Design of Photocatalytic Reactors

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Design of

Photocatalytic Reactors

PROEFSCHRIFT

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

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

in het openbaar te verdedigen op woensdag 30 oktober 2013 om 12:30 door

Mahsa MOTEGH

scheikundig ingenieur geboren te Teheran

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Dit proefschrift is goedgekeurd door de promotor: Prof. dr. ir. M.T. Kreutzer

Copromotor: Dr. ir. J.R. van Ommen

Samenstelling promotiecommissie:

Rector Magnificus voorzitter

Prof. dr. ir. M.T. Kreutzer Technische Universiteit Delft, promotor Dr. ir. J.R. van Ommen Technische Universiteit Delft, copromotor Prof. dr. ir. G. Mul Universiteit Twente

Prof. dr. H.J. Heeres Rijksuniversiteit Groningen

Prof. dr. J. Marugan Rey Juan Carlos University, Möstoles, Spain Prof. dr. ir. C.R. Kleijn Technische Universiteit Delft

Prof. dr. ir. A.I. Stankiewicz Technische Universiteit Delft

Prof. dr. ir. P.W. Appel Technische Universiteit Delft, reservelid

This work was financially supported by Delft University of Technology.

ISBN 978-94-6186-219-8

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Summary

Photocatalysis is a photochemical reaction induced by photon–absorption of a solid material, a "photocatalyst", that remains unchanged during the reaction. Photocatal-ysis has a wide variety of applications, e.g., degrading contaminants in aqueous so-lutions and in air, oxidizing liquid hydrocarbons, and reducing carbon dioxide into valuable hydrocarbons. It has been successfully applied at lab scale and many ad-vancements are achieved with respect to photocatalyst development and the effect of different parameters such as pH, temperature, catalyst loading, and light intensity on the photoreaction kinetics of various compounds. Yet, there are several issues to be resolved for the technology to be widely implemented at large scale. The current limited industrial application of the technology is attributed to, among other factors, the difficulty of quantifying and predicting the photonic efficiency at different steps of the chain of photocatalytic events. Moreover, the strategies for the scale–up of photocatalytic reactors are scarce. There is a lack of guidelines on how to carry out experimental studies, and how to design and operate photocatalytic reactors. This thesis focuses on addressing these issues in multiphase slurry photocatalytic reactors. In this work, we first focused on providing experimentalists with simple guidelines to properly measure kinetic data in well-mixed slurry photoreactors. Whereas in such reactors concentrations are independent of location, the light distribution may still be inhomogeneous. As the light travels through the photoreactor, it is scattered and absorbed by the photocatalyst particles and its intensity drops; since photons initiate the photoreaction, this results in a non–uniform reaction rate in the photoreactor. We calculated the local volumetric rate of photon absorption based on a so-called two-flux model. This model assumes that photocatalyst particles absorb and scatter photons, but scattering happens only in a direction opposite to the incident light. Based on the analysis of the rate of photon absorption, we developed analytical expressions that calculate the minimum optical thickness that is required to ensure no photon transmits through the reactor unused, both for low and for high photon fluxes. We concluded that for a reliable determination of the photoreaction rate, an optically differential photoreactor is needed. In such a photoreactor, the optical thickness is sufficiently

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xii Summary

small for the gradient in the rate of photon absorption to be less than 5%.

In a photocatalytic reaction, the absorbed photons excite the electrons in photocatalyst particles, generating electron–hole pairs. The electron–hole pairs then initiate a set of redox reactions, or recombine to lose the absorbed energy to heat. Many photocat-alytic processes require a supply of oxygen for the progression of the photocatphotocat-alytic chain of events. The role of oxygen is to remove the excited electrons in order to sup-press the recombination of electron–hole pairs. In practice, the aeration is done either externally in a recirculating–flow photoreactor, or internally via sparging air or oxygen into the slurry photoreactor. Considering that bubbles scatter photons significantly, the main research question was whether there is any advantage to separating the aeration and photoreaction units in a photoreactor setup. Thus, we aimed to determine at what gas fractions and bubble diameters, bubbles start having a significant effect on the photonic efficiency in a bubbly slurry photocatalytic reactor. Bubbles scatter the light mainly in the forward direction, and the two–flux model fails to consider that. To cap-ture the scattering characteristics of bubbles, we developed a new optical model. We devised a bidirectional scattering model that accounts for scattering in both forward and backward directions. Based on the photon balances, we showed that for typical values of gas fraction and bubble diameter in bubbly slurry photoreactors, the effect of bubbles on the photon–absorption and photoreaction rate is negligible. Therefore, there is no advantage to separating the aeration and photoreaction units in a photore-actor setup. Moreover, the same guidelines for design and operation of two–phase slurries can be applied to bubbly slurry photocatalytic reactors.

Following the analysis of photonic efficiencies in well–mixed photoreactors, we looked into the extent of diffusion limitations in unstirred photoreactors. As men-tioned previously, the gradient in the rate of photon absorption results in a gradient in the photoreaction rate throughout the photoreactor. This consequently leads to a non-uniform concentration field in the photoreactor. Of course, vigorous stirring can eliminate such concentration gradients, but we find many examples of unstirred pho-tocatalytic reactors for which neither forced nor natural convection is reported. Obvi-ously, when the mass transport is not fast enough to keep up with photocatalysis, the overall reaction rate changes, and the measured kinetic data are obscured by diffusion limitations. Similar criteria were also developed for optically thin reactors. By apply-ing a two–flux model, we showed that the effect of diffusion limitation in rectangular optically thick photoreactors is negligible when the Damkohler number based on re-actor depth in the direction of incident light is smaller than the 10% of the product of optical thickness and the exponent that describes how the reaction rate varies with intensity.

Finally, this thesis presents a case study for the scale–up of photocatalytic reactors for water remediation purposes. A successful implementation of photocatalysis at large–scale calls for an interdisciplinary view over the interplay between all the im-portant parameters that affect the capture and utilisation of photons in a photoreactor.

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Summary xiii

Moreover, the engineering aspects of photocatalysis in terms of contacting patterns and mass transfer rates must be optimized to develop useful design procedures for the scale–up of photocatalytic reactors. In this case study, we chose the reactor configu-ration (i.e., rectangular slurry bubble column) as such to ensure a good mass transfer rate, a high photocatalytic surface area per reactor volume, and a high reactor surface– area–to–volume ratio for a good capture of sunlight. By implementing a bidirectional scattering model, we calculated the local rate of photon absorption and the photonic ef-ficiencies for different steps of the photoreaction. The outcome of photonic efficiency studies revealed that the electron–hole trapping at the surface of the photocatalyst, and the surface reaction efficiency are the bottlenecks of the overall photonic efficiency. Future research efforts must be focused on improving these efficiencies. Despite the low photonic efficiencies, we showed that implementing the principles of process in-tensification, the large scale degradation of cyanide to below its allowable emission threshold set by European legislation is achievable.

Throughout this thesis, we focused on implementing and developing simple models to capture the most relevant phenomena in (bubbly) slurry photocatalytic reactors. We developed analytical expressions and a set of easy-to-calculate criteria for the design and operation of photoreactors. Based on such criteria, this study helps answering some of the main questions related to analysis, design and scale–up of photocatalytic reactors. Finally, based on the analysis of photonic efficiencies, the limiting steps in the overall photonic efficiency were identified. Future research shall indeed focus on improving the efficiency of these limiting steps to make photocatalysis feasible for large–scale applications.

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Samenvatting

Fotokatalyse is een proces waarbij een fotochemische reactie in gang wordt gezet door absorptie van fotonen door een vaste stof, een fotokatalysator, die tijdens de reactie onveranderd blijft. Fotokatalyse heeft een breed toepassingsgebied, zoals afbraak van verontreinigingen in waterige oplossingen en in lucht, oxidatie van vloeibare koolwa-terstoffen en reductie van koolstofdioxide tot waardevolle koolwakoolwa-terstoffen. Het is met succes toegepast op laboratoriumschaal en er is aanzienlijke vooruitgang geboekt op het gebied van de ontwikkeling van fotokatalysatoren en het effect van verschil-lende parameters zoals pH, temperatuur, katalysator concentratie, lichtintensiteit op de kinetica van de fotoreactie van verschillende verbindingen. Om tot grootschalige toepassingen van deze technologie te kunnen komen moeten er nog een aantal kwest-ies worden opgelost. De huidige beperkte industriële toepassing van deze technologie wordt onder andere toegeschreven aan de moeilijkheid om de efficiëntie van fotonen tijdens de verschillende fasen in de keten van fotokatalytische stappen te kwantificeren en te voorspellen. Verder zijn er weinig opschalingsstrategieën voor fotokatalytische reactoren voorhanden. Er is gebrek aan richtlijnen voor het uitvoeren van experi-mentele studies, en voor het ontwerpen en het opereren van fotokatalytische reactoren. Dit proefschrift behandelt deze vraagstukken voor fotokatalytische slurriereactoren. In dit proefschrift wordt in eerst aandacht besteed aan het opstellen van eenvoudige richtlijnen voor het uitvoeren van experimenten om op een juiste en geschikte manier kinetische gegevens te meten in goedgemengde fotokatalytische slurriereac-toren. Hoewel in dergelijke reactoren concentraties plaatsonafhankelijk zijn, kan de lichtverdeling toch inhomogeen zijn. Het licht dat zich door de reactor voortplant wordt op zijn pad verstrooid en geabsorbeerd door de katalysatordeeltjes, waardoor de intensiteit afneemt. Omdat fotonen de fotoreactie starten, resulteert dit voor de re-actor niet in een uniforme reactiesnelheid. We hebben de lokale volumetrische foton– absorptiesnelheid berekend op basis van een twee–flux model. Dit model gaat er van uit dat fotokatalysatordeeltjes fotonen absorberen en verstrooien, met de restrictie dat verstrooiing alleen optreedt in de richting tegengesteld aan de richting van het inval-lende licht. Op basis van de foton–absorptiesnelheid hebben we analytische

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xvi Samenvatting

jkingen afgeleid die de minimale optische dikte berekenen die vereist is om er zeker van te zijn dat er geen fotonen ongebruikt de reactor verlaten, zowel voor lage als voor hoge fotonenflux. We concludeerden hieruit dat voor een betrouwbare bepaling van de fotoreactiesnelheid een optisch geschikte fotoreactor nodig is. In zo’n fotoreactor is de optische dikte klein genoeg om de gradiënt in de foton–absorptiesnelheid kleiner te laten zijn dan 5%.

In een fotokatalytische reactie exciteren geabsorbeerde fotonen elektronen in fo-tokatalysatoren, waarbij paren van elektronen en gaten ontstaan. Deze zogenaamde elektron–gat–paren initiëren een aantal redoxreacties of recombineren waarbij de geabsorbeerde energie als warmte vrijkomt. Veel fotokatalytische processen hebben voor hun voortgang een toevoer van zuurstof nodig. Zuurstof verwijdert de geëxci-teerde elektronen waardoor het effect van recombinatie wordt onderdrukt. In de prak-tijk vindt beluchting extern plaats voor een reactor waarbij het water wordt rondge-pompt, of intern via het bubbelen van lucht of zuurstof door de vloeistoffase in het geval van een slurriereactor. Omdat belletjes fotonen aanzienlijk verstrooien was de belangrijkste onderzoeksvraag of het scheiden van de beluchting en de fotoreactie in de fotoreactor voordelen zou opleveren. Daarom hebben we bepaald bij welke gasfrac-tie en belletjesgrootte deze belletjes een significant effect op de fotonenefficiëngasfrac-tie in een slurriereactor beginnen te krijgen. Belletjes verstrooien het licht voornamelijk in de voorwaartse richting en dit wordt in het twee–flux–model juist niet meegenomen. Om toch de verstrooiingseigenschappen van bellen te beschouwen, hebben we een nieuw optisch model ontwikkeld. We ontworpen een verstrooiingsmodel dat zowel met voorwaartse als met achterwaartse verstrooiing rekening houdt. Gebaseerd op fo-tonenbalansen laten we zien dat voor gasfracties en belgroottes typisch voor beluchte slurriereactoren, het effect van bellen op de foton–absorptie en fotoreactiesnelheid verwaarloosbaar is. Daarom zijn er geen voordelen van het scheiden van beluchting en fotoreactie in fotoreactoren. Dezelfde richtlijnen voor het ontwerp en gebruik van twee–fase slurriereactoren kan dus toegepast worden op drie–fase slurriereactoren. Naar aanleiding van de analyse van foton–efficiëntie in perfect gemengde fotoreac-toren, hebben we gekeken naar de mate waarin niet–geroerde fotoreactoren diffusie– gelimiteerd zijn. Zoals eerder opgemerkt resulteert de gradiënt in foton–absorptie in een gradiënt in fotoreactiesnelheid. De consequentie hiervan is dat er een niet– uniforme concentratieverdeling in de fotoreactor ontstaat. Krachtig roeren kan natu-urlijk concentratiegradiënten uitsluiten, maar er bestaan vele voorbeelden van niet– geroerde fotokatalytische reactoren waarvoor geforceerde noch natuurlijke convectie wordt beschreven. Als de stofoverdracht niet snel genoeg is om gelijke tred te houden met de fotokatalyse zal uiteraard de reactiesnelheid variëren en worden de gemeten kinetische waardes vertroebeld door diffusielimitering. Vergelijkbare criteria werden ook ontwikkeld voor optisch dunne reactoren. We hebben door een twee–flux–model toe te passen het effect van limitering door diffusie in een optisch dikke fotoreactor met een rechthoekige doorsnede bestudeerd. Dit effect blijkt verwaarloosbaar als het

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Samenvatting xvii

Damköhler–getal, gebaseerd op de reactordiepte in de richting van de invallende licht-bundel, kleiner is dan 10% van het product van de optische dikte en de exponent die de variatie van de reactiesnelheid met de lichtintensiteit beschrijft.

Aan het eind van dit proefschrift wordt een case–study over het opschalen van fo-tokatalytische reactoren voor waterzuivering gepresenteerd. Succesvolle implemen-tatie van fotokatalyse op grote schaal vraagt om interdisciplinair inzicht in de interac-ties tussen alle belangrijke parameters die absorptie en efficiënt gebruik van fotonen in een fotoreactor beïnvloeden. Verder dienen de technische aspecten van fotokatalyse in termen van contactpatronen en stofoverdrachtssnelheden te worden geoptimaliseerd om bruikbare ontwerpprocedures voor het opschalen van fotoreactoren te kunnen on-twikkelen. In deze case–study hebben we de reactorconfiguratie zo gekozen (een slurrie–bellenkolom met een rechthoekige doorsnede) dat goede stofoverdracht, een hoog fotokatalytisch oppervlak per reactorvolume en een hoge oppervlakte/volume verhouding van de reactor worden gegarandeerd. Door gebruik te maken van het twee–richtingen–verstrooiingsmodel konden de lokale foton–absorptiesnelheid en de fotonenefficiëntie van de verschillende stappen van de fotoreactie worden uitgerekend. Het resultaat hiervan laat zien dat het verlies van elektron–gat–paren aan het oppervlak van de fotokatalysator en de efficiëntie van de oppervlaktereacties de bottleneck van de algehele fotonenefficiëntie vormen. Toekomstig onderzoek moet worden toegespitst op de verhoging van deze efficiënties. Ondanks deze lage fotonenefficiëntie hebben we laten zien dat door toepassing van procesintensificatie de afbraak van cyanide tot beneden de door de EU toegestane emissiegrenswaarden op grote schaal mogelijk is. In dit proefschrift hebben we de nadruk gelegd op het toepassen en ontwikkelen van eenvoudige modellen waarmee de meest relevante verschijnselen in een fotokatalytis-che slurriereactor kunnen worden beschreven. We hebben analytisfotokatalytis-che uitdrukkingen en een set eenvoudig te berekenen criteria voor het ontwerpen en opereren van fo-toreactoren ontwikkeld. Deze studie draagt door het gebruik van deze criteria bij aan het beantwoorden van een aantal hoofdvragen gerelateerd aan de analyse, het ontwerp en de opschaling van fotokatalytische reactoren. Gebaseerd op de analyses van de fotonenefficiëntie, konden uiteindelijk de limiterende stappen in de algehele fotonen-efficiëntie worden vastgesteld. Toekomstig onderzoek moet er op gericht zijn de ef-ficiëntie van de limiterende stappen te verbeteren en daardoor fotokatalyse op grote schaal toepasbaar te maken.

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1. Introduction

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2 Chapter 1

1.1 Technological challenges for the industrial

imple-mentation of photoreactors

A photocatalytic reaction is a photochemical reaction in which a light-absorbing cat-alyst, a so-called photocatcat-alyst, enhances the rate of a reaction by providing a more energy-efficient reaction pathway. A photocatalytic reaction starts when the photons with sufficient energy – an energy greater than the band gap of photocatalyst – are absorbed by a photocatalyst and consequently excite the electrons into the conduc-tion band, leaving positive holes in the valence band of photocatalyst. The gener-ated electron–hole pair, if not recombined, engages in a set of redox reactions at the surface of the photocatalyst, referred to as a photoreaction. Photocatalysis has been successfully applied to degrade contaminants in aqueous solutions1,2_{, oxidize organic}

contaminants in air3_{, oxidize liquid hydrocarbons}4–6_{, reduce carbon dioxide into}

valu-able hydrocarbons7_{, and other processes}8–11_.

Photons play a vital role in photocatalytic reactions, as in the absence of photons no photocatalytic reaction occurs and the rate of photoreaction depends on how many photons are absorbed by the photocatalyst. As light passes through a photoreactor, its intensity decays as a result of absorption and scattering events by photocatalyst or other particles in the reactor. Consequently, the photon distribution and the rate of photon absorption is not constant throughout the photoreactor, even in ideally-mixed photoreactors. Therefore, it is important to quantify the amount of photons in the photoreactor as a function of position. The quantification of photon distribution pro-file is not only important in photocatalytic reactions, but also in applications such as production of algae in photo-bioreactors.

Many of the photocatalytic reactions in liquid phase follow an oxidative pathway. This means that the generated holes, through the excitation of electrons, will either directly or via the formation of OH radicals oxidize the reactants. These types of reactions require oxygen for the progression of the photocatalytic chain of events. The role of oxygen is to remove the excited electrons in order to delay or inhibit the recombination of the electron-hole pairs and the loss of absorbed energy. Therefore, oxygen must be sparged into the slurry in continuous operations, specially when the concentration of reactants is higher than ppm levels. A suitable configuration for aerated photocatalytic reactors is a slurry bubble column reactor, as depicted in Fig. 1.1.

Despite the successful small-scale implementation of photocatalytic technology pro-cesses, their industrial implementation is hindered due to the lack of sound scale–up guidelines. Developing such guidelines require the correct interpretation of measured kinetic data and quantum efficiencies at lab scale, and translating this information from lab-scale experiments to industrial scale. The correct evaluation and translation of lab-scale data is tied to a sound understanding of fundamental phenomena and their interplay in photocatalytic reactors. These phenomena mainly include the change in

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Introduction 3

air

slurry

bubble

liquid

photocatalyst

Fig. 1.1 A slurry bubble column in which bubbles are dispersed from the bottom region via a gas sparser into a pool of liquid with suspended photocatalyst particles.

the rate of photon absorption throughout the photoreactor, and its consequent effect in inducing diffusion limitations in the photoreactor.

Before we go into details of the objectives of this thesis, let us begin with a short overview of kinetics and light distribution in slurry photocatalytic reactors. This will give enough background to formulate several key questions that are addressed in the following chapters.

1.2 Photoreaction kinetics

The rate of a photoreaction depends not only on the concentration of chemical species but also on that of photons. The common practice is to report the photoreaction rate in terms of the volumetric rate of photon absorption, ea(rD f .C; ea/). However, many

kinetic expressions are reported in literature that solely consider the initial intensity of the illumination source. Such expressions do not provide the intrinsic kinetic rate and if used in a different geometry or for scale up, may result in an unexpected efficiency

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4 Chapter 1

drop. The photoreaction rate is a complex function of ea. At low light intensities,

the photoreaction rate is reported to have a linear dependence on the ea, however, at

medium to high intensities, the dependence is reported to be square root11–15. The reason is that at high intensities, the rate of electron-hole pair generation becomes higher than the reaction at the surface of the photocatalyst. Thus, the recombination of generated electron–hole pairs becomes prominent and the energy of photons is lost, which explains the switch from linear to square–root dependence of reaction rate on ea. In any photoreactor, however, usually both regimes coexist, with high intensities

close to the illumination source diminishing as light travels through the slurry farther from the source. Thus, a proper kinetic rate expression must take this phenomenon into account.

Accurate, but complex kinetic expressions can be achieved by Quasi-steady-state ap-proximations (QSSA) for photocatalytic reactions16_{. In this thesis, we used a}

sim-plified version of such expressions for the limiting case of strongly adsorbing com-pounds17_{in the form of,}

rD k1f .C /g.ea/D k1f .C /k2 1Cp1C 2ea=k2 (1.1)

where f .C / is the part that describes the dependency of reaction rate on concentration and g.ea/ the dependency on the rate of photon absorption.

It is not always possible to separate the concentration dependency from the photon– absorption–rate dependency, but Eq. (1.1) provides a good minimal representation of the important features in photocatalytic reactions. In Eq. (1.1), for small values of ea g.ea/ reduces to ea, hence, a linear dependence, and for large values of ea it

reduces to .2k2ea/1=2, thus, a square–root dependence. The cross-over at ea

k2= marks the rate of absorption per unit slurry volume where recombination of

electrons and holes becomes prominent with respect to surface reaction; In Eq. (1.1), k2depends on material properties and roughly scales with the inverse particle size, and

is the volume fraction of catalyst particles that converts the units of eafrom moles of

photon per unit volume of slurry to moles of photon per unit volume of particle. The parameter represents the wavelength-dependent probability that a photon creates an electron/hole pair.

1.3 Radiative Models

Radiative models are required to calculate the rate of photon absorption and predict the kinetics of a photoreaction. The rate of photoreaction depends not only on the con-centration of reactants, but also on the volumetric rate of photon absorption (ea). In

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Introduction 5

this section we describe different radiative models for the quantification of the amount of absorbed photons by photocatalysts.

1.3.1 Radiative Transfer Equation (RTE) in Participating Media

As light travelling in a certain direction passes through participating media, it goes through scattering and absorption events that cause a gradient in intensity in that di-rection. A part of light is lost due to the absorption by disperse particles and perhaps the continuous medium, and a part is lost as it scatters out of the direction of inci-dent light. At high temperatures, there can be a gain in intensity owing to emission, but photocatalytic reactions are not operated at high temperatures. Another source of intensity gain is when the photons from all other directions are scattered into the direc-tion of incident light (See Fig. 1.2). This gain term is accounted for by integrating over the product of all the photons coming from different directions with the probability of these photons being scattered into the direction of interest. The probability of scatter-ing from a certain direction into another is denoted as the scatterscatter-ing phase function. As a result of this integration, the RTE becomes an integro–differential equation, and its rigorous numerical solution is usually achieved by two main groups of procedures:

(a) Probabilistic methods such as Monte Carlo simulations in which the fate of a sta-tistically meaningful number of photons are followed from their point of emission till they are either absorbed or exit the media18,19_.

(b) Discretization methods such as the Discrete Ordinate Method (DOM) which in-volves the transformation of the RTE into a system of algebraic equations that describe the transport of photons. It is solved by following the direction of prop-agation starting from the boundary condition values20,21_.

The solution of the RTE provides the intensity of light in all directions, from which the rate of photon absorption can be calculated as:

ea.s; t /D Z Z D4 I.s; ; t /d : (1.2)

where, is the monochromic absorption coefficient at wavelength .

1.3.2 Simplified radiative models based on geometric optics

In the simplified models presented here, our approach to model the propagation of light in the medium is based on geometric or ‘ray’ optics. This approach does not include ‘wave’ optics and treats light as rays that propagate through the liquid, the

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6 Chapter 1

(

s

)

I

_λ

, ,t

Ω

ds

s

(

s

)

d

I

_λ

, ,t

_Ω

+

I

λ

Loss via

Absorption

Gain due to

In-‐scattering

Gain due to

Emission

Loss via

Out-‐scattering

Ω : Solid an

gle

(direction

of propaga

tion)

Fig. 1.2 A beam of monochromic light of intensity I.s; ; t / travelling in an absorbing-,

emitting-, scattering medium in the direction of along a path s and wavelength . I.s; ; t /

and I.s; ; t /C dIare the intensities at s, and sC ds, respectively, with dIrepresenting

the net gain in the spectral intensity. Out-scattering takes some photons out from propagation direction into all other directions, while in-scattering causes an increase of intensity due to

the scattering of photons from other directions 0into the direction of interest .

bubbles and the particles. In geometric optics approximation, the surface of the par-ticle that light interacts with are treated as a normal surface. It is an excellent ap-proximation when the particle sizes are large with respect to the wavelength of the light. In the following models, further simplifications are considered with respect to the angular distribution of scattered rays. Although approximate, these simple models can provide a physical understanding and an immediate grasp of the key parameters that play a role in the design and scale–up of photocatalytic reactors22,23_{. Moreover,}

the inherent analytical solution of these models to the rate of photon absorption helps developing design guidelines for such reactors.

Lambert-Beer (Zero Scattering)

If the light passes through a fully homogeneous media, it can be partially absorbed (unless the media is non-absorbing), but it does not scatter. Such phenomena can be expressed via the simple and famous Lambert-Beer law, dI=dsD I. However, passing through non–homogeneous media,

e.g., slurries, the light scatters at any heterogeneous interface24. In typical slurry photoreactors, there is significant scattering as well as absorption. The Lambert-Beer law of light propagation cannot be employed to describe the light intensity distribution in slurry photoreactor, as by neglecting the scattering effect, it overestimates the rate of photon absorption in the photoreactor23_.

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Introduction 7

Unidirectional Scattering (Two-Flux) Model

The two-flux model (TFM)25_{is a 1–D model that considers when a photon hits}

a particle, only scattering or absorption occurs. The scattering probability is given by the particles scattering albedo, !. This model enforces a significant simplification on the angular distribution of scattered photons. In TFM, it is assumed that scattering only occurs in the direction opposite to the incident. Photon balances can be set up based on such assumptions for a unidirectional light of intensity I0 entering an infinitely wide slab of slurry with thickness

L. The solution of these photon balances results in analytical expressions for the light intensity in the forward and backward directions. The rate of photon absorption is then simply calculated as the net gradient of light intensity in both directions22,25_{. This model serves as good approximation of the rate of photon}

absorption and is useful in developing design rule of thumbs for two-phase slurry photocatalytic reactors22_.

Six Flux Model

The six-flux approximation (SFM)23 _{is a 3–D model considering the effect}

of both absorption and scattering. In SFM, it is assumed that scattering occurs in any of the six directions of Cartesian coordinate according to a certain probability factor. These probability factors are derived via a trial and error best fit procedure to the numerical solution of full RTE. For symmetry considerations, the probability of scattering along any of the four directions of the plane normal to the direction of incident light is the same23. Having these probability factors, photon balances are set up in 3 dimensions (6 directions) for a unidirectional light of intensity I0 entering an infinitely wide slab of

slurry with thickness L. Also here, analytical expressions are driven for the light intensity in 6 directions and the net gradient of light intensity provides the rate of photon absorption23_{. This model is more complex, especially since to}

develop the probability factors, one needs to numerically solve the RTE anyway.

1.3.3 Optical properties

Here, we review the relevant optical properties of particles in slurry systems that are required to setup the RTE. The absorption coefficient and the scattering coefficient , which are both expressed per unit length travelled through the slurry, indicate the tendency towards absorption and scattering of photons by photocatalyst particles in the slurry, respectively. These properties are wavelength dependent and therefore, when averaging is necessary, intensity averaged properties must be used, for instance,

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8 Chapter 1

DR Id =R Id . Two other properties to consider are the extinction coefficient

ˇ and the scattering albedo ! defined as,

ˇD C ; !D =ˇ (1.3)

where ˇ is expressed per unit length of slurry and ! is dimensionless. The scattering albedo expresses the relative absorption strength: from !D 0 for absorption–only to !D 1 for scattering–only.

A common dimensionless term in photocatalysis is the optical thickness, denoting how likely scattering and absorption events occur as light travels through the slurry, and is expressed as

D ˇL (1.4)

in which L is the length of the reactor in the direction of flight of the incident photons. In optically thick reactors, hardly any photon penetrates all the way through the slurry. In optically thin photoreactors, many photons pass through the reactor unused. While photocatalyst absorb and scatter light, bubbles, if present in the reactor, only scatter light. Davis26 has shown that when a beam of light illuminates a spherical bubble, the bubble scatters the photons mainly in the forward direction, as shown in Fig. 1.3. It has been shown that also prolate spheroidal bubbles scatter mainly in the forward direction27_{. As is shown in this thesis, the scattering coefficient of a swarm of}

bubbles depends on the gas fraction, bubble diameter, and the probability of scattering in the backward direction (i.e, direction opposite to incident).

Table 1.1 presents the optical properties of some commonly used photocatalysts at wavelength =335 nm and at photocatalyst loading of 0.5 g L 1. The optical prop-erties are wavelength dependent. For information on the optical propprop-erties of the photocatalysts in the full UV–A spectrum can be found elsewhere28–30_{. The optical}

properties of a swarm of bubbles is calculated assuming a gas fraction of 20% and bubble diameter of 4 mm.

1.4 Gaps and objectives

Slurry photocatalytic reactors are commonly used and studied in lab– to pilot–scale applications. Optimum operating conditions have been reported in literature for a spe-cific reaction on a particular photocatalyst in a photoreactor of certain geometry illu-minated by a specific lamp19,31–34_{. These conditions vary for different photoreactions}

and photocatalysts, making the design of photoreactors ambiguous. Many questions arise when considering the design of photoreactors, e.g.,

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Introduction 9

bubble

Fig. 1.3 The angular distribution of scattered rays around a single bubble. The peak in the forward direction indicates the tendency of bubbles to scatter the light in the forward (direction of incident) direction.

Table 1.1 Optical properties of some common photocatalysts and bubbles

Particle ˇ (cm 1) Extinction coefficient ( ) Scattering albedo Pf( ) Forward– scattering probability Anatase Aldrich* _18.5 _0.54 _0.91 Degussa P25* 34 0.59 0.82 40%TiO2(Aldrich)/SiO2* 0.955 0.83 0.90 Hombikat UV100* 13 0.52 0.86 Bubbles** _0.0375 ₁ _0.95

* _{The Optical properties of photocatalysts are reported at wavelength}

D335nm, at photocatalyst loading of 0.5 g L 1.

**_{The optical properties of bubbles are calculated at gas fraction of}

g=20% for

bubbles with average diameter of dB=4 mm.

(b) What operating conditions are optimum for studying the kinetics of photocatalytic reactions?

(c) What operating conditions are optimal for maximising the photonic efficiency in photocatalytic reactors?

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10 Chapter 1

(d) Are there analytical expressions that teach about the maximum achievable pho-tonic efficiency in a photocatalytic reactor?

(e) What are the dimensionless parameters that determine the maximum achievable efficiency?

(f) Can simplified radiative transfer models provide a good approximation of the pho-tonic performance of photocatalytic reactors?

The goal of this thesis is to develop a generic predictive tool based on unique criteria across different photoreactions and photocatalysts that estimates the photonic efficiency and optimum operating conditions in photoreactors. Answering the above–mentioned key questions will help developing guidelines for the design, operation, and scale–up of slurry photocatalytic reactors.

Bubbles in photoreactors suppress the electron-hole recombination by removing the excited electrons from the photocatalyst surface, and thus, they improve the photonic efficiency. However, bubbles may as well adversely affect the photonic efficiency since they scatter the photons significantly. Therefore, many researchers aerate the slurry externally via pumping air into the storage tank as a part of recirculating-flow photoreactor19,35,36_{. Some other aerated the reactor directly in a slurry bubble column}

configuration at pilot–scale37–39_{, and reported an optimum gas holdup and}

photocat-alyst loading. The effect of bubbles on the scattering of photons and the eventual photonic efficiency in slurry photocatalysis was not studied. Some efforts were made to incorporate the effect of scattering by bubbles on the radiation profile in photo– bioreactors, involving the numerical solution of the radiative transfer equation40,41_.

However, there were no criteria in literature that indicate when bubbles start to have a negative effect on the photonic efficiency as a result of extensive scattering. We aim to quantify the effect of bubbles on the loss of photons via scattering. So much is unknown in terms of:

(a) Is there a possibility for the scattered photons to be yet absorbed by the photocat-alyst in the reactor? Or do they escape the photoreactor?

(b) What is the extent at which bubbles scatter light?

(c) What is the angular distribution of scattered photons by a bubble?

(d) In there a simplified radiative model that can capture the scattering behaviour of bubbles? Or shall a new one be developed?

(e) What bubble characteristics affect the extent of scattering in photoreactors?

(f) For typical slurry bubble column photocatalytic reactors what is the maximum loss of overall photonic efficiency caused by scattering by bubbles?

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Introduction 11

If the loss of photons due to scattering by bubbles proves negligible, the positive ef-fect of bubbles on delaying the electron-hole recombination can improve the photonic efficiency in photoreactors. Moreover, in this case, the design rules that are developed for two–phase slurry photocatalytic reactors can be directly applied to the design of three–phase slurry bubble columns.

Some researchers run photocatalytic experiments with numerous number of particles in liquid (i.e., high optical thicknesses) without stirring the reactor42–44. This can lead to diffusion limitations in the reactor, due to the pronounced gradient in the rate of photon absorption in optically thick photoreactors (See Fig. 1.4). Therefore, the gathered kinetic data from experiments in such photoreactors may not be reliable, as the reaction rate is controlled by the diffusion rate. The objective of our investigation is to determine when meaningful kinetic data can be collected from experiments in unstirred photoreactors. For that one needs to know:

(a) When and under what operating conditions can one neglect the diffusion limita-tions in unstirred slurry photocatalytic reactors?

(b) What are the pertinent dimensionless numbers?

(c) Can we provide an analytical expression that predicts the concentration profile as a function of time in unstirred slurry photocatalytic reactors?

Addressing these questions helps developing a criterion to teach whether the exper-imental procedures for studying quantum efficiencies or kinetics are appropriate, or otherwise to set the experimental conditions in such manner to get meaningful data from the experiments. Furthermore, it helps estimating the residence time required to reach a certain conversion in these systems.

Finally, there are very few successful implementations of photocatalytic reactors at large scale. Even though a great body of literature exists on the fundamental aspects of photocatalysis such as kinetics and photonic efficiencies, the developed strategies for the scale–up of photocatalytic reactors are scarce45–48_{. There is simply a lack of}

real–case implementation that has translated the derived kinetic rate expressions at lab scale to large–scale operations. In this thesis, our final goal is to address this issue by presenting a scale–up case study based on the analytical radiative model that we developed for multiphase slurry photocatalytic reactors.

1.5 Outline of the thesis

This thesis consists of an introduction, four related chapters published in or submitted to international journals, and a final chapter on the conclusions and outlook of the

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12 Chapter 1

Fig. 1.4 The profile of the rate of photon absorption ea and the consequent gradient in the

concentration Ciin optically thick photoreactors as a function of reactor depth x. In this figure,

ıris the thickness of reaction region, where the eais significant, ıdis the depletion region over

which the gradient in Ci between reaction region and dark region is evident. The dark region

is the part of reactor where hardly any photon is present. Here, C0is the initial concentration,

Ci.t / is the equilibrium concentration at the edge of reaction region, and I0is the initial light

intensity.

work.

A brief summary of the chapters is given bellow:

Chapter II presents the results of a model study on a two–phase liquid–solid slurry photocatalytic reactors. In this chapter, we quantify the photon losses in each step of the photocatalytic chain of events based on the two–flux model. We develop analytical expressions that provide criteria on when and under what operating conditions the photon losses at each step of the chain of events become larger than 5%, and present a summary of the resulting photonic efficiencies. Finally, we provide guidelines for the appropriate operating condition in slurry photocatalytic reactors to either maximize the photonic efficiency or study kinetics.

Chapter III discusses the effect of bubbles in three-phase slurry bubble columns (SBC) on the scattering of light and the rate of photon absorption. In this chapter, we develop a new analytical radiative model that can accurately capture the optical properties of bubbles, but also those of photocatalytic particles. Based on this model,

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Introduction 13

we report an analytical expression that teaches when the scattering by bubbles results in photon losses of less than five percent as a function of dimensionless bubble scattering coefficient. Further, we summarize the bubble characteristics that affect the overall photonic efficiency in slurry bubble column photoreactors.

Chapter IV addresses the diffusion limitations in unstirred slurry photocatalytic reactors. Diffusion limitations are induced due to the gradient in the rate of photon absorption and photoreaction throughout such photoreactors. In this chapter, we introduce an analytical expression that teaches under what operating conditions in terms of optical thickness and photocatalyst properties diffusion limitations can be neglected in unstirred photocatalytic reactors. Moreover, we address the analytical solution to the concentration gradient at all times in such photoreactors that helps determining the average conversion as a function of residence time.

Chapter V provides a design for a large-scale slurry bubble column photocatalytic re-actor to degrade organic pollutants in a waste-water stream of an Integrated Gasifier Combined Cycle (IGCC) power plant. The photoreactor is aimed at degrading 99% of inlet cyanide to bring its level below the allowable emission threshold set by the Euro-pean Commission. The goal of this case study is to present how one can translate the kinetic data derived at lab–scale experiments to the design of a large–scale photocat-alytic reactor. In this chapter, an effective design with respect to reactor configuration, frontal area, and photonic efficiency is presented.

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Introduction 15

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[34] I. J. Ochuma, O. O. Osibo, R. P. Fishwick, S. Pollington, A. Wagland, J. Wood, and J. M. Winterbot-tom. Three-phase photocatalysis using suspended titania and titania supported on a reticulated foam monolith for water purification. Catalysis Today, 128(1-2 SPEC. ISS.):100–107, 2007.

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[36] M. L. Satuf, R. J. Brandi, A. E. Cassano, and O. M. Alfano. Scaling-up of slurry reactors for the photocatalytic degradation of 4-chlorophenol. Catalysis Today, 129(1-2 SPEC. ISS.):110–117, 2007. [37] D. S. Bhatkhande, S. B. Sawant, J. C. Schouten, and V. G. Pangarkar. Photocatalytic degradation of chlorobenzene using solar and artificial uv radiation. Journal of Chemical Technology and Biotech-nology, 79(4):354–360, 2004.

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aminopyrim-16 Chapter 1

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2. Photocatalytic-reactor

effi-ciencies and simplified

ex-pressions to assess their

rele-vance in kinetic experiments

§

The purpose of this chapter is to provide experimentalists with simple guidelines to properly measure kinetic data from well-mixed photoreactors. Whereas in such reactors concentrations are independent of location, the light distribution will still be inhomogeneous. We use a 1D description of the reactor, and consider both low and high light intensities, leading to a linear and square root dependence of reaction rate on the local volumetric rate of photon absorption, respectively. The two-flux approximation is used to describe the local volumetric rate of pho-ton absorption; even for optically thin reactors (i.e., low catalyst loadings), using Lambert-Beer – neglecting scattering by the catalyst particles – would lead to erroneous results. Analytical expressions are derived for the minimum optical thickness that is required to ensure that upon irradiating the front wall of the reactor no photons escape the reactor at the back. Limiting

values are 3:5 for low photon fluxes and 6:5 for high photon fluxes. For a reliable

deter-mination of the reaction rate, a maximum optical thickness, in the range 0.1–0.55, is calculated. At a smaller optical thickness, the small gradients in the photon absorption rate do not affect the volume-averaged reaction rate by more than 5%, that is, that the reactor then operates in an optically differential mode.

§_{Published as: M. Motegh, J. Cen, P. W. Appel, J. R. van Ommen, M. T. Kreutzer. Photocatalytic-reactor} ef-ficiencies and simplified expressions to assess their relevance in kinetic experiments. Chemical Engineering Journal, 207-208, 1, 2012,doi: 10.1016/j.cej.2012.07.023.

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20 Chapter 2

2.1 Introduction

Kinetic data from photoreactors are frequently obscured by the fact that light distri-bution is not homogenous in these reactors. Contrary to the concentration field that is easily leveled out by mixing, the field of local volumetric rate of photon absorption (ea) is non-homogeneous. This makes it impossible to use the common stirred tank

(CSTR) approximation that reactor conditions are equal to outflux conditions. In most reactors, gradients in photon absorption exist from high rates on the lamp side (either positioned on one side in a one-dimensional scenario or centrally in a spherical or cylindrical geometry) to low rates far from the lamp. These gradients seriously im-pede the possibility to use simple kinetic interpretations of the data. Many of these simplifications are, however, useful. One particularly relevant example is the design of experiments such that photons that enter on one side never leave the reactor on the other side. Then, effectiveness of the catalyst could be described by counting how many molecules are converted per photon that enters the reactor. Another example occurs in developing kinetic expressions (i.e., rD f .C; ea/ using the rate of photon

absorption per volume. In that case, one would like to use as homogeneous an ea-field

as possible: the volume-averaging of eawould otherwise complicate the derivation of

an accurate kinetic rate expression from the experimental data. In conclusion, gradi-ents of light intensity inside the photoreactor, if not accounted for, introduce errors in the interpretation of experimental data.

Photocatalysis in slurry systems has been successfully applied to degrade contami-nants in aqueous solutions, oxidize liquid hydrocarbons, and many other processes1–4. In all these applications of the technology, suitable photocatalyst loadings for optimal reactor operation are often experimentally determined5–10_{. Furthermore, several}

stud-ies have compared the quantum efficiency of different photocatalysts at equal catalyst loadings11–13_{. An equal catalyst loading does not imply, however, that the reactors are}

identical in optical characteristics and behavior: different catalysts often have differ-ent optical properties. At presdiffer-ent, what is missing is a set of easy-to-calculate criteria, using the relevant dimensionless groups, that determine whether the optical reactor characteristics and operation procedures are appropriate for the measurement of quan-tum efficiency and/or the development of kinetic expressions. This certainly does not help when comparing results from different papers.

The purpose of the present chapter is to introduce such general criteria for reactor operation and design. Our main objective is to present simple rules that can be used by experimentalists, with a focus on clear expressions that teach when a step in the photocatalytic chain of events starts to introduces (efficiency) losses larger than, say, 5%. This is in full analogy to similar simplified expressions in reaction engineering for the effects on reaction rates due to axial dispersion14_{, mass transfer}15_{, heat}

trans-fer16_{, to mention just a few. We will introduce, inevitably, simplifications ourselves}

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Photocatalytic-reactor efficiencies and simplified expressions to assess their

relevance in kinetic experiments 21

fields. Understanding flow fields in reaction engineering comes from both simplified analysis and CFD calculations; similarly the radiation transfer equation (RTE) is best addressed by a one-dimensional description, augmented with full optics calculations. Herein, we shall make extensive use of the two-flux approximation (TFA), which has the benefit of including scattering and absorption phenomena, but reduces complexity by simplifying scattering in all possible directions to scattering in only one direction: upon hitting a photocatalyst particle, light is either absorbed or it is scattered in the direction opposite to the incident one.

The chapter is organized as follows: first, the one-dimensional description using the two-flux approximation is briefly summarized, with emphasis on the empirical optical properties that needs to be measured or taken from literature, and on appropriate forms of the rate expression that can be used. The resulting reactor model is analyzed to determine, for each step in the photocatalytic chain of events, the losses with respect to full quantum efficiency (i.e., one reaction per photon). The resulting expressions for these losses then allow the formulation of criteria for the condition to keep these losses smaller than 5%. These criteria are most useful for experimentalists, and are summarized in Table 2.1. Finally, we calculate the maximum optical thickness for which the photon absorption rate can be assumed constant, to reliably determine the reaction rate.

2.2 1D reactor model

2.2.1 Local volumetric rate of photon absorption

To model a photocatalytic reactor, the conservation equations of radiation, momentum, and chemical species must be solved simultaneously. Here, we assume fully mixed reactors, and focus on the coupling between the radiation and chemical species conser-vation equations. The conserconser-vation equation for radiation is the Radiative Transport Equation (RTE). The conservation equation of chemical species is coupled to the RTE via the influence of the rate of photon absorption on the kinetics of a photoreaction. The usual practice is to report the rate of photon absorption eaper unit liquid volume

for homogeneous catalysis and per unit suspended slurry for heterogeneous cataly-sis17_.

Solving for eais complicated when scattering of light occurs: one has to consider the

possibility of scattering in every direction at each collision. One can use a random-walk model (i.e., isotropic scattering) to simplify matters, but that only works if many collisions occur before a photon is absorbed, say, for poorly absorbing, highly scatter-ing particles that would make for poor photocatalysts anyway. The other extreme sit-uation would be zero scattering. In that case, the Lambert-Beer (L-B) law adequately

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22 Chapter 2

describes the local light intensity I in the reactor, from which ea is readily obtained

as the gradient of light intensity in its direction of propagation. In typical photoreac-tors, however, there is significant scattering but also significant absorption. In such cases, simplified models of pseudo-unidirectional scattering (two-flux approximation) or pseudo-hexadirectional scattering (six-flux model) are more suitable.

Before we describe the unidirectional model, we briefly review the relevant optical properties of slurries of photocatalytic particles. We need to know the absorption coefficient and the scattering coefficient , which are both expressed per unit length travelled through the slurry medium. It should be noted that these properties depend on photon wavelength . We treat monochromatic light here and note that mean values are obtained for polychromatic light as, for instance, DR d =R d. In this work,

we will mostly use the extinction coefficient ˇ and the scattering albedo !,

ˇD C ; !D =ˇ (2.1)

where ˇ is also expressed per unit length travelled through the medium and ! is di-mensionless. The scattering albedo expresses the relative absorption strength: from !D1 for scattering-only to !D0 for absorption-only. Most photocatalysts have values that are between these extremes, ! 0:7 typically. These optical properties are read-ily obtained (see e.g. Ref. 18,19), in dilute suspensions such that multiple scattering events can be ignored. While one may use literature values, it should be noted that the extent of agglomeration of the particles has a large effect: large agglomerates catch much less light, as most particles are in the shadow of others inside the agglomerate, and for a given material ˇ scales with the inverse of particle size20_.

In the two-flux approximation (TFA)20_{, it is assumed that scattering occurs only in}

the direction opposite to the incident one. For unidirectional light with intensity I0,

that enters a flat-plate container holding a slurry medium, we solve the RTE for for-ward and backfor-ward light intensity which yields for ea, the volumetric rate of photon

absorption20_.

eaD ˇI0a

beˇ xC ce ˇ x (2.2)

where aD Œ.1 C u/! 1, bD uŒ1 ! C .1 !2/1=2, and cD 1 C ! C .1 !2/1=2 are dimensionless coefficients that depend on the scattering albedo and the optical thickness through u_De 2Œ 1C.1 !2/1=2=Œ1C.1 !2/1=2. The optical thickness is a dimensionless parameter that signifies how many scattering and absorption likely occur when light travels through the entire depth of the reactor, and is expressed as

D ˇL (2.3)

in which L is the length of the reactor in the direction of flight of the incident photons. For thick reactors, hardly any photons will penetrate all the way into the slurry. In that

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Photocatalytic-reactor efficiencies and simplified expressions to assess their

relevance in kinetic experiments 23

0 1 2 3 4 5 0 . 0 0 . 5 1 . 0 ea / I0 (-) x  x ( - ) 0.8 0.95 ω =₀ 0.4 0.6 (a) 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 0 0 . 5 1 . 0 e a / I 0 ( -) 0.95 0.6 ω_{= 0} 0.8 0.4 x  x ( - ) (b) 0 1 2 3 4 5 0 . 0 0 . 5 1 . 0 e a / I 0 /( 1 -q ( )) (-) x  x ( - ) ω= 0 0.4 0.6 0.8 0.95 (c) 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 0 0 . 5 1 . 0 ea / I0 / (1 -q ( )) ( -) 0.95 0.6 ω_{= 0} 0.8 0.4 x  x ( - ) (d)

Fig. 2.1 (a), (b) The dimensionless local volumetric rate of photon absorption, ea=ˇI0 vs.

local optical thickness of photoreactor, xD ˇx for photoreactors with total optical thickness

of (a) D 5 (b) D 0:5 at different scattering albedos (i.e., ratio of scattering to extinction,

!D =ˇ). (c), (d) The corrected dimensionless local volumetric rate of photon absorption,

ea=ˇI0=.1 q.!// vs. local optical thickness of photoreactor, .xDˇx/ for photoreactors with

total optical thickness of (c) _{D 5 (d) D 0:5 at different scattering albedos.}

case, u!0 and thus b!0 , so the profile of I and earesembles the common

Lambert-Beer exponential decay, with an important difference: the higher the scattering albedo, the more light is scattered back, out of the reactor (see Fig. 2.1(a)). In fact, the relative amount that is backscattered out of the slurry is given by q.!/D !Œ1 C coth./.1 !2_/1=2 1_{. Fig. 2.1(c) shows that correcting for these “lost” photons by dividing by}

1 q.!/ indeed collapses all the curves only a single one for D 5. In contrast, for thin reactors, backscattering to the lamp is not the only way that photons escape the slurry: the other losses occur on the side opposite to the light source with photons transmitting out of the reactor. As a result, the curves do not collapse onto a single curve by accounting for the backscattering loss only. In fact, the constant b in Eq. (2.2) does not tend to zero, and the situation is more complex, as is shown in Fig. 2.1 (b),(d) for _{D 0:5.}

Design of Photocatalytic Reactors

Design of

Photocatalytic Reactors

Mahsa MOTEGH

Contents

Summary

Samenvatting

1. Introduction

1.1

Technological challenges for the industrial

imple-mentation of photoreactors

air

slurry

slurry

bubble

liquid

photocatalyst

1.2

Photoreaction kinetics

1.3

Radiative Models

1.3.1

Radiative Transfer Equation (RTE) in Participating Media

1.3.2

Simplified radiative models based on geometric optics

(

s

)

I

, ,t

Ω

ds

s

(

s

)

d

I

, ,t

Ω

+

I

Loss via

Absorption

Gain due to

In-­‐scattering

Gain due to

Emission

Loss via

Out-­‐scattering

Ω : Solid an

gle

(direction

of propaga

tion)

1.3.3

Optical properties

1.4

Gaps and objectives

bubble

1.5

Outline of the thesis

References

2. Photocatalytic-reactor

effi-ciencies and simplified

ex-pressions to assess their

rele-vance in kinetic experiments

§

2.1

Introduction

2.2

1D reactor model

2.2.1

Local volumetric rate of photon absorption

_Ω

In-‐scattering

Out-‐scattering