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Kinetic analysis of the partial synthesis of artemisinin: Photooxygenation to the intermediate hydroperoxide

Kinetic analysis of the partial synthesis of artemisinin: Photooxygenation to the intermediate... The price of the currently best available antimalarial treatment is driven in large part by the limited availability of its base drug compound artemisinin. One approach to reduce the artemisinin cost is to efficiently integrate the partial synthesis of artemisinin starting from its biological precursor dihydroartemisinic acid (DHAA) into the production process. The optimal design of such an integrated process is a complex task that is easier to solve through simulations studies and process modelling. In this article, we present a quantitative kinetic model for the photooxygenation of DHAA to an hydroperoxide, the essential initial step of the partial synthesis to artemisinin. The photooxygenation reactions were studied in a two-phase photo-flow reactor utilizing Taylor flow for enhanced mixing and fast gas-liquid mass transfer. A good agreement of the model and the experimental data was achieved for all combinations of photosensitizer concentration, photon flux, fluid velocity and both liquid and gas phase compositions. Deviations between simulated predictions and measurements for the amount of hydroperoxide formed are 7.1 % on average. Consequently, the identified and parameterized kinetic model is exploited to investigate different behaviors of the reactor under study. In a final step, the kinetic model is utilized to suggest attractive operating windows for future applications of the photooxygenation of DHAA exploiting reaction rates that are not affected by mass transfer limitations. Keywords Artemisinin · Singlet oxygen · Photooxygenation · Kinetic analysis · Taylor flow Introduction S. Triemer and M. Schulze have contributed equally. A. Seidel-Morgenstern Malaria causes around 230 million infections and more than seidel@mpi-magdeburg.mpg.de 400.000 deaths each year [1] – although it is preventable and S. Triemer treatable. Medications containing derivatives of artemisinin, triemer@mpi-magdeburg.mpg.de a secondary metabolite of the plant Artemisia annua,show high efficacy against the disease and cause only low side effects, making these treatments a key in this global effort. Max Planck Institute for Dynamics of Complex technical Systems, Sandtorstraße 1, 39106 Magdeburg, Germany Due to their high price, however, especially the people, who suffer most of the disease – the population in the Institute of Energy and Process Systems Engineering, Technische Universitat ¨ Braunschweig, Langer Kamp 19B, sub-Saharan region – do not have full access to artemisinin- 38106 Braunschweig, Germany based combination therapies (ACTs). Center of Pharmaceutical Engineering, Technische Universitat ¨ Until today, artemisinin is mainly produced by extraction Braunschweig, Franz-Liszt-Straße 35a, 38106 Braunschweig, of the plant A. annua [2]. As an alternative, semi-synthetic Germany processes for artemisinin production were developed [3, Institute of Chemical Engineering, Ulm University, 4] and applied in industrial scale [5, 6] starting from Albert-Einstein-Allee 11, 89081 Ulm, Germany fermentation with genetically engineered yeasts. The final Institute for Applied Materials - Electrochemical production step is the reaction from dihydroartemisinic acid Technologies, Karlsruhe Institute of Technology, (DHAA) to artemisinin. DHAA is a biological precursor Adenauerring 20b, 76131 Karlsruhe, Germany to artemisinin and obtained as major byproduct from the Lehrstuhl fur ¨ Chemische Verfahrenstechnik, extraction. By applying a similar reaction step as in the Otto-von-Guericke-Universitat, ¨ Universitatsplatz ¨ 2, 39106 Magdeburg, Germany semi-synthetic production, it can be utilized as an additional 642 J Flow Chem (2021) 11:641–659 Fig. 1 Partial synthesis of hν artemisinin starting from dihydroartemisinic acid: Illustration of mass transfer, photon transfer and reaction O O 2 2 kinetics H + hν H H + O + O H H H O O OH + OH HO H Dihydroartemisinic Artemisinin Terary acid (DHAA) hydroperoxide (PO ) source for artemisinin [7] increasing the yield of artemisinin all involved units [18]. To the best of our knowledge, a com- retrieved from the plant. prehensive model is not available for the artemisinin partial In both approaches the synthesis from DHAA to synthesis so far [19]. To be predictive, the model needs to artemisinin plays a crucial role. Thus, a good understanding describe the major characteristics and phenomena of the of the reaction mechanism and the main factors of influence process. However, multi-phase flow and photon emission in is of large interest. The partial synthesis starting from chemical reactors are 3D phenomena that can be described DHAA (Fig. 1) proceeds via an initial photooxygenation either based on first principles yielding complex models or forming a tertiary hydroperoxide as main intermediate [8, by reducing the complexity with simplifications limiting the 9]. In the presence of strong acids, this hydroperoxide model applicability [20–23]. (PO ) undergoes a Hock-cleavage, a second oxidation and The aim of this contribution is to provide a first quan- subsequent cyclization reactions forming artemisinin as titative model for the reaction kinetics of the photooxi- main product [10, 11]. The first step, the photooxygenation, dation of dihydroartemisinic acid to the intermediate ter- is initiated by formation of singlet oxygen in situ. tiary hydroperoxide PO . The model combines a detailed Photosensitization requiring light irradiation and a matching description of the reaction kinetics with mass and photon dye is widely applied at lab- and industrial-scale [5, 6, 12] transfer. Focus in the model development was to obtain a for this purpose due to its reduced need for reactants and model structure, which is reliable but at the same time as higher selectivity. To achieve a fast and selective conversion simple as possible, to allow for analysis of the production of DHAA to artemisinin, the reactor system and the reaction process, its limitation and model-based optimization. The conditions need to provide high mass transfer of oxygen, model was parameterized by steady-state experiments of the strong mixing and efficient irradiation within the reactor photooxygenation in a continuous photo-flow reactor. The volume. These requirements were met by applying small- ferrioxalate actinometer was utilized to quantify the inci- scaled reactor systems operated under slug flow conditions dent photon flux in the reactor – an essential quantity in the [13, 14] as displayed in Fig. 1. reaction kinetics of the photooxygenation. The challenging To obtain an optimal overall process of artemisinin pro- identification of the kinetic parameters was supported by an duction, the partial synthesis step needs to be designed iterative strategy applying model-based experimental design with respect to all upstream and downstream units. For this to ensure large parameter sensitivities and reduce the exper- task, model-based tools have been proven essential in aca- imental workload [24]. In the following, we first introduce demia and the pharmaceutical industry [15, 16] to facilitate the reaction mechanism and the experimental setup we used system understanding and control [17]. The description of to study the kinetics. We explain the mathematical tools and the process chain constitutes a highly complex mathemat- how they are combined based on the applied experimen- ical problem with multiple process variables, degrees of tal setting to yield a predictive model with reliable kinetic freedom and at the same time various constraints, e.g. on constants for the photooxidation of DHAA. To demonstrate product quality and process safety. For each unit within the the potential of the model, we use it in the end to derive process, a model is required, which predicts the units’ beha- promising experimental regimes for future lab and industrial viors well but is also simple to enable joint optimization of implementation of the photooxygenation. J Flow Chem (2021) 11:641–659 643 Fig. 2 Simplified reaction network of the photooxygenation of *DCA PO dihydroartemisinic acid OH (DHAA) to the desired h HO hydroperoxide PO –the key intermediate in the artemisinin DCA partial synthesis. 9,10-Dicynanoanthracene (DCA) serves as photosensitizer 2 PO in the in situ formation of singlet OH O OH HO oxygen Dihydroartemisinic acid (DHAA) PO O OH HO Reaction network of the photooxygenation H-shift matching an ene-type reaction mechanism known as of dihydroartemisinic acid Schenk-reaction [30]. In the range of the double bond, H- atoms in three different positions can be abstracted forming The photooxygenation of dihydroartemisinic acid (DHAA) three different hydroperoxides. Due to the cis-effect of the to hydroperoxides proceeds via two main reaction steps ene-type reaction, the tertiary hydroperoxide PO is the main product. PO is also the intermediate to artemisinin (Fig. 2): and so the desired product of the photooxygenation. 1. photosensitized formation of singlet oxygen and All formed hydroperoxides are semi-stable species which 2. ene-type reaction to an hydroperoxide. undergo several rearrangement and degradation reactions In photosensitization, a photoactive molecule, the photo- leading to total decomposition within several weeks [11]. sensitizer, absorbs light of a corresponding wavelength and transfers that energy to an oxygen molecule exciting it in its singlet state [12]. In this study we used 9,10- Kinetic steady-state experiments dicyanoanthracene (DCA), which is a widely applied photo- in a photo-flow reactor sensitizer due to its high efficiency, strong chemical stability and absorbance in the visible spectrum [25]. The photooxygenation of dihydroartemisinic acid (DHAA) After absorption of light in the blue region (400– requires efficient irradiation of the reactant solution and 500 nm) DCA is excited to a singlet state following a sufficient supply of oxygen to investigate the kinetics of complex network of different quenching processes [26, 27]. the reaction steps. Milli-scaled flow reactors in Taylor In the main pathway, singlet state DCA is quenched by flow mode offer high surface area between gas and liquid triplet oxygen forming one molecule of singlet oxygen. phase and efficient irradiation of the substrate due to the The residual triplet state allows the formation of another small channel depths. This makes this type of reactors molecule of singlet oxygen reducing DCA to its ground suitable to study the kinetics of photoreactions [31–33]. state. Parallel quenching processes, e.g. fluorescence or The experimental conditions including toluene as solvent, phosphorescence, lead to deactivation of DCA without 9,10-dicyanoanthracene (DCA) as photosensitizer and a forming singlet oxygen. Depending on the solvent, the temperature of -20 C were adapted from [14] due to the dissolved oxygen concentration and the presence of optimal yields for artemisinin observed in this study. To additional quenchers, the overall quantum yield of singlet exclude dynamics from the kinetic analysis, the reactor oxygen formation with DCA might vary significantly [27]. has to enter a steady-state before sampling or evaluating A maximum quantum yield of singlet oxygen is reported in online-measurement data. the range of 1.56–1.71 in benzene extrapolated to indefinite In the following, the applied reactor setup and the pro- oxygen concentration [27–29]. cedure of the photooxygenation experiments are introduced Once singlet oxygen is formed, it either reacts with briefly. For details on materials, the equipment and sample DHAA or it is quenched back to its triplet state. The reaction analysis, the interested reader is referred to the Supporting of DHAA with singlet oxygen proceeds via 1,5-sigmatropic Information (SI). LED 644 J Flow Chem (2021) 11:641–659 Continuous photo-flow reactor system experiments, the gas/liquid ratio was set to 4:1 (v/v) - equal to a gas holdup of β = 0.8. The total flow rate was varied The photooxygenation of DHAA was investigated in an in- between 1–2 ml/min at 7 bar absolute system pressure, house-made tubular reactor system, Fig. 3. The photoreactor ensuring Taylor flow conditions in all experiments. The consisted of wrapped transparent tubing (FEP, ID 0.8 mm) photoreactor was operated at -20 C, while all the up- and immersed in a cooling liquid connected to a thermostat. The downstream equipment was kept at room temperature. length of the photoreactor (2–10 m) was chosen according To ensure steady-state operation of the reactor system, to the residence time range of interest. Two LED modules one set of experimental conditions was kept for a duration emitting blue light (417 nm) irradiated the photoreactor of at least 5 times of the estimated residence time in the from both sides in all experiments. The irradiation intensity whole reactor before sampling the liquid effluent at the was set relative to the maximum emitted optical power end of the reaction line. The concentrations of DHAA and of the LED modules (21 W per module) by adjusting the the formed hydroperoxides were determined by quantitative current in the power supply. In the following we refer to this H-NMR. setting as LED power P . LED The liquid and the gas feed were dosed continuously by a syringe pump and mass flow controllers, respectively. Both Measurement of the provided photon flux feed streams were contacted in a T-mixer and then entered by chemical actinometry the photoreactor. After irradiation, the gas and liquid phase are split in a membrane phase separator. The residual gas The initial step of the photooxygenation of DHAA is the stream is measured with a flow meter. The liquid stream is light-induced formation of singlet oxygen, where photons collected and analyzed offline. The pressure in the reaction must be considered as stoichiometric reagent. Chemical line was controlled by two back-pressure regulators at the actinometry is a well-established tool to investigate the gas and the liquid side. incident photon flux in complex reactor geometries, where other methods as radiometry are not easily applicable [34]. Steady-state experiments for the photooxygenation It is an integral method yielding an average value of the of DHAA in Taylor flow conditions incident photon flux over the irradiation period. In this study, we used potassium ferrioxalate as acti- The feed solution consisting of DHAA and DCA dissolved nometer – also known as the Hatchard-Parker-Actinometer in toluene was connected to the reactor system and dosed [35] – to characterize the photon flux reaching the reac- together with a gas stream containing either pure oxygen or tor in our experimental setup. This actinometer is the most oxygen/nitrogen mixtures through the reactor system. In all established one [36] and used also for characterization of FC F N2 01 Residual gas FC Reactor O2 P T P coil 2 02 02 Product soluon Feed 7 bar Photoreactor 20°C -20°C Fig. 3 Continuous photo-flow reactor setup applied for the kinetic investigation of the photooxygenation of dihydroartemisinic acid. The liquid and gas feed are pumped at Taylor flow conditions through the reaction line (ID: 0.8 mm) kept at -20 C and irradiated by blue LED light (417 nm) LED J Flow Chem (2021) 11:641–659 645 Act flow reactors [37, 38] due to its wide range of absorption The quantum yield Φ and the Napierian absorption Act in the UV and visible spectrum, easy preparation and han- coefficient κ of ferrioxalate at irradiation wavelength 417 nm dling. As Roibu et al. [39] showed, the absorbed amount are given in the SI – together with details on the calculation of photons differs depending on the set flow conditions. of the actinometer conversion and the determination of the To mimic the radiation conditions in the photooxygena- incident photon flux. The relation of absorbed and incident tion experiments, all actinometric measurements shown in photon flux based on the Lambert-Beer law is introduced this study were performed in continuous mode in Tay- in the following section on model development for the lor flow conditions. The procedure of measurements with photooxygenation of DHAA. ferrioxalate and their analysis were adapted from Wriedt et al. [38]. Process model for the photooxygenation Experimental procedure of actinometric of dihydroartemisinic acid measurements The difficulty in obtaining reliable reaction kinetics for A 0.15M solution of ferrioxalate was prepared freshly the photooxygenation of dihydroartemisinic acid (DHAA) on the day of the experiment. The actinometer solution lies in the interaction of the chemical reaction network was pumped together with nitrogen as inert phase in slug with photon and mass transfer processes. Both phenomena flow pattern through the irradiated reactor at 7 bar system are complex to describe and depend strongly on the pressure. The gas holdup β was 0.8 in all experiments reactor system applied. Accordingly, the identified process – equal to the flow conditions in the photooxygenation model is assembled from two main parts. The kinetic experiments. The two-phase-flow was pumped through the model describes the (photo-induced) chemical reactions photoreactor resulting in a residence time of 6–12 s in the and is independent of the process setup. The reactor irradiated section (2 m length). After achieving stable flow model, instead, reproduces the fluid dynamics of the two- conditions for at least 5 min, 3 samples of the liquid effluent phase flow, including the interfacial transfer equations, stream were collected. and is dependent on the photo-flow reactor system used. Each sample was diluted 25-fold with 0.05M sulfuric Both components of the process model, that integrates acid before combining it with a buffer solution of 0.1% the kinetics into the reactor model, are introduced in phenanthroline solution in 0.05M sulfuric acid containing the following subsections. In the end, a short theoretical 0.06M sodium acetate. After 30 min the absorption of background on how we identified the process model and the sample was measured at 510 nm with a UV/Vis estimated and assessed its model parameters is outlined. spectrometer to determine the formed amount of Fe(II) The interested reader is referred to the Supporting oxalate and calculate the actinometer conversion. In Information (SI) for a more thorough motivation and addition, samples of the reactor effluent without irradiation derivation of the reactor model. Likewise, more details on were collected and processed likewise to the irradiated the strategy leading to the identified process model can be samples to determine actinometer conversion due to found in the SI. ambient light. Details on materials, sample workup and analysis are Kinetic rate equations for the photooxygenation given in the SI. The reaction scheme of the kinetic model is shown in Determination of the incident photon flux Fig. 2. The tertiary hydroperoxide PO is the species of interest, i.e., it is further converted to artemisinin. Act The conversion of ferrioxalate X in the linear region of The two secondary hydroperoxides PO and PO are 2 3 the actinometer only depends on the constant quantum yield lumped together to the byproduct species PO .Inthe Act Φ at the irradiation wavelength of 417 nm, the optical conducted photooxygenation experiments, the recovery of path length l and the volumetric incident photon flux L the measured products PO and PO make up around 95 % opt p 1 y during irradiation in the photoreactor with a residence time of the total amount of reacted DHAA. The missing 5 % τ . Following the procedure and the model introduced in are attributed to rearrangement and degradation products Wriedt et al. 2018 [38], L is obtained by solving Eq. 1 formed between sampling and NMR analysis (Section 6). To numerically, based on the known residence time and the cover these additional and presently chemically unidentified measured actinometer conversion, products and the respective reactions, an additional species PO is introduced, which is produced from PO and PO . x 1 y Act Act dX Φ Act Act Identical reaction rate constants are assumed. This approach 417 nm −κ [Act] (1−X )l 0 opt 417 nm = L 1 − e .(1) is motivated by the lack of data on species and reactions, as dτ [Act] 0 646 J Flow Chem (2021) 11:641–659 it allows to lump the unknown and unquantifiable reactions scope, or mechanistically motivated [42]. The mechanistic and side products. This approach may be replaced by a justification lies in the fact that “in a single photon more detailed mechanism once more is known on the absorption process, the rate of the photosensitizer activation side reactions. Alternatively, separate loss reactions might step (primary event) is proportional to the rate of energy lead to additional complications during the identification absorbed” [42]. The formation rate of singlet oxygen might of their reaction constants and would therefore make be expressed as a physical interpretation difficult. Hence, the chemical r = Φ L , (7) 1 1 O O p reaction network is 2 2 PO 1 with the local volumetric rate of photon absorption L and DHAA+ O −−→ PO , 2 1 the quantum yield of singlet oxygen Φ , i.e., the number k O PO y DHAA+ O −−→ PO , 2 y of singlet oxygen molecules formed divided by the number 1/τ of absorbed photons. 1 3 O −−→ O , 2 2 Different mechanistic networks for the formation of PO x PO −−→ PO , singlet oxygen by DCA in various solvents have been 1 x PO derived in literature [26, 27]. Here, we neglect implications PO −−→ PO , (2) y x on the quantum yield by extraneous species, e.g. solvent with kinetic rate constants k , i ∈{PO , PO , PO },and the quenching, as they are unknown and would encompass i 1 y x lifetime of singlet oxygen τ . The corresponding reaction the unfavorable situation that the quantum yield does not rates are expressed as elementary reactions [40], resulting in tend to zero with vanishing oxygen concentration [21, 26, the following rates of formation: 27]. The quantum yield of singlet oxygen can then be stated as r = k [DHAA][ O ], (3a) PO PO 2 1 1 1 [O ] r = k [DHAA][ O ], (3b) PO PO 2 y y Φ1 = , (8) k [O ]+ k l1 2 l2 r = k ([PO ]+[PO ]).(3c) PO PO 1 y x x where k and k are lumped kinetic parameters that l1 l2 Since singlet oxygen is a very reactive and short-lived combine diverse rate constants [27]. The concentration of species, the steady-state-assumption is applied, triplet oxygen concentration in Eq. 8 has been replaced by ! the concentration of dissolved oxygen as singlet oxygen d[ O ] 1 1 1 ∼ ∼ = 0 = r1 −(k +k )[DHAA][ O ]− [ O ], PO PO 2 2 O 1 y occurs merely in trace quantities [21, 33]. dz τ (4) Connecting the reaction kinetics to the rate of photon where r is the formation rate of singlet oxygen. O absorption Combining (3) with (4), yields The interaction between radiative transfer and reaction k [DH AA] PO r = r , (5a) PO kinetics is visualized in Fig. 4. The reaction rates in 1 O ˜ ˜ 1 + (k + k )[DH AA] PO PO Eqs. 6 and 7 depend on the local volumetric rate of k [DH AA] PO r = r1 , (5b) PO y O ˜ ˜ 1 + (k + k )[DH AA] PO PO 1 y r = k ([PO ]+[PO ]), (5c) PO PO 1 y x x with the kinetic constants normalized to the lifetime of singlet oxygen k = k τ ,i ∈{PO , PO }.(6) i i Δ 1 y The lifetime of singlet oxygen in toluene τ is 33.2 μsat- 20 , extrapolated from available data in the range from 5 to 90 [41]. Photosensitized formation of singlet oxygen Fig. 4 Interaction between radiative transfer and reaction kinetics; L : In photosensitized processes, expressions for reaction a local volumetric incident photon flux, L : local volumetric rate of rates are either empirically derived, thus having limited photon absorption, c: vector holding concentrations of present species J Flow Chem (2021) 11:641–659 647 Table 1 Summary of key assumptions applied to describe the reactor behavior The relative pressure drop over the reactor is small (0.1–0.5 bar at 7 bar operating pressure). Consequently, the momentum balance is neglected [51]. Due to the isothermal operation of the reactor, there are no internal temperature gradients. Thus, energy balances are not considered. The flow is one-dimensional (z axis). Hence, ideal mixing in radial direction is assumed [22, 52]. Diffusion is not considered. The operation of the setup is in steady-state. The liquid phase is incompressible. The density is calculated by a simple mixture density of the solvent plus the excess volume caused by the addition of DHAA. Material exchange between the phases is based on the linear approach to mass transfer. The gas phase can be described by an ideal gas mixture, i.e., the Taylor bubbles are well mixed. The dissolved oxygen concentration is derived from Henry’s law. photon absorption L that results from the radiative effect of a decreasing gas holdup due to reaction progress transfer equation (RTE). The L , in turn, depends on on the average path length [39] is neglected. The reaction the concentrations of the chemical species c. A common kinetics are therefore related to the averaged L ,which is assumption is that photons are predominantly absorbed constant over the whole reactor length. Accordingly, the by the photosensitizer, i.e. c = (c ) , leading actinometric measurements used to characterize the irradia- DCA to the substantial simplification that the RTE and the tion conditions in the reactor also provide an average value chemical kinetics are decoupled and can therefore be solved of the incident photon flux over the reactor length, see Eq. 1. independently. However, the L remains a complex function of position and time, that is highly dependent on the Reactor model individual reactor geometry, the physical properties of the participating media and the flow conditions [43]. The reactor model connects the intrinsic reaction rates with If nontransient light intensity is assumed, an averaged L the physical phenomena occurring within the reactor line, is derived from the Beer-Lambert law [44], namely the specific flow conditions and mass transfer. The key assumptions for the description of the reactor behavior L = L (1 − exp [−κc l ]), (9) p DCA opt are stated in Table 1. In a reliable reactor model, the gas with the the local volumetric incident photon flux L ,the p and liquid phase as well as the mass transfer between them Napierian absorption coefficient of the absorbing species need to be quantified. In the following, we first derive the κ , the photosensitizer concentration c , and the optical DCA balance equations for each phase separately based on the path length l . The concentration of DCA was assumed opt two-fluid model, and subsequently describe the interfacial to be constant throughout the whole reactor. Please note mass transfer between the gas and the liquid phase. that Eq. 9 does not explicitly include the irradiation from two sides as the here used reactor setup would suggest. Description of fluid dynamics with the two-fluid model Due to the symmetric configuration of the capillary reactor, however, the superposition of the light emission from two The core idea of the two-fluid model (indices g and l for sides is implicitly alleviated in L . In addition, an error gas and liquid phase, respectively) is to balance each phase resulting from this simplified description is balanced by individually and close their balances by interfacial transfer considering the optical path length as one of the parameters equations. A more detailed motivation for the two-fluid to be estimated, Eq. 21. model can be found in the SI, Section 5.1.2. The local volumetric incident photon flux L is defined p Resulting from the simplifications in Table 1,the as the absolute incident photon flux q related to the material balance of a species i in the liquid phase in terms irradiated volume of the reaction solution V : l of concentration c along the reactor coordinate z becomes L = . (10) V dc 1 1,i = O l i 2 = (r + δ j ), δ = , (11) i i O i In complex reactor geometries, the local rate of photon dz u 0, else absorption might differ significantly within the reactor vol- where u is the liquid phase velocity, r is the net rate ume altering the local reaction rates. In this study, L was l i of reaction and j is the transfer of oxygen from the assumed to be constant. The assumption of homogeneous O gas to the liquid phase. The species i is in the set illumination is commonly made in microreactor modelling, {DHAA, PO , PO , PO , O }. The delta function δ ensures resulting in good model-data fits [45]. This includes that the 1 y x 2 i 648 J Flow Chem (2021) 11:641–659 that the oxygen transfer is solely active in the balance for law (SI, Sec. 5.1.4) and is taken from literature [48]. dissolved oxygen. The mass transfer coefficient k a in Eq. 18 is affected For the gas phase, a material balance over oxygen and by several reactor-dependent and fluid properties, that are the total gas flow V is considered. The former in terms of summarized in a contribution from the Taylor bubble caps molar fraction x is and a contribution from the liquid film between reactor wall and Taylor bubble [49]. The contribution by the film dx RT =− (1 − α)Aj (1 − x ), (12) O O was observed to be dominant [49], leading to k a ∝ 2 2 dz pV D u /L /d with the diffusion coefficient of oxygen O UC 2 g and the material balance over the total gas flow reads D and the length of a unit cell L consisting of the gas O UC dV RT g bubble and the liquid slug [50]. For no information about =− (1 − α)Aj . (13) the geometry of the unit cell is readily available, we simply dz p consider a dependence of the mass transfer coefficient on In Eqs. 12 and 13, R is the universal gas constant, the superficial gas velocity: T temperature, p total pressure, and A the known cross- sectional area of the channel. The gas fraction α is a k a = k a u , (19) l l key characteristic of the two-fluid model, which assigns a relative area to any of the phases: introducing a constant k a. A A g l α = , 1 − α = , and A = A + A , (14) g l A A The process model: Combining the kinetics where A and A are the unspecified cross-sectional areas with the reactor model g l covered by the gas phase flow V and the liquid phase flow ˙ The integration of the chemical kinetics, Eq. 5,and themass V , respectively. The phase velocities can then be expressed transfer relation, Eq. 18, into the material balances (11), (12) as and (13) provides the governing equations of the process ˙ ˙ ˙ ˙ V V V V g g l l u = = ,u = = . (15) g l model for both the liquid and the gas phase: A αA A (1 − α)A g l 1 − A ˜ ˜ (k + k )[DH AA] To solve the material balances in Eqs. 11, 12 and 13,the d[DHAA] C0 [O ] PO PO 2 1 y = − dz k [O ]+ k ˜ ˜ V l1 2 l2 1 + (k + k )[DH AA] unknown gas fraction α must be determined. To this end, we l PO PO 1 y utilize an established simplification of the two-fluid model L (1 − exp [−κc l ]) , p DCA opt – the drift flux model [46, 47] (further details in SI, Sec. 5.1.3). Its constitutive equation relates α to the known gas 1 − A d[PO ] C [O ] k [DH AA] 1 0 2 PO holdup β , dz k [O ]+ k ˜ ˜ V l1 2 l2 1 + (k + k )[DH AA] l PO PO 1 y α = β, (16) L (1 − exp [−κc l ]) − k [PO ] , p DCA opt PO 1 with 1 − A ˜ d[PO ] k [DH AA] C [O ] PO y 0 2 y ˙ ˙ dz k [O ]+ k ˜ ˜ V l1 2 l2 1 + (k + k )[DH AA] V V l PO PO g g 1 y β = = . (17) ˙ ˙ ˙ V V + V g l L (1 − exp [−κc l ]) − k [PO ] , p DCA opt PO y The distribution factor C might be taken from literature or 1 − A d[PO ] C experimentally determined. In this study, C was estimated x 0 = k ([PO ]+[PO ]), PO 1 y dz by measurement of the residence time after tracer injection 1 − A ˜ ˜ (SI, Sec. 6.1). (k + k )[DH AA] d[O ] C [O ] PO PO 2 0 2 1 y = − dz k [O ]+ k ˜ ˜ V l1 2 l2 1 + (k + k )[DH AA] l PO PO 1 y Interfacial oxygen transfer s ∞ L (1 − exp [−κc l ]) + k a u ([O ] −[O ]) , p DCA opt l 2 2 Mass transfer of oxygen from the gas into the liquid phase dx RT β 2 ∞ =− 1 − A(1 − x )k a u ([O ] −[O ]), O l 2 2 2 g dz pV C is modeled according to g 0 dV g RT β ∞ ∞ =− 1 − Ak a u ([O ] −[O ]), (20) j = k a([O ] −[O ]), (18) l 2 2 O l 2 2 dz p C where [O ] is the saturation concentration of oxygen in with initial conditions the liquid phase and k a is the volumetric transfer coefficient ([DHAA], [PO ], [PO ], [PO ], [O ], [x ], [V ]) (0) 1 y x 2 O g based on the specific gas-liquid interfacial surface area = ([DHAA] , 0, 0, 0, [O ] , x , V ) . a. The saturation concentration is calculated by Henry’s 0 2 O ,0 g,0 2 J Flow Chem (2021) 11:641–659 649 The vector of unknown model parameters of the process influences. Subsequently, the reaction behaviour of the model, that needs to be identified, is photooxygenation is analyzed qualitatively on the basis of the experimental data. ˜ ˜ (k a, k ,k , k , k ,k ,l ) . (21) In the second part, the experimental data is used l l1 l2 PO PO PO opt 1 y x to identify the kinetic model parameters and assess Identification of the model parameters the suitability of the previously made assumptions. The parameterized model is finally applied to understand and by Model-based Design of Experiments identify the rate-determining effects in dependence on the reaction conditions offered. Identifying a reliable process model is a challenging problem, particularly in (bio-)chemical engineering where Quantification of the incident volumetric photon often reaction kinetics are not known apriori.Evenif flux L the stoichiometries have been established, the mathematical rate laws might not be readily revealed [40]. For the Relation between L and the set LED power identification of a reliable mathematical model, a systematic procedure is therefore key [53, 54]. One major tool in The actinometric measurements with ferrioxalate were this process is the model-based design of experiments (MBDoE). MBDoE facilitates model identification by performed in Taylor flow conditions as the later presented photooxygenation experiments. In Fig. 5a, the obtained planning experiments with high informative output under the consideration of the formulated model candidates, actinometer conversions are depicted. The experimental operation window of LED settings and residence time in thereby reducing development time and cost [55–57]. In the study case at hand, we primarily used MBDoE the irradiated section was limited to a narrow range of 6– 12 s and 10–25%LED by physical and technical constraints for the enhanced precision of parameter estimates. Here, [38]. Precipitation occurred in all samples obtained at LED MBDoE aims at minimizing the covariance matrix of the model parameters, a measure for the quantification of the settings higher than 25%LED. Therefore, these data were excluded from further analysis. The conversions obtained parametric uncertainties, by maximizing the parameter sen- sitivities on the measured outputs [58]. Having collected without precipitation show an expected linear dependence on the residence times. the measurement data of the optimally planned experiment, the parameters of the proposed model candidate(s) were Based on the obtained actinometer conversion and the known quantum yield of ferrioxalate, the volumetric estimated. Parameter estimation was performed using the maximum likelihood approach to obtain a match between incident photon flux (L ) was determined separately for each data point based on Eq. 1. The optical path length was model outputs and the experimental data. Next to an evalu- assumed to be equal to the channel diameter of 0.8 mm. The ation of the model-data fit, the model parameters and their average values for each LED setting are depicted in Fig. 5b. estimates were assessed by checking their identifiability The incident photon flux shows a strong linear depen- and by the calculation of confidence intervals. Identifiabil- dence on the LED power at lower set values. The measured ity of parameters ensures that the model parameters can incident photon fluxes deviate from that dependence due to be uniquely determined from the available measurement data [58, 59], and is therefore a necessity for a reliable the aforementioned observed precipitation during the exper- iment. The linear behavior is a known property of LEDs interpretation of parameter values. We used the profile like- lihood approach that yields improved confidence intervals and also given in the reference data-sheet of the LED mod- ules applied. Therefore, a linear relation is used to connect for the model parameters besides conclusions about param- eter identifiability [60, 61]. More information about the the volumetric incident photon flux with the LED power as additional model equation introducing L as proportionality MBDoE and the profile likelihood approach is outlined in factor, the SI. L = L · P . (22) p p LED Results and Discussion Relation between L and the unknown optical path length In the following first part, the experimental data is shown, which was later on used to parameterize the developed The determination of the incident photon flux from process model. Here, the actinometric measurements are actinometric measurements strongly depends on the value discussed, which yielded a relation for the incident set for the optical path length l , which either has to opt volumetric photon flux L – a key parameter in the model be estimated or measured to take partial absorption into to disentangle kinetic parameters from reactor-dependent account, Eq. 9. In our actinometric data set shown above, 650 J Flow Chem (2021) 11:641–659 Fig. 5 Results of actinometric measurements at two-phase slug flow conditions: a Actinometer conversion in dependence on set LED power P and residence LED time in the irradiated section of the photoreactor, b Volumetric incident photon absorption determined based on measured actinometer conversion (l = opt 0.8 mm) the path length was found to be insensitive. That is, for each The parameterized relation in Eq. 24 was used in the model path length assumed (e.g. 0.8 mm as shown above), values to link the knowledge from the actinometric measurements for the incident photon flux and the resulting proportionality with the photooxygenation experiments. factor L could be found, which fit the experimental actinometric data equally well. Qualitative assessment of the reaction behaviour The complex irradiation geometry of our applied reactor of the photooxygenation (Fig. 3), however, also makes it difficult to predict the path length from theoretical considerations due to The main goal of this contribution is to provide a kinetic the combination of a wide emission angle of the LED model for the photooxygenation of dihydroartemisinic acid modules, illumination from two sides, reflection within the to the desired intermediate hydroperoxide PO .Inthe photoreactor casing and Taylor flow conditions. following, a subset of the experimental data is shown to As an alternative, the optical path length can be set illustrate qualitative trends of the reaction behavior in Fig. 6. as an additional parameter to be estimated based on the Due to the applied model-based design of experiments, experimental data of the photooxygenation of DHAA. A the kinetics were studied selectively at conditions that relation between incident photon flux and path length is assured highest sensitivity of the kinetic parameters to be developed from the actinometric measurements and then estimated. That is why the experimental conditions of the used as additional model equation in the analysis of the datashowninFig. 6 change between the subplots. photooxygenation. Each data point is the result of a separate experiment in The absorbed and the incident volumetric photon flux steady-state. The experimental results are compared based are connected by Beer-Lambert law, as shown in Eq. 23. on the superficial residence time defined by the initial gas The relation contains two unknown parameters; L as the and liquid flow rates: proportionality factor between the the absorbed volumetric photon flux and the set LED power and [Act]. [Act] can be τ = . (25) ˙ ˙ V + V l g,0 interpreted as an average concentration of the ferrioxalate during irradiation. Both parameters were estimated by first The superficial residence time underestimates the real for various assumed lengths of the optical determining L residence time in the system: Due to O consumption, the path (as in Fig. 5 for 0.8 mm) from experimental data and gas flow rate decreases with the increasing conversion of then by fitting the exponential expression of Eq. 23 to these DHAA. Therefore, the real residence time does not only obtained values of L (details are given in SI): depend on the initial flow settings but also on the reaction progress. To compare the amount of unknown products a a formed in the photooxygenation, an additional quantity, the L L p p L = = P , (23) recovery, is introduced, which is defined as the ratio of p LED −κ [Act]l −κ [Act]l Act opt Act opt 1 − e 1 − e known components of the reaction mixture and the initially L added amount of DHAA: mol −5 8.893 · 10 [DHAA]+[PO ]+[PO ] 1 y L s %LED L = . (24) Recovery = · 100 %. (26) −1 −23.935 cm ·l opt [DHAA] 1 − e 0 J Flow Chem (2021) 11:641–659 651 The photooxygenation of DHAA is a fast reaction reaching full DHAA conversion in less than 5 min residence time in the irradiated section (Fig. 6a). The desired tertiary hydroperoxide PO reaches a yield of 85 %, while the secondary hydroperoxides are formed with a yield of 8 %. These obtained numbers are in accordance with previous studies, which observed a yield of PO up to 90 % [7, 14] under comparable conditions. The concentration-time- profiles agree in shape with the mixed zero and first reaction order, which was proposed in the model. The recovery of the reactant decreased from 100 % at short residence time to 92 % when full conversion was reached. We assume that this decrease is caused by rearrangement and degradation reactions of the formed hydroperoxides as observed in previous mechanistic studies by Brown et al. [8, 9, 11]. This non-detectable amount of formed products was treated as additional species PO in the model in order to close the overall mass balance. When the light intensity increases, the reaction acceler- ates without affecting the final yields (Fig. 6b). This is in correspondence with the proposed reaction network since the incident photon flux affects only the formation of sin- glet oxygen. The ratio of the reaction rates of PO and PO 1 x is constant and equal to the ratio of the corresponding rate constants k and k . The constant recovery in respect PO 1 POX to light intensity indicates that the consecutive rearrange- ment and degradation of PO and PO are independent of 1 x irradiation. Based on the model structure, the reaction rate is supposed to increase linearly with the incident photon flux. Doubling the LED power from 50% to 100%, however, results only in an 1.5 fold increase of the effective initial rate PO formation (from 0.174 mol/l/minto0.257 mol/l/min at τ = 0.55 min). That is, at the high irradiation intensities, the proposed linearity is not observed in our experimental data. The effect may result from oxygen mass transfer between gas and liquid phase, which is slower than the high reaction rates under strong irradiation and thus limit the overall observed reaction rate. In Fig. 6c, the photosensitizer concentration and gas phase composition was varied while the superficial resi- dence time was kept constant. Again both parameters only influence the reaction rate while the total recovery was unaffected. A 3-fold increase of the catalyst concentra- tion yielded a 2-fold increase in PO concentration formed. Assuming an optical path length equal to the channel diam- Fig. 6 Behavior of the photooxygenation of dihydroartemisinic acid eter of 0.8 mm, an approx. 3-fold rise in light absorption to the desired hydroperoxide PO at varied reaction conditions (incl. initial concentration of DHAA): a Concentration of DHAA, and, thus, in the reaction rate is expected according to Beer- the formed hydroperoxides and the observed reactant recovery in Lambert law. The lower increase observed in the experi- dependence on the superficial residence time b Dependence of PO ments might indicate that the light passes the reactor on formation on provided light intensity c Effect of varied photosensitizer a longer path length resulting in high absorption and thus concentration and gas phase composition at the inlet at constant lower sensitivity on the catalyst concentration. A decrease superficial residence time 652 J Flow Chem (2021) 11:641–659 in O content in the gas phase results in approx. 20% lower the involved parameters with the measurement information yield of PO at otherwise similar reaction conditions. Based at hand. A potential reduction of the correlation by MBDoE on this data, it cannot be concluded yet if that significant did not predict to significantly disentangle the strong con- decrease is caused by a lower O quantum yield or by nection between the parameters. One related problem lies slower mass transfer due to reduced equilibrium concentra- in the mathematical structure of the quantum yield rela- tion of oxygen in the liquid phase. For this conclusion, the tion. Its parameters are theoretically identifiable, but cannot quantitative analysis based on a parameterized and validated be determined properly if noisy data is utilized, i.e. differ- model of the photooxygenation is required. ent parameter sets can explain the outcome equally well [62]. Accordingly, parameter estimation runs showed that Identification of the process model parameters physically reasonable values of the quantum yield of singlet and quantitative assessment of the model-data fit oxygen, i.e., values below 2, could not be retrieved. Conse- quentially, the unknown quantum yield parameters were set The process model developed to describe the photooxy- to literature values, taken from [27] for DCA in benzene: genation behaviour contains seven unknown parameters to k = 0.641 and k = 0.0119 mol/L. l1 l2 be identified with experimental data, Eq. 21.Two of the Hence, five parameters to be estimated were left: The parameters, the mass transfer coefficient k a and the optical mass transfer coefficient k a, the three chemical kinetic l l ˜ ˜ path length l , are related to the applied reactor setup. The constants k , k and k , and the optical path opt PO PO PO 1 y x other five parameters are kinetic rate constants, which are length l . The results of the parameter estimation and opt of the subsequent quantitative assessment of the derived independent of the experimental setup. During the model identification process, a local sensi- model parameters and the model-data fit are summarized tivity analysis revealed (SI) that the kinetic parameters of in Table 2. The measurement error variance estimated 2 2 2 the chemical reactions forming the intermediate hydroper- from regression statistics (SI) σ ˆ = 2.73e-4 mol /L is ˜ ˜ oxides, k and k , are heavily correlated with the k satisfactorily low. Correspondingly, the relative deviation PO PO l1 1 y parameter of the quantum yield relation for singlet oxygen, between the predicted and measured concentration of the Eq. 8. Thus, it becomes impractical to uniquely determine key intermediate PO is 7.09 %. The good model-data fit is Table 2 Goodness of fit and estimated parameter values and spreads, Eq. 21, for the developed process model, Eqs. 20. The confidence intervals are based on the profile likelihood (SI) Model-data fit Symbol Unit Value Description 2 2 SSE mol /l 0.1799 sum of squared errors 2 2 2 σ ˆ mol /l 2.73e − 4 measurement error variance % 7.09 averaged relative deviation of PO Estimated parameters − + Symbol Unit Value COD CI CI 95 95 k a 1/cm min 1.094 0.093 1.046 1.148 −1 k Lmol 7.130 0.173 6.555 7.790 PO −1 k Lmol 0.644 0.306 0.550 0.747 PO k 1/min 0.0249 0.369 0.0204 0.0296 PO l cm 0.178 0.107 0.169 0.188 opt Fixed parameters (quantum yield, Eq. 8) Symbol Unit Value Reference k – 0.641 DCA in benzene [27] l1 −1 k mol l 0.0119 DCA in benzene [27] l2 −1 −1 κ 1mol cm 12841.98 see Supporting Information C – 1.02 see Supporting Information † n PO 1 data (y − y ) /y /n PO ,i PO ,i PO 1 1 1 i PO ,i + − ˆ ˆ COD: coefficient of dispersion, COD = (CI − CI )/θ , θ : estimated value 95 95 +/− CI : ±95% confidence interval 95 J Flow Chem (2021) 11:641–659 653 Fig. 7 Match of experimental data with simulated results based on the photoreactor of each data point. Triangle, diamond and square markers parametrized process model for all quantities measured at the reactor represent data from Fig. 6a. The dashed lines mark 20 % deviations outlet. The grey scale illustrates the superficial residence time in the visualized in the parity plots in Fig. 7 which show a good To further assess the quality of the identified model, match between experimental results and simulated data relative deviations of PO over four important process over the whole range of investigated superficial residence parameters, that is, the initial DHAA concentration, the times. Exemplarily, the data points appearing in Fig. 6a LED light power, the photosensitizer concentration, and the are marked in Figs. 7a, b and c accordingly. In contrast molar fraction of oxygen, were investigated (SI). The results to DHAA and PO , the key chemical species on the route suggest that the existent deviations are mainly caused by towards artemisinin, the data of PO is less matched because measurement noise and errors that inherently occur during for two reasons. On the one hand, the optimizer tends to the measurement procedure but not by systematic model favor higher concentrations per definition of the objective discrepancy. function, i.e., the likelihood function. On the other hand, the Following the profile likelihood approach, all five PO concentrations are closer to zero, where the signal-to- estimated parameters in the developed process model are noise ratio is increased. identifiable (SI). Next to a coefficient of dispersion (COD) 654 J Flow Chem (2021) 11:641–659 95 % confidence intervals (CI) for the estimated parameters and their estimates are in plausible ranges. The required are stated in Table 2. simplification on fluid dynamics and photon transfer, It can be noted that the chemical kinetic constants have namely the application of the two-fluid model and the larger CODs and are, loosely spoken, more uncertain in their neglect of absorption rate distribution, offers a good estimates than the mass transfer coefficient and the optical description of the observed process behavior. path length. On the whole, each of the parameters shows an Albeit, we want to emphasize that for a reliable acceptable spread suggesting that their expected values can utilization and interpretation of the identified process model be reliably used for further model-based investigation. the following aspects need to be taken into account. The rate constants for the formation of the desired Neglecting the distribution of the local volumetric rate of hydroperoxide PO and the byproducts were normed, Eq. 6, photon absorption is a strong simplification affecting the to ease the parameter estimation process. Based on the reaction system on various levels. In particular, a gradient known life time of singlet oxygen in toluene (33.2 μsat-20 in the absorbed photon flux will cause a non-uniform [41]) the absolute rate constants of the reactions of DHAA distribution of the rate of singlet oxygen production within with O to the hydroperoxides, Eq. 3, can be obtained: the liquid slug, resulting in a potential diffusion limitation of the overall reaction rate. The absorbed photon flux 5 −1 −1 k = 2.15 · 10 Lmol s , PO itself is influenced by the gas holdup and photosensitizer −1 5 −1 k = 0.19 · 10 Lmol s . PO concentration. Both quantities decrease with reaction time due to oxygen consumption and photobleaching and Both values are in the same order of magnitude as rate constants published for other investigated ene-type reactions therefore affect the absorbed photon flux. We also want to point to the fact that a reliable description of the two- [33, 63, 64]. The reaction to the desired hydroperoxide is phase flow is essential. A global sensitivity analysis of about 10-fold faster than the reaction to the byproducts. This important model parameters (details in SI) showed, that the matches with the favored selectivity of PO observed in the distribution parameter C , that links the relative motion of photooxygenation experiments. For Taylor flow fluid dynamics and mass transfer the different phases, Eq. 16, is highly sensitive. A variation of C in the model induces a considerable change in the in microchannels, there are various relations for the mass transfer coefficient available that vary substantially simulated PO concentration. Lastly, the identified model and all parameters are only valid for a temperature of - among each other [65]. In the study case at hand, initial superficial velocities between 120 cm/min and 350 cm/min 20 C. Studying the complex influence of temperature on the reaction system including the mass transfer and flow appear, resulting in volumetric mass transfer coefficients −1 −1 conditions is beyond the scope of this paper and a task for of approximately 12 min to 20 min . These values lie future studies. within the range of k a values predicted from correlations available in the literature [65]. Exploitation of the process model to analyse Intuitively, the length of the optical path l = 0.178 cm opt different operating regimes seems to be large at first sight as it is greater than twice the tube diameter of 0.08 cm. In a single circular tube The identified and fully-parameterized model can now be geometry with perpendicular irradiation, the optical path length can be assumed to be between channel diameter d used to understand the process behavior and identify opti- mal operation windows. In the following, three characteris- as upper boundary and the ratio A/d as lower boundary depending on the collimation of the incident light [66]. tic operating situations are illustrated that differ in the cause that limits or partially limits the process dynamics: light Both boundaries, however, are based on the hypothesis that light enters the tubing from one side and is lost after irradiance, substrate DHAA or mass transfer. The possible fourth operating regime – the kinetically controlled domain leaving it. In the considered photoreactor instead, two light without any other limitation – does not occur under the sources are installed in a closed box of stainless steel, investigated conditions. resulting in reflection of the light beam back to the reactor. In Figs. 8 and 9, the dynamic behavior of the system’s Furthermore, as the reactor itself is symmetric (compare key quantities, product concentrations, gas flow rate and with Fig. 3), leaving light beams on one side can re-enter gas phase composition are drawn over the reactor length. the reactor tubing on the other side. In particular in the tube convolutions around the poles in the reactor box, optical The thin vertical line marks the exit of the photoreactor and thus the end of light irradiance. The discontinuities in path lengths significantly exceeding twice the tube diameter are very plausible. the curves at the reactor exit are induced by a temperature jump from reactor to ambient temperature. Experimental In conclusion, the model developed to describe the photooxygenation of DHAA provides a good fit with the data are plotted at the sampling position downstream to the photoreactor exit. experimental data. All model parameters are identifiable J Flow Chem (2021) 11:641–659 655 rates are large in the beginning, see Fig. 8a, but is recovered with decreasing reaction rate values. Obviously, mass transfer does not substantially hinder the process dynamics. In contrast, both the light-limiting and the substrate-limiting regime can be observed in Fig. 8a. Here, a pseudo-inflection point might be determined that describes the transition bet- ween the two regimes that are often observed in photoredox catalysis [21]. At the inflection point, the reaction switches from a pseudo-zero-order reaction with the reaction rate at its maximum to a first-order reaction. Mathematically, the inflection point is defined as the half-maximum kinetic reaction rate. Accordingly, with = r = r + r , PO PO PO 1 y Eq. 5, the light-limiting regime is controlled by a max ˜ ˜ (k + k )[DHAA] 1 : r = Φ L = r , PO PO PO 1 y O p PO (27) and the substrate-limited regime by ˜ ˜ ˜ ˜ (k + k )[DHAA] 1 : r = Φ1 L (k + k )[DHAA]. PO PO PO PO PO 1 y O p 1 y (28) In this study, the inflection point is therefore at [DHAA]≈ 0.129 mol/L. In the DHAA graph in Fig. 8a this inflection point is passed shortly beyond the intersection between the DHAA and the PO curve. To the left of it, it follows zero- order kinetics, and to the right of the inflection point, it approaches first order kinetics. A complementary process characteristic is shown in Fig. 9. In this case, the gas phase consists of both oxygen and nitrogen; see the molar concentration of oxygen in Fig. 9b. From the curve of dissolved oxygen in Fig. 9b, it readily can be observed that the system quickly runs into Fig. 8 Propagation of concentrations, oxygen molar fraction and gas mass transfer limitations. The level of dissolved oxygen flow along the reactor coordinate showing no mass transfer limitations −1 −1 settles down to an equilibrium stage that continuously (conditions: [DHAA] =0.23moll , [DCA]= 0.85 mmol l , P = 100%LED, x = 1). The thin vertical line marks the reactor decreases as the molar fraction of oxygen in the gas phase LED O ,0 outlet drops and therefore correspondingly the solubility limit of oxygen that is determined by Henry’s law. Note that despite the elevated temperature beyond the photoreactor, In the first case example, the gas phase consists solely of the dissolved oxygen concentration does not reach again oxygen, as can be observed in Fig. 8b. The volumetric gas the initial dissolved oxygen concentration because of the flow decreases along the reaction line in the photoreactor decreased molar fraction of oxygen. Along the whole since oxygen is consumed in the liquid phase due to the reactor line, the process runs above the inflection point, i.e. chemical reactions and continuously supplied from the gas above [DHAA]≈ 0.129 mol/L, see Fig. 9a. This implicates phase, Fig. 8b. The negative slope of the PO concentration that the DHAA curve in the same figure follows pseudo- curve after reaching its maximum concentration, Fig. 8a, zero-order kinetics. The additional bending of the actual is owed to the consecutive loss reactions, Eq. 2,thatalso straight line is caused by the low availability of oxygen in continue to go on downstream of the reactor in contrast the liquid phase that affects the quantum yield of singlet to the photo-induced reactions. The further discontinuity oxygen, Eq. 8, and reduces the maximum reaction rate, downstream leading to an even higher negative slope is Eq. 27. Thus, here, the process is partially limited by mass caused by a slow down of the reaction medium due to a transfer, i.e. the mass transfer rate is approximately equal diameter jump of the tubing. Noteworthy is the behaviour to the rate of the bulk kinetics, preventing a more efficient of the dissolved oxygen in Fig. 8b. The dissolved oxygen is conversion of DHAA. rapidly consumed at the inlet of the photoreactor as reaction 656 J Flow Chem (2021) 11:641–659 Fig. 10 Prediction of mass transfer limited regimes for the photooxy- genation of DHAA. The Hatta number is given in dependence on the provided volumetric rate of photon absorption L and the mass transfer −1 coefficent for different O concentrations (contour lines, in mol L ) −1 and for DHAA = 0.5 mol L . The grey rectangle approximately covers the experimental space explored in this article which causes the chemical reaction to take place only at the phase boundary. Critical Hatta values are Ha ≥ 3, strong mass transfer limitation, Ha ≤ 0.3, kinetic regime, no limitation by mass transfer. In the study case at hand, the Hatta number [68] is defined as (SI) ˜ ˜ (k + k )[DHAA] 1 1 PO PO 1 y Ha = D L . 2 p ˜ ˜ k k [O ]+ k l l1 2 l2 1 + (k + k )[DHAA] PO PO 1 y (29) The diffusion coefficient of oxygen in toluene may be taken 2 −1 ◦ Fig. 9 Propagation of concentrations, oxygen molar fraction and gas from [69] and has a value of 2.4860e − 09 m s at −20 C. flow along the reactor coordinate showing mass transfer limitations The limits of the Hatta regimes are drawn as contours in −1 −1 (conditions: [DHAA] =0.48moll , [DCA]= 0.60 mmol l , Fig. 10. P = 100%LED, x = 0.51). The thin vertical line marks the LED O ,0 Generally speaking, with decreasing DHAA concentra- reactor outlet tions all contour lines move towards the ordinate. As obser- ved in the previous section, the conducted experiments, visua- lized as the grey rectangle, lie around the lower Hatta limit where behaviors from dynamics partially limited by mass Identification of mass transfer limited regimes transfer to dynamics not limited by mass transfer appear. for the photooxygenation of dihydroartemisinic acid The analysis for the process behavior so far was linked to Conclusion the applied reactor setup. The identified kinetic constants for the photooxygenation can also be used to predict suitable In this study we provide a mechanistic kinetic model operation regimes for other process settings to prevent that for the photooxygenation of dihydroartemisinic acid – the mass transfer of oxygen limits the overall reaction rate. Such important initial step in the partial synthesis to artemisinin. a classification can be stated with the Hatta number. Based The experimental study on the reaction kinetics was on the two-film theory, the Hatta number relates the rate conducted in a continuous flow photoreactor utilizing of chemical reaction in the liquid phase to the diffusion Taylor flow. The reaction kinetics are combined with a rate across the phase boundary [67]. The higher the Hatta simplified process model taking photon and mass transfer number, the faster is the reaction in comparison to diffusion, into account. To characterize the light input of the reactor, J Flow Chem (2021) 11:641–659 657 the photooxygenation experiments were complemented by article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not actinometric measurements yielding a relation between the included in the article’s Creative Commons licence and your intended incident photon flux and the unknown optical path length, use is not permitted by statutory regulation or exceeds the permitted which was integrated in the process model. use, you will need to obtain permission directly from the copyright The model achieves a good fit between the model outputs holder. To view a copy of this licence, visit http://creativecommons. org/licenses/by/4.0/. and the experimental results from steady-state experiments for a wide range of different critical process parameters. Therefore, the made assumptions and the simplifications, including the two-fluid-model provide a suitable description References for the main process characteristics. Nevertheless, assuming a spatially independent rate of photon absorption within 1. World malaria report 2020 (2020) 20 years of global progress and the reactor is a strong simplification of the reaction system challenges. Tech. rep., World Health Organization, Geneva 2. Lapkin AA, Plucinski PK, Cutler M (2006) Comparative applied, considering its geometrical complexity and the assessment of technologies for extraction of artemisinin. J Nat large value obtained for the average path length. Thus, Prod 69(11):1653–1664. https://doi.org/10.1021/np060375j extending the model by more detailed descriptions of the 3. Paddon CJ, Westfall PJ, Pitera DJ, Benjamin K, Fisher K, McPhee photon transport inside the reactor as well as of the fluid D, Leavell MD, Tai A, Main A, Eng D, Polichuk DR, Teoh KH, Reed DW, Treynor T, Lenihan J, Jiang H, Fleck M, Bajad S, Dang dynamics might improve the predictability of the model. G, Dengrove D, Diola D, Dorin G, Ellens KW, Fickes S, Galazzo By analyzing the process behavior, different regimes J, Gaucher SP, Geistlinger T, Henry R, Hepp M, Horning T, Iqbal of operation were identified where the process is limited T, Kizer L, Lieu B, Melis D, Moss N, Regentin R, Secrest S, by either absorbed photon flux, substrate concentration or Tsuruta H, Vazquez R, Westblade LF, Xu L, Yu M, Zhang Y, Zhao L, Lievense J, Covello PS, Keasling JD, Reiling KK, Renninger mass transfer. Due to is potential to describe the main NS, Newman JD (2013) High-level semi-synthetic production of photooxygenation characteristics, the developed model is the potent antimalarial artemisinin. Nature 496(7446):528–532. seen as an essential building block for future investigations https://doi.org/10.1038/nature12051 on the partial synthesis of arteminsinin. It provides a good 4. Ro DK, Paradise EM, Ouellet M, Fisher KJ, Newman KL, Ndungu JM, Ho KA, Eachus RA, Ham TS, Kirby J, Chang MCY, Withers starting point for kinetic studies of the subsequent acid- ST, Shiba Y, Sarpong R, Keasling JD (2006) Production of the catalyzed reaction sequence finally yielding artemisinin. antimalarial drug precursor artemisinic acid in engineered yeast. The model can be used also as a valuable building block Nature 440(7086):940–943. https://doi.org/10.1038/nature04640 in optimizing the whole process chain from extraction or 5. Turconi J, Griolet F, Guevel R, Oddon G, Villa R, Geatti A, Hvala M, Rossen K, Goller ¨ R, Burgard A (2014) Semisynthetic fermentation to artemisinin purification in the end. artemisinin, the chemical path to industrial production. Org Pro- Supplementary Information The online version contains supplemen- cess Res Dev 18(3):417–422. https://doi.org/10.1021/op4003196 tary material available at https://doi.org/10.1007/s41981-021-00181-2. 6. Burgard A, Gieshoff T, Peschl A, Horstermann ¨ D, Keleschovsky C, Villa R, Michelis S, Feth MP (2016) Optimisation of the photo- Acknowledgements We gratefully acknowledge the support by the chemical oxidation step in the industrial synthesis of artemisinin. Max Planck Society and the Center of Pharmaceutical Engineering Chem Eng J 294:83–96. https://doi.org/10.1016/j.cej.2016.02.085 (PVZ), Braunschweig. S.T. and M.S. are also grateful to the 7. Triemer S, Gilmore K, Vu GT, Seeberger PH, Seidel-Morgenstern International Max Planck Research School “Advanced Methods in A (2018) Literally green chemical synthesis of artemisinin Process and Systems Engineering” (IMPRS ProEng). B.W. and D.Z. from plant extracts. Angew Chem Int Ed 57(19):5525–5528. gratefully acknowledge the financial support provided by the German https://doi.org/10.1002/anie.201801424 Research Foundation (ZI 1502/4-1). We would like to thank Karyna 8. Sy LK, Brown GD, Haynes R (1998) A novel endoperoxide and Oliynyk for performing the actinometric measurements. We are also related sesquiterpenes from Artemisia annua which are possibly grateful to the Otto-von-Guericke University and especially Dr. Liane derived from allylic hydroperoxides. Tetrahedron 54(17):4345– Hilfert and Sabine Hentschel for performing the NMR analysis of the 4356. https://doi.org/10.1016/S0040-4020(98)00148-3 reaction samples. 9. Sy LK, Ngo KS, Brown GD (1999) Biomimetic syn- thesis of arteannuin h and the 3,2-rearrangement of Funding Open Access funding enabled and organized by Projekt allylic hydroperoxides. Tetrahedron 55(52):15127–15140. DEAL. https://doi.org/10.1016/S0040-4020(99)00987-4 10. Roth RJ, Acton N (1989) A simple conversion of artemisinic acid into artemisinin. J Nat Prod 52(5):1183–1185. Declarations https://doi.org/10.1021/np50065a050 11. Sy LK, Brown GD (2002) The mechanism of the spontaneous Conflict of Interests The authors declare that they have no conflict of autoxidation of dihydroartemisinic acid. Tetrahedron 58(5):897– interest. 908. https://doi.org/10.1016/S0040-4020(01)01193-0 Open Access This article is licensed under a Creative Commons 12. DeRosa M (2002) Photosensitized singlet oxygen and Attribution 4.0 International License, which permits use, sharing, its applications. Coord Chem Rev 233-234:351–371. adaptation, distribution and reproduction in any medium or format, as https://doi.org/10.1016/S0010-8545(02)00034-6 long as you give appropriate credit to the original author(s) and the 13. Lev ´ esque F, Seeberger PH (2012) Continuous-flow synthesis source, provide a link to the Creative Commons licence, and indicate of the anti-malaria drug artemisinin. Angew Chem Int Ed if changes were made. The images or other third party material in this 51(7):1706–1709. https://doi.org/10.1002/anie.201107446 658 J Flow Chem (2021) 11:641–659 14. Kopetzki D, Lev ´ esque F, Seeberger PH (2013) A continuous-flow 32. Aillet T, Loubiere ` K, Dechy-Cabaret O, Prat L (2016) process for the synthesis of artemisinin. Chem Eur J 19(17):5450– Microreactors as a tool for acquiring kinetic data on pho- 5456. https://doi.org/10.1002/chem.201204558 tochemical reactions. Chem Eng Technol 39(1):115–122. 15. Klatt KU, Marquardt W (2009) Perspectives for pro- https://doi.org/10.1002/ceat.201500163 cess systems engineering—Personal views from academia 33. Loponov KN, Lopes J, Barlog M, Astrova EV, Malkov AV, and industry. Comput Chem Eng 33(3):536–550. Lapkin AA (2014) Optimization of a scalable photochemical https://doi.org/10.1016/j.compchemeng.2008.09.002 reactor for reactions with singlet oxygen. Org Process Res Dev 16. Kroll P, Hofer A, Ulonska S, Kager J, Herwig C 18(11):1443–1454. https://doi.org/10.1021/op500181z (2017) Model-based methods in the biopharmaceuti- 34. Wriedt B, Ziegenbalg D (2020) Common pitfalls in cal process lifecycle. Pharm Res 34(12):2596–2613. chemical actinometry. J Flow Chem 10(1):295–306. https://doi.org/10.1007/s11095-017-2308-y https://doi.org/10.1007/s41981-019-00072-7 17. Schenkendorf R, Gerogiorgis D, Mansouri S, Gernaey K (2020) 35. Hatchard CG, Parker CA (1956) A new sensitive chemical Model-based tools for pharmaceutical manufacturing processes. actinometer - II. Potassium ferrioxalate as a standard chemical Processes 8(1):49. https://doi.org/10.3390/pr8010049 actinometer. Proc R Soc Lond A Math Phys Sci 235(1203):518– 18. Smith R (2014) Chemical process: design and integration, 1st edn., 536. https://doi.org/10.1098/rspa.1956.0102 Wiley, Hoboken 36. Kuhn HJ, Braslavsky SE, Schmidt R (2004) Chemical actinometry 19. Zhang XW, Zhao X, Liu KH, Sub HM (2020) Kinet- (IUPAC Technical Report). Pure Appl Chem 76(12):2105–2146. ics study on reaction between dihydroartemisinic acid and https://doi.org/10.1351/pac200476122105 singlet oxygen: An essential step to photochemical syn- 37. Aillet T, Loubiere K, Dechy-Cabaret O, Prat L (2014) Accurate thesis of artemisinin. Chin J Chem Phys 33(2):145–150. measurement of the photon flux received inside two continuous https://doi.org/10.1063/1674-0068/cjcp2002021 flow microphotoreactors by actinometry. Int J Chem React Eng 20. Cassano AE, Martin CA, Brandi RJ, Alfano OM (1995) Photore- 12(1):257–269. https://doi.org/10.1515/ijcre-2013-0121 actor analysis and design: fundamentals and applications. Ind Eng 38. Wriedt B, Kowalczyk D, Ziegenbalg D (2018) Exper- Chem Res 34(7):2155–2201. https://doi.org/10.1021/ie00046a001 imental determination of photon fluxes in multilayer 21. Bloh JZ (2019) A holistic approach to model the kinet- capillary photoreactors. ChemPhotoChem 2(10):913–921. ics of photocatalytic reactions. Front Chem 7:128. https://doi.org/10.1002/cptc.201800106 https://doi.org/10.3389/fchem.2019.00128 39. Roibu A, Van Gerven T, Kuhn S (2020) Photon transport 22. Angeli P, Gavriilidis A (2008) Hydrodynamics of Taylor flow in and hydrodynamics in gas-liquid flows. Part 1: Characterization small channels: A review. Proc Inst Mech Eng C J Mech Eng Sci of Taylor Flow in a Photo Microreactor. ChemPhotoChem p 222(5):737–751. https://doi.org/10.1243/09544062JMES776 cptc.202000065. https://doi.org/10.1002/cptc.202000065 23. Gupta R, Fletcher D, Haynes B (2009) On the CFD modelling of 40. Levenspiel O (1999) Chemical reaction engineering, 3rd edn. Taylor flow in microchannels. Chem Eng Sci 64(12):2941–2950. Wiley, New York https://doi.org/10.1016/j.ces.2009.03.018 41. Bregnhøj M, Westberg M, Jensen F, Ogilby PR (2016) Solvent- 24. Schenkendorf R, Xie X, Rehbein M, Scholl S, Krewer U dependent singlet oxygen lifetimes: Temperature effects implicate (2018) The impact of global sensitivities and design measures tunneling and charge-transfer interactions. Phys Chem Chem Phys in model-based optimal experimental design. Processes 6(4):27. 18(33):22946–22961. https://doi.org/10.1039/C6CP01635A https://doi.org/10.3390/pr6040027 42. Munoz-Batista ˜ MJ, Ballari MM, Kubacka A, Alfano OM, 25. Olea AF, Worrall DR, Wilkinson F, Williams SL, Abdel-Shafi Fernandez-Garc ´ ´ ıa M (2019) Braiding kinetics and spectroscopy AA (2002) Solvent effects on the photophysical properties of in photo-catalysis: The spectro-kinetic approach. Chem Soc Rev 9,10-dicyanoanthracene. Phys Chem Chem Phys 4(2):161–167. 48(2):637–682. https://doi.org/10.1039/C8CS00108A https://doi.org/10.1039/b104806f 43. Modest MF (2013) Radiative heat transfer, 3rd edn. Academic 26. Araki Y, Dobrowolski DC, Goyne TE, Hanson DC, Jiang Press, New York ZQ, Lee KJ, Foote CS (1984) Chemistry of singlet oxy- 44. Parnis JM, Oldham KB (2013) Beyond the Beer–Lambert gen. 47. 9,10-Dicyanoanthracene-sensitized photooxygenation of law: The dependence of absorbance on time in photo- alkyl-substituted olefins. J Am Chem Soc 106(16):4570–4575. chemistry. J Photochem Photobiol A Chem 267:6–10. https://doi.org/10.1021/ja00328a045 https://doi.org/10.1016/j.jphotochem.2013.06.006 27. Kanner RC, Foote CS (1992) Singlet oxygen production from 45. Meir G, Leblebici ME, Fransen S, Kuhn S, Van Gerven T singlet and triplet states of 9,10-dicyanoanthracene. J Am Chem (2020) Principles of co-axial illumination for photochemical Soc 114(2):678–681. https://doi.org/10.1021/ja00028a040 reactions: Part 1. Model development. J Adv Manuf Process 2(2). 28. Dobrowolski DC, Ogilby PR, Foote CS (1983) Chemistry https://doi.org/10.1002/amp2.10044 of singlet oxygen. 39. 9,10-Dicyanoanthracene,-sensitized for- 46. Nicklin D (1962) Two-phase bubble flow. Chem Eng Sci mation of singlet oxygen. J Phys Chem 87(13):2261–2263. 17(9):693–702. https://doi.org/10.1016/0009-2509(62)85027-1 https://doi.org/10.1021/j100236a001 47. Zuber N, Findlay JA (1965) Average volumetric concentration 29. Scurlock RD, Ogilby PR (1993) Production of singlet oxygen in two-phase flow systems. J Heat Transf 87(4):453–468. (1 g O2) by 9,10-dicyanoanthracene and acridine: Quantum https://doi.org/10.1115/1.3689137 yields in acetonitrile. J Photochem Photobiol A Chem 72(1):1–7. 48. Wu X, Deng Z, Yan J, Zhang Z, Zhang F, Zhang Z (2014) https://doi.org/10.1016/1010-6030(93)85077-L Experimental Investigation on the Solubility of Oxygen in 30. Breitmaier E, Jung G (2012) Organische Chemie: Grundlagen, Toluene and Acetic Acid. Ind Eng Chem Res 53(23):9932–9937. Verbindungsklassen, Reaktionen, Konzepte, Molekulstruktur, ¨ https://doi.org/10.1021/ie5014772 Naturstoffe, Syntheseplanung, Nachhaltigkeit, 7th edn. Georg 49. van Baten J, Krishna R (2004) CFD simulations of mass transfer Thieme Verlag, Stuttgart from Taylor bubbles rising in circular capillaries. Chem Eng Sci 31. Su Y, Hessel V, Noel ¨ T (2015) A compact pho- 59(12):2535–2545. https://doi.org/10.1016/j.ces.2004.03.010 tomicroreactor design for kinetic studies of gas-liquid 50. Vandu C, Liu H, Krishna R (2005) Mass transfer from Taylor photocatalytic transformations. AIChE J 61(7):2215–2227. bubbles rising in single capillaries. Chem Eng Sci 60(22):6430– https://doi.org/10.1002/aic.14813 6437. https://doi.org/10.1016/j.ces.2005.01.037 J Flow Chem (2021) 11:641–659 659 51. Kreutzer MT, Kapteijn F, Moulijn JA (2005) Fast gas– liquid– 61. Rooney WC, Biegler LT (2001) Design for model parame- solid reactions in monoliths: A case study of nitro-aromatic ter uncertainty using nonlinear confidence regions. AIChE J hydrogenation. Catal Today 8 47(8):1794–1804. https://doi.org/10.1002/aic.690470811 52. Gupta R, Fletcher D, Haynes B (2010) Taylor flow 62. Holmberg A (1982) On the practical identifiability in microchannels: a review of experimental and com- of microbial growth models incorporating Michaelis- putational work. J Comput Multiph Flows 2(1):1–31. Menten type nonlinearities. Math Biosci 62(1):23–43. https://doi.org/10.1260/1757-482X.2.1.1 https://doi.org/10.1016/0025-5564(82)90061-X 53. Franceschini G, Macchietto S (2008) Model-based design of 63. Griesbeck AG, Adam W, Bartoschek A, El-Idreesy TT (2003) experiments for parameter precision: State of the art. Chem Eng Photooxygenation of allylic alcohols: Kinetic comparison of Sci 63(19):4846–4872. https://doi.org/10.1016/j.ces.2007.11.034 unfunctionalized alkenes with prenol-type allylic alcohols, 54. Gernaey KV, Gani R (2010) A model-based systems approach to ethers and acetates. Photochem Photobiol Sci 2(8):877–881. pharmaceutical product-process design and analysis. Chem Eng https://doi.org/10.1039/B302255B Sci 65(21):5757–5769. https://doi.org/10.1016/j.ces.2010.05.003 64. Zhang W, Hibiki T, Mishima K (2010) Correlations of two-phase 55. Flassig RJ, Sundmacher K (2012) Optimal design of frictional pressure drop and void fraction in mini-channel. Int J stimulus experiments for robust discrimination of biochem- Heat Mass Transf 13 ical reaction networks. Bioinformatics 28(23):3089–3096. 65. Haase S, Murzin DY, Salmi T (2016) Review on hydrody- https://doi.org/10.1093/bioinformatics/bts585 namics and mass transfer in minichannel wall reactors with 56. Galvanin F, Ballan CC, Barolo M, Bezzo F (2013) A gen- gas–liquid Taylor flow. Chem Eng Res Des 113:304–329. eral model-based design of experiments approach to achieve https://doi.org/10.1016/j.cherd.2016.06.017 practical identifiability of pharmacokinetic and pharmacody- 66. Roibu A, Fransen S, Leblebici ME, Meir G, Van Ger- namic models. J Pharmacokinet Pharmacodyn 40(4):451–467. ven T, Kuhn S (2018) An accessible visible-light acti- https://doi.org/10.1007/s10928-013-9321-5 nometer for the determination of photon flux and optical 57. Abt V, Barz T, Cruz-Bournazou MN, Herwig C, Kroll P, Moller ¨ J, pathlength in flow photo microreactors. Sci Rep 8(1):5421. Portner ¨ R, Schenkendorf R (2018) Model-based tools for optimal https://doi.org/10.1038/s41598-018-23735-2 experiments in bioprocess engineering. Curr Opin Chem Biol 67. Bourne JR (2003) Mixing and the selectivity of chem- 22:244–252. https://doi.org/10.1016/j.coche.2018.11.007 ical reactions. Org Process Res Dev 7(4):471–508. 58. Walter E, Pronzato L (1997) Identification of parametric models https://doi.org/10.1021/op020074q from experimental data. Communications and control engineering. 68. Su Y, Straathof NJW, Hessel V, Noel ¨ T (2014) Photochemical Springer, London transformations accelerated in continuous-flow reactors: basic 59. Janzen ´ DLI, Bergenholm L, Jirstrand M, Parkinson J, Yates concepts and applications. Chem Eur J 20(34):10562–10589. J, Evans ND, Chappell MJ (2016) Parameter identifiability https://doi.org/10.1002/chem.201400283 of fundamental pharmacodynamic models. Front Physiol 7. 69. Schumpe A, Luehring P (1990) Oxygen diffusivities in https://doi.org/10.3389/fphys.2016.00590 organic liquids at 293.2 K. J Chem Eng Data 35(1):24–25. 60. Raue A, Kreutz C, Maiwald T, Bachmann J, Schilling M, https://doi.org/10.1021/je00059a007 Klingmuller ¨ U, Timmer J (2009) Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics 25(15):1923– Publisher’s note Springer Nature remains neutral with regard to 1929. https://doi.org/10.1093/bioinformatics/btp358 jurisdictional claims in published maps and institutional affiliations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Flow Chemistry Springer Journals

Kinetic analysis of the partial synthesis of artemisinin: Photooxygenation to the intermediate hydroperoxide

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Abstract

The price of the currently best available antimalarial treatment is driven in large part by the limited availability of its base drug compound artemisinin. One approach to reduce the artemisinin cost is to efficiently integrate the partial synthesis of artemisinin starting from its biological precursor dihydroartemisinic acid (DHAA) into the production process. The optimal design of such an integrated process is a complex task that is easier to solve through simulations studies and process modelling. In this article, we present a quantitative kinetic model for the photooxygenation of DHAA to an hydroperoxide, the essential initial step of the partial synthesis to artemisinin. The photooxygenation reactions were studied in a two-phase photo-flow reactor utilizing Taylor flow for enhanced mixing and fast gas-liquid mass transfer. A good agreement of the model and the experimental data was achieved for all combinations of photosensitizer concentration, photon flux, fluid velocity and both liquid and gas phase compositions. Deviations between simulated predictions and measurements for the amount of hydroperoxide formed are 7.1 % on average. Consequently, the identified and parameterized kinetic model is exploited to investigate different behaviors of the reactor under study. In a final step, the kinetic model is utilized to suggest attractive operating windows for future applications of the photooxygenation of DHAA exploiting reaction rates that are not affected by mass transfer limitations. Keywords Artemisinin · Singlet oxygen · Photooxygenation · Kinetic analysis · Taylor flow Introduction S. Triemer and M. Schulze have contributed equally. A. Seidel-Morgenstern Malaria causes around 230 million infections and more than seidel@mpi-magdeburg.mpg.de 400.000 deaths each year [1] – although it is preventable and S. Triemer treatable. Medications containing derivatives of artemisinin, triemer@mpi-magdeburg.mpg.de a secondary metabolite of the plant Artemisia annua,show high efficacy against the disease and cause only low side effects, making these treatments a key in this global effort. Max Planck Institute for Dynamics of Complex technical Systems, Sandtorstraße 1, 39106 Magdeburg, Germany Due to their high price, however, especially the people, who suffer most of the disease – the population in the Institute of Energy and Process Systems Engineering, Technische Universitat ¨ Braunschweig, Langer Kamp 19B, sub-Saharan region – do not have full access to artemisinin- 38106 Braunschweig, Germany based combination therapies (ACTs). Center of Pharmaceutical Engineering, Technische Universitat ¨ Until today, artemisinin is mainly produced by extraction Braunschweig, Franz-Liszt-Straße 35a, 38106 Braunschweig, of the plant A. annua [2]. As an alternative, semi-synthetic Germany processes for artemisinin production were developed [3, Institute of Chemical Engineering, Ulm University, 4] and applied in industrial scale [5, 6] starting from Albert-Einstein-Allee 11, 89081 Ulm, Germany fermentation with genetically engineered yeasts. The final Institute for Applied Materials - Electrochemical production step is the reaction from dihydroartemisinic acid Technologies, Karlsruhe Institute of Technology, (DHAA) to artemisinin. DHAA is a biological precursor Adenauerring 20b, 76131 Karlsruhe, Germany to artemisinin and obtained as major byproduct from the Lehrstuhl fur ¨ Chemische Verfahrenstechnik, extraction. By applying a similar reaction step as in the Otto-von-Guericke-Universitat, ¨ Universitatsplatz ¨ 2, 39106 Magdeburg, Germany semi-synthetic production, it can be utilized as an additional 642 J Flow Chem (2021) 11:641–659 Fig. 1 Partial synthesis of hν artemisinin starting from dihydroartemisinic acid: Illustration of mass transfer, photon transfer and reaction O O 2 2 kinetics H + hν H H + O + O H H H O O OH + OH HO H Dihydroartemisinic Artemisinin Terary acid (DHAA) hydroperoxide (PO ) source for artemisinin [7] increasing the yield of artemisinin all involved units [18]. To the best of our knowledge, a com- retrieved from the plant. prehensive model is not available for the artemisinin partial In both approaches the synthesis from DHAA to synthesis so far [19]. To be predictive, the model needs to artemisinin plays a crucial role. Thus, a good understanding describe the major characteristics and phenomena of the of the reaction mechanism and the main factors of influence process. However, multi-phase flow and photon emission in is of large interest. The partial synthesis starting from chemical reactors are 3D phenomena that can be described DHAA (Fig. 1) proceeds via an initial photooxygenation either based on first principles yielding complex models or forming a tertiary hydroperoxide as main intermediate [8, by reducing the complexity with simplifications limiting the 9]. In the presence of strong acids, this hydroperoxide model applicability [20–23]. (PO ) undergoes a Hock-cleavage, a second oxidation and The aim of this contribution is to provide a first quan- subsequent cyclization reactions forming artemisinin as titative model for the reaction kinetics of the photooxi- main product [10, 11]. The first step, the photooxygenation, dation of dihydroartemisinic acid to the intermediate ter- is initiated by formation of singlet oxygen in situ. tiary hydroperoxide PO . The model combines a detailed Photosensitization requiring light irradiation and a matching description of the reaction kinetics with mass and photon dye is widely applied at lab- and industrial-scale [5, 6, 12] transfer. Focus in the model development was to obtain a for this purpose due to its reduced need for reactants and model structure, which is reliable but at the same time as higher selectivity. To achieve a fast and selective conversion simple as possible, to allow for analysis of the production of DHAA to artemisinin, the reactor system and the reaction process, its limitation and model-based optimization. The conditions need to provide high mass transfer of oxygen, model was parameterized by steady-state experiments of the strong mixing and efficient irradiation within the reactor photooxygenation in a continuous photo-flow reactor. The volume. These requirements were met by applying small- ferrioxalate actinometer was utilized to quantify the inci- scaled reactor systems operated under slug flow conditions dent photon flux in the reactor – an essential quantity in the [13, 14] as displayed in Fig. 1. reaction kinetics of the photooxygenation. The challenging To obtain an optimal overall process of artemisinin pro- identification of the kinetic parameters was supported by an duction, the partial synthesis step needs to be designed iterative strategy applying model-based experimental design with respect to all upstream and downstream units. For this to ensure large parameter sensitivities and reduce the exper- task, model-based tools have been proven essential in aca- imental workload [24]. In the following, we first introduce demia and the pharmaceutical industry [15, 16] to facilitate the reaction mechanism and the experimental setup we used system understanding and control [17]. The description of to study the kinetics. We explain the mathematical tools and the process chain constitutes a highly complex mathemat- how they are combined based on the applied experimen- ical problem with multiple process variables, degrees of tal setting to yield a predictive model with reliable kinetic freedom and at the same time various constraints, e.g. on constants for the photooxidation of DHAA. To demonstrate product quality and process safety. For each unit within the the potential of the model, we use it in the end to derive process, a model is required, which predicts the units’ beha- promising experimental regimes for future lab and industrial viors well but is also simple to enable joint optimization of implementation of the photooxygenation. J Flow Chem (2021) 11:641–659 643 Fig. 2 Simplified reaction network of the photooxygenation of *DCA PO dihydroartemisinic acid OH (DHAA) to the desired h HO hydroperoxide PO –the key intermediate in the artemisinin DCA partial synthesis. 9,10-Dicynanoanthracene (DCA) serves as photosensitizer 2 PO in the in situ formation of singlet OH O OH HO oxygen Dihydroartemisinic acid (DHAA) PO O OH HO Reaction network of the photooxygenation H-shift matching an ene-type reaction mechanism known as of dihydroartemisinic acid Schenk-reaction [30]. In the range of the double bond, H- atoms in three different positions can be abstracted forming The photooxygenation of dihydroartemisinic acid (DHAA) three different hydroperoxides. Due to the cis-effect of the to hydroperoxides proceeds via two main reaction steps ene-type reaction, the tertiary hydroperoxide PO is the main product. PO is also the intermediate to artemisinin (Fig. 2): and so the desired product of the photooxygenation. 1. photosensitized formation of singlet oxygen and All formed hydroperoxides are semi-stable species which 2. ene-type reaction to an hydroperoxide. undergo several rearrangement and degradation reactions In photosensitization, a photoactive molecule, the photo- leading to total decomposition within several weeks [11]. sensitizer, absorbs light of a corresponding wavelength and transfers that energy to an oxygen molecule exciting it in its singlet state [12]. In this study we used 9,10- Kinetic steady-state experiments dicyanoanthracene (DCA), which is a widely applied photo- in a photo-flow reactor sensitizer due to its high efficiency, strong chemical stability and absorbance in the visible spectrum [25]. The photooxygenation of dihydroartemisinic acid (DHAA) After absorption of light in the blue region (400– requires efficient irradiation of the reactant solution and 500 nm) DCA is excited to a singlet state following a sufficient supply of oxygen to investigate the kinetics of complex network of different quenching processes [26, 27]. the reaction steps. Milli-scaled flow reactors in Taylor In the main pathway, singlet state DCA is quenched by flow mode offer high surface area between gas and liquid triplet oxygen forming one molecule of singlet oxygen. phase and efficient irradiation of the substrate due to the The residual triplet state allows the formation of another small channel depths. This makes this type of reactors molecule of singlet oxygen reducing DCA to its ground suitable to study the kinetics of photoreactions [31–33]. state. Parallel quenching processes, e.g. fluorescence or The experimental conditions including toluene as solvent, phosphorescence, lead to deactivation of DCA without 9,10-dicyanoanthracene (DCA) as photosensitizer and a forming singlet oxygen. Depending on the solvent, the temperature of -20 C were adapted from [14] due to the dissolved oxygen concentration and the presence of optimal yields for artemisinin observed in this study. To additional quenchers, the overall quantum yield of singlet exclude dynamics from the kinetic analysis, the reactor oxygen formation with DCA might vary significantly [27]. has to enter a steady-state before sampling or evaluating A maximum quantum yield of singlet oxygen is reported in online-measurement data. the range of 1.56–1.71 in benzene extrapolated to indefinite In the following, the applied reactor setup and the pro- oxygen concentration [27–29]. cedure of the photooxygenation experiments are introduced Once singlet oxygen is formed, it either reacts with briefly. For details on materials, the equipment and sample DHAA or it is quenched back to its triplet state. The reaction analysis, the interested reader is referred to the Supporting of DHAA with singlet oxygen proceeds via 1,5-sigmatropic Information (SI). LED 644 J Flow Chem (2021) 11:641–659 Continuous photo-flow reactor system experiments, the gas/liquid ratio was set to 4:1 (v/v) - equal to a gas holdup of β = 0.8. The total flow rate was varied The photooxygenation of DHAA was investigated in an in- between 1–2 ml/min at 7 bar absolute system pressure, house-made tubular reactor system, Fig. 3. The photoreactor ensuring Taylor flow conditions in all experiments. The consisted of wrapped transparent tubing (FEP, ID 0.8 mm) photoreactor was operated at -20 C, while all the up- and immersed in a cooling liquid connected to a thermostat. The downstream equipment was kept at room temperature. length of the photoreactor (2–10 m) was chosen according To ensure steady-state operation of the reactor system, to the residence time range of interest. Two LED modules one set of experimental conditions was kept for a duration emitting blue light (417 nm) irradiated the photoreactor of at least 5 times of the estimated residence time in the from both sides in all experiments. The irradiation intensity whole reactor before sampling the liquid effluent at the was set relative to the maximum emitted optical power end of the reaction line. The concentrations of DHAA and of the LED modules (21 W per module) by adjusting the the formed hydroperoxides were determined by quantitative current in the power supply. In the following we refer to this H-NMR. setting as LED power P . LED The liquid and the gas feed were dosed continuously by a syringe pump and mass flow controllers, respectively. Both Measurement of the provided photon flux feed streams were contacted in a T-mixer and then entered by chemical actinometry the photoreactor. After irradiation, the gas and liquid phase are split in a membrane phase separator. The residual gas The initial step of the photooxygenation of DHAA is the stream is measured with a flow meter. The liquid stream is light-induced formation of singlet oxygen, where photons collected and analyzed offline. The pressure in the reaction must be considered as stoichiometric reagent. Chemical line was controlled by two back-pressure regulators at the actinometry is a well-established tool to investigate the gas and the liquid side. incident photon flux in complex reactor geometries, where other methods as radiometry are not easily applicable [34]. Steady-state experiments for the photooxygenation It is an integral method yielding an average value of the of DHAA in Taylor flow conditions incident photon flux over the irradiation period. In this study, we used potassium ferrioxalate as acti- The feed solution consisting of DHAA and DCA dissolved nometer – also known as the Hatchard-Parker-Actinometer in toluene was connected to the reactor system and dosed [35] – to characterize the photon flux reaching the reac- together with a gas stream containing either pure oxygen or tor in our experimental setup. This actinometer is the most oxygen/nitrogen mixtures through the reactor system. In all established one [36] and used also for characterization of FC F N2 01 Residual gas FC Reactor O2 P T P coil 2 02 02 Product soluon Feed 7 bar Photoreactor 20°C -20°C Fig. 3 Continuous photo-flow reactor setup applied for the kinetic investigation of the photooxygenation of dihydroartemisinic acid. The liquid and gas feed are pumped at Taylor flow conditions through the reaction line (ID: 0.8 mm) kept at -20 C and irradiated by blue LED light (417 nm) LED J Flow Chem (2021) 11:641–659 645 Act flow reactors [37, 38] due to its wide range of absorption The quantum yield Φ and the Napierian absorption Act in the UV and visible spectrum, easy preparation and han- coefficient κ of ferrioxalate at irradiation wavelength 417 nm dling. As Roibu et al. [39] showed, the absorbed amount are given in the SI – together with details on the calculation of photons differs depending on the set flow conditions. of the actinometer conversion and the determination of the To mimic the radiation conditions in the photooxygena- incident photon flux. The relation of absorbed and incident tion experiments, all actinometric measurements shown in photon flux based on the Lambert-Beer law is introduced this study were performed in continuous mode in Tay- in the following section on model development for the lor flow conditions. The procedure of measurements with photooxygenation of DHAA. ferrioxalate and their analysis were adapted from Wriedt et al. [38]. Process model for the photooxygenation Experimental procedure of actinometric of dihydroartemisinic acid measurements The difficulty in obtaining reliable reaction kinetics for A 0.15M solution of ferrioxalate was prepared freshly the photooxygenation of dihydroartemisinic acid (DHAA) on the day of the experiment. The actinometer solution lies in the interaction of the chemical reaction network was pumped together with nitrogen as inert phase in slug with photon and mass transfer processes. Both phenomena flow pattern through the irradiated reactor at 7 bar system are complex to describe and depend strongly on the pressure. The gas holdup β was 0.8 in all experiments reactor system applied. Accordingly, the identified process – equal to the flow conditions in the photooxygenation model is assembled from two main parts. The kinetic experiments. The two-phase-flow was pumped through the model describes the (photo-induced) chemical reactions photoreactor resulting in a residence time of 6–12 s in the and is independent of the process setup. The reactor irradiated section (2 m length). After achieving stable flow model, instead, reproduces the fluid dynamics of the two- conditions for at least 5 min, 3 samples of the liquid effluent phase flow, including the interfacial transfer equations, stream were collected. and is dependent on the photo-flow reactor system used. Each sample was diluted 25-fold with 0.05M sulfuric Both components of the process model, that integrates acid before combining it with a buffer solution of 0.1% the kinetics into the reactor model, are introduced in phenanthroline solution in 0.05M sulfuric acid containing the following subsections. In the end, a short theoretical 0.06M sodium acetate. After 30 min the absorption of background on how we identified the process model and the sample was measured at 510 nm with a UV/Vis estimated and assessed its model parameters is outlined. spectrometer to determine the formed amount of Fe(II) The interested reader is referred to the Supporting oxalate and calculate the actinometer conversion. In Information (SI) for a more thorough motivation and addition, samples of the reactor effluent without irradiation derivation of the reactor model. Likewise, more details on were collected and processed likewise to the irradiated the strategy leading to the identified process model can be samples to determine actinometer conversion due to found in the SI. ambient light. Details on materials, sample workup and analysis are Kinetic rate equations for the photooxygenation given in the SI. The reaction scheme of the kinetic model is shown in Determination of the incident photon flux Fig. 2. The tertiary hydroperoxide PO is the species of interest, i.e., it is further converted to artemisinin. Act The conversion of ferrioxalate X in the linear region of The two secondary hydroperoxides PO and PO are 2 3 the actinometer only depends on the constant quantum yield lumped together to the byproduct species PO .Inthe Act Φ at the irradiation wavelength of 417 nm, the optical conducted photooxygenation experiments, the recovery of path length l and the volumetric incident photon flux L the measured products PO and PO make up around 95 % opt p 1 y during irradiation in the photoreactor with a residence time of the total amount of reacted DHAA. The missing 5 % τ . Following the procedure and the model introduced in are attributed to rearrangement and degradation products Wriedt et al. 2018 [38], L is obtained by solving Eq. 1 formed between sampling and NMR analysis (Section 6). To numerically, based on the known residence time and the cover these additional and presently chemically unidentified measured actinometer conversion, products and the respective reactions, an additional species PO is introduced, which is produced from PO and PO . x 1 y Act Act dX Φ Act Act Identical reaction rate constants are assumed. This approach 417 nm −κ [Act] (1−X )l 0 opt 417 nm = L 1 − e .(1) is motivated by the lack of data on species and reactions, as dτ [Act] 0 646 J Flow Chem (2021) 11:641–659 it allows to lump the unknown and unquantifiable reactions scope, or mechanistically motivated [42]. The mechanistic and side products. This approach may be replaced by a justification lies in the fact that “in a single photon more detailed mechanism once more is known on the absorption process, the rate of the photosensitizer activation side reactions. Alternatively, separate loss reactions might step (primary event) is proportional to the rate of energy lead to additional complications during the identification absorbed” [42]. The formation rate of singlet oxygen might of their reaction constants and would therefore make be expressed as a physical interpretation difficult. Hence, the chemical r = Φ L , (7) 1 1 O O p reaction network is 2 2 PO 1 with the local volumetric rate of photon absorption L and DHAA+ O −−→ PO , 2 1 the quantum yield of singlet oxygen Φ , i.e., the number k O PO y DHAA+ O −−→ PO , 2 y of singlet oxygen molecules formed divided by the number 1/τ of absorbed photons. 1 3 O −−→ O , 2 2 Different mechanistic networks for the formation of PO x PO −−→ PO , singlet oxygen by DCA in various solvents have been 1 x PO derived in literature [26, 27]. Here, we neglect implications PO −−→ PO , (2) y x on the quantum yield by extraneous species, e.g. solvent with kinetic rate constants k , i ∈{PO , PO , PO },and the quenching, as they are unknown and would encompass i 1 y x lifetime of singlet oxygen τ . The corresponding reaction the unfavorable situation that the quantum yield does not rates are expressed as elementary reactions [40], resulting in tend to zero with vanishing oxygen concentration [21, 26, the following rates of formation: 27]. The quantum yield of singlet oxygen can then be stated as r = k [DHAA][ O ], (3a) PO PO 2 1 1 1 [O ] r = k [DHAA][ O ], (3b) PO PO 2 y y Φ1 = , (8) k [O ]+ k l1 2 l2 r = k ([PO ]+[PO ]).(3c) PO PO 1 y x x where k and k are lumped kinetic parameters that l1 l2 Since singlet oxygen is a very reactive and short-lived combine diverse rate constants [27]. The concentration of species, the steady-state-assumption is applied, triplet oxygen concentration in Eq. 8 has been replaced by ! the concentration of dissolved oxygen as singlet oxygen d[ O ] 1 1 1 ∼ ∼ = 0 = r1 −(k +k )[DHAA][ O ]− [ O ], PO PO 2 2 O 1 y occurs merely in trace quantities [21, 33]. dz τ (4) Connecting the reaction kinetics to the rate of photon where r is the formation rate of singlet oxygen. O absorption Combining (3) with (4), yields The interaction between radiative transfer and reaction k [DH AA] PO r = r , (5a) PO kinetics is visualized in Fig. 4. The reaction rates in 1 O ˜ ˜ 1 + (k + k )[DH AA] PO PO Eqs. 6 and 7 depend on the local volumetric rate of k [DH AA] PO r = r1 , (5b) PO y O ˜ ˜ 1 + (k + k )[DH AA] PO PO 1 y r = k ([PO ]+[PO ]), (5c) PO PO 1 y x x with the kinetic constants normalized to the lifetime of singlet oxygen k = k τ ,i ∈{PO , PO }.(6) i i Δ 1 y The lifetime of singlet oxygen in toluene τ is 33.2 μsat- 20 , extrapolated from available data in the range from 5 to 90 [41]. Photosensitized formation of singlet oxygen Fig. 4 Interaction between radiative transfer and reaction kinetics; L : In photosensitized processes, expressions for reaction a local volumetric incident photon flux, L : local volumetric rate of rates are either empirically derived, thus having limited photon absorption, c: vector holding concentrations of present species J Flow Chem (2021) 11:641–659 647 Table 1 Summary of key assumptions applied to describe the reactor behavior The relative pressure drop over the reactor is small (0.1–0.5 bar at 7 bar operating pressure). Consequently, the momentum balance is neglected [51]. Due to the isothermal operation of the reactor, there are no internal temperature gradients. Thus, energy balances are not considered. The flow is one-dimensional (z axis). Hence, ideal mixing in radial direction is assumed [22, 52]. Diffusion is not considered. The operation of the setup is in steady-state. The liquid phase is incompressible. The density is calculated by a simple mixture density of the solvent plus the excess volume caused by the addition of DHAA. Material exchange between the phases is based on the linear approach to mass transfer. The gas phase can be described by an ideal gas mixture, i.e., the Taylor bubbles are well mixed. The dissolved oxygen concentration is derived from Henry’s law. photon absorption L that results from the radiative effect of a decreasing gas holdup due to reaction progress transfer equation (RTE). The L , in turn, depends on on the average path length [39] is neglected. The reaction the concentrations of the chemical species c. A common kinetics are therefore related to the averaged L ,which is assumption is that photons are predominantly absorbed constant over the whole reactor length. Accordingly, the by the photosensitizer, i.e. c = (c ) , leading actinometric measurements used to characterize the irradia- DCA to the substantial simplification that the RTE and the tion conditions in the reactor also provide an average value chemical kinetics are decoupled and can therefore be solved of the incident photon flux over the reactor length, see Eq. 1. independently. However, the L remains a complex function of position and time, that is highly dependent on the Reactor model individual reactor geometry, the physical properties of the participating media and the flow conditions [43]. The reactor model connects the intrinsic reaction rates with If nontransient light intensity is assumed, an averaged L the physical phenomena occurring within the reactor line, is derived from the Beer-Lambert law [44], namely the specific flow conditions and mass transfer. The key assumptions for the description of the reactor behavior L = L (1 − exp [−κc l ]), (9) p DCA opt are stated in Table 1. In a reliable reactor model, the gas with the the local volumetric incident photon flux L ,the p and liquid phase as well as the mass transfer between them Napierian absorption coefficient of the absorbing species need to be quantified. In the following, we first derive the κ , the photosensitizer concentration c , and the optical DCA balance equations for each phase separately based on the path length l . The concentration of DCA was assumed opt two-fluid model, and subsequently describe the interfacial to be constant throughout the whole reactor. Please note mass transfer between the gas and the liquid phase. that Eq. 9 does not explicitly include the irradiation from two sides as the here used reactor setup would suggest. Description of fluid dynamics with the two-fluid model Due to the symmetric configuration of the capillary reactor, however, the superposition of the light emission from two The core idea of the two-fluid model (indices g and l for sides is implicitly alleviated in L . In addition, an error gas and liquid phase, respectively) is to balance each phase resulting from this simplified description is balanced by individually and close their balances by interfacial transfer considering the optical path length as one of the parameters equations. A more detailed motivation for the two-fluid to be estimated, Eq. 21. model can be found in the SI, Section 5.1.2. The local volumetric incident photon flux L is defined p Resulting from the simplifications in Table 1,the as the absolute incident photon flux q related to the material balance of a species i in the liquid phase in terms irradiated volume of the reaction solution V : l of concentration c along the reactor coordinate z becomes L = . (10) V dc 1 1,i = O l i 2 = (r + δ j ), δ = , (11) i i O i In complex reactor geometries, the local rate of photon dz u 0, else absorption might differ significantly within the reactor vol- where u is the liquid phase velocity, r is the net rate ume altering the local reaction rates. In this study, L was l i of reaction and j is the transfer of oxygen from the assumed to be constant. The assumption of homogeneous O gas to the liquid phase. The species i is in the set illumination is commonly made in microreactor modelling, {DHAA, PO , PO , PO , O }. The delta function δ ensures resulting in good model-data fits [45]. This includes that the 1 y x 2 i 648 J Flow Chem (2021) 11:641–659 that the oxygen transfer is solely active in the balance for law (SI, Sec. 5.1.4) and is taken from literature [48]. dissolved oxygen. The mass transfer coefficient k a in Eq. 18 is affected For the gas phase, a material balance over oxygen and by several reactor-dependent and fluid properties, that are the total gas flow V is considered. The former in terms of summarized in a contribution from the Taylor bubble caps molar fraction x is and a contribution from the liquid film between reactor wall and Taylor bubble [49]. The contribution by the film dx RT =− (1 − α)Aj (1 − x ), (12) O O was observed to be dominant [49], leading to k a ∝ 2 2 dz pV D u /L /d with the diffusion coefficient of oxygen O UC 2 g and the material balance over the total gas flow reads D and the length of a unit cell L consisting of the gas O UC dV RT g bubble and the liquid slug [50]. For no information about =− (1 − α)Aj . (13) the geometry of the unit cell is readily available, we simply dz p consider a dependence of the mass transfer coefficient on In Eqs. 12 and 13, R is the universal gas constant, the superficial gas velocity: T temperature, p total pressure, and A the known cross- sectional area of the channel. The gas fraction α is a k a = k a u , (19) l l key characteristic of the two-fluid model, which assigns a relative area to any of the phases: introducing a constant k a. A A g l α = , 1 − α = , and A = A + A , (14) g l A A The process model: Combining the kinetics where A and A are the unspecified cross-sectional areas with the reactor model g l covered by the gas phase flow V and the liquid phase flow ˙ The integration of the chemical kinetics, Eq. 5,and themass V , respectively. The phase velocities can then be expressed transfer relation, Eq. 18, into the material balances (11), (12) as and (13) provides the governing equations of the process ˙ ˙ ˙ ˙ V V V V g g l l u = = ,u = = . (15) g l model for both the liquid and the gas phase: A αA A (1 − α)A g l 1 − A ˜ ˜ (k + k )[DH AA] To solve the material balances in Eqs. 11, 12 and 13,the d[DHAA] C0 [O ] PO PO 2 1 y = − dz k [O ]+ k ˜ ˜ V l1 2 l2 1 + (k + k )[DH AA] unknown gas fraction α must be determined. To this end, we l PO PO 1 y utilize an established simplification of the two-fluid model L (1 − exp [−κc l ]) , p DCA opt – the drift flux model [46, 47] (further details in SI, Sec. 5.1.3). Its constitutive equation relates α to the known gas 1 − A d[PO ] C [O ] k [DH AA] 1 0 2 PO holdup β , dz k [O ]+ k ˜ ˜ V l1 2 l2 1 + (k + k )[DH AA] l PO PO 1 y α = β, (16) L (1 − exp [−κc l ]) − k [PO ] , p DCA opt PO 1 with 1 − A ˜ d[PO ] k [DH AA] C [O ] PO y 0 2 y ˙ ˙ dz k [O ]+ k ˜ ˜ V l1 2 l2 1 + (k + k )[DH AA] V V l PO PO g g 1 y β = = . (17) ˙ ˙ ˙ V V + V g l L (1 − exp [−κc l ]) − k [PO ] , p DCA opt PO y The distribution factor C might be taken from literature or 1 − A d[PO ] C experimentally determined. In this study, C was estimated x 0 = k ([PO ]+[PO ]), PO 1 y dz by measurement of the residence time after tracer injection 1 − A ˜ ˜ (SI, Sec. 6.1). (k + k )[DH AA] d[O ] C [O ] PO PO 2 0 2 1 y = − dz k [O ]+ k ˜ ˜ V l1 2 l2 1 + (k + k )[DH AA] l PO PO 1 y Interfacial oxygen transfer s ∞ L (1 − exp [−κc l ]) + k a u ([O ] −[O ]) , p DCA opt l 2 2 Mass transfer of oxygen from the gas into the liquid phase dx RT β 2 ∞ =− 1 − A(1 − x )k a u ([O ] −[O ]), O l 2 2 2 g dz pV C is modeled according to g 0 dV g RT β ∞ ∞ =− 1 − Ak a u ([O ] −[O ]), (20) j = k a([O ] −[O ]), (18) l 2 2 O l 2 2 dz p C where [O ] is the saturation concentration of oxygen in with initial conditions the liquid phase and k a is the volumetric transfer coefficient ([DHAA], [PO ], [PO ], [PO ], [O ], [x ], [V ]) (0) 1 y x 2 O g based on the specific gas-liquid interfacial surface area = ([DHAA] , 0, 0, 0, [O ] , x , V ) . a. The saturation concentration is calculated by Henry’s 0 2 O ,0 g,0 2 J Flow Chem (2021) 11:641–659 649 The vector of unknown model parameters of the process influences. Subsequently, the reaction behaviour of the model, that needs to be identified, is photooxygenation is analyzed qualitatively on the basis of the experimental data. ˜ ˜ (k a, k ,k , k , k ,k ,l ) . (21) In the second part, the experimental data is used l l1 l2 PO PO PO opt 1 y x to identify the kinetic model parameters and assess Identification of the model parameters the suitability of the previously made assumptions. The parameterized model is finally applied to understand and by Model-based Design of Experiments identify the rate-determining effects in dependence on the reaction conditions offered. Identifying a reliable process model is a challenging problem, particularly in (bio-)chemical engineering where Quantification of the incident volumetric photon often reaction kinetics are not known apriori.Evenif flux L the stoichiometries have been established, the mathematical rate laws might not be readily revealed [40]. For the Relation between L and the set LED power identification of a reliable mathematical model, a systematic procedure is therefore key [53, 54]. One major tool in The actinometric measurements with ferrioxalate were this process is the model-based design of experiments (MBDoE). MBDoE facilitates model identification by performed in Taylor flow conditions as the later presented photooxygenation experiments. In Fig. 5a, the obtained planning experiments with high informative output under the consideration of the formulated model candidates, actinometer conversions are depicted. The experimental operation window of LED settings and residence time in thereby reducing development time and cost [55–57]. In the study case at hand, we primarily used MBDoE the irradiated section was limited to a narrow range of 6– 12 s and 10–25%LED by physical and technical constraints for the enhanced precision of parameter estimates. Here, [38]. Precipitation occurred in all samples obtained at LED MBDoE aims at minimizing the covariance matrix of the model parameters, a measure for the quantification of the settings higher than 25%LED. Therefore, these data were excluded from further analysis. The conversions obtained parametric uncertainties, by maximizing the parameter sen- sitivities on the measured outputs [58]. Having collected without precipitation show an expected linear dependence on the residence times. the measurement data of the optimally planned experiment, the parameters of the proposed model candidate(s) were Based on the obtained actinometer conversion and the known quantum yield of ferrioxalate, the volumetric estimated. Parameter estimation was performed using the maximum likelihood approach to obtain a match between incident photon flux (L ) was determined separately for each data point based on Eq. 1. The optical path length was model outputs and the experimental data. Next to an evalu- assumed to be equal to the channel diameter of 0.8 mm. The ation of the model-data fit, the model parameters and their average values for each LED setting are depicted in Fig. 5b. estimates were assessed by checking their identifiability The incident photon flux shows a strong linear depen- and by the calculation of confidence intervals. Identifiabil- dence on the LED power at lower set values. The measured ity of parameters ensures that the model parameters can incident photon fluxes deviate from that dependence due to be uniquely determined from the available measurement data [58, 59], and is therefore a necessity for a reliable the aforementioned observed precipitation during the exper- iment. The linear behavior is a known property of LEDs interpretation of parameter values. We used the profile like- lihood approach that yields improved confidence intervals and also given in the reference data-sheet of the LED mod- ules applied. Therefore, a linear relation is used to connect for the model parameters besides conclusions about param- eter identifiability [60, 61]. More information about the the volumetric incident photon flux with the LED power as additional model equation introducing L as proportionality MBDoE and the profile likelihood approach is outlined in factor, the SI. L = L · P . (22) p p LED Results and Discussion Relation between L and the unknown optical path length In the following first part, the experimental data is shown, which was later on used to parameterize the developed The determination of the incident photon flux from process model. Here, the actinometric measurements are actinometric measurements strongly depends on the value discussed, which yielded a relation for the incident set for the optical path length l , which either has to opt volumetric photon flux L – a key parameter in the model be estimated or measured to take partial absorption into to disentangle kinetic parameters from reactor-dependent account, Eq. 9. In our actinometric data set shown above, 650 J Flow Chem (2021) 11:641–659 Fig. 5 Results of actinometric measurements at two-phase slug flow conditions: a Actinometer conversion in dependence on set LED power P and residence LED time in the irradiated section of the photoreactor, b Volumetric incident photon absorption determined based on measured actinometer conversion (l = opt 0.8 mm) the path length was found to be insensitive. That is, for each The parameterized relation in Eq. 24 was used in the model path length assumed (e.g. 0.8 mm as shown above), values to link the knowledge from the actinometric measurements for the incident photon flux and the resulting proportionality with the photooxygenation experiments. factor L could be found, which fit the experimental actinometric data equally well. Qualitative assessment of the reaction behaviour The complex irradiation geometry of our applied reactor of the photooxygenation (Fig. 3), however, also makes it difficult to predict the path length from theoretical considerations due to The main goal of this contribution is to provide a kinetic the combination of a wide emission angle of the LED model for the photooxygenation of dihydroartemisinic acid modules, illumination from two sides, reflection within the to the desired intermediate hydroperoxide PO .Inthe photoreactor casing and Taylor flow conditions. following, a subset of the experimental data is shown to As an alternative, the optical path length can be set illustrate qualitative trends of the reaction behavior in Fig. 6. as an additional parameter to be estimated based on the Due to the applied model-based design of experiments, experimental data of the photooxygenation of DHAA. A the kinetics were studied selectively at conditions that relation between incident photon flux and path length is assured highest sensitivity of the kinetic parameters to be developed from the actinometric measurements and then estimated. That is why the experimental conditions of the used as additional model equation in the analysis of the datashowninFig. 6 change between the subplots. photooxygenation. Each data point is the result of a separate experiment in The absorbed and the incident volumetric photon flux steady-state. The experimental results are compared based are connected by Beer-Lambert law, as shown in Eq. 23. on the superficial residence time defined by the initial gas The relation contains two unknown parameters; L as the and liquid flow rates: proportionality factor between the the absorbed volumetric photon flux and the set LED power and [Act]. [Act] can be τ = . (25) ˙ ˙ V + V l g,0 interpreted as an average concentration of the ferrioxalate during irradiation. Both parameters were estimated by first The superficial residence time underestimates the real for various assumed lengths of the optical determining L residence time in the system: Due to O consumption, the path (as in Fig. 5 for 0.8 mm) from experimental data and gas flow rate decreases with the increasing conversion of then by fitting the exponential expression of Eq. 23 to these DHAA. Therefore, the real residence time does not only obtained values of L (details are given in SI): depend on the initial flow settings but also on the reaction progress. To compare the amount of unknown products a a formed in the photooxygenation, an additional quantity, the L L p p L = = P , (23) recovery, is introduced, which is defined as the ratio of p LED −κ [Act]l −κ [Act]l Act opt Act opt 1 − e 1 − e known components of the reaction mixture and the initially L added amount of DHAA: mol −5 8.893 · 10 [DHAA]+[PO ]+[PO ] 1 y L s %LED L = . (24) Recovery = · 100 %. (26) −1 −23.935 cm ·l opt [DHAA] 1 − e 0 J Flow Chem (2021) 11:641–659 651 The photooxygenation of DHAA is a fast reaction reaching full DHAA conversion in less than 5 min residence time in the irradiated section (Fig. 6a). The desired tertiary hydroperoxide PO reaches a yield of 85 %, while the secondary hydroperoxides are formed with a yield of 8 %. These obtained numbers are in accordance with previous studies, which observed a yield of PO up to 90 % [7, 14] under comparable conditions. The concentration-time- profiles agree in shape with the mixed zero and first reaction order, which was proposed in the model. The recovery of the reactant decreased from 100 % at short residence time to 92 % when full conversion was reached. We assume that this decrease is caused by rearrangement and degradation reactions of the formed hydroperoxides as observed in previous mechanistic studies by Brown et al. [8, 9, 11]. This non-detectable amount of formed products was treated as additional species PO in the model in order to close the overall mass balance. When the light intensity increases, the reaction acceler- ates without affecting the final yields (Fig. 6b). This is in correspondence with the proposed reaction network since the incident photon flux affects only the formation of sin- glet oxygen. The ratio of the reaction rates of PO and PO 1 x is constant and equal to the ratio of the corresponding rate constants k and k . The constant recovery in respect PO 1 POX to light intensity indicates that the consecutive rearrange- ment and degradation of PO and PO are independent of 1 x irradiation. Based on the model structure, the reaction rate is supposed to increase linearly with the incident photon flux. Doubling the LED power from 50% to 100%, however, results only in an 1.5 fold increase of the effective initial rate PO formation (from 0.174 mol/l/minto0.257 mol/l/min at τ = 0.55 min). That is, at the high irradiation intensities, the proposed linearity is not observed in our experimental data. The effect may result from oxygen mass transfer between gas and liquid phase, which is slower than the high reaction rates under strong irradiation and thus limit the overall observed reaction rate. In Fig. 6c, the photosensitizer concentration and gas phase composition was varied while the superficial resi- dence time was kept constant. Again both parameters only influence the reaction rate while the total recovery was unaffected. A 3-fold increase of the catalyst concentra- tion yielded a 2-fold increase in PO concentration formed. Assuming an optical path length equal to the channel diam- Fig. 6 Behavior of the photooxygenation of dihydroartemisinic acid eter of 0.8 mm, an approx. 3-fold rise in light absorption to the desired hydroperoxide PO at varied reaction conditions (incl. initial concentration of DHAA): a Concentration of DHAA, and, thus, in the reaction rate is expected according to Beer- the formed hydroperoxides and the observed reactant recovery in Lambert law. The lower increase observed in the experi- dependence on the superficial residence time b Dependence of PO ments might indicate that the light passes the reactor on formation on provided light intensity c Effect of varied photosensitizer a longer path length resulting in high absorption and thus concentration and gas phase composition at the inlet at constant lower sensitivity on the catalyst concentration. A decrease superficial residence time 652 J Flow Chem (2021) 11:641–659 in O content in the gas phase results in approx. 20% lower the involved parameters with the measurement information yield of PO at otherwise similar reaction conditions. Based at hand. A potential reduction of the correlation by MBDoE on this data, it cannot be concluded yet if that significant did not predict to significantly disentangle the strong con- decrease is caused by a lower O quantum yield or by nection between the parameters. One related problem lies slower mass transfer due to reduced equilibrium concentra- in the mathematical structure of the quantum yield rela- tion of oxygen in the liquid phase. For this conclusion, the tion. Its parameters are theoretically identifiable, but cannot quantitative analysis based on a parameterized and validated be determined properly if noisy data is utilized, i.e. differ- model of the photooxygenation is required. ent parameter sets can explain the outcome equally well [62]. Accordingly, parameter estimation runs showed that Identification of the process model parameters physically reasonable values of the quantum yield of singlet and quantitative assessment of the model-data fit oxygen, i.e., values below 2, could not be retrieved. Conse- quentially, the unknown quantum yield parameters were set The process model developed to describe the photooxy- to literature values, taken from [27] for DCA in benzene: genation behaviour contains seven unknown parameters to k = 0.641 and k = 0.0119 mol/L. l1 l2 be identified with experimental data, Eq. 21.Two of the Hence, five parameters to be estimated were left: The parameters, the mass transfer coefficient k a and the optical mass transfer coefficient k a, the three chemical kinetic l l ˜ ˜ path length l , are related to the applied reactor setup. The constants k , k and k , and the optical path opt PO PO PO 1 y x other five parameters are kinetic rate constants, which are length l . The results of the parameter estimation and opt of the subsequent quantitative assessment of the derived independent of the experimental setup. During the model identification process, a local sensi- model parameters and the model-data fit are summarized tivity analysis revealed (SI) that the kinetic parameters of in Table 2. The measurement error variance estimated 2 2 2 the chemical reactions forming the intermediate hydroper- from regression statistics (SI) σ ˆ = 2.73e-4 mol /L is ˜ ˜ oxides, k and k , are heavily correlated with the k satisfactorily low. Correspondingly, the relative deviation PO PO l1 1 y parameter of the quantum yield relation for singlet oxygen, between the predicted and measured concentration of the Eq. 8. Thus, it becomes impractical to uniquely determine key intermediate PO is 7.09 %. The good model-data fit is Table 2 Goodness of fit and estimated parameter values and spreads, Eq. 21, for the developed process model, Eqs. 20. The confidence intervals are based on the profile likelihood (SI) Model-data fit Symbol Unit Value Description 2 2 SSE mol /l 0.1799 sum of squared errors 2 2 2 σ ˆ mol /l 2.73e − 4 measurement error variance % 7.09 averaged relative deviation of PO Estimated parameters − + Symbol Unit Value COD CI CI 95 95 k a 1/cm min 1.094 0.093 1.046 1.148 −1 k Lmol 7.130 0.173 6.555 7.790 PO −1 k Lmol 0.644 0.306 0.550 0.747 PO k 1/min 0.0249 0.369 0.0204 0.0296 PO l cm 0.178 0.107 0.169 0.188 opt Fixed parameters (quantum yield, Eq. 8) Symbol Unit Value Reference k – 0.641 DCA in benzene [27] l1 −1 k mol l 0.0119 DCA in benzene [27] l2 −1 −1 κ 1mol cm 12841.98 see Supporting Information C – 1.02 see Supporting Information † n PO 1 data (y − y ) /y /n PO ,i PO ,i PO 1 1 1 i PO ,i + − ˆ ˆ COD: coefficient of dispersion, COD = (CI − CI )/θ , θ : estimated value 95 95 +/− CI : ±95% confidence interval 95 J Flow Chem (2021) 11:641–659 653 Fig. 7 Match of experimental data with simulated results based on the photoreactor of each data point. Triangle, diamond and square markers parametrized process model for all quantities measured at the reactor represent data from Fig. 6a. The dashed lines mark 20 % deviations outlet. The grey scale illustrates the superficial residence time in the visualized in the parity plots in Fig. 7 which show a good To further assess the quality of the identified model, match between experimental results and simulated data relative deviations of PO over four important process over the whole range of investigated superficial residence parameters, that is, the initial DHAA concentration, the times. Exemplarily, the data points appearing in Fig. 6a LED light power, the photosensitizer concentration, and the are marked in Figs. 7a, b and c accordingly. In contrast molar fraction of oxygen, were investigated (SI). The results to DHAA and PO , the key chemical species on the route suggest that the existent deviations are mainly caused by towards artemisinin, the data of PO is less matched because measurement noise and errors that inherently occur during for two reasons. On the one hand, the optimizer tends to the measurement procedure but not by systematic model favor higher concentrations per definition of the objective discrepancy. function, i.e., the likelihood function. On the other hand, the Following the profile likelihood approach, all five PO concentrations are closer to zero, where the signal-to- estimated parameters in the developed process model are noise ratio is increased. identifiable (SI). Next to a coefficient of dispersion (COD) 654 J Flow Chem (2021) 11:641–659 95 % confidence intervals (CI) for the estimated parameters and their estimates are in plausible ranges. The required are stated in Table 2. simplification on fluid dynamics and photon transfer, It can be noted that the chemical kinetic constants have namely the application of the two-fluid model and the larger CODs and are, loosely spoken, more uncertain in their neglect of absorption rate distribution, offers a good estimates than the mass transfer coefficient and the optical description of the observed process behavior. path length. On the whole, each of the parameters shows an Albeit, we want to emphasize that for a reliable acceptable spread suggesting that their expected values can utilization and interpretation of the identified process model be reliably used for further model-based investigation. the following aspects need to be taken into account. The rate constants for the formation of the desired Neglecting the distribution of the local volumetric rate of hydroperoxide PO and the byproducts were normed, Eq. 6, photon absorption is a strong simplification affecting the to ease the parameter estimation process. Based on the reaction system on various levels. In particular, a gradient known life time of singlet oxygen in toluene (33.2 μsat-20 in the absorbed photon flux will cause a non-uniform [41]) the absolute rate constants of the reactions of DHAA distribution of the rate of singlet oxygen production within with O to the hydroperoxides, Eq. 3, can be obtained: the liquid slug, resulting in a potential diffusion limitation of the overall reaction rate. The absorbed photon flux 5 −1 −1 k = 2.15 · 10 Lmol s , PO itself is influenced by the gas holdup and photosensitizer −1 5 −1 k = 0.19 · 10 Lmol s . PO concentration. Both quantities decrease with reaction time due to oxygen consumption and photobleaching and Both values are in the same order of magnitude as rate constants published for other investigated ene-type reactions therefore affect the absorbed photon flux. We also want to point to the fact that a reliable description of the two- [33, 63, 64]. The reaction to the desired hydroperoxide is phase flow is essential. A global sensitivity analysis of about 10-fold faster than the reaction to the byproducts. This important model parameters (details in SI) showed, that the matches with the favored selectivity of PO observed in the distribution parameter C , that links the relative motion of photooxygenation experiments. For Taylor flow fluid dynamics and mass transfer the different phases, Eq. 16, is highly sensitive. A variation of C in the model induces a considerable change in the in microchannels, there are various relations for the mass transfer coefficient available that vary substantially simulated PO concentration. Lastly, the identified model and all parameters are only valid for a temperature of - among each other [65]. In the study case at hand, initial superficial velocities between 120 cm/min and 350 cm/min 20 C. Studying the complex influence of temperature on the reaction system including the mass transfer and flow appear, resulting in volumetric mass transfer coefficients −1 −1 conditions is beyond the scope of this paper and a task for of approximately 12 min to 20 min . These values lie future studies. within the range of k a values predicted from correlations available in the literature [65]. Exploitation of the process model to analyse Intuitively, the length of the optical path l = 0.178 cm opt different operating regimes seems to be large at first sight as it is greater than twice the tube diameter of 0.08 cm. In a single circular tube The identified and fully-parameterized model can now be geometry with perpendicular irradiation, the optical path length can be assumed to be between channel diameter d used to understand the process behavior and identify opti- mal operation windows. In the following, three characteris- as upper boundary and the ratio A/d as lower boundary depending on the collimation of the incident light [66]. tic operating situations are illustrated that differ in the cause that limits or partially limits the process dynamics: light Both boundaries, however, are based on the hypothesis that light enters the tubing from one side and is lost after irradiance, substrate DHAA or mass transfer. The possible fourth operating regime – the kinetically controlled domain leaving it. In the considered photoreactor instead, two light without any other limitation – does not occur under the sources are installed in a closed box of stainless steel, investigated conditions. resulting in reflection of the light beam back to the reactor. In Figs. 8 and 9, the dynamic behavior of the system’s Furthermore, as the reactor itself is symmetric (compare key quantities, product concentrations, gas flow rate and with Fig. 3), leaving light beams on one side can re-enter gas phase composition are drawn over the reactor length. the reactor tubing on the other side. In particular in the tube convolutions around the poles in the reactor box, optical The thin vertical line marks the exit of the photoreactor and thus the end of light irradiance. The discontinuities in path lengths significantly exceeding twice the tube diameter are very plausible. the curves at the reactor exit are induced by a temperature jump from reactor to ambient temperature. Experimental In conclusion, the model developed to describe the photooxygenation of DHAA provides a good fit with the data are plotted at the sampling position downstream to the photoreactor exit. experimental data. All model parameters are identifiable J Flow Chem (2021) 11:641–659 655 rates are large in the beginning, see Fig. 8a, but is recovered with decreasing reaction rate values. Obviously, mass transfer does not substantially hinder the process dynamics. In contrast, both the light-limiting and the substrate-limiting regime can be observed in Fig. 8a. Here, a pseudo-inflection point might be determined that describes the transition bet- ween the two regimes that are often observed in photoredox catalysis [21]. At the inflection point, the reaction switches from a pseudo-zero-order reaction with the reaction rate at its maximum to a first-order reaction. Mathematically, the inflection point is defined as the half-maximum kinetic reaction rate. Accordingly, with = r = r + r , PO PO PO 1 y Eq. 5, the light-limiting regime is controlled by a max ˜ ˜ (k + k )[DHAA] 1 : r = Φ L = r , PO PO PO 1 y O p PO (27) and the substrate-limited regime by ˜ ˜ ˜ ˜ (k + k )[DHAA] 1 : r = Φ1 L (k + k )[DHAA]. PO PO PO PO PO 1 y O p 1 y (28) In this study, the inflection point is therefore at [DHAA]≈ 0.129 mol/L. In the DHAA graph in Fig. 8a this inflection point is passed shortly beyond the intersection between the DHAA and the PO curve. To the left of it, it follows zero- order kinetics, and to the right of the inflection point, it approaches first order kinetics. A complementary process characteristic is shown in Fig. 9. In this case, the gas phase consists of both oxygen and nitrogen; see the molar concentration of oxygen in Fig. 9b. From the curve of dissolved oxygen in Fig. 9b, it readily can be observed that the system quickly runs into Fig. 8 Propagation of concentrations, oxygen molar fraction and gas mass transfer limitations. The level of dissolved oxygen flow along the reactor coordinate showing no mass transfer limitations −1 −1 settles down to an equilibrium stage that continuously (conditions: [DHAA] =0.23moll , [DCA]= 0.85 mmol l , P = 100%LED, x = 1). The thin vertical line marks the reactor decreases as the molar fraction of oxygen in the gas phase LED O ,0 outlet drops and therefore correspondingly the solubility limit of oxygen that is determined by Henry’s law. Note that despite the elevated temperature beyond the photoreactor, In the first case example, the gas phase consists solely of the dissolved oxygen concentration does not reach again oxygen, as can be observed in Fig. 8b. The volumetric gas the initial dissolved oxygen concentration because of the flow decreases along the reaction line in the photoreactor decreased molar fraction of oxygen. Along the whole since oxygen is consumed in the liquid phase due to the reactor line, the process runs above the inflection point, i.e. chemical reactions and continuously supplied from the gas above [DHAA]≈ 0.129 mol/L, see Fig. 9a. This implicates phase, Fig. 8b. The negative slope of the PO concentration that the DHAA curve in the same figure follows pseudo- curve after reaching its maximum concentration, Fig. 8a, zero-order kinetics. The additional bending of the actual is owed to the consecutive loss reactions, Eq. 2,thatalso straight line is caused by the low availability of oxygen in continue to go on downstream of the reactor in contrast the liquid phase that affects the quantum yield of singlet to the photo-induced reactions. The further discontinuity oxygen, Eq. 8, and reduces the maximum reaction rate, downstream leading to an even higher negative slope is Eq. 27. Thus, here, the process is partially limited by mass caused by a slow down of the reaction medium due to a transfer, i.e. the mass transfer rate is approximately equal diameter jump of the tubing. Noteworthy is the behaviour to the rate of the bulk kinetics, preventing a more efficient of the dissolved oxygen in Fig. 8b. The dissolved oxygen is conversion of DHAA. rapidly consumed at the inlet of the photoreactor as reaction 656 J Flow Chem (2021) 11:641–659 Fig. 10 Prediction of mass transfer limited regimes for the photooxy- genation of DHAA. The Hatta number is given in dependence on the provided volumetric rate of photon absorption L and the mass transfer −1 coefficent for different O concentrations (contour lines, in mol L ) −1 and for DHAA = 0.5 mol L . The grey rectangle approximately covers the experimental space explored in this article which causes the chemical reaction to take place only at the phase boundary. Critical Hatta values are Ha ≥ 3, strong mass transfer limitation, Ha ≤ 0.3, kinetic regime, no limitation by mass transfer. In the study case at hand, the Hatta number [68] is defined as (SI) ˜ ˜ (k + k )[DHAA] 1 1 PO PO 1 y Ha = D L . 2 p ˜ ˜ k k [O ]+ k l l1 2 l2 1 + (k + k )[DHAA] PO PO 1 y (29) The diffusion coefficient of oxygen in toluene may be taken 2 −1 ◦ Fig. 9 Propagation of concentrations, oxygen molar fraction and gas from [69] and has a value of 2.4860e − 09 m s at −20 C. flow along the reactor coordinate showing mass transfer limitations The limits of the Hatta regimes are drawn as contours in −1 −1 (conditions: [DHAA] =0.48moll , [DCA]= 0.60 mmol l , Fig. 10. P = 100%LED, x = 0.51). The thin vertical line marks the LED O ,0 Generally speaking, with decreasing DHAA concentra- reactor outlet tions all contour lines move towards the ordinate. As obser- ved in the previous section, the conducted experiments, visua- lized as the grey rectangle, lie around the lower Hatta limit where behaviors from dynamics partially limited by mass Identification of mass transfer limited regimes transfer to dynamics not limited by mass transfer appear. for the photooxygenation of dihydroartemisinic acid The analysis for the process behavior so far was linked to Conclusion the applied reactor setup. The identified kinetic constants for the photooxygenation can also be used to predict suitable In this study we provide a mechanistic kinetic model operation regimes for other process settings to prevent that for the photooxygenation of dihydroartemisinic acid – the mass transfer of oxygen limits the overall reaction rate. Such important initial step in the partial synthesis to artemisinin. a classification can be stated with the Hatta number. Based The experimental study on the reaction kinetics was on the two-film theory, the Hatta number relates the rate conducted in a continuous flow photoreactor utilizing of chemical reaction in the liquid phase to the diffusion Taylor flow. The reaction kinetics are combined with a rate across the phase boundary [67]. The higher the Hatta simplified process model taking photon and mass transfer number, the faster is the reaction in comparison to diffusion, into account. To characterize the light input of the reactor, J Flow Chem (2021) 11:641–659 657 the photooxygenation experiments were complemented by article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not actinometric measurements yielding a relation between the included in the article’s Creative Commons licence and your intended incident photon flux and the unknown optical path length, use is not permitted by statutory regulation or exceeds the permitted which was integrated in the process model. use, you will need to obtain permission directly from the copyright The model achieves a good fit between the model outputs holder. To view a copy of this licence, visit http://creativecommons. org/licenses/by/4.0/. and the experimental results from steady-state experiments for a wide range of different critical process parameters. Therefore, the made assumptions and the simplifications, including the two-fluid-model provide a suitable description References for the main process characteristics. Nevertheless, assuming a spatially independent rate of photon absorption within 1. World malaria report 2020 (2020) 20 years of global progress and the reactor is a strong simplification of the reaction system challenges. Tech. rep., World Health Organization, Geneva 2. Lapkin AA, Plucinski PK, Cutler M (2006) Comparative applied, considering its geometrical complexity and the assessment of technologies for extraction of artemisinin. J Nat large value obtained for the average path length. Thus, Prod 69(11):1653–1664. https://doi.org/10.1021/np060375j extending the model by more detailed descriptions of the 3. Paddon CJ, Westfall PJ, Pitera DJ, Benjamin K, Fisher K, McPhee photon transport inside the reactor as well as of the fluid D, Leavell MD, Tai A, Main A, Eng D, Polichuk DR, Teoh KH, Reed DW, Treynor T, Lenihan J, Jiang H, Fleck M, Bajad S, Dang dynamics might improve the predictability of the model. G, Dengrove D, Diola D, Dorin G, Ellens KW, Fickes S, Galazzo By analyzing the process behavior, different regimes J, Gaucher SP, Geistlinger T, Henry R, Hepp M, Horning T, Iqbal of operation were identified where the process is limited T, Kizer L, Lieu B, Melis D, Moss N, Regentin R, Secrest S, by either absorbed photon flux, substrate concentration or Tsuruta H, Vazquez R, Westblade LF, Xu L, Yu M, Zhang Y, Zhao L, Lievense J, Covello PS, Keasling JD, Reiling KK, Renninger mass transfer. Due to is potential to describe the main NS, Newman JD (2013) High-level semi-synthetic production of photooxygenation characteristics, the developed model is the potent antimalarial artemisinin. Nature 496(7446):528–532. seen as an essential building block for future investigations https://doi.org/10.1038/nature12051 on the partial synthesis of arteminsinin. It provides a good 4. Ro DK, Paradise EM, Ouellet M, Fisher KJ, Newman KL, Ndungu JM, Ho KA, Eachus RA, Ham TS, Kirby J, Chang MCY, Withers starting point for kinetic studies of the subsequent acid- ST, Shiba Y, Sarpong R, Keasling JD (2006) Production of the catalyzed reaction sequence finally yielding artemisinin. antimalarial drug precursor artemisinic acid in engineered yeast. The model can be used also as a valuable building block Nature 440(7086):940–943. https://doi.org/10.1038/nature04640 in optimizing the whole process chain from extraction or 5. Turconi J, Griolet F, Guevel R, Oddon G, Villa R, Geatti A, Hvala M, Rossen K, Goller ¨ R, Burgard A (2014) Semisynthetic fermentation to artemisinin purification in the end. artemisinin, the chemical path to industrial production. Org Pro- Supplementary Information The online version contains supplemen- cess Res Dev 18(3):417–422. https://doi.org/10.1021/op4003196 tary material available at https://doi.org/10.1007/s41981-021-00181-2. 6. Burgard A, Gieshoff T, Peschl A, Horstermann ¨ D, Keleschovsky C, Villa R, Michelis S, Feth MP (2016) Optimisation of the photo- Acknowledgements We gratefully acknowledge the support by the chemical oxidation step in the industrial synthesis of artemisinin. Max Planck Society and the Center of Pharmaceutical Engineering Chem Eng J 294:83–96. https://doi.org/10.1016/j.cej.2016.02.085 (PVZ), Braunschweig. S.T. and M.S. are also grateful to the 7. Triemer S, Gilmore K, Vu GT, Seeberger PH, Seidel-Morgenstern International Max Planck Research School “Advanced Methods in A (2018) Literally green chemical synthesis of artemisinin Process and Systems Engineering” (IMPRS ProEng). B.W. and D.Z. from plant extracts. Angew Chem Int Ed 57(19):5525–5528. gratefully acknowledge the financial support provided by the German https://doi.org/10.1002/anie.201801424 Research Foundation (ZI 1502/4-1). We would like to thank Karyna 8. Sy LK, Brown GD, Haynes R (1998) A novel endoperoxide and Oliynyk for performing the actinometric measurements. We are also related sesquiterpenes from Artemisia annua which are possibly grateful to the Otto-von-Guericke University and especially Dr. Liane derived from allylic hydroperoxides. Tetrahedron 54(17):4345– Hilfert and Sabine Hentschel for performing the NMR analysis of the 4356. https://doi.org/10.1016/S0040-4020(98)00148-3 reaction samples. 9. Sy LK, Ngo KS, Brown GD (1999) Biomimetic syn- thesis of arteannuin h and the 3,2-rearrangement of Funding Open Access funding enabled and organized by Projekt allylic hydroperoxides. Tetrahedron 55(52):15127–15140. DEAL. https://doi.org/10.1016/S0040-4020(99)00987-4 10. Roth RJ, Acton N (1989) A simple conversion of artemisinic acid into artemisinin. J Nat Prod 52(5):1183–1185. Declarations https://doi.org/10.1021/np50065a050 11. Sy LK, Brown GD (2002) The mechanism of the spontaneous Conflict of Interests The authors declare that they have no conflict of autoxidation of dihydroartemisinic acid. Tetrahedron 58(5):897– interest. 908. https://doi.org/10.1016/S0040-4020(01)01193-0 Open Access This article is licensed under a Creative Commons 12. DeRosa M (2002) Photosensitized singlet oxygen and Attribution 4.0 International License, which permits use, sharing, its applications. Coord Chem Rev 233-234:351–371. adaptation, distribution and reproduction in any medium or format, as https://doi.org/10.1016/S0010-8545(02)00034-6 long as you give appropriate credit to the original author(s) and the 13. Lev ´ esque F, Seeberger PH (2012) Continuous-flow synthesis source, provide a link to the Creative Commons licence, and indicate of the anti-malaria drug artemisinin. Angew Chem Int Ed if changes were made. The images or other third party material in this 51(7):1706–1709. https://doi.org/10.1002/anie.201107446 658 J Flow Chem (2021) 11:641–659 14. Kopetzki D, Lev ´ esque F, Seeberger PH (2013) A continuous-flow 32. Aillet T, Loubiere ` K, Dechy-Cabaret O, Prat L (2016) process for the synthesis of artemisinin. Chem Eur J 19(17):5450– Microreactors as a tool for acquiring kinetic data on pho- 5456. https://doi.org/10.1002/chem.201204558 tochemical reactions. Chem Eng Technol 39(1):115–122. 15. Klatt KU, Marquardt W (2009) Perspectives for pro- https://doi.org/10.1002/ceat.201500163 cess systems engineering—Personal views from academia 33. Loponov KN, Lopes J, Barlog M, Astrova EV, Malkov AV, and industry. Comput Chem Eng 33(3):536–550. Lapkin AA (2014) Optimization of a scalable photochemical https://doi.org/10.1016/j.compchemeng.2008.09.002 reactor for reactions with singlet oxygen. Org Process Res Dev 16. Kroll P, Hofer A, Ulonska S, Kager J, Herwig C 18(11):1443–1454. https://doi.org/10.1021/op500181z (2017) Model-based methods in the biopharmaceuti- 34. Wriedt B, Ziegenbalg D (2020) Common pitfalls in cal process lifecycle. Pharm Res 34(12):2596–2613. chemical actinometry. J Flow Chem 10(1):295–306. https://doi.org/10.1007/s11095-017-2308-y https://doi.org/10.1007/s41981-019-00072-7 17. Schenkendorf R, Gerogiorgis D, Mansouri S, Gernaey K (2020) 35. Hatchard CG, Parker CA (1956) A new sensitive chemical Model-based tools for pharmaceutical manufacturing processes. actinometer - II. Potassium ferrioxalate as a standard chemical Processes 8(1):49. https://doi.org/10.3390/pr8010049 actinometer. Proc R Soc Lond A Math Phys Sci 235(1203):518– 18. Smith R (2014) Chemical process: design and integration, 1st edn., 536. https://doi.org/10.1098/rspa.1956.0102 Wiley, Hoboken 36. Kuhn HJ, Braslavsky SE, Schmidt R (2004) Chemical actinometry 19. Zhang XW, Zhao X, Liu KH, Sub HM (2020) Kinet- (IUPAC Technical Report). Pure Appl Chem 76(12):2105–2146. ics study on reaction between dihydroartemisinic acid and https://doi.org/10.1351/pac200476122105 singlet oxygen: An essential step to photochemical syn- 37. Aillet T, Loubiere K, Dechy-Cabaret O, Prat L (2014) Accurate thesis of artemisinin. Chin J Chem Phys 33(2):145–150. measurement of the photon flux received inside two continuous https://doi.org/10.1063/1674-0068/cjcp2002021 flow microphotoreactors by actinometry. Int J Chem React Eng 20. Cassano AE, Martin CA, Brandi RJ, Alfano OM (1995) Photore- 12(1):257–269. https://doi.org/10.1515/ijcre-2013-0121 actor analysis and design: fundamentals and applications. Ind Eng 38. Wriedt B, Kowalczyk D, Ziegenbalg D (2018) Exper- Chem Res 34(7):2155–2201. https://doi.org/10.1021/ie00046a001 imental determination of photon fluxes in multilayer 21. Bloh JZ (2019) A holistic approach to model the kinet- capillary photoreactors. ChemPhotoChem 2(10):913–921. ics of photocatalytic reactions. Front Chem 7:128. https://doi.org/10.1002/cptc.201800106 https://doi.org/10.3389/fchem.2019.00128 39. Roibu A, Van Gerven T, Kuhn S (2020) Photon transport 22. Angeli P, Gavriilidis A (2008) Hydrodynamics of Taylor flow in and hydrodynamics in gas-liquid flows. Part 1: Characterization small channels: A review. Proc Inst Mech Eng C J Mech Eng Sci of Taylor Flow in a Photo Microreactor. ChemPhotoChem p 222(5):737–751. https://doi.org/10.1243/09544062JMES776 cptc.202000065. https://doi.org/10.1002/cptc.202000065 23. Gupta R, Fletcher D, Haynes B (2009) On the CFD modelling of 40. Levenspiel O (1999) Chemical reaction engineering, 3rd edn. Taylor flow in microchannels. Chem Eng Sci 64(12):2941–2950. Wiley, New York https://doi.org/10.1016/j.ces.2009.03.018 41. Bregnhøj M, Westberg M, Jensen F, Ogilby PR (2016) Solvent- 24. Schenkendorf R, Xie X, Rehbein M, Scholl S, Krewer U dependent singlet oxygen lifetimes: Temperature effects implicate (2018) The impact of global sensitivities and design measures tunneling and charge-transfer interactions. Phys Chem Chem Phys in model-based optimal experimental design. Processes 6(4):27. 18(33):22946–22961. https://doi.org/10.1039/C6CP01635A https://doi.org/10.3390/pr6040027 42. Munoz-Batista ˜ MJ, Ballari MM, Kubacka A, Alfano OM, 25. Olea AF, Worrall DR, Wilkinson F, Williams SL, Abdel-Shafi Fernandez-Garc ´ ´ ıa M (2019) Braiding kinetics and spectroscopy AA (2002) Solvent effects on the photophysical properties of in photo-catalysis: The spectro-kinetic approach. Chem Soc Rev 9,10-dicyanoanthracene. Phys Chem Chem Phys 4(2):161–167. 48(2):637–682. https://doi.org/10.1039/C8CS00108A https://doi.org/10.1039/b104806f 43. Modest MF (2013) Radiative heat transfer, 3rd edn. Academic 26. Araki Y, Dobrowolski DC, Goyne TE, Hanson DC, Jiang Press, New York ZQ, Lee KJ, Foote CS (1984) Chemistry of singlet oxy- 44. Parnis JM, Oldham KB (2013) Beyond the Beer–Lambert gen. 47. 9,10-Dicyanoanthracene-sensitized photooxygenation of law: The dependence of absorbance on time in photo- alkyl-substituted olefins. J Am Chem Soc 106(16):4570–4575. chemistry. J Photochem Photobiol A Chem 267:6–10. https://doi.org/10.1021/ja00328a045 https://doi.org/10.1016/j.jphotochem.2013.06.006 27. Kanner RC, Foote CS (1992) Singlet oxygen production from 45. Meir G, Leblebici ME, Fransen S, Kuhn S, Van Gerven T singlet and triplet states of 9,10-dicyanoanthracene. J Am Chem (2020) Principles of co-axial illumination for photochemical Soc 114(2):678–681. https://doi.org/10.1021/ja00028a040 reactions: Part 1. Model development. J Adv Manuf Process 2(2). 28. Dobrowolski DC, Ogilby PR, Foote CS (1983) Chemistry https://doi.org/10.1002/amp2.10044 of singlet oxygen. 39. 9,10-Dicyanoanthracene,-sensitized for- 46. Nicklin D (1962) Two-phase bubble flow. Chem Eng Sci mation of singlet oxygen. J Phys Chem 87(13):2261–2263. 17(9):693–702. https://doi.org/10.1016/0009-2509(62)85027-1 https://doi.org/10.1021/j100236a001 47. Zuber N, Findlay JA (1965) Average volumetric concentration 29. Scurlock RD, Ogilby PR (1993) Production of singlet oxygen in two-phase flow systems. J Heat Transf 87(4):453–468. (1 g O2) by 9,10-dicyanoanthracene and acridine: Quantum https://doi.org/10.1115/1.3689137 yields in acetonitrile. J Photochem Photobiol A Chem 72(1):1–7. 48. Wu X, Deng Z, Yan J, Zhang Z, Zhang F, Zhang Z (2014) https://doi.org/10.1016/1010-6030(93)85077-L Experimental Investigation on the Solubility of Oxygen in 30. Breitmaier E, Jung G (2012) Organische Chemie: Grundlagen, Toluene and Acetic Acid. Ind Eng Chem Res 53(23):9932–9937. Verbindungsklassen, Reaktionen, Konzepte, Molekulstruktur, ¨ https://doi.org/10.1021/ie5014772 Naturstoffe, Syntheseplanung, Nachhaltigkeit, 7th edn. Georg 49. van Baten J, Krishna R (2004) CFD simulations of mass transfer Thieme Verlag, Stuttgart from Taylor bubbles rising in circular capillaries. Chem Eng Sci 31. Su Y, Hessel V, Noel ¨ T (2015) A compact pho- 59(12):2535–2545. https://doi.org/10.1016/j.ces.2004.03.010 tomicroreactor design for kinetic studies of gas-liquid 50. Vandu C, Liu H, Krishna R (2005) Mass transfer from Taylor photocatalytic transformations. AIChE J 61(7):2215–2227. bubbles rising in single capillaries. Chem Eng Sci 60(22):6430– https://doi.org/10.1002/aic.14813 6437. https://doi.org/10.1016/j.ces.2005.01.037 J Flow Chem (2021) 11:641–659 659 51. Kreutzer MT, Kapteijn F, Moulijn JA (2005) Fast gas– liquid– 61. Rooney WC, Biegler LT (2001) Design for model parame- solid reactions in monoliths: A case study of nitro-aromatic ter uncertainty using nonlinear confidence regions. AIChE J hydrogenation. Catal Today 8 47(8):1794–1804. https://doi.org/10.1002/aic.690470811 52. Gupta R, Fletcher D, Haynes B (2010) Taylor flow 62. Holmberg A (1982) On the practical identifiability in microchannels: a review of experimental and com- of microbial growth models incorporating Michaelis- putational work. J Comput Multiph Flows 2(1):1–31. Menten type nonlinearities. Math Biosci 62(1):23–43. https://doi.org/10.1260/1757-482X.2.1.1 https://doi.org/10.1016/0025-5564(82)90061-X 53. Franceschini G, Macchietto S (2008) Model-based design of 63. Griesbeck AG, Adam W, Bartoschek A, El-Idreesy TT (2003) experiments for parameter precision: State of the art. Chem Eng Photooxygenation of allylic alcohols: Kinetic comparison of Sci 63(19):4846–4872. https://doi.org/10.1016/j.ces.2007.11.034 unfunctionalized alkenes with prenol-type allylic alcohols, 54. Gernaey KV, Gani R (2010) A model-based systems approach to ethers and acetates. Photochem Photobiol Sci 2(8):877–881. pharmaceutical product-process design and analysis. Chem Eng https://doi.org/10.1039/B302255B Sci 65(21):5757–5769. https://doi.org/10.1016/j.ces.2010.05.003 64. Zhang W, Hibiki T, Mishima K (2010) Correlations of two-phase 55. Flassig RJ, Sundmacher K (2012) Optimal design of frictional pressure drop and void fraction in mini-channel. Int J stimulus experiments for robust discrimination of biochem- Heat Mass Transf 13 ical reaction networks. Bioinformatics 28(23):3089–3096. 65. Haase S, Murzin DY, Salmi T (2016) Review on hydrody- https://doi.org/10.1093/bioinformatics/bts585 namics and mass transfer in minichannel wall reactors with 56. Galvanin F, Ballan CC, Barolo M, Bezzo F (2013) A gen- gas–liquid Taylor flow. Chem Eng Res Des 113:304–329. eral model-based design of experiments approach to achieve https://doi.org/10.1016/j.cherd.2016.06.017 practical identifiability of pharmacokinetic and pharmacody- 66. Roibu A, Fransen S, Leblebici ME, Meir G, Van Ger- namic models. J Pharmacokinet Pharmacodyn 40(4):451–467. ven T, Kuhn S (2018) An accessible visible-light acti- https://doi.org/10.1007/s10928-013-9321-5 nometer for the determination of photon flux and optical 57. Abt V, Barz T, Cruz-Bournazou MN, Herwig C, Kroll P, Moller ¨ J, pathlength in flow photo microreactors. Sci Rep 8(1):5421. Portner ¨ R, Schenkendorf R (2018) Model-based tools for optimal https://doi.org/10.1038/s41598-018-23735-2 experiments in bioprocess engineering. Curr Opin Chem Biol 67. Bourne JR (2003) Mixing and the selectivity of chem- 22:244–252. https://doi.org/10.1016/j.coche.2018.11.007 ical reactions. Org Process Res Dev 7(4):471–508. 58. Walter E, Pronzato L (1997) Identification of parametric models https://doi.org/10.1021/op020074q from experimental data. Communications and control engineering. 68. Su Y, Straathof NJW, Hessel V, Noel ¨ T (2014) Photochemical Springer, London transformations accelerated in continuous-flow reactors: basic 59. Janzen ´ DLI, Bergenholm L, Jirstrand M, Parkinson J, Yates concepts and applications. Chem Eur J 20(34):10562–10589. J, Evans ND, Chappell MJ (2016) Parameter identifiability https://doi.org/10.1002/chem.201400283 of fundamental pharmacodynamic models. Front Physiol 7. 69. Schumpe A, Luehring P (1990) Oxygen diffusivities in https://doi.org/10.3389/fphys.2016.00590 organic liquids at 293.2 K. J Chem Eng Data 35(1):24–25. 60. Raue A, Kreutz C, Maiwald T, Bachmann J, Schilling M, https://doi.org/10.1021/je00059a007 Klingmuller ¨ U, Timmer J (2009) Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics 25(15):1923– Publisher’s note Springer Nature remains neutral with regard to 1929. https://doi.org/10.1093/bioinformatics/btp358 jurisdictional claims in published maps and institutional affiliations.

Journal

Journal of Flow ChemistrySpringer Journals

Published: Sep 1, 2021

Keywords: Artemisinin; Singlet oxygen; Photooxygenation; Kinetic analysis; Taylor flow

References