Research Note Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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110th Anniversary: Commentary: CFD as a Modeling Tool for Fixed Bed Reactors Behnam Partopour and Anthony G. Dixon*
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Department of Chemical Engineering, Worcester Polytechnic Institute, Worcester, Massachusetts 01609, United States ABSTRACT: Computational fluid dynamics (CFD) is a valuable tool in the modeling of fixed bed reactors. In particular, resolved-particle CFD in which a bed of particles is simulated directly, without invoking a porous media representation, is being used to probe reaction systems and understand the complexities of reactions in heterogeneous systems. Some reviews are now available, and the number of publications is growing. In this contribution, a broad perspective is attempted on what are some of the key issues, what problems should be solved for further progress, and what new techniques might be applied. Topics discussed are the numerical generation and meshing and simulation of beds of complex particle shapes, coupling microkinetics with resolved-particle CFD, validation with in situ experimental methods, and some suggestions for the possible role of visualization techniques and machine learning in the interpretation of the large amounts of information generated by CFD. fixed bed properties is their intrusive nature. Most experimental efforts for measuring the structural properties or temperature distribution could easily lead to deformation of the original packing (e.g., placing thermocouples in different positions in the bed). More importantly, understanding the wall effects using experimental tools is very challenging. Fixed beds show a discontinuity-like behavior near the tube wall, radial voidage is at a maximum, and heat and mass transfer are hard to characterize. These are good enough reasons to be skeptical of the existing fixed bed correlations and their validity range. We like to emphasize that this is not a rejection of experimental measurements, in fact they play an essential role in fixed bed modeling, and we come back to this later. On the other hand, modern computer-based tools enable very detailed simulation of flow within the most complex geometries. Computer generation of packings coupled with the reaction and transport equations of computational fluid dynamics (CFD) provides information regarding velocity components, temperature, and species concentration within each cell of the computational domain. Dixon and co-workers in the early 2000s showed the possibility of particle-resolved CFD simulations of fixed bed reactors for a small number of particles;2,3 since then, many publications have investigated the applications of such CFD simulations for fixed beds,4 and the number of studies is only growing faster thanks to the exponential growth in computational power. Today, it is possible to simulate fixed beds of hundreds of particles within a
F
ixed bed reactors are at the heart of the chemical industry. After decades of research and innovation in reaction engineering, realistic alternatives to fixed beds for many processes are yet to be found. Billions of dollars of (bio)chemicals are produced via fixed beds, annually. The main challenge is to design optimized fixed beds for each process. Understanding the flow and its interaction with the reaction and transport is the major limiting factor in optimization and scale up of fixed bed reactors. Even in the presence of the most optimized, that is, highly selective and reactive, catalysts, fixed beds could still have low yield due to poor heat and mass transfer. Local transport phenomena can also significantly affect the catalyst dynamics (e.g., deactivation). That is why reliable models are essential for the design and optimization space. However, fixed bed models are far from perfect. In other words, there are not many models that can accurately describe reactors under realistic conditions, especially for beds of low tube-to-particle diameter ratio (N), in which tube wall effects have a strong influence on transport and reaction. This is because of strong assumptions in the models, such as plug flow, homogeneity, constant transport coefficients, etc. as well as widely scattered literature correlations for many of the parameters, such as pressure drop and heat transfer.1 The complex geometry of low-N fixed beds is one of the main barriers to successful models. The packing structure varies for different particle shapes and different N. The radial variation of voidage (we believe this term should become standard and replace “porosity” when it comes to fixed bed structure to avoid confusion with catalyst particle porosity), controls the velocity profile and radial heat transfer which have been shown to be dominant factors in fixed bed performance. The major drawback of experimental methods for evaluating © XXXX American Chemical Society
Received: Revised: Accepted: Published: A
December 24, 2018 March 22, 2019 March 27, 2019 March 27, 2019 DOI: 10.1021/acs.iecr.8b06380 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Research Note
Industrial & Engineering Chemistry Research
Figure 1. Methodology for particle-resolved CFD simulations of fixed beds.
several computational methods were developed early on for packing of spherical particles, generating packings of nonspherical particles remained as an important issue for a long time. Lower computational power, lack of accurate contact detection and force model algorithms and difficulties with volumetric meshing of the particle−particle and wall−particle contact areas contributed to the problem. Today, there are different options available for generating packed beds of nonspherical particles. Discrete Element Method (DEM) based software can handle arbitrary particle shapes based on computationally expensive multisphere approximations, although rigorous contact models have been developed for cylinders.5,6 Physics libraries based on rigid body dynamics and surface meshes are capable of fast and robust packing of arbitrary particle shapes,7,8 such as cylinders of different aspect ratios, rings, trilobes, and other shapes involving internal voids and external features. The final static geometry of the packing is the main interest in fixed bed simulations, and several studies have shown that both DEM and Physics Library models can reproduce the properties of these geometries within acceptable margins of error. For the volumetric mesh generation, the main issue has been handling of the particle−particle and particle−wall contacts. In the case of spherical particles with only point contacts, different local geometry modification methods (e.g., bridges and caps) have been shown to be valid options. For nonspherical particles for which the contacts can be a point,
reasonable time, and there are multiple commercial and opensource finite volume platforms available. Sophisticated methods have been developed to address issues regarding the numerical generation of the packed beds, handling the meshing problems, and adding complex reaction kinetics to the CFD simulations. It seems that we have reached a point where the technical issues are largely addressed, and resolved-particle CFD simulation of fixed beds has become state of the art, with only limitations in computer power preventing the simulation of full-scale realistic fixed beds. Now, we believe it is time to evaluate the existing methodologies and discuss the applications of these rigorous simulations to obtain robust chemical reaction engineering (CRE) models (see Figure 1). Here we will briefly point out some of the most important technical aspects of the CFD simulations, the existing opportunities, and some directions that we believe need the attention of the researchers in the field. While we do not expect particleresolved simulations to be a substitute for effective medium simulations of large industrial fixed bed reactors in the near future, they can be invaluable in developing insight into the reactor performance and correlations for the parameters, such as for heat and mass transfer, that are needed.
1. NUMERICAL GENERATION OF PACKED BEDS AND MESHING Numerical generation of the packed beds of particles is one of the most challenging aspects of the simulations. Although B
DOI: 10.1021/acs.iecr.8b06380 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Research Note
Industrial & Engineering Chemistry Research
Microkinetic models are supposed to be accurate globally, even for extreme conditions. However, some detailed experimental studies10 as well as resolved-particle CFD simulations11 cast doubt on that. One major drawback is that many microkinetic models are only validated for differential reactors (very low conversion) and isothermal conditions. First-principle-derived microkinetic models that rely only on DFT calculations for kinetic constants could also contain large errors.12 Even small errors in calculated activation energy can exponentially increase the uncertainty in the overall rate. These effects might not be observed in simple differential or CSTR models for which temperature and species gradients are small or negligible. However, they become significant under integral fixed bed CFD simulations,13 or in a real reactor set up. We believe that in the absence of comprehensively validated microkinetic models, lumped kinetic models that are widely used in industry, for example, for steam methane reforming,14 may often result in more accurate simulations even if restricted to the range of conditions for which they were fitted.
line, or a surface, generating individual bridges is extremely challenging. To date, the best valid option is the local smoothing9 (equivalent to the caps or flattening approach for spherical particles). The method does a good job of keeping the radial and bulk voidage of the packing intact. However, more studies are needed to evaluate the accuracy of the heat transfer at the contact areas for this approach, for nonspherical particles.
2. EFFECTS OF PARTICLE SHAPES Most CFD studies of fixed beds have reported results for packings of spheres and some on packings of cylinders. In fact, there is an imbalance between the number of DEM/physicsbased simulations of packing of nonspherical particles and actual CFD simulations for them, due to the difficulties of meshing such complex geometries, particularly in the neighborhood of particle−particle contacts. Nonetheless, it has been shown that the local and bulk properties (e.g., radial voidage, particle orientation distribution) of these structures are very different from each other. More CFD studies are needed to address the impacts of these properties on the flow, transport, and reaction in the fixed bed, particularly because industrial fixed beds quite often use nonspherical particles (e.g., Raschig rings for ethylene partial oxidation, methanol partial oxidation to formaldehyde, and particles with internal holes and/or external lobes for steam methane reforming, etc.). CFD studies can contribute to the development of parametric correlations for radial voidage and structural properties of packed beds of nonspherical particles, and with modern meshing methods8 it is likely that CFD simulations will soon be contributing more extensively to develop correlations for heat and mass transfer and flow properties.
4. EXPERIMENTAL VALIDATION Experimental validation of fixed bed CFD simulations is the most essential part in developing models. Without conducting detailed experiments, it is almost impossible to identify the sources of error and evaluate the accuracy of these models. More studies have been carried out to evaluate the performance of the CFD simulations for heat transfer and pressure drop, and fewer for reaction. Indeed, it is hard to locally measure the species profile within the reactor without deforming the fixed bed structure. However, at present profile reactors seem to be the best choice. A few new studies have been published that evaluated the performance of the CFD simulations.11,15,16 These studies focused on comparing CFD versus experimental data obtained from in situ profile measurements. The results have been invaluable and provided new insights into the fixed bed performance (e.g., inadequacy of some microkinetic models). A very important point is to distinguish between using experimental tools for validation of CFD models and using them for developing correlations for fixed beds. As was mentioned earlier intrusive experiments cannot be trusted when the goal is to generate empirical correlations because the bed structure is already changed. However, this is not a problem when it comes to validation of CFD models. A CFD simulation can be carried out according to the experimental setup, including all the intrusive measurement devices. Once the simulation is validated for that specific configuration, then new simulations can be carried out for intact (uninstrumented) fixed bed configurations. CFD-driven approaches are currently appearing to test pressure drop calculations, to develop correlations for particle−fluid heat and mass transfer correlations. Conventional effective medium models can be evaluated, while CFD plays a part in developing new approaches to fixed bed heat transfer.17
3. COUPLING REACTION KINETICS WITH CFD Probably one of the most important factors that distinguishes CFD simulations of fixed bed reactors from single-phase CFD simulations is the necessity of coupling heterogeneous reactions to the flow simulations. This area has had much attention of researchers during the past few years. Currently, both lumped semiempirical and complex microkinetic models can be added to the simulations. There are two major methodologies for coupling the kinetics with CFD: (1) adding the reactions as boundary conditions for the flow at the particle solid−fluid external interfacein these simulations no reaction is explicitly represented inside the catalyst particles; (2) explicitly modeling reaction and diffusion within the catalyst particles using effective diffusivity models, and coupling transport across the particle−fluid interface. The former approach could be valid for very fast reactions where the reaction is limited by the internal diffusion. However, the latter is more realistic, and it is necessary for slow reactions. When the reaction is added via boundary conditions, extra caution should be taken. In this approach, usually, the reaction flux vector is set up outward into the fluid region and therefore, the heat flux direction would also be outward into the flow. However, this is numerically incorrect; the heat flux could be directed inward toward the solid catalyst particles as well. Choosing the right kinetic model is extremely important for CFD simulation of fixed beds. Almost all studies have shown sharp gradients of temperature and species in 3-dimensional simulations. In such cases, the most important question would be “is the kinetic model still valid under the operating conditions?”
5. VISUALIZATION, MACHINE LEARNING, AND FIXED BED CFD CFD simulations generate massive amounts of data. A great deal of future research will depend on the ability to efficiently represent and interpret large volumes of complex data. The discussion in this section is intended to identify an important C
DOI: 10.1021/acs.iecr.8b06380 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Research Note
Industrial & Engineering Chemistry Research
(5) Kodam, M.; Bharadwaj, R.; Curtis, J.; Hancock, B.; Wassgren, C. Cylindrical Object Contact Detection for Use in Discrete Element Method Simulations. Part I−Contact Detection Algorithms. Chem. Eng. Sci. 2010, 65, 5852. (6) Feng, Y. T.; Han, K.; Owen, D. R. J. A Generic Contact Detection Framework for Cylindrical Particles in Discrete Element Modelling. Comp. Meth. Appl. Mech. Eng. 2017, 315, 632. (7) Boccardo, G.; Augier, F.; Haroun, Y.; Ferre, D.; Marchisio, D. L. Validation of a Novel Open-source Work-flow for the Simulation of Packed-bed Reactors. Chem. Eng. J. 2015, 279, 809. (8) Partopour, B.; Dixon, A. G. An Integrated Workflow for Resolved-Particle Packed Bed Models with Complex Particle Shapes. Powder Technol. 2017, 322, 258. (9) Eppinger, T.; Seidler, K.; Kraume, M. DEM-CFD Simulations of Fixed Bed Reactors with Small Tube to Particle Diameter Ratios. Chem. Eng. J. 2011, 166, 324. (10) Korup, O.; Goldsmith, C. F.; Weinberg, G.; Geske, M.; Kandemir, T.; Schlogl, R.; Horn, R. Catalytic Partial Oxidation of Methane on Platinum Investigated by Spatial Reactor Profiles, Spatially Resolved Spectroscopy, and Microkinetic Modeling. J. Catal. 2013, 297, 1. (11) Wehinger, G. D.; Kraume, M.; Berg, B.; Korup, O.; Mette, K.; Schlögl, R.; Behrens, M.; Horn, R. Investigating Dry Reforming of Methane with Spatial Reactor Profiles and Particle-Resolved CFD Simulations. AIChE J. 2016, 62, 4436. (12) Döpking, S.; Plaisance, C. P.; Strobusch, D.; Reuter, K.; Scheurer, C.; Matera, S. Addressing Global Uncertainty and Sensitivity in First-Principles Based Microkinetic Models by an Adaptive Sparse Grid Approach. J. Chem. Phys. 2018, 148, 034102. (13) Partopour, B.; Dixon, A. G. Resolved-Particle Fixed Bed CFD with Microkinetics for Ethylene Oxidation. AIChE J. 2017, 63, 87. (14) Xu, J.; Froment, G. F. Methane Steam Reforming, Methanation and Water-Gas Shift: I. Intrinsic Kinetics. AIChE J. 1989, 35, 88. (15) Behnam, M.; Dixon, A. G.; Wright, P. M.; Nijemeisland, M.; Stitt, E. H. Comparison of CFD Simulations to Experiment under Methane Steam Reforming Reacting Conditions. Chem. Eng. J. 2012, 207, 690. (16) Dong, Y.; Geske, M.; Korup, O.; Ellenfeld, N.; Rosowski, F.; Dobner, C.; Horn, R. What Happens in a Catalytic Fixed-Bed Reactor for n-Butane Oxidation to Maleic Anhydride? Insights from Spatial Profile Measurements and Particle Resolved CFD Simulations. Chem. Eng. J. 2018, 350, 799. (17) Behnam, M.; Dixon, A. G.; Nijemeisland, M.; Stitt, E. H. A New Approach to Fixed Bed Radial Heat Transfer Modeling Using Velocity Fields from Computational Fluid Dynamics Simulations. Ind. Eng. Chem. Res. 2013, 52, 15244. (18) Stitt, H.; Marigo, M.; Wilkinson, S.; Dixon, A. G. How Good is Your Model? “Just because the results are in colour − it doesn’t mean they are right. Johnson Matthey Technol. Rev. 2015, 59, 74. (19) Munzner, T. Visualization Analysis and Design; AK Peters/CRC Press: 2014. (20) Wang, J.-X.; Xiao, H. Data-Driven CFD Modeling of Turbulent Flows through Complex Structures. Int. J. Heat Fluid Flow 2016, 62, 138. (21) Bansal, S.; Roy, S.; Larachi, F. Support Vector Regression Models for Trickle Bed Reactors. Chem. Eng. J. 2012, 207, 822. (22) Park, S.; Na, J.; Kim, M.; Lee, J. M. Multi-objective Bayesian Optimization of Chemical Reactor Design using Computational Fluid Dynamics. Comput. Chem. Eng. 2018, 119, 25.
area for future research, without being too prescriptive. Up to now, the data has been explored by routine visualization techniques or simple data analysis. Traditional visualization techniques, other than being colorful and nice, can only provide limited information. In particular, three-dimensional visualizations are often hard to understand and potentially misleading.18 Two-dimensional surface contour plots provide limited information. Today, there are advanced visualization techniques that can help to explore the data locally and provide an interactive visualization front end for the users. These methods can be leveraged for presentation of the results of CFD simulations. Choosing the right colormaps for the contour plots could significantly impact the understanding of the results by human beings. There have been studies about human cognitive ability and visualization techniques that should be noted by the community. For example, Munzner19 suggests the use of multiple-hue continuous colormaps with monotonically increasing luminance, instead of the popular rainbow color maps prevalent in the literature. When it comes to data analysis, we have always looked for familiar patterns, those of which we have been already aware. The data are analyzed by traditional methods, a big part of the data set is ignored, and most of the results are averaged over different sections of the geometry. That means millions of data points, hundreds of hours of simulation time, and possibly much valuable information about local phenomena is thrown away, to reduce the data set to something that can be analyzed by human cognitive processes. In other words, the current approach for analyzing CFD data is not efficient at all. The new machine learning algorithms provide us valuable tools to investigate the “big data” provided by CFD with less bias and more flexibility. Examples include the use of neural networks for deep learning of physical phenomena such as modeling turbulent flow,20 data mining, and pattern recognition from historical data from existing processes (particularly for industrial applications), support vector regression models for feature selection, for example modeling trickle bed reactors,21 and multiobjective Bayesian optimization22 which have all been applied to chemical reactor design and catalyst discovery and selection in recent years. Identifying all correlated variables, the hidden patterns in the data, and generating data driven predictive models for fixed bed reactors are major challenges for the future.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Anthony G. Dixon: 0000-0002-7443-3656 Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Dixon, A. G. Fixed Bed Catalytic Reactor Modelling − the Radial Heat Transfer Problem. Can. J. Chem. Eng. 2012, 90, 507. (2) Dixon, A. G.; Nijemeisland, M. CFD as a Design Tool for Fixedbed Reactors. Ind. Eng. Chem. Res. 2001, 40, 5246. (3) Dixon, A. G.; Nijemeisland, M.; Stitt, E. H. Packed Tubular Reactor Modeling and Catalyst Design using Computational Fluid Dynamics. Adv. Chem. Eng. 2006, 31, 307. (4) Jurtz, N.; Kraume, M.; Wehinger, G. D. Advances in Fixed-bed Reactor Modeling using Particle-resolved Computational Fluid Dynamics (CFD). Rev. Chem. Eng. 2019, 35, 139. D
DOI: 10.1021/acs.iecr.8b06380 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
