Article pubs.acs.org/IECR
Analysis of External and Internal Mass Transfer at Low Reynolds Numbers in a Multiple-Slit Packed Bed Microstructured Reactor for Synthesis of Methanol from Syngas Hamidreza Bakhtiary-Davijany,† Farbod Dadgar,‡ Fatemeh Hayer,† Xuyen Kim Phan,† Rune Myrstad,§ Hilde J. Venvik,*,† Peter Pfeifer,∥ and Anders Holmen† †
Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway School of Chemical Science and Engineering, KTH Royal Institute of Technology, SE-10044, Stockholm, Sweden § SINTEF Materials and Chemistry, NO-7465 Trondheim, Norway ∥ Institute for Micro Process Engineering, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, DE-76344 Eggenstein-Leopoldshafen, Germany ‡
ABSTRACT: The possibility of mass transfer limitations in an integrated micro packed bed reactor−heat exchanger (IMPBRHE) for methanol synthesis was experimentally investigated. Experiments were performed with three different particle size distributions (50−200 μm) of a Cu-based catalyst at 80 bar and 215−270 °C. Negligible effects of pore diffusion limitations on the performance of the reactor under methanol synthesis conditions for catalyst particle diameters up to 125 μm were found. Due to a very low Reynolds numbers (∼1) and dominance of molecular diffusion, variation of the total pressure was applied as a suitable technique to alter the diffusivities of reactants in the gas mixture by dilution, while keeping the reactant flow and partial pressure constant. No significant change in the CO conversion was observed in the temperature range 235−255 °C, pressure range 50−90 bar, and for reactant contact times of 105−308 ms·g/mL. The same procedure was applied to a laboratory fixed bed reactor with similar results. Possible heat transfer effects associated with the dilution were shown to be negligible. We therefore conclude that both reactor systems operate in the absence of external mass transfer limitations.
■
INTRODUCTION Simultaneous occurrence of chemical reactions and physical phenomena such as mass transfer is a common case in heterogeneous catalysis. It usually creates a complicated picture which should be treated carefully in order to evaluate the performance of the process under study. It applies both when measuring intrinsic reaction rates and during optimization of industrial reactors.1−5 Mass transfer is often divided into two categories: external mass transfer or film diffusion, which includes transfer of reactants from the bulk of the gas phase to the surface of catalyst, and internal mass transfer or pore diffusion, which takes into account the intraparticle transport within the catalyst pores. Since the net rate of a chemical reaction could be strongly affected by mass transfer limitations, their minimization is important to the design and operation of chemical processes. Microstructured reactors are known for superior heat and mass transfer properties, and are hence potentially better candidates for kinetic investigations than conventional fixed beds.2−4 They are also claimed to perform efficiently in compact production of synthetic fuels and chemicals because of the elimination of mass and heat transfer limitations.6−8 This should, however, be experimentally verified via appropriate methods. Depending on the characteristics of the reactor under study, the type of active metal and the catalyst loading mode into the channels (wall-coated or packed), or even reaction conditions such as temperature, the dominant mechanism of mass transfer could be different. This means that each case has to be treated specifically. As will be further discussed below, the © 2012 American Chemical Society
established methodologies suggested in the literature are not necessarily applicable. The standard method for the examination of the external mass transfer limitation in packed beds working in a turbulent flow regime (10 < Re < 2000) is the change of the gas flow rate at constant (reactant) residence time through varying the catalyst mass or bed length. According to film theory, the bulk phase is assumed to be perfectly mixed and any possible resistance would occur in the stagnant layer over the outer surface of the catalyst particles.1 Within this layer, the mass transfer mainly proceeds by diffusion, whereas convection dominates in the bulk of gas. If the flow velocity increases, the thickness of the boundary layer is reduced because of the increased turbulence, and external mass transfer is consequently enhanced. Alternatively, varying the particle size can also be applied, but it is often hard to achieve a well-defined particle size distribution.9 In addition, possible effects of pore diffusion could also play a role. These issues make the particle size variation to be a less practical and conclusive option. In wall-coated microchannels, the flow regime is laminar with typical Reynolds numbers of about 1 and molecular diffusion normal to the channel walls is the dominant mass transfer mechanism. However, the stagnant film concept is in principle not applicable to laminar flow,9−11 and hence test methods Received: Revised: Accepted: Published: 13574
January 5, 2012 August 23, 2012 October 1, 2012 October 1, 2012 dx.doi.org/10.1021/ie300039a | Ind. Eng. Chem. Res. 2012, 51, 13574−13579
Industrial & Engineering Chemistry Research
Article
other than flow variation should be used. Different methods for determining mass transfer limitations in wall-coated microchannel reactors were recently reviewed and discussed by Walter et al.11 Variation of the total pressure and change of inert gas type have been suggested as methods for examination of external mass transfer limitations, and were tested for steam reforming of methanol in a wall-coated microchannel reactor.9 The possibility of accompanying internal diffusion effects has to be carefully considered when applying these strategies. Also for a packed bed microchannel configuration, such as the one used in this study, is the situation different from that of commercial packed beds subject to turbulent flow regimes. Although the flow resistance by the catalyst particles as well as the formation of a boundary layer may theoretically apply, the flow regime may be different. From the conditions, the average Reynolds numbers in this study can be estimated to ∼1. This implies that the mixing effects associated with turbulent flows are negligible and flow velocity variation cannot be applied. Keeping the channel dimensions fixed, the other possible factor for evaluating mass transfer could be manipulation of the diffusivities. The molecular diffusivity is a function of pressure and temperature as well as the composition of the gas. As both reaction kinetics and diffusivity are affected, changing the temperature will not produce explicit conclusions on the mass transfer. At high pressure, however, one way to change the diffusivity without affecting kinetics is to increase the concentration of an inert gas while maintaining the inlet partial pressure of reactants by increasing the total pressure as discussed above. The methanol synthesis is an exothermic reaction limited by equilibrium. The reactions involved include the water gas shift (1) and hydrogenations of CO (2) and CO2 (3), of which only two are independent reactions: CO + H 2O ↔ H 2 + CO2
(1)
CO + 2H 2 ↔ CH3OH
(2)
CO2 + 3H 2 ↔ CH3OH + H 2O
(3)
work in a category that makes it reasonable to carefully assess the mass transfer experimentally. Graaf et al.12 examined the internal mass transport limitations experimentally in low-pressure (15−50 bar) methanol synthesis using an industrial Cu/ZnO/Al2O3 catalyst. They concluded that the observed reaction rates are strongly affected for large particle diameters (4.2 mm). For smaller particles (150−200 μm), they corrected for the contribution of internal diffusion limitations to their kinetic rate expressions for the methanol synthesis.16 Later on, Lommerts et al.5 applied a more elaborate theoretical approach to investigate the diffusion limitation effects, but reached conclusions similar to both the experimental investigations and the Thiele modulus concept on the presence of pore diffusion limitations in the methanol synthesis. The extent of pore diffusion limitations is a factor of the particle size and structure, catalyst activity (time on stream), syngas composition, temperature, and pressure. Under commercial methanol synthesis conditions, however, diffusion limitations become considerable at above approximately 510 K and the effectiveness factor can be as low as 0.4 under unfavorable conditions.17 For the frequently applied catalyst pellets with 5 mm particle diameter, Seyfert and Luft18 reported an effectiveness factor of 0.75 at 538 K and 80 bar. We have previously studied the heat transfer properties, pressure drop, and fluid flow characteristics19 as well as reaction performance20 of our integrated micro packed bed reactor− heat exchanger (IMPBRHE) in the synthesis of methanol over copper-based catalysts. In this work we investigate the possibility of external mass transfer limitations in the IMPBRHE as well as a conventional tubular packed bed reactor under fully laminar conditions. Changes in diffusivity were generated through dilution by inert gases combined with adjustment of the total pressure to keep reactant flow and partial pressure constant. To eliminate contributions from pore diffusion limitations in the IMPBRHE, methanol synthesis experiments were also performed with varying catalyst particle size.
■
MATERIALS AND METHODS The experiments were carried out in a setup consisting of a reactant feed system with mass flow controllers, two parallel reactors, and product analysis. The stainless steel IMPBRHE was made by the Institute for Micro Process Engineering (IMVT) at the Karlsruhe Institute of Technology (KIT). It consists of eight parallel slits of 800 μm × 8 mm cross section and 60 mm length equipped with hexagonally arranged pillars. Each reaction slit is sandwiched between two cross-flow oil slits. More detailed information on the IMPBRHE fabrication and geometry has been published elsewhere.19 A high temperature oil thermostat (Julabo HT30) was used to maintain the reaction temperature. Temperatures were measured on the surface of the outer slit wall. The stainless steel fixed bed reactor (FBR) was 1/2 in. in diameter, and the catalyst bed temperature was measured using a movable thermocouple along the reactor axis. The FBR temperature was maintained by an electrical furnace regulated against a thermocouple placed on the outer reactor wall. In the external mass transfer experiments, both the IMPBRHE and the FBR were packed with a powdered Cu/ ZnO/support commercial catalyst with a particle diameter of 50−80 μm. The pore diffusion limitation experiments in the IMPBRHE were carried out using a homemade Cu/ZnO/ Al2O3 catalyst, synthesized by a standard coprecipitation
In large scale methanol synthesis, pore diffusion is often a limiting phenomenon due to the large catalyst pellet size, which decreases the reactor productivity12 while at the same time limiting the heat release from the reactions to control the reactor temperature. Lommerts et al. showed that an increase in particle diameter from 1 to 5 mm could result in a 40% reduction in the rate of methanol formation.5 On the contrary, because of high gas velocities and dominance of turbulent flow, i.e., ideal mixing, film diffusion is unlikely to impose restrictions.1,13 Aiming at experimental verification of pore diffusion limitations in the methanol synthesis, Graaf et al.12 assumed the absence of film diffusion limitation in a fixed bed reactor with a particle size of 150−200 μm. They rationalized this assumption by analyzing the lower limit of the Sherwood number for the relevant Reynolds number range to find negligible concentration (and temperature) differences between the bulk of the gas and the catalyst surface. Furthermore, most criteria in the literature are typically deduced from single, first order, and irreversible reactions.1,14,15 Application of these criteria to a system of at least two parallel reversible reactions is difficult and imposes several assumptions and simplifications. Moreover, the specific slit geometry with pillar structures as well as the smaller average particle size and low Reynolds number (both about half the value of Graaf et al.12) places our 13575
dx.doi.org/10.1021/ie300039a | Ind. Eng. Chem. Res. 2012, 51, 13574−13579
Industrial & Engineering Chemistry Research
Article
method. Metal solutions of Cu(NO 3 ) 2 ·2.5H 2 O, Zn(NO3)2·6H2O, and Al(NO3)3·9H2O as well as sodium carbonate and sodium acetate solutions were prepared separately using deionized water. Metals and sodium carbonate solutions were simultaneously added to the sodium acetate solution while maintaining stirring, 50 °C temperature, and pH 7. The precipitate was then separated and thoroughly washed with deionized water to remove possible remaining sodium, further dried in air at 110 °C, and then calcined at 400 °C for 2 h. The resulting catalyst was sieved to three different particle size fractions (50−80, 80−125, and 125−200 μm). The procedures for catalyst loading into the IMPBRHE and in situ reduction have been described elsewhere.19 Due to a relatively long time required for catalyst loading, leak detection, and reduction procedures, the data points for each reactor were taken using a single batch of catalyst but after ensuring similar activity levels as previous experiments with the same catalyst.19,20 The feed and product gases were analyzed by gas chromatography (Agilent 5890 GC) in online mode, while the liquid products were analyzed offline. Premixed synthesis gas containing H2/CO/CO2/N2 (65/25/ 5/5) was introduced after the reduction and pressure buildup to the desired pressure level (50 or 80 bar) was performed. Either helium or argon was added as dilutant, and the total pressure was adjusted to maintain the inlet partial pressure of the premixed syngas constant, i.e., equal to 50 or 80 bar in the undiluted case. Three temperature levels (235, 245, and 255 °C) and three different contact times (105, 160, and 308 ms·g/ mL) were applied for each syngas pressure. After adjusting the experimental conditions (flow/T/P), 3−5 h was allowed for stabilization. The contact time was defined as the ratio of catalyst mass to the premixed syngas volumetric flow rate at standard temperature and pressure; i.e., the mass flow rate of reaction gas was the same with and without the Ar/He dilution.
conversion values displayed in the rest of the plots have therefore been compensated for the extent of deactivation at the point of measurement, using either linear or exponential fits, depending on the deactivation pattern. The investigation of phenomena contributing to catalyst deactivation is in progress and will be discussed elsewhere. Figure 2 has been included to indicate the equilibrium conversion as a function of temperature for the two syngas
Figure 2. Calculated (HYSYS estimate) equilibrium CO conversion against temperature at two different operating pressures for a feed gas composition of H2/CO/CO2/N2 = 65/25/5/5.
pressures applied experimentally. The conversion values at 255 °C, the highest temperature applied in the IMPBHRE, are approximately 54 and 66% for the 50 and 80 bar syngas pressures, respectively. As shown below, a few data points for the highest temperatures and contact times applied approach the equilibrium conversion, but most data are obtained under conditions well away from equilibrium. In Figure 3, the CO conversion is shown against the IMPBRHE slit temperature at a contact time of 172 ms·g/mL
■
RESULTS The observed fluctuations in all measured conversions were found to be within an acceptable reproducibility window (±10%). Figure 1 shows the relative CO conversion against time on stream for two different runs using the commercial catalyst. A slow continuous decrease in the catalyst activity was observed during the approximately 230 h on stream. The
Figure 3. CO conversion vs slit temperature in the IMPBRHE for three different catalyst particle size ranges under syngas feed (H2/CO/ CO2/N2 = 65/25/5/5) at 172 ms·g/mL contact time and 80 bar.
and 80 bar. All three particle sizes give comparable CO conversions, but that of the largest particle size (125−200 μm) is slightly lower than those of the two smaller particle size ranges (50−80 and 80−125 μm), for which it is hard to distinguish any difference.
Figure 1. Relative CO conversion against time on stream for the Cu/ ZnO-based commercial catalyst in the IMPBRHE for two different experimental runs under feed gas composition H2/CO/CO2/N2 = 65/ 25/5/5 at 80 bar and 255 °C. 13576
dx.doi.org/10.1021/ie300039a | Ind. Eng. Chem. Res. 2012, 51, 13574−13579
Industrial & Engineering Chemistry Research
Article
Figure 4 compares the conversion of carbon monoxide at 50 bar of premixed synthesis gas feed in the IMPBRHE at different
Figure 6. CO conversion vs peak temperature in the laboratory FBR for diluted (open symbols) and undiluted (filled symbols) syngas feed at 80 bar (H2/CO/CO2/N2 = 65/25/5/5). Dilution by inert gas (Ar) was accompanied by a pressure increase to maintain constant reactant contact time (160 ms·g/mL). Figure 4. CO conversion vs slit temperature in the IMPBRHE for diluted (open symbols) and undiluted (filled symbols) syngas feed at 50 bar (H2/CO/CO2/N2 = 65/25/5/5). Dilution by inert gas (Ar or He) was accompanied by a pressure increase to maintain constant reactant contact times (160 or 308 ms·g/mL).
temperatures for the undiluted (filled symbols) and diluted (open symbols) cases. Using argon or helium as dilutant, the total pressure was increased to 56.4 or 90 bar, respectively. The conversion levels obtained for two different residence times are practically independent of the difference in reactant diffusivity introduced by the dilution. Figure 5 presents similar data for
Figure 7. Temperature profile along the laboratory FBR axis at 235 °C peak temperature for diluted (open symbols) and undiluted (filled symbols) syngas feed at 80 bar (H2/CO/CO2/N2 = 65/25/5/5). Dilution by inert gas (Ar) was accompanied by a pressure increase to maintain constant reactant contact time (160 ms·g/mL).
peak temperature of 235 °C are shown. The nonisothermal behavior of the two cases seems to be more or less identical.
■
DISCUSSION Concerning possible pore diffusion limitations, these are normally considered less likely the smaller the particle size. However, for particles in the range 150−200 μm, a slight influence on the methanol synthesis reaction kinetics was reported by Graaf et al.5,12 This is in agreement with our experimental data, which show negligible effects of pore diffusion limitations for particles less than 125 μm on the performance of the IMPBRHE under the conditions applied. Such limitations cannot, however, be completely excluded for the largest particle size fraction applied upon approaching 270 °C. As mentioned, the experiments were designed to vary the diffusion coefficients. Lommerts et al.5 compared estimated binary diffusion coefficients with experimental values for relevant pairs reported by Marrero and Mason.21 The outcome was that the equation suggested by Fuller et al.22 produces a slightly better prediction than the one by Chapman and Enskog23 at high pressures, and was hence applied in our calculations. The calculations indicate that CO2 has the lowest diffusivity and should be a limiting component if diffusion
Figure 5. CO conversion vs slit temperature in the IMPBRHE for diluted (open symbols) and undiluted (filled symbols) syngas feed at 80 bar (H2/CO/CO2/N2 = 65/25/5/5). Dilution by inert gas (Ar) was accompanied by a pressure increase to maintain constant reactant contact times (105, 160, or 308 ms·g/mL).
the premixed syngas at 80 bar, without and with dilution by Ar and with increase of the total pressure to 90.2 bar. Again, the conversion remainswithin experimental errorconstant upon manipulating the gas phase transport for three different contact times. Figure 6 shows the conversion of CO against the peak temperature in the fixed bed reactor for 80 bar of premixed syngas, undiluted as well as under Ar dilution and total pressure elevation to 90.2 bar. The reactant conversion is unaffected by changes in reactant transport also in this case. In Figure 7, the temperature profiles along the axis of the fixed bed reactor at a 13577
dx.doi.org/10.1021/ie300039a | Ind. Eng. Chem. Res. 2012, 51, 13574−13579
Industrial & Engineering Chemistry Research
Article
mixture are unlikely to occur in the IMPBRHE, but should possibly be checked more carefully in the FBR with its poorer heat transfer capability.
limitations exist. According to mechanistic discussions in the literature, CO2 is also the source of carbon during methanol formation.16,24 However, the fraction of CO2 in the feed gas is low and it is to a large extent formed via the water gas shift reaction, meaning that the supply from the gas phase may not be the main source of CO2 under steady state. The diffusion and supply of CO to the surface may be critical at high conversion, and the diffusion coefficient of CO in the gas mixture was therefore chosen in our calculations. Figure 8
■
CONCLUSION Possible internal and external mass transfer limitations in an integrated micro packed bed reactor−heat exchanger (IMPBRHE) for the synthesis of methanol from syngas were experimentally investigated. The IMPBRHE was found to operate free of pore diffusion limitations, at least for catalyst particle sizes below 125 μm. Once this was established, changes in diffusivity through both variation of the inert gas partial pressure and change of the inert gas type could applied to investigate the existence of external mass transfer limitations under fully laminar flow conditions (Re ∼ 1). The reactor performance remained unchanged upon a significant decrease in the CO diffusion coefficient over a wide range of operating temperatures and pressures. A similar behavior was observed in a laboratory scale fixed bed reactor. Hence, it may be concluded that external mass transfer limitations exist neither in the IMPBRHE nor in the FBR under relevant conditions. For the purpose of compact production of methanol, the results of this study show that the productivity of the IMPBRHE is not affected by mass transfer limitations, although very low Reynolds numbers are involved.
Figure 8. Calculated CO diffusivities in undiluted and diluted experiments.
■ ■
compares the calculated CO diffusivity values at 255 °C between the reference conditions of synthesis gas mixtures at different pressures (different CO partial pressures) and the corresponding Ar/He dilution experiments with total pressure increase. A reduction of ∼35% in the estimated CO diffusivity values was obtained by Ar or He dilution of 50 bar of premixed syngas to 56.4 or 90.0 bar total pressure, respectively, as well as Ar dilution of 80 bar of premixed syngas to 90.2 bar total pressure. In the case of severe diffusion limitations, the measured conversion levels (i.e., observed reaction rates) should drop accordingly with a similar ratio as the diffusion coefficient. The conditions applied in the IMPBRHE fall well within the window of “real” operating conditions of the methanol synthesis. Short residence times down to 105 ms·g/mL ensure that a wide range of flow velocities has been considered. Possible heat transport effects due to the dilution and pressure increase could be associated with the method used here. Calculations show negligible differences between the thermal conductivity of the gas mixtures under the different conditions, 0.158 W/(m·K) for the premixed syngas at 80 bar and 0.1603 W/(m·K) under dilution by argon and pressure elevation to 90.2 bar. However, a somewhat higher total heat storage capacity exists for the diluted feed due to the higher total mass flow. The FBR temperature profiles shown in Figure 7 do not indicate significant effects on thermal behavior from the dilution−pressure increase procedure. Interaction of the dilutant gas with the catalyst surface may also affect heat transfer, and in principle, possible cooling effects from the reaction gas mixture may affect the conversion and temperature distribution results. Concerning the IMPBRHE, the authors recently investigated its key characteristics in terms of thermal behavior.19 Superior heat removal capability of the IMPBRHE under realistic methanol synthesis operating conditions and regardless of the amount of heat released by the reaction was found from both experimental and modeling results. Therefore, effects on the productivity due to cooling by the reaction gas
AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS This publication forms a part of the “Remote Gas” project, performed under the strategic Norwegian Research program PETROMAKS. The authors acknowledge the partners, Statoil, UOP, Bayerngas Norge, Aker Solutions, DNV, and the Research Council of Norway (168223/S30), for support. H.J.V. also acknowledges the financing by Statoil ASA through the Gas Technology Centre (NTNU-SINTEF) (www.ntnu.no/ gass/). The authors finally acknowledge UOP for providing the synthesis procedure for the Cu/ZnO/Al2O3 catalyst.
■
REFERENCES
(1) Satterfield, C. N. Mass Transfer in Heterogeneous Catalysis; MIT Press: Cambridge, MA, 1969. (2) Görke, O.; Pfeifer, P.; Schubert, K. Kinetic study of ethanol reforming in a microreactor. Appl. Catal., A: Gen. 2009, 360, 232. (3) Hessel, V.; Hardt, S.; Lowe, H. Chemical Micro Process Engineering: Fundamentals, Modelling and Reactions; Wiley-VCH Verlag: Weinheim, Germany, 2004. (4) Schubert, K.; Bier, W.; Brandner, J.; Fichtner, M.; Franz, C.; Linder, G. Presented at the 2nd International Conference on Microreaction Technology, New Orleans, LA, March 8−12, 1998. (5) Lommerts, B. J.; Graaf, G. H.; Beenackers, A. A. C. M. Mathematical modeling of internal mass transport limitations in methanol synthesis. Chem. Eng. Sci. 2000, 55, 5589. (6) Jarosch, K. T.; Tonkovich, A. L. Y.; Perry, S. T.; Kuhlmann, D.; Wang, Y. In Microreactor Technology and Process Intensification; ACS Symposium Series 914; American Chemical Society: Washington, DC, 2005. (7) Myrstad, R.; Eri, S.; Pfeifer, P.; Rytter, E.; Holmen, A. Fischer− Tropsch synthesis in a microstructured reactor. Catal. Today 2009, 147, S301. (8) Pfeifer, P.; Haas-Santo, K.; Görke, O. Application and Operation of Microreactors for Fuel Conversion. In Micro Process Engineering: A 13578
dx.doi.org/10.1021/ie300039a | Ind. Eng. Chem. Res. 2012, 51, 13574−13579
Industrial & Engineering Chemistry Research
Article
Comprehensive Handbook, 1st ed.; Hessel, V., Renken, A., Schouten, J. C., Yoshida, J., Eds.; Wiley-VCH Verlag: Weinheim, Germany, 2009; Vol. 2. Devices, Reactions and Applications. (9) Kölbl, A.; Pfeifer, P.; Fichtner, M.; Kraut, M.; Schubert, K.; Liauw, M. A.; Emig, G. Examination of External Mass Transport in a Microchannel Reactor by Pressure Variation. Chem. Eng. Technol. 2004, 27, 671. (10) Hidajat, K.; Aracil, D. J.; Carberry, J. J.; Kenney, C. N. Interphase fluid-particle mass transport at low Reynolds numbers. Catal. Lett. 1995, 30, 213. (11) Walter, S.; Malmberg, S.; Schmidt, B.; Liauw, M. A. Mass transfer limitations in microchannel reactors. Catal. Today 2005, 110, 15. (12) Graaf, G. H.; Scholtens, H.; Stamhuis, E. J.; Beenackers, A. A. C. M. Intra-particle diffusion limitations in low-pressure methanol synthesis. Chem. Eng. Sci. 1990, 45, 773. (13) Lee, S. Methanol Synthesis Technology, 1st ed.; CRC Press Inc.: Boca Raton, FL, 1990. (14) Ertl, G.; Knozinger, H.; Schuth, F.; Weitkamp, J. Handbook of Heterogenous Catalysis, 2nd ed.; Wiley-VCH: Weinheim, Germany, 2008. (15) Mears, D. E. Tests for Transport Limitations in Experimental Catalytic Reactors. Ind. Eng. Chem. Process Des. Dev. 1971, 10, 541. (16) Graaf, G. H.; Stamhuis, E. J.; Beenackers, A. A. C. M. Kinetics of low-pressure methanol synthesis. Chem. Eng. Sci. 1988, 43, 3185. (17) Hansen, J. B.; Højlund Nielsen, P. E. Methanol Synthesis. In Handbook of Heterogeneous Catalysis; Wiley-VCH: Weinheim, Germany, 2008. (18) Seyfert, W.; Luft, G. Untersuchungen zur Methanolsynthese im Mitteldruckbereich. Chem. Ing. Tech. 1985, 57. (19) Bakhtiary-Davijany, H.; Hayer, F.; Phan, X. K.; Myrstad, R.; Venvik, H. J.; Pfeifer, P.; Holmen, A. Characteristics of an Integrated Micro Packed Bed Reactor-Heat Exchanger for methanol synthesis from syngas. Chem. Eng. J. (Amsterdam, Neth.) 2011, 167, 496. (20) Bakhtiary-Davijany, H.; Hayer, F.; Kim, P. X.; Myrstad, R.; Pfeifer, P.; Venvik, H. J.; Holmen, A. Performance of a multi-slit packed bed microstructured reactor in the synthesis of methanol: Comparison with a laboratory fixed-bed reactor. Chem. Eng. Sci. 2011, 66, 6350. (21) Marrero, T. R.; Mason, E. A. Gaseous diffusion coefficients. J. Phys. Chem. Ref. Data 1972, 1, 3. (22) Fuller, E. N.; Schettler, P. D.; Giddings, J. C. A new method for prediction of binary gas phase diffusion coefficients. Ind. Eng. Chem. 1966, 58, 18. (23) Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1954. (24) Bussche, K. M. V.; Froment, G. F. A Steady-State Kinetic Model for Methanol Synthesis and the Water Gas Shift Reaction on a Commercial Cu/ZnO/Al2O3Catalyst. J. Catal. 1996, 161, 1.
13579
dx.doi.org/10.1021/ie300039a | Ind. Eng. Chem. Res. 2012, 51, 13574−13579
