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Modeling, Simulation and Optimization of Multiphase Micropacked-Bed Reactors

and Capillary Sonoreactors

Francisco José Navarro Brull

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Departamento de Química Física Facultad de Ciencias

Modeling, Simulation and Optimization of Multiphase Micropacked-Bed Reactors

and Capillary Sonoreactors

Francisco José Navarro Brull

Tesis presentada para aspirar al grado de DOCTOR POR LA UNIVERSIDAD DE ALICANTE

MENCIÓN DE DOCTOR INTERNACIONAL DEL PROGRAMA DE DOCTORADO EN CIENCIA DE MATERIALES

Dirigida por:

Roberto Gómez Torregrosa

Partially funded by the EU project MAPSYN (Microwave, Acoustic and Plasma SYNtheses) under grant agreement No. CP-IP 309376 of the European Union Seventh Framework Program, the Novartis-MIT Centre for Continuous Manufacturing (USA), and the University of Alicante.

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D. Roberto Gómez Torregrosa, catedrático de Química Física de la Universidad de Alicante,

CERTIFICA:

Que el trabajo con título “Modeling, Simulation and Optimization of Multiphase Micropacked-Bed Reactors and Capillary Sonoreactors”, presentado por Francisco José Navarro Brull, ingeniero químico, para aspirar al grado de Doctor con mención internacional dentro del programa de doctorado de Ciencia de Materiales, ha sido realizado en el Departamento de Química Física de la Universidad de Alicante bajo mi supervisión.

Y para que así conste a los efectos oportunos, se firma el presente certificado en Alicante, a 23 de julio de 2018.

Roberto Gómez Torregrosa

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Thesis structure

Section I – Objectives, Hypotheses and Summary... 3 Section II – Published work... 33

• Chapter I: Phase-field Method and Fractal Analysis to Capture and Quantify Multiphase-flow Phenomena... 35

• Chapter II: Modeling Pore-scale Two-phase Flow: on How to Avoid Gas Channeling Phenomena in Micropacked-Bed Reactors via Catalyst Wettability Modification... 45

• Chapter III: Reduction of Dispersion in Ultrasonically-Enhanced Micropacked Beds... 75

• Chapter IV: Experimental Assessments of Micropacked-bed sonoreactors ... 95 Section III – Unpublished work... 109

• Chapter V: Mathematical Models for the Design and Optimization of Sonoreactors...111

• Chapter VI: Analysis and Limitations of Traditional Sonoreactors...119

• Chapter VII: Scaled-up Designs of Micropacked-bed and Capillary Sonoreactors...135

• Chapter VIII: Toward a Holistic Simulation of Reactive Multiphase flows in porous media...161 Section IV – General Conclusions...175 Annex – (ES) ...

Modelado, simulación y optimización de reactores multifásicos miniaturizados de lecho fijo y sonorreactores capilares

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SECTION I

Objectives, Hypotheses and Summary

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3

Modeling, Simulation and Optimization of Multiphase Micropacked-Bed Reactors and Capillary Sonoreactors

In the last decades, miniaturized flow chemistry has promised to bring the benefits of process intensification, continuous manufacturing and greener chemistry to the fine chemical industry. However, miniaturized catalytic processes where gas, liquid, and solids are involved have always been impeded by two main drawbacks: multiphase-flow maldistribution and clogging of capillary reactors.

Consequently, the objectives of this thesis are to:

• Improve the physical understanding of multiphase micropacked-bed reactors via modeling and simulation

• Bring innovative solutions that reduce gas-channeling and dispersion in micropacked-bed reactors via passive or active methods (e.g. power ultrasound)

• Establish a fast prototyping methodology for the acoustic design of sonoreactors

• Design efficient sonoreactors with wide vibrating areas

• Enable capillary flow reactors to handle a high concentration of suspended solids

First principle models have been used to capture the complexity of multiphase flow and optimize the use of power ultrasound within this broad area of research.

Novel sonochemical reactors were prototyped, built and tested following the unique insights given by a modeling and simulation approach.

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Based on previous observations found in the literature, the hypotheses that were assumed in this thesis are the following:

• Micropacked-bed multiphase flow regimes are mainly dominated by viscous stress and interfacial tension forces, leading to gas preferential channels whose presence cannot be diminished by increasing flow rates

• Modifications of the wettability of the substrate or the usage of ultrasonic irradiation can increase the gas–liquid interaction enhancing the overall performance of the micropacked-bed reactors

• The blockage of capillary reactors handling solids in flow can be prevented by high-power ultrasound and cavitation

• The scale-up of traditional sonoreactors is limited by acoustic design principles

• Modeling and simulation can accelerate the innovation process by providing unique insights at the physicochemical level allowing the fast prototyping of chemical reactors

Thesis Background and Funding

This research was initiated and partially funded by the EU project MAPSYN (Microwave, Acoustic and Plasma SYNtheses) developed in the group of Photochemistry and Electrochemistry of Semiconductors (GFES) at the University of Alicante (Spain), under grant agreement No. CP-IP 309376 of the European Union Seventh Framework Program. The modeling and simulation capabilities developed during this period helped to initiate a collaboration with the Jensen Research Group (MIT, USA). The potential benefits of ultrasound applied to flow chemistry were demonstrated thanks to a 9-month research stay and a posterior collaboration as a research affiliate. Prototyping and experimental costs were covered by the Novartis-MIT Centre for Continuous Manufacturing.

Finally, the proper acoustic design and scalability of sonoreactors was examined thanks to GFES research group at the University of Alicante (Spain). The author wants to express his gratitude to everyone who has contributed to this research, especially Prof. Roberto Gómez, Prof. Klavs Jensen, and Prof. Andrew Teixeira.

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Section I

5

Summary

Introduction

The rise of environmental awareness combined with new and more restrictive legislation promotes the redefinition of traditional chemical processes [1]. In conventional catalyst design, the increase of performance for heterogeneous reactions commonly focuses on the active phase, its dispersion, and its interaction with the support [2,3]. While the active phase plays an essential role, new trends in materials science have promoted an increase in the theoretical understanding of catalysts. With the aid of advances in technology and computational design, rational catalyst design (Figure 1) is a new multi-level approach analyzing all the factors to be considered within a heterogeneous catalyst reaction. The optimization of multiple scales is therefore addressed from the active site level (surface-science and theoretical calculations) to the design of the chemical reactor where the process will be carried out.

Figure 1. Rational catalyst design integrates a holistic approach in order to optimize the performance of catalytic reactions. Reprinted (adapted) with permission from [3]. Copyright 2012 American Chemical Society.

For example, selective hydrogenation of alkynes to alkenes is a crucial step in the synthesis of bulk and fine chemicals, especially vitamins A and E [4–9]. The lack of selectivity will cause an over-hydrogenation to alkanes, reason why semi- hydrogenations are carried out traditionally on a lead-poisoned Pd-CaCO3

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Summary

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catalyst known as Lindlar’s catalyst [10]. Furthermore, limited-sized batch reactors with low conversions are the conventional approach for the production of such alkenes due to the need for reaction control. Thus, catalytic semi- hydrogenations experience production limitations due to mass transport [11] and selectivity problems that often require high quantities of solvent and limited pressure. Continuous micro-/mili-reactors have arisen in this context as a promising alternative to conventional batch reactors [12–16]. The miniaturization of flow devices enables greener and more effective chemical production methods [17–19]. Although it is beyond the scope of this work to provide an extensive analysis of miniaturized reactor technologies, it is important to point out their main advantages and disadvantages to choose a proper catalytic reactor to carry out a semi-hydrogenation reaction [11,20].

Micro- vs Milli-reactor Technology

Process intensification is one of the most promising areas of study since it could enable novel reaction methods by scaling down the dimensions of chemical reactors [14,21]. The advantages of miniaturization rely on the internal diameter of the reactor channel that sorts these devices into two categories: microfluidic and millifluidic reactors [22].

Both micro- and milli-reactors exhibit significant advantages over traditional reactors because the reaction conditions in the miniaturized channels noticeably differ from those in large-scale reactors [23,24]. Micro-reactors —also known as Lab on a Chip— reduce the diameter of the reactor channels to tens/hundreds of micrometers [17,25], whereas millireactors usually increase the range up to a few millimeters [22]. In both cases, the flow conditions change radically. At these scales, laminar flow —i.e. low Reynolds number— is obtained and phenomena such as diffusion, among others, become critical. The high increase of the surface- to-volume ratio allows them to sustain fast exothermic reactions under controlled conditions, which significantly improves organic synthetic processes [19].

Segmented flow regimes [26] can enhance the mixing of reactants, significantly reducing the volume of solvents required leading to greener and more economical production methods, with higher yields of target products.

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Section I

7

The miniaturization of chemical processes, as part of process intensification [27–29], has been facing an increasing demand in the fine chemistry sector and, more specifically, in the pharmaceutical industry [14]. However, there is always a technical tradeoff between these milli- and micro-scales [30], where the heat- and mass transfer coefficients to be obtained can significantly differ (see Table 1). The reactor type and scale determine the temperature control and operation time

—i.e. residence time/flow rate— ensuring efficient mixing and high operating pressures [16,31].

Table 1. Differences between micro- and millifluidic devices [22].

Advantages Disadvantages

Microfluidic reactor

(10 – 500 µm of internal reactor diameter)

• High heat transfer and surface-to- volume ratios

• Good heat transfer capabilities

• Ideally suited for optimizing reaction conditions

• Efficient mixing

• Microchannels suffer from restricted flow capacity

• High-pressure drop

• Tendency to block/clog

Millifluidic reactor (500 µm – 1-10 mm of internal reactor diameter)

• Improved flow capacities

• Lower pressure drop

• Reduced clogging risk

• Preparation of multigram to multikilogram quantities

• Possibility to work with micropacked- bed reactors

• Lower heat transfer surface

• Poorer heat transfer capabilities

For example, gas-liquid-solid reaction systems (to carry out alkyne semi- hydrogenations) can be classified according to their different contacting principles [32]:

• continuous-phase microreactors: where gas and liquid phases are not intermixed and their interfaces are well defined along the reaction channel;

• dispersed-phase microreactors: where a mixture of one of the fluids into the other is generated using appropriate inlets or micromixers.

Within this classification, three reactor types (Figure 2) are commonly found in literature [33], namely:

• Falling film microreactor

• Micropacked-bed reactors

• Capillary reactors

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Summary

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Figure 2. Microreactor devices to carry out gas-liquid-solid reactions. Reprinted with permission from [34,35]. Copyright © 2008 and 2013. Elsevier Science S.A.

Falling film microreactors (Figure 2a) offer excellent heat removal capabilities due to their large area-per-unit volume (20,000 m2·m-3) [36]. Exothermic reactions that are inaccessible due to safety constraints become possible. However, their use in hydrogenations is limited because of the relatively slow liquid-side mass transfer [37] and, particularly, the short residence times that this type of continuous-phase microreactors provides [38]. Operating costs can become also prohibiting when special treatments or replacements are needed to face catalyst deactivation on the active surfaces [39]. On the contrary, capillary reactors and micropacked-bed reactors (Figure 2b and 2c, respectively) are widely used in the literature [40–42]

and, therefore, will be the focus of this thesis.

Micropacked-bed reactors

Micropacked-bed reactors, with particle sizes usually in the range of 50-400 μm, are well known because of their versatility for testing catalysts [20,32,43–46].

Among their advantages, these miniaturized packed-bed reactors have unique heat- and mass transfer characteristics thanks to high surface-to-volume ratios that the miniaturization of the reaction channel and catalyst particles provides.

However, kinetic and transport phenomena rely on the complex gas-liquid-solid hydrodynamics of these reactors [22]. When the catalyst particles are smaller than

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Section I

9

~500 μm, the liquid-gas flow regime is determined by viscous stress and interfacial tension rather than by gravity and inertial forces [47,48]. Additionally, the reduction of particle size entails a substantial pressure drop that is difficult to overcome since a numbering-up strategy ―i.e. adding multiple reactor channels―

will tend to cause flow maldistribution. A standard option is to scale-up the design and to increase the inner diameters in the order of 1-10 mm) [16,20]. However, gas phase flows preferentially through the bed and near the wall due to the inevitable local increase in porosity [47]. Consequently, poor radial-mass transfer coefficients are achieved, especially as the reactor diameter increases [49].

Micropacked-bed reactors present the following hydrodynamic behavior [47,50]

when compared to trickle-bed reactors that have catalyst pellets around 1-3 mm of diameter (Figure 3):

• bed is usually saturated with liquid due to strong capillary forces;

• gas exclusively flows through the packed-bed along preferential channels;

• pre-wetting of the system or modification of flow rates do not significantly affect the path once the flow is stabilized.

Figure 3. Conceptualized representation of the hydrodynamic behavior for a macro-scale packed-bed reactor or trickle-bed reactor (top) and a miniaturized packed-bed reactor (bottom). The pie chart shows the volumetric fraction of solid, liquid and gas in the bed (reciprocal of porosity, liquid and gas holdup, respectively).

Reprinted (adapted) with permission from [51] Copyright (2017) American Chemical Society

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Summary

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Consequently, the reduction of particle size modifies the nature of preferential flow paths or “channels” being formed (see Figure 3). In this way, modeling strategies for trickle-bed reactors, which have been based on empirical hypotheses [52], cannot be generally extended to miniaturized devices dominated by viscous stresses and interfacial tension forces [53].

Modeling and Simulation of Gas-channeling Phenomena

In the literature, several authors have applied visualization techniques in order to gain a physical understanding of micropacked-bed media [54–58]. Marquez et al. carried out gas-liquid flow visualization studies through a micro-fabricated plate with different pillar array geometries [56]. This work highlighted how some critical parameters ―fluid viscosity ratio, surface tension, and geometry including wettability― determine the hydrodynamics of these miniaturized systems [59,60].

To simulate the bubble breakup and coalescence through a porous medium, the Phase Field Method (PFM) is preferred given its clear physical basis that provides more accurate and efficient results [61,62]. To have a better understanding of the formation of preferential channels in micropacked-bed reactors, this computational model has been validated against the experimental data set performed by Marquez. Ethanol and polyethylene glycol 200 (PEG-200) were simulated using the constructed micro-fluidic 2D geometry made of ⌀ 120 μm micro-pillar polydimethylsiloxane (PDMS). As described by the authors [56], they modified the wettability of the PDMS with a plasma treatment, which was transferred to the model varying the contact angle.

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Section I

11

Figure 4. Direct visualization of experimental [56] and simulation results (right and left panels in a, b and c, respectively). For the sake of visual comparison, a similar color code is maintained for both sets of panels (gas slugs in black, micro- pillars in grey and liquid phase in white). A comparison measuring the self-similarity of the results is given by computing the fractal dimension of the three flow patterns (d). Reprinted (adapted) with permission from [51]. Copyright (2017) American Chemical Society

The simulated flow patterns reproduced the liquid enclosures inside the gas bubbles as well as the fingering movement of the gas (Figure 4). The Phase Field Method is able to reproduce the experimental micro-scale results. Particularly, the contact angle modifies the gas slugs increasing or decreasing the formation of preferential channels (Figure 4a vs b). The placement of obstacles nearby the gas and liquid inlets created enough perturbation to obtain characteristic flow paths within the reduced simulation domain. To quantify the statistical self-similarity between flow patterns, the fractal dimension was computed by subsampling the experimental and simulation results. Despite the complexity of the transient flow under study, the fractal dimension of the simulated gas-flow patterns is contained within the interquartile range of the experimental data set. The expected differences are attributed to the inlet configuration and inhomogeneous geometry and material wettability [63], which are common uncertainties found experimentally [56]. This agreement points to the fact that PFM is a powerful tool able to capture and foresee the fundamental physical characteristics of the two-phase flow on the scale of the micropacked-bed.

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Summary

12

Wettability Control of Micropacked-bed Reactors

Mass transfer coefficients of micropacked-beds are intimately linked to gas- liquid interactions ―where gas-channeling phenomena are to be avoided― [64,65].

If one tries to reduce the high-pressure drop by increasing the reactor diameter, the mass transfer coefficients are significantly reduced due to the preferential paths being formed near the wall. Albeit flow regime maps can be depicted for each application, there is still a plethora of parameters ―i.e. liquid and gas velocities, physical properties of the fluids, characteristics of the solid surfaces, inherent construction errors or even the design of the fluid inlets― that cannot be taken into account in simple models [66].

For instance, the combined effect of capillary forces, viscous forces and wettability (impact of the contact angle) had not been elucidated until very recently with the aid of Hele-Shaw cell geometries [67–69]. These studies are part of numerous efforts to understand multiphase flows through porous media similar to microparticulate packed-beds in other areas of research: oil recovery [70,71]

and geological carbon dioxide sequestration [72,73], among others [74]. In liquid- liquid porous application domains, preferential channels are usually classified as either capillary or viscous fingering [75]. The capillary number (Ca ≅ 𝜇𝜇u/𝛾𝛾) is used to discern which kind of fingering may occur, where 𝛾𝛾 is the surface tension, 𝜇𝜇 the viscosity and u the velocity magnitude of the fluid being displaced. Interestingly, for capillary flow regimes (𝐶𝐶𝐶𝐶 ≪ 1), decreasing the surface wettability of the particles can help to reduce flow maldistribution to some extent [67,76–78].

The Phase Field Method (PFM) was used to identify key parameters that can significantly reduce gas-channeling problems such as the packed-bed geometry and wettability. It is usually accepted that the catalyst support and solvent should be chosen to properly wet the catalyst surface since it is at the solid-liquid interface where the hydrogenation reaction takes place. The proper choice of catalyst support and solvent is not trivial and modifies the wettability of the surface [79]. When the wettability is misguidedly increased, gas-channeling (Figure 5) occurs.

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Section I

13

Figure 5. Simulation results of an organic solvent and H2 through a randomly packed-bed of particles 100 μm in diameter (mean-centered). Results are calculated for (left) 45º and (right) 75º contact angle values, the latter leading to reduction of gas channeling. The gas phase is represented in red and the liquid in blue. Green colors correspond to the gas-liquid interface, while small white arrows indicate the velocity field. Reprinted (adapted) with permission from [51]. Copyright (2017) American Chemical Society

Radial-mass transfer problems can appear due to the affinity of the liquid to the surface of the substrate. Therefore, the wettability needs to be diminished.

The existence of the observed critical value of the contact angle around 60º can be explained by the geometrical arrangement of the packed-bed [78]. In a close- packed arrangement, wettability is reduced above the 60-75º region, increasing the probability of violent injections of fluid invading the porous structure (also known as Haines jumps) [78]. Thus, reducing the wettability of the particle surface to a certain extent (60 to 90º for capillary-driven flow regimes) can lead to flow regimes where the gas-liquid-solid interaction is homogenously increased. These findings can be primarily used for the design of new catalysts/beds that improve the hydrodynamics in micropacked-beds at different scales, ultimately reducing the existing mass transfer unknowns and limitations.

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Summary

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Reduction of Dispersion in Ultrasonically-Enhanced Micropacked-beds

Micropacked-bed reactors for multiphase catalyst testing are limited by their complex and poorly understood hydrodynamics [40,49,50,55,65]. The beneficial increase of catalytic surface area and liquid holdup (~75%) is counteracted by the formation of gas preferential channels, which significantly reduces gas-liquid interaction [80] and mass transfer. This unpredictable nature of gas- and wall- channeling phenomena is directly linked to the randomly-packed skeleton of particles within the bed. Consequently, poor radial mass transfer coefficients are achieved, especially when the particle diameter is below 500 μm and the reactor diameter increases [49,66]. Decreasing the surface wettability of the particles can help to reduce flow maldistribution to some extent [67,68]. Unfortunately, increasing gas and liquid flow rates cannot eliminate the strong and stable gas- channels produced by viscous forces [49]. However, in oil-recovery systems, where these unfavorable viscous conditions exist, ultrasound irradiation has been successfully used to modify the porous structure showing 10% to 50%

enhancement in permeation [81–84]. Within this context, the use of acoustic energy in multiphase porous media is a novel approach to reduce gas-channeling mass transfer limitations in micropacked-bed reactors for heterogeneously catalyzed processes.

High-power ultrasound applications [85–88] are usually operated in the low- frequency region (20-80 kHz) and is typically applied in two ways: via ultrasonic baths [89] (indirect transmission of acoustic power) or by directly contacting the medium with ultrasonic horns or transducers [76,90–93]. An efficient acoustic design will maximize the amplitude of vibrations at areas of interest by creating standing waves along the resonant structure [88]. However, the proper design of a sonoreactor will be dependent on the operating frequency of interest, construction material(s), assembly, and geometry. To guarantee the correct transmission of acoustic power into the reactor medium, a guideline [94] with the following steps was followed: i) frequency and transducer selection; ii) analytic dimensioning; iii) numerical modeling and design; and iv) final frequency tuning.

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Section I

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Figure 6. Cross-sectional view of a micropacked-bed sonoreactor system attached to a commercial ultrasonic transducer (APC International, Ltd.). At 38 kHz, the acoustic power was efficiently transmitted to the reactor chamber. The red-blue color code indicates positive and negative acoustic pressure, whereas gray scale indicates the displacement of solid materials; orange disks define the piezoelectric ceramics.

Reprinted (adapted) with permission from [51]. Copyright (2017) American Chemical Society

The designed micropacked-bed sonotrode system resonated at 38.0 kHz consuming a maximum of 20 W of load power (Figure 6). The horizontal stepped design provided sufficient displacement gains as illustrated in darker colors. To accurately measure the dispersion and liquid holdup in the multiphase system, a residence time distribution (RTD) setup [48,95,96] was used. The micropacked- bed sonoreactor (Figure 6) had a length of 100 mm and inner-outer diameters of 3.175 and 6.35 mm, respectively. The bed was packed with stainless steel beads of diameter 0.2 mm, and both water and nitrogen were fed continuously into the system at flow rates of 1-5 mL·min-1 and 10-20 sccm, respectively. Bed porosity, determined by weight, was 0.37. No statistical difference was observed between the particle size distribution of fresh and sonicated packing materials. Repeated tracer-response curves were combined and deconvoluted to obtain highly reproducible quantitative dispersion and residence time data.

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Summary

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Figure 7. RTD curves for a two-phase flow micropacked-bed reactor. Sonicated and silent experiment results confirm significant hydrodynamic changes likely due to the reduction of gas-channeling phenomena. Reprinted (adapted) with permission from [51]. Copyright (2017) American Chemical Society

Experimental residence time distributions revealed two orders of magnitude reduction in dispersion with ultrasound (Figure 7), allowing for nearly plug-flow behavior at high flow rates in the bed. Under silent conditions, viscous and capillary forces promote the formation of a segregated flow where much of the gas flows near the reactor wall. In this worst-case scenario [49], unequal velocity gradients appear radially and the tracer distributes unevenly resulting in a substantial tail in the RTD. High-power ultrasound continuously modified the preferential gas channels, significantly reducing the axial dispersion. The benefits of using ultrasound can be attributed to pore-scale phenomena occurring at the gas-liquid interface. The transmitted acoustic energy dynamically modifies the porous structure (partial fluidization) and capillary pressure, disturbing the hydrodynamic resistances and allowing eventual intercalation of the gas phase.

An additional setup was used to directly visualize the effects of power ultrasound on the fluid dynamics of co-current flow. Combined with experimental pressure drop readings, the analyses suggest that ultrasonication of packed-beds may induce minor bed vibrations capable of overcoming capillary and viscous forces to induce bubble break-up and bed homogenization. The efficient use of ultrasound can unlock new pathways for multiphase reactor design and use, enabling the partial fluidization of micropacked-beds.

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Section I

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Low-power Ultrasound to Fluidize and Unclog Capillary Reactors

Capillary reactors can exhibit practical advantages over microreactors as they allow higher throughput and better solid management [22,41]. By reducing the diameter of the reactor to the order of millimeters instead of tens/hundreds of micrometers, the high surface-to-volume ratio of milli-scale reactors is still able to sustain reactions under fine controlled conditions. Examples of the versatility of using commercial capillary tubing and fittings instead of lab-on-a-chip devices have been recently published for fine chemistry on demand in the pharmaceutical industry [97]. Yet, the handling of solids (catalysts, reagents, precipitation of products or by-products) is still one of the main drawbacks limiting their operating window [98]. During reaction, the capillary tubing or connectors can be irreversibly clogged by the formation of solid aggregates or precipitates [99,100].

Figure 8. The Teflon-stacked sono-microreactor was proposed early in the literature [98,101] to handle solid forming reactions (a). Authors assumed that the main unclogging mechanism was due to cavitation. Uneven displacements and acoustic pressure distribution (colored scale in b and c) were obtained when analyzing its acoustic performance.

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Summary

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Acoustic irradiation is an active method to handle solids and avoid clogging in continuous-flow capillary systems [30,100,102], typically applied in the form of ultrasonic baths [103]. The main clogging mechanisms usually involve bridging, fouling or particle deposition [99,104,105]. The usage of power ultrasound to prevent or remediate the blockage of capillary sonoreactors has often been related to cavitation (see Figure 8) [98] as in the case of ultrasonic cleaning applications [106–110]. However, recent acoustic applications to micropacked-bed reactors [111] might indicate that additional mechanisms can produce partial particle fluidization. For instance, purely vibratory forces have been traditionally applied to avoid the formation of jams in hoppers or silos [112,113]. Recent understanding of the physics of granular materials such as arch or bridge formation [114,115], particle stress distributions [116,117] and the use of internal or external energy sources can be reapplied to different scales of interest [113].

High-speed microscopic imaging can be used to understand how ultrasonic irradiation at 51 kHz promotes the local fluidization of a clog formed by ~100 𝜇𝜇m KCl crystals (see Figure 9). Low-power sonication (1W) can prevent and avoid clog formation when there exists a sudden reduction of capillary cross-sectional area. This proof-of-concept visualization illustrates the importance of having a proper distribution of vibrating surfaces rather than a high amplitude at specific points that may induce cavitation. However, the selection of ultrasonic irradiation systems is usually not regarded as determinant since their effects are commonly a means, not an end. However, an understanding of the acoustic design variables and their influence should be taken into account when optimizing the effects of ultrasound instead of just adjusting the applied frequency once the device is mounted [101].

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Section I

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Figure 9. Clogging and unclogging: pressure drop (a) signal and high-speed visualization (b) for a controlled geometry restriction (1.09 mm ID reduced to 0.63 mm over 6 mm of length). The sonication system upstream the capillary restriction (c) fluidizes the 90-150 μm KCl particles suspended by removing and avoiding further clogs (1 ml/min of KCl-saturated water, 51 kHz and 1 W of power).

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Summary

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Scaled-Up Designs of Micropacked-Bed and Capillary Sonoreactors

Possible drawbacks of millireactors are multiphase flow maldistribution, inefficient reactant mixing, and clogging of capillary tubing [22]. Ultrasonic irradiation has been successfully implemented not only to prevent clogging in capillaries but also because of mass transport enhancement [18,76,98,100,104,118].

The immersion of the capillaries in ultrasonic baths is the traditional approach [119]. However, the attachment of capillary tubing to high-power ultrasound transducers [76,91–93], or near ultrasonic probes [89], has recently been found to improve solid handling during the production of active pharmaceutical ingredients [41,120]. To this end, Langevin-type transducers (also known as half-wave or sandwich transducers) provide high electro-acoustical efficiency and relatively low heat generation [93]. Tapered sonotrodes, as used in ultrasonic horns, amplify the acoustic energy by reducing the vibrational cross-sectional area. Devices involving high-energy conversion at low ultrasound frequency (20-80 kHz) are known in the literature as power ultrasound.

The scale-up of sonoreactors [121,122] remains one of the challenges in process intensification for pharmaceutical crystallization [123]. The acoustic field generated within the reactor chamber strongly depends on how the entire device resonates. Ultrasonic horns are usually designed to maximize their vibration modes longitudinally and at a specific frequency [124,125]. Analytical approaches using Langevin equation [126–128] or electromechanical equivalent circuits can be a good starting point for the design of sonoreactors [94]. However, the wider the sonicated area is, the more likely to have vibration modes that form a patterned distribution of nodes and antinodes [129]. By means of the Finite Element Method (FEM), 3D simulations were carried out for modeling the acoustic field inside the reactor, the vibrations of the solid, and the electro-mechanical properties of the transducer. With the addition of slits and the described computer design optimization method, longer extensions of sonoreactors can be achieved.

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Section I

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Figure 10. Cross-sectional simulation view of a micropacked-bed sonoreactor (a) and its scaled-up version (b). The slits (b) guide the sound propagation across the solid whose displacement is represented in the black-white scale. Nodes and antinodes distribute according to the wavelength λ [m], which approximately corresponds to the ratio between the speed of sound (c [m/s]) in the material and the applied frequency (f [Hz]). The acoustic pressure in the porous media corresponds to the colored scale, showing the severe attenuation at the extremes of the sonotrode (a).

The micropacked-bed sonoreactor [111] was scaled-up by a factor of 5 according to its length (Figure 10). The introduction of slits improves the uniformity of vibrations and acoustic pressure within the region of interest. The scaled-up sonotrode acts as a waveguide which also increases the amplitude by reducing the cross-sectional area. Therefore, wider reactor diameters are also possible as shown in the simulation results (Figure 10b) assuming that damping in the media is not too severe [92]. Otherwise, the mechanic energy will be mainly transmitted close to the antinodes that vibrate perpendicularly to the reactor surface.

The simulation approach was validated and used to prototype a variety of acoustic designs. For example, a novel helicoidal capillary sonoreactor was proposed to potentially enable a high concentration of solid particles in miniaturized flow chemistry (Figure 11).

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Summary

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Figure 11. Cylindrical (a, c) and helicoidal (d) sonoreactors showing the different simulated displacement distributions achieved (grey scale), which are validated by tracking the motion response of particles at the surface (b, e). The resonant frequency of the models for the assembled prototypes were all around 28 kHz. The attenuated acoustic pressure (red to blue color scale) indicates the main longitudinal direction of the vibration mode (a).

The simulation results match the experimental observations showing an increase of amplitude and homogenization of the displacement field (Figure 11).

The helicoidal capillary sonoreactor distributes the standing waves patterns created along a cylindrical sonotrode transmission (Figure 11a and 11b compared to 11d and 11e). The displacement field distribution in this design is therefore improved (Figure 11c compared to 11d) even at an applied low-frequency ultrasound of 28 kHz. The advantages of this design were validated using a second drill bit with 370 mm instead of 160 mm of total helicoidal length. More importantly, perhaps, the first principle modeling and rationalization approach validated here unlocks the scale-up of high-power low-frequency ultrasound sonoreactors.

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Section I

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Toward a Holistic Simulation of Reactive Multiphase Flows in Porous Media

Two-phase flows in micropacked-bed reactors were simulated at the pore-scale in this thesis. A physically-based model, named Phase Field Method (PFM), was able to reproduce hydrodynamic experiments found in the literature (see Figure 9). With only one simulation domain, the PFM modifies the fluid properties as a function of an order or phase parameter (𝜙𝜙). A diffuse interface separating the two phases is then obtained by minimizing the mixing potential energy of the system. This allows an accurate physical simulation including topological changes

―e.g., bubble breakup and coalescence through the porous medium [61,130].

However, modeling mass transfer phenomena is challenging due to the concentration discontinuities that appear at the interface. In the literature, two common strategies have been found that use a one-domain formulation but still capture the concentration jump at the diffuse interface:

• Yang and Mao [131,132] transformed the concentrations, molecular diffusivities, mass transfer time and velocities solving the domain as continuous.

• Haroun et al. [133] added a flux term that accounts for the concentration jump at the interface.

Several examples of multiphase reactive flows were published by using these modeling approaches [131,134–137]. Yet, pore-scale models require a detailed geometry and mesh of the micropacked-bed structure. For larger domains or time- scales another approach is necessary. Darcy's law or a suitable generalization is commonly used to this end. These meso-scale or Darcy-scale models neglect the complex structure of the bed and multiphase topology by treating the system as a porous domain. This way, the Navier–Stokes equation will only describe the flow in void (or free) regions, while the Darcy–Brinkman equation can be proposed to capture the porous flow through the micropacked-bed [138]. The porosity increase at the wall and the variation of permeability through the micropacked- bed can be captured using wall porosity functions and the Kozeny equation, respectively. In the literature, similar multiscale models have been used to solve reactive flow in complex media [139–141]. For example, certain modeling frameworks establish different spatial and temporal domains [142–145] as it is

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usually necessary for CO2 sequestration, oil recovery or other research areas that include subsurface flows [146,147].

Figure 12. Multiscale modeling approach of micropacked-bed reactors. Pore-scale and meso-scale simulations can be combined to understand, improve and predict reactor performance.

A modeling framework, where the PFM is used at both scales, can be proposed for modeling micropacked-bed reactors (Figure 12). Significative preferential channels for both phases are present at the pore- and meso- scale level, causing a relatively poor radial dispersion. The inevitable increase of the porosity near the wall and the design of reactor inlets leads to an interplay with the strong capillary and viscous forces present in the micropacked-bed. As the reactor diameter increases, preferential channels can even create hotspots where the yield of a selective hydrogenation will be significantly reduced.

It should be noted that the proposed meso-scale approach needs experimental validation [74,138,148]. In addition, the strategies to include the effect of capillary pressure in unsaturated porous media are still an open area of research [63,149,150]. However, these early simulation results capture the radial mass transfer limitations shown when testing the catalyst performance in micropacked- bed reactors [49]. With experimental techniques such as X-ray microtomography or magnetic resonance imaging, there is no doubt that there will be exciting research opportunities. The advances in both numerical methods and computational power are transforming and accelerating the innovation process in chemical engineering and materials science.

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