

unit Pa·s m2 W/(m·K) J/(kg·K) m2/s H2, CO H2, CO2 H2, Ar H2, H2O H2, C8H18 H2, C3H8 H2, CH4 CO, CO2 CO, Ar CO, H2O CO, C8H18 CO, C3H8 CO, CH4 CO2, Ar CO2, H2O CO2, C8H18 CO2, C3H8 CO2, CH4 Ar, H2O Ar, C8H18 Ar, C3H8 Ar, CH4 H2O, C8H18 H2O, C3H8 H2O, CH4 C8H18, C3H8 C8H18, CH4 C3H8, CH4

3408

5921 −05

2.04 × 10 0.185 3.00 × 10−11 0.113 1974 1.74 1.46 1.79 2.00 6.20 9.86 1.56 3.62 4.39 5.76 1.50 2.57 4.80 3.38 4.61 1.15 2.03 3.92 5.61 1.34 2.39 4.69 1.93 3.22 5.80 9.14 2.59 2.83

× × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−06 10−06 10−06 10−06 10−07 10−07 10−06 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−08 10−07 10−07

7668 −05

0.00143T1.75 1/2 P(MAB )[(∑ vA )1/3 + (∑ vB)1/3 ]2

11758 −05

2.04 × 10

2.04 × 10

2.04 × 10

2.05 × 10

0.113 1974

0.1131 1974

0.1128 1973

0.1132 1974

1.72 1.44 1.77 1.97 6.12 9.73 1.54 3.57 4.33 5.68 1.48 2.53 4.74 3.33 4.55 1.14 2.00 3.87 5.54 1.32 2.35 4.62 1.90 3.18 5.72 9.02 2.55 2.79

× × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−06 10−06 10−06 10−06 10−07 10−07 10−06 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−08 10−07 10−07

1.70 1.43 1.75 1.96 6.06 9.64 1.52 3.54 4.29 5.63 1.47 2.51 4.69 3.30 4.51 1.13 1.98 3.84 5.48 1.31 2.33 4.58 1.88 3.15 5.67 8.94 2.53 2.77

× × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−06 10−06 10−06 10−06 10−07 10−07 10−06 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−08 10−07 10−07

1.77 1.49 1.83 2.04 6.32 1.01 1.59 3.69 4.47 5.87 1.53 2.62 4.89 3.45 4.70 1.18 2.07 4.00 5.72 1.36 2.43 4.77 1.96 3.28 5.91 9.32 2.64 2.89

× × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−06 10−06 10−06 10−06 10−07 10−06 10−06 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−08 10−07 10−07

1.66 1.40 1.71 1.91 5.93 9.42 1.49 3.46 4.19 5.50 1.43 2.45 4.59 3.23 4.40 1.10 1.94 3.75 5.36 1.28 2.28 4.48 1.84 3.08 5.54 8.74 2.47 2.71

× × × × × × × × × × × × × × × × × × × × × × × × × × × ×

15762 −05

2.03 × 10−05

0.1126 1974 10−06 10−06 10−06 10−06 10−07 10−07 10−06 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−08 10−07 10−07

1.72 1.45 1.78 1.98 6.15 9.77 1.54 3.59 4.35 5.70 1.49 2.55 4.76 3.35 4.57 1.14 2.01 3.89 5.56 1.33 2.37 4.64 1.91 3.19 5.75 9.06 2.57 2.81

× × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−06 10−06 10−06 10−06 10−07 10−07 10−06 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−08 10−07 10−07

value was calculated to be 50 and 376 W/(m2·K) for steam and water, respectively. Saturated water was used in the coolant channel, and the calculation based on the heat generation (see the next section) showed that water was dominant over steam. Therefore, the value of 100 W/(m2·K) specified for the simulation. Heat transfer between the reactor body and the ambient was assumed to be by natural convection as the reactor was installed inside an oven with no forced convection. In our previous work,28 the coefficient of local heat transfer to the ambient (hambient) was determined in such a way that CO conversions at the exit and the temperatures at the center of the catalyst loading area of the reactant flow channel were calculated by varying the values of the coefficient hambient, and the value of 0.1 W/(m2·K) was selected due to the least average errors. Since a reactor was installed inside the same oven with the previous work, the value was used without modification. Gas density was calculated as a function of temperature, pressure, and composition under the assumption of the ideal gas law. Viscosity, thermal conductivity, and heat capacity were assumed to be constant. Detailed information on the parameters for physical properties are presented in Table 3. In order to calculate the profiles of CO conversion and temperature, Galerkin’s method42 was applied, and 963,524 free

Physical properties were available in a process simulator (UniSim Design Suite, Honeywell Inc.), and binary diffusion coefficient (Dik) was calculated using the following equation:37 Dik =

9287 −05

(1)

In the case of catalytic fixed-bed reactors, the overall heat transfer coefficients range between 100 and 300 W/(m2· K).38−40 In the case of heat transfer coefficients for the catalytic bed, the correlation of hcat = 38 + (0.0255 + 0.055G)Tw (where G is flow rate/area in kg/(m2·s) and Tw is the wall temperature in °C)38 can be used and the calculated values was ca. 44 W/ (m2·K), under the experimental conditions in the present study. In addition, our previous work19 also showed that local heat transfer value in the catalytic bed was close to 150 W/(m2·K). Therefore, local heat transfer coefficient for the catalytic bed was specified to 100 W/(m2·K), and the effectiveness of the specified value was corroborated by comparison of simulated temperature profiles in the bed to experimental observation (will be discussed later). Local heat transfer coefficient for the coolant channel was calculated using the correlation41 of Nu = 1.86(Re•Pr)1/3(DH/ L)1/3 which can be applied to infernal and laminar flow, and the D


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Figure 2. Comparison of (a) CO conversion, and the selectivities of (b) C1, (c) C2−4, and (d) C5+, between experimental data and simulation results.

Figure 3. Temperature profiles along the axis of the catalytic bed when the SV was (a) 7668, (b) 9287, (c) 11758, and (d) 15762 mL/(gcat·h); the other conditions are referred to Table 1. The positions of temperature measurements are 70, 140, and 200 mm from the inlet.

tetrahedral grids were defined. Other details about the computational methods in COMSOL Multiphysics are available in the reference.29,43,44 The main reaction for FTS can be schematically written as nCO + 2nH2 → -(CH2)n- + nH2O, where -(CH2)n- is the methylene group polymerizing into a hydrocarbon chain. While the CO consumption rate was used in our previous work29 to evaluate the temperature gradient with the minimum computational load, it is also important to describe the selectivity of hydrocarbon products as the production of methane should be minimized. For this purpose, the production rates for lumped chain length distributions (C1, C2−4, and C5+) were derived, while each lump was written using the representative chain number in order to satisfy carbon-mole balance during simulation:

reaction for C2 − 4 production (R C2−4): 3CO + 7H 2 → C3H8 + 3H 2O

reaction for C5 + production (R C5+): 8CO + 17H 2 → C8H18 + 8H 2O

Then, the values of the parameters were estimated by fitting selectivity data, which was obtained using our previous reactor module. Because the same catalyst was used in the present work, the reaction rates were used without further modification: R C1 =

reaction for C1 production (R C1): CO + 3H 2

k C1PCOPH2 (1 + K COPCO + K H2PH2)2

R C2 ‐ 4 =

→ CH4 + H 2O E

(2)

k C2−4PCOPH2 (1 + K COPCO + K H2PH2)2

(3)


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Figure 4. Profiles of (a) CO conversion and (b) temperature in the catalytic bed, and cross sectional view of (c) CO conversion and (d) temperature at the packing depth of 300 mm when the SV was specified to be 15762 mL/(gcat·h) (cf. Table 1). The values at the top and bottom of the color bar represent the maximum and minimum, respectively.

R C5+ =

The units of ki, KH2, and KCO are mol/(kgcat·s·bar2), bar−1, and bar−1, respectively, and the gas constant (R) is 8.314 J/ (mol·K).

k C5 +PCOPH2 (1 + K COPCO + K H2PH2)2

(4)

where −5

k C1 = 2.78 × 10

4. RESULTS AND DISCUSSION

⎡ 121 000 ⎛ 1 1 ⎞⎤ ⎜ ⎟⎥ exp⎢ − − ⎣ R ⎝T 503.15 ⎠⎦

In order to validate the effectiveness of the developed model, the simulation results of conversion, selectivities, and temperature were compared with experimental data under the conditions listed in Table 1 (cf. Figures 2 and 3). The means of absolute relative residuals (MARR) [%], defined as 100 × (∑i |(yi ,exp − yi ,calc )/yi ,exp |)/Nexp·, for CO conversion,

⎡ 163 000 ⎛ 1 1 ⎞⎤ ⎜ ⎟⎥ k C2−4 = 1.17 × 10−5 exp⎢ − − ⎝ ⎣ R T 503.15 ⎠⎦ ⎡ 64 000 ⎛ 1 1 ⎞⎤ ⎜ ⎟⎥ − k C5 + = 3.69 × 10−5 exp⎢ − ⎣ R ⎝T 503.15 ⎠⎦

the selectivities of C1, C2−4, C5+, and the temperature are 9.80, 8.02, 5.06, 1.53, and 1.57, respectively, while their corresponding values for the relative standard deviation of individual errors are 2.70, 3.46, 5.64, 0.70, and 1.34, respectively. As shown in the figures and the values of errors, the developed model satisfactorily described the experimental data. Especially in the temperature profile, the effectiveness of the local heat transfer coefficient for the catalytic bed was corroborated on the basis of individual errors between simulated results and experimental data.

⎡ 24 600 ⎛ 1 1 ⎞⎤ ⎜ ⎟⎥ K H2 = 1.91 × 10−4 exp⎢ − ⎣ R ⎝T 503.15 ⎠⎦ ⎡ 19 300 ⎛ 1 1 ⎞⎤ ⎜ ⎟⎥ K CO = 8.73 × 10−2 exp⎢ − ⎝ ⎣ R T 503.15 ⎠⎦ F


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Industrial & Engineering Chemistry Research As the space velocity (SV) increased, CO conversion decreased, while the selectivities were not significantly changed owing to the similar temperature profiles in the catalytic bed (cf. Figure 3). Note that, the production rate which is a product of conversion and feed flow rate was high despite low conversion at high SV. In other words, the higher the SV, the greater was the amount of heat released by the reaction in the operating windows of the present study. Regardless of the increased heat generation, heat transfer rates by the microchannel-based coolant channel were sufficiently large for limiting the temperature increase to less than 10 °C under all experimental conditions. In addition, the strong heat removal performance of the cooling channel prevented the formation of a thermal peak close to the inlet of the catalytic bed, unlike that usually observed in conventional fixed bed reactors.19 The effects of thermal intensification are discussed in the literature,28,45−47 where the specific area of a heat-exchanger reactor of structure similar to that of a modular reactor with microchannel-based coolant channels in the present study45 is up to 320 times that of conventional batch reactors with double jackets. Figure 4 shows the three-dimensional profiles of CO conversion and temperature in the catalytic bed as calculated by the CFD model. The profiles of all the catalytic bed channels were maintained identical owing to the high heat transfer rates. Within a catalytic bed, heat removal took place over almost the entire cross section, and thus, the temperature difference between the center and the edge of each bed was less than 5 °C (cf. Figure 4d). As the latent heat of pressurized water was used in the cooling channel, the total amount of heat transferred from the catalytic bed to the cooling channel was calculated using COMSOL Multiphysics, and then, the value was applied to a process simulator (UniSim Design Suite, Honeywell Inc.) in order to check the vapor fraction at the outlet of the cooling channel. Under all experimental conditions, the vapor fraction was less than 4%, indicating that the amount of water was more than enough to remove the heat generated by the reaction. Considering the high heat transfer rate affected by the microchannel-based cooling channel and the sufficient amount of pressurized water, it was decided that the size of each catalytic bed could be increased to the appropriate size of one module. It was determined that the inert fraction, which was 67% in the experiment, could be decreased to 0%. Figure 5 shows the simulation results when the height of each catalytic bed was increased to 10 mm and the inert fraction was specified to be 0. The temperature was increased by up to 50 °C even when the SV was low (cf. Figure 5a), as heat generation increased (cf. Figure 5b) owing to the increase in the volume to twice the original size. Interestingly, while the degree of the temperature peak increased with little change in the location of the peak owing to the increase in heat generation in the conventional fixed bed reactor, the maximum temperature did not change greatly in the modular reactor because of the high heat transfer rate. Meanwhile, the location of temperature peak shifted from the inlet of the reactor to the exit, and the band for the maximum temperature widened (cf. contour plot in the upper right of Figure 5a). This feature indicates that a wider range of catalytic bed is used in the modular reactor, as compared to that in the conventional reactor, and thus, the performance of the module is enhanced despite the reduced bed volume. Further, note that the vapor fraction increased up to 15% (cf. 4% in the reference case) even with increased heat

Figure 5. (a) Temperature profiles along the axis of the catalytic bed when the SV was varied (upper right is the contour plot), and (b) averaged heat flux of catalytic bed which was calculated as total heat flux at the boundaries of the bed divided by total heat transfer area, when the height of each catalytic bed was increased to 10 mm (twice of the original size) and the inert fraction was assumed to be 0 (only catalyst was loaded); coolant inlet pressure was specified to 2.8 MPa and the corresponding saturated temperature was 230.7 °C, while the feed temperature was 233 °C.

generation rates, indicating that the enhanced heat removal capacity efficiently uses the latent heat of the cooling media. As the temperature profile is directly related to the selectivity of the hydrocarbon products, the values were also evaluated as shown in Figure 6. In the FT process, methane, which is produced mostly at high temperatures, is an undesired product, especially when the syngas is obtained by the reforming of methane. In the modular reactor, even with increased heat generation, methane selectivity was maintained at approximately 10%, indicating that the widened range of high temperature insignificantly affects its selectivity. When the high temperature range was wide (middle range of SV values), the selectivity of C5+ decreased slightly (less than 5%P), and when the SV was further increased, the values increased again owing to the reduced range of the high-temperature band (cf. Figure 5a). Although selectivity was maintained, the yield decreased with increasing SV because of the decrease in the conversion as shown in Figure 6c. However, the production rate shown in Figure 6d, calculated as a product of the conversion and yield, revealed that the optimal space velocity should be determined in terms of high productivity.

5. CONCLUSIONS Reaction rates for the lumped chain length distribution for the FTS reaction were applied for a CFD modeling of a modular G


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Figure 6. Effects of SV on (a) CO conversion (regressed line: y = 89.2−8.06 × 10−4x − 6.68 × 10−8x2), (b) selectivity of C1, C2−4, and C5+ (regressed lines: y = 10.8 + 6.03 × 10−6x + 1.05 × 10−9x2, y = 20.5 + 5.40 × 10−4x − 2.78 × 10−8x2, y = 68.7−5.46 × 10−4x + 2.68 × 10−8x2 for C1, C2−4, and C5+, respectively), (c) yield of C1, C2−4, and C5+, and (d) C5+ production rate, when the height of each catalytic bed was increased to 10 mm and the inert fraction was assumed to be 0. Values in (c) and (d) were calculated using regressed lines in (b).

DiT = thermal diffusion coefficient of species i, kg/(m·s) Dik = multicomponent Maxwell−Stefan diffusivities of species i and k, m2/s F = volume force, N/m3 h = local heat transfer coefficient, W/(m2·K) I = identity matrix ji = mass flux of species i, kg/(m2·s) ki = reaction rate constant of species i, mol/(kgcat·s·bar2) Ki = adsorption equilibrium constant of species i, bar−1 M1/2 AB = harmonic mean of molar mass of species A and B, kg/ mol Mn = mean molar mass, kg/mol Nu = Nusselt number, dimensionless P = pressure, bar Pi = partial pressure of species i, bar Pr = Prandtl number, dimensionless Q = heat source term, W/m3 Qbr = mass source term, kg/(m3·s) q0 = heat flux, W/m2 Re = Reynolds number, dimensionless Ri = reaction rate of species i, mol/(m3·s) SV = space velocity, mL/(gcat·h) T = temperature, °C u = velocity vector, m/s xi = mole fraction of species i, dimensionless

reactor with microchannel-based coolant channels. The validity of the developed model was corroborated by comparing the results with experimental data, and further analysis showed that the high heat transfer rate resulting from the high specific surface area could maintain the temperature profile close to isothermal conditions. CFD modeling could provide useful insights into the dynamics of the suggested module and be used as a tool to predict how the increase of size of the catalytic bed, decrease in the inert fraction, and change in other operating conditions affect the performance of the reaction module. Consequently, the proposed approach and the simulation results may be applicable in the design of an economically optimal reaction module for commercial production.

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AUTHOR INFORMATION

Corresponding Authors

*Tel: +82-42-860-7671. Fax: +82-42-860-7388. E-mail: [email protected]. *Tel: +82-31-219-2383. Fax: +82-31-219-2395. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) under “Energy Efficiency & Resources Programs” (Project Nos. 2010201010008A and 20153010092090) of the Ministry of Trade, Industry & Energy, Republic of Korea and the Human Resources Development of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Trade, Industry & Energy (No. 20154010200820).

Greek letters

εP κ κbr μ ρ νi ωi

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porosity, dimensionless thermal conductivity, W/(m·K) permeability of the porous medium, m2 dynamic viscosity, kg/(m·s) fluid density, kg/m3 diffusion volume of species i mass fraction of species i, dimensionless

Subscript

NOMENCLATURE CP = heat capacity, J/(kg·K) DH = hydraulic diameter, m Dim = mixture-averaged diffusion coefficient of species i, m2/ s

ambient cat coolant i H

ambient atmosphere catalytic beds coolant channels species DOI: 10.1021/acs.iecr.6b02359 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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