Model‐based equipment design for the biphasic production of 5‐hydroxymethylfurfural in a tubular reactor

Funding information German Research FoundationDeutsche Forschungsgemeinschaft, Grant/Award Number: EXC2186 Abstract Herein, a novel concept for the acid catalyzed dehydration of fructose (FRC) to 5-hydroxymethylfurfural (5-HMF) in a biphasic tubular reactor is presented. Reaction kinetic models were developed based on experiments performed in a newly developed lab-scale autoclave that enables a decoupled investigation of singlephase reaction and 5-HMF mass transfer. Our reaction kinetic models allow an accurate description of the biphasic reaction. Subsequently, we integrate the reaction kinetic models in the model-based design of a tailored reactor unit. This reactor unit employs the concept of in-situ extraction in a countercurrent flow of a monodisperse droplet swarm within a continuous aqueous phase. From reactor calculations, we obtain a maximum 5-HMF yield of 76% at full FRC conversion. Countercurrent in-situ extraction enables over 99% 5-HMF recovery in the organic phase.


| INTRODUCTION
The efficient production and purification of the important platform chemical 5-hydroxymethylfurfural (5-HMF) represents a challenging task. 5-HMF contains reactive alcohol and aldehyde functional groups leading to the formation of undesired byproducts, namely humins. 1 Promising concepts envisage an integrated process of reaction and in situ extraction in order to increase the overall product yield. 2,3 Torres et al 4 proposed a countercurrent Graesser extractor 5 for the continuous production of 5-HMF from fructose (FRC). In their study, significant reduction of 5-HMF production costs can be achieved using the concept of countercurrent in-situ extraction. Recent experimental studies on the continuous production Several kinetic models for the acid catalyzed dehydration of FRC to 5-HMF and levulinic acid (LA) have been proposed. 1 In our study, we use sulfuric acid (H 2 SO 4 ), as this catalyst showed very good activity in previous investigations. 10 The kinetic model for H 2 SO 4 catalyzed FRC dehydration by Fachri et al 10  To extend the data for the H 2 SO 4 catalyzed FRC dehydration to even lower temperatures, we investigate the reaction in a temperature range of T = (378 to 408) K. We compare two different kinetic models differing in the description of the side reactions. Both models are extended by a detailed description of the extraction of 5-HMF from the aqueous phase into an organic solvent. In our study we use 2-methyltetrahydrofuran (2-MTHF) as solvent because it has advantageous attributes such as acidic stability, low boiling point and low ecotoxicity. 12 Furthermore, the solvent system 2-MTHF/water features a stable miscibility gap in the temperature range of T = (293 to 423) K. 13 The mass transfer model is developed by conducting extraction experiments at the relevant reaction temperatures.
Comprehensive models for biphasic tubular reactors for liquid-liquid reactions can be found in literature. [14][15][16][17] These models have in common that the column is separated in several stages which are modeled as a cascade of ideally stirred tank reactors. It is typically assumed that the liquid phases are in equilibrium and hence mass transfer can be neglected. Moreover, fluid dynamics are not modeled in detail and the phase ratio in the reactor has to be estimated. Our herein presented model explicitly considers mass transfer as well as fluid dynamics in the biphasic countercurrent reactor. Levulinic acid (LA) (purity >99%) was purchased from Sigma Aldrich (Steinheim, Germany). Water-free sodium sulfate (Na 2 SO 4 ) (purity >99%) was purchased at VWR chemicals (Darmstadt, Germany). We used bidistilled water for all experimental solutions.

| Experimental set up
All experiments are conducted in a custom made lab-scale reactor (premex GmbH, Lyss, Switzerland, see Figure 1). The design of the reactor is inspired by Nitsch et al. 18,19 The nominal volume of the reactor is 0.5 × 10 −3 m 3 . The reactor is equipped with two independent stirrers (1,2) for the convection of the organic and aqueous phase. All biphasic experiments are conducted with a stable phase boundary, hence glass internals (3) are installed to provide stable flow conditions. Two glass windows allow visual control of the phase boundary (4). The vessel is manufactured from C-22 Hastelloy in order to withstand inorganic acids. The reactor has a maximum design temperature of 423 K and a maximum design pressure of 15 MPa. Temperature inside the reactor is measured with a type-K thermocouple.
The reactor is equipped with a heating jacket that is controlled with a PID controller implemented in a custom made LabView program (ver. In our investigations, concentrations of reactants and products are small on a molar basis. Therefore, we neglect changes in total liquid volume due to water formation of the dehydration reaction. We give attention to the volume of each sample being always in the range of 0.1% of the total liquid volume in the autoclave. In order to minimize the sampling error caused by residual liquid in the tubing of the sampling port, air from the sampling syringe is used to flush the sampling port.
To determine the influence of temperature and the presence of

| Single-phase reaction kinetics
Experimental and modeled concentration data is used to calculate the conversion of FRC (X FRC ), and selectivity (S i ) and yield (Y i ) of the detectable products in the HPLC analysis according to the following equations: The respective total carbon yield is calculated with We compare two different reaction pathways in this work to describe the time-dependent concentration profiles of the singlephase reaction (see Figure 2). Details on the system of rate equations for both models and the formulation of the system of ordinary differential equations (ODE) can be found in section 3 of the Supporting Information. Parameter values for pre-exponential factors and activation energies are determined using the MATLAB software package (build 2018Ra). 21 We perform a least squares minimization between experimental and modeling data using the lsqnonlin function. Following the approach proposed by Fachri et al 10  Investigations on 5-HMF formation in absence of water where 5-HMF is assumed to be stable also show that humins production is suppressed. 25-27

| Calculation of partition coefficients and modeling of mass transfer
The calculation of the mass transfer rate requires knowledge of the equilibrium state which can be represented by the partition coefficient 5 K. We calculate K based on data obtained in the equilibrium measurements described in Section 2.3 with The concentration of 5-HMF in the aqueous phase C eq HMF,aq is directly obtained from HPLC measurements. Raman spectroscopy is calibrated in mole fractions, hence the measured data has to be multiplied with the respective molar density of the organic phase at the respective temperature. To account for the temperature sensitivity of the molar density in the binary system 2-MTHF/water, we use the PC-SAFT 6P model from 28 in Aspen Plus ver. 8.8. 29 5-HMF mole fractions in the organic phase are in the range of 1 mol%. Assuming an F I G U R E 2 Kinetic models used in this work to describe the single-and biphasic reaction. Model 1 with second order side reaction (this work) and Model 2 with two independent first order side reactions (according to Reference 10) ideal mixture we estimated the influence of 5-HMF on molar density of the organic phase to be less than 0.5%.
The change in 5-HMF concentration due to mass transfer in both the aqueous and organic phase can be calculated with. 5 Similar to Raman spectroscopy, FT-IR spectroscopy is calibrated in mole fractions. To obtain values for C HMF,aq we multiply the measured mole fractions with the molar density of the aqueous phase at the respective temperature using the PC-SAFT 6P model in Aspen Plus ver. 8.8. 28 We use values for the partition coefficient K at 383 and 393 K from equilibrium measurements. The mass transfer rate R 5-HMF is calculated from the interfacial area for mass transfer per unit volume a and the overall mass transfer coefficient k od . All mass transfer experiments are performed at a stable phase boundary, hence the interfacial area for mass transfer per unit volume can be calculated from the autoclave's diameter D A and the liquid volume To account for the change in V org with increasing temperature, we use the PC-SAFT 6P model from 28 to calculate V org at 383 and 393 K.
Values for k od are determined via least squares minimization in MATLAB. 21 Both differential Equations (8) and (9) are solved using the ode45 solver. 21 Initial concentrations for C HMF,aq (t = 0) and C HMF,org (t = 0) are obtained from measured data in the aqueous and organic phase. We solve the following optimization problem using the fminsearch function in MATLAB 21 min kod X n total n = 1 C HMF,aq,calc,n − C HMF,aq,meas,n À Á 2 + C HMF,org,calc,n −C HMF,org,meas,n À with n total being the total number of experimental data points for each individual experiment.
Mass transfer experiments are performed at equal Reynolds numbers in both the aqueous and the organic phase. The Reynolds number is calculated from The

| Reactor model development
We  To reduce the complexity of the system, we assume no internal circulation inside the droplets occurs and the droplets do not deform. 32 For this case, the free sedimentation velocity v 0 of a single droplet is only dependent on the two liquid phase's densities ρ c and ρ d , the droplet diameter d p and the drag coefficient c D . The velocity is then calculated from 32 : where the drag coefficient c D is given by The kinematic relationship of a droplet swarm and the absolute Consequently, the fluid dynamics are specified by Equations (13)- (15) and (17), correlating the fluid dynamic and process parameters.

| Concentration profile
The temporal behavior of the spatial concentration profile is modeled by the partial differential equation system On the left hand side of the equation, the change of concentration per time is given. The first term on the right hand side describes the mass transport due to convection in axial direction of the column. The corresponding velocities of the continuous and disperse phase result from the calculation of the fluid dynamics.
The second term on the right hand side of Equations (18) and (19) describes the mass transport due to axial back mixing or dispersion, which is physically generated by the flow of the droplets for pulsated sieve tray columns shows a variation in 5-HMF yield of less than 1%.
The third terms on the right hand side of Equations (18) and (19) are source terms as r i designates the reaction rate of the particular component. Depending on the reaction kinetic mechanism of the dehydration reaction and the mass transfer rate _ n HMF (see Equation (21) Due to the nonlinear source terms occurring in the first reaction kinetic model, deriving an analytical solution of the coupled PDE system is impossible. Therefore, we semi-discretize the PDE system in space to obtain an ordinary differential equation (ODE) system in time. 34 As the space-discretization leads to an ill-conditioned block triagonal matrix depending on the mesh size of the discretization, the resulting ODE system is stiff. 34 We use the MATLAB solver of carbon assigned to humins formation (see Equation (4)) is also captured well by both models.
In addition to experiments starting from FRC as substrate, we also performed experiments starting from a mixture of FRC and 5-HMF.
The rational behind these experiments is to provide high initial con- A comparison of the obtained kinetic parameters for both kinetic models along with parameters reported in literature is done in the following. Table 1 lists the parameters for both kinetic models developed in this work compared with parameters from Fachri et al, 10 Girisuta et al, 36

| Biphasic reaction
In order to validate both models with respect to their performance in the biphasic reaction, a biphasic experiment is conducted according At long reaction times both models overpredict the 5-HMF concentration in the organic phase. The concentration in the organic phase is measured with inline Raman spectroscopy. At reaction times longer than 20 min, we find an increase in scattering of the data compared to the data in the range of 0-20 min. We assume this is due to a fluorescence effect caused by soluble humins species. This fluorescence effect corrupts the signal and can lead to an erroneous quantification of 5-HMF. 40 Considering that our kinetic models were not adjusted to the experimental data of the biphasic reaction, the quality of the model prediction is acceptable. In the following, we will use both reaction kinetic models developed in this work to describe the reaction in a single and biphasic tubular reactor.

| Single-phase reactor
The results from the modeled selectivity of the single-phase reaction are depicted in Figure 11. We perform calculations for the single- with increasing temperature, which is in good agreement to previously reported results. 10,41,42 An explanation for this different temperature sensitivity of Model 1 and Model 2 can be found by comparison of the activation energies for both models. The coupled side reaction in Model 1 has the highest activation energy of all reaction steps which results in an increased selectivity to humins at high temperatures. 35 The activation energy for 5-HMF rehydration to LA and FA on the other hand is smallest, which is in agreement to Swift et al 41 and Fachri et al. 10 Rehydration to LA is therefore suppressed at high temperatures.
However, in Model 1 the reduced rate in rehydration of 5-HMF to LA and FA is not able to compensate the increase in humins formation rate, thus resulting in an overall lower 5-HMF selectivity at high temperatures.
The structure of Model 2 is similar to already reported kinetic models. 10,41 Because our obtained activation energies are also comparable (see Table 1), the reduced rate of 5-HMF rehydration to LA and FA at high temperatures is able to compensate for the higher selectivity to humins formed directly from FRC. In the case of FRC dehydration catalyzed by HCl modeled according to Swift et al, 41 the reduced formation of LA and FA can even overcompensate the higher selectivity to humins, leading to higher 5-HMF yields at higher temperatures.
Using H 2 SO 4 as catalyst according to Fachri et al, 10 the increase of 5-HMF selectivity with increasing temperature is less pronounced.
We also attempted to integrate a further side reaction to humins in Model 1 starting only from 5-HMF to yield a more accurate description of the temperature sensitivity on 5-HMF selectivity (results not shown). However, the resulting parameters from the data regression for the parallel reaction of 5-HMF to humins had very large confidence intervals which made the obtained parameters questionable.
The differences in the 5-HMF selectivity also reflects in the overall yield, which is presented in Figure 12 for both kinetic models. The maximum yield for both kinetic models is obtained at about 70% conversion which is in good agreement to our experimental data (see  To account for the effect of droplet diameter on 5-HMF yield in a technical relevant range, 9 we provide data of a sensitivity study in section 10 of the Supporting Information. At the herein investigated reaction conditions, the increase in 5-HMF yield due to smaller droplets is less than 1%.

| Biphasic countercurrent reactor
Selectivity for 5-HMF in the biphasic reactor is discussed as a function of conversion ( Figure 14). Compared to single phase operation, the decrease in selectivity with increasing conversion is significantly lower which can be attributed to the in-situ extraction of Despite the differences in the solvent system and temperature, the results from our modeling studies conducted with Model 1 are comparable to these experimental results. 6,7,43 The 5-HMF yield in the biphasic tubular reactor calculated with Model 2 is lower, which is due to the structure of the kinetic model. In Model 2, the formation of humins from FRC is modeled as an isolated parallel reaction, which sets a limitation to the overall 5-HMF yield. 4 Shimanouchi et al 6 also differentiate between the 5-HMF yield in the MIBK phase and the total 5-HMF yield and find that almost 50% of the produced 5-HMF remains in the aqueous phase. Due to the efficient countercurrent extraction in the herein developed tubular reactor, over 99% of the produced 5-HMF is present in the organic phase (see Supporting Information). This is in good agreement to results reported by Sindermann et al 31 for countercurrent extraction of 5-HMF on a technical scale. We believe this is a major benefit of our concept with regard to an overall 5-HMF production process.
Employing the concept of a countercurrent in-situ extraction, downstream processing of the aqueous phase can be significantly simplified Compared to single-phase operation, LA and FA selectivity is also significantly decreased. Based on calculations with Model 1, LA and FA yield is reduced from 67 to 14% and with Model 2 from 47 to 9%.
Despite the lower LA and FA yield with Model 2, the total carbon yield (calculated with Equation (6) Model 2 allows a more consistent description of the temperature sensitivity for product distribution in the single-phase system (see Section 4.4.1). Model 1 on the other hand enables the calculation of higher 5-HMF yields in biphasic systems, which is more in line with recent results from experiments in microreactors. 6,7,20,43 A logical next step is therefore to combine the beneficial attributes of both models by providing further data at higher reaction temperatures and more detailed analytics for the inline characterization of humins. Based on these data we develop reaction kinetic models for the description of the aqueous phase reaction.

| CONCLUSION
Furthermore, the lab-scale reactor enables us to investigate partition coefficients and mass transfer of 5-HMF from the aqueous into the organic phase in the same temperature range as in the singlephase reaction experiments. We subsequently extend the reaction kinetic models by including a detailed description of 5-HMF mass transfer from the aqueous into the organic phase. Experimental validation reveals that both reaction kinetic models developed in this study allow a satisfying prediction of the biphasic reaction.
For technical scale-up of this biphasic reaction, we propose a countercurrent tubular reactor as an integrated unit operation for the production of 5-HMF from FRC.
Our one-dimensional rate model calculates a dynamic concentration profile over the reactor height. The formation of 5-HMF in the aqueous phase and the extraction of 5-HMF into the organic phase is described by the validated reaction kinetic models developed in this work. Moreover, we consider technical scale fluid dynamics by a detailed description of the dispersed phase applying models for droplet swarm sedimentation.
From our reactor modeling study we obtain a maximum 5-HMF yield of 76% at 100% FRC conversion. A further advantage of this reactor concept is the very efficient extraction of 5-HMF (>99%) which facilitates downstream processing of the aqueous phase.