Multiscale modelling strategy for structured catalytic reactors
Introduction
Structured reactors play a key role in the design of intensified multiphase processes in chemical engineering (Pangarkar et al., 2008). In contrast to classical fixed beds, which are random packings of catalytically active particles, structured reactors can be purposefully designed on all scales from the catalyst level up to the reactor level (Kreutzer et al., 2006). For, say, spherical non-porous catalyst particles, the structure of a fixed bed has only one design parameter, which is the size of the particles. It determines the size of the available catalyst surface and thereby the reaction rate and catalyst efficiency; small particles are preferred here. The particle size also determines the interparticle length, which has a strong impact on the total pressure drop of the reactor; large particles are preferred in order to keep the pressure loss low. Selecting the particle size therefore is a compromise between maximising the catalyst efficiency and minimising the pressure loss. Application of porous or non-spherical particles adds some degrees of freedom to the design, but it does not allow to design mass transport and reaction independently.
In a structured packing, the design of the structure introduces many new degrees of freedom for reactor design, allowing to decouple the hydrodynamic state (pressure drop), the reaction rate (catalyst efficiency) and the transport of heat and mass (reaction control) to a wide extent (Pangarkar et al., 2008). Thus, in a structured reactor these processes can be adjusted in order to control the temperature and concentration profiles along the flow path, thereby improving selectivity and conversion, and avoiding local temperature peaks.
According to Cybulski and Moulijn, (2006), structured reactors can be categorised into monolithic reactors, membrane reactors and arranged reactors (see Fig. 1). Numerous contributions about the modelling and simulation of monolithic reactors have been published, including modelling of specific details and simulations of complete reactors (e.g. Chen et al., 2008, Tischer and Deutschmann, 2002). Also, a wide range of contributions on modelling of membrane reactors is available (e.g. Marcano and Tsotsis, 2002). With regard to arranged reactors, many contributions treat the modelling of gas–liquid systems in structured packings (see Pangarkar et al., 2008), which are widely applied, for example in reactive distillation. However, only a few publications treat arranged reactors for heterogeneously catalysed gas-phase reactions. von Scala et al. (1999) investigated flow paths in Katapak-M packings and estimated pressure drops from CFD simulations of the structure for single phase flow. Their model-based results correspond very well with experimental data. Petre et al. (2003) proposed a computational method for a priori estimation of the pressure drop in a structured packing by analysis of dissipation rates in recurrent structure elements. Calis et al. (2001) focussed on regular fixed bed channels with very low tube-to-particle-diameter ratio. They applied CFD simulations to predict pressure drop correlations, which showed reasonable agreement with experimental results. However, none of these contributions treats mass and heat transfer in arranged, parallel passage reactors, which is the focus of this work.
Like all structured reactors, arranged reactors are multiscale systems; the geometrical design of the structure determines the processes of transport and reaction on this scale and has a strong impact on the behaviour of the complete reactor on a larger scale. Thus, the ability to describe the processes on a small scale and transfer this knowledge to the reactor scale is a prerequisite for a purposeful reactor design. While the simulation of the processes on the scale of the repeating structures can be done with established methods such as computational fluid dynamics (CFD), the same level of detail cannot be applied to the description of the whole reactor due to high computational costs. Instead, reduced reactor models are required, which reflect the essential behaviour on the small scale, but which are computationally cheap and thus applicable to the simulation of the complete reactor.
In this contribution, we propose a multiscale hierarchy of three model levels for the design and analysis of structured reactors (Fig. 2). Each model describes the reactor or a part of it on a different level of detail and is tailored for specific tasks:
- •
The detailed model describes one or several repeating sections of the structure in all geometric details. It is not only applicable for the analysis and design of the structure, but it also allows to estimate heat and mass transport parameters needed to transfer the essential characteristics of the structure to the reduced models (see below).
- •
The zone model neglects exact geometrical details. Instead, it considers discrete volumes in which the reaction takes place. It is useful, e.g. for designing the reactor-wide flow pattern.
- •
The phase model has spatially homogenised reactive and non-reactive phases, coupled by interphase mass and heat transfer. It is suitable to describe the spatially distributed reactor behaviour and its interaction with surrounding devices in a computationally efficient way. It can be applied for optimisation of the reactor and its integration into complex devices.
None of these models is entirely new. The novelty of this contribution is the hierarchy of coherent and compatible models; results obtained with one of the models can be transferred to other elements of the model hierarchy. Furthermore, the application of the models covers a wide spectrum of tasks ranging from the design of the structure up to the heat integration and optimal control of the complete reactor. It is the latter aspect, in particular, which makes the proposed hierarchy a powerful and useful tool.
In this contribution, we derive and discuss the three models illustrated in Fig. 2, thereby focussing on a flat bed reforming reactor that is used as an indirect internal reforming unit in high temperature molten carbonate fuel cell (MCFC) systems (Bischoff and Huppmann, 2002, Pfafferodt et al., 2010). Its purpose is to reform the fuel gas (usually a methane/steam mixture) to a certain conversion before the gas mixture is fed to the fuel cells. They are inserted into the fuel cell stack at certain intervals, so they absorb heat from the fuel cells they are attached to. The elementary cell of this arranged reactor is shown in Fig. 3 left. It consists of two corrugated metal sheets, which are aligned in a staggered way, forming small chambers. In some of these, cylindrical catalyst particles are inserted.
Because the derivations of the zone and the phase models are motivated by the simulation results obtained from their preceding models, we discuss the models directly together with their results and some examples of typical applications. The detailed model and the zone model have already been published elsewhere in detail (Pfafferodt et al., 2008). For the sake of completeness, we repeat the most important aspects of these models here, so the reader can follow the argumentation, and refer to the mentioned publications for further details. Because the phase model has not been published elsewhere, we discuss its derivation in detail.
In Section 5, we also discuss how this hierarchical modelling approach can be transferred to other arranged, parallel passage reactors such as Katapak structures.
Section snippets
The detailed model
This model describes the hydrodynamic and chemical behaviour in the elementary cell of the catalytic reactor on a small scale. It can be used to evaluate the performance of different geometrical structures. Furthermore, it is an important tool for the estimation of parameters that are required in the subsequently discussed zone and phase models. The class of detailed models is only briefly described here. For detailed information about the example, the reader is referred to the work of
The zone model
The zone model is a reduced model that is based on the findings from the detailed model. It describes the processes on the scale of the structures in a reduced way. Thus, the complete reactor, or at least a large part of it, can be simulated. The zone model is suitable to design a complete structured reactor with respect to the flow field, catalyst distribution and pressure drop.
The phase model
The phase model represents the next reduction level of a structured reactor. Its derivation is based on the zone model, and it adopts the idea of two different zones present in the reactor. However, it is not necessary to set up and solve the zone model of a reactor in order to develop the corresponding phase model. This model can be applied to simulate spatially distributed states in a complete structured reactor in a very efficient way. It can also be coupled with models of other,
Conclusions
The proposed modelling strategy for arranged, parallel passage structured reactors covers a wide range of applications that are relevant for the design of such systems. The detailed model can be used to estimate important parameters of a given geometry of the elementary cells, for example coefficients of mass and energy transport or anisotropic permeabilities. This makes it a valuable tool for the design of the structure. The zone model describes a complete structured reactor or large parts of
Nomenclature
- aI
Interfacial area between R/N-zone per volume (m−1)
- A
Surface (m2)
- ci
Concentration of species i (mol m−3)
- c1, c2
Ergun coefficients (dimensionless)
- ct
Total concentration (mol m−3)
- cp
Average molar heat capacity (J mol−1 K−1)
- cp,i
Molar heat capacity species i (J mol−1 K−1)
- d
Characteristic length (m)
- d2
Height of reforming reactor (m)
- fi,k
Volume force acting on species i (N mol−1)
- gi
Mass flux density of species i (mol m−2 s−1)
- h
Volumetric enthalpy density (J m−3)
- hi
Molar enthalpy species i (J mol−1)
- hI
Enthalpy flux density
References (31)
- et al.
Operating experience with a 250 kWel molten carbonate fuel cell (MCFC) power plant
Journal of Power Sources
(2002) - et al.
CFD modeling and experimental validation of pressure drop and flow profile in a novel structured catalytic reactor packing
Chemical Engineering Science
(2001) - et al.
Mathematical modeling of monolith catalysts and reactors for gas phase reactions
Applied Catalysis A—General
(2008) - et al.
A comparison of lumped and distributed models of monolith catalytic combustors
Chemical Engineering Science
(1995) - et al.
A numerical comparison of alternative three-phase reactors with a conventional trickle-bed reactor. The advantages of countercurrent flow for hydrodesulfurization
Chemical Engineering Science
(1999) - et al.
Shouldn't catalysts shape up? Structured reactors in general and gas–liquid monolith reactors in particular
Catalysis Today
(2006) - et al.
Reactor development for conversion of natural gas to liquid fuels: a scale-up strategy relying on hydrodynamic analogies
Chemical Engineering Science
(1996) - et al.
CFD modelling and calculation of dynamic two-phase flow in columns equipped with structured packing
Transactions IChemE Part A
(2007) - et al.
Momentum transfer at the boundary between a porous medium and a homogeneous fluid—I. Theoretical development
International Journal of Heat Mass Transfer
(1995) - et al.
Pressure drop through structured packings: breakdown into the contributing mechanisms by CFD modeling
Chemical Engineering Science
(2003)
Modelling of Katapak reactor for hydrogenation of anthraquinones
Chemical Engineering Science
Heat transfer measurements and simulation of Katapak-M catalyst supports
Chemical Engineering Science
A new approach to fluid separation modelling in the columns equipped with structured packings
Chemical Engineering Journal
Transport Phenomena, Rev.
Cited by (11)
Architecture model proposal of innovative intelligent manufacturing in the chemical industry based on multi-scale integration and key technologies
2020, Computers and Chemical EngineeringCitation Excerpt :Specifically, new advances in research methods and approaches have emerged to meet the requirements of establishing relationships between molecular structures on nano-, micro-, meso‑, and macroscale (e.g., equipment) processes(J. Li, Huang, 2014). These advances include simulation methods for different scales (e.g., molecular-scale computational chemistry simulation, mesoscopic-scale structural simulation(Ferkl et al., 2017; Sitprasert et al., 2011), computational fluid dynamics simulation, and dynamic process simulation at the equipment scale (Heidebrecht et al., 2011; Sivec et al., 2019; N. Yang et al., 2011)), non-contact measurement technology, and high-performance computing capabilities. Therefore, the interconnection, coupling, and transmission mechanisms among multiple scales are becoming a hotspot in scientific research and engineering technology applications and constitute the basic characteristics of interconnected chemical engineering.
Multiscale structures in particle–fluid systems: Characterization, modeling, and simulation
2019, Chemical Engineering ScienceCitation Excerpt :Several characteristic scales naturally exist between the vastly different global and atomic scales, and the complex phenomena at these intermediate scales have drawn great attention from different disciplines. A number of general reviews serve as gateways into the rapidly expanding literature on multiscale behavior and research approaches in process engineering (Li and Kwauk, 2003; Ge et al., 2007; van der Hoef et al., 2008; Charpentier, 2009; Dudukovic, 2009; Van den Akker, 2010; Heidebrecht et al., 2011; Li et al., 2013; Joshi and Nandakumar, 2015; Li and Huang, 2018). The partition of characteristic scales proposed by Li et al. (2005a; 2016b), as shown in Fig. 1, is representative of the scale structure assigned by process engineers.
Hydrodynamics and mass transfer in multiphase monolithic reactors with different distributors: An experimental and modeling study
2018, Chemical Engineering and Processing: Process IntensificationCitation Excerpt :In recent years, the multiphase monolithic reactors have received wide attention and are regarded as an intensification replacement of conventional multiphase reactors (e.g., trickle beds and slurry bubble columns) in the catalysis community, due to the low pressure drop and high mass transfer coefficients [1–10].
Modeling of diffusion and reaction in monolithic catalysts for the methanol-to-propylene process
2013, Fuel Processing TechnologyCitation Excerpt :Process intensification is currently a fashionable subject in the field of chemical process industry, which aims to optimize capital, energy, environmental and safety benefits in the design of chemical process plants [7]. As a way to process intensification, there has been an increasing interest to employ structured catalysts and reactors for two-phase (gas–solid) [8,9] and multiphase (gas–liquid–solid) reactions [10,11]. According to the spatial configurations, structured catalysts and reactors can be divided into monoliths, corrugated sheet (or gauze), knitted wires and open-celled foams.
Comparison among monolithic and randomly packed reactors for the methanol-to-propylene process
2012, Chemical Engineering JournalCitation Excerpt :Nevertheless, particular attention has to be paid, especially during the scale-up process, to the limitation of back-mixing, the prevention of catalyst attrition and the separation of entrained fines. As a way to process intensification, a fashionable subject in the field of chemical process industry aiming to optimize capital investment, energy, environmental and safety benefits in the design of chemical process plants [7], there has been an increasing interest to employ structured catalysts and reactors for two-phase (gas–solid) [8,9] and multiphase (gas–liquid–solid) reactions [10,11]. According to the spatial configurations, structured catalysts and reactors can be divided into monoliths, corrugated sheet (or gauze), knitted wires and open-celled foams.
Intensifying the Fischer-Tropsch Synthesis by reactor structuring - A model study
2012, Chemical Engineering JournalCitation Excerpt :Typical challenges in a slurry reactor are reducing backmixing and optimizing solids separation, while in a multi-tubular fixed bed reactor these are improving temperature gradients and catalyst effectiveness. Several methods have been proposed to structure the systems with a fixed catalyst structure [1–8] and systems with a mobile catalyst [9–13]. In each of these approaches, structuring introduces extra degrees of freedom to optimize the design objectives independently [14].