Modelling studies of enantioselective extraction of an amino acid derivative in slug flow capillary microreactors

This work shows that enantioselective liquid–liquid extraction in microreactors is attractive for chiral separation. A precise control over the residence time in microreactors results in high enantiopurities and low host inventories. Mathematical modelling has been presented to describe the experimental results on the enantioselective extraction of an aqueous racemic amino acid derivative (3,5-dinitrobenzoyl-(R,S)-leucine) with a cinchona alkaloid chiral host in 1-octanol using a slug flow capillary microreactor (at an aqueous to organic flow ratio of 1:1). A good agreement between the model predictions and experimental results was obtained by taking the enhancement of the mass transfer rates due to the reactions in the aqueous and organic phases into account. An enantiomeric excess of the (S)-enantiomer higher than the equilibrium value was observed especially at shorter residence times due to kinetic effects. The observed phenomena could be explained by an instantaneous rate of the complexation of the (S)-enantiomer with the host and a finite rate of the complexation of the (R)enantiomer. The developed model was used to determine guidelines for multi-stage operation in microreactors in order to increase yield and enantiopurity.


Introduction
In the last few decades, the demand for enantiopure compounds has increased rapidly [1][2][3][4][5]. For example, in pharmaceutical industries this is due to the often different biological activity of each enantiomer leading to different pharmacological activities and different pharmacokinetic or toxicity effects [1][2][3][4]. Racemic production followed by chiral separation is currently being used for the majority of the synthetic single enantiomer products [6,7].
Crystallization and chromatographic methods seem to be the most advanced for chiral separations [8,12,14]. The main drawbacks of crystallization-based chiral separation methods are a limited flexibility and solid handling [8,35,37,41]. Chromatography-based methods have been demonstrated on small scale [8,14]. Although modifications allow for continuous operation on the preparative scale, this method is technically relatively complicated and suffers from high capital cost [6,8,16].
In enantioselective liquid-liquid extraction (ELLE), a solution of a racemic mixture is contacted with an immiscible solution containing a chiral host. The host complexates preferentially with one of the enantiomers. ELLE is an alternative when classical resolution using crystallization is not possible [44,45]. Several experimental and modelling studies on ELLE for the separation of a racemic mixture to obtain an enantiopure compound have been reported [6,[46][47][48][49][50][51][52][53][54]. Advantages of ELLE include the ease of scale up and the possibility to use one host family for the separation of multiple racemates [8,35,43].
The proof of concept for ELLE in a continuous centrifugal contactor separator (CCCS) has been reported [32,33,[46][47][48]. For example, ELLE of 3,5-dinitrobenzoyl-(R,S)-leucine (DNB-(R,S)-Leu) with a cinchona alkaloid (CA) host in 1,2-dichloroethane (1,2-DCE) has been demonstrated in a single CCCS. An (S)-enantiomer excess (ee org ) of 34% and a yield of 61% were obtained [32]. With six CCCS devices in series, operated countercurrently, up to 98% ee was obtained [33]. However, a large host inventory was present due to the high hold-up of the organic phase in the CCCS devices, indicating a significant cost increase.
Alternatives to a CCCS for continuous ELLE have been reported with the use of intensified columns and microreactors [25,26,44]. Kockmann and co-workers [25,26] have reported the use of intensified columns for similar systems (ELLE of DNB-(R,S)-Leu with a CA host). The process involved countercurrent operation with stirring and pulsation, resulting in a large number of stages and a good separation with an ee of up to 98.6% and 85.8% for the (R)-and (S)-enantiomers, respectively [26]. Microreactors operated under slug flow are another alternative for ELLE, with advantages including a precise process control, an enhanced extraction efficiency, a reduced reactor volume, a low host and solvent inventory, and easy scaling-up [55][56][57][58][59][60][61][62][63]. Such slug flow microreactors offer a superior control over the temperature and residence time [64,65]. Both are critical for obtaining a high operational selectivity in chiral separation [66]. The mass transfer and extraction rates are enhanced by internal circulation in the droplets and liquid slugs [67]. Microreactors for ELLE have simple setups without moving parts and are relatively easy to scale up to pharmaceutical production scales [60,68].
Recently, we have investigated ELLE in capillary microreactors under slug flow operation for the enantioselective extraction of an aqueous solution of DNB-(R,S)-Leu ( Fig. 1) with a cinchona alkaloid host that was applied in organic solvents including 1,2-DCE and 1-octanol [44]. The experiments showed that the concentration of the enantiomers at the microreactor outlet turned out to be a function of the residence time for a given aqueous to organic flow ratio and enantiomer/host intake. Interestingly, when using 1-octanol as the solvent, the (S)-enantiomer excess in the organic phase was higher at short residence times than the ee at equilibrium. This finding indicates that non-equilibrium ELLE operation in microreactors may have high potential for future application. A detailed mass transfer and extraction analysis to identify the factors responsible for the above findings is thus the main purpose of this work.

ELLE in capillary microreactors
The extraction procedure and experimental apparatus have been described in detail previously [44]. Here a brief overview is provided, with the flow and ELLE schematics shown in Fig. 2. The aqueous phase inlet consisted of 1 mM DNB-(R,S)-leu in 0.1 M phosphate buffer (pH 6.58) and organic phase inlet 1 mM CA in 1-octanol. Extraction experiments were operated in the slug flow regime using capillary microreactors made of polytetrafluoroethylene (PTFE) tubing with an inner diameter of 0.8 mm, under conditions as shown in Table 1. After extraction in the microreactor, the immiscible liquids were separated at the end of the microreactor using a Y-splitter consisting of a PTFE exit and a glass exit. Phase separation is based on the preferential wettability (i.e., the aqueous phase prefers glass, the organic phase PTFE). The compositions of the aqueous phase at the microreactor inlet and outlet were analyzed via HPLC.
As can be seen in Table 1, the extraction was carried out in the microreactor of different lengths at an aqueous to organic flow ratio of 1:1. The residence time (τ) was between 22 and 905 s, which is defined as where V c , d c and L c are the volume, inner diameter and length of the capillary microreactor, respectively. Q aq and Q org denote the volumetric flow rates of the aqueous and organic phases, respectively.

Determination of ELLE equilibrium constants in batch reactors
Here, batch experiments with 1-octanol as solvent are described. The experiments were carried out in 20 mL glass flasks. A series of 10 mL unbuffered aqueous DNB-(R,S)-Leu solutions with a concentration in a range of (0.5-3.2) × 10 −4 mol/L were mixed with 1 mL 1octanol to determine the physical partitioning over the phases in the absence of CA. Stirring was done with a Teflon bar for 14 h. Afterwards, both phases were allowed to settle for one hour and separated. The pH of the aqueous phase was measured and its composition was analyzed by HPLC. The enantiomer concentration in the organic phase was calculated according to the mass balance.
The complexation constants for the reactions between each enantiomer and CA were determined using reactive extraction. 1 mL buffered (pH 6.58) racemic aqueous DNB-(R,S)-leu solution (1 mM) and 1 mL of host solution (1 mM) were mixed in 20 mL glass flasks under stirring using a Teflon bar for 14 h. After equilibrium and settling, both phases were separated. The enantiomer concentration in the aqueous phase was analyzed by HPLC. The organic phase concentration was calculated according to the mass balance.

Analytical procedure
Concentrations of the enantiomers in the aqueous phase were measured using HPLC (Shimadzu SIL-20A) equipped with a chiral column (Astec/Chirobiotic T). The eluent was a 3:1 (v/v) mixture of acetonitrile and methanol with 0.25 vol.% triethylamine and 0.25 vol.% acetic acid. The pH of the aqueous phase was measured using an InoLab pH 730 pH-meter equipped with a SenTix 81 probe (WTW, Germany).

Model development
The scheme of the extraction mechanism is similar to the model used and validated by Schuur et al. [35,70], see Fig. 3. DNB-(R,S)-Leu is a weak acid [70], so it exists in the aqueous phase in the neutral and dissociated forms. Only the neutral form is transported to the organic phase and can combine with the host.
The component balance of the (S)-enantiomer in the aqueous phase when flowing in the microreactor reads . The corresponding balances for the organic phase read

Calculation of the molar fluxes
In mass transfer applications, the fluxes between different phases are usually calculated using one of two widely used models: the film model or the penetration model [71]. The fluxes are obtained from solving a set of equations that describe the combined effects of diffusive transport and reactions in a particular phase near the interface. Applying the film model, we have for the aqueous phase

R
denotes its local production rate, x is the distance from the interface and δ is the so-called film thickness of the film model. Analogously, for the organic phase a set of equations, one for each component (i.e., S, R, C, SC or RC; Fig. 3), can be written. Both sets can then be solved simultaneously for the gradients at the interface that allow for the calculation of the interfacial fluxes. The equations for the two phases are coupled at the interface by the solubility condition The partition coefficient (m) was determined from physical extraction experiments in the absence of a pH buffer in batch reactors, using DNB-(R,S)-Leu solutions with a concentration in a range of (0.5-3.2) × 10 −4 M (Section 2.3). m was found to be a constant of 26.73 according to Eq. (7). The constant value of m is reasonable and also applicable in the current microreactor study that dealt with a diluted enantiomer concentration in both the organic and aqueous phases. For example, ELLE experiments in microreactors (and the subsequent modelling thereof) were performed for an inlet aqueous concentration of DNB-(R,S)-Leu at 1 mM in the presence of a buffer (pH 6.58). Under such pH conditions (≫pK a ), each enantiomer was present in the aqueous phase predominantly in the dissociated form ( Fig. 3) and thus the concentration of each enantiomer in the neutral form therein was at a very low level (ca. on the order of 10 −7 M).
The solution of coupled sets of nonlinear differential equations in the form of Eq. (6) can be circumvented by using the concept of chemical enhancement factors. Then, the mass transfer rates can be obtained from the physical fluxes, i.e. without reaction, augmented by the enhancement factors. The partial fluxes can be written in the following form for the aqueous phase S aq  aq bulk  aq I  , ,, and for the organic phase where the overall mass transfer coefficients of the (S)-and (R)-enantiomers follow from

Bulk phase concentrations
In the aqueous phase, the ionization reactions (see Fig. 3) are assumed to be very fast and to be always at equilibrium [72]. Then, the aqueous liquid bulk phase concentrations follow from the dissociation equilibria  (16) and the component balances for the enantiomers: In the organic phase, the reaction is also assumed to be fast enough that the complex formation is always at equilibrium:    (20) The organic phase bulk concentrations can be calculated from Eqs. (19) and (20) together with the component balance of the host (i.e., no dissolution of the host and its complex forms in the aqueous phase; see Fig. 3).

Interfacial area
The interfacial area (a) in slug flow was calculated [67], based on our experimental measurements on the droplet lengths (3.57 ± 0.15 mm) and slug lengths (3.53 ± 0.04 mm) using Given the fixed 1:1 aqueous to organic flow ratio used, a was found to be almost constant (ca. 2488 ± 46 m 2 /m 3 ).

Overall mass transfer coefficient
In our previous work [67], the overall physical mass transfer coefficient without reaction for the investigated microreactor under slug flow operation has been developed based on the penetration theory and additional contribution of internal circulation as Eq. (23) is for the case of the (S)-enantiomer (and similarly for the (R)-enantiomer). To allow for mass transfer enhancement due to the chemical reactions in both phases, the enhancement factors have to be incorporated. Thus, the overall mass transfer coefficient with chemical reactions is obtained for the case of the (S)-enantiomer as Eqs. (23) and (24) are applicable for the current chiral extraction system, given 1:1 aqueous to organic flow ratio, Fourier number typically < 0.1, and the fact that the extraction performance at a constant temperature indeed turned out to be just a function of the residence time (i.e., independent of the flow rate or microreactor length; cf. Appendix A).

Enhancement factor
Enhancement factors according to the film model can be calculated by solving the simultaneous sets of differential equations (Eq. (6)) for the aqueous phase or similar ones for the organic phase. Fortunately, fairly accurate estimation methods are available to calculate the enhancement factors. Generally, these methods obtain an approximate analytical solution by applying a suitable linearization of the differential equations.
Regarding the complexation of each enantiomer with the host in the organic phase, using the results of Onda et al. [73] rewritten in our notation gives for the (R)-enantiomer where the equilibrium constant is contained in the parameter g R and the second-order forward reaction rate constant (k 2,R ) in the parameter ϕ R . The parameters are defined in the Nomenclature section. Note that here the complexation is assumed first order with respect to the enantiomer and the host, respectively. In the limiting case where the reaction rate in the film is much faster than the diffusion rate, Eq. (25) simplifies to the so-called enhancement factor for an instantaneous reaction [74]: Similarly, the enhancement factor for an instantaneous reaction in the case of the (S)-enantiomer reads The dissociation of each enantiomer in the aqueous phase is assumed in equilibrium everywhere in the aqueous phase. Accordingly, , .
∞ Eaq, is a constant under the present conditions (pH 6.58) and denotes the instantaneous enhancement factor for the dissociation of the (S)-or (R)-enantiomer in the aqueous phase (see Appendix B for details). Here, the diffusivities of each enantiomer in its neutral and dissociated forms are assumed equal for a first approximation (i.e.,

Activity coefficient
The activity coefficients (γ) of the ionic species in the aqueous solution were obtained from the Debye-Hückel law [75].
where z x is the charge number of the ion species x. The values of the constants p and q for the aqueous sodium chloride solutions at 25˚C were taken here as an approximation (i.e., p = 0.5115 and q = 1.316) [75]. The ionic strength (I) is calculated according to where C x denotes the molarity (mol/L) of the ionic species x. Since the concentrations of the enantiomers in the neutral forms were very low in this study (ca. on the order of 10 −7 M), their activity coefficients are assumed to be 1.

Physical properties of the system
The physical properties of the solvent and chemicals used are shown in Tables 2 and 3 Here D A B , represents the diffusivity of solute A in solvent B. The solvent viscosity (μ B ) is in cP, the solute molar volume at the normal boiling point (ν A ) is in cm 3 /mol and φ B represents the solvent association (being 2.6 for water, 1.9 for methanol, 1.5 for ethanol and 1 for unassociated solvents) [76]. Since the diffusivity approximation using the Wilke-Chang equation is applicable for solvents like water, low alcohol (e.g., methanol, ethanol) and unassociated ones, the enantiomer and host diffusivities in 1-octanol were approximated following the Stokes-Einstein equation (Eq. (32)), using the corresponding diffusivities in water Table 2 Physical properties of the solvents used (T = 25˚C) [78]. and 1,2-DCE as a reference, respectively [77].
The diffusivities of host (C) and its combined form (SC or RC) are assumed to be equal for a first approximation, given the much larger molar volume of host than that of the enantiomer.

Numerical solution method
The concentrations of the enantiomers in the microreactor were obtained by numerically solving the reactor equations (Eqs. (2)-(5)) in an outer loop. A stepwise approach was employed where the microreactor was divided into n equally-spaced segments (see Fig. 4). At sufficiently large values of n, the concentrations can be taken constant within each segment k (k = 1, 2, …, n), given negligible amount of extraction therein. From the concentrations in the two phases, the mass transfer rates of the components were calculated using the methods of Sections 3.1-3.3. The mass transfer rates were obtained iteratively in an inner loop. They were used to update the host and enantiomer concentrations at the outlet of the segment to account for the extraction within the segment in order to fulfil the mass balance. The modelling then proceeded to the next segment. This numeric approximation converges at sufficiently large n values (see Appendix C for more detailed discussion). The mathematical formulation was translated to computer codes and solved using Matlab software (version R2016a, The Mathworks Inc.).

Equilibrium extraction
The equilibrium constants for the complexation reaction between DNB-(R,S)-Leu and CA in the 1-octanol system are shown in Table 4. The value of K S is higher than K R , indicating that the host CA preferentially complexates with the (S)-enantiomer over the (R)-enantiomer similar to the 1,2-DCE system as reported by Schuur et al. [70]. Also the intrinsic selectivity, defined as K S /K R , is comparable in 1octanol and 1,2-DCE, with values of 3.24 and 3.43, respectively [70]. With this selectivity nine equilibrium stages are required to obtain at least 99% ee in both phases under total reflux conditions according to the Fenske equation [70]. In a first approach the complexation reactions were assumed to proceed in the instantaneous reaction regime for both enantiomers (model I). The system was thus modelled using the method described in Section 3.4, where the enhancement factors of the (R)-and (S)-enantiomers in the organic phase were obtained from Eqs. (26) and (27), respectively. The relative standard deviation (RSD) between the modelled and experimental values was taken as the indicator for the quality of the model performance, which is calculated by where N is the number of data points. y i model, and y i exp, denote the modelled and experimental values of the parameter (in this case being the enantiomer concentration or the enantiomeric excess) at a specific data point i, respectively. With model I, the aqueous phase exit concentration of the (S)-enantiomer was modelled with an RSD of 10.2%. The fit is better at relatively short residence times and a slight larger deviation exists at relatively large residence times approaching equilibrium (Fig. 5). The corresponding concentrations of the (R)-enantiomer were predicted better, with an RSD of 4.6%.
An important parameter in enantiomeric separation is the enantiomeric excess (ee), defined for the current system as The observed and modelled ee data are shown in Fig. 6. The modelled values show large deviations from the experimental data. Also the predicted ee org shows a faulty qualitative behavior with a small initial increase whereas a considerable initial decrease was observed experimentally. A detailed analysis of the results showed that the deviations of the ee are mainly due to an underestimation in the modelled values at relatively large residence times (see Fig. 5). In other words, a good modelling of the ee is highly sensitive to the prediction accuracy of the enantiomer concentration.

Model II: instantaneous complexation rate for the (S)-enantiomer and finite complexation rate for the (R)-enantiomer
The observed deviations with model I, both in the exit concentrations and the ee values, suggest that the complexation rate of the (R)enantiomer is not fast enough to be taken as instantaneous. Therefore in model II, the complexation of the (R)-enantiomer is taken to proceed with a finite rate. The complexation of the (S)-enantiomer is still assumed to proceed instantaneously. In more detail, the system was modelled using the method described in Section 3.4. The enhancement factor of the (S)-enantiomer in the organic phase was obtained from Eq. (27), and that of the (R)-enantiomer was obtained from Eq. (25) based on an assumed value of the second-order forward reaction rate constant (k 2,R ) for its complexation with the host. In the modelling, the optimized value of k 2,R was determined, at which the deviation between the model prediction and the measured ee org value (expressed as the sum of the squares of residuals (SSR); see definition in Eq. (36)) reached its minimum.   The optimized value of k 2,R with a 95% confidence interval was found as (5 ± 1.1) × 10 5 L/(mol·s). The 95% confidence interval was estimated based on the following equation [ where SSR min and SSR 95% are the minimum value of SSR related to the ee org and the value of SSR at a 95% confidence level, respectively. The function F represents the F-distribution. With the estimated SSR 95% from Eq. (37), the corresponding lower and upper limits of k 2,R in the confidence interval were subsequently obtained from the modelling. With this model II, the aqueous phase exit concentrations as well as the ee org and ee aq were modelled satisfactory, see Fig. 7a and 7b, respectively. Importantly, the ee org values now have a correct qualitative and quantitative behavior as a function of the residence time. The relative standard deviations of the predicted values as compared to the measured data were 5.7% and 10.3% for the ee org and ee aq , respectively ( Table 5). The improved performance of model II can be attributed mainly to a more accurate representation of the exit concentration of the (R)-enantiomer, especially at relatively short residence times (Fig. 7a).
The optimized value of k 2,R at 5 × 10 5 L/(mol·s) implies that the rate of complexation of the (R)-enantiomer is intrinsically fast. This is Table 4 Equilibrium constants involved in ELLE of DNB-(R,S)-Leu with CA in 1-octanol at room temperature.

Parameter
Value Dimension     supported by the results of separate observations with batch reactors (not shown here) where equilibrium was reached within 1 min after mixing of equal amounts of the aqueous and organic phases. The reaction regime of the complexation of the (R)-enantiomer in relation to the mass transfer rate in the organic phase can be identified by considering the Hatta number (Ha R ) and the enhancement factor (E R org , ). Both numbers are plotted versus the residence time in Fig. 8 according to model II. Generally, the rate of the reaction is considered instantaneous compared to the rate of mass transfer if Ha R ≫ E R org , [73]. From Fig. 8, it is clear that this criterion is satisfied only at relatively long residence times (e.g., at τ > 50 s). Especially at short residence times, the reaction regime for the complexation of the (R)-enantiomer was in either the slow or fast complexation regime [80], but not in the instantaneous regime.
The experimental observations and the results of model II show that at short residence times, a high ee org can be achieved. Importantly, the ee org values found here are much higher than the values at equilibrium conditions (i.e., obtained at sufficiently long residence times). These results could be obtained with the microreactor because it allows for slug flow operation with short residence times and an intrinsically narrow residence time distribution [81]. With short residence times, the extraction rate of the (R)-enantiomer was determined by both the physical mass transfer rate as well as the complexation rate. At the same time the extraction rate of the (S)-enantiomer was completely mass transfer limited (given the instantaneous complexation rate assumed). Therefore, it is the kinetic effect of the (R)-enantiomer complex formation that primarily caused the high ee org at short residence times. In other words, at such short residence times the intrinsic complexation rate of each enantiomer, when compared with the physical mass transfer rate, showed a large difference, which resulted in a more favorable enrichment of the (S)-enantiomer. Thus, a higher ee org values than the equilibrium ones were obtained. The results obtained here with model II further suggest that such chiral separations can be realized in a highly controllable and predictive way in slug flow microreactors.

Process simulation for multi-stage ELLE operation
Using the current microreactor system, a high ee org can be achieved by performing chiral extraction at short residence times. However, the yield of the (S)-enantiomer is very low then [44]. To improve the yield, a multi-stage ELLE operation is suggested. Here two options for multistage operation are modelled and discussed.
The first option is a cross flow configuration where the aqueous stream continuously flows from one stage to the next and fresh organic feed is supplied at each stage (Fig. 9). The flow rate ratios between the organic and aqueous phases are kept the same in all stages (i.e., at 1:1). The exit concentrations for each stage were obtained using model II. The overall ee org and the overall yield of the (S)-enantiomer were obtained from Eqs. (35) and (38), respectively.
The performance of cross flow extraction was assessed by varying the total number of stages from 1 to 5 and using a residence time per stage of 4, 10, 22.6 or 45.2 s. At shorter residence times, it is possible to obtain a higher overall ee org than the equilibrium value, see Fig. 10. Smaller residence times per stage yield higher ee org values. The overall yield of the (S)-enantiomer increases with an increase of the total number of stages due to additional extraction per stage. The overall ee org decreases with an increasing number of stages since, from the second stage onwards, the aqueous phase is more and more enriched with the (R)-enantiomer. Under such circumstances, the extraction of the (R)-enantiomer is increasingly important compared with the extraction of the (S)-enantiomer. Noteworthy, such decrease in the overall ee org is not very pronounced at the shortest residence time modelled (i.e., τ = 4 s per stage). Whereas for τ = 45.2 s or 22.6 s per stage, the extraction should be stopped at stage 3 or 4, respectively, since the organic effluent at the next stage is already slightly enriched with the (R)-enantiomer.
From Fig. 10, it further appears that by operating at shorter residence times per stage, a higher overall ee org is obtained at the cost of a lower overall yield of the (S)-enantiomer. Thus, a proper selection of the residence time and total number of stages is needed for obtaining the desired yield of the (S)-enantiomer and ee org . Typically, at the operational conditions relevant to this figure, an overall yield of the (S)enantiomer over 60% and an overall ee org over 53% are obtained by operation at 4 s per stage in a five-stage cross flow configuration.
The second option for multi-stage operation is an overall countercurrent flow configuration. Inside each microreactor, we still have cocurrent slug flow of the two phases in equal flow rate. The fresh organic feed enters the first stage and flows continuously through the next stages. The aqueous feed enters at the last stage and flows in the opposite direction, see Fig. 11. Model II was again used successively for each stage to calculate the overall system performance, in combination with a trial and error method (i.e., the modelling started with a guess of the aqueous phase inlet concentrations at the first stage, until the modelled aqueous inlet at the last stage matched the fresh aqueous feed composition). Fig. 12 depicts the effects of the total number of stages and the residence time on the overall ee org and yield of the (S)-enantiomer. Again, the total number of stages was varied from 1 to 5 and the residence time per stage was taken as 4, 10, 22.6 or 45.2 s. With countercurrent flow conditions the overall yield of the (S)-enantiomer increases and the overall ee org seems to decrease with an increase of the total number of stages (the latter is especially true if the residence time per stage or the total number of stages is kept short). Similarly, the overall yield of the (S)-enantiomer increases and the overall ee org decreases with an increase of the residence time. Interestingly, the overall ee org is higher than the equilibrium value in all 5 stages modelled only at relatively short residence time operations (e.g., τ = 4 or 10 s per stage), which could be partly explained by the facts that the equilibrium value still increases with an increase of the total number of stages while the overall ee org tends to decrease with an increase of the residence time per stage. Typically, an overall yield of the (S)-enantiomer of more than 50% and an overall ee org of approximately 54% are obtained by operation at 4 s per stage in a five-stage countercurrent flow configuration. Although this extraction performance is slightly inferior to that in cross flow configuration under otherwise equivalent operation Fig. 8. Ha R and E R,org as a function of the residence time according to model II. Susanti et al. Chemical Engineering Journal 354 (2018) [378][379][380][381][382][383][384][385][386][387][388][389][390][391][392] conditions, the countercurrent flow configuration is more attractive in terms of reduced solvent and host uses. In Fig. 13 the single-stage operation is compared with a five-stage countercurrent operation. The total residence time is the same for the two systems. Five-stage operation provides a higher overall yield of the (S)-enantiomer and a higher overall ee org . This effect is caused by a higher local ee org in multi-stage operation due to the shorter residence time per stage. Also in the multi-stage operation larger concentration difference between the phases are found resulting in a higher amount of extraction.
The results shown in this section illustrate the usefulness of process modelling of single-and multi-stage operations. It facilitates a screening process to identify the microreactor arrangement, flow ratio of the phases and operational conditions to obtain a high overall yield and enantiomeric excess. It has to be mentioned that the modelled multistage operation is not optimized, given the used 1:1 aqueous to organic ratio (a pre-requisite for the validity of the overall physical or chemical mass transfer coefficient equations; cf. Eqs. (23) and (24)) [67]. To obtain a favorable ee of each enantiomer (e.g., close to 100%) in practical operations, the cross flow configuration might use a different aqueous-organic flow ratio per stage, and the countercurrent flow configuration might prefer to feed the aqueous racemic solution at the middle stage together with the wash water and organic feed added at the opposite ends of the stages [54]. In this respect, model II still needs to be improved with the inclusion of a more general mass transfer correlation valid for various aqueous-to-organic flow ratios, which requires additional mass transfer study in slug flow microreactors and is under our ongoing work.

Conclusions
This work presents a modelling study of the enantioselective extraction of an aqueous racemic 3,5-dinitrobenzoyl-(R,S)-leucine (1 mM) with cinchona alkaloid as the chiral host (1 mM) in 1-octanol in capillary microreactors (with an internal diameter of 0.8 mm) under slug flow operation at an aqueous to organic flow ratio of 1:1. A good agreement between the model predictions and results of extraction experiments (in terms of the exit enantiomer concentrations and enantiomeric excess) was obtained, by combining in the model the physical mass transfer rate of each enantiomer with the enhancement factor expressions that account for the aqueous dissociation of each enantiomer and its complexation with the host in the organic phase. An enantiomeric excess of the (S)-enantiomer higher than the equilibrium value was observed experimentally at shorter residence times in microreactors, which could be explained by an instantaneous rate of the complexation of the (S)-enantiomer with the host and a finite rate of the complexation of the (R)-enantiomer. In the model, an optimized second-order forward reaction rate constant at around 5 × 10 5 L/ (mol·s) was found for the complexation of the (R)-enantiomer and has to be verified in future kinetic studies.
The model developed in this work can be used for the prediction of the enantioselective extraction performance in single-and multi-stage operations under slug flow in capillary microreactors. Thus, the model allows a pre-screening for the identification of the relevant operational conditions and multi-stage operation scheme towards obtaining high overall yield and ee of the enantiomer, as demonstrated in the illustration examples dealing with cross flow and countercurrent flow configurations up to five stages. However, the current model still needs to be improved in order to expand its validity for other conditions (e.g., for the aqueous-to-organic flow ratios other than 1:1 and other microreactor geometries). This is particularly relevant for performance   Table 1. predictions when using countercurrent multi-stage setups including washing, feeding and stripping sections with the objective to separate racemates in both enantiomers in high yields [54].

Acknowledgements
This work was supported by the STW (through Project 11404: Chiral Separations by Kinetic Extractive Resolution in Microfluidic Devices). Input from all user committee members of the project are gratefully acknowledged.
Appendix A. . Extraction performance as a function of the residence time ELLE experiments in microreactors were conducted at a constant temperature of ca. 23°C. The extraction performance (e.g., characterized by the enantiomer concentration in the aqueous phase at the microreactor outlet) was found just a function of the residence time (i.e., independent of the   Table 1. For a given axial location along the microreactor, the dissociation reaction of each enantiomer in the aqueous phase is assumed to be very fast (i.e., the reaction rate is instantaneous as compared with the physical transport rate of each enantiomer), so that the equilibrium was approached at all points therein. Then, according to the film theory, the total mass balance of the (S)-enantiomer in the film region of the aqueous side (Fig. B.1) is given by [74] Table 1.  Here due to the use of a buffer system (pH = 6.58), the concentration of H + throughout the film region and the bulk region in the aqueous phase is assume to be constant.
Appendix C. . Number of segments along the microreactor and its effect on the model convergence In the modelling, the microreactor was divided axially into n equally-spaced segments. If n is sufficiently large, the extracted amount of each enantiomer into the organic phase in one segment k (k = 1, 2, …, n) is negligibly small compared with its total amount present in the aqueous phase at the inlet of this segment. Then, the concentrations of the (S)-and (R)-enantiomers in each phase, and the concentration of host in the organic phase can be assumed constant throughout each segment k during the respective modelling step. Before the modelling proceeded to the next segment k+1, the concentration values at the outlet of the segment k (equal to the corresponding ones at the inlet of the next segment) should be updated according to the extracted amount, in order to satisfy the mass balance. It is easily understood that if n value is large enough, the modelled concentration profile approaches the actual one (as illustrated in Fig. C.1).
The value of n should be also selected that the model solution convergence has been achieved. The modelled concentration quickly converges to a constant value (i.e., the correct solution) upon increasing n much above 100 for all residence time values relevant to our experiments. Thus, a sufficiently large value of n (> 10,000) was used in the modelling for a comparison with the experimental measurements. Despite the large number of segments in use, the model is still efficient since the calculation time to solve the model was relatively short (on the order of minutes).
It should be noted that the modelling can be also performed using the state-of-the-art ordinary different equation (ODE) solvers in Matlab, which might be more efficient in terms of reduced number of steps and thus more appropriate for more demanding calculations such as countercurrent ELLE in microreactors involving a large number of stages.  Table 1.