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Challenges in transfer of gas-liquid reactions from batch to continuous operation: dimensional analysis and simulations for aerobic oxidation

Challenges in transfer of gas-liquid reactions from batch to continuous operation: dimensional... The transfer of gas-liquid reactions from conventional batch processes into continuous operation using milli and micro reactors is claimed as an important step towards process intensification. Importantly, this transfer step should be realized in an early phase of process development, already, in order to minimize research efforts towards the undesired operation strategy. The main challenge of this approach, therefore, arises from lack of knowledge in the early stage of process development and the resulting system with high degrees of freedom. This contribution presents an approach to tackle this challenge by means of mathematical modelling and simulation for the aerobic oxidation of 9,10-dihydroanthracene (DHA) catalyzed by polyoxometalates (POMs) being used as example for gas-liquid reactions. The reaction was chosen as it provides sufficient complexity, since it consists of three consec- utive oxidation steps of DHA and a parallel catalytic redox-cycle according to a Mars-van-Krevelen mechanism. It also provides the challenge of unknown reaction kinetics, which have been estimated in this contribution. The dimensionless balance equations for reactor modeling are derived and parametrized based on early stage experimental results obtained in batch operation mode. The discrimination between batch and continuous operation was performed by means of characteristic dimensionless numbers using the identical mathematical model for comparability reasons. The model was used to perform sensitivity studies with emphasis on the interplay between mass transfer characteristics and reaction kinetics for both the batch and continuous operation mode. The simulation results show that the performance of both operation modes mainly depend on the oxidation state of the POM catalyst, which is caused by the differences in oxygen availability. Therefore, results obtained in batch operation mode are prone to be masked by mass transfer issues, which affects catalyst and reactor development at the same time and may thus cause maldevelopments. With respect to process development it can thus be concluded that the transfer from batch to continuous operation together with mathematical modeling is important in an early phase, already, in order to detect limitations misleading the development. Finally, even simple models with roughly estimated parameters from preliminary experiments are shown to be sufficient in the early phase and can systematically be improved, in the subsequent phases. . . . . Keywords Multiphase reaction Mathematical modelling Flow chemistry Liquid phase oxidation POM catalyst Article highlights • Batch-wise and continuously operated reactors are compared based on Introduction dimensionless reactor models and sensitivity analysis. � The dimensionless mass-transfer parameter is introduced to distinguish Over the last two decades, milli and micro reactors receive an between reactors operated in batch and continuous mode. increasing attention due to the possibilities to shorten the way � Catalyst re-oxidation even limits slow Mars-van-Krevelen driven reac- tions, due to low oxygen availability. from lab to the market. Milli and micro reactors can be scaled- up by numbering-up and the small characteristic lengths pro- * Jens Friedland vide a good reaction control and thermal management [1]. For jens.friedland@uni-ulm.de the production of fine chemicals and pharmaceutical products, the application of small-scale continuous reactors are already Robert Güttel part of the reaction engineer’s toolbox [2]. However, investi- robert.guettel@uni-ulm.de gations in batch reactors are still the method of choice for highly viscous and sticky suspensions or for reaction mixtures Institute of Chemical Engineering, Ulm University, Albert-Einstein-Allee 11, 89091 Ulm, Germany probably producing precipitates, where easy cleaning is 626 J Flow Chem (2021) 11:625–640 favored over high reaction control [3]. Sometimes flow chem- used in reactor design and scale-up. Romanainen and Salmi istry is claimed to be superior in general [4], although there are worked on the simulation of tank reactors and bubble col- still challenges remaining, which can be circumvented by umns, where they implemented gas-liquid reactions applying using batch reactors (e.g. chemical compatibility, clogging film theory [23, 24]. The focus was put on different strategies and fouling) [5]. to solve the material balance numerically, which led to the Currently, liquid phase oxidations are under intensive in- conclusion, that a simultaneous calculation of bulk and film vestigation, because the standard processes for the conversion might be favorable, however, this strategic approach shows of petroleum-based raw materials will be substituted by bio- some instability for the numerical solution [23]. They also derived raw materials in future [6]. Aerobic oxidation of or- showed the application, demonstrating the simulation ap- ganic substrates is particularly attractive, since it allows for proach for the chlorination of butanoic acid in a bubble col- functionalizing organic molecules and their implementation umn. A penetration model was implemented by van Elk et al., into a renewable chemical value chain. This typical applica- who tried to overcome the asymptotic cases usually applied tion, however, comes along with hazardous risks if the reac- and demonstrated the possibility to cover more realistic appli- tion ignites, which becomes severe for large volume batch cation scenarios with a dynamic model [25]. Nevertheless, it is reactors [7]. One approach to minimize the risk of explosion state of the art to apply simplified model equations or its an- or ignition is the utilization of the small characteristic diame- alytical solutions to characterize a gas-liquid reaction system ters provided in milli or micro reactors, which can be chosen [30]. For instance, second order reactions [26] or the influence to be below the safe diameters of the explosive reaction mix- on reactant depletion in a batch reactor [27] are investigated ture [8, 9], however, microreactors are not inherently safe [9]. based in the film model. However, Kucka et al. already de- Therefore, hazardous operation windows are usually avoided. rived expressions for the characteristics of the above men- One of the most frequently used approaches is to operate tioned models and the surface renewal model [28]. In their below the limiting oxygen concentration (LOC) of the organic investigation, different methods for the determination of reac- solvent and/or reagents used in a chemical reaction [10]. tion kinetics are applied to experimental results from a stirred Despite these advantages for continuous operation in milli cell reactor and used to evaluate the reaction of CO with or micro reactors, the batch reactor is often chosen in the early Monoethanolamine (MEA). In the early stage of process de- stages of process development, due to the simpler handling velopment, however, the reaction kinetics might even be un- and flexibility of operation conditions. Further reasons for known and need to be estimated from preliminary experimen- preferring the batch against the flow reactor, especially for tal results. Markoš et al., for instance, present a very detailed gas-liquid reactions, are the complexity and the realization dimensionless model based on the film theory for the oxida- of the desired flow pattern for realistic reaction mixtures. In tion of xylene. They point out that the agreement between addition, the specific mass transfer properties depend on many simulation and experimental results depends on the quality factors, such as physical properties of the fluids [11–13], the of the used kinetics [31]. This is not surprising, since uncer- flow pattern itself and the reactor geometry, which induce tainties are expected to affect simulation results from rigorous significant uncertainties in the mass transfer correlations and models. It has to be emphasized, however, that the benefit of predictability [14–16]. Nevertheless, flow reactors offer the modeling and simulation is not restricted to well-known sys- opportunity to apply spectroscopic methods providing spatial tems, but also suitable for extrapolation and even for explora- concentration profiles, which is improving the knowledge tion towards unknown reaction systems. Modeling and simu- gain during process development [17, 18]. Furthermore, the lation studies for those systems with high degree of freedom, understanding of fluid dynamics and mixing inside the milli though, is rare. Modelling and simulation for even more com- and micro channels is improved, recently [19, 20]. This prog- plex systems currently investigated, like three-phase systems, ress together with the combination of computational fluid dy- are far behind the experimental development [32, 33]. A most namics (CFD) and spectroscopic methods allows to analyze recent investigation by Kappe and Coworkers is a positive the mass transfer characteristics and thus minimize the uncer- example at the matured stage of investigation in the field of tainties in prediction [21, 22]. aerobic oxidation [34]. Nevertheless, the work shows the ef- During development of gas-liquid reaction processes math- fort, which is necessary to keep astride experiments and sim- ematical models play a key role for scale-up and reactor de- ulation, resulting in a fit-for-purpose process model in an early sign (e.g. [23–28]), which need to be adapted to the specific stage of development. They combined reaction experiments case. Therefore, the design and operation parameters of the with two-directional computational fluid dynamics (CFD) reactor, as well as the kinetic parameters of the reactions and simulation for the selective oxidation of diphenyl sulfide to mass transfer are required. Furthermore, a mass transfer model diphenyl sulfoxide applying a copper catalyst. The residence suitable for the problem has to be chosen [29]. In case of well- time distribution was characterized by a pulse experiment and known systems, the relevant information is available and the the mass transfer coefficient was estimated using Higbie’s model can be validated by experimental data, before being penetration model. Thus, the investigation is combining the J Flow Chem (2021) 11:625–640 627 experimental investigations and simulation in order to scale the phase boundary, while the macro or reactor scale covers and predict possible process conditions. Eventually, the coex- the balances for the fluid bulk. istence of suitable models with experimental effort should be a The example reaction chosen justifies the assumption of characteristic commitment in reaction engineering. isothermal conditions, since the adiabatic temperature rise of The present contribution provides a sensitivity study based the reaction mixture is small (21 K) and therefore, heat bal- on modeling and simulation for the transfer of gas-liquid re- ances are neglected. Furthermore, film theory is assumed to actions from batch to continuous operation with emphasis on describe the transport processes in proximity of the phase the particularities in an early phase of process development. boundary, in order to allow for illustrative presentation of Therefore, the dimensionless material balances are derived the simulation results. Concerning the temporal behavior, and parametrized based on experimental results obtained in steady-state conditions are assumed for the meso scale bal- batch operation mode. The discrimination between batch ances. In contrast, unsteady-state balances are formulated for and continuous operation was performed by means of the macro scale, which allows to utilize the residence time to characteristic dimensionless numbers using the identical be used as comparison basis for both reactor types. mathematical model for comparability reasons. The aerobic oxidation of 9,10-dihydroanthracene (DHA) catalyzed by Balance equations polyoxometalates (POMs) is used as an example reaction, being subject of recent research efforts in catalyst [35, 36] Based on the main assumptions, the material balance at the and reactor [37] development. The chosen example provides meso scale can be formulated according to Eq. (1)foraflat sufficient complexity in order to demonstrate the potential of geometry of the liquid film with a thickness of δ ,in order to the model-driven batch-to-conti approach in early stages of derive the profile of the concentration of component A in the process development, since an organic reactant undergoes liquid film c as function of the spatial coordinate x. The rate i,L consecutive oxidation steps catalyzed by POMs via a Mars- r of reaction j in the liquid film is a function of the spatial j,L van-Krevelen (MvK) mechanism. In addition, neither the re- coordinate x, as well, as it depends on the concentrations of the action mechanism, nor the kinetics are known in sufficient reactants. Furthermore, D refers to the diffusion coefficient i,L detail, which is usually the case, if catalyst development is in the liquid phase, while ν holds for the stoichiometric co- i,j in the focus of the research. efficients. We show that a model-based exploration of the complex d c i;L gas-liquid system is possible, despite the presence of uncer- 0 ¼ D þ ∑ ν r ð1Þ i;L i; j j;L dx tainties. In particular, we observed that the oxidation state of the POM catalyst is the crucial factor in the transfer from batch The boundary condition at the gas-liquid interface (x =0)is to continuous operation, which is caused by the differences in provided in Eq. (3), which assumes no chemical reaction tak- oxygen availability. Importantly, this observation is not easily ing place in the gas film. Here, k refers to the gas sided mass i,G accessible by experiments, only, but requires support by transfer coefficient and c to the concentration at the gas- i;L modeling and simulation. We therefore demonstrate that even liquid interface. Furthermore, Henry’s law is used to convert simple models with roughly estimated parameters from pre- the partial pressure of component A in the gas phase p into i i,G liminary experiments are very important tools for a the respective equilibrium concentration c with the simulation-driven transfer from batch to continuous operation i,G,eq Henry-coefficient H according to Eq. (2). For components already in an early stage of process development. with negligible vapor pressures (H = 0) the boundary condi- tion can be simplified to Eq. (4) leading to the absence of mass transfer across the gas-liquid interface. At the interface be- Modelling tween the liquid film and the liquid bulk (x = δ ) the concen- tration has to be a continuous function and thus Eq. (5)is used General concept as respective boundary condition. Note that the bulk fluid is assumed to be well mixed in direction of the coordinate x In order to describe the “batch-to-conti” transformation on a according to the film theory. comparable basis the following approach is used to set up the balance equations. In particular, both the stirred tank reactor p ¼ H c ð2Þ i i;G;eq i;G operated in batch mode (bSTR) and the continuously operated dc plug flow reactor (cPFR) are modeled based on the equal i;L D ¼ k H c −c ð3Þ i;L i;G i i;G;eq i;L meaning of reaction time t in the batch reactor and residence dx x¼0 time τ in the plug flow reactor. Furthermore, the reactor model dc i;L consists of the combination of balance equations at two length D ¼ 0 ð4Þ i;L dx x¼0 scales: The meso scale refers to the balances in proximity of 628 J Flow Chem (2021) 11:625–640 c ðÞ x ¼ δ ¼ c ð5Þ i;L L i;L;b The dimensionless time θ is obtained as the ratio between the reaction time τ and the overall reaction time τ in both At the macro scale Eqs. (6)and (7) describe the material reactor types (Eq. (14)). The dimensionless reaction rate ω balances of the gas and liquid bulk, respectively. Note that the is defined with respect to a reference reaction rate r accord- ref left side of both equations refer to the accumulation in the bulk ingtoEq.(15). It has to be mentioned that the reference fluid. In case of the bSTR τ refers to the time dimension and reaction rate can arbitrarily be chosen and corresponds to the thus the reaction time, while it corresponds to the residence kinetics of the virtual reaction as stated in Eq. (31) for the time τ = z/u with z being the spatial coordinate in flow di- TP present contribution, as will be discussed below in detail. rection and u the two-phase velocity of gas and liquid in the TP cPFR. Therefore, the variable τ quantifies the reaction time for τ θ ¼ ð14Þ both the bSTR and cPFR, which allows for direct comparison of the results obtained for both reactors with respect to reac- j;L ω ¼ ð15Þ tion time. j ref dc a i;G;eq G;L Furthermore, the Hatta number Ha and the Damköhler ¼ −H k c −c ð6Þ i i;G i;G;eq i;L dτ ε number Da are defined (Eqs. (16)and (17)). It becomes ob- dc J a i;L;b i;δ G;L vious that the chosen reference reaction rate determines the ¼ þ ∑ ν r ð7Þ i; j j;L;b dτ ε meaning of the values obtained for Ha and Da and thus re- L j quires a closer look as discussed in detail below (see Eq. (31)). dc i;L J ¼ −D ð8Þ For Ha the assumption of film theory with k = D /δ allows i;δ i;L i,L i,L L dx x¼δ to eliminate the liquid film thickness δ . The Biot number Bi L i relates the gas and liquid sided mass transfer to each other (Eq. The right side of Eq. (6) describes the mass transfer be- (18)). Finally, the Hinterland ratio Hi relates the liquid volume tween the gas bulk and the gas-liquid interface according to V to the volume of the liquid film V and can be expressed L L,f the boundary condition introduced in Eq. (3) with the specific using the film theory and geometric considerations as shown gas-liquid interfacial surface area a = A /V , the gas G,L G,L R in Eq. (19). holdup ε = V /V and the reactor volume V . In Eq. (7) G G R R chemical reaction in the liquid bulk r is considered, which 2 j,L,b δ r D r ref 1;L ref 2 L Ha ¼ ¼ ð16Þ equals r (x = δ ). Furthermore, J refers to the mass flux j,L L i,δ D c c 1;L 1;ref 1;ref 1;L density of component A between the liquid film and the liquid bulk according to Eq. (8). The balance equations at the macro r τ ref Da ¼ ð17Þ scale thus correspond to an initial value problem with the I 1;ref initial conditions provided in Eqs. (9)and (10). H k H k i i;G i i;G Bi ¼ δ ¼ ð18Þ i L c ðÞ τ ¼ 0¼ c ð9Þ i;G;eq i;G;eq;0 D k i;L i;L c ðÞ τ ¼ 0¼ c ð10Þ i;L i;L;0 V ε k L L 1;L Hi ¼ ¼ ð19Þ V a D L; f G;L 1;L The resulting dimensionless material balance at the meso Dimensionless balance equations scale is shown in Eq. (20) with the corresponding boundary conditions in Eqs. (21)and (22). Note that steady-state is The dimensionless form of the balance equations is derived assumed for these balance equations. based on the following definitions. First, the concentrations and initial conditions are transformed into residual fractions f d f i;L i;L 0 ¼ þ Ha ∑ ν ω ð20Þ according to Eqs. (11)and (12)with c chosen as the refer- i; j j 1,ref 2 D dχ 1;L j ence concentration. Furthermore, the dimensionless spatial df coordinate χ in the film is defined as indicated in Eq. (13). i;L ¼ Bi f −f ð21Þ i;m i;L i;G dχ χ¼0 c c c i;L i;L;b i;G;eq f ¼ f ¼ f ¼ ð11Þ i;L i;L;b i;G c c c 1;ref 1;ref 1;ref f ðÞ χ ¼ 1¼ f ð22Þ i;L i;L;b c c i;L;0 i;G;eq;0 κ ¼ κ ¼ i;L i;G ð12Þ At the macro scale Eqs. (23)and (24) are derived accord- c c 1;ref 1;ref ingly with the initial conditions provided in Eqs. (25)and (26). For further simplification, we assume that the gas phase con- χ ¼ ð13Þ sists of one single component only, which leads to constant J Flow Chem (2021) 11:625–640 629 value for f as indicated in Eq. (23). Finally, we assume an according to the stoichiometric Eqs. (R1)to (R3)[36]. The i,G ideal segmented flow pattern for the gas-liquid two-phase by-product water is sufficiently soluble in N,N- flow in the cPFR (see Fig. 1) with well-mixed gas and liquid dimethylformamid (DMF) used as solvent, in which the slugs and neglecting the film between the gas slug and the chemical reaction takes place. All reaction steps are assumed wall. Note that one unit cell can be regarded as control volume to be catalyzed by a POM ({Ba V O }), which provides 4 14 38 for the segmented flow model assuming the unit cell length oxygen to the organic substrate and is re-oxidized by molec- being much smaller than the reactor length. ular oxygen based on a MvK mechanism (Eq. (R4)). df D ε Da Bi i;G i;L L I 1;m C H þfg Ba V O →C H þ H O * 14 12 4 14 38 14 10 2 ¼ − f −f ¼ 0 ð23Þ i;G i;L dθ D 1−ε Ha Hi 1;L L þfg Ba V O ðR1Þ 4 14 37 df df D Da i;L;b i;L I i;L ¼ − þ Da ∑ ν ω ð24Þ I i; j j C H þfg Ba V O →C H O þfg Ba V O ðR2Þ 14 10 4 14 38 14 10 4 14 37 dθ D Ha Hi dχ 1;L j χ¼1 C H O þ2Bfg a V O →C H O þ H O 14 10 4 14 38 14 8 2 2 f ðÞ θ ¼ 0¼ κ ð25Þ i;G i;G þ2Bfg a V O ðR3Þ 4 14 37 f ðÞ θ ¼ 0¼ κ ð26Þ i;L i;L;b fg Ba V O þ 0:5O →fg Ba V O ðR4Þ 4 14 37 2 4 14 38 This reaction network is highly relevant, due to the impor- tance of anthraquinone in the chemical value chain, being currently produced by cycloaddition or coupling reactions, Implementation and simulation e.g. by Friedel-Crafts-reaction of benzene and phthalic anhy- dride. From theoretical point of view and more relevant to the Challenges from reaction network and catalysis current study, the reaction network provides several interest- ing features. Importantly, the consecutive character is well The example reaction chosen for this study is the oxidation of understood in chemical reaction engineering, which provides 9,10-dihydroanthracene (C H ) to anthraquinone 14 12 the basis in order to perform fundamental studies. One aspect (C H O ) via the intermediates anthracene (C H )and 14 8 2 14 10 arises from the POM being present in the liquid phase in form anthrone (C H O) using gaseous oxygen as reactant 14 10 −1 of clusters in the size of 3025 g mol , which can therefore be considered as a molecular, rather than a solid catalyst. This renders the system being homogeneously catalyzed, for which the theoretical framework of non-catalytic gas-liquid reactions can be applied counterintuitively. In particular, the implemen- tation of the MvK mechanism in modeling of gas-liquid reac- tions is not yet performed in scientific literature to the best of our knowledge. Another interesting aspect is motivated by the typical chal- lenge in research for derivation of kinetic data, where exper- iments have to be designed despite a significant lack of knowl- edge on the reaction system, especially in an early stage of research. For multi-phase reactions, in particular, care has to be taken in order to avoid the obtained kinetic data to be falsified by heat and mass transfer issues. Even though several rules of thumb are available to tackle this challenge (e.g. the Weisz-Prater criterion in heterogeneous catalysis), these rules are usually applicable to very simplified reaction systems on- ly. In this context the reaction system chosen is too complex and still not fully understood, neither mechanistically, nor with respect to the reaction kinetics. On top of this, the varia- tion of the POM based catalyst during research progress may affect both the reaction mechanism and the kinetics, which hampers the transfer of knowledge gained so far. Fig. 1 Model for the unit cell in a segmented flow (Taylor-flow) regime, The scientific key question for experimental derivation of with the unit cell consisting of one gas bubble and one liquid slug, as well as an illustration of the two film model at the meso scale reliable kinetic data are the concentration and temperature 630 J Flow Chem (2021) 11:625–640 Table 2 Assumed profiles in proximity of the gas-liquid interface, since they Stoichiometric Eq. Reaction kinetics reaction kinetics allow to distinguish reaction kinetics from the effects of trans- port limitations. Operando techniques are not capable to solve (R1) r =k c c 1 1 2 7 these issues completely yet [22, 38], since resolution of those (R2) r =k c c 2 2 3 7 profiles is still a matter of research [39, 40]. Therefore, model- (R3) r =k c c 3 3 4 7 ing and simulation is a promising approach, in order to sup- (R4) r =k c c 4 ref 1 8 port the design of experiments and interpretation of the results, as will be demonstrated in the present contribution. data. Note that the effect of reaction temperature is included Reaction system in k , only, for the presented isothermal balance equations. ref r ¼ k c c re f re f 1;re f cat;re f For implementation, the matrix of stoichiometric coeffi- ð27Þ with c ¼ c and c ¼ c þ c 1;re f 1;G;eq;0 cat;re f 7;L;b 8;L;b cients is derived from the stoichiometric reaction Eqs. (R1)to(R4) as summarized in Table 1. In addition, the We have chosen this type of reference reaction kinetics, as components A are also numbered in the following for it involves the gaseous reactant on the one hand, which has to simplification of the notation. Note that oxygen is pres- be transported across the gas-liquid interface. On the other ent in the gas phase and also soluble in the liquid, hand, it also includes the concentration of a reactant fed with while all other components are considered to be present the liquid phase, being the catalyst in this case. The reference in the liquid phase only, due to a negligible vapor pres- kinetics thus put the most important reactants of the complex sure of the organic reactants and the catalyst. reaction network in the center of the considerations, being the The kinetics involved for the occurring reactions are not catalyst in the focus of ongoing research. It has to be men- known yet and thus require to be estimated. Therefore, we tioned again that the choice of the reference reaction kinetics chose a simple approach assuming all reactions to be irrevers- depends on the individual case and can even describe a virtual ible and first order in the respective reactants (Table 2). In reaction not taking place in real experiments, since it is only particular, the catalyst is considered to take part in each reac- required to derive the dimensionless balance equations. After tion, either as oxygen donor or acceptor according to the MvK all, the meaning of the specific values for the dimensionless mechanism. numbers is defined by the choice of the reference. Reaction (R4) is chosen as the reference, being first order both in oxygen and catalyst concentration according to Eq. Parametrization (27). Therefore, the initial equilibrium concentration of mo- lecular oxygen in the gas bulk corresponds to the reference For parametrization the dimensionless numbers Da and Ha concentration c , which is also used for definition of the I 1,ref are estimated based on experiments performed in the bSTR by dimensionless numbers and variables above. Furthermore, Lechner et al. [36]. The overall reaction time in those exper- the total catalyst concentration, comprising the oxidized and iments was τ ¼ 7 h, with an initial oxygen partial pressure of reduced state, is considered as c , which is constant cat,ref p ¼ 8 bar as well as the initial concentration of component throughout the reaction progress. The kinetic constant of the O ;0 −3 reference reaction k needs to be scaled for sensitivity analy- A of c =45.8 mol m and of the catalyst of c = ref 2 2,L,b,0 7,L,b,0 −3 sis during simulation experiments or to meet experimental 0.9 mol m in the liquid phase. Components A to A and A 3 6 8 Table 1 Matrix of stoichiometric A Component Chemical formula Stoichiometric Eq. coefficients of the reaction system i (the solvent DMF is implemented (R1) (R2) (R3) (R4) as inert component A ) A oxygen O 00 0 −0.5 1 2 A 9,10-dihydroanthracene C H −10 0 0 2 14 12 A anthracene C H 1 −10 0 3 14 10 A anthrone C HO0 1 −10 4 14 10 A anthraquinone C H O 00 1 0 5 14 8 2 A water HO1 0 1 0 6 2 A catalyst, oxidized {Ba V O } −1 −1 −21 7 4 14 38 A catalyst, reduced {Ba V O}1 1 2 −1 8 4 14 37 J Flow Chem (2021) 11:625–640 631 −1 are not present in the reactor initially, while the total liquid of magnitude for ε ≈ 0.5 and a ≈ 1000 m typical for L G,L −5 3 volume was V =5 ·10 m . The authors report an initial segmented flow (including liquid film surrounding the conversion of component A obtained after a reaction time bubbles) in channels of 1.6 mm (1/16 in.) diameter, as well −3 of Δτ =1 h of Δc =11.45 mol m , as well as a formation as for δ ≈ 40 μm (rough estimate from k a values from 2,L,b L L G,L −3 of component A of Δc =5.95 mol m and A of [15]), gives Hi ≈ 12.5. In contrast, a Hinterland ratio of 4 4,L,b 5 −3 Δc =5.50 mol m . From these changes in concentration Hi ≈ 250 is obtained for the used bSTR with ε ≈ 0.5, 5,L,b L −1 the number of catalytic cycles of the catalyst, which is the a ≈ 50 m and δ ≈ 40 μm (agitated tank with small G,L L turn-over number (TON), can be calculated according to Eq. energy input, c.f. [46]). (28). Note, that the first term in the numerator represents all Hi ¼ ð29Þ turn-overs in the first reaction. a δ G;L L ν Δc þ ν Δc þ Δc þ ν Δc O ;R1 2;L;b O ;R2 4;L;b 5;L;b O ;R3 5;L;b 2 2 2 TON ¼ Note that Da is not suitable to distinguish between the cat;re f operation strategies, as it relates the reaction time with the ð28Þ intrinsic reaction kinetics, which is identical for both reactors. In contrast, Ha quantifies the mass transfer characteristics and With the Henry coefficient of O in DMF of H ≈ 5 2 O ;DMF may thus weakly depend on the reactor type chosen, only. −8 −3 −1 10 mol m Pa [41, 42], as well as the estimated orders of The interplay between reaction in the bulk and the profiles magnitudes for the diffusion coefficient of O in the liquid in the film can illustratively be discussed based on the mass −9 2 −1 phase of D ≈ 5  10 m s [43] and for the liquid film O ;L transport parameter T (Eq. (30)). Comparison with Eq. (24) thickness of δ ≈ 40 μm, Table 3 summarizes the relevant exhibits that this parameter describes the transport of the lim- values for the dimensionless numbers of a typical experiment iting component supplied by the gas phase A from the liquid in a bSTR. The diffusivity of all other components is assumed film into the liquid bulk and therefore links the meso and to be five times smaller, compared to oxygen diffusivity, how- macroscale with each other. It also becomes obvious from ever, diffusivities for the catalyst are unavailable and might be Eq. (24) that for high values of T the gradient of the residual even smaller than for the Anthracene derivates fraction at χ = 1 can be small for constant flux densities, which −9 2 −1 (D ¼ D ≈ 1  10 m s [44, 45]). Furthermore, the A ;L A ;L 3 5 results in flat profiles for A in the film. gas-sided mass transfer is assumed to be not limiting (Bi → ∞). Da τ k a I 1;L G;L T ¼ ¼ ð30Þ Ha Hi ε Reactor comparison This parameter is also suitable for fundamental studies on the batch-to-conti approach, since it allows a direct compari- Interestingly, the dimensionless balance equations allow to son of results obtained for various values of Hi, Ha,and Da express the difference between bSTR and cPFR by the on a common basis by lumping the individual effects. In other value for Hi only, since Eq. (19) can be rewritten to Eq. words, since all these parameters are affected by changing the (29) assuming film theory. It becomes obvious that Hi operation strategy from batch to continuous operation, the consists of properties strongly depending on the reactor proper comparison would require to perform an intensive type used and is thus suitable to distinguish between batch study with these three parameters. Lumping the individual or continuous operation. In particular, Hi becomes small effects in T reduces the parameter space without losing for segmented flow in the cPFR, due to the high values for significance. specific interfacial surface area. The estimation of the order Table 3 Estimated reference values and dimensionless numbers from a typical experiment performed in a bSTR by Lechner et al. [36] Property Equation Value −3 Reference concentrations c ¼ p H 0.04 mol m 1;ref O ;0 O ;DMF 2 2 −3 Catalyst concentration c ¼ c þ c 0.9 mol m cat;ref 7;L;b 8;L;b TON c cat;ref −3 −3 −1 Reference reaction rate r ¼ 9.4·10 mol m s ref Δτ r 3 −1 −1 ref Reference kinetic constant k ¼ 0.262 m mol s ref c c 1;ref cat;ref Damköhler number Eq. (17) ≈ 6000 Hatta number Eq. (16) ≈ 0.274 632 J Flow Chem (2021) 11:625–640 Implementation and simulation constants require to amount to k =2.28 · −5 3 −1 −1 10 m mol s for j ∈ {1, 2, 3}. The model equations are implemented to Matlab (version r k c c 1;0 1 2;L;b;0 cat;ref R2019b) and solved with ode15s (4th order backward differ- ¼ ¼ ω ¼ 0:1 ð33Þ 1;0 r k c c ref ref 1;ref cat;ref entiation formula - BDF) in order to perform a sensitivity r c 1;0 1;ref analysis by simulation experiments. The simulations focus −5 −1 k ¼ k ¼ 2:28  10 s ð34Þ 1 ref r c on the comparison between bSTR and cPFR, which are dis- ref 2;L;b;0 tinguished based on Hi, while keeping all other parameters Figure 2 shows the simulation results for the bSTR under equal for comparability reasons. Furthermore, the initial con- base case conditions. The observed profiles of the residual ditions used in the above-mentioned experiment are applied fractions for the organic reactants as function of reaction time for simulations, as well. The diffusion coefficients of all (Fig. 2a) are typical for the consecutive reaction considered in Anthracene derivates and the catalyst in the liquid phase are this example and agree qualitatively with experimental results assumed to be equal for simplicity reasons, though this as- [36]. After 7 h of reaction (θ = 1) the conversion of A reaches sumption may induce errors in the obtained results. We there- ca. 88%, while the yield for all anthracene derivates is com- fore focus the discussion of the results on the trends observed, parable in the range of 25 to 35%. The high numbers for the rather than on the interpretation of specific numbers. residual fractions are caused by the low solubility of O in For evaluation of the reactor performance, following defi- DMF and thus a small value for c . One may conclude that 1,ref nitions are used for conversion X of component A and the the solubility of O appears to be one important factor respon- yield Y towards component A (Eq. (31)). The degree of re- i i sible for the long reaction times required in the experiments in duction of the catalyst α is quantified by Eq. (32). order to achieve reasonable conversions. In Fig. 2c the corre- f f c c sponding profiles of the oxidized and reduced catalyst species 2;L;b 2;L;b i;L;b i;L;b and Y ¼ ¼ X ¼ 1− ¼ 1− ð31Þ c κ c κ are shown. The initially fully oxidized catalyst is reduced rap- 2;L;b;0 2;L 2;L;b;0 2;L idly in the very early stage of the reaction and remains at a cat;red 8;L;b α ¼ ¼ ð32Þ rather constant residual fraction of the oxidized state of f ≈ 7,L,b f c þ c 7;L;b 8;L;b cat;ref 16 thereafter. The profiles of the residual fraction of oxygen and the degree of reduction of the catalyst α at the meso scale are shown in Fig. 2b for three different reaction times θ , θ I II and θ indicated in Fig. 2a (corresponding to ca. 30 min, 3.5 h III and 7 h). Obviously, the degree of reduction of the catalyst is Results and discussion constant in the liquid film, as well. The oxygen profile, how- ever, declines almost linearly from the phase boundary at χ = Base case 0 towards the liquid bulk at χ = 1, which agrees with the expectations from the small Ha used for the simulations. The base case assumes that the dimensionless initial The almost constant degree of reduction of the catalyst α at rates of the reactions (R1)to(R3)amountto ω =0.1 j,0 meso and macro scale renders the apparent kinetics for (R1) to for j ∈ {1, 2, 3}, which means that those reactions are (R3) being first order in concentration of the respective organ- slower than the reference reaction (R4). This scenario ic reactant. The oxygen availability in the liquid phase, how- corresponds to the typical approximation used in homo- ever, is the limiting factor for the re-oxidation of the catalyst in geneous catalysis, which neglects the formation of con- (R4) and hence for the overall reaction process. In particular, centration gradients of the molecular catalyst. Indeed, it the residual fraction of oxygen in the liquid bulk amounts to is known from experiments, that the specific chemistry ca. 0.2 only. Considering that the reaction mainly takes place of catalytic steps is a delicate task (c.f. [19]), but is in the bulk for the large Hi used in the simulations, the limiting typically neglected. In the present example, however, effect of oxygen availability is not surprising. Importantly, the the catalyst is stoichiometrically involved in the reac- catalyst is provided in large excess with respect to oxygen tion, due to the MvK mechanism proposed. Therefore, (κ = 22.9) and therefore the degree of reduction α is rather 7,L certainly pronounced gradients in oxidized and reduced independent on the reaction progress and limited to ca. 0.3. catalyst species may evolve, depending on the reaction The negligible differences in the profiles observed at the meso rates. The assumption limits those gradients on the one scale are caused by the slight changes of α with reaction time hand, but offers the respective discussion at the same at the macro scale. time. Therefore, this approach allows to shed light on The simulation results for the base case in the cPFR are the importance of the spatial distribution of the catalyst shown in Fig. 3, providing qualitatively similar profiles com- oxidation state within the reactor on the measured re- pared to the bSTR with a slightly higher conversion for A of sults. In order to fulfill the assumption, the kinetic J Flow Chem (2021) 11:625–640 633 Fig. 2 Simulation results for bSTR operation (with Da = 6000, Ha = spatial profiles of residual fractions in the film at three selected reaction 0.274, Hi =250, T = 320); residual fractions of (a) organic reactants and times: (θ )initial,(θ ) intermediate, (θ ) final phase I II III (c) catalyst species as function of dimensionless reaction time θ;(b) ca. 95% and yields in the range of 14 to 59% for all organic differences in the oxygen profile in the film can directly be products. The degree of reduction of the catalyst is also almost attributed to the mass transport parameter T. constant in the film (Fig. 3b) and with reaction time (Fig. 3c), The degree of catalyst reduction α can be predicted de- but lower than in the bSTR. Furthermore, the profiles at the pending on the reaction extent assuming that the rate of cata- meso scale are not affected by the reaction time. Compared to lyst reduction in reactions (R1) to (R3) equals the rate of re- the bSTR, however, the profile of oxygen residual fraction in oxidation in (R4). This assumption, expressed in Eq. (35), the film is almost constant and close to unity (ca. 95%) even in requires negligible changes in degree of reduction with spatial the liquid bulk. Hence, the oxygen availability is hardly lim- coordinate and reaction time. After introduction of the reac- iting, which consequently means that the re-oxidation rate of tion kinetics (Table 2) and the definition of the reduction de- the catalyst in the bulk can be regarded as the limiting factor. gree (Eq. (32)) Eqs. (36)to(38) can be derived, respectively. The differently pronounced oxygen profiles in the film in the base case simulations can be explained by the parameter T, 0 ¼ ∑ ν r ð35Þ 7; j j j¼1 which is significantly smaller for the bSTR (T = 320) bSTR compared to the CFPR (T = 6400). It has to be mentioned cPFR k c c ref 1;G;eq 8;L;b that the convection and reaction terms in Eq. (24) are rather ¼ c k c þ k c þ 2 k c ð36Þ unaffected by the reactor choice given by the similar profiles 7;L;b 1 2;L;b 2 3;L;b 3 4;L;b of the residual fractions with reaction time. Therefore, the Fig. 3 Simulation results for cPFR operation (with Da = 6000, Ha = spatial profiles of residual fractions in the film at three selected reaction 0.274, Hi =12.5, T = 6394), residual fractions of (a) organic reactants times: (θ )initial,(θ ) intermediate, (θ ) final phase I II III and (c) catalyst species as function of dimensionless reaction time θ;(b) 634 J Flow Chem (2021) 11:625–640 simulations is possible, since the errors induced by unknown k c c ¼ c −c k c þ k c þ 2 k c ref 1;G;eq 8;L;b cat;ref 8;L;b 1 2;L;b 2 3;L;b 3 4;L;b kinetics and further simplifying assumptions contribute equal- ð37Þ ly to the obtained results for both reactors. From Table 4 it can be observed that the simulation is capable of predicting the k c þ k c þ 2 k c 1 2;L;b 2 3;L;b 3 4;L;b α ¼ ð38Þ trend of the experimental data, while the specific values devi- k c þ k c þ k c þ 2 k c ref 1;G;eq 1 2;L;b 2 3;L;b 3 4;L;b ate to a certain extent. The discrepancy can be explained by the fact that the reaction kinetics are not known and therefore Equation (38) provides the basis for an estimate of the approximated by simple power-law approaches. On the other expected degree of reduction, in order to design and interpret hand, this simple approach obviously allows to gain meaning- experimental results. Most importantly, the relevance of oxy- ful insights into the reaction system and the reactor behavior. gen solubility and re-oxidation rate becomes apparent both Figure 4 provides the direct comparison of both reactor expressed by the term k c , since increasing this term ref 1,G,eq types based on the profiles of the organic reactants with reac- leads to a decrease in the degree of reduction, which is bene- tion time obtained by simulations. The observed trends are ficial for the reactor performance. Even though this conclusion comparable for bSTR and cPFR, exhibiting a declining resid- is drawn based on the specific reaction kinetics assumed in the ual fraction for A , negligible values for A , and monotonously present example, it is of general importance for similar reac- 2 3 increasing values for A . Component A exhibits a profile 5 4 tion systems and other kinetics, as well. Eventually, the rela- typical for intermediates in consecutive reactions. The tionship shows that in-situ measurements of the catalyst state resulting profiles in residual fractions thus agree with the ex- will give a further insight into the underlying kinetics. pectations associated with the chosen values for the dimen- sionless reaction rates in a consecutive reaction network. Kinetics The detailed comparison reveals that the cPFR exhibits better performance with respect to conversion of A and yield In order to represent the experimental results reported by of A obtained at reaction time of θ = 1. Comparing the reac- Lechner et al. [36] the dimensionless reaction rates have been tion time required to reach a conversion of X =0.2 and the adjusted according to the following values: ω =0.5, ω = 1,0 2,0 yield in A at that reaction time, the cPFR (θ =0.15, 5 cPFR 25, and ω = 5. Note that these values are not obtained by 3,0 Y = 0.11) outperforms the bSTR (θ =0.25, 5,cPFR bSTR fitting to experimental data, due to lack of knowledge in reac- tion kinetics. Instead, emphasis is on studying the order of magnitude effects of the reaction rates on the observations. The chosen values mean that the rate of reaction (R1) is lim- iting, while the selectivity towards the intermediate (A and A ) and final (A ) products are governed by the respective 4 5 dimensionless reaction rates. In particular, A formation is expected to be hardly detectable, since it is directly converted into A given by the high ω /ω ratio. 4 2,0 1,0 The direct comparison of experimental and simulation re- sults obtained for both the bSTR and cPFR reactor is summa- rized in Table 4 and depicted in Fig. 4. Note that the simula- tions are based on identical parametrization, except for Hi for both reactor types. Therefore, the direct comparison based on Table 4 Comparison of reactor performance in simulation and experiment [36] for both reactor types (no cPFR experiments with fluidic residence time τ > 1 h available) fl Simulation Experiment Reaction time Reactor X /% Y /% X /% Y /% 5 5 θ=1 bSTR 60 55 57 40 cPFR 87 85 –– θ=0.13 bSTR 12 4 22 14 cPFR 18 9 21* 15* Fig. 4 Residual fractions of the organic reactants as function of *operating cPFR with fluidic residence time of τ =54 min dimensionless reaction time θ;(a)bSTR(Hi =250); (b)cPFR(Hi =12.5) fl J Flow Chem (2021) 11:625–640 635 Y = 0.11) clearly. The reason for this observation has to is first order in oxygen. Finally, it has to be considered that the 5,bSTR be related to the value of Hi, since this parameter distinguishes oxygen demand depends on the reaction extent, due to differ- between both reactor types, only. In particular, Hi is respon- ences in stoichiometry and the intrinsic rate of reactions (R1) sible for oxygen availability in the liquid bulk and hence for to (R3) and thus changes with reaction time (e.g. Eq. (38)). the degree of reduction of the catalyst, as discussed for the The interplay of these factors is therefore responsible for base case. Therefore, the profiles of the oxygen residual frac- the observed profiles and renders the cPFR beneficial for ki- tion together with the degree of reduction as function of reac- netic experiments, because mass transport limitations are less tion time are depicted in Fig. 5 for cPFR and bSTR. pronounced. Interestingly, the simulation results exhibiting a Obviously, the degree of reduction is significantly lower in higher oxygen saturation and smaller degree of reduction in the cPFR reaching a maximum value of about 15%, while that the cPFR agree in principle with experimental observations. in the bSTR even exceeds 50%. This observation is associated The POM catalyst used in the experiments changes color from with the oxygen residual fraction, which is rather constant orange to green upon increasing degree of reduction and even with reaction time at ca. 0.9 and 0.2 for the cPFR and bSTR, becomes colorless after decomposition, which justifies the respectively. Interestingly, the oxygen residual fraction is rath- predictions from simulations qualitatively. er constant, while the degree of reduction exhibit significant changes with reaction time. This can be explained by the high Sensitivity analysis in mass transfer value for ω , which means that the catalyst reduction in re- 2,0 action (R2) is twenty-five times faster than the catalyst re- The effect of mass transfer is studied based on the lumped oxidation in reaction (R4) under initial conditions. mass transport parameter T introduced in Eq. (30). For sensi- Therefore, the oxygen consuming re-oxidation reaction is lim- tivity analysis this parameter is varied between 30 and 120′ iting in the simulated cases and the profile of reduction degree 000, while each value is justified by typical conditions for is governed by the rates of reactions (R1) to (R3). On the other either bSTR or cPFR. As basis for a meaningful range of T hand, the oxygen transport through the film is limiting due to the film thickness was varied between 2 and 400 μm, which the high value for Hi in the bSTR, which leads to pronounced even covers values beyond the expected boundaries for bSTR profiles in oxygen residual fraction in the film and thus low and typical flow regimes in cPFR. We thereby account for values in the bulk. This limits the re-oxidation, as well, which uncertainties in estimation of T by broadening of the consid- ered value range and avoid the complexity arising from more accurate determination at the same time. Figure 6 depicts the impact of the mass transport parameter T on the maximum degree of catalyst reduction in the bulk achieved within the reaction time and the conversion of component A after 55 min (θ=0.13) and7h(θ = 1) of reaction. The solid lines correspond to typical conditions for each reactor type, while the dashed lines indicate the extrapolation towards unusual conditions, in order to support the direct comparison of batch and continuous operation. For illustration, the range of T cor- responding to the film thickness between 2 and 400 μmis indicated for the bSTR and the cPFR, as well. It becomes apparent that both reactor types overlap in the range of 250 < T < 2000, which correspond to extrapolated values for each and therefore unlikely operation conditions. The degree of maximum reduction appears to be a function of the mass transport parameter T only, but does not depend on the reactor type, since the α (T) profiles of cPFR and max bSTR are clearly overlapping. Furthermore, it appears that extrapolation over the whole range of T leads to identical profiles irrespective of the reactor type. It can also be observed that the reduction degree is constant for the typical operation range in the cPFR, but exhibits a strong sensitivity towards the mass transport parameter for the bSTR. Importantly, the max- imum reduction degree is very small and the average value therefore even smaller for the cPFR. Consequently, the cata- Fig. 5 Catalyst oxidation state and oxygen residual fraction as function of dimensionless reaction time θ;(a)bSTR(Hi =250); (b)cPFR(Hi =12.5) lyst can be assumed to be homogeneously distributed in the 636 J Flow Chem (2021) 11:625–640 A , as well, but form the reduced catalyst species stoichiomet- rically at the same time. For additional information, the reader is referred to the supporting information, where the degree of reduction and the rates are plotted for the highest and lowest value of the mass transport parameter, respectively. Interestingly, the conversion in the cPFR is constant in the typical operation window, while it increases for smaller T values. The dimensionless formulation of the balance equa- tions hampers a clear argumentation of this unexpected obser- vation. Importantly, the mass transport parameter T results from lumping of the degrees of freedom of the reactor opera- tion expressed by Hi, Ha and Da , which allows different sets of those degrees of freedom to yield identical T values. For instance, a reduction of Hi from 250 to 12.5 for bSTR to cPFR can be compensated by a decrease in Da from 10 to 0.5 in order to maintain T/Ha = 400. The relation T/Da , representing mass transfer into and the reaction within liquid bulk, changes from T/Da = 0.4 in the first to T/Da = 8 in the I I second case. This means that the interplay between reaction in Fig. 6 Maximum degree of catalyst reduction α and conversion in A the bulk and the processes in the liquid film play an important max 2 in the liquid bulk as function of the mass transport parameter T for the role for the performance of the chosen reactor. Therefore, bSTR (squares) and cPFR (circles) with typical (solid lines, filled sym- fundamental differences between both cases exist depending bols) and extrapolated (dashed lines, open symbols) operation range; lines on the specific parametrization, though the balance equations are shown to guide the eye, typical range in film thickness δ related to are identical. Along this argumentation, an increase in Ha mass transport parameter T is indicated by bars for both reactor types leads to a decrease in T at constant Da and Hi, which is associated with an increasing enhancement factor E and there- liquid phase in the oxidized state, which corresponds to the fore an improved mass flux of oxygen across the gas-liquid typical assumption for molecular catalysts in homogeneous interface. In the same vein, a reduction in T induces the gra- catalysis. In contrast, the degree of reduction reaches very dient of the residual fractions at χ = 1 to raise (see Eq. (24)), high values for the bSTR, which lead to the irreversible deac- which enhances the mass flux into the bulk, as well. tivation of the POM-based catalyst by decomposition. According to Eq. (30)small T values can be achieved for fast Therefore, gradients in the concentration of oxidized and re- reactions, expressed by high values for Ha and small values duced catalyst species probably develop. The reason for the for Da , and cause gradients at the meso scale to develop. high degrees of reduction is the limited availability of oxygen Therefore, large values of T allow to neglect gradients in the for re-oxidation for low values of T and thus reasonable mass film and thus to assume intrinsic conditions, while decreasing transfer limitations for oxygen. Hence, the cPFR is beneficial T values lead to deviation from intrinsic operating points. The for kinetic measurements, due to absence of severe mass trans- latter situation thus requires more sophisticated models for fer limitations at high T values. Considering the conversion, analysis of experimental data, while a one-dimensional, the results for the bSTR raise with increasing T and asymptot- pseudo-homogeneous model is sufficient for the intrinsic case. ically reach those of the cPFR and therefore intrinsic condi- It also becomes apparent that a straight-forward argumenta- tions. Furthermore, the sensitivity towards the mass transport tion of the obtained results based on the dimensionless num- parameter is more expressed in the bSTR. bers only, is misleading, due to the interdependencies of their The sensitivity of both the conversion and degree of reduc- definitions. tion in the bSTR indicate that a correlation between both ex- ists: with decreasing degree of reduction the conversion in- Variation of kinetics in the reaction network creases. This is most probably caused by the enhanced oxygen availability for higher values of the mass transport parameter The impact of the kinetics in the consecutive reaction network and thus improved re-oxidation of the catalyst by reaction is studied in two scenarios. In scenario I the kinetics of reac- (R4), which is first order in O . This leads to a higher concen- tion (R1) is varied according to ω = ∈ [0.005, 5], while the 2 1,0 tration of the oxidized catalyst species A and thus an in- kinetics of reaction (R2) and (R3) are kept constant at ω = 7 2,0 creased rate for the oxidation of A via reaction (R1), which 25 and ω = 5. This scenario therefore covers various cases 2 3,0 is first order in A and A . The rates of the consecutive reac- relating the reduction of the catalyst in reaction (R1) to its re- 2 7 tions (R2) and (R3) profit from the increasing concentration of oxidation in reaction (R4). Within the consecutive network J Flow Chem (2021) 11:625–640 637 reaction (R1) is thus always limiting, since reaction (R2) is at α > 0.6. Hence, in comparison to the cPFR the yield in the max least five times faster. It has to be considered, however, that bSTR is obviously limited by the re-oxidation of the catalyst. reaction (R2) and (R3) require oxygen stoichiometrically, as In particular, the available oxygen is mainly consumed by well, and thus contribute to catalyst reduction. reaction (R1) and (R2), since ω /ω = 5, and thus reaction 2,0 3,0 The obtained simulation results (Fig. 7a) exhibit similar (R3) suffers from oxygen depletion, which becomes more and almost negligible degrees of reduction for bSTR and severe for high ω values. 1,0 cPFR for very small values of ω associated with similar Scenario II extends the previous analysis by variation of the 1,0 values for conversion and yield. Therefore, oxygen availabil- rates of reaction (R1) to (R3) proportionally, according to ity appears to be not limiting, neither in the molecular form ω =0.5 m, ω =25 m and ω =5 m with the activity ratio 1,0 2,0 3,0 required for the catalyst re-oxidation, nor in form of the oxi- m = ∈ [0.1, 10]. It therefore scales all reactions contributing to dized catalyst needed for reaction (R1) to (R3), which renders catalyst reduction equally and thus relates the overall rates of the reaction rates being intrinsic. With increasing values for catalyst reduction and re-oxidation to each other. Hence, the ω the degree of reduction raises for both the bSTR and the factor m expresses the activity ratio of the reduction and the re- 1,0 cPFR, while the increase is significantly more pronounced for oxidation half-cycle during the MvK mechanism. The direct the bSTR. This can be explained by the increasing demand of comparison to scenario I is possible for m = 1 and indicated in oxygen in reaction (R1) to (R3) induced by the higher reaction Fig. 7 as dashed vertical line. rates, leading to the re-oxidation of the catalyst becoming The results in Fig. 7b exhibit an increasing degree of re- limiting. The difference between both reactors is caused by duction with raising activity ratio, since the re-oxidation half- the mass transfer parameter T, which is significantly smaller cycle of the catalyst becomes limiting. Furthermore, both the for the bSTR as discussed above. This leads to more pro- bSTR and the cPFR exhibit similar values of catalyst reduc- nounced mass transfer limitations and therefore to a lower tion degree, conversion and yield for m < 0.25, while the de- oxygen availability. In addition to the observations at the mac- viation becomes more pronounced for raising m. This can ro scale shown in Fig. 7a gradients develop in the liquid film again by explained by the smaller mass transport parameter as discussed above for the base case. T in the bSTR, which limits the oxygen availability required The conversion X and yield Y raises with ω for the cPFR for catalyst re-oxidation. Importantly, higher m values mean 5 1,0 and reaches unity asymptotically. Furthermore, both values that catalyst re-oxidation is hampered under reference condi- are very similar indicating a high selectivity towards compo- tions at maximum oxygen availability already. During reac- nent A after the reaction time of θ = 1. In contrast, the con- tion oxygen is consumed and thus the catalyst reduction de- version raises, while the yield exhibits a maximum for the gree becomes even more sensitive towards mass transport bSTR, which means that the selectivity towards the interme- restrictions. Interestingly, the selectivity towards component diate components A and A increases with ω . The observed A is high for both reactors expressed by the slight deviation 3 4 1,0 5 maximum and subsequent decline in yield is associated with between conversion and yield, since all reactions suffer pro- an increasing trend of the degree of catalyst reduction beyond portionally from the higher reduction degree of the catalyst. Fig. 7 Impact of reaction rate constants in the reaction network on the conversion X, the yield Y and the maximum degree of catalyst reduction α ;(a) 5 max impact of ω ;(b) impact of the activity ratio m of the reduction and the re-oxidation half-cycle during the MvK mechanism 1,0 638 J Flow Chem (2021) 11:625–640 The lower selectivity as well as the deviation of the maximum macro scale, respectively. The parameterization is performed value for conversion and yield observed in the bSTR from the using experimental results obtained in a bSTR during the early expected value of one for irreversible reactions indicates that stage of catalyst development. Importantly, the discrimination the catalyst re-oxidation limits the reactor performance in that of the bSTR and the cPFR is realized by means of character- case. istic dimensionless numbers using the identical mathematical The results of the kinetic study exhibit a very similar be- model for comparability reasons. The uncertainties typical for havior of the bSTR and the cPFR in the intrinsic regime, as an early stage in process development are accounted for by expected, which is beneficial for experimental investigation of sensitivity analyses carried out for the reaction kinetics and the kinetic parameters or catalyst development. The low values mass transport parameter T. for conversion and yield can easily be compensated by in- It was revealed that the maximum degree of catalyst reduc- creasing residence time in this regime. Under non-intrinsic tion strongly correlates with the mass transport parameter, but conditions, however, pronounced gradients and oxygen trans- not directly with the reactor type. This is expected from the port limitations develop, which lead to several challenges in identical set of balance equations used and the re-oxidation of evaluation of experimental data. In case that catalyst re- the catalyst chosen to be the reference reaction. The mass oxidation is limiting, for instance, the experimental determi- transport parameter, though, can directly be linked to charac- nation of conversion and yield of the organic reactants be- teristic values for both types of reactor operation and can thus comes rather meaningless. Instead, emphasis should be put be used for respective discrimination. The results also show on the additional determination of the catalyst reduction de- that the mass transport parameter is suitable to determine, gree, in order to evaluate the information obtained from the whether the reactor is operated under (nearly) intrinsic condi- product composition data (see Eq. (38)). tions or in a regime, where mass transfer, catalyst re−/oxida- Catalyst development often aims at increasing the activity tion and chemical reaction are interfering. Importantly, even with respect to conversion of the organic reactants, which is rather slow reactions may suffer from mass transfer limitations expressed by increasing ω in scenario I. Interestingly, the in a bSTR and therefore require cPFR experiments for kinetic 1,0 results clearly show that an increase in activity is not neces- studies, which can be concluded from our results. sarily correlated with the measured conversion or yield, which For the POM catalyzed aerobic oxidation of DHA we iden- in particular holds for the non-intrinsic case with severe mass tified the catalyst reduction degree as the most important as- transport limitations. Obviously, the choice of an appropriate pect to be considered in the design of the process. It appears to reactor and operations conditions become very important to determine the significance of the experimental results with provide a correlation between experimental results and devel- respect to catalyst activity improvement obtained under non- opment aims. The results in Fig. 7a, obtained for catalyst intrinsic conditions. Therefore, catalyst development needs to aim at sufficiently fast re-oxidation of the reduced catalyst activity ranging over three orders of magnitude, clearly under- line the benefits of the cPFR for that purpose. species in order to avoid limitations or even catalyst decom- From Fig. 7b it can be concluded that catalyst development position. Furthermore, oxygen availability in the liquid phase requires a holistic approach, emphasizing both the reduction supports catalyst re-oxidation and can be improved by en- and re-oxidation half cycle. In other words, improving the hancing the interfacial surface area, as well as higher oxygen activity towards conversion of the organic reactants require a solubility by the choice of appropriate solvents. Finally, the proportional increase in catalyst re-oxidation activity, as well. results indicate that determining the catalyst oxidation state Otherwise, the re-oxidation step becomes limiting and thus the in-situ is of superior importance in addition to the analysis catalyst reduction degree increases towards rather high values of the product spectrum, in order to quantify the catalyst per- in the non-intrinsic case. This leads to pronounced gradients formance. hampering the evaluation of the experimental data and even to The study illustrates that even simple reactor models with irreversible decomposition of POM catalysts. roughly estimated parameters from preliminary experiments are sufficient in the early phase of process development. Such models are capable to resolve the complex interactions be- Conclusions tween mass transfer and reaction steps and thereby allow to identify the bottle-neck in the significance of experimental The present contribution investigates the transfer from batch data. They can also be used for design of appropriate experi- to continuous operation under uncertainties for the POM cat- ments and even for exploration of the feasibility of novel alyzed aerobic oxidation of DHA as an example for gas-liquid process windows. Hence, process development profits from reactions. The study is based on a mathematical model assum- both the transfer of experimental studies from batch to contin- ing film theory, which consists of dimensionless balance uous operation and mathematical modeling in an early phase, equations for the liquid film and the liquid bulk at meso and already. J Flow Chem (2021) 11:625–640 639 Supplementary Information The online version contains supplementary 9. 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Challenges in transfer of gas-liquid reactions from batch to continuous operation: dimensional analysis and simulations for aerobic oxidation

Journal of Flow Chemistry , Volume 11 (3) – Sep 1, 2021

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Abstract

The transfer of gas-liquid reactions from conventional batch processes into continuous operation using milli and micro reactors is claimed as an important step towards process intensification. Importantly, this transfer step should be realized in an early phase of process development, already, in order to minimize research efforts towards the undesired operation strategy. The main challenge of this approach, therefore, arises from lack of knowledge in the early stage of process development and the resulting system with high degrees of freedom. This contribution presents an approach to tackle this challenge by means of mathematical modelling and simulation for the aerobic oxidation of 9,10-dihydroanthracene (DHA) catalyzed by polyoxometalates (POMs) being used as example for gas-liquid reactions. The reaction was chosen as it provides sufficient complexity, since it consists of three consec- utive oxidation steps of DHA and a parallel catalytic redox-cycle according to a Mars-van-Krevelen mechanism. It also provides the challenge of unknown reaction kinetics, which have been estimated in this contribution. The dimensionless balance equations for reactor modeling are derived and parametrized based on early stage experimental results obtained in batch operation mode. The discrimination between batch and continuous operation was performed by means of characteristic dimensionless numbers using the identical mathematical model for comparability reasons. The model was used to perform sensitivity studies with emphasis on the interplay between mass transfer characteristics and reaction kinetics for both the batch and continuous operation mode. The simulation results show that the performance of both operation modes mainly depend on the oxidation state of the POM catalyst, which is caused by the differences in oxygen availability. Therefore, results obtained in batch operation mode are prone to be masked by mass transfer issues, which affects catalyst and reactor development at the same time and may thus cause maldevelopments. With respect to process development it can thus be concluded that the transfer from batch to continuous operation together with mathematical modeling is important in an early phase, already, in order to detect limitations misleading the development. Finally, even simple models with roughly estimated parameters from preliminary experiments are shown to be sufficient in the early phase and can systematically be improved, in the subsequent phases. . . . . Keywords Multiphase reaction Mathematical modelling Flow chemistry Liquid phase oxidation POM catalyst Article highlights • Batch-wise and continuously operated reactors are compared based on Introduction dimensionless reactor models and sensitivity analysis. � The dimensionless mass-transfer parameter is introduced to distinguish Over the last two decades, milli and micro reactors receive an between reactors operated in batch and continuous mode. increasing attention due to the possibilities to shorten the way � Catalyst re-oxidation even limits slow Mars-van-Krevelen driven reac- tions, due to low oxygen availability. from lab to the market. Milli and micro reactors can be scaled- up by numbering-up and the small characteristic lengths pro- * Jens Friedland vide a good reaction control and thermal management [1]. For jens.friedland@uni-ulm.de the production of fine chemicals and pharmaceutical products, the application of small-scale continuous reactors are already Robert Güttel part of the reaction engineer’s toolbox [2]. However, investi- robert.guettel@uni-ulm.de gations in batch reactors are still the method of choice for highly viscous and sticky suspensions or for reaction mixtures Institute of Chemical Engineering, Ulm University, Albert-Einstein-Allee 11, 89091 Ulm, Germany probably producing precipitates, where easy cleaning is 626 J Flow Chem (2021) 11:625–640 favored over high reaction control [3]. Sometimes flow chem- used in reactor design and scale-up. Romanainen and Salmi istry is claimed to be superior in general [4], although there are worked on the simulation of tank reactors and bubble col- still challenges remaining, which can be circumvented by umns, where they implemented gas-liquid reactions applying using batch reactors (e.g. chemical compatibility, clogging film theory [23, 24]. The focus was put on different strategies and fouling) [5]. to solve the material balance numerically, which led to the Currently, liquid phase oxidations are under intensive in- conclusion, that a simultaneous calculation of bulk and film vestigation, because the standard processes for the conversion might be favorable, however, this strategic approach shows of petroleum-based raw materials will be substituted by bio- some instability for the numerical solution [23]. They also derived raw materials in future [6]. Aerobic oxidation of or- showed the application, demonstrating the simulation ap- ganic substrates is particularly attractive, since it allows for proach for the chlorination of butanoic acid in a bubble col- functionalizing organic molecules and their implementation umn. A penetration model was implemented by van Elk et al., into a renewable chemical value chain. This typical applica- who tried to overcome the asymptotic cases usually applied tion, however, comes along with hazardous risks if the reac- and demonstrated the possibility to cover more realistic appli- tion ignites, which becomes severe for large volume batch cation scenarios with a dynamic model [25]. Nevertheless, it is reactors [7]. One approach to minimize the risk of explosion state of the art to apply simplified model equations or its an- or ignition is the utilization of the small characteristic diame- alytical solutions to characterize a gas-liquid reaction system ters provided in milli or micro reactors, which can be chosen [30]. For instance, second order reactions [26] or the influence to be below the safe diameters of the explosive reaction mix- on reactant depletion in a batch reactor [27] are investigated ture [8, 9], however, microreactors are not inherently safe [9]. based in the film model. However, Kucka et al. already de- Therefore, hazardous operation windows are usually avoided. rived expressions for the characteristics of the above men- One of the most frequently used approaches is to operate tioned models and the surface renewal model [28]. In their below the limiting oxygen concentration (LOC) of the organic investigation, different methods for the determination of reac- solvent and/or reagents used in a chemical reaction [10]. tion kinetics are applied to experimental results from a stirred Despite these advantages for continuous operation in milli cell reactor and used to evaluate the reaction of CO with or micro reactors, the batch reactor is often chosen in the early Monoethanolamine (MEA). In the early stage of process de- stages of process development, due to the simpler handling velopment, however, the reaction kinetics might even be un- and flexibility of operation conditions. Further reasons for known and need to be estimated from preliminary experimen- preferring the batch against the flow reactor, especially for tal results. Markoš et al., for instance, present a very detailed gas-liquid reactions, are the complexity and the realization dimensionless model based on the film theory for the oxida- of the desired flow pattern for realistic reaction mixtures. In tion of xylene. They point out that the agreement between addition, the specific mass transfer properties depend on many simulation and experimental results depends on the quality factors, such as physical properties of the fluids [11–13], the of the used kinetics [31]. This is not surprising, since uncer- flow pattern itself and the reactor geometry, which induce tainties are expected to affect simulation results from rigorous significant uncertainties in the mass transfer correlations and models. It has to be emphasized, however, that the benefit of predictability [14–16]. Nevertheless, flow reactors offer the modeling and simulation is not restricted to well-known sys- opportunity to apply spectroscopic methods providing spatial tems, but also suitable for extrapolation and even for explora- concentration profiles, which is improving the knowledge tion towards unknown reaction systems. Modeling and simu- gain during process development [17, 18]. Furthermore, the lation studies for those systems with high degree of freedom, understanding of fluid dynamics and mixing inside the milli though, is rare. Modelling and simulation for even more com- and micro channels is improved, recently [19, 20]. This prog- plex systems currently investigated, like three-phase systems, ress together with the combination of computational fluid dy- are far behind the experimental development [32, 33]. A most namics (CFD) and spectroscopic methods allows to analyze recent investigation by Kappe and Coworkers is a positive the mass transfer characteristics and thus minimize the uncer- example at the matured stage of investigation in the field of tainties in prediction [21, 22]. aerobic oxidation [34]. Nevertheless, the work shows the ef- During development of gas-liquid reaction processes math- fort, which is necessary to keep astride experiments and sim- ematical models play a key role for scale-up and reactor de- ulation, resulting in a fit-for-purpose process model in an early sign (e.g. [23–28]), which need to be adapted to the specific stage of development. They combined reaction experiments case. Therefore, the design and operation parameters of the with two-directional computational fluid dynamics (CFD) reactor, as well as the kinetic parameters of the reactions and simulation for the selective oxidation of diphenyl sulfide to mass transfer are required. Furthermore, a mass transfer model diphenyl sulfoxide applying a copper catalyst. The residence suitable for the problem has to be chosen [29]. In case of well- time distribution was characterized by a pulse experiment and known systems, the relevant information is available and the the mass transfer coefficient was estimated using Higbie’s model can be validated by experimental data, before being penetration model. Thus, the investigation is combining the J Flow Chem (2021) 11:625–640 627 experimental investigations and simulation in order to scale the phase boundary, while the macro or reactor scale covers and predict possible process conditions. Eventually, the coex- the balances for the fluid bulk. istence of suitable models with experimental effort should be a The example reaction chosen justifies the assumption of characteristic commitment in reaction engineering. isothermal conditions, since the adiabatic temperature rise of The present contribution provides a sensitivity study based the reaction mixture is small (21 K) and therefore, heat bal- on modeling and simulation for the transfer of gas-liquid re- ances are neglected. Furthermore, film theory is assumed to actions from batch to continuous operation with emphasis on describe the transport processes in proximity of the phase the particularities in an early phase of process development. boundary, in order to allow for illustrative presentation of Therefore, the dimensionless material balances are derived the simulation results. Concerning the temporal behavior, and parametrized based on experimental results obtained in steady-state conditions are assumed for the meso scale bal- batch operation mode. The discrimination between batch ances. In contrast, unsteady-state balances are formulated for and continuous operation was performed by means of the macro scale, which allows to utilize the residence time to characteristic dimensionless numbers using the identical be used as comparison basis for both reactor types. mathematical model for comparability reasons. The aerobic oxidation of 9,10-dihydroanthracene (DHA) catalyzed by Balance equations polyoxometalates (POMs) is used as an example reaction, being subject of recent research efforts in catalyst [35, 36] Based on the main assumptions, the material balance at the and reactor [37] development. The chosen example provides meso scale can be formulated according to Eq. (1)foraflat sufficient complexity in order to demonstrate the potential of geometry of the liquid film with a thickness of δ ,in order to the model-driven batch-to-conti approach in early stages of derive the profile of the concentration of component A in the process development, since an organic reactant undergoes liquid film c as function of the spatial coordinate x. The rate i,L consecutive oxidation steps catalyzed by POMs via a Mars- r of reaction j in the liquid film is a function of the spatial j,L van-Krevelen (MvK) mechanism. In addition, neither the re- coordinate x, as well, as it depends on the concentrations of the action mechanism, nor the kinetics are known in sufficient reactants. Furthermore, D refers to the diffusion coefficient i,L detail, which is usually the case, if catalyst development is in the liquid phase, while ν holds for the stoichiometric co- i,j in the focus of the research. efficients. We show that a model-based exploration of the complex d c i;L gas-liquid system is possible, despite the presence of uncer- 0 ¼ D þ ∑ ν r ð1Þ i;L i; j j;L dx tainties. In particular, we observed that the oxidation state of the POM catalyst is the crucial factor in the transfer from batch The boundary condition at the gas-liquid interface (x =0)is to continuous operation, which is caused by the differences in provided in Eq. (3), which assumes no chemical reaction tak- oxygen availability. Importantly, this observation is not easily ing place in the gas film. Here, k refers to the gas sided mass i,G accessible by experiments, only, but requires support by transfer coefficient and c to the concentration at the gas- i;L modeling and simulation. We therefore demonstrate that even liquid interface. Furthermore, Henry’s law is used to convert simple models with roughly estimated parameters from pre- the partial pressure of component A in the gas phase p into i i,G liminary experiments are very important tools for a the respective equilibrium concentration c with the simulation-driven transfer from batch to continuous operation i,G,eq Henry-coefficient H according to Eq. (2). For components already in an early stage of process development. with negligible vapor pressures (H = 0) the boundary condi- tion can be simplified to Eq. (4) leading to the absence of mass transfer across the gas-liquid interface. At the interface be- Modelling tween the liquid film and the liquid bulk (x = δ ) the concen- tration has to be a continuous function and thus Eq. (5)is used General concept as respective boundary condition. Note that the bulk fluid is assumed to be well mixed in direction of the coordinate x In order to describe the “batch-to-conti” transformation on a according to the film theory. comparable basis the following approach is used to set up the balance equations. In particular, both the stirred tank reactor p ¼ H c ð2Þ i i;G;eq i;G operated in batch mode (bSTR) and the continuously operated dc plug flow reactor (cPFR) are modeled based on the equal i;L D ¼ k H c −c ð3Þ i;L i;G i i;G;eq i;L meaning of reaction time t in the batch reactor and residence dx x¼0 time τ in the plug flow reactor. Furthermore, the reactor model dc i;L consists of the combination of balance equations at two length D ¼ 0 ð4Þ i;L dx x¼0 scales: The meso scale refers to the balances in proximity of 628 J Flow Chem (2021) 11:625–640 c ðÞ x ¼ δ ¼ c ð5Þ i;L L i;L;b The dimensionless time θ is obtained as the ratio between the reaction time τ and the overall reaction time τ in both At the macro scale Eqs. (6)and (7) describe the material reactor types (Eq. (14)). The dimensionless reaction rate ω balances of the gas and liquid bulk, respectively. Note that the is defined with respect to a reference reaction rate r accord- ref left side of both equations refer to the accumulation in the bulk ingtoEq.(15). It has to be mentioned that the reference fluid. In case of the bSTR τ refers to the time dimension and reaction rate can arbitrarily be chosen and corresponds to the thus the reaction time, while it corresponds to the residence kinetics of the virtual reaction as stated in Eq. (31) for the time τ = z/u with z being the spatial coordinate in flow di- TP present contribution, as will be discussed below in detail. rection and u the two-phase velocity of gas and liquid in the TP cPFR. Therefore, the variable τ quantifies the reaction time for τ θ ¼ ð14Þ both the bSTR and cPFR, which allows for direct comparison of the results obtained for both reactors with respect to reac- j;L ω ¼ ð15Þ tion time. j ref dc a i;G;eq G;L Furthermore, the Hatta number Ha and the Damköhler ¼ −H k c −c ð6Þ i i;G i;G;eq i;L dτ ε number Da are defined (Eqs. (16)and (17)). It becomes ob- dc J a i;L;b i;δ G;L vious that the chosen reference reaction rate determines the ¼ þ ∑ ν r ð7Þ i; j j;L;b dτ ε meaning of the values obtained for Ha and Da and thus re- L j quires a closer look as discussed in detail below (see Eq. (31)). dc i;L J ¼ −D ð8Þ For Ha the assumption of film theory with k = D /δ allows i;δ i;L i,L i,L L dx x¼δ to eliminate the liquid film thickness δ . The Biot number Bi L i relates the gas and liquid sided mass transfer to each other (Eq. The right side of Eq. (6) describes the mass transfer be- (18)). Finally, the Hinterland ratio Hi relates the liquid volume tween the gas bulk and the gas-liquid interface according to V to the volume of the liquid film V and can be expressed L L,f the boundary condition introduced in Eq. (3) with the specific using the film theory and geometric considerations as shown gas-liquid interfacial surface area a = A /V , the gas G,L G,L R in Eq. (19). holdup ε = V /V and the reactor volume V . In Eq. (7) G G R R chemical reaction in the liquid bulk r is considered, which 2 j,L,b δ r D r ref 1;L ref 2 L Ha ¼ ¼ ð16Þ equals r (x = δ ). Furthermore, J refers to the mass flux j,L L i,δ D c c 1;L 1;ref 1;ref 1;L density of component A between the liquid film and the liquid bulk according to Eq. (8). The balance equations at the macro r τ ref Da ¼ ð17Þ scale thus correspond to an initial value problem with the I 1;ref initial conditions provided in Eqs. (9)and (10). H k H k i i;G i i;G Bi ¼ δ ¼ ð18Þ i L c ðÞ τ ¼ 0¼ c ð9Þ i;G;eq i;G;eq;0 D k i;L i;L c ðÞ τ ¼ 0¼ c ð10Þ i;L i;L;0 V ε k L L 1;L Hi ¼ ¼ ð19Þ V a D L; f G;L 1;L The resulting dimensionless material balance at the meso Dimensionless balance equations scale is shown in Eq. (20) with the corresponding boundary conditions in Eqs. (21)and (22). Note that steady-state is The dimensionless form of the balance equations is derived assumed for these balance equations. based on the following definitions. First, the concentrations and initial conditions are transformed into residual fractions f d f i;L i;L 0 ¼ þ Ha ∑ ν ω ð20Þ according to Eqs. (11)and (12)with c chosen as the refer- i; j j 1,ref 2 D dχ 1;L j ence concentration. Furthermore, the dimensionless spatial df coordinate χ in the film is defined as indicated in Eq. (13). i;L ¼ Bi f −f ð21Þ i;m i;L i;G dχ χ¼0 c c c i;L i;L;b i;G;eq f ¼ f ¼ f ¼ ð11Þ i;L i;L;b i;G c c c 1;ref 1;ref 1;ref f ðÞ χ ¼ 1¼ f ð22Þ i;L i;L;b c c i;L;0 i;G;eq;0 κ ¼ κ ¼ i;L i;G ð12Þ At the macro scale Eqs. (23)and (24) are derived accord- c c 1;ref 1;ref ingly with the initial conditions provided in Eqs. (25)and (26). For further simplification, we assume that the gas phase con- χ ¼ ð13Þ sists of one single component only, which leads to constant J Flow Chem (2021) 11:625–640 629 value for f as indicated in Eq. (23). Finally, we assume an according to the stoichiometric Eqs. (R1)to (R3)[36]. The i,G ideal segmented flow pattern for the gas-liquid two-phase by-product water is sufficiently soluble in N,N- flow in the cPFR (see Fig. 1) with well-mixed gas and liquid dimethylformamid (DMF) used as solvent, in which the slugs and neglecting the film between the gas slug and the chemical reaction takes place. All reaction steps are assumed wall. Note that one unit cell can be regarded as control volume to be catalyzed by a POM ({Ba V O }), which provides 4 14 38 for the segmented flow model assuming the unit cell length oxygen to the organic substrate and is re-oxidized by molec- being much smaller than the reactor length. ular oxygen based on a MvK mechanism (Eq. (R4)). df D ε Da Bi i;G i;L L I 1;m C H þfg Ba V O →C H þ H O * 14 12 4 14 38 14 10 2 ¼ − f −f ¼ 0 ð23Þ i;G i;L dθ D 1−ε Ha Hi 1;L L þfg Ba V O ðR1Þ 4 14 37 df df D Da i;L;b i;L I i;L ¼ − þ Da ∑ ν ω ð24Þ I i; j j C H þfg Ba V O →C H O þfg Ba V O ðR2Þ 14 10 4 14 38 14 10 4 14 37 dθ D Ha Hi dχ 1;L j χ¼1 C H O þ2Bfg a V O →C H O þ H O 14 10 4 14 38 14 8 2 2 f ðÞ θ ¼ 0¼ κ ð25Þ i;G i;G þ2Bfg a V O ðR3Þ 4 14 37 f ðÞ θ ¼ 0¼ κ ð26Þ i;L i;L;b fg Ba V O þ 0:5O →fg Ba V O ðR4Þ 4 14 37 2 4 14 38 This reaction network is highly relevant, due to the impor- tance of anthraquinone in the chemical value chain, being currently produced by cycloaddition or coupling reactions, Implementation and simulation e.g. by Friedel-Crafts-reaction of benzene and phthalic anhy- dride. From theoretical point of view and more relevant to the Challenges from reaction network and catalysis current study, the reaction network provides several interest- ing features. Importantly, the consecutive character is well The example reaction chosen for this study is the oxidation of understood in chemical reaction engineering, which provides 9,10-dihydroanthracene (C H ) to anthraquinone 14 12 the basis in order to perform fundamental studies. One aspect (C H O ) via the intermediates anthracene (C H )and 14 8 2 14 10 arises from the POM being present in the liquid phase in form anthrone (C H O) using gaseous oxygen as reactant 14 10 −1 of clusters in the size of 3025 g mol , which can therefore be considered as a molecular, rather than a solid catalyst. This renders the system being homogeneously catalyzed, for which the theoretical framework of non-catalytic gas-liquid reactions can be applied counterintuitively. In particular, the implemen- tation of the MvK mechanism in modeling of gas-liquid reac- tions is not yet performed in scientific literature to the best of our knowledge. Another interesting aspect is motivated by the typical chal- lenge in research for derivation of kinetic data, where exper- iments have to be designed despite a significant lack of knowl- edge on the reaction system, especially in an early stage of research. For multi-phase reactions, in particular, care has to be taken in order to avoid the obtained kinetic data to be falsified by heat and mass transfer issues. Even though several rules of thumb are available to tackle this challenge (e.g. the Weisz-Prater criterion in heterogeneous catalysis), these rules are usually applicable to very simplified reaction systems on- ly. In this context the reaction system chosen is too complex and still not fully understood, neither mechanistically, nor with respect to the reaction kinetics. On top of this, the varia- tion of the POM based catalyst during research progress may affect both the reaction mechanism and the kinetics, which hampers the transfer of knowledge gained so far. Fig. 1 Model for the unit cell in a segmented flow (Taylor-flow) regime, The scientific key question for experimental derivation of with the unit cell consisting of one gas bubble and one liquid slug, as well as an illustration of the two film model at the meso scale reliable kinetic data are the concentration and temperature 630 J Flow Chem (2021) 11:625–640 Table 2 Assumed profiles in proximity of the gas-liquid interface, since they Stoichiometric Eq. Reaction kinetics reaction kinetics allow to distinguish reaction kinetics from the effects of trans- port limitations. Operando techniques are not capable to solve (R1) r =k c c 1 1 2 7 these issues completely yet [22, 38], since resolution of those (R2) r =k c c 2 2 3 7 profiles is still a matter of research [39, 40]. Therefore, model- (R3) r =k c c 3 3 4 7 ing and simulation is a promising approach, in order to sup- (R4) r =k c c 4 ref 1 8 port the design of experiments and interpretation of the results, as will be demonstrated in the present contribution. data. Note that the effect of reaction temperature is included Reaction system in k , only, for the presented isothermal balance equations. ref r ¼ k c c re f re f 1;re f cat;re f For implementation, the matrix of stoichiometric coeffi- ð27Þ with c ¼ c and c ¼ c þ c 1;re f 1;G;eq;0 cat;re f 7;L;b 8;L;b cients is derived from the stoichiometric reaction Eqs. (R1)to(R4) as summarized in Table 1. In addition, the We have chosen this type of reference reaction kinetics, as components A are also numbered in the following for it involves the gaseous reactant on the one hand, which has to simplification of the notation. Note that oxygen is pres- be transported across the gas-liquid interface. On the other ent in the gas phase and also soluble in the liquid, hand, it also includes the concentration of a reactant fed with while all other components are considered to be present the liquid phase, being the catalyst in this case. The reference in the liquid phase only, due to a negligible vapor pres- kinetics thus put the most important reactants of the complex sure of the organic reactants and the catalyst. reaction network in the center of the considerations, being the The kinetics involved for the occurring reactions are not catalyst in the focus of ongoing research. It has to be men- known yet and thus require to be estimated. Therefore, we tioned again that the choice of the reference reaction kinetics chose a simple approach assuming all reactions to be irrevers- depends on the individual case and can even describe a virtual ible and first order in the respective reactants (Table 2). In reaction not taking place in real experiments, since it is only particular, the catalyst is considered to take part in each reac- required to derive the dimensionless balance equations. After tion, either as oxygen donor or acceptor according to the MvK all, the meaning of the specific values for the dimensionless mechanism. numbers is defined by the choice of the reference. Reaction (R4) is chosen as the reference, being first order both in oxygen and catalyst concentration according to Eq. Parametrization (27). Therefore, the initial equilibrium concentration of mo- lecular oxygen in the gas bulk corresponds to the reference For parametrization the dimensionless numbers Da and Ha concentration c , which is also used for definition of the I 1,ref are estimated based on experiments performed in the bSTR by dimensionless numbers and variables above. Furthermore, Lechner et al. [36]. The overall reaction time in those exper- the total catalyst concentration, comprising the oxidized and iments was τ ¼ 7 h, with an initial oxygen partial pressure of reduced state, is considered as c , which is constant cat,ref p ¼ 8 bar as well as the initial concentration of component throughout the reaction progress. The kinetic constant of the O ;0 −3 reference reaction k needs to be scaled for sensitivity analy- A of c =45.8 mol m and of the catalyst of c = ref 2 2,L,b,0 7,L,b,0 −3 sis during simulation experiments or to meet experimental 0.9 mol m in the liquid phase. Components A to A and A 3 6 8 Table 1 Matrix of stoichiometric A Component Chemical formula Stoichiometric Eq. coefficients of the reaction system i (the solvent DMF is implemented (R1) (R2) (R3) (R4) as inert component A ) A oxygen O 00 0 −0.5 1 2 A 9,10-dihydroanthracene C H −10 0 0 2 14 12 A anthracene C H 1 −10 0 3 14 10 A anthrone C HO0 1 −10 4 14 10 A anthraquinone C H O 00 1 0 5 14 8 2 A water HO1 0 1 0 6 2 A catalyst, oxidized {Ba V O } −1 −1 −21 7 4 14 38 A catalyst, reduced {Ba V O}1 1 2 −1 8 4 14 37 J Flow Chem (2021) 11:625–640 631 −1 are not present in the reactor initially, while the total liquid of magnitude for ε ≈ 0.5 and a ≈ 1000 m typical for L G,L −5 3 volume was V =5 ·10 m . The authors report an initial segmented flow (including liquid film surrounding the conversion of component A obtained after a reaction time bubbles) in channels of 1.6 mm (1/16 in.) diameter, as well −3 of Δτ =1 h of Δc =11.45 mol m , as well as a formation as for δ ≈ 40 μm (rough estimate from k a values from 2,L,b L L G,L −3 of component A of Δc =5.95 mol m and A of [15]), gives Hi ≈ 12.5. In contrast, a Hinterland ratio of 4 4,L,b 5 −3 Δc =5.50 mol m . From these changes in concentration Hi ≈ 250 is obtained for the used bSTR with ε ≈ 0.5, 5,L,b L −1 the number of catalytic cycles of the catalyst, which is the a ≈ 50 m and δ ≈ 40 μm (agitated tank with small G,L L turn-over number (TON), can be calculated according to Eq. energy input, c.f. [46]). (28). Note, that the first term in the numerator represents all Hi ¼ ð29Þ turn-overs in the first reaction. a δ G;L L ν Δc þ ν Δc þ Δc þ ν Δc O ;R1 2;L;b O ;R2 4;L;b 5;L;b O ;R3 5;L;b 2 2 2 TON ¼ Note that Da is not suitable to distinguish between the cat;re f operation strategies, as it relates the reaction time with the ð28Þ intrinsic reaction kinetics, which is identical for both reactors. In contrast, Ha quantifies the mass transfer characteristics and With the Henry coefficient of O in DMF of H ≈ 5 2 O ;DMF may thus weakly depend on the reactor type chosen, only. −8 −3 −1 10 mol m Pa [41, 42], as well as the estimated orders of The interplay between reaction in the bulk and the profiles magnitudes for the diffusion coefficient of O in the liquid in the film can illustratively be discussed based on the mass −9 2 −1 phase of D ≈ 5  10 m s [43] and for the liquid film O ;L transport parameter T (Eq. (30)). Comparison with Eq. (24) thickness of δ ≈ 40 μm, Table 3 summarizes the relevant exhibits that this parameter describes the transport of the lim- values for the dimensionless numbers of a typical experiment iting component supplied by the gas phase A from the liquid in a bSTR. The diffusivity of all other components is assumed film into the liquid bulk and therefore links the meso and to be five times smaller, compared to oxygen diffusivity, how- macroscale with each other. It also becomes obvious from ever, diffusivities for the catalyst are unavailable and might be Eq. (24) that for high values of T the gradient of the residual even smaller than for the Anthracene derivates fraction at χ = 1 can be small for constant flux densities, which −9 2 −1 (D ¼ D ≈ 1  10 m s [44, 45]). Furthermore, the A ;L A ;L 3 5 results in flat profiles for A in the film. gas-sided mass transfer is assumed to be not limiting (Bi → ∞). Da τ k a I 1;L G;L T ¼ ¼ ð30Þ Ha Hi ε Reactor comparison This parameter is also suitable for fundamental studies on the batch-to-conti approach, since it allows a direct compari- Interestingly, the dimensionless balance equations allow to son of results obtained for various values of Hi, Ha,and Da express the difference between bSTR and cPFR by the on a common basis by lumping the individual effects. In other value for Hi only, since Eq. (19) can be rewritten to Eq. words, since all these parameters are affected by changing the (29) assuming film theory. It becomes obvious that Hi operation strategy from batch to continuous operation, the consists of properties strongly depending on the reactor proper comparison would require to perform an intensive type used and is thus suitable to distinguish between batch study with these three parameters. Lumping the individual or continuous operation. In particular, Hi becomes small effects in T reduces the parameter space without losing for segmented flow in the cPFR, due to the high values for significance. specific interfacial surface area. The estimation of the order Table 3 Estimated reference values and dimensionless numbers from a typical experiment performed in a bSTR by Lechner et al. [36] Property Equation Value −3 Reference concentrations c ¼ p H 0.04 mol m 1;ref O ;0 O ;DMF 2 2 −3 Catalyst concentration c ¼ c þ c 0.9 mol m cat;ref 7;L;b 8;L;b TON c cat;ref −3 −3 −1 Reference reaction rate r ¼ 9.4·10 mol m s ref Δτ r 3 −1 −1 ref Reference kinetic constant k ¼ 0.262 m mol s ref c c 1;ref cat;ref Damköhler number Eq. (17) ≈ 6000 Hatta number Eq. (16) ≈ 0.274 632 J Flow Chem (2021) 11:625–640 Implementation and simulation constants require to amount to k =2.28 · −5 3 −1 −1 10 m mol s for j ∈ {1, 2, 3}. The model equations are implemented to Matlab (version r k c c 1;0 1 2;L;b;0 cat;ref R2019b) and solved with ode15s (4th order backward differ- ¼ ¼ ω ¼ 0:1 ð33Þ 1;0 r k c c ref ref 1;ref cat;ref entiation formula - BDF) in order to perform a sensitivity r c 1;0 1;ref analysis by simulation experiments. The simulations focus −5 −1 k ¼ k ¼ 2:28  10 s ð34Þ 1 ref r c on the comparison between bSTR and cPFR, which are dis- ref 2;L;b;0 tinguished based on Hi, while keeping all other parameters Figure 2 shows the simulation results for the bSTR under equal for comparability reasons. Furthermore, the initial con- base case conditions. The observed profiles of the residual ditions used in the above-mentioned experiment are applied fractions for the organic reactants as function of reaction time for simulations, as well. The diffusion coefficients of all (Fig. 2a) are typical for the consecutive reaction considered in Anthracene derivates and the catalyst in the liquid phase are this example and agree qualitatively with experimental results assumed to be equal for simplicity reasons, though this as- [36]. After 7 h of reaction (θ = 1) the conversion of A reaches sumption may induce errors in the obtained results. We there- ca. 88%, while the yield for all anthracene derivates is com- fore focus the discussion of the results on the trends observed, parable in the range of 25 to 35%. The high numbers for the rather than on the interpretation of specific numbers. residual fractions are caused by the low solubility of O in For evaluation of the reactor performance, following defi- DMF and thus a small value for c . One may conclude that 1,ref nitions are used for conversion X of component A and the the solubility of O appears to be one important factor respon- yield Y towards component A (Eq. (31)). The degree of re- i i sible for the long reaction times required in the experiments in duction of the catalyst α is quantified by Eq. (32). order to achieve reasonable conversions. In Fig. 2c the corre- f f c c sponding profiles of the oxidized and reduced catalyst species 2;L;b 2;L;b i;L;b i;L;b and Y ¼ ¼ X ¼ 1− ¼ 1− ð31Þ c κ c κ are shown. The initially fully oxidized catalyst is reduced rap- 2;L;b;0 2;L 2;L;b;0 2;L idly in the very early stage of the reaction and remains at a cat;red 8;L;b α ¼ ¼ ð32Þ rather constant residual fraction of the oxidized state of f ≈ 7,L,b f c þ c 7;L;b 8;L;b cat;ref 16 thereafter. The profiles of the residual fraction of oxygen and the degree of reduction of the catalyst α at the meso scale are shown in Fig. 2b for three different reaction times θ , θ I II and θ indicated in Fig. 2a (corresponding to ca. 30 min, 3.5 h III and 7 h). Obviously, the degree of reduction of the catalyst is Results and discussion constant in the liquid film, as well. The oxygen profile, how- ever, declines almost linearly from the phase boundary at χ = Base case 0 towards the liquid bulk at χ = 1, which agrees with the expectations from the small Ha used for the simulations. The base case assumes that the dimensionless initial The almost constant degree of reduction of the catalyst α at rates of the reactions (R1)to(R3)amountto ω =0.1 j,0 meso and macro scale renders the apparent kinetics for (R1) to for j ∈ {1, 2, 3}, which means that those reactions are (R3) being first order in concentration of the respective organ- slower than the reference reaction (R4). This scenario ic reactant. The oxygen availability in the liquid phase, how- corresponds to the typical approximation used in homo- ever, is the limiting factor for the re-oxidation of the catalyst in geneous catalysis, which neglects the formation of con- (R4) and hence for the overall reaction process. In particular, centration gradients of the molecular catalyst. Indeed, it the residual fraction of oxygen in the liquid bulk amounts to is known from experiments, that the specific chemistry ca. 0.2 only. Considering that the reaction mainly takes place of catalytic steps is a delicate task (c.f. [19]), but is in the bulk for the large Hi used in the simulations, the limiting typically neglected. In the present example, however, effect of oxygen availability is not surprising. Importantly, the the catalyst is stoichiometrically involved in the reac- catalyst is provided in large excess with respect to oxygen tion, due to the MvK mechanism proposed. Therefore, (κ = 22.9) and therefore the degree of reduction α is rather 7,L certainly pronounced gradients in oxidized and reduced independent on the reaction progress and limited to ca. 0.3. catalyst species may evolve, depending on the reaction The negligible differences in the profiles observed at the meso rates. The assumption limits those gradients on the one scale are caused by the slight changes of α with reaction time hand, but offers the respective discussion at the same at the macro scale. time. Therefore, this approach allows to shed light on The simulation results for the base case in the cPFR are the importance of the spatial distribution of the catalyst shown in Fig. 3, providing qualitatively similar profiles com- oxidation state within the reactor on the measured re- pared to the bSTR with a slightly higher conversion for A of sults. In order to fulfill the assumption, the kinetic J Flow Chem (2021) 11:625–640 633 Fig. 2 Simulation results for bSTR operation (with Da = 6000, Ha = spatial profiles of residual fractions in the film at three selected reaction 0.274, Hi =250, T = 320); residual fractions of (a) organic reactants and times: (θ )initial,(θ ) intermediate, (θ ) final phase I II III (c) catalyst species as function of dimensionless reaction time θ;(b) ca. 95% and yields in the range of 14 to 59% for all organic differences in the oxygen profile in the film can directly be products. The degree of reduction of the catalyst is also almost attributed to the mass transport parameter T. constant in the film (Fig. 3b) and with reaction time (Fig. 3c), The degree of catalyst reduction α can be predicted de- but lower than in the bSTR. Furthermore, the profiles at the pending on the reaction extent assuming that the rate of cata- meso scale are not affected by the reaction time. Compared to lyst reduction in reactions (R1) to (R3) equals the rate of re- the bSTR, however, the profile of oxygen residual fraction in oxidation in (R4). This assumption, expressed in Eq. (35), the film is almost constant and close to unity (ca. 95%) even in requires negligible changes in degree of reduction with spatial the liquid bulk. Hence, the oxygen availability is hardly lim- coordinate and reaction time. After introduction of the reac- iting, which consequently means that the re-oxidation rate of tion kinetics (Table 2) and the definition of the reduction de- the catalyst in the bulk can be regarded as the limiting factor. gree (Eq. (32)) Eqs. (36)to(38) can be derived, respectively. The differently pronounced oxygen profiles in the film in the base case simulations can be explained by the parameter T, 0 ¼ ∑ ν r ð35Þ 7; j j j¼1 which is significantly smaller for the bSTR (T = 320) bSTR compared to the CFPR (T = 6400). It has to be mentioned cPFR k c c ref 1;G;eq 8;L;b that the convection and reaction terms in Eq. (24) are rather ¼ c k c þ k c þ 2 k c ð36Þ unaffected by the reactor choice given by the similar profiles 7;L;b 1 2;L;b 2 3;L;b 3 4;L;b of the residual fractions with reaction time. Therefore, the Fig. 3 Simulation results for cPFR operation (with Da = 6000, Ha = spatial profiles of residual fractions in the film at three selected reaction 0.274, Hi =12.5, T = 6394), residual fractions of (a) organic reactants times: (θ )initial,(θ ) intermediate, (θ ) final phase I II III and (c) catalyst species as function of dimensionless reaction time θ;(b) 634 J Flow Chem (2021) 11:625–640 simulations is possible, since the errors induced by unknown k c c ¼ c −c k c þ k c þ 2 k c ref 1;G;eq 8;L;b cat;ref 8;L;b 1 2;L;b 2 3;L;b 3 4;L;b kinetics and further simplifying assumptions contribute equal- ð37Þ ly to the obtained results for both reactors. From Table 4 it can be observed that the simulation is capable of predicting the k c þ k c þ 2 k c 1 2;L;b 2 3;L;b 3 4;L;b α ¼ ð38Þ trend of the experimental data, while the specific values devi- k c þ k c þ k c þ 2 k c ref 1;G;eq 1 2;L;b 2 3;L;b 3 4;L;b ate to a certain extent. The discrepancy can be explained by the fact that the reaction kinetics are not known and therefore Equation (38) provides the basis for an estimate of the approximated by simple power-law approaches. On the other expected degree of reduction, in order to design and interpret hand, this simple approach obviously allows to gain meaning- experimental results. Most importantly, the relevance of oxy- ful insights into the reaction system and the reactor behavior. gen solubility and re-oxidation rate becomes apparent both Figure 4 provides the direct comparison of both reactor expressed by the term k c , since increasing this term ref 1,G,eq types based on the profiles of the organic reactants with reac- leads to a decrease in the degree of reduction, which is bene- tion time obtained by simulations. The observed trends are ficial for the reactor performance. Even though this conclusion comparable for bSTR and cPFR, exhibiting a declining resid- is drawn based on the specific reaction kinetics assumed in the ual fraction for A , negligible values for A , and monotonously present example, it is of general importance for similar reac- 2 3 increasing values for A . Component A exhibits a profile 5 4 tion systems and other kinetics, as well. Eventually, the rela- typical for intermediates in consecutive reactions. The tionship shows that in-situ measurements of the catalyst state resulting profiles in residual fractions thus agree with the ex- will give a further insight into the underlying kinetics. pectations associated with the chosen values for the dimen- sionless reaction rates in a consecutive reaction network. Kinetics The detailed comparison reveals that the cPFR exhibits better performance with respect to conversion of A and yield In order to represent the experimental results reported by of A obtained at reaction time of θ = 1. Comparing the reac- Lechner et al. [36] the dimensionless reaction rates have been tion time required to reach a conversion of X =0.2 and the adjusted according to the following values: ω =0.5, ω = 1,0 2,0 yield in A at that reaction time, the cPFR (θ =0.15, 5 cPFR 25, and ω = 5. Note that these values are not obtained by 3,0 Y = 0.11) outperforms the bSTR (θ =0.25, 5,cPFR bSTR fitting to experimental data, due to lack of knowledge in reac- tion kinetics. Instead, emphasis is on studying the order of magnitude effects of the reaction rates on the observations. The chosen values mean that the rate of reaction (R1) is lim- iting, while the selectivity towards the intermediate (A and A ) and final (A ) products are governed by the respective 4 5 dimensionless reaction rates. In particular, A formation is expected to be hardly detectable, since it is directly converted into A given by the high ω /ω ratio. 4 2,0 1,0 The direct comparison of experimental and simulation re- sults obtained for both the bSTR and cPFR reactor is summa- rized in Table 4 and depicted in Fig. 4. Note that the simula- tions are based on identical parametrization, except for Hi for both reactor types. Therefore, the direct comparison based on Table 4 Comparison of reactor performance in simulation and experiment [36] for both reactor types (no cPFR experiments with fluidic residence time τ > 1 h available) fl Simulation Experiment Reaction time Reactor X /% Y /% X /% Y /% 5 5 θ=1 bSTR 60 55 57 40 cPFR 87 85 –– θ=0.13 bSTR 12 4 22 14 cPFR 18 9 21* 15* Fig. 4 Residual fractions of the organic reactants as function of *operating cPFR with fluidic residence time of τ =54 min dimensionless reaction time θ;(a)bSTR(Hi =250); (b)cPFR(Hi =12.5) fl J Flow Chem (2021) 11:625–640 635 Y = 0.11) clearly. The reason for this observation has to is first order in oxygen. Finally, it has to be considered that the 5,bSTR be related to the value of Hi, since this parameter distinguishes oxygen demand depends on the reaction extent, due to differ- between both reactor types, only. In particular, Hi is respon- ences in stoichiometry and the intrinsic rate of reactions (R1) sible for oxygen availability in the liquid bulk and hence for to (R3) and thus changes with reaction time (e.g. Eq. (38)). the degree of reduction of the catalyst, as discussed for the The interplay of these factors is therefore responsible for base case. Therefore, the profiles of the oxygen residual frac- the observed profiles and renders the cPFR beneficial for ki- tion together with the degree of reduction as function of reac- netic experiments, because mass transport limitations are less tion time are depicted in Fig. 5 for cPFR and bSTR. pronounced. Interestingly, the simulation results exhibiting a Obviously, the degree of reduction is significantly lower in higher oxygen saturation and smaller degree of reduction in the cPFR reaching a maximum value of about 15%, while that the cPFR agree in principle with experimental observations. in the bSTR even exceeds 50%. This observation is associated The POM catalyst used in the experiments changes color from with the oxygen residual fraction, which is rather constant orange to green upon increasing degree of reduction and even with reaction time at ca. 0.9 and 0.2 for the cPFR and bSTR, becomes colorless after decomposition, which justifies the respectively. Interestingly, the oxygen residual fraction is rath- predictions from simulations qualitatively. er constant, while the degree of reduction exhibit significant changes with reaction time. This can be explained by the high Sensitivity analysis in mass transfer value for ω , which means that the catalyst reduction in re- 2,0 action (R2) is twenty-five times faster than the catalyst re- The effect of mass transfer is studied based on the lumped oxidation in reaction (R4) under initial conditions. mass transport parameter T introduced in Eq. (30). For sensi- Therefore, the oxygen consuming re-oxidation reaction is lim- tivity analysis this parameter is varied between 30 and 120′ iting in the simulated cases and the profile of reduction degree 000, while each value is justified by typical conditions for is governed by the rates of reactions (R1) to (R3). On the other either bSTR or cPFR. As basis for a meaningful range of T hand, the oxygen transport through the film is limiting due to the film thickness was varied between 2 and 400 μm, which the high value for Hi in the bSTR, which leads to pronounced even covers values beyond the expected boundaries for bSTR profiles in oxygen residual fraction in the film and thus low and typical flow regimes in cPFR. We thereby account for values in the bulk. This limits the re-oxidation, as well, which uncertainties in estimation of T by broadening of the consid- ered value range and avoid the complexity arising from more accurate determination at the same time. Figure 6 depicts the impact of the mass transport parameter T on the maximum degree of catalyst reduction in the bulk achieved within the reaction time and the conversion of component A after 55 min (θ=0.13) and7h(θ = 1) of reaction. The solid lines correspond to typical conditions for each reactor type, while the dashed lines indicate the extrapolation towards unusual conditions, in order to support the direct comparison of batch and continuous operation. For illustration, the range of T cor- responding to the film thickness between 2 and 400 μmis indicated for the bSTR and the cPFR, as well. It becomes apparent that both reactor types overlap in the range of 250 < T < 2000, which correspond to extrapolated values for each and therefore unlikely operation conditions. The degree of maximum reduction appears to be a function of the mass transport parameter T only, but does not depend on the reactor type, since the α (T) profiles of cPFR and max bSTR are clearly overlapping. Furthermore, it appears that extrapolation over the whole range of T leads to identical profiles irrespective of the reactor type. It can also be observed that the reduction degree is constant for the typical operation range in the cPFR, but exhibits a strong sensitivity towards the mass transport parameter for the bSTR. Importantly, the max- imum reduction degree is very small and the average value therefore even smaller for the cPFR. Consequently, the cata- Fig. 5 Catalyst oxidation state and oxygen residual fraction as function of dimensionless reaction time θ;(a)bSTR(Hi =250); (b)cPFR(Hi =12.5) lyst can be assumed to be homogeneously distributed in the 636 J Flow Chem (2021) 11:625–640 A , as well, but form the reduced catalyst species stoichiomet- rically at the same time. For additional information, the reader is referred to the supporting information, where the degree of reduction and the rates are plotted for the highest and lowest value of the mass transport parameter, respectively. Interestingly, the conversion in the cPFR is constant in the typical operation window, while it increases for smaller T values. The dimensionless formulation of the balance equa- tions hampers a clear argumentation of this unexpected obser- vation. Importantly, the mass transport parameter T results from lumping of the degrees of freedom of the reactor opera- tion expressed by Hi, Ha and Da , which allows different sets of those degrees of freedom to yield identical T values. For instance, a reduction of Hi from 250 to 12.5 for bSTR to cPFR can be compensated by a decrease in Da from 10 to 0.5 in order to maintain T/Ha = 400. The relation T/Da , representing mass transfer into and the reaction within liquid bulk, changes from T/Da = 0.4 in the first to T/Da = 8 in the I I second case. This means that the interplay between reaction in Fig. 6 Maximum degree of catalyst reduction α and conversion in A the bulk and the processes in the liquid film play an important max 2 in the liquid bulk as function of the mass transport parameter T for the role for the performance of the chosen reactor. Therefore, bSTR (squares) and cPFR (circles) with typical (solid lines, filled sym- fundamental differences between both cases exist depending bols) and extrapolated (dashed lines, open symbols) operation range; lines on the specific parametrization, though the balance equations are shown to guide the eye, typical range in film thickness δ related to are identical. Along this argumentation, an increase in Ha mass transport parameter T is indicated by bars for both reactor types leads to a decrease in T at constant Da and Hi, which is associated with an increasing enhancement factor E and there- liquid phase in the oxidized state, which corresponds to the fore an improved mass flux of oxygen across the gas-liquid typical assumption for molecular catalysts in homogeneous interface. In the same vein, a reduction in T induces the gra- catalysis. In contrast, the degree of reduction reaches very dient of the residual fractions at χ = 1 to raise (see Eq. (24)), high values for the bSTR, which lead to the irreversible deac- which enhances the mass flux into the bulk, as well. tivation of the POM-based catalyst by decomposition. According to Eq. (30)small T values can be achieved for fast Therefore, gradients in the concentration of oxidized and re- reactions, expressed by high values for Ha and small values duced catalyst species probably develop. The reason for the for Da , and cause gradients at the meso scale to develop. high degrees of reduction is the limited availability of oxygen Therefore, large values of T allow to neglect gradients in the for re-oxidation for low values of T and thus reasonable mass film and thus to assume intrinsic conditions, while decreasing transfer limitations for oxygen. Hence, the cPFR is beneficial T values lead to deviation from intrinsic operating points. The for kinetic measurements, due to absence of severe mass trans- latter situation thus requires more sophisticated models for fer limitations at high T values. Considering the conversion, analysis of experimental data, while a one-dimensional, the results for the bSTR raise with increasing T and asymptot- pseudo-homogeneous model is sufficient for the intrinsic case. ically reach those of the cPFR and therefore intrinsic condi- It also becomes apparent that a straight-forward argumenta- tions. Furthermore, the sensitivity towards the mass transport tion of the obtained results based on the dimensionless num- parameter is more expressed in the bSTR. bers only, is misleading, due to the interdependencies of their The sensitivity of both the conversion and degree of reduc- definitions. tion in the bSTR indicate that a correlation between both ex- ists: with decreasing degree of reduction the conversion in- Variation of kinetics in the reaction network creases. This is most probably caused by the enhanced oxygen availability for higher values of the mass transport parameter The impact of the kinetics in the consecutive reaction network and thus improved re-oxidation of the catalyst by reaction is studied in two scenarios. In scenario I the kinetics of reac- (R4), which is first order in O . This leads to a higher concen- tion (R1) is varied according to ω = ∈ [0.005, 5], while the 2 1,0 tration of the oxidized catalyst species A and thus an in- kinetics of reaction (R2) and (R3) are kept constant at ω = 7 2,0 creased rate for the oxidation of A via reaction (R1), which 25 and ω = 5. This scenario therefore covers various cases 2 3,0 is first order in A and A . The rates of the consecutive reac- relating the reduction of the catalyst in reaction (R1) to its re- 2 7 tions (R2) and (R3) profit from the increasing concentration of oxidation in reaction (R4). Within the consecutive network J Flow Chem (2021) 11:625–640 637 reaction (R1) is thus always limiting, since reaction (R2) is at α > 0.6. Hence, in comparison to the cPFR the yield in the max least five times faster. It has to be considered, however, that bSTR is obviously limited by the re-oxidation of the catalyst. reaction (R2) and (R3) require oxygen stoichiometrically, as In particular, the available oxygen is mainly consumed by well, and thus contribute to catalyst reduction. reaction (R1) and (R2), since ω /ω = 5, and thus reaction 2,0 3,0 The obtained simulation results (Fig. 7a) exhibit similar (R3) suffers from oxygen depletion, which becomes more and almost negligible degrees of reduction for bSTR and severe for high ω values. 1,0 cPFR for very small values of ω associated with similar Scenario II extends the previous analysis by variation of the 1,0 values for conversion and yield. Therefore, oxygen availabil- rates of reaction (R1) to (R3) proportionally, according to ity appears to be not limiting, neither in the molecular form ω =0.5 m, ω =25 m and ω =5 m with the activity ratio 1,0 2,0 3,0 required for the catalyst re-oxidation, nor in form of the oxi- m = ∈ [0.1, 10]. It therefore scales all reactions contributing to dized catalyst needed for reaction (R1) to (R3), which renders catalyst reduction equally and thus relates the overall rates of the reaction rates being intrinsic. With increasing values for catalyst reduction and re-oxidation to each other. Hence, the ω the degree of reduction raises for both the bSTR and the factor m expresses the activity ratio of the reduction and the re- 1,0 cPFR, while the increase is significantly more pronounced for oxidation half-cycle during the MvK mechanism. The direct the bSTR. This can be explained by the increasing demand of comparison to scenario I is possible for m = 1 and indicated in oxygen in reaction (R1) to (R3) induced by the higher reaction Fig. 7 as dashed vertical line. rates, leading to the re-oxidation of the catalyst becoming The results in Fig. 7b exhibit an increasing degree of re- limiting. The difference between both reactors is caused by duction with raising activity ratio, since the re-oxidation half- the mass transfer parameter T, which is significantly smaller cycle of the catalyst becomes limiting. Furthermore, both the for the bSTR as discussed above. This leads to more pro- bSTR and the cPFR exhibit similar values of catalyst reduc- nounced mass transfer limitations and therefore to a lower tion degree, conversion and yield for m < 0.25, while the de- oxygen availability. In addition to the observations at the mac- viation becomes more pronounced for raising m. This can ro scale shown in Fig. 7a gradients develop in the liquid film again by explained by the smaller mass transport parameter as discussed above for the base case. T in the bSTR, which limits the oxygen availability required The conversion X and yield Y raises with ω for the cPFR for catalyst re-oxidation. Importantly, higher m values mean 5 1,0 and reaches unity asymptotically. Furthermore, both values that catalyst re-oxidation is hampered under reference condi- are very similar indicating a high selectivity towards compo- tions at maximum oxygen availability already. During reac- nent A after the reaction time of θ = 1. In contrast, the con- tion oxygen is consumed and thus the catalyst reduction de- version raises, while the yield exhibits a maximum for the gree becomes even more sensitive towards mass transport bSTR, which means that the selectivity towards the interme- restrictions. Interestingly, the selectivity towards component diate components A and A increases with ω . The observed A is high for both reactors expressed by the slight deviation 3 4 1,0 5 maximum and subsequent decline in yield is associated with between conversion and yield, since all reactions suffer pro- an increasing trend of the degree of catalyst reduction beyond portionally from the higher reduction degree of the catalyst. Fig. 7 Impact of reaction rate constants in the reaction network on the conversion X, the yield Y and the maximum degree of catalyst reduction α ;(a) 5 max impact of ω ;(b) impact of the activity ratio m of the reduction and the re-oxidation half-cycle during the MvK mechanism 1,0 638 J Flow Chem (2021) 11:625–640 The lower selectivity as well as the deviation of the maximum macro scale, respectively. The parameterization is performed value for conversion and yield observed in the bSTR from the using experimental results obtained in a bSTR during the early expected value of one for irreversible reactions indicates that stage of catalyst development. Importantly, the discrimination the catalyst re-oxidation limits the reactor performance in that of the bSTR and the cPFR is realized by means of character- case. istic dimensionless numbers using the identical mathematical The results of the kinetic study exhibit a very similar be- model for comparability reasons. The uncertainties typical for havior of the bSTR and the cPFR in the intrinsic regime, as an early stage in process development are accounted for by expected, which is beneficial for experimental investigation of sensitivity analyses carried out for the reaction kinetics and the kinetic parameters or catalyst development. The low values mass transport parameter T. for conversion and yield can easily be compensated by in- It was revealed that the maximum degree of catalyst reduc- creasing residence time in this regime. Under non-intrinsic tion strongly correlates with the mass transport parameter, but conditions, however, pronounced gradients and oxygen trans- not directly with the reactor type. This is expected from the port limitations develop, which lead to several challenges in identical set of balance equations used and the re-oxidation of evaluation of experimental data. In case that catalyst re- the catalyst chosen to be the reference reaction. The mass oxidation is limiting, for instance, the experimental determi- transport parameter, though, can directly be linked to charac- nation of conversion and yield of the organic reactants be- teristic values for both types of reactor operation and can thus comes rather meaningless. Instead, emphasis should be put be used for respective discrimination. The results also show on the additional determination of the catalyst reduction de- that the mass transport parameter is suitable to determine, gree, in order to evaluate the information obtained from the whether the reactor is operated under (nearly) intrinsic condi- product composition data (see Eq. (38)). tions or in a regime, where mass transfer, catalyst re−/oxida- Catalyst development often aims at increasing the activity tion and chemical reaction are interfering. Importantly, even with respect to conversion of the organic reactants, which is rather slow reactions may suffer from mass transfer limitations expressed by increasing ω in scenario I. Interestingly, the in a bSTR and therefore require cPFR experiments for kinetic 1,0 results clearly show that an increase in activity is not neces- studies, which can be concluded from our results. sarily correlated with the measured conversion or yield, which For the POM catalyzed aerobic oxidation of DHA we iden- in particular holds for the non-intrinsic case with severe mass tified the catalyst reduction degree as the most important as- transport limitations. Obviously, the choice of an appropriate pect to be considered in the design of the process. It appears to reactor and operations conditions become very important to determine the significance of the experimental results with provide a correlation between experimental results and devel- respect to catalyst activity improvement obtained under non- opment aims. The results in Fig. 7a, obtained for catalyst intrinsic conditions. Therefore, catalyst development needs to aim at sufficiently fast re-oxidation of the reduced catalyst activity ranging over three orders of magnitude, clearly under- line the benefits of the cPFR for that purpose. species in order to avoid limitations or even catalyst decom- From Fig. 7b it can be concluded that catalyst development position. Furthermore, oxygen availability in the liquid phase requires a holistic approach, emphasizing both the reduction supports catalyst re-oxidation and can be improved by en- and re-oxidation half cycle. In other words, improving the hancing the interfacial surface area, as well as higher oxygen activity towards conversion of the organic reactants require a solubility by the choice of appropriate solvents. Finally, the proportional increase in catalyst re-oxidation activity, as well. results indicate that determining the catalyst oxidation state Otherwise, the re-oxidation step becomes limiting and thus the in-situ is of superior importance in addition to the analysis catalyst reduction degree increases towards rather high values of the product spectrum, in order to quantify the catalyst per- in the non-intrinsic case. This leads to pronounced gradients formance. hampering the evaluation of the experimental data and even to The study illustrates that even simple reactor models with irreversible decomposition of POM catalysts. roughly estimated parameters from preliminary experiments are sufficient in the early phase of process development. Such models are capable to resolve the complex interactions be- Conclusions tween mass transfer and reaction steps and thereby allow to identify the bottle-neck in the significance of experimental The present contribution investigates the transfer from batch data. They can also be used for design of appropriate experi- to continuous operation under uncertainties for the POM cat- ments and even for exploration of the feasibility of novel alyzed aerobic oxidation of DHA as an example for gas-liquid process windows. Hence, process development profits from reactions. The study is based on a mathematical model assum- both the transfer of experimental studies from batch to contin- ing film theory, which consists of dimensionless balance uous operation and mathematical modeling in an early phase, equations for the liquid film and the liquid bulk at meso and already. J Flow Chem (2021) 11:625–640 639 Supplementary Information The online version contains supplementary 9. 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Journal

Journal of Flow ChemistrySpringer Journals

Published: Sep 1, 2021

Keywords: Multiphase reaction; Mathematical modelling; Flow chemistry; Liquid phase oxidation; POM catalyst

References