A Lattice Boltzmann Approach to Multi-Phase Surface Reactions with Heat Effects

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A Lattice Boltzmann Approach to Multi-Phase Surface

Reactions with Heat Effects

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A Lattice Boltzmann Approach to Multi-Phase Surface

Reactions with Heat Effects

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op woensdag 23 oktober om 10:00 uur

door

Mohammad Reza KAMALI

M.Sc. Chemical Engineer, Lappeenranta University of Technology, Finland B.Sc. Chemical Engineer, Iran University of Science and Technology, Iran

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Samenstelling promotiecommissie:

Rector Magnificus, voorzitter

Prof. dr. ir. H.E.A. van den Akker, Technische Universiteit Delft, promotor

Prof. dr. S. Sundaresan, Princeton University, promotor

Prof. dr. ir. F. Kapteijn, Technische Universiteit Delft Dr. ir. J.R. van Ommen, Technische Universiteit Delft Prof. dr. ir. J.J. Derksen, University of Aberdeen

Prof. dr. F. Toschi, Technische Universiteit Eindhoven Prof. dr. -ing. G. Brenner, Technische Universität Clausthal Prof. dr. R.F. Mudde (reserve lid) Technische Universiteit Delft

The outstanding contributions of Dr. ir. J.J.J. Gillissen as a mentor is highly appreciated.

The financial support of the Dutch Technology Foundation STW, the Applied Science Division of the Netherlands Organization for Scientific Research (NWO) is gratefully acknowledged. The author wish to also thank Islamic Developement Bank for awarded scholarship through "Merit Scholarship Programme for High Technology".

Cover design: M.A. Mohsen Mohammadi, Gilar Design Studio (www.gilar.net) Persian handwriting: Masih Kamali

Cover keywords: Hafez’s tomb, phase segregation, taylor bubble flow, partial wetting flow in porous media and inclined channel. Printed by: GVO drukkers & vormgevers B.V. | Ponsen & Looijen

ISBN 978-94-6186-222-8

Copyright c_{2013 by M. R. Kamali}

All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilised in any formor by anymeans, electronic ormechanical, including protocopying, recording or any information storage and retrieval system, without written permission of the author. (Author’s email: mdrzkamali@gmail.com)

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8 Conclusions And Contributions 119 9 Perspectives And Recomendations 125 A D2Q9 And D3Q19 Lattice Topologies 129 B EOS In Shan And Chen Model And Maxwell-Rule 131 C Coupling Physical And LB Units 135 D On Spurious Velocities In Shan And Chen Method 137 E Chapman-Enskog Expansion Of The Pseudo-Temperature Variable 141 F Calculation Of Heat Capacity From Equation Of State (EOS) 143 G Diffusivity And Schmidt Number In FTS 147 H Solubilities Of Gas Components In FTS Liquid 149 I Thermal Boundary Conditions 153 I.1 Validation of implementation of isothermal boundary conditions . . . 154

I.2 Validation of implementation of constant heat flux boundary conditions . . 154

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Acknowledgements 175

List of Journal Publications 179

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Summary

A Lattice Boltzmann Approach to Multi-Phase Surface Reactions

with Heat Effects.

Mohammad Reza KAMALI, Delft University of Technology

The aim of the present research was to explore the promises and shift the limits of the numerical framework of lattice Boltzmann (LB) for studying the physics behind multi-component two-phase heterogeneous non-isothermal reactive flows under industrial conditions. An example of such an industrially relevant topic is the Fischer-Tropsch Syn-thesis (FTS) in the Gas-to-Liquid (GtL) conversion process of methane. The research described in this thesis was carried out in the context of a twin project supported by Shell and STW on structured reactors for Fischer-Tropsch and the meso-scale flow and transport phenomena and catalysis aspects therein.

The complexity of such multi-component two-phase heterogeneous reactive flow sys-tems with thermal effects was a good reason for splitting the topic up into a number of constitutive elements which were tackled individually. The various LB methods available in the literature dealing with all these separate elements were studied; the most promising methods were identified, improved where needed, and implemented in a three-dimensional code structure which was then validated against theory and/or experiment.

At the start of the development of this numerical infrastructure, we implemented an incompressible single-phase LB based flow solver. This was used for analysing in 2-D the flow and for detecting stagnation zones in cross-flow structured packings for tubular fixed bed reactors. This study was combined with an experimental and modelling investigation comparing the heat transfer characteristics of different types of packings in such reactors. Further details of this analysis are provided in Chapter 2 of this thesis.

Then, the LB approach was extended for dealing with multi-component gas-liquid flows over solid surfaces. The pseudo-potential concept due to Shan and Chen (1993) was identified as being the promising method, as it describes the interaction of components and interaction in more fundamental terms and does not require a separate equation for

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tracking the phase interfaces. In this concept, the various components each have their own particle distribution function governed by an own Boltzmann equation. Inter-particle forces are defined in the format of potential functions for each of the components; the interactions between the various components and phases are controlled by parameters denoted as coupling strength. These potential functions should reflect some equation of state (EOS). For the interaction of fluid components with the solid boundaries, a similar approach was considered. These component-component and component-wall pseudo po-tentials and the pertinent coupling strengths are responsible for phase separation, surface tension, density ratio between phases, contact angle and so on; the values of all these continuum variables follow from the selected potential functions and coupling strengths.

The original Shan & Chen concept was introduced for two EOSs only (ideal gas and Van der Waals) and suffered from numerical instabilities for density ratios in excess of, say, 10. More recently, Yuan and Schaefer (2006) came up with improvements allowing the use of different EOSs (such as Carnahan-Starling and Redlich-Kwong) with a positive effect on the numerical stability at higher density ratios. Implementing such modifications resulted in successful simulations of two-phase systems with density ratios as high as 1,000 –depending on the EOS used and on the reduced temperature.

The code developed so far was capable of dealing with single- and multiple-component systems with various density ratios and wettability properties. It was used for studying a variety of cases including a spontaneous phase separation process between two phases, the rise of a single bubble in a liquid pool, fully wetting (Taylor) and partially wetting segmented flows in a straight tube, and almost non-wetting/partially wetting droplet flow in inclined micro-channels. The outcome of these simulations compared favourably with available literature data or experiments. Particularly with respect to the motion of a Taylor bubble through a tube, a comprehensive quantitative analysis was performed tackling different aspects of the bubble and its motion. This validation study comprised the analysis of the variations of liquid film thickness, bubble to liquid velocity ratio, and bubble shape with the Capillary number; also the pressure field in the thin liquid film between bubble and tube wall was evaluated. Further background on this multi-component multi-phase flow solver and the details of the validation studies performed are described in Chapters 3-4 of this thesis.

Solving the energy conservation equation in two-phase systems with phase change phe-nomena included was another step in improving the potential of the current LB approach with the view of the project objectives. In this approach, next to the ones used in the multi-component system, an additional distribution function was introduced for a pseudo-temperature scalar variable ρT . This variable recovers the macroscopic conservation of energy in two-phase mixtures. The rest of the distribution functions take care of the mass and the momentum conservation of the multi-component system. Heats of reaction, enthalpy change associated with phase change, and diffusive transport of enthalpy are all taken into account; the dependence of enthalpy on pressure, which is usually a small effect in most non-isothermal flows encountered in chemical reaction systems, is ignored

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Summary xiii

however. The energy equation was coupled with the LB equations for species transport and the potential interaction forces through the EOS by using the local pseudo-temperature field. In order to control the noise associated with the fluctuations in the pseudo-temperature in the vicinity of the diffused interface, a robust regularized spline algorithm was introduced in the coupling between pseudo-temperature and density. The proposed scheme was used for simulating some benchmark problems the results of which were validated against available analytical solutions. An extensive explanation on this thermal two-phase model and its applications are provided in Chapter 5 of this thesis.

As another important element of this research, the potential of the current multi-component LB methodology for solving the advection-diffusion equation for multiple species was assessed. This study showed –for various velocities and for various values of the ratio of the diffusivities of solvent and solute –that the accuracy of our multi-component LB methodology is high. Of course, this accuracy depends on the spatial resolution, expressed in terms of the diffusion depth per grid spacing. Furthermore, we investigated the accuracy of this model by simulating the mass transfer of a gas-like com-ponent across a gas-liquid interface at a moderate density ratio of the two phases and at a moderate value of Henry’s coefficient. Further details can be found in Chapter 6 of this thesis.

Finally, the current approach was used for simulating the complex interplay of diffusion and surface reaction in a multi-component gas-liquid catalytic chemical reactor under (for the time being) isothermal conditions. The current lattice Boltzmann technique was capable of reproducing quite realistically, at satisfactory temporal and spatial resolution, the combination of species transport across a phase interface, a chemical reaction at a catalytic surface, and the resulting phase change due to the surface reaction. This was observed after careful comparison of the simulation data with analytical models.

We simulated a simplified isothermal 1-D Fischer-Tropsch Synthesis in which hydrogen and carbon monoxide reacted to water and paraffin C15 at a catalytic flat surface with an

educated simplification of the reaction kinetics. This four-component gas-liquid surface reaction with a liquid film covering a catalytic surface from the very beginning resulted in a gradually increasing thickness of the liquid layer as well as in quite realistic species concentration profiles in liquid and gas phases. In our simulated model, the tracked hy-drocarbon was representative of all the possible carbon chain products in such a reaction. In the end, by combining all temporally resolved species concentrations with empirical Anderson-Schulz-Flory (ASF) model and by determining the chain growth probabilities, the pertinent carbon chain products were calculated for the range C1− C60. The

exten-sive description of this multi-component multi-phase surface reaction study is given in Chapter 7 of this thesis.

Finally, Chapters 8 and 9 present the overall conclusions of this project and an outlook for further work.

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Samenvatting

Een rooster Boltzmann aanpak voor meer-fasen, oppervlakte

re-acties met warmte effecten.

Mohammad Reza KAMALI, Technische Universiteit Delft

Het doel van dit proefschrift is om de Lattice Boltzmann (LB) techniek te gebruiken en de grenzen ervan te verleggen voor niet-isotherme, heterogene, reactieve, twee-fasen systemen met meerdere componenten, zoals die voorkomen in industriële toepassingen. Een voorbeeld van een industriële toepassing is Fischer-Tropsch synthese (FTS) voor de Gas-to-Liquids (GtL) conversie van methaan. Dit werk, financieel ondersteund door Shell en STW, is onderdeel van een samenwerking, waarin we onderzoek doen naar gestruc-tureerde reactoren voor Fischer-Tropsch synthese op meso-schaal, waarbij vloeistoftrans-port fenomenen en katalyse een rol spelen.

De complexiteit van gemengde, reactieve, meer-fasen stromingen met temperatuur afhankelijke eigenschappen was een goede reden om het onderwerp op te delen in een aantal gekoppelde vraagstukken, die individueel zijn aangepakt. De in de literatuur beschikbare LB-methoden zijn bestudeerd; de meest veelbelovende methoden voor deze vraagstukken zijn in kaart gebracht, waar noodzakelijk aangepast, en toegepast in een driedimensionaal numeriek model, welke vervolgens is gevalideerd met behulp van theorie en experimenten.

We zijn de ontwikkeling van dit numerieke model gestart met de implementatie van een enkel-fase LB-model voor niet-compressibele fluïda. Deze aanpak is gebruikt om een tweedimensionale analyse uit te voeren op de uniformiteit van het stromingsveld in cross-flow gestructureerde pakkingen voor gepakte bed reactoren. Dit werk heeft een experimentele en een numerieke component, waarin we warmtetransport en warmteover-dracht van verschillende typen pakkingen met elkaar vergelijken. De details van dit werk staan beschreven in Hoofdstuk 2 van dit proefschrift.

Vervolgens werd de LB-methode uitgebreid naar een meer-componenten systeem, welke gasvloeistof stromen over een vaste wand mogelijk maakte. Het pseudopotentiaal model

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van Shan and Chen (1993) werd geïdentificeerd als de meest veelbelovende methode om dit te bereiken, aangezien het de interacties tussen de componenten op een funda-mentele manier beschouwt en er geen extra vergelijking vereist zijn voor het volgen van de grensvlakken tussen de fasen. In dit model worden de verschillende componenten, elk door een verdelingsfunctie gerepresenteerd, beschreven volgens een aparte Boltzmann vergeli-jking. Krachten tussen de componenten worden in de vorm van potentiaalfuncties geïm-plementeerd, waarbij de grootte van de krachten tussen de componenten wordt bepaald door de zogeheten koppeling sterktes. De vorm van de potentiaalfuncties wordt dusdanig gekozen, dat het systeem zich gedraagt volgens een voorgeschreven toestandsvergelijking (TV). Voor de interactie tussen de componenten en de vaste wanden is een soortgelijke aanpak gebruikt. De pseudopotentialen voor de interacties tussen de componenten en tussen de componenten en de wanden, samen met de relevante koppeling sterktes zijn ve-rantwoordelijk voor de fasescheiding, de oppervlaktespanning, de dichtheidsverhoudingen tussen de fasen, de contacthoeken, enz. De waarden van al deze continuümgrootheden volgen uit de geselecteerde potentiaalfuncties en de koppeling sterktes.

Het originele Shan & Chen model werd geïntroduceerd voor twee TV’s (ideaal gas en Van der Waals) en leed aan numerieke instabiliteiten voor dichtheidsverhoudingen groter dan ongeveer 10. Recentelijk kwamen Yuan en Schaefer (2006) met een implementatie van verschillende TV’s (zoals Carnahan-Starling en Redlich-Kwong), welke grotere dichthei-dsverhouding mogelijk maakte door een verbetering van de numerieke stabiliteit. Imple-mentatie van dergelijke wijzigingen resulteerde in succesvolle simulaties van twee-fasen systemen met dichtheidsverhoudingen van ongeveer 1000, afhankelijk van de gebruikte TV’s en van de koppeling sterktes.

De tot dusver ontwikkelde code is toepasbaar op systemen met één enkele of meerdere componenten met verschillende dichtheidsverhoudingen en bevochtigingseigenschappen. De code is gebruikt voor het bestuderen van verschillende vraagstukken, waaronder een spontane scheiding tussen twee fasen, de stijging van een gasbel in een vloeistofbad, een volledig bevochtigde (Taylor ) stroming en een gedeeltelijk bevochtigende (segmented ) stroming in een recht kanaal, en een vrijwel niet bevochtigende en een gedeeltelijk be-vochtigende druppel stroming in een schuin kanaal. De resultaten van deze simulaties stemden overeen met de beschikbare experimentele en numerieke data in de literatuur. Vooral de beweging van een Taylorbel door een kanaal is uitgebreide kwantitatief geanal-yseerd, waarbij verschillende aspecten van de bewegende bel zijn onderzocht. Dit vali-datie onderzoek omvat de analyse van de met het Capillair getal variÃńrende vloeistof-filmdikte, bel tot vloeistof snelheidsverhouding en bel vorm; ook het drukprofiel in de dunne vloeistoffilm tussen de bel en de kanaalwand is onderzocht. Verdere achtergronden met betrekking tot deze meer-componenten, meer-fasen code en de details van de validatie onderzoeken zijn beschreven in de Hoofdstukken 3-4 van dit proefschrift.

De energiebehoudsvergelijking is opgelost voor twee-fasen systemen met faseverander-ing. Gelet op de projectdoelstellingen was dit een verdere stap in het verbeteren van de mogelijkheden van het huidige Lattice Boltzmann model. Naast de distributiefuncties

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Samenvatting xvii

voor de verscheidene componenten is er bij deze benadering een aanvullende distribu-tiefunctie geïntroduceerd voor een scalaire pseudotemperatuur variabele ρT . Deze vari-abele herstelt macroscopisch energiebehoud in twee-fasen mengsels. De overige distribu-tiefuncties waarborgen massa- en impulsbehoud van het meer-componenten systeem. Er is rekening gehouden met reactiewarmtes, enthalpieveranderingen van faseveranderingen en diffusief enthalpietransport. De drukafhankelijkheid van de enthalpie - normaalge-sproken klein voor niet isotherme stromingen in chemische reactiesystemen - is echter verwaarloosd.

De energievergelijking is gekoppeld aan de LB-vergelijkingen voor massa- en impuls-behoud door middel van de toestandsvergelijking (TV), waarbij gebruik is gemaakt van het lokale pseudotemperatuur veld. In de nabijheid van het diffuse grensvlak treden fluctuaties op in de lokale pseudotemperatuur. Om de ruis van deze fluctuaties te onder-drukken werd een robuust geregulariseerd spline algoritme gebruikt in de koppeling tussen de pseudotemperatuur en de dichtheid. Dit schema werd gebruikt om benchmark prob-lemen te simuleren, waarvan de resultaten werden gevalideerd aan de hand van bekende analytische oplossingen. Deze methode en de toepassingen ervan staan verder beschreven in Hoofdstuk 5 van dit proefschrift.

In dit onderzoek werd ook bekeken of de huidige meer-component LB-methode geschikt is om de advectie-diffusievergelijking voor meerdere componenten op te lossen. Op ba-sis van de resultaten voor diverse snelheden en diffusiecoëfficiënten blijkt dat onze meer-component LB-methode een hoge nauwkeurigheid heeft. Uiteraard hangt de nauwkeurigheid af van de ruimtelijke resolutie, uitgedrukt in de verhouding tussen de diffusiediepte en de roosterperiode. Verder hebben we de nauwkeurigheid van het model ook bekeken, door de massaoverdracht te simuleren van een gasachtige component over een grenslaag tussen gas en vloeistof, bij representatieve waarden van de dichtheidsverhouding van de twee fases en van de Henry coëfficiënt. Verdere details staan beschreven in Hoofdstuk 6.

De huidige benadering is tenslotte gebuikte om de complexe interactie van diffusie en oppervlakte reacties te simuleren in een meer-componenten gasvloeistof katalytische chemische reactor, (voorlopig) onder isotherme condities. De huidige LB-methode was tamelijk realistisch in staat om, bij voldoende tijdelijke en ruimtelijke resolutie, de com-binatie van materiaaltransport door een fasegrensvlak, een chemische reactie op een kat-alytisch oppervlak, en de faseovergang ten gevolge van de oppervlaktereactie te simuleren. Dit werd geobserveerd na een nauwkeurige vergelijking van de simulatiegegevens met an-alytische modellen.

We simuleerden een versimpeld, isothermisch, eendimensionaal Fischer-Tropsch syn-theseproces, waarbij waterstof en koolstof reageren tot water en paraffine C15 op een

katalytisch oppervlak met een gefundeerde vereenvoudiging van de reactiekinetiek. Deze viercomponenten gasvloeistof reactie, waarbij het katalytische oppervlak vanaf het begin bedekt wordt door een vloeistoflaag, resulteerde in een geleidelijk toenemende dikte van de vloeistoflaag, en in tamelijk realistische concentratieprofielen van de componenten in de

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vloeistof- en gasfasen. In ons gesimuleerde model was de getraceerde koolwaterstof repre-sentatief voor alle mogelijke koolstofproducten in de Fischer-Tropsch reactie. Uiteindelijk werden de relevante koolstofproducten berekend in het bereik C1 − C60 door alle, in de

tijd opgeloste componentconcentraties met het empirische Anderson-Schulz-Flory (ASF) model te combineren en de kansen op ketengroei te berekenen. De uitgebreide beschri-jving van deze studie naar meer-componenten, meer-fase oppervlaktereacties is te vinden in Hoofdstuk 7 van dit proefschrift.

Hoofdstuken 8 en 9, tenslotte, bespreken de conclusies van dit project en een visie voor toekomstige werkzaamheden.

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Chapter 1

1.1 Introduction to XtL technology

XtL (Gas-to-Liquids, GtL; Coal-to-Liquids, CtL; Biomass-to-Liquids, BtL) technology is a method of producing liquefied hydrocarbons from raw materials such as coal, biomass and natural gas. These processes first of all comprise a unit for the production of synthesis gas (syngas) which is a mixture of mainly CO and H2. Such a syngas production unit

could be a gasifier for conversion of coal and biomass or auto thermal reforming or partial oxidation or a steam reformer for conversion of natural gas. In the next step, the syngas produced is converted into liquid which is a mixture of hydrocarbons, from methane to heavy waxes, through Fischer-Tropsch synthesis (FTS).

Being not limited to a certain range of raw materials, XtL technology has many advantages for energy production. In the early days, synthesis gas was obtained by gasification of coal. It was first done at an industrial scale by Germany during World War 2; later on, substantial developments took place in South-Africa when this country was facing an oil boycott in the 1980’s. These days, CtL has become appealing, especially for countries rich in coal but limited in oil reserves (such as China).

As another incentive for developing and applying XtL technology, one can name in the conversion of natural gas into liquid hydrocarbons especially at the time of decreasing oil reserves. Compared to oil, natural gas is much cleaner. However, usually the gas reserves are located in remote areas making transportation a challenging job. In fact, getting the gas to markets is very difficult because the transportation requires extreme conditions (₋₁₃₀◦C,10_{− 20 bar), dedicated ships and a dedicated receiving terminal. For} this reason, gas associated with oil is often flared. The Fischer-Tropsch route offers an attractive alternative by converting the natural gas to liquid fuels that can be transported with the existing tanker fleet. Moreover, the synthetic oil obtained in this way is much cleaner than crude oil.

Yet another reward in using XtL technology comes from its application in producing liquid bio-fuels obtained by gasification of biomass followed by Fischer-Tropsch synthesis. In these processes it is possible to use wide range of bio materials including solid bio-waste (agricultural, forest or municipal), grasses, woods, and/or algae for production of biofuel. This would make these processes attractive compared to the ones which use fossil fuels, due to to higher yield and the possibility of using by-product plant waste for process

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energy. Moreover, the diesel produced in BtL has high quality with high cetane number and low sulfur content (IEF report in 2010) .

1.2 Fischer-Tropsch synthesis in XtL technology

As described before, an important step in XtL technology is the Fischer-Tropsch synthesis (FTS). In this reaction, H2 and CO are converted into hydrocarbons (mainly paraffins

and olefins) and water over a cobalt or iron based catalyst. A simple stoichiometric reac-tion of this kind is can be:

nCO + (2n + 1)H2 −→ CnH2n+2+ nH2O

FTS is extremely exothermic with the heat of reaction being approximately -170 kJ/mol. Operating conditions are typically 10_{−60 bar and 200−350}◦C. FTS is usually performed in continuous reactor types for both economical and safety reasons. In existing reactors, the temperature and the H2/CO ratio must be kept within narrow ranges, since the

se-lectivity of the reactor is strongly dependent on these variables. In order to control the temperature under the exothermic conditions of this reaction, there are strong require-ments on the heat withdrawal capability of such reactors. The need of high conversion requires high gas-to-liquid and liquid-to-solid mass transfer rates. To obtain high selec-tivity, short diffusion distances are preferred. Acceptable pressure drop and easy catalyst replacement are additional constraints. Typical current FTS reactors are fluidized beds, slurry bubble columns, and multi-tubular fixed bed reactors (Krishna and Sie 1994, Kr-ishna and Sie 2000, Sie and KrKr-ishna 1999). Among these reactors, the multi-tubular fixed bed reactors have an advantage of less back mixing, catalyst attrition and separation problems. Multi-tubular fixed bed reactors with the tubes being packed with catalyst particles is commercially abundant. However, studies show that the deployment of struc-tured reaction environments instead of spherical particles within these may turn them even more efficient. This may be due to improved heat and mass transfer properties, a lower pressure drop, higher active catalyst hold-ups (with a proper design by an optimized thickness layer of the catalyst), simpler scale-up rules, and higher productivity (Vervloet et al. 2009, Pangarkar 2010). The favourable structures according to these authors are Closed Cross Flow Structure (CCFS) and Open Cross Flow Structure (OCFS) on which the next chapter will elaborate in greater detail.

1.3 Application of lattice Boltzmann simulations

A detailed computational (CFD) analysis is an important step in understanding the flow behaviour and eventually designing the multi-tubular fixed bed reactors aimed for the Fischer-Tropsch synthesis. The challenges involved in the application of computational methods come from multiple aspects. In terms of physics, the problem in hand comprises

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1.4. General background of LB and history of LB simulations in the group 3

multiple challenging subjects to be addressed. The cartoon below (Figure1.1) schemati-cally shows the FTS reaction provided that it is performed in a single tube of the reactor in which the walls are coated with a catalyst.

Figure 1.1: Schematic representation of FTS reaction in a tube coated with the catalyst particles.

Apart from the multi-phase flow challenges such as gas-liquid flow in complex geome-tries, the dynamics of the gas-liquid interface, the gas-liquid-solid contact point motion, liquefaction and phase change, pressure drop and so on, there are multiple other issues to take into account in the presence of chemical reactions. For instance, one can think of mass transport within the gas phase (reactants), gas-liquid mass transfer, diffusion of reactants through the liquid phase, and gas-liquid-solid mass transport (diffusion of re-actants through liquid products and into porous catalysts), non-linear multi-component gas-liquid surface reactions, and multi-phase heat transfer and evaporation/condensation due to thermal effects (such as an exothermic reaction). Lattice Boltzmann (LB) simu-lations may be very useful for such detailed simusimu-lations. One of the main advantages of LB simulations –demonstrated throughout the different chapters of this thesis –is in their ability to lump most of these physical, physico-chemical and chemical phenomena in a single recipe.

1.4 General background of LB and history of LB

sim-ulations in the group

Lattice Boltzmann (LB) method has bases in the Boltzmann’s theory which considers gases to be composed of interacting particles which stream (following the equation of mo-tion) and collide (like billiard balls) and can be described by classical mechanics. However, the tremendous amount of particles will cause noises in this analyses making it necessary to come up with some simplifications in the definitions to be able to use this concept for description of real fluids. Having been originated from the lattice gas automata (LGA), LB method allows to use Boltzmann’s theory for such a description by assuming the fluids to be composed of fictitious particles with a certain density distribution function at discrete space, time, and particle velocities. Another simplification comes through approximation of the collision operator (when the particles collide) with the Bhatnagar-Gross-Krook (BGK) relaxation term which allows the method to be more efficient. More detailed description of the method and its application is elaborated in different chapters of this thesis.

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As a relatively new CFD technique, the LB method has been used for simulations of multiple real-life applications. A number of such studies performed in the former Kramers Laboratorium voor Fysische Technologie, nowadays integrated in the Transport Phenomena Group of the Department of Chemical Engineering at Delft University of Technology, are summarized below:

First, Derksen et al. used LB to simulate the flow past a circular cylinder at Reynolds numbers between 0.3 and 120 and arrived at a good agreement with experimental data reported in literature. Then, Derksen and Van den Akker (Derksen and Van Den Akker 1999) used a LB implementation of a Large Eddy Simulation (LES) to study the turbulent flow behaviour driven by a Rushton Turbine. The results obtained in this study covered a range of flow field characteristics such as the distribution of the turbulent kinetic energy and the energy dissipation rate. In this paper, for the first time in the lab, an immersed boundary method was successfully implemented to mimic the effect of the complex no-slip boundary condition of the impeller on the flow. Later on, Derksen and Van den Akker (Derksen and Van Den Akker 2000) used the developed LB technique to perform Large Eddy simulations on a reverse flow cyclone which resulted in a rather accurate prediction of the averaged flow field in the system; in addition, the vortex core precession frequency found in these simulations agreed pretty well with experimental data.

Next, Ten Cate (Ten Cate 2002) studied a crystallization process under turbulent conditions in a baffled industrial crystallizer by doing Large Eddy simulations with the help of LB techniques. The local turbulence information obtained from LES results was used for detailed DNS studies on very large numbers of particles to determine the local crystal-crystal collision frequencies and intensities. Further, the LB method was used by Hollander (Hollander 2002) to study agglomeration in stirred vessels. Rhode (Rhode 2004) focused on extending LB methods for flow simulations in systems involving moving complex no-slip boundaries and particularly on local mesh refinement techniques. He performed a detailed assessment on the accuracy, mass and momentum conservation and on the applicability of these extensions. Hartmann (Hartmann 2005) studied the turbulent flow and mixing and the dissolution of solid particles in a Rushton turbine stirred vessel by means of LB techniques. Van Wageningen (Van Wageningen 2005) used the LB method to simulate the flow behaviour in static mixer reactors. This data together with experiments was used to design such reactors for the purpose of separating copper from waste water streams.

Throughout these years, the main focus of the group was on the turbulent flow in single-phase flowand on the motion of solid particles in a turbulent fluid. Exception-ally, Derksen and Van den Akker (Derksen and Van Den Akker 2007) used an interface-capturing LB method (He et al. 1999, Zhang et al. 2000) for the simulation of liquid-liquid dispersions under turbulent conditions.

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1.5. Scope of this work 5

1.5 Scope of this work

In the current study, as a new path of research in the group, a pseudo-potential multi-component multi-phase LB approach based on (Shan and Chen 1993) is extended to study various aspects of gas-liquid and gas-liquid-solid reactive flows. The particular focus in this project is on the detailed numerical investigation of non-isothermal multi-component gas-liquid flow over catalytic surfaces. The study is aimed at a better understanding of this type of flow leading to optimized designs of the structured packings in multi-tubular fixed bed Fischer-Tropsch reactors which is an important option for XtL (Gas-to-Liquids, GtL; Coal-to-Liquids, CtL; Biomass-to-Liquids, BtL) technology.

1.6 Outline and structure of this thesis

In order to cover the scope and motivation of this work described before, this doctoral thesis comprises several papers published or to be published in scientific journals in the following order:

Chapter 2 of this thesis provides some background on the application of cross flow structured catalytic packings for tubular fixed bed reactors operated in co-current gas-liquid flow conditions. In this chapter, this type of packing is compared with some alter-native packings such as a random bed, a knitted wire structure and an Aluminum-foam structure by using experiments and concluded that cross flow structured packings have higher overall heat transfer characteristics. Chapter 2 further elaborates on LB numerical simulations performed by the developed in-house code of single phase flow in some sim-plified 2-D geometries of Cross Flow Structured Packings (CCFS) which provide details of velocity distributions, rather inhomogeneous, inside the packing elements. These LB simulations show that these inhomogeneities in the flow which can influence the reac-tor efficiency, depend on the geometrical parameters such as the packing width-to-height ratio.

It is important to mention that throughout this thesis we developed, validated and used a pseudo-potential multi-component multi-phase LB based technique for simulation of gas-liquid flows. In our method the forcing scheme and non-ideal equationn of state (EOS) for fluids are accommodated using the Shan and Chen method. In Chapter 3, details of using such a multiphase flow solver for some gas-liquid flow simulations, with rather high liquid to gas density ratios, are presented. Given the importance of using structured packings as discussed in Chapter 2, Chapter 3 presents a dispersed gas(vapour)-liquid flow simulation in an inclined micro-channel with two expanding bends (obtained by simplification of CCFS packings). This chapter further deals with multiple gas-liquid case studies such as the simulation of single bubble rise in an unconfined liquid and Taylor bubble motion in a straight micro channel. These case studies have been performed for different non-ideal fluids (obeying different equations of state) and each of them is aimed at validating different aspects of the gas-liquid flow simulation toolbox developed.

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and the pertinent contact line motion. This issue is an important element for multi-phase flow simulations in structured packings while the surfaces are coated with catalyst par-ticles resulting in a partially wetting system. As the gas bubble immersed in a partially wetting liquid moves over a no-slip solid wall, the contact angle at the fluid-solid inter-face changes by the capillary number in the system. In this chapter, the variation of the dynamic contact angle with the capillary number obtained from the LB simulations was compared with experimental data from the literature. Our results presented in this chapter indicate that in the LB simulation, the contact line moves over the no-slip surface due to evaporation at the nose and condensation at the tail of the bubble. This is in contrast to reality where slip at the contact line facilitates the bubble motion. We show that by controlling the extent of phase transition the simulations can be brought into close agreement with experimental data from the literature.

In Chapter 5, the details of species transport - an essential aspect of FTS - in the current pseudo-potential multi-component multi-phase approach are discussed. The chapter includes multiple validation cases of convection-diffusion processes and compares the results of LB simulations with analytical solutions. Species transport in a single phase and across a gas-liquid interface is studied in this section. The relaxation time is used to tune the required ratio between diffusivity of solute species in a solvent to the diffusivity of solvent species in the solvent (tested for the ratios up to 1000). In flow systems, this ratio can be extended to accommodate the Schmidt number representing the ratio of diffusivity of solute in the solvent to kinematic viscosity of the solvent.

Simulation of surface reactions in multi-component gas-liquid systems with the help of the current LB method is the topic of Chapter 6. This chapter deals with the formu-lation, implementation, and validation of lattice Boltzmann techniques capable of repro-ducing, among other things, species transport across a phase interface, combined with a chemical reaction at a catalytic surface and a phase change due to the surface reaction, which all are relevant to the Fischer-Tropsch Synthesis (FTS) described in Chapter 2. The chapter presents validations of different kinds all related to a simplified one-dimensional isothermal FTS with a liquid film covering a catalytic surface and gradually growing due to the surface reaction.

Chapter 7 illustrates the details of an LB based model proposed for simulating multi-component two-phase thermal flows. As mentioned earlier, the FTS is a highly exothermic reaction and the heat transport properties of the structured packings are very crucial for applying these packing elements in real-life reactors. While the LB method almost exclu-sively has been developed and applied for isothermal flows, the main focus of this chapter is to propose an extension to the LB method to be used for non-isothermal conditions. This extension employs multiple distribution functions, one for a pseudo-temperature variable and the rest for various species. Non-ideal equations of state (EOS) are accommodated using the Shan and Chen method (Shan and Chen 1993). The evolution equation for the pseudo-temperature variable is constructed in such a manner that in the continuum limit one recovers the well-known macroscopic energy conservation equation for the mixtures. Heats of reaction, enthalpy changes associated with phase change and diffusive transport of enthalpy are all taken into account; the dependence of enthalpy on pressure, however,

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1.6. Outline and structure of this thesis 7

which is usually a minor effect in most non-isothermal flows encountered in chemical reac-tion systems, is ignored. The energy equareac-tion is coupled to the LB equareac-tions for species transport through the EOS. Thermal boundary conditions were implemented following the scheme proposed by Zou & He (Zou and He 1997). The proposed scheme is validated against simple test problems for which analytical solutions can readily be obtained.

Finally, Chapter 8 reflects on the pieces of work described in the previous chapters and provides a summary of main conclusions and a perspective for future work.

In addition to the chapters mentioned before, the thesis comprises multiple appendices; each of them may be used as supplementary material presenting details as to the methods presented throughout the thesis.

Note from the author

The different chapters in this thesis are stand-alone journal publications and thus can be read individually. As a result, some explanations and paragraphs may appear more than once.

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Chapter 2 Intensification Of Co-Current

Gas-Liquid Reactors Using Structured

Catalytic Packings: A Multiscale

Approach

2

2.1 Abstract

Cross-flow structured packings for tubular fixed bed reactors operated with co-current gas-liquid flow perform significantly better in terms of overall heat transfer than a randomly packed bed (glass beads), knitted wire packing, and Al-foam structure at a range of gas and liquid flow rates. This is mainly the result of radial directed convective transport of heat, realized by the channel structure of the cross-flow packings. A pseudo-homogeneous 2-D (two-dimensional) plug flow model is found inadequate to quantify variations in over-all heat transfer for experiments with different packing orientations and different gap sizes between the packing structure and the cooling wall, because it does not take directed con-vective transport of heat into account. Numerical simulations are performed to investigate in detail the fluid flow inside the packing. The geometry is defined as sheets separating layers of diagonal channels. For simplicity we assume no fluid exchange between different layers and we approximate the flow in the individual layers as 2-D. The simulated velocity distribution inside the packing is highly inhomogeneous, showing regions of almost zero flow. These inhomogeneities in the flow are shown to depend on geometrical parameters, such as the packing width-to-height ratio and can have strong impact on reactor efficiency.

2_{This chapter is published as: D. Vervloet, M.R. Kamali, J.J.J. Gillissen, J. Nijenhuis, H.E.A. van den}

Akker, F. Kapteijn, J.R. van Ommen “Intensification Of Co-Current Gas-Liquid Reactors Using Struc-tured Catalytic Packings: A Multiscale Approach”, Catalysis Today, Volume 147, SUPPL., September 2009, Pages S138-S143, doi:10.1016/j.cattod.2009.07.015

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2.2 Introduction

Heterogeneous catalysis plays a key role in many processes in the chemical industry. Of-ten the reactants and the products exist in different phases, which can cause inefficiencies because of poor reactant-catalyst contacting, e.g. bypassing, maldistribution, and in-complete wetting. The introduction of structure in reactors is essential to optimize the performance with respect to the phenomena and dynamics that govern at various scales in the reactor, ranging from molecular (catalyst) level to reactor scale (Cybulski and Moulijn 2006). It is expected that imposing structure on the reaction environment of three-phase tubular fixed bed reactors can lead to significant improvements in reactor performance (Kapteijn et al. 1999). The motivation for using structured geometries in tubular reactors is to control the fluid flow paths in the reaction environment, hereby (1) improving gas-liquid-solid contacting in order to maximally exploit catalytic perfor-mance, (2) establishing flow dynamics that minimize axial mixing in order to obtain narrow residence time distributions, and (3) maximizing mixing in the radial direction in order to improve heat transport from the reaction mixture to the wall. The latter one is particularly important for the reaction kinetics that strongly depend on tempera-ture and concentration variations, such as the highly exothermal Fischer-Tropsch reaction (de Deugd, Chougule, Kreutzer, Meeuse, Grievink, Kapteijn and Moulijn 2003, De Deugd, Kapteijn and Moulijn 2003). Realizing uniform radial temperature and concentration pro-files in a tubular fixed bed reactor can greatly improve the reactor performance (Pangarkar et al. 2009). Structured packings based on cross-flow geometries are a good candidate for securing these objectives, while preserving a relatively large surface area and low pres-sure drop (Pangarkar et al. 2008). Understanding the fluid dynamics of these systems is imperative for design purposes, such as mass/heat transfer rates, residence time distribu-tion, fluid hold-up, and consequently conversion. In this chapter we investigate the heat transfer characteristics and flow dynamics of structured packings based on a cross-flow geometry for co-current operated tubular fixed bed reactors.

2.2.1 Structured packings for tubular fixed bed reactors

Radial heat transfer in tubular reactors can be significantly improved through the intro-duction of a geometry that allows for cross-flow in the reaction environment. Cross-flow is convective flow of reactants that has a component perpendicular to the axial reactor direction, which improves the heat transfer by means of radial convective transport in addition to the generally small radial conductive heat transport. This can be realized by choosing a geometry that consists of slanted channels. Figure 2.1 shows a schematic view of a possible flow path in an axial cross-section of a randomly packed bed and a cross-flow structured geometry. Depending on the type of cross-flow structure (CFS) mixing of the reactant flows from different channels can take place at various locations. Two types of CFS are distinguished: (1) the open CFS (OCFS) and (2) the closed CFS (CCFS). Examples of these types of structures are Katapak-MK and Mellapak, developed and manufactured by Sulzer . An OCFS packing consists of a stack of corrugated plates

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2.2. Introduction 11

Figure 2.1: Possible flow paths of reactants (co-current, top-down) through an axial cross-section of a randomly packed bed (left) and a cross-flow structured geometry (right).

with alternating angle configuration (e.g. 45◦ and -45◦. The channels are formed by the corrugations in the sheets. In this case the reactants in the channels are allowed to mix with those of the channels from a neighbouring plate at cross-sections and in the gap between the reactor wall and the packing structure (see Figure2.2). In a CCFS geometry mixing between the channels of two neighbouring plates is prohibited, due to the presence of flat sheets between the corrugated sheets (see Figure 2.2). Evaluation of the mixing

Figure 2.2: Visualization of the OCFS (left) and CCFS (right) structures

zones leads to the visualization of the possible flow paths in the OCFS and CCFS pack-ings, which is depicted in Figure 2.3. Three types of flow paths exist inside the OCFS packing: (a) flow through the centre of the packing moving to the neighbouring layer at each cross-section, (b) flow through the gap between the packing and the reactor wall, and (c) flow through the channels of the packing exiting the channel at the reactor wall and entering a new channel. For the CCFS packing flow type (a) is blocked by the flat sheets; hence only flow types (b) and (c) take place. The actual flow through the packings is a combination of all possible flows.

Note that although the fluids follow a tortuous flow path, this does not automatically imply that plug flow conditions cannot exist. All tortuous flow paths through the packings are of the same length, and therefore plug flow conditions can exist. Deviations from plug flow may arise through either (1) bypassing of the flow through the gap or (2) uneven flow distribution through the channels. Photos of the constructed packings are given in Figure 2.4.

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(a) OCFS (b) OCFS, CCFS (c) OCFS, CCFS

Figure 2.3: Types of flow through an axial cross-section of the packing: (a) flow through the center of the packing moving to the neighboring layer at each cross-section, (b) flow through the gap between the packing and the reactor wall, and (c) flow through the channels of the packing exiting the channel at the reactor wall and entering a new channel.

Figure 2.4: Photos of the OCFS (left) and CCFS (right) packings

2.2.2 Multi-scale approach

We approach the challenges that are associated with the transport phenomena on different length-scales, i.e. the tubular scale (meso-scale) and the channel scale (micro-scale). The strengths of both numerical and experimental work are combined. Reactor operation and performance characteristics in a conceptual process design, i.e. the macro-scale, will not be addressed in this chapter.

2.3 Meso-scale - Experimental

The meso-scale deals with phenomena that take place at length-scales ranging from the tube diameter to tube length. The results of heat transfer experiments at different gas and liquid velocities are shown for the OCFS and CCFS packings, compared to those of

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2.3. Meso-scale - Experimental 13

a randomly packed bed, an open foam packing, and a knitted wire packing.

In order to measure the overall heat transfer coefficient (Uov) of the packings a

cus-tom built set-up is used to measure the gas and liquid temperatures at the entrance and exit of the tube. The temperature profiles at various axial locations in the tube are also monitored. Figure 2.5 shows a schematic representation of the set-up. The column (5.0 cm ), which consists of an insulated pre-column (1.0 m long) and a cooling column (80 cm long), is loaded with a specific packing type. The function of the pre-column is to eliminate any possible entrance effects in the flow. Gas (N2) and liquid (isopar-M, an

Figure 2.5: Schematic representation of the set-up to measure the radial temperature profiles at various locations in the tube in three radial directions.

organic liquid with diesel-like properties) are heated to 65◦C and fed to the pre-column. When the mixture enters the cooling column, heat is transferred to the cooling liquid (water), cooling the mixture to approximately 30 ◦C, depending on the flow rates and the packing properties. Inside the tube the temperature profile is measured by arrays of seven thermocouples (type K) at various axial locations. The radial temperature profiles are measured in three different directions. Measurements were performed with different packings and different packing orientations at superficial liquid velocities ranging from 5 (m/s) to 22 (m/s) and superficial gas velocities ranging from 0.4 (m/s) to 2.6 (m/s). Several packing properties are listed in Table 2.1: the porosity (), the hydraulic channel diameter (dh), the specific surface per reactor volume (av), and the static contribution of

the material to the radial effective thermal conductivity (λstatic).

The overall heat transfer coefficient, Uov, is calculated using the logarithmic mean

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Table 2.1: Investigated packings and parameters.

Packing type Material dh av λstatic

(-) (mm) (m−1) (W m−1 K−1)

Glass beads Silica 0.4 0.9 2000 0.08

Knitted wire Stainless steel 0.9 1.9 1930 1-3

Open foam Aluminium 0.9 2.4 1900 20-25

OCFS Stainless steel 0.84 1.8 1885 2-4

CCFS Stainless steel 0.95 1.6 2400 1

2.3.1 Results and discussion

The results for different packings operated at different superficial gas and liquid velocities are shown in Figure 2.6, adapted from Pangarkar et al. (Pangarkar 2009). In general the overall heat transfer increases strongly with the liquid flow rate, and is only weakly dependent (OCFS, knitted wire) or independent (Al-foam, CCFS) on the gas flow rate. The CFS geometries are found to transfer up to 2.5 times more heat than other packings depending on the flow conditions. At the highest gas velocities the set-up could not be operated with the glass beads due to pressure drop limitations.

We conjecture from the observed increase in the overall heat transfer coefficient of the CFS packings that the promotion of radial heat transfer by means of directed convective transport plays an important role.

The effect of periodic redistribution of the flow inside a structured geometry due to stacking of elements can be seen in Figure 2.7. In this figure the effect of the OCFS packing orientation in the stack, i.e. all packing elements in the same orientation or in alternating 90◦ rotated orientation, is presented in terms of overall heat transfer.

In all cases an alternated rotation of the packing elements yields a higher overall heat transfer coefficient by 15–60%. Similar results were obtained for the CCFS packing.

The effect of small variations in the gap size is shown in Figure 2.8. Three categories of OCFS packings with different gap sizes have been studied: _{∼ 0.1 mm, ∼ 0.3 mm, and} ∼ 0.5 mm.

The effect of the gap size on the overall heat transfer is not significant for low superficial gas velocities. At the largest superficial gas velocity the largest gap size is found to show a 37–54% higher overall heat transfer than that of the medium gap size. Also a narrow gap results in a better heat transfer. A general approach to quantify the effects of radial heat transport and wall heat transfer resistance is given by the two-dimensional pseudohomogeneous plug flow model (Von Scala et al. 1999). This model has also been applied in a similar study by Schildhauer et al. (Schildhauer et al. 2009). The curvature of temperature (T ) over the axial (z) and radial (r) positions (Eq. 2.1) of a tube (radius R) depends on the superficial velocities (u), specific heats (Cp, assumed constant), and

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2.3. Meso-scale - Experimental 15 0 200 400 600 800 1000 1200 1400 U ov (W.m −2 .K −1 ) CCFS OCFS Al−foam Knitted wire Glass beads 22 mm/s 0.4 m/s 22 mm/s 2.6 m/s 5 mm/s 2.6 m/s 5 mm/s 0.4 m/s U L = U G =

Figure 2.6: Calculated overall heat transfer, Uov, at various superficial gas and liquid velocities for

different packings.

radial heat conductivity (λe,r, assumed constant and isotropic) and the wall heat transfer

coefficient αw, assumed constant).

(uLCp,LρL + uGCp,GρG) ∂T ∂z = λe,r ∂2_T ∂r2 + 1 r ∂T ∂r (2.1) With boundary conditions: constant and isotropic) and the wall heat transfer coefficient (αw, assumed constant). z = 0 : T = Tin; r = 0 : ∂T ∂r = 0; r = R :−λe,r ∂T ∂r = αw(Tr=R− Tw) (2.2) Furthermore, it is assumed that all phases (G, L, S) at any one point in the reactor are at the same temperature and that the gas- and liquid phases are in the plug flow regime. Key parameters λe,r and αw are determined by the packing structure and fluid flow properties.

These are estimated by fitting Eq. 2.1 on the measured temperature profile, averaged for all three radial directions at every axial position in the tube. Since the cross-flow structures are not isotropic, i.e. the flow- and heat transfer properties are not the same in all radial directions, the significance of this model for CFS packings is doubtful. It was not attempted to separate the effective radial heat transfer coefficient for the different

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Figure 2.7: Overall heat transfer coefficient, Uov, for different OCFS packing orientations, i.e. same

orientation and alternating orientation at different superficial gas and liquid velocities.

Figure 2.8: Overall heat transfer coefficient, Uov, for OCFS with different gap sizes: ∼ 0.1 mm, ∼ 0.3

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2.4. Micro-scale - Numerical Approach 17

radial directions. In Figure2.9 the normalized radial temperature profile of an arbitrarily chosen experiment is depicted, as well as the resulting fit on Eq. 2.1.

0 0.005 0.01 0.015 0.02 0.025

0.4 0.42 0.44

Radial distance from center (m)

Normalized T (−)

Experimental Model

Figure 2.9: Normalized radial temperature profile, (T _{− T}c)/(Tin− Tc), of a heat transfer experiment

with OCFS packings (z = 35 (cm) from inlet, UL = 18 (mm/s),UG = 1.5 (m/s)) and fitted model.

Clearly, the (parabolic) partial differential equation does not give a representative description of the temperature profile inside the reactor loaded with OCFS packings. The Kolmogorov–Smirnov test also rejects the hypothesis that the residuals are normally distributed at a 95% confidence level. A similar result was found for the CCFS packings. CFS geometries show an increased heat transfer performance, which is not captured by the applied model. This indicates that the radial transport of heat does not follow a random path, and that directed convective transport of heat is a major contributor of the heat transport mechanism. Currently, we are developing such a model that takes directed convective transport of heat into account. A good understanding of the fluid flow is crucial to progress in this direction. For this purpose we use numerical tools.

2.4 Micro-scale - Numerical Approach

We use the Lattice Boltzmann (LB) method to numerically simulate the fluid flow inside the packing. The LB scheme used is based on the single relaxation time BGK (Bhat-nagar–Gross–Krook) approximation (Bhatnagar et al. 1954), defined on the D2Q9

(two-dimensional, nine velocity components) lattice structure (Succi 2001). In the simulations, all relevant length-scales are resolved, from the packing geometry down to the individual channels.

The motivation for using this particular method for this particular problem is threefold. First, with the help of the LB method the complex geometry in the structured packing can be handled easily. Second, implementing parallel codes is straight forward, which is desirable for the highly demanding calculations in structured packings. Third, LB can simply handle the variety of mesoscopic forces and multi-physics involved in the type of processes in which structured packings are applied (such as Fischer-Tropsch synthesis) (Succi 2001).

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2.4.1 Problem description

We study single-phase, gravity driven flow through the CCFS packing. This packing consists of layers, which are composed of diagonal channels. The layers are separated by flat sheets, which inhibit fluid mixing between the different layers. Therefore, we believe that the flow in these layers are independent and can be approximated as 2-D. We have simulated the flow inside four different layers. Figure 2.10b and Table 2.2 show the investigated 2-D domains and the geometrical parameters used in the simulations.

It is noted that the simulated, single-phase hydrodynamics might differ from the multi-phase hydrodynamics inside the real reactor. We are currently extending the simulation code to two-phase flow. Nevertheless, the single-phase results can provide guidelines for packing optimization and more accurate two-phase flow simulations and experiments.

Isopar-M (liquid) with a kinematic viscosity of 3.8_×10−6 (m2/s) was considered to flow inside the packing. The Reynolds number equals 140 (based on liquid inlet velocity and reactor diameter).

Table 2.2: Parameters of the 2-D geometries based on the CCFS packing.

2-D Layer unit I II III IV

DP acking mm 28.6 35.7 42.9 50

DReactor mm 35.7 42.9 50 57.1

Total Grid 64000 76800 89600 102400

Reactor height=229 (mm); packing height=85.7 (mm); gap width= 3.57 (mm); packing channel di-ameter=7.14 (mm); channels diagonal angle= al-ternating 45◦, -45◦ 45º DPacking L P a c k in g L R e a c to r DReactor Gap DChannel II III LayerI I IV III II z x 45º DPacking L P a c k in g L R e a c to r DReactor Gap DChannel II III Layer I I IV III II z x (a) (b)

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2.4. Micro-scale - Numerical Approach 19

2.4.2 Results and discussion

Figure 2.11 shows the liquid streamlines in the different CCFS layers for single-phase (liquid) flow. The flow in the packing is inhomogeneous and in some channels the liquid remains stagnant. This mal-functioning of the packing can lead to drastic reduction in the catalyst efficiency. Furthermore, it can reduce the convective heat transfer in the packing element and increase the possibility of hot spot formation in the catalytic bed.

Figure 2.12shows the distribution of the x-component of the fluid velocity inside four different simulated 2-D layers. From this figure the velocity vectors in the channels as well as in the gap regions can be observed. The x-component of the fluid velocity is the main source of radial heat transfer inside the packing element. Comparing the velocity distributions in different layers shows that the stagnant zones are more pronounced in the off-central layers of the CCFS packing, for which the layer width-to-height ratio is low. An inhomogeneous flow field implies inhomogeneous and poorer heat transport inside the packing. This problem might be reduced by decreasing the height of the stacked packing elements in order to promote mixing between them.

The 2-D velocity fields shown in Figure 2.12 are based on simulations of individual layers, without considering the interactions between them. However, in reality, fluid exiting the diagonal channels, hits the reactor wall, changes direction and moves into the adjacent layers. This interaction between layers promotes the flow to pass through different layers of the packing element. Flow may also bypass the packing following a path in the gap region. The relative importance of these different possible flow paths depends on the gap- and channel-size as well as on the flow rate and pressure drop over the packing. Good reaction efficiency depends on homogeneous heat and flow distribution inside the packing which is achievable by optimizing the before mentioned parameters.

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1

(a) (b) (c) (d)

Figure 2.11: Streamlines in different layers (a) layer I; (b) layer II; (c) layer III; (d) layer IV. The coordinates are scaled in lattices units, where 160 units correspond to the diameter of the central reactor layer.

2.5 Conclusions

CFS packings perform much better in terms of overall heat transfer than the investigated randomly packed bed, foam packing, and the knitted wire packing in tubular reactors. This is largely the consequence of the presence of directed convective transport of the fluid flow through the channel geometry. Periodic redistribution of the liquid by alternating the packing orientation has a positive effect on the overall heat transfer. A large gap size between the packing structure and the cooling wall is shown to be beneficial for the overall heat transfer at large superficial gas velocities. At low superficial gas velocities the effect of different gap sizes on the overall heat transfer is negligible. A general 2-D heat transport model, based on pseudo-homogeneous plug flow, is found inadequate to describe the radial temperature profile inside the tube. The deviations between model and experimental results occur because the model assumes radial symmetry, and does not take direction oriented transport of heat into account. Numerical experiments are performed to investigate the fluid flow inside the packing in detail. The geometry is defined as sheets separating layers of diagonal channels. For simplicity we assume no fluid exchange between different layers and we approximate the flow in the individual layers as 2-D. The simulated velocity distribution inside the packing is highly inhomogeneous, showing regions of almost zero flow. These inhomogeneities, which can strongly impact reactor efficiency, are shown to depend on geometrical parameters, such as the packing

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width-to-2.5. Conclusions 21

(a) (b) (c) (d)

Figure 2.12: x-Component of velocity vectors in different CCFS layers: (a) layer I; (b) layer II; (c) layer III; (d) layer IV. The coordinates are scaled in lattices units, where 160 units correspond to the diameter of the central reactor layer. The velocities are scaled based on the reference vector in the top middle of the figure.

height ratio. Currently, we are working towards full 3-D simulations. These will enable us to study more complicated geometries like the OCFS packing or an array of packings with alternating orientation.

List of symbols

av packing surface per volume (m−1)

Cp specific heat (J kg−1 K) dh hydraulic diameter (m) r radial coordinate (m) R tube radius (m) t time (s) T temperature (K) u fluid velocity (m s−1)

Uov overall heat transfer coefficient (W m−2 K)

z axial coordinate (m)

Greek Symbols:

αw Wall heat transfer coefficient (W m−2 K)

porosity (-)

λ heat conduction coefficient (W m−1 K)

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Chapter 3 Simulating Gas-Liquid Flows By Means

Of A Pseudo-Potential Lattice

Boltzmann Method

3

3.1 Abstract

Dispersed gas (vapour) - liquid flow through an inclined micro-channel with bends has suc-cessfully been simulated, i.e. without numerical difficulties, by means of a two-phase Lat-tice Boltzmann method. Combining in this method the Shan-Chen (Shan and Chen 1993) pseudo-potential interaction model with the Yuan & Schaefer (Yuan and Schaefer 2006a) proposal for dealing with non-ideal equations of state makes high density ratios achiev-able. This approach also allows simulation of gas-liquid flows without explicitly having to track the phase interfaces. Rather, a potential function related to the equation of state for vapour-liquid equilibrium, a coupling strength representing attraction or repulsion between species, and a relaxation time scale take care of micro and meso scale phenom-ena such as phase separation and interfacial tension as well as interphase transport and multi-phase flow. In addition, fluid-wall interaction (contact angle) is taken into account by selecting proper potential functions and coupling strengths. As far as the phase be-haviour is concerned, we assessed our method by studying the phase separation process and by validating against Maxwell’s equilibrium rule. Qualitative validation of our ap-proach of gas-liquid flow has been done by comparing against experimental data on single bubble rise. Detailed simulations were carried out for an individual Taylor bubble in a channel the results of which compared favourably to literature data.

3_{This chapter is published as: M.R. Kamali, H.E.A. van den Akker, ”Simulating Gas-Liquid Flows}

By Means Of A Pseudo-Potential Lattice Boltzmann Method”, Industrial and Engineering Chemistry Research, 2013, 52 (33), pp 11365-11377, DOI: 10.1021/ie303356u

A Lattice Boltzmann Approach to Multi-Phase Surface Reactions with Heat Effects

A Lattice Boltzmann Approach to Multi-Phase Surface

Reactions with Heat Effects

A Lattice Boltzmann Approach to Multi-Phase Surface

Reactions with Heat Effects

Mohammad Reza KAMALI

Contents

Summary

A Lattice Boltzmann Approach to Multi-Phase Surface Reactions

with Heat Effects.

Samenvatting

Een rooster Boltzmann aanpak voor meer-fasen, oppervlakte

re-acties met warmte effecten.

Chapter 1

1.1

Introduction to XtL technology

1.2

Fischer-Tropsch synthesis in XtL technology

1.3

Application of lattice Boltzmann simulations

1.4

General background of LB and history of LB

sim-ulations in the group

1.5

Scope of this work

1.6

Outline and structure of this thesis

Note from the author

Chapter 2

Intensification Of Co-Current

Gas-Liquid Reactors Using Structured

Catalytic Packings: A Multiscale

Approach

2

2.1

Abstract

2.2

Introduction

2.2.1

Structured packings for tubular fixed bed reactors

2.2.2

Multi-scale approach

2.3

Meso-scale - Experimental

2.3.1

Results and discussion

2.4

Micro-scale - Numerical Approach

2.4.1

Problem description

2.4.2

Results and discussion

2.5

Conclusions

List of symbols

Chapter 3

Simulating Gas-Liquid Flows By Means

Of A Pseudo-Potential Lattice

Boltzmann Method

3

3.1

Abstract