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CFD modeling of a compact reactor for methanol synthesis: Maximizing productivity with increased thermal controllability
International Journal of Heat and Mass Transfer 145 (2019) 118776
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
CFD modeling of a compact reactor for methanol synthesis: Maximizing productivity with increased thermal controllability Minji Son a, Yesol Woo b, Geunjae Kwak c, Yun-Jo Lee c, Myung-June Park b,d,⇑ a
Engineering Research Institute, Ajou University, Suwon 16499, Republic of Korea Department of Energy Systems Research, Ajou University, Suwon 16499, Republic of Korea c C1 Gas Conversion Research Group, Carbon Resources Institute, Korea Research Institute of Chemical Technology (KRICT), Daejeon 34114, Republic of Korea d Department of Chemical Engineering, Ajou University, Suwon 16499, Republic of Korea b
a r t i c l e
i n f o
Article history: Received 1 July 2019 Received in revised form 22 August 2019 Accepted 21 September 2019
Keywords: Methanol Computational fluid dynamics Modeling Compact reactor Thermal control
a b s t r a c t A kinetic model for methanol synthesis was validated for a conventional fixed-bed reactor at the minipilot scale by determining a heat transfer coefficient to fit the experimental data satisfactorily. To enhance the thermal controllability of the reaction system, a compact reactor, which utilizes heat transfer with both cooling media and cool feed gas, was introduced. The analysis of detailed profiles of mass, momentum, and heat was conducted by applying the developed kinetic model to the computational fluid dynamics modeling approach. While the accumulation of heat was observed in a conventional reactor because of its limited heat transfer capability, a compact reactor could efficiently remove the generated heat. The space velocity and feed temperature were manipulated to increase the production rate while unstable thermal behavior was prevented, and it was clearly shown that the proposed reactor could produce twice the methanol, with its peak temperature maintained below the conventional one. When the diameter of the catalytic bed in the compact reactor was increased, the reaction remained in the kinetic regime, resulting in high methanol productivity as well as maximum utilization of the bed. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Catalytic conversion of syngas (mixtures of CO and H2) to hydrocarbons and alcohols is one of the most important processes for improving the carbon cycling with increasing energy demand and environmental concern [1,2]. Methanol is an excellent fuel in its own right and a versatile product, as it can be used directly in fuel cells for electricity production and as a gasoline substituent. Furthermore, it can be upgraded to either dimethyl ether (DME), which is a diesel substituent, or chemical building blocks for ethylene and propylene by the methanol-to-olefin process [3–6]. Nowadays, methanol is commercially synthesized over Cu/ZnO/Al2O3 catalysts under low pressure (5–10 MPa) and low temperature (473.15–573.15 K); methanol can be formed via highly exothermic hydrogenation of CO and CO2, and the water-gas-shift reaction is included in the overall process [7]. Because the methanol synthesis reaction is exothermic and reversible, low temperature causes high conversion with a slow reaction rate, leading to the requirement of a large amount of catalyst. Meanwhile, high temperature improves ⇑ Corresponding author at: Department of Energy Systems Research, Ajou University, Suwon 16499, Republic of Korea. E-mail address: [email protected] (M.-J. Park). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118776 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
the rate of reaction, while a temperature that is too high decreases the conversion of CO and CO2 owing to the failure of equilibrium conversion [8] and deteriorates the thermal stability of the reactor. Therefore, implementing high temperatures at the entrance of the reactor for high reaction rate and then reducing the temperature gradually towards the exit to increase thermodynamic equilibrium conversion is one of the most significant issues in methanol synthesis reactor configuration [9]. The traditional method for methanol production is based on the direct combination of CO, CO2, and H2 gases in a catalytic packed bed reactor; a conventional methanol reactor is a shell and tube heat exchanger with multiple tubes packed with catalyst pellets. Saturated water circulates through the shell side of the reactor to remove the generated heat of reaction. Because of the equilibrium behavior of the reactions, methanol conversion in the conventional reactor is maintained to be low, and most of the unreacted syngas should be recycled in the process [10]. To overcome the limits of conventional reactors, a variety of advanced reactors have been suggested. Velardi and Barresi [11] applied a network of three catalytic fixed bed reactors to promote the performance of exothermic and equilibrium-limited synthesis reactions, and evaluate the effects of operating parameters, such as switching time, inlet velocity, and inlet temperature on productivity. Rahimpour and
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M. Son et al. / International Journal of Heat and Mass Transfer 145 (2019) 118776
Nomenclature A CP D Dm i DTi Dik F I ji Mn Q Qbr r
heat transfer area, m2 heat capacity, J/(kg∙K) diameter, m mixture-averaged diffusion coefficient of species i, m2/s thermal diffusion coefficient of species i, kg/(m∙s) multicomponent Maxwell-Stefan diffusivities of species i and k, m2/s volume force, N/m3 identity matrix mass flux of species i, kg/(m2∙s) mean molar mass, kg/mol heat source term, W/m3 mass source term, kg/(m3s) radius, m
Alizadehhesari [9] developed a membrane dual-type methanol reactor system to compare its performance with the conventional dual-type methanol synthesis reactor and showed that the developed reactor resulted in a favorable temperature profile for a long catalyst lifetime. Samimi et al. [12] applied a water permselective membrane in the reverse water-gas-shift reactor, which was installed prior to the methanol synthesis reactor, and showed that the methanol production rate was significantly increased in addition to the benefit that no additional water separator was required in the process. Rahmatmand et al. [13] introduced a novel methanol synthesis process configuration, where adiabatic and plate watercooled reactor replace a two stage conventional reactor system, and mathematical modeling corroborated the validity of the process by improving the catalyst durability. Samimi et al. [14] proposed three configurations with cooling system (water-cooled, gas-cooled, and double-cooled reactors) and showed that the gascooled reactor yielded more methanol than the other reactors under similar reaction conditions. However, their analysis assumed an average temperature in the radial direction; thus, detailed profiles of local conversion and temperature were not considered. In the present study, a variation of the bayonet reactor, called the compact reactor, was suggested, and its performance was compared to those of the conventional reactor with respect to temperature control and productivity. A computational fluid dynamics (CFD) simulation was applied to retrieve detailed distributions of conversion and temperature for a more complicated description of the proposed reactor than the conventional one. It is worth noting that, when the length to diameter ratio is high, averaged temperature profiles in radial direction may not be much different from those based on radial temperature gradient. However, as the size of the tube increases, a limited heat transfer rate in radial direction due to heat transfer resistance may result in temperature increase in a tube, especially close to the center. In addition, the scale-up of a compact reactor introduced in the present study is not based on the multi-tubular configuration but the increase of the tube size, and thus, too much increase of tube radius may lead to thermal instability. Therefore, it is important to investigate the radial gradient of the catalytic tube. Finally, the developed model was used to evaluate the effects of operating conditions and design parameters on the performance of the structure. 2. Experimental and modeling methods 2.1. Catalyst preparation A commercial catalyst (Cu/ZnO/Al2O3, Dalian Reak Science, RK05) was used in pilot-scale methanol synthesis experiments. The
Ri SV u xi z
reaction rate of species i, mol/(m3∙s) space velocity, mL/(gcath) velocity vector, m/s mole fraction of species i, dimensionless packing depth, m
Greek letters eP porosity, dimensionless j thermal conductivity, W/(mK) jbr permeability of the porous medium, m2 l dynamic viscosity, Pas q fluid density, kg/m3 xi mass fraction of species i, dimensionless
commercial methanol catalyst has a molar ratio of Cu/Zn/ Al = 60/30/10, a cylindrical pellet (5 mm diameter and 5 mm height), and a bulk density of 1.1–1.3 kg/L. The fresh catalyst (0.77 kg) was physically mixed with 1.60 kg of a-alumina ball (5 mm diameter) before loading into the reactor tube to prevent an abrupt temperature increase. The mixed catalysts were loaded into the tube reactor. Prior to methanol synthesis, the loaded catalyst was reduced at 250 °C for 5 h in a flow of 5% H2 balanced with N2. 2.2. Experimental setup A schematic of the pilot-scale methanol synthesis system is shown in Fig. 1. The reactor is basically a vertical shell and tube heat exchanger in which methanol catalyst is packed in the vertical tubes and tubes are being surrounded by saturated water. The heat of the exothermic reaction is transferred to the saturated water, and steam is produced. The heated water and steam are subsequently cooled through the heat exchanger and transferred to a water vessel. The reaction temperature can be easily controlled by controlling the system pressure of the shell side in the closed cooling loop system. The experiments concerning the pilot-scale methanol synthesis were carried out in a loop reactor with product separation and internal recycling (see Fig. 1). The model synthesis gas (H2:CO:CO2:N2 = 58.4:6.0:9.1:26.5 mol%) was premixed and dosed into the reactor. The inlet gas was preheated and converted over a fixed bed of commercial methanol catalyst. The resulting product mixture (unreacted gases, methanol, and H2O) was cooled, and the liquid products were first separated under a pressure of 50 bar and then, in the second step, transferred to a methanol storage tank near atmospheric pressure. The liquid phase was collected as crude methanol comprising methanol and water. The separated gas was recycled by means of a recycle compressor, following by mixing with fresh feed gas. The recycled gas was partly purged to prevent an accumulation of inert trace gases, such as CH4 and N2. 2.3. Kinetic modeling Overall reaction mechanism for methanol synthesis are as follows:
CO hydrogenation : CO þ 2H2 ¢
CH3 OH
ð1Þ
CO2 hydrogenation : CO2 þ 3H2 ¢ CH3 OH þ H2 O
ð2Þ
Reverse water-gas shift : CO2 þ H2 ¢ CO þ H2 O
ð3Þ
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M. Son et al. / International Journal of Heat and Mass Transfer 145 (2019) 118776
Fig. 1. Scheme of experimental system (mini-pilot scale), where a single tube (inner diameter = 0.038 m (1.5 in), length = 1.5 m) with a shell was used as a reactor for 10 kg/day production of methanol. Experimental conditions: Pressure, SV, and temperature (both inlet and wall) were specified to be 5 MPa, 6771 mL/(gcath), and 210 °C, respectively, and feed composition was set to be H2:CO:CO2:N2 = 58.4:6.0:9.1:26.5 mol%.
The reactions rates are available in our previous work [15], as follows:
r CO
h i 1:5 0:5 kA K CO f CO f H2 f CH3 OH = K P;A f H2 ¼ 0:5 ð1 þ K CO f CO Þ 1 þ K 0:5 H2 f H 2 þ K H 2 O f H2 O
r RWGS
r CO2
h i kB K CO2 f CO2 f H2 f CO f H2 O =K P;B ¼ 0:5 1 þ K CO2 f CO2 1 þ K 0:5 H2 f H2 þ K H2 O f H2 O
h i 1:5 1:5 kC K CO2 f CO2 f H2 f H2 O f CH3 OH = K P;C f H2 ¼ 0:5 1 þ K CO2 f CO2 1 þ K 0:5 H2 f H2 þ K H 2 O f H 2 O
ð4Þ
where T is in Kelvin while the units of both K P;A and K P;C are MPa2, and K P;B is dimensionless. The validity of the reaction rate equations was corroborated by using experimental data in a mini-pilot reaction system (Fig. 1). 2.4. CFD modeling
ð5Þ
ð6Þ
Here, f denotes the fugacity, which was calculated using the generalized correlations for the fugacity coefficient in the literature [16], and Kp represents the reaction equilibrium constant. The reported values of the kinetic parameters (Table 1) were used without any modification, except the reaction equilibrium constants, which were obtained by fitting the data in a process simulator (UniSim Design Suite, Honeywell Inc.), as follows:
CFD modeling of the reactors was conducted using COMSOL Multiphysics 5.3 (COMSOL, Inc.), and the scheme of the two reactors are provided in Fig. 2. The capacities of both reactors were 50 kg/day of production (5 times larger than the mini-pilot in Fig. 1). While a single tube reactor was used in the experimental study (cf. Section 2.2) for the validation of the kinetic model, a multi-tubular reactor was considered in the simulation study since
Table 1 Kinetic parameters for a lab-scale methanol synthesis reactor. Parameters
Units
kA
mol/(kgcatsMPa1.5)
kB
mol/(kgcatsMPa)
ð7Þ
kC
mol/(kgcatsMPa1.5)
K H2 O
MPa1
2090 2:018 T
ð8Þ
K CO
MPa1
log K P;C ¼ logK P;A þ logK P;B
ð9Þ
log K P;A ¼
4817 9:83 T
log K P;B ¼
1
K CO2
MPa
K H2
MPa1
Values
Remarks 9
113;711 RT
5:95 10 exp 1:16 1011 exp 126;573 RT 2:24 106 exp 68;252 RT 3:80 10-10 exp 80;876 RT 8:00 10-6 exp -6
58;015 RT
[15]
[17]
67;439 RT
1:02 10 exp 2:71 102 exp 6291 RT
[18]
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M. Son et al. / International Journal of Heat and Mass Transfer 145 (2019) 118776
(a)
Syngas feed (tube)
It is worth noting that, since the latent heat of the saturated water was used for cooling, the coolant shell was assumed to be isothermal condition with no balances considered, while momentum and energy balance equations for the syngas feed, which contributes to the cooling of the catalytic bed, were solved in the inner tube of the compact reactor. In addition, boiling phenomenon which may occur in the coolant shell was assumed to be negligible for simplicity.
(b) Catalyc tube
3. Results and discussion
Cross-seconal view
Syngas feed Coolant (shell)
Catalyc tube Inner tube
Coolant
Reactor effluent
Fig. 2. Scheme of (a) conventional multi-tubular fixed-bed reactor (inner diameter and length of a tube (packing depth) are 0.038 m (1.5 in) and 2.2 m, respectively, and inner diameter of a shell is 0.1 m) and (b) compact reactor proposed in this study (radii of inner, middle, and outermost tubes are 0.035, 0.077, and 0.085 m, respectively, and the length of the middle tube is 2.2 m), for 50 kg/day production of methanol (5 times larger capacity than the mini-pilot system in the experiments).
it is most widely used configuration for the scale-up in industrial applications. However, since the limited capacity of the cooling shell in the conventional reactor may result in the thermal instability, different configuration of compact reactor was introduced, and its performance was compared to the conventional one with the catalytic bed volumes of two reactor configurations maintained to be same. The conventional reactor (Fig. 2a) is a multi-tubular shell and tube reactor, and the total number of tubes was set to 3. The reactions took place in the tube side where the catalysts were loaded, and cooling water in the shell side controlled the reaction temperature. The compact reactor (Fig. 2b) is a variation of the bayonet-type reactor, consisting of 3 tubes. In the outermost tube, the cooling water flowed to control the reaction temperature, while the catalysts were loaded in the middle tube. The feed gas flowed upward to absorb the heat generated from the catalytic bed after being injected at the bottom of the inner tube and then entered the catalytic bed to flow downward. The temperature of the catalytic bed was simultaneously controlled by preheating with cool feed gas in the inner tube and by cooling with coolant media (cooling water in this work) flowing in the outermost tube. The following built-in modules from the COMSOL Multiphysics were used to consider the mass, energy, and momentum balances, respectively, of the reactant flow channel: ‘‘Transport of Concentrated Species,” ‘‘Heat Transfer in Fluids,” and ‘‘Free and Porous Media Flow”. The reactor body, which was made of stainless steel (SUS 316L), was analyzed using the ‘‘Heat Transfer in Solids” module assuming the existence of heat conduction, that is, by excluding heat transfer by radiation. Detailed stationary equations for each module are presented in Table 2 and symbols can be found in the Nomenclature section. In order to calculate the profiles of CO conversion and temperature, Galerkin’s method [19] was applied, and free tetrahedral grids were defined. Balance equations were calculated using the parallel direct sparse solver interface (PARDISO), which applies parallel computing methods on shared-memory and distributedmemory multiprocessors [20], was used to improve the computation speed.
Fig. 3 shows the comparison of the conversions and temperature profile between experimental data and simulated results, along with the statistics, such as mean of absolute relative residuhP i N als (MARR), defined as M ¼ 100 yi;sim yi;exp =yi;exp =N i (N: number of experimental data), and relative standard deviation of individual errors (RSDE), defined as rhffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 i PN 100 =ðN 1Þ. Another design parameter in i yi;sim M the reactor model was the overall heat transfer coefficient between the catalytic bed and coolant shell, whose value was determined to be 70 W/(m2K) by minimizing the errors of conversion and temperature profiles in a balanced manner. It should be noticed that, there existed the trade-off between CO conversion and CO2/H2 conversions, as shown in Fig. 3; in other words, by increasing the errors of CO conversion, those for CO2 and H2 conversions could be decreased. Since the degree of CO conversion was higher than the others, more focus was made on the CO conversion, and thus, relative error of CO conversion was determined to be much lower than the others. In addition, although relative errors were different between the objective elements, their absolute errors which was defined as the absolute deviation of the simulated values from the experimental data in %P (percent point) were similar; the values of absolute errors for CO, CO2 and H2 conversions were 4.2, 5.4, and 4.9 %P, respectively. It is shown that the simulated results coincide with the measured data, validating the effectiveness of the developed model. Fig. 4 shows the profiles of CO conversion and temperature in the tubes of the conventional multi-tubular fixed-bed reactor. Simulation conditions were determined, such that the production rate of methanol was 50 kg/day; pressure and GHSV were specified to be 5 MPa and 5000 mL/(gcath), respectively, and the inlet and wall temperatures were set to be 150 and 240 °C, respectively. Feed composition was set to be H2:CO:CO2:N2 = 66.7:19.6:9.1:4.6 mol %. The physical properties specified in the present study were available from the process simulator and are provided in Table 3. Conversion increased along the reactor axis and reached 43.2% (averaged) at the reactor exit (peak conversion was 51.3%). It should be noted that, as shown in the cross-sectional view at z = 0.6 m, conversion at the center was lower than that close to the wall, due to high linear velocity at the center. The temperature profile along the center of the reactor axis showed an increase from the reactor inlet, and after reaching the maximum value (305.5 °C), it decreased to 288.1 °C at the reactor exit. Detailed CFD results showed a different temperature gradient pattern in the radial direction at different positions along the reactor axis. Near the inlet of the tube, the feed gas close to the wall was heated by heat transfer with the media in the shell, while the heat was not fully transferred to the center of the tube, resulting in a lower temperature at the center (convex down parabolic curve as shown in the left diagram in Fig. 4c). At z (packing depth) = 0.6 m, because the conversion increased from the center to the wall in the radial direction, the reaction rate also increased despite the decreased flow rate of the gas (the rate is determined as the multiplication of the conversion and flow rate), leading to an
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M. Son et al. / International Journal of Heat and Mass Transfer 145 (2019) 118776 Table 2 Detailed stationary equations used in each part of the module. Name
Balance equations
Remarks
Transport of concentrated species
r ji þ r ðqxi uÞ ¼ Ri
Mass balance for the catalytic bed
where m rM n T rT ji ¼ qDm i rxi þ qxi Di M n þ Di T P 1 P 1 xk xi Dm ; Mn ¼ i ¼ ð1 xi Þ k–1 Dik i Mi (mixture-averaged diffusion model) 1=2
1 0:00143T 1:75 ðM 1 i þM k Þ Di;k ¼ 1=3 1=3 2 Pðmi þmk Þ P Ri ¼ stoichiometry r j MW i (rj: j-th reaction with j = CO, CO2, RWGS)
Heat transfer in fluids
qC P rT ¼ r ðjrT Þ þ Q
Energy balance for the catalytic bed
where P Q¼ Hj r j (heat of reaction j) Heat transfer in solids Free and porous media flow
0 ¼ r ðjrT Þ þ Q (with heat transfer by radiation negligible) h i 2l q l l u T eP ðu rÞ eP ¼ F jbr þ Q br u þ r PI þ eP ru þ ru 3eP ðr uÞI
r ðquÞ ¼ Q br
Energy balance for the reactor body Momentum balance for the catalytic bed
(Brinkman equation is for porous media region, while ‘‘Laminar flow” equation is used for free media region)
Inlet of catalytic bed Outlet of catalytic bed
Solid boundary condition
Boundary conditions
Remarks
u ¼ U 0 n P = 50 bar h i nT pI þ l ru þ ðruÞT 23 lðr uÞI n ¼ b p0
For momentum Constant pressure For momentum
b p 0 p0 , u t ¼ 0 n qDm i rwi ¼ 0 n ðjrT Þ ¼ 0
For mass For heat transfer
n ðjrT Þ ¼ 0
For heat transfer
MARR CO 7.4% CO2 33.5% H2 30.6%
(a) MARR = 3.2% RSDE = 1.4%
(b) Fig. 3. Comparison between simulated results and experimental data for (a) conversions and (b) temperature. Experimental conditions are given in the caption of Fig. 1.
increase in the temperature from the center. Then, the temperature decreased due to the heat transfer with the shell (binodal curve as shown in the middle diagram in Fig. 4c). In the later part of the reactor axis, the generated heat accumulated in the tube and the
temperature at the center reached maximum, while the temperature near the wall was close to the wall temperature (convex up parabolic curve as shown in the right diagram in Fig. 4c). As discussed above, the conventional tubular reactor showed the problem with the removal of heat around the center of the tube due to limited heat transfer capacity. To increase the heat transfer capacity, a compact reactor, which is a variation of the bayonet reactor, was suggested; the cooling is conducted by the cooling media in the shell as well as the cool feed gas in the inner tube (Fig. 2b). Fig. 5 shows the CFD results in the catalyst packing tube (middle tube), under the same simulation conditions in the conventional reactor except the feed gas temperature of 30 °C (cf. inlet temperature represents the one at the inlet of the catalyst packing tube, while the feed gas temperature denotes the one at the inlet of the inner tube). As for the conversion, the averaged value increased along the axis of the catalytic bed (averaged conversion at the exit was 48.4%, while the maximum value of local conversion was 49.8%). The radial gradient showed that the conversion at r = ri,middle is lower than that close to the outermost tube (ro,middle), owing to the temperature difference between the outermost and inner tube. This feature is maintained over the entire catalytic bed. It is worth noting that the radial gradient in the compact reactor was influenced more dominantly by the temperatures of inner and outermost tubes than the difference in linear velocities in the radial direction, while that in the conventional tube was affected by the linear velocity distribution. The temperature of the feed gas increased from 30 to approximately 130 °C (close to the inlet temperature in the conventional reactor) on account of the heat transfer from the catalytic bed. In the early part of the bed, the pattern of the radial temperature gradient was similar to that of the conversion gradient, while, in the middle of the bed (z = 1.1 m), the accumulated heat was removed by both the coolant in the outermost tube and the feed gas in
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(a)
(b)
z = 0.3 m
z = 0.3 m
z = 0.6 m
z = 0.6 m
Cross-seconal view
z = 0.9 m
z = 0.9 m
(c)
Fig. 4. Profiles of (a) CO conversion and (b) temperature in the tubes of the conventional multi-tubular fixed-bed reactor along the axis of catalyst packing. Cross-sectional view for radial distribution was shown at z (packing depth) = 0.6 m. (c) Radial temperature gradient at z = 0.3 (left), 0.6 (middle), and 0.9 (right).
Table 3 Physical properties specified in the CFD modeling. Symbol
Unit
Value
l eP jbr j
Pas
1:613 10-2 1.397
CP
– m2 W/(mK) J/(kgK)
1:000 10-12 0.1205 2.525
the inner tube, leading to the maximum temperature between ri, middle and ro,middle. In addition to the introduction of the cool feed gas, the higher heat transfer capacity of the compact reactor compared with the conventional reactor is attributed to the larger heat transfer area of the compact reaction [13.1 m2 (compact) vs. 7.72 m2 (conventional)]. As a result, the peak temperature was 284 °C, compared to 305.5 °C in the conventional reactor. Overall, since the reaction was in the thermodynamic regime rather than the kinetic regime, the lower peak temperature of the compact reactor resulted in higher conversion and a larger methanol production rate than the conventional reactor for the same space velocity. Because the heat transfer capacity of the proposed reactor was larger than that of the conventional reactor, the space velocity was increased to evaluate the effects of increased heat generation on the conversion and temperature profiles. Fig. 6a shows the CO conversion of the compact reactor (sky-blue colored bar with the label of Comp-30) decreasing with increasing SV more significantly than
the conventional reactor does (gray colored bar with the label of Conventional in the legend). Meanwhile, CO2 conversion of the compact reactor increased with increasing SV, while the conventional reactor showed insignificant change in CO2 conversion (Fig. 6b). Because the amount of CO2 was smaller than CO, the effects of SV on H2 conversion were similar to that on CO conversions (Fig. 6c). This feature is attributable to the increased flow rate (amount) of the feed gas in the compact reactor leading to a greater absorption of the heat generated in the catalytic bed, thus decreasing the inlet temperature as a result of thermodynamic behavior (Fig. 6e). In the case of the conventional reactor, the inlet temperature was fixed for all SVs, and the peak temperature was almost same (the locations of peak temperature moved from the inlet to the outlet with increasing SV, data not shown). As a result, the methanol productivity of the conventional reactor increased because the degree of the increase in the flow rate (amount) was higher than that of the decrease in the conversion. In the opposite manner, the methanol production in the compact reactor decreased slightly with increasing SV. To increase the methanol productivity in the compact reactor, the inlet temperature was increased to 60 °C (orange-colored bar with the legend of Comp-60), and it was observed that the conversion increased compared to the case of Tfeed = 30 °C, except that the conversion for SV/SVref = 1.0 could not be calculated due to the fact that the increase in the peak temperature was too much. Further increase in the feed temperature increased the methanol productivity. Although the maximum value was obtained at the highest SV and feed temperature, a conversion too low under these condi-
M. Son et al. / International Journal of Heat and Mass Transfer 145 (2019) 118776
(a)
7
(b)
Cross-seconal view
ro,middle
r=0 ro,inner ri,middle
Fig. 5. Profiles of (a) CO conversion, (b) temperature in the compact reactor proposed in this study. Cross-sectional view for radial distribution was shown at z (packing depth) = 1.1 m.
Fig. 6. Effects of the space velocity on (a) CO conversion, (b) CO2 conversion, (c) H2 conversion, (d) productivity, (e) inlet temperature, and (f) peak temperature, under different feed temperature of the compact reactor and at Tinlet = 150 °C in the conventional reactor. SVref was specified to be 5000 mL/(gcath). The labels ‘‘Conventional” and ‘‘Comp” in the legend represent the conventional and compact reactor, respectively, and the number denotes the value of the feed temperature in the compact reactor. The red dashed line corresponds to the conversion of the conventional reactor under the reference condition.
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M. Son et al. / International Journal of Heat and Mass Transfer 145 (2019) 118776
tions may increase the separation cost significantly. Therefore, the appropriate conditions might be SV/SVref = 2.0 and Tfeed = 90 °C, because it provides CO and H2 conversion similar to those under the reference conditions of the conventional reactor (cf. red dashed line in Fig. 6a and 6c), while the productivity is similar to the case of SV/SVref = 3.0 and Tfeed = 120 °C. To increase the productivity, in addition to the increase in SV, an increase in the diameter of the catalytic bed was considered. Fig. 7 shows the effects of the diameter on the performance of the compact reactor. It is shown that CO and H2 conversions decreased with increasing diameter with the SV fixed at 5000 mL/(gcath), while CO2 conversion increased slightly (Fig. 7a). This feature is attributable to the decrease in the inlet temperature when the flow rate was increased with increasing diameter for constant SV (Fig. 7b). However, despite the decreased conversion, the productivity increased owing to the increase in the feed gas. To better asses the reactor efficiency, the productivity per CO conversion was calculated as shown in Fig. 7b, and it was clearly shown that, the increase of the tube diameter enhanced the efficiency. Fig. 7c and 7d show the axial profiles of CO conversion and temperature for the conventional and compact reactors with different diameters. In the case of the conventional reactor, because the early
part of the catalytic bed played the role of preheating the feed gas, the reaction started at approximately z = 0.5 m. Meanwhile, although the inlet temperature of the compact reactor was lower than that of the conventional reactor, the reaction started at approximately z = 0.2 m because the temperature near the wall of the outermost tube was maintained close to the wall temperature (240 °C) (Fig. 7e). Because of the high heat transfer capacity of the compact reactor, peak temperatures in both axial and radial directions were maintained below that of the conventional reactor. Overall, if similar CO conversion is assumed, the diameter of the catalytic bed can be increased by 40% over that of the reference case while the productivity is increased approximately 1.7 times compared to the reference case (2 times compared to the conventional reactor). In the conventional reactor and the compact reactor with the reference diameter, the reaction reached equilibrium in the middle of the catalytic bed and was controlled thermodynamically thereafter (Fig. 7f). This indicates that the conversion was limited by the equilibrium, and the bed was not fully used. When the diameter was increased by 20%, the reaction reached equilibrium near the exit of the bed, and further increase maintained the reaction in the kinetic regime over the entire bed. This feature also supports the merits of the compact reactor.
(a)
(b)
(c)
(d)
(e)
(f) D/Dref = 1.0
D/Dref = 1.2
Equilibrium line
D/Dref = 1.4
D/Dref = 1.6
Fig. 7. Effects of the diameter on (a) conversions and productivity, (b) productivity per CO conversion, and peak and inlet temperature, axial profiles of (c) CO conversion and (d) temperature, (e) radial profiles of temperature at z (packing depth) = 1.8 m, and (f) temperature vs. conversion profiles, under the condition of Tfeed = 30 °C and SV = 5000 mL/(gcath). The legend ‘‘Conventional” and ‘‘Comp” represent the conventional and compact reactor, respectively, and the number denotes the ratio of D/Dref where Dref = 0.035 m.
M. Son et al. / International Journal of Heat and Mass Transfer 145 (2019) 118776
4. Conclusions The kinetic model was successfully validated by comparing simulated results with experimental data in a fixed-bed reactor at the mini-pilot scale. To explain how the capability of thermal control in a compact reactor was enhanced by the introduction of an additional heat transfer system (preheating of the feed gas in the inner tube), detailed profiles of mass, momentum, and heat were analyzed using the model. Further analysis on the effects of operating conditions and a design parameter for the structure showed that the productivity could be increased by a factor of two while the temperature was maintained below the peak temperature of the conventional reactor. In addition, due to the increased heat capacity, the diameter of the catalytic bed in the compact reactor could be increased, leading to the maximal utilization of the bed by maintaining the reaction in the kinetic regime. In conclusion, the CFD model in this work could be effectively used to analyze the physicochemical behavior of the advanced catalytic reactor and provide useful information on the determination of design parameters. Declaration of Competing Interest None. Acknowledgements This research was supported by the National Strategic ProjectCarbon Upcycling of the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (MSIT), the Ministry of Environment (ME), and the Ministry of Trade, Industry and Energy (MOTIE) (2017M3D8A2084259). Support was also received from the C1 Gas Refinery Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Science, ICT & Future Planning (2018M3D3A1A01055765) and from the Human Resources Development of the KETEP grant funded by the Ministry of Trade, Industry & Energy of the Korean Government (No. 20154010200820). References [1] M.E. Dry, The Fischer-Tropsch process: 1950–2000, Catal. Today 71 (2002) 227–241.
9
[2] C. Song, Global challenges and strategies for control, conversion and utilization of CO2 for sustainable development involving energy, catalysis, adsorption and chemical processing, Catal. Today 115 (2006) 2–32. [3] M. Bertau, H.J. Wernicke, F. Schmidt, U.-D. Standt, F. Seyfried, S. Buchholz, G. Busch, M. Winterberg, L. Reichelt, C. Pätzold, S. Pohl, L. Plass, J. Roes, M. Steffen, G. Sandstede, A. Heinzel, S. Hippmann, D. Holtmann, F. Sonntag, T. Veith, J. Schrader, Methanol utilisation technologies, in: M. Bertau, H. Offermanns, L. Plass, F. Schmidt, H.-.J. Wernicke (Eds.), Methanol: The Basic Chemical and Energy Feedstock of the Future: Asinger’s Vision Today, Springer, Berlin Heidelberg, Berlin, Heidelberg, 2014, pp. 327–601. [4] B. Denise, R.P.A. Sneeden, C. Hamon, Hydrocondensation of carbon dioxide: IV, J. Mol. Catal. 17 (1982) 359–366. [5] P. Mizsey, E. Newson, T.B. Truong, P. Hottinger, The kinetics of methanol decomposition: a part of autothermal partial oxidation to produce hydrogen for fuel cells, Appl. Catal. A: Gen. 213 (2001) 233–237. [6] M. Sedighi, M. Ghasemi, A. Jahangiri, Catalytic performance of CeAPSO-34 molecular sieve with various cerium content for methanol conversion to olefin, Korean J. Chem. Eng. 34 (2017) 997–1003. [7] G.A. Olah, A. Goeppert, G.K.S. Prakash, Beyond Oil and Gas: The Methanol Economy, second ed., 2009. [8] M.R. Rahimpour, M. Lotfinejad, Enhancement of methanol production in a membrane dual-type reactor, Chem. Eng. Technol. 30 (2007) 1062–1076. [9] M.R. Rahimpour, K. Alizadehhesari, Enhancement of carbon dioxide removal in a hydrogen-permselective methanol synthesis reactor, Int. J. Hydrogen Energy 34 (2009) 1349–1362. [10] M. Farsi, A. Jahanmiri, Dynamic modeling of a H2O-permselective membrane reactor to enhance methanol synthesis from syngas considering catalyst deactivation, J. Nat. Gas Chem. 21 (2012) 407–414. [11] S.A. Velardi, A.A. Barresi, Methanol synthesis in a forced unsteady-state reactor network, Chem. Eng. Sci. 57 (2002) 2995–3004. [12] F. Samimi, N. Hamedi, M.R. Rahimpour, Green methanol production process from indirect CO2 conversion: RWGS reactor versus RWGS membrane reactor, J. Environ. Chem. Eng. 7 (2019) 102813. [13] B. Rahmatmand, M.R. Rahimpour, P. Keshavarz, Introducing a novel process to enhance the syngas conversion to methanol over Cu/ZnO/Al2O3 catalyst, Fuel Process. Technol. 193 (2019) 159–179. [14] F. Samimi, M. Feilizadeh, M. Ranjbaran, M. Arjmand, M.R. Rahimpour, Phase stability analysis on green methanol synthesis process from CO2 hydrogenation in water cooled, gas cooled and double cooled tubular reactors, Fuel Process. Technol. 181 (2018) 375–387. [15] N. Park, M.J. Park, Y.J. Lee, K.S. Ha, K.W. Jun, Kinetic modeling of methanol synthesis over commercial catalysts based on three-site adsorption, Fuel Process. Technol. 125 (2014) 139–147. [16] J.M. Smith, H.C. Van Ness, M.M. Abbott, Introduction to Chemical Engineering Thermodynamics, seventh ed., McGraw-Hill, New York, 2005. [17] G.H. Graaf, E.J. Stamhuis, A.A.C.M. Beenackers, Kinetics of low-pressure methanol synthesis, Chem. Eng. Sci. 43 (1988) 3185–3195. [18] A. Coteron, A.N. Hayhurst, Kinetics of the synthesis of methanol from CO + H2 and CO + CO2 + H2 over copper-based amorphous catalysts, Chem. Eng. Sci. 49 (1994) 209–221. [19] S.C. Brenner, L.R. Scott, The Mathematical Theory of Finite Element Methods, second ed., Springer-Verlag, New York, 2002. [20] O. Schenk, K. Gärtner, Solving unsymmetric sparse systems of linear equations with PARDISO, Future Gener. Comp. Sy. 20 (2004) 475–487.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
CFD modeling of a compact reactor for methanol synthesis: Maximizing productivity with increased thermal controllability Minji Son a, Yesol Woo b, Geunjae Kwak c, Yun-Jo Lee c, Myung-June Park b,d,⇑ a
Engineering Research Institute, Ajou University, Suwon 16499, Republic of Korea Department of Energy Systems Research, Ajou University, Suwon 16499, Republic of Korea c C1 Gas Conversion Research Group, Carbon Resources Institute, Korea Research Institute of Chemical Technology (KRICT), Daejeon 34114, Republic of Korea d Department of Chemical Engineering, Ajou University, Suwon 16499, Republic of Korea b
a r t i c l e
i n f o
Article history: Received 1 July 2019 Received in revised form 22 August 2019 Accepted 21 September 2019
Keywords: Methanol Computational fluid dynamics Modeling Compact reactor Thermal control
a b s t r a c t A kinetic model for methanol synthesis was validated for a conventional fixed-bed reactor at the minipilot scale by determining a heat transfer coefficient to fit the experimental data satisfactorily. To enhance the thermal controllability of the reaction system, a compact reactor, which utilizes heat transfer with both cooling media and cool feed gas, was introduced. The analysis of detailed profiles of mass, momentum, and heat was conducted by applying the developed kinetic model to the computational fluid dynamics modeling approach. While the accumulation of heat was observed in a conventional reactor because of its limited heat transfer capability, a compact reactor could efficiently remove the generated heat. The space velocity and feed temperature were manipulated to increase the production rate while unstable thermal behavior was prevented, and it was clearly shown that the proposed reactor could produce twice the methanol, with its peak temperature maintained below the conventional one. When the diameter of the catalytic bed in the compact reactor was increased, the reaction remained in the kinetic regime, resulting in high methanol productivity as well as maximum utilization of the bed. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Catalytic conversion of syngas (mixtures of CO and H2) to hydrocarbons and alcohols is one of the most important processes for improving the carbon cycling with increasing energy demand and environmental concern [1,2]. Methanol is an excellent fuel in its own right and a versatile product, as it can be used directly in fuel cells for electricity production and as a gasoline substituent. Furthermore, it can be upgraded to either dimethyl ether (DME), which is a diesel substituent, or chemical building blocks for ethylene and propylene by the methanol-to-olefin process [3–6]. Nowadays, methanol is commercially synthesized over Cu/ZnO/Al2O3 catalysts under low pressure (5–10 MPa) and low temperature (473.15–573.15 K); methanol can be formed via highly exothermic hydrogenation of CO and CO2, and the water-gas-shift reaction is included in the overall process [7]. Because the methanol synthesis reaction is exothermic and reversible, low temperature causes high conversion with a slow reaction rate, leading to the requirement of a large amount of catalyst. Meanwhile, high temperature improves ⇑ Corresponding author at: Department of Energy Systems Research, Ajou University, Suwon 16499, Republic of Korea. E-mail address: [email protected] (M.-J. Park). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118776 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
the rate of reaction, while a temperature that is too high decreases the conversion of CO and CO2 owing to the failure of equilibrium conversion [8] and deteriorates the thermal stability of the reactor. Therefore, implementing high temperatures at the entrance of the reactor for high reaction rate and then reducing the temperature gradually towards the exit to increase thermodynamic equilibrium conversion is one of the most significant issues in methanol synthesis reactor configuration [9]. The traditional method for methanol production is based on the direct combination of CO, CO2, and H2 gases in a catalytic packed bed reactor; a conventional methanol reactor is a shell and tube heat exchanger with multiple tubes packed with catalyst pellets. Saturated water circulates through the shell side of the reactor to remove the generated heat of reaction. Because of the equilibrium behavior of the reactions, methanol conversion in the conventional reactor is maintained to be low, and most of the unreacted syngas should be recycled in the process [10]. To overcome the limits of conventional reactors, a variety of advanced reactors have been suggested. Velardi and Barresi [11] applied a network of three catalytic fixed bed reactors to promote the performance of exothermic and equilibrium-limited synthesis reactions, and evaluate the effects of operating parameters, such as switching time, inlet velocity, and inlet temperature on productivity. Rahimpour and
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M. Son et al. / International Journal of Heat and Mass Transfer 145 (2019) 118776
Nomenclature A CP D Dm i DTi Dik F I ji Mn Q Qbr r
heat transfer area, m2 heat capacity, J/(kg∙K) diameter, m mixture-averaged diffusion coefficient of species i, m2/s thermal diffusion coefficient of species i, kg/(m∙s) multicomponent Maxwell-Stefan diffusivities of species i and k, m2/s volume force, N/m3 identity matrix mass flux of species i, kg/(m2∙s) mean molar mass, kg/mol heat source term, W/m3 mass source term, kg/(m3s) radius, m
Alizadehhesari [9] developed a membrane dual-type methanol reactor system to compare its performance with the conventional dual-type methanol synthesis reactor and showed that the developed reactor resulted in a favorable temperature profile for a long catalyst lifetime. Samimi et al. [12] applied a water permselective membrane in the reverse water-gas-shift reactor, which was installed prior to the methanol synthesis reactor, and showed that the methanol production rate was significantly increased in addition to the benefit that no additional water separator was required in the process. Rahmatmand et al. [13] introduced a novel methanol synthesis process configuration, where adiabatic and plate watercooled reactor replace a two stage conventional reactor system, and mathematical modeling corroborated the validity of the process by improving the catalyst durability. Samimi et al. [14] proposed three configurations with cooling system (water-cooled, gas-cooled, and double-cooled reactors) and showed that the gascooled reactor yielded more methanol than the other reactors under similar reaction conditions. However, their analysis assumed an average temperature in the radial direction; thus, detailed profiles of local conversion and temperature were not considered. In the present study, a variation of the bayonet reactor, called the compact reactor, was suggested, and its performance was compared to those of the conventional reactor with respect to temperature control and productivity. A computational fluid dynamics (CFD) simulation was applied to retrieve detailed distributions of conversion and temperature for a more complicated description of the proposed reactor than the conventional one. It is worth noting that, when the length to diameter ratio is high, averaged temperature profiles in radial direction may not be much different from those based on radial temperature gradient. However, as the size of the tube increases, a limited heat transfer rate in radial direction due to heat transfer resistance may result in temperature increase in a tube, especially close to the center. In addition, the scale-up of a compact reactor introduced in the present study is not based on the multi-tubular configuration but the increase of the tube size, and thus, too much increase of tube radius may lead to thermal instability. Therefore, it is important to investigate the radial gradient of the catalytic tube. Finally, the developed model was used to evaluate the effects of operating conditions and design parameters on the performance of the structure. 2. Experimental and modeling methods 2.1. Catalyst preparation A commercial catalyst (Cu/ZnO/Al2O3, Dalian Reak Science, RK05) was used in pilot-scale methanol synthesis experiments. The
Ri SV u xi z
reaction rate of species i, mol/(m3∙s) space velocity, mL/(gcath) velocity vector, m/s mole fraction of species i, dimensionless packing depth, m
Greek letters eP porosity, dimensionless j thermal conductivity, W/(mK) jbr permeability of the porous medium, m2 l dynamic viscosity, Pas q fluid density, kg/m3 xi mass fraction of species i, dimensionless
commercial methanol catalyst has a molar ratio of Cu/Zn/ Al = 60/30/10, a cylindrical pellet (5 mm diameter and 5 mm height), and a bulk density of 1.1–1.3 kg/L. The fresh catalyst (0.77 kg) was physically mixed with 1.60 kg of a-alumina ball (5 mm diameter) before loading into the reactor tube to prevent an abrupt temperature increase. The mixed catalysts were loaded into the tube reactor. Prior to methanol synthesis, the loaded catalyst was reduced at 250 °C for 5 h in a flow of 5% H2 balanced with N2. 2.2. Experimental setup A schematic of the pilot-scale methanol synthesis system is shown in Fig. 1. The reactor is basically a vertical shell and tube heat exchanger in which methanol catalyst is packed in the vertical tubes and tubes are being surrounded by saturated water. The heat of the exothermic reaction is transferred to the saturated water, and steam is produced. The heated water and steam are subsequently cooled through the heat exchanger and transferred to a water vessel. The reaction temperature can be easily controlled by controlling the system pressure of the shell side in the closed cooling loop system. The experiments concerning the pilot-scale methanol synthesis were carried out in a loop reactor with product separation and internal recycling (see Fig. 1). The model synthesis gas (H2:CO:CO2:N2 = 58.4:6.0:9.1:26.5 mol%) was premixed and dosed into the reactor. The inlet gas was preheated and converted over a fixed bed of commercial methanol catalyst. The resulting product mixture (unreacted gases, methanol, and H2O) was cooled, and the liquid products were first separated under a pressure of 50 bar and then, in the second step, transferred to a methanol storage tank near atmospheric pressure. The liquid phase was collected as crude methanol comprising methanol and water. The separated gas was recycled by means of a recycle compressor, following by mixing with fresh feed gas. The recycled gas was partly purged to prevent an accumulation of inert trace gases, such as CH4 and N2. 2.3. Kinetic modeling Overall reaction mechanism for methanol synthesis are as follows:
CO hydrogenation : CO þ 2H2 ¢
CH3 OH
ð1Þ
CO2 hydrogenation : CO2 þ 3H2 ¢ CH3 OH þ H2 O
ð2Þ
Reverse water-gas shift : CO2 þ H2 ¢ CO þ H2 O
ð3Þ
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M. Son et al. / International Journal of Heat and Mass Transfer 145 (2019) 118776
Fig. 1. Scheme of experimental system (mini-pilot scale), where a single tube (inner diameter = 0.038 m (1.5 in), length = 1.5 m) with a shell was used as a reactor for 10 kg/day production of methanol. Experimental conditions: Pressure, SV, and temperature (both inlet and wall) were specified to be 5 MPa, 6771 mL/(gcath), and 210 °C, respectively, and feed composition was set to be H2:CO:CO2:N2 = 58.4:6.0:9.1:26.5 mol%.
The reactions rates are available in our previous work [15], as follows:
r CO
h i 1:5 0:5 kA K CO f CO f H2 f CH3 OH = K P;A f H2 ¼ 0:5 ð1 þ K CO f CO Þ 1 þ K 0:5 H2 f H 2 þ K H 2 O f H2 O
r RWGS
r CO2
h i kB K CO2 f CO2 f H2 f CO f H2 O =K P;B ¼ 0:5 1 þ K CO2 f CO2 1 þ K 0:5 H2 f H2 þ K H2 O f H2 O
h i 1:5 1:5 kC K CO2 f CO2 f H2 f H2 O f CH3 OH = K P;C f H2 ¼ 0:5 1 þ K CO2 f CO2 1 þ K 0:5 H2 f H2 þ K H 2 O f H 2 O
ð4Þ
where T is in Kelvin while the units of both K P;A and K P;C are MPa2, and K P;B is dimensionless. The validity of the reaction rate equations was corroborated by using experimental data in a mini-pilot reaction system (Fig. 1). 2.4. CFD modeling
ð5Þ
ð6Þ
Here, f denotes the fugacity, which was calculated using the generalized correlations for the fugacity coefficient in the literature [16], and Kp represents the reaction equilibrium constant. The reported values of the kinetic parameters (Table 1) were used without any modification, except the reaction equilibrium constants, which were obtained by fitting the data in a process simulator (UniSim Design Suite, Honeywell Inc.), as follows:
CFD modeling of the reactors was conducted using COMSOL Multiphysics 5.3 (COMSOL, Inc.), and the scheme of the two reactors are provided in Fig. 2. The capacities of both reactors were 50 kg/day of production (5 times larger than the mini-pilot in Fig. 1). While a single tube reactor was used in the experimental study (cf. Section 2.2) for the validation of the kinetic model, a multi-tubular reactor was considered in the simulation study since
Table 1 Kinetic parameters for a lab-scale methanol synthesis reactor. Parameters
Units
kA
mol/(kgcatsMPa1.5)
kB
mol/(kgcatsMPa)
ð7Þ
kC
mol/(kgcatsMPa1.5)
K H2 O
MPa1
2090 2:018 T
ð8Þ
K CO
MPa1
log K P;C ¼ logK P;A þ logK P;B
ð9Þ
log K P;A ¼
4817 9:83 T
log K P;B ¼
1
K CO2
MPa
K H2
MPa1
Values
Remarks 9
113;711 RT
5:95 10 exp 1:16 1011 exp 126;573 RT 2:24 106 exp 68;252 RT 3:80 10-10 exp 80;876 RT 8:00 10-6 exp -6
58;015 RT
[15]
[17]
67;439 RT
1:02 10 exp 2:71 102 exp 6291 RT
[18]
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M. Son et al. / International Journal of Heat and Mass Transfer 145 (2019) 118776
(a)
Syngas feed (tube)
It is worth noting that, since the latent heat of the saturated water was used for cooling, the coolant shell was assumed to be isothermal condition with no balances considered, while momentum and energy balance equations for the syngas feed, which contributes to the cooling of the catalytic bed, were solved in the inner tube of the compact reactor. In addition, boiling phenomenon which may occur in the coolant shell was assumed to be negligible for simplicity.
(b) Catalyc tube
3. Results and discussion
Cross-seconal view
Syngas feed Coolant (shell)
Catalyc tube Inner tube
Coolant
Reactor effluent
Fig. 2. Scheme of (a) conventional multi-tubular fixed-bed reactor (inner diameter and length of a tube (packing depth) are 0.038 m (1.5 in) and 2.2 m, respectively, and inner diameter of a shell is 0.1 m) and (b) compact reactor proposed in this study (radii of inner, middle, and outermost tubes are 0.035, 0.077, and 0.085 m, respectively, and the length of the middle tube is 2.2 m), for 50 kg/day production of methanol (5 times larger capacity than the mini-pilot system in the experiments).
it is most widely used configuration for the scale-up in industrial applications. However, since the limited capacity of the cooling shell in the conventional reactor may result in the thermal instability, different configuration of compact reactor was introduced, and its performance was compared to the conventional one with the catalytic bed volumes of two reactor configurations maintained to be same. The conventional reactor (Fig. 2a) is a multi-tubular shell and tube reactor, and the total number of tubes was set to 3. The reactions took place in the tube side where the catalysts were loaded, and cooling water in the shell side controlled the reaction temperature. The compact reactor (Fig. 2b) is a variation of the bayonet-type reactor, consisting of 3 tubes. In the outermost tube, the cooling water flowed to control the reaction temperature, while the catalysts were loaded in the middle tube. The feed gas flowed upward to absorb the heat generated from the catalytic bed after being injected at the bottom of the inner tube and then entered the catalytic bed to flow downward. The temperature of the catalytic bed was simultaneously controlled by preheating with cool feed gas in the inner tube and by cooling with coolant media (cooling water in this work) flowing in the outermost tube. The following built-in modules from the COMSOL Multiphysics were used to consider the mass, energy, and momentum balances, respectively, of the reactant flow channel: ‘‘Transport of Concentrated Species,” ‘‘Heat Transfer in Fluids,” and ‘‘Free and Porous Media Flow”. The reactor body, which was made of stainless steel (SUS 316L), was analyzed using the ‘‘Heat Transfer in Solids” module assuming the existence of heat conduction, that is, by excluding heat transfer by radiation. Detailed stationary equations for each module are presented in Table 2 and symbols can be found in the Nomenclature section. In order to calculate the profiles of CO conversion and temperature, Galerkin’s method [19] was applied, and free tetrahedral grids were defined. Balance equations were calculated using the parallel direct sparse solver interface (PARDISO), which applies parallel computing methods on shared-memory and distributedmemory multiprocessors [20], was used to improve the computation speed.
Fig. 3 shows the comparison of the conversions and temperature profile between experimental data and simulated results, along with the statistics, such as mean of absolute relative residuhP i N als (MARR), defined as M ¼ 100 yi;sim yi;exp =yi;exp =N i (N: number of experimental data), and relative standard deviation of individual errors (RSDE), defined as rhffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 i PN 100 =ðN 1Þ. Another design parameter in i yi;sim M the reactor model was the overall heat transfer coefficient between the catalytic bed and coolant shell, whose value was determined to be 70 W/(m2K) by minimizing the errors of conversion and temperature profiles in a balanced manner. It should be noticed that, there existed the trade-off between CO conversion and CO2/H2 conversions, as shown in Fig. 3; in other words, by increasing the errors of CO conversion, those for CO2 and H2 conversions could be decreased. Since the degree of CO conversion was higher than the others, more focus was made on the CO conversion, and thus, relative error of CO conversion was determined to be much lower than the others. In addition, although relative errors were different between the objective elements, their absolute errors which was defined as the absolute deviation of the simulated values from the experimental data in %P (percent point) were similar; the values of absolute errors for CO, CO2 and H2 conversions were 4.2, 5.4, and 4.9 %P, respectively. It is shown that the simulated results coincide with the measured data, validating the effectiveness of the developed model. Fig. 4 shows the profiles of CO conversion and temperature in the tubes of the conventional multi-tubular fixed-bed reactor. Simulation conditions were determined, such that the production rate of methanol was 50 kg/day; pressure and GHSV were specified to be 5 MPa and 5000 mL/(gcath), respectively, and the inlet and wall temperatures were set to be 150 and 240 °C, respectively. Feed composition was set to be H2:CO:CO2:N2 = 66.7:19.6:9.1:4.6 mol %. The physical properties specified in the present study were available from the process simulator and are provided in Table 3. Conversion increased along the reactor axis and reached 43.2% (averaged) at the reactor exit (peak conversion was 51.3%). It should be noted that, as shown in the cross-sectional view at z = 0.6 m, conversion at the center was lower than that close to the wall, due to high linear velocity at the center. The temperature profile along the center of the reactor axis showed an increase from the reactor inlet, and after reaching the maximum value (305.5 °C), it decreased to 288.1 °C at the reactor exit. Detailed CFD results showed a different temperature gradient pattern in the radial direction at different positions along the reactor axis. Near the inlet of the tube, the feed gas close to the wall was heated by heat transfer with the media in the shell, while the heat was not fully transferred to the center of the tube, resulting in a lower temperature at the center (convex down parabolic curve as shown in the left diagram in Fig. 4c). At z (packing depth) = 0.6 m, because the conversion increased from the center to the wall in the radial direction, the reaction rate also increased despite the decreased flow rate of the gas (the rate is determined as the multiplication of the conversion and flow rate), leading to an
5
M. Son et al. / International Journal of Heat and Mass Transfer 145 (2019) 118776 Table 2 Detailed stationary equations used in each part of the module. Name
Balance equations
Remarks
Transport of concentrated species
r ji þ r ðqxi uÞ ¼ Ri
Mass balance for the catalytic bed
where m rM n T rT ji ¼ qDm i rxi þ qxi Di M n þ Di T P 1 P 1 xk xi Dm ; Mn ¼ i ¼ ð1 xi Þ k–1 Dik i Mi (mixture-averaged diffusion model) 1=2
1 0:00143T 1:75 ðM 1 i þM k Þ Di;k ¼ 1=3 1=3 2 Pðmi þmk Þ P Ri ¼ stoichiometry r j MW i (rj: j-th reaction with j = CO, CO2, RWGS)
Heat transfer in fluids
qC P rT ¼ r ðjrT Þ þ Q
Energy balance for the catalytic bed
where P Q¼ Hj r j (heat of reaction j) Heat transfer in solids Free and porous media flow
0 ¼ r ðjrT Þ þ Q (with heat transfer by radiation negligible) h i 2l q l l u T eP ðu rÞ eP ¼ F jbr þ Q br u þ r PI þ eP ru þ ru 3eP ðr uÞI
r ðquÞ ¼ Q br
Energy balance for the reactor body Momentum balance for the catalytic bed
(Brinkman equation is for porous media region, while ‘‘Laminar flow” equation is used for free media region)
Inlet of catalytic bed Outlet of catalytic bed
Solid boundary condition
Boundary conditions
Remarks
u ¼ U 0 n P = 50 bar h i nT pI þ l ru þ ðruÞT 23 lðr uÞI n ¼ b p0
For momentum Constant pressure For momentum
b p 0 p0 , u t ¼ 0 n qDm i rwi ¼ 0 n ðjrT Þ ¼ 0
For mass For heat transfer
n ðjrT Þ ¼ 0
For heat transfer
MARR CO 7.4% CO2 33.5% H2 30.6%
(a) MARR = 3.2% RSDE = 1.4%
(b) Fig. 3. Comparison between simulated results and experimental data for (a) conversions and (b) temperature. Experimental conditions are given in the caption of Fig. 1.
increase in the temperature from the center. Then, the temperature decreased due to the heat transfer with the shell (binodal curve as shown in the middle diagram in Fig. 4c). In the later part of the reactor axis, the generated heat accumulated in the tube and the
temperature at the center reached maximum, while the temperature near the wall was close to the wall temperature (convex up parabolic curve as shown in the right diagram in Fig. 4c). As discussed above, the conventional tubular reactor showed the problem with the removal of heat around the center of the tube due to limited heat transfer capacity. To increase the heat transfer capacity, a compact reactor, which is a variation of the bayonet reactor, was suggested; the cooling is conducted by the cooling media in the shell as well as the cool feed gas in the inner tube (Fig. 2b). Fig. 5 shows the CFD results in the catalyst packing tube (middle tube), under the same simulation conditions in the conventional reactor except the feed gas temperature of 30 °C (cf. inlet temperature represents the one at the inlet of the catalyst packing tube, while the feed gas temperature denotes the one at the inlet of the inner tube). As for the conversion, the averaged value increased along the axis of the catalytic bed (averaged conversion at the exit was 48.4%, while the maximum value of local conversion was 49.8%). The radial gradient showed that the conversion at r = ri,middle is lower than that close to the outermost tube (ro,middle), owing to the temperature difference between the outermost and inner tube. This feature is maintained over the entire catalytic bed. It is worth noting that the radial gradient in the compact reactor was influenced more dominantly by the temperatures of inner and outermost tubes than the difference in linear velocities in the radial direction, while that in the conventional tube was affected by the linear velocity distribution. The temperature of the feed gas increased from 30 to approximately 130 °C (close to the inlet temperature in the conventional reactor) on account of the heat transfer from the catalytic bed. In the early part of the bed, the pattern of the radial temperature gradient was similar to that of the conversion gradient, while, in the middle of the bed (z = 1.1 m), the accumulated heat was removed by both the coolant in the outermost tube and the feed gas in
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M. Son et al. / International Journal of Heat and Mass Transfer 145 (2019) 118776
(a)
(b)
z = 0.3 m
z = 0.3 m
z = 0.6 m
z = 0.6 m
Cross-seconal view
z = 0.9 m
z = 0.9 m
(c)
Fig. 4. Profiles of (a) CO conversion and (b) temperature in the tubes of the conventional multi-tubular fixed-bed reactor along the axis of catalyst packing. Cross-sectional view for radial distribution was shown at z (packing depth) = 0.6 m. (c) Radial temperature gradient at z = 0.3 (left), 0.6 (middle), and 0.9 (right).
Table 3 Physical properties specified in the CFD modeling. Symbol
Unit
Value
l eP jbr j
Pas
1:613 10-2 1.397
CP
– m2 W/(mK) J/(kgK)
1:000 10-12 0.1205 2.525
the inner tube, leading to the maximum temperature between ri, middle and ro,middle. In addition to the introduction of the cool feed gas, the higher heat transfer capacity of the compact reactor compared with the conventional reactor is attributed to the larger heat transfer area of the compact reaction [13.1 m2 (compact) vs. 7.72 m2 (conventional)]. As a result, the peak temperature was 284 °C, compared to 305.5 °C in the conventional reactor. Overall, since the reaction was in the thermodynamic regime rather than the kinetic regime, the lower peak temperature of the compact reactor resulted in higher conversion and a larger methanol production rate than the conventional reactor for the same space velocity. Because the heat transfer capacity of the proposed reactor was larger than that of the conventional reactor, the space velocity was increased to evaluate the effects of increased heat generation on the conversion and temperature profiles. Fig. 6a shows the CO conversion of the compact reactor (sky-blue colored bar with the label of Comp-30) decreasing with increasing SV more significantly than
the conventional reactor does (gray colored bar with the label of Conventional in the legend). Meanwhile, CO2 conversion of the compact reactor increased with increasing SV, while the conventional reactor showed insignificant change in CO2 conversion (Fig. 6b). Because the amount of CO2 was smaller than CO, the effects of SV on H2 conversion were similar to that on CO conversions (Fig. 6c). This feature is attributable to the increased flow rate (amount) of the feed gas in the compact reactor leading to a greater absorption of the heat generated in the catalytic bed, thus decreasing the inlet temperature as a result of thermodynamic behavior (Fig. 6e). In the case of the conventional reactor, the inlet temperature was fixed for all SVs, and the peak temperature was almost same (the locations of peak temperature moved from the inlet to the outlet with increasing SV, data not shown). As a result, the methanol productivity of the conventional reactor increased because the degree of the increase in the flow rate (amount) was higher than that of the decrease in the conversion. In the opposite manner, the methanol production in the compact reactor decreased slightly with increasing SV. To increase the methanol productivity in the compact reactor, the inlet temperature was increased to 60 °C (orange-colored bar with the legend of Comp-60), and it was observed that the conversion increased compared to the case of Tfeed = 30 °C, except that the conversion for SV/SVref = 1.0 could not be calculated due to the fact that the increase in the peak temperature was too much. Further increase in the feed temperature increased the methanol productivity. Although the maximum value was obtained at the highest SV and feed temperature, a conversion too low under these condi-
M. Son et al. / International Journal of Heat and Mass Transfer 145 (2019) 118776
(a)
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(b)
Cross-seconal view
ro,middle
r=0 ro,inner ri,middle
Fig. 5. Profiles of (a) CO conversion, (b) temperature in the compact reactor proposed in this study. Cross-sectional view for radial distribution was shown at z (packing depth) = 1.1 m.
Fig. 6. Effects of the space velocity on (a) CO conversion, (b) CO2 conversion, (c) H2 conversion, (d) productivity, (e) inlet temperature, and (f) peak temperature, under different feed temperature of the compact reactor and at Tinlet = 150 °C in the conventional reactor. SVref was specified to be 5000 mL/(gcath). The labels ‘‘Conventional” and ‘‘Comp” in the legend represent the conventional and compact reactor, respectively, and the number denotes the value of the feed temperature in the compact reactor. The red dashed line corresponds to the conversion of the conventional reactor under the reference condition.
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M. Son et al. / International Journal of Heat and Mass Transfer 145 (2019) 118776
tions may increase the separation cost significantly. Therefore, the appropriate conditions might be SV/SVref = 2.0 and Tfeed = 90 °C, because it provides CO and H2 conversion similar to those under the reference conditions of the conventional reactor (cf. red dashed line in Fig. 6a and 6c), while the productivity is similar to the case of SV/SVref = 3.0 and Tfeed = 120 °C. To increase the productivity, in addition to the increase in SV, an increase in the diameter of the catalytic bed was considered. Fig. 7 shows the effects of the diameter on the performance of the compact reactor. It is shown that CO and H2 conversions decreased with increasing diameter with the SV fixed at 5000 mL/(gcath), while CO2 conversion increased slightly (Fig. 7a). This feature is attributable to the decrease in the inlet temperature when the flow rate was increased with increasing diameter for constant SV (Fig. 7b). However, despite the decreased conversion, the productivity increased owing to the increase in the feed gas. To better asses the reactor efficiency, the productivity per CO conversion was calculated as shown in Fig. 7b, and it was clearly shown that, the increase of the tube diameter enhanced the efficiency. Fig. 7c and 7d show the axial profiles of CO conversion and temperature for the conventional and compact reactors with different diameters. In the case of the conventional reactor, because the early
part of the catalytic bed played the role of preheating the feed gas, the reaction started at approximately z = 0.5 m. Meanwhile, although the inlet temperature of the compact reactor was lower than that of the conventional reactor, the reaction started at approximately z = 0.2 m because the temperature near the wall of the outermost tube was maintained close to the wall temperature (240 °C) (Fig. 7e). Because of the high heat transfer capacity of the compact reactor, peak temperatures in both axial and radial directions were maintained below that of the conventional reactor. Overall, if similar CO conversion is assumed, the diameter of the catalytic bed can be increased by 40% over that of the reference case while the productivity is increased approximately 1.7 times compared to the reference case (2 times compared to the conventional reactor). In the conventional reactor and the compact reactor with the reference diameter, the reaction reached equilibrium in the middle of the catalytic bed and was controlled thermodynamically thereafter (Fig. 7f). This indicates that the conversion was limited by the equilibrium, and the bed was not fully used. When the diameter was increased by 20%, the reaction reached equilibrium near the exit of the bed, and further increase maintained the reaction in the kinetic regime over the entire bed. This feature also supports the merits of the compact reactor.
(a)
(b)
(c)
(d)
(e)
(f) D/Dref = 1.0
D/Dref = 1.2
Equilibrium line
D/Dref = 1.4
D/Dref = 1.6
Fig. 7. Effects of the diameter on (a) conversions and productivity, (b) productivity per CO conversion, and peak and inlet temperature, axial profiles of (c) CO conversion and (d) temperature, (e) radial profiles of temperature at z (packing depth) = 1.8 m, and (f) temperature vs. conversion profiles, under the condition of Tfeed = 30 °C and SV = 5000 mL/(gcath). The legend ‘‘Conventional” and ‘‘Comp” represent the conventional and compact reactor, respectively, and the number denotes the ratio of D/Dref where Dref = 0.035 m.
M. Son et al. / International Journal of Heat and Mass Transfer 145 (2019) 118776
4. Conclusions The kinetic model was successfully validated by comparing simulated results with experimental data in a fixed-bed reactor at the mini-pilot scale. To explain how the capability of thermal control in a compact reactor was enhanced by the introduction of an additional heat transfer system (preheating of the feed gas in the inner tube), detailed profiles of mass, momentum, and heat were analyzed using the model. Further analysis on the effects of operating conditions and a design parameter for the structure showed that the productivity could be increased by a factor of two while the temperature was maintained below the peak temperature of the conventional reactor. In addition, due to the increased heat capacity, the diameter of the catalytic bed in the compact reactor could be increased, leading to the maximal utilization of the bed by maintaining the reaction in the kinetic regime. In conclusion, the CFD model in this work could be effectively used to analyze the physicochemical behavior of the advanced catalytic reactor and provide useful information on the determination of design parameters. Declaration of Competing Interest None. Acknowledgements This research was supported by the National Strategic ProjectCarbon Upcycling of the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (MSIT), the Ministry of Environment (ME), and the Ministry of Trade, Industry and Energy (MOTIE) (2017M3D8A2084259). Support was also received from the C1 Gas Refinery Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Science, ICT & Future Planning (2018M3D3A1A01055765) and from the Human Resources Development of the KETEP grant funded by the Ministry of Trade, Industry & Energy of the Korean Government (No. 20154010200820). References [1] M.E. Dry, The Fischer-Tropsch process: 1950–2000, Catal. Today 71 (2002) 227–241.
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