Article pubs.acs.org/IECR
Multiscale and Multiphase Model of Fixed Bed Reactors for Fischer− Tropsch Synthesis: Intensification Possibilities Study Marko Stamenić,† Vladimir Dikić,† Miloš Mandić,† Branislav Todić,‡ Dragomir B. Bukur,‡,§ and Nikola M. Nikačević*,† †
Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, Belgrade 11000, Serbia Chemical Engineering Program, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar § Artie McFerrin Department of Chemical Engineering, Texas A&M University, MS 3122, College Station, Texas 77843-3122, United States ‡
S Supporting Information *
ABSTRACT: A multiphase fixed-bed reactor (FBR) model for Fischer−Tropsch Synthesis has been developed. A high level of details is considered for description of the phenomena on the reactor and particle scale. Detailed kinetics is used, with parameters estimated from experiments with a cobalt-based catalyst. Model robustness has been validated using literature data. Performance analysis was made for a conventional scale FBR with egg-shell distribution of catalyst and a millimeter-scale FBR with small particles and uniform distribution. In both cases, diffusion limitations are almost eliminated due to use of small diffusion lengths. For similar qualitative results, a milli-scaled design would result in a significantly lower reactor volume, but the capital costs could be high due to large wall area and a vast number of tubes. Heat removal is efficient in both cases, and pressure drop in the milliscale reactor is low due to the use of a shorter bed and lower velocity.
1. INTRODUCTION Fischer−Tropsch synthesis (FTS) is a catalytic reaction in which synthesis gas, a mixture of carbon monoxide (CO) and hydrogen (H2), is converted into a range of hydrocarbons, mainly alkanes and alkenes, which can further be processed to fuels and/or value-added chemicals. In its almost one hundred year history FTS has been conducted mainly at two temperature ranges: from 320 to 350 °C known as high temperature FTS (HTFTS), and from 200 to 250 °C known as low temperature FTS (LTFTS).1−3 Four types of reactors have been used in commercial processing: (1) circulating fluidized bed reactor; (2) bubbling fluidized bed reactor; (3) tubular fixed bed reactor and (4) slurry phase reactor, all of which have their own advantages and drawbacks.1,4,5 Catalysts based on cobalt (Co) or iron (Fe) have mostly been used for FTS. Since the subject of this article is modeling and simulation study of a multitubular fixed bed reactor with Co catalyst for LTFTS, further attention will be focused on this type of reactor. The main advantages of using a fixed bed reactor (FBR) for LTFTS are easy separation of the products from the catalyst © XXXX American Chemical Society
and relatively easy scale-up, while the main drawbacks are associated with high pressure drop and heat removal, the latter being important since FTS is a highly exothermic reaction. The proper choice of design and operating parameters should lead to achieving high productivity and selectivity of the desired products, and at the same time minimizing the aforementioned negative effects. Having in mind that LTFTS in a FBR is a gas−liquid−solid operation involving hundreds of species it is obvious that modeling of such system is a challenging task. The phenomena one has to take into account are mass, heat and momentum transfer on the reactor and catalyst particle scale, phase equilibrium, and detailed kinetics of the process. In such a complex system one needs carefully to select a desired level of Received: Revised: Accepted: Published: A
June 15, 2017 August 11, 2017 August 15, 2017 August 15, 2017 DOI: 10.1021/acs.iecr.7b02467 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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good agreement, which justified the use of such a detailed model. Nevertheless, several simplifications were used in this study; that is, external resistance to mass and heat transfer was neglected, as well as the existence of liquid phase outside the catalyst particle. Especially the latter one is potentially significant as the liquid inside the reactor can influence two very important features of the FBR: heat transfer to the reactor wall and pressure drop. Although the liquid phase flow was mainly disregarded in models of the FBRs for FTS, in some studies the presence of liquid phase was taken into account through correlations for heat transfer coefficient and/or pressure drop.12,16,23,24 Brunner et al.16 showed that the liquid inside the reactor significantly contributes to the overall heat transfer coefficient. The same authors studied three different correlations for the friction factor, used in an Ergun-like pressure drop expression, and found that the Tallmadge’s correlation26 gives the most reliable results over the range of operating conditions which was investigated. An alternative approach for accounting for the presence of liquid phase was proposed by Lee et al.20 The authors developed a 2D pseudohomogeneous model that considers continuity and momentum equations for the gas−liquid mixture on the reactor scale. The mixture properties were calculated based on the volume fraction of each phase in the mixture. The authors concluded that a more comprehensive model, which takes into account the existence of the liquid phase inside the reactor, would be more useful in the reactor design assessment. External (fluid-particle) resistance to mass and heat transfer was generally neglected in previous studies. An exception to this trend can be found in the early work of Atwood and Bennett,6 and, more recently, in the study of Yang et al.27 The authors used a simple reaction rate expression with catalyst effectiveness factor, in a 1D pseudohomogeneous model, neglecting the existence of the liquid phase. Simple correlations based on particle Reynolds number were used to calculate fluid−particle transfer coefficients. Results from these studies showed that for low values of gas velocities inside the FBR considerable difference can occur between the temperature at the particle surface and that of the bulk fluid,6 and that external mass transfer limitations can influence the product slate.27 Requirements regarding heat removal and pressure drop imply that the reactor tube diameter should be in the range of 2−5 cm, while the catalyst particle diameter should be in the range of 1−3 mm.1 Several experimental studies showed that under typical industrial conditions diffusion limitations severely influence performance of the catalyst.28,29 Post et al.28 demonstrated that the CO conversion decreases significantly with increase in particle size, due to limited mobility of reactant molecules inside the catalyst pores. Iglesia et al.29,30 considered the influence of diffusion limitations on the selectivity of FTS. On the basis of their experimental work a method was developed for preparation of an egg-shell type catalyst, with a thin layer of active material near the surface of the particle that would minimize the observed negative effects of diffusion limitations, but fulfill the requirements regarding pressure drop. Several more recent experimental and modeling studies confirmed the benefits of using the egg-shell type catalyst distribution.31−33 A negative impact of diffusion limitations on catalyst selectivity is even more pronounced with the use of state-of-the-art modern catalysts, as shown in the work of Mandic et al.34 The authors developed a single particle model
details in a model, in order to obtain reliable simulation results that may be used for analysis, design, and further optimization. A number of studies in the literature deal with the modeling of FBRs for FTS.6−24 In the majority of these studies a pseudohomogeneous model was used, meaning that the existence of concentration and temperature gradients inside the catalyst particle was neglected. In several of these studies, diffusion limitations were accounted for via the use of an effectiveness factor (η) calculated through Thiele module (φ), using simple kinetics for CO consumption.6,11,15−18 All results showed that, under typical FTS conditions, the value of η can be significantly lower than 1, implying the negative influence of diffusion limitations. However, since detailed kinetics of FTS was not accounted for, these studies did not consider the effect of diffusion limitations on the product slate (the composition of the outlet stream). Since heat removal is an important aspect in the design of FBRs for FTS, in several studies the authors employed 2D pseudohomogeneous models in order to account for radial gradients of concentrations and, especially, temperature inside the reactor.7,10,11,14,16−18,20 These studies were aimed to give better representation of temperature profiles inside the reactor, which could be used in the assessment of hot spot formation and/or temperature runaway. Although some authors10,11 reported differences in results when applying a 1D and 2D approach, a general conclusion about the advantages of applying a 2D approach cannot be drawn from these studies, as many factors influence the temperature profile inside the reactor. Generally, the use of 1D models could be appropriate for narrower tubes, while for the ones above 5 cm, a 2D model should be the choice.1 In contrast to the above-mentioned studies, several authors utilized heterogeneous models for modeling of FBR for FTS,9,21,23 that is, concentration and temperature profiles inside the catalyst particle were accounted for. Ermolaev et al.21 used a 2D heterogeneous model combined with simple power law kinetics to evaluate the performance of a FBR in terms of CO conversion, C5+ productivity, temperature profiles and hot spot formation. Results showed that the model overpredicts CO conversion at lower GHSVs, which was attributed to neglecting the resistance to mass transfer in the liquid film surrounding the catalyst particle. A more comprehensive approach was presented in the recent study of Ghouri et al.23 in which detailed kinetics developed by Todic et al.25 for a highly active Co catalyst was used. The particle diffusion model was employed in order to obtain temperature profiles and concentration profiles for reactants inside the catalyst particle. Perhaps the most comprehensive study so far, regarding the complexity of the mathematical description applied, was done by Wang et al.9 The authors developed a 1D heterogeneous model, including detailed kinetics model for Fe-catalyst accounting for hydrocarbons up to C50. The catalyst particle was assumed to be filled with wax (liquid products of FTS) and Fick’s law was employed to describe the diffusion through the catalyst particle. Modified Soave−Redlich−Kwang (SRK) equation of state was used to describe equilibrium between concentrations in the bulk-gas and the liquid at the catalyst surface. The authors highlighted the need to establish an appropriate procedure for solving model equations having such detailed representation of the process. The influence of several parameters (tube diameter, recycle ratio, cooling fluid temperature and inlet pressure) on the performance of FBR was analyzed and compared with experimental data, resulting in a B
DOI: 10.1021/acs.iecr.7b02467 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research to study the effects of particle shape, size, catalyst distribution, and process conditions on catalyst effectiveness factor and methane selectivity inside a particle. Results stressed the benefits of using the egg-shell catalyst distribution with catalyst layer thickness up to 0.13 mm or lower, and H2/CO molar ratio lower than stoichiometric to avoid the negative impact of diffusion limitations on the catalyst selectivity. With the development of contemporary catalysts the possibilities for intensification of the FTS have emerged, motivating investigations for potential use of micro- or millistructured reactors,35,36 for which the negative effects of diffusion limitations and heat removal would be suppressed by reducing the scale of the system. In the work of Guettel et al.12 mathematical modeling was used for comparison of the performance of four different types of reactors: FBR and slurry reactor as representatives of conventional reactors, and monolith and microstructured reactors as representatives of a small-scale design. Results clearly indicated that the small-scale reactors can compete with, or even outperform the conventional reactors in terms of catalytic effectiveness, but in order to match productivity per reactor volume, the use of a highly active catalyst is necessary. In the present work, we developed a new 1D multiscale and multiphase (heterogeneous) mathematical model for FTS in a FBR. Extensive literature review revealed the importance of interplay of various phenomena, on the reactor and particle scale, on the performance of a FBR for FTS. To study and comprehend these interplays, we considered a high level of details in description of the phenomena occurring in a FBR. This included incorporating a detailed kinetic model, considering gas and liquid flow inside the FBR, taking into account external (interfacial) and internal (intraparticle) mass and heat transfer, and accounting for nonideal phase equilibrium. To the best of our knowledge, such a comprehensive model for FTS in a FBR has not been published so far. The goal was to develop a reliable model that could be applicable in a broad range of design and operating parameters. Such a model offers the possibility of in depth analysis of the influence of various parameters on the qualitative and quantitative performance of a FBR. This includes obtaining a complete product slate (based on detailed kinetics) and temperature profiles both inside the catalyst particle and throughout the reactor, distribution of components between gas and liquid phase, and pressure drop and liquid holdup from full momentum balances for gas and liquid phase (instead of using empirical correlations). The model was used to simulate and analyze in detail two fixed-bed reactor designs: a centimeter scale (conventional) FBR with egg-shell distribution of catalyst and a millimeter scale FBR with small particles and uniform distribution of catalyst. This comparative analysis presents potential for intensification of industrial-scale fixed bed reactors for FTS.
distributed equally among all tubes, thus they all have the same boundary conditions (one tube is modeled, as a representative). • Catalyst particles are of the egg-shell type, that is, a catalyst is deposited as a layer at the outer part of the pellet, while the components are not diffusing into the core (nonporous core). Diffusion inside the catalyst particle is described using Fick’s law (convective transfer is neglected). Multicomponent diffusion is not taken into account in a catalyst layer, since it is assumed that higher hydrocarbons (component C25+, i.e., wax) are prevailing due to low volatility. It is also assumed that all pores are interconnected and of uniform size (surface diffusion and micropore diffusion is not considered). • The outer surface of the particle is assumed to be totally wetted with the liquid. Hence, two interfaces can be distinguished for each particle: the gas−liquid interface and the liquid−solid interface. A simplified representation of a single catalyst particle with egg-shell distribution and its surrounding with gas−liquid and liquid−solid boundaries is shown in Figure 1. A qualitative concentration profile of a single reactant (products would have the opposite trend) is also presented in Figure 1.
Figure 1. Schematic representation of a single catalyst pellet and its surroundings.
• Reaction rates are calculated for a total of 116 components: CO, H2, H2O, CH4, and olefins and paraffins from C2 to C57. • In the material balances olefin and paraffin molecules up to C24 are lumped in a common C component (C2, C3, ...), while all hydrocarbons having 25 and more carbon atoms are grouped into one pseudocomponent (C25+), giving a total of 28 components. • Plug-flow pattern through the packed bed is assumed for both gas and liquid phases. • Radial gradients inside the reactor are neglected. However, heat transfer in the radial direction (to reactor wall) is taken into account through the use of an overall
2. MATHEMATICAL MODEL 2.1. Model Assumptions. Since FTS in a FBR is a threephase operation, mathematical representation of the phenomena occurring in a FBR includes material, energy, and momentum balance for the gas, liquid, and solid phase. Assumptions used in derivation of the model are listed below. • Reactants (CO and H2) enter the reactor tube filled with spherical catalyst particles. It is assumed that gas is C
DOI: 10.1021/acs.iecr.7b02467 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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heat transfer coefficient, calculated using empirical correlations. • The temperature of the tube wall is assumed to be constant along the reactor. This assumption is valid for pressurized boiling water, with a high flow rate. Thus, the temperature boundary condition for all tubes of a multitubular reactor is the same. • The same assumptions and equations are used for the modeling of a millimeter scale packed bed reactor; that is, phenomena like capillary and microfluidic effects are considered to be negligible. Additional assumptions are stated in particular parts of the model representation. 2.2. Model Equations. Generally, in a 1D heterogeneous model for FBR, two scales and thus two spatial domains can be defined: the tube domain (denoted as the reactor domain in the following text) and the catalyst particle domain. In this work, these domains are presented in a dimensionless form. On the reactor scale, the spatial domain is represented by axial coordinate z, according to eq 1: z=
Z , L
017 mol %) and methane (≈ 1 mol %). On the other hand, the liquid phase consists mainly (≈ 50 mol %) of C25+ hydrocarbons, while the rest is water (≈ 10%), hydrocarbons with more than 10 carbon atoms and dissolved reactants. The predicted distribution of products is in good agreement with the literature findings.37,57,58 It is worth noticing that the use of a simpler approach, in which equilibrium constant K is approximated with Henry’s constants for inorganic species and C1−C3, and vapor pressures for C4+ predicts a similar composition in the gas and the liquid phase, although the K values differ considerably for almost all species. M
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with changes in process conditions. The model is very robust and correctly predicts trends resulting from changes of process conditions over a wide range, regardless of whether conditions are changed simultaneously or one at a time. Two sets of design configurations are simulated, with the same operating conditions (except for inlet velocities), in order to explore intensification possibilities for industrial-scale FBR. The first FBR considers egg-shell catalyst distribution in a centimeter (conventional) scale reactor, and the second utilizes small particles with uniform catalyst distribution in a millimeter scale reactor. Conclusions from this analysis are • Centi- and milli-scale multitubular FBRs provided similar qualitative performance, in terms of CO conversion, selectivity, and productivity. For the same inlet flow rate and similar amount of catalyst used, milli-multitubular FBR has approximately 2.5 smaller total volume than the conventional scale reactor. On the other hand, it has significantly higher number of tubes which results in at least 37% larger reactor wall area, indicating higher capital costs for the smaller scale facility. • Calculated values for the effectiveness factor are similar and higher than 100% for both types of FBRs indicating that for the selected catalyst design there are no considerable negative impacts of diffusion resistances. This is also supported by relatively low values for methane selectivity (around 5.7%), which indicates a lack of significant intraparticle diffusion limitations; • Because of higher catalyst loading (mass of catalyst per reactor volume) and lower liquid velocities, higher values for liquid holdup are obtained for the milli-FBR (6.71% compared to 4.65% for the centi-FBR). Although higher liquid holdup is obtained and considerably smaller particle sizes are used, the total pressure drop was smaller in the case of milli-FBR as a consequence of shorter reactor length (2 against 12 m) and lower gas and liquid velocities; • Slightly better heat removal was achieved in a millimeterscale FBR, as a consequence of using a smaller tube diameter. Heat removal in a conventional FBR with eggshell catalyst distribution is also efficient; the maximum temperature rise was less than 3.5 K; • For the specified operating and design conditions, external resistances to mass transfer are found to be negligible; moreover, it was concluded that temperature gradients inside the catalyst particle/layer were insignificant and that the particle is essentially isothermal; • Some negative effects of diffusion limitations on selectivity were observed even within thin layers of catalyst; that is, for egg-shell layer thickness of 0.1 mm the H2/CO molar ratio inside the catalyst layer increased from 2 at the surface to 2.6 at the inner layer boundary, and the local CH4 formation rate increased by 21%, leading to higher CH4 selectivity. For the milli-scale system, with 0.4 mm diameter catalyst particles, the increase of H 2 /CO ratio and consequently CH 4 formation rate is even more pronounced, because of the use of a thicker catalyst layer. Therefore, for highly active catalysts and typical operating conditions, one should avoid using thicker catalyst layers, to keep the diffusion limitations at the acceptable level. The comprehensive modeling approach allows in depth analysis of the various phenomena taking place on the reactor
end of the catalyst layer close to reactor inlet. In the milli-FBR, where the catalyst particle radius is 0.2 mm, the H2/CO molar ratio at the center of the particle and near the reactor inlet is more than 3. It has been reported that, for larger particles, that is, catalyst layers, H2/CO can rise to very high values, above 20.34 The influence of local conditions inside the catalyst, a direct consequence of diffusion resistance, on rates of CO disappearance and CH4 formation is shown in Figure 7. It can be seen that both rates increase with the distance from the particle surface. As mentioned above, the CO reaction rate increases inside the particle because of negative order kinetics, that is, the inhibition by CO is reduced as its concentration decreases. As a result, the effectiveness factor based on the CO rate is higher than 100% (see Table 3). As it can be seen in the right-hand side of Figure 7, CO consumption rate is somewhat higher for the mili-FBR, which is a consequence of higher H2/ CO ratio (see Figure 6), that is, lower CO concentration. As stated above, this leads to the overall higher CO conversion and C5+ production in milli-scale reactor (aside to more catalyst in milli-FBR). Methane reaction rate also increases in the particle because of the higher H2/CO favoring chain termination reactions. When these two reaction rates are compared, the increase is higher (in relative terms) for the CH4 formation rate. Close to the reactor inlet CO disappearance rate increases about 13% in centimeter-FBR and more than 21% in millimeter-FBR along the catalyst layer. At the same time the CH4 formation rate increases around 21% in centi-FBR and 39% in milli-FBR, due to higher H2/CO increase in the milli-FBR (see Figure 6). This effect on reaction rates is less pronounced toward the reactor outlet as a consequence of lower bulk concentrations of the reactants. In addition, the CH4 reaction rate is reduced because of a higher concentration of water (the latter inhibits the methane reaction rate−see eq 38). Therefore, H2/CO molar ratio is one of the crucial parameters to control for having desirable FBR performance. Increasing H2/CO leads to higher CO conversion and thus C5+ production, while on the other hand it increases selectivity toward undesirable products. Desired selectivity can be controlled also with thin catalyst layers and low temperatures, which on the other hand decrease productivity per reactor volume. All of these opposite effects raise an opportunity for a rigorous optimization study, which may be valuable tool for FBR reactor design.
4. CONCLUSIONS A new 1D multiscale and multiphase (heterogeneous) mathematical model for FTS in a FBR has been developed. Compared to existing models in the literature, fewer simplifications have been made and phenomena such as external and internal mass/heat transfer, phase equilibrium, and kinetics are described at a detailed level. Moreover, liquid holdup and pressure drop are obtained using momentum balance equations for the gas and the liquid phase inside the reactor, instead of using empirical correlations for this purpose. The kinetics of FTS is obtained from experiments with a stateof-the-art cobalt-based catalyst, representative of recent developments in FTS catalysis. The model’s predictive capabilities have been verified by comparison with available literature data on FTS in FBRs. The model provides a good quantitative match for SCH4 and C5+ selectivities and follows the trends for CO conversion variation N
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and particle scale and their influence on the reactor performance. The developed model will be used for sensitivity analysis, in which all important design and operating parameters will be varied, as well as in rigorous optimization, that may be useful for both theoretical and practical design purposes.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b02467. Properties from equation of state (EOS); interfacial mass and heat transfer coefficients; intraparticle diffusion and conduction; overall heat transfer coefficient (to reactor tube wall); drag forces; equilibrium and Henry’s constants and activity coefficients; reaction rates, Tables S1, S2 (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Tel.: +381113303652. ORCID
Nikola M. Nikačević: 0000-0003-1135-5336 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research was made possible by a grant (NPRP Grant No. 7-559-2-211) from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.
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REFERENCES
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DOI: 10.1021/acs.iecr.7b02467 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.iecr.7b02467 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
