Development of the VARICOL Process for the Resolution of Racemic Menthol

Abstract

This paper reports the chiral separation of menthol enantiomers using the VARICOL process to improve productivity. Amylose 3,5-dimethylphenylcarbamate coated on silica gel was employed as the chiral stationary phase, and n-hexane/2-propanol (95/5, v/v) was used as the eluent. To design and optimize the VARICOL process, a linear driving-force model was developed to predict the separation performance. Separation regions of the conventional simulated moving bed (SMB) and VARICOL processes were evaluated and compared. It was found that, under an outlet purity requirement of 95.0%, the five-column VARICOL process has a separation region comparable to that of the six-column conventional SMB process. As an illustrative example, a five-column VARICOL unit and a six-column conventional SMB unit, both operating under the same conditions, were employed to resolve the menthol racemate. Purities for both the extract and raffinate were above 95.0%, and a productivity of 0.400 g_racemate/(L_CSP∙min) and a solvent consumption of 0.355 L/g_racemate were achieved in the VARICOL process. Productivity increased by 20% while solvent consumption maintained relative to the conventional SMB process, though product purities decreased slightly.

1. Introduction

l-menthol, a naturally occurring cyclic monoterpene alcohol [1], is recognized as one of the most important flavors currently [2]. As estimated recently, its global production is more than 34,000 metric tons [3], and its demand is still increasing. It is widely used in candies, chewing gums, cigarettes, cosmetics and pharmaceuticals [4,5]. l-menthol contains three chiral centers in its molecular structure, which leads to seven other optical isomers, including d-menthol, d,l-isomenthol, d,l-neomenthol and d,l-neoisomenthol, as shown in Figure 1. These isomers display an unpleasant smell and are less effective for inducing the cooling sensation when applied to the body’s skin [2,3]. Though d,l-menthol is also marketed since it shows no toxicity [6,7], it is less desirable than l-menthol.

As a natural product, l-menthol is present in mint with almost absolute optical purity [1]. In the past, isolation from corn mint oil was the only approach for the production of l-menthol [3]. The price of l-menthol fluctuates violently due to the surging demand and unstable yield. This has promoted the development in synthesis of optically pure l-menthol. Approximately 60% of the l-menthol in the end-use market is derived from chemical synthesis at present [3]. Symrise, Takasago and BASF are the main suppliers of synthetic l-menthol in the world [3,4].

The Symrise process uses thymol as the starting material. A mixture of the four racemic pairs, containing approximately 60% d,l-menthol, 26% d,l-neomenthol, 12% d,l-isomenthol and 2% d,l-neoisomenthol, is obtained by hydrogenation of thymol [8]. l-menthol is subsequently isolated from this mixture after a series of achiral and chiral separation procedures. Achiral separation gives d,l-menthol by distillation, followed by chiral separation of d,l-menthol using the preferential crystallization method to give enantiomerically pure l-menthol as the final product. In the chiral separation process, d,l-menthol is first esterified to give d,l-menthylbenzoate. The racemic esters are then resolved by seeding optically pure ester crystals into the supersaturated solution of d,l-menthylbenzoate. Finally, d-menthol and l-menthol are obtained after hydrolysis [9]. d-menthol, along with the other three racemates, is recycled to the hydrogenation section to re-establish the thermodynamic equilibrium [8]. The enantio-separation of racemic menthol is complex, comprising esterification, enantioselective crystallization and hydrolysis. The esterification is essential because enantiomerically pure d-menthol and l-menthol can not be obtained simply by seeding in racemic menthol solutions [3]. Moreover, the operating conditions of preferential crystallization should be strictly controlled. Enzymatic catalysis may be an alternative strategy for the chiral separation of racemic menthol [10,11,12,13,14].

Chromatography is a promising technique for chiral separation [15,16,17,18,19], with simulated moving bed (SMB) as its continuous form [20,21]. Several fixed beds packed with adsorbent particles are connected in series in an SMB unit, with four inlet and outlet lines, eluent, feed, raffinate and extract, connected between the columns. With periodical switching of these inlet and outlet lines in the direction of fluid flow in this technique, the countercurrent contact of the fluid and adsorbent particles in the true moving bed (TMB) concept is achieved to reinforce the mass transfer. Higher productivity and less solvent consumption compared with batch chromatography make it an attractive method used in sugar refinement [22,23], medicine manufacturing [24,25,26] and biological production purifications [27,28,29] since firstly proposed by Universal Oil Products (UOP) in 1961.

A variety of non-conventional modes of SMB were proposed to further improve the performance of SMB [30,31], including Varicol [32,33,34], Modicon [35,36], Powerfeed [37,38], partial-discard [39,40], outlet stream fractionation and feed-back [41,42], and solvent gradient [43,44]. Among these variants, Varicol was proposed and industrialized by NOVASEP. Figure 2 compares the difference between conventional SMB and VARICOL in operation mode by taking a specific shifting scheme as an example. For both conventional SMB and VARICOL, packed columns located between different inlet and outlet lines have different functions in separation, and thus can be divided into four zones. Zone I is located between the eluent line and the extract line, and is responsible for the regeneration of the stationary phase. Zone II is located between the extract line and the feed line, and is responsible for the purification of the more-adsorbed component. Zone III is located between the feed line and the raffinate line, and is responsible for the purification of the less-adsorbed component. Zone IV is located between the raffinate line and the eluent line, and is responsible for the regeneration of the mobile phase. Conventional SMB and VARICOL have the same position of inlet and outlet lines, and thereby, the same initial column configurations. In the conventional SMB process, all the inlet and outlet ports shift in the direction of fluid flow for a column simultaneously every particular time interval, namely a switching period. The column configuration remains constant as 1/2/2/1 during the operation. In contrast, in a VARICOL process, the inlet and outlet ports shift asynchronously. The period is further divided into subintervals by these individual shifting, and the column configuration varies within a period. After a quarter of a period as the first subinterval, the extract line shifts downstream for a column, with the column configuration changing into 2/1/2/1. Subsequently, after a quarter of a period as the second subinterval, the feed line shifts downstream for a column, with the column configuration changing into 2/2/1/1. Then, after a quarter of a period as the third subinterval, the eluent line shifts downstream for a column, with the column configuration changing into 1/2/1/2. Finally, after a quarter of a period as the fourth subinterval, the raffinate line shifts downstream for a column, with the column configuration changing back into 1/2/2/1. With this shifting scheme, VARICOL process has an average column configuration of 1.5/1.75/1.5/1.25.

The asynchronous shifting of the inlet and outlet ports offers a greater degree of freedom for the operation of the VARICOL process. Consequently, with the same column numbers, the VARICOL process can achieve better separation performance than the conventional SMB process under suitable design. This also gives rise to a possibility of achieving the same purities for extract and raffinate with a reduced number of columns using the VARICOL process [32,45,46]. SMB separation process with fewer columns is beneficial for the following reasons [20]. First of all, fewer fixed beds, tubes and valves are used for the equipment setup, and therefore, less device cost and extra-column dead volume. Moreover, a smaller amount of adsorbent is required, especially for chiral separation, because of the high price of the chiral stationary phase. In addition, fewer packing and re-packing efforts are essential. Packed columns should have equivalent hydrodynamic characteristics to ensure symmetry. However, the packing procedure can be irreproducible. Therefore, the packing procedure is always very tedious and time-consuming, and re-packing should be performed for the columns with poor reproductivity.

In our previous work, the conventional simulated moving bed technique was used for the resolution of menthol racemate, and menthol enantiomers with purity above 99.0% can be obtained [47]. Considering the high demand for l-menthol, improving the productivity of the SMB unit is of great importance. This work aims to explore the potential of the VARICOL process for the enantioseparation of the racemic menthol at a reduced product purity target, taking into account the diverse application purposes of l-menthol. Amylose 3,5-dimethylphenylcarbamate coated on silica gel was used as the chiral stationary phase, with n-hexane/2-propanol (95/5, v/v) serving as the mobile phase. Mathematical models were developed to describe the dynamics of the VARICOL process, where mass transfer resistance and axial dispersion were taken into account. The separation regions of the VARICOL processes were estimated by simulations. The superiority of the VARICOL process in terms of separation performance compared with conventional SMB was investigated. Experiments were carried out for the resolution of racemic menthol by conventional SMB and VARICOL process respectively, and the predicted separation performance was compared with the experimental results.

2. Theoretical Analysis

2.1. Mathematical Models of the VARICOL Process

Mathematical modeling is an effective approach for the understanding and design of the SMB separation process. The SMB process can be modeled by two strategies: the TMB strategy and the SMB strategy [22,48]. The first one makes an analogy between the SMB and TMB processes, considering the movement of the solid phase in the opposite direction of the liquid phase [25,49,50]. The steady state of the TMB operation is predicted by a set of ordinary differential equations. The second one describes the real intermittent behavior of the SMB process, considering the periodical shifting of the injection and collection lines [51,52]. The cyclic steady state of the SMB operation is predicted by a set of partial differential equations. Less computation time is required for the TMB strategy, yet acceptable prediction results can be obtained by the TMB strategy only when the column numbers in each zone are at least two, because of the great deviation between the SMB process and TMB process with low total column numbers [53]. The SMB strategy is used in this paper because the total column numbers considered in the current work are five or six. Mass transfer and axial dispersion are taken into account in the model, which contains the following equations [52,54].

Mass balance over a volume element in the liquid phase is as follows:

$${\displaystyle \frac{\partial c_{i,k}}{\partial t}}+{\displaystyle \frac{u_k}{\epsilon }}{\displaystyle \frac{\partial c_{i,k}}{\partial z}}+{\displaystyle \frac{1-\epsilon }{\epsilon }}{\displaystyle \frac{6}{d_{\mathrm{p}}}}K\left(q_{i,k}^{*}-q_{i,k}\right)=D_{\mathrm{ax},k}{\displaystyle \frac{{\partial }^2{c}_{i,k}}{\partial z^2}}$$

(1)

Mass balance over a volume element in the solid phase is as follows:

$${\displaystyle \frac{\partial q_{i,k}}{\partial t}}={\displaystyle \frac{6}{d_{\mathrm{p}}}}K\left(q_{i,k}^{*}-q_{i,k}\right)$$

(2)

where the subscript $i$ ($i$ = 1, 2) refers to the species in the racemate, with 1 and 2 representing the less-retained and more-retained enantiomers, d-menthol and l-menthol, respectively, and the subscript $k$ ($k$ = 1, 2, …, $N_{\mathrm{C}}$) refers to the column number. $N_{\mathrm{C}}$ is the total column number. $c_{i,k}$ and $q_{i,k}$ are the concentrations in the liquid phase and solid phase, respectively. $q_{i,k}^{*}$ is the saturated solid phase concentration corresponding to the liquid phase concentration. $\epsilon$ is the bulk porosity of the fixed bed. $u_k$ is the superficial velocity. $D_{\mathrm{ax},k}$ is the axial dispersion coefficient. $K$ is the overall mass transfer coefficient. $d_{\mathrm{p}}$ is the particle diameter of the chiral stationary phase. $z$ is the axial coordination of the SMB column. $t$ is the time variable.

The binary adsorption isotherm of the menthol enantiomer can be described by the modified linear + Langmuir model [47].

$$q_i^{*}=H_i{c}_i+{\displaystyle \frac{Q_{\mathrm{m}\mathrm{a}\mathrm{x}}{b}_i{c}_i}{1+{\displaystyle \sum _{i=1}^2{b}_i{c}_i}}}$$

(3)

where $H_i$ is the Henry parameter for the linear adsorption site, while $Q_{\mathrm{m}\mathrm{a}\mathrm{x}}$ and $b_i$ are the Langmuir parameters for the non-linear adsorption site.

The superficial velocity is as follows:

$$u_k={\displaystyle \frac{Q_j}{\frac{\pi }{4}{d}_{\mathrm{C}}^2}}$$

(4)

where the subscript $j$ ($j$ = I, II, III, IV) refers to the zone number in the VARICOL unit. $Q_j$ is the flow rate in the packed bed. $d_{\mathrm{C}}$ is the column diameter.

The axial dispersion can be estimated by the Peclet number:

$$Pe={\displaystyle \frac{u_k{L}_{\mathrm{C}}}{\epsilon D_{\mathrm{a}\mathrm{x},k}}}$$

(5)

where $Pe$ is the Peclet number, which is a dimensionless number. $L_{\mathrm{C}}$ is the column length.

Initial conditions for the partial differential equations are as follows:

$${\left.c_{i,k}\right|}_{t=0,z}=0$$

(6)

$${\left.q_{i,k}\right|}_{t=0,z}=0$$

(7)

Boundary conditions for the partial differential equations are as follows:

$$D_{\mathrm{a}\mathrm{x},k}{\left.\left({\displaystyle \frac{\partial c_{i,k}}{\partial z}}\right)\right|}_{t,z=0}={\displaystyle \frac{u_k}{\epsilon }}\left({\left.c_{i,k}\right|}_{t,z=0}-c_{i,k,\mathrm{in}}\right)$$

(8)

$${\left.\left({\displaystyle \frac{\partial c_{i,k}}{\partial z}}\right)\right|}_{t,z=L_{\mathrm{C}}}=0$$

(9)

where $c_{i,k,\mathrm{in}}$ is the inlet concentration of the packed bed.

Mass balance between two connected columns is given for different cases.

When no stream enters or exits between the two columns,

$$c_{i,k+1,\mathrm{in}}={\left.c_{i,k}\right|}_{t,z=L_{\mathrm{C}}}$$

(10)

When only one stream enters or exits between the two columns,

For the eluent node,

$$Q_{\mathrm{I}}=Q_{\mathrm{I}\mathrm{V}}+Q_{\mathrm{D}}$$

(11)

$$c_{i,k+1,\mathrm{in}}={\displaystyle \frac{Q_{\mathrm{I}\mathrm{V}}}{Q_{\mathrm{I}}}}{\left.c_{i,k}\right|}_{t,z=L_{\mathrm{C}}}$$

(12)

For the extract node,

$$Q_{\mathrm{I}\mathrm{I}}=Q_{\mathrm{I}}-Q_{\mathrm{X}}$$

(13)

$$c_{i,k+1,\mathrm{in}}={\left.c_{i,k}\right|}_{t,z=L_{\mathrm{C}}}$$

(14)

$$c_{i,\mathrm{X}}={\left.c_{i,k}\right|}_{t,z=L_{\mathrm{C}}}$$

(15)

For the feed node,

$$Q_{\mathrm{I}\mathrm{I}\mathrm{I}}=Q_{\mathrm{I}\mathrm{I}}+Q_{\mathrm{F}}$$

(16)

$$c_{i,k+1,\mathrm{in}}={\displaystyle \frac{Q_{\mathrm{I}\mathrm{I}}}{Q_{\mathrm{I}\mathrm{I}\mathrm{I}}}}{\left.c_{i,k}\right|}_{t,z=L_{\mathrm{C}}}+{\displaystyle \frac{Q_{\mathrm{F}}}{Q_{\mathrm{I}\mathrm{I}\mathrm{I}}}}{c}_{i,\mathrm{F}}$$

(17)

For raffinate nodes,

$$Q_{\mathrm{I}\mathrm{V}}=Q_{\mathrm{I}\mathrm{I}\mathrm{I}}-Q_{\mathrm{R}}$$

(18)

$$c_{i,k+1,\mathrm{in}}={\left.c_{i,k}\right|}_{t,z=L_{\mathrm{C}}}$$

(19)

$$c_{i,\mathrm{R}}={\left.c_{i,k}\right|}_{t,z=L_{\mathrm{C}}}$$

(20)

When two streams enter and exit between the two columns, the following occurs.

The eluent port and extract port gather at the same node when Zone I contains no column. The mass balance of this node can not be obtained simply by combining Equations (11)–(15) because of the special design of the node, which will be introduced in Section 3.1 of this article.

$$c_{i,k+1,\mathrm{in}}={\displaystyle \frac{Q_{\mathrm{I}\mathrm{V}}-Q_{\mathrm{I}}+Q_{\mathrm{I}\mathrm{I}}}{Q_{\mathrm{I}\mathrm{I}}}}{\left.c_{i,k}\right|}_{t,z=L_{\mathrm{C}}}$$

(21)

$$c_{i,\mathrm{X}}={\left.c_{i,k}\right|}_{t,z=L_{\mathrm{C}}}$$

(22)

When Zone IV contains no column, the raffinate port and eluent port gather at the same node.

$$c_{i,k+1,\mathrm{in}}={\displaystyle \frac{Q_{\mathrm{I}\mathrm{V}}}{Q_{\mathrm{I}}}}{\left.c_{i,k}\right|}_{t,z=L_{\mathrm{C}}}$$

(23)

$$c_{i,\mathrm{R}}={\left.c_{i,k}\right|}_{t,z=L_{\mathrm{C}}}$$

(24)

where $Q_{\mathrm{D}}$, $Q_{\mathrm{X}}$, $Q_{\mathrm{F}}$ and $Q_{\mathrm{R}}$ are the flow rates of desorbent, extract, feed and raffinate, respectively. $c_{i,\mathrm{X}}$ and $c_{i,\mathrm{R}}$ are the concentrations in the extract and raffinate stream, respectively.

2.2. Numerical Solving of the Model Equations

The mathematical model describing the dynamics of the VARICOL process consists of partial differential equations and nonlinear algebraic equations. gPROMS software with version 4.0.0, developed by Process System Enterprise, was applied to numerically solve the equations. The axial domains of all columns were discretized by orthogonal collocation on finite elements method (OCFEM) with third order over uniform grids. In our preliminary works, different interval numbers ranging from 10 to 100 were used for numerical solvation, and the effect of interval number on prediction accuracy and CPU time was studied. An interval number of 60 for discretization was selected, since it can minimize the computation efforts while ensuring the prediction accuracy of internal concentration profiles. The absolute and relative tolerance were set as 10⁻⁵.

2.3. VARICOL Separation Performance Parameters

Parameters, including purity, productivity and solvent consumption, were defined for performance evaluation.

The purity of the extract is defined as the mass percentage of the more-adsorbed species in both enantiomers contained in the extract stream over a cycle during cyclic steady state. The purity of the raffinate is defined as the mass percentage of the less-adsorbed species in both enantiomers contained in the raffinate stream over a cycle during cyclic steady state.

$$PUR={\displaystyle \frac{\overline{c_{1,\mathrm{R}}}}{{\displaystyle \sum _{i=1}^2\overline{c_{i,\mathrm{R}}}}}}$$

(25)

$$PUX={\displaystyle \frac{\overline{c_{2,\mathrm{X}}}}{{\displaystyle \sum _{i=1}^2\overline{c_{i,\mathrm{X}}}}}}$$

(26)

The productivity is defined as the amount of racemate resolved by the VARICOL process per volume of chiral stationary phase per unit of time.

$$PR={\displaystyle \frac{Q_{\mathrm{F}}{\displaystyle \sum _{i=1}^2{c}_{i,\mathrm{F}}}}{\left(1-\epsilon \right)N_{\mathrm{C}}{V}_{\mathrm{C}}}}$$

(27)

where $V_{\mathrm{C}}$ is the volume of the column.

The solvent consumption is defined as the total volume of solvent used in both inlet streams per amount of racemate resolved by the VARICOL process.

$$SC={\displaystyle \frac{Q_{\mathrm{D}}+Q_{\mathrm{F}}}{Q_{\mathrm{F}}{\displaystyle \sum _{i=1}^2{c}_{i,\mathrm{F}}}}}$$

(28)

2.4. Design of the VARICOL Process

To obtain relatively optimized separation performance, flow rates in each zone and shifting scheme, including initial column configurations and individual shifting time for all ports, should be suitably designed. In the VARICOL process, the shifting of an inlet or outlet port can be either upstream or downstream. If an inlet or outlet line is shifted upstream for one column, a downstream shifting for two columns is required for it in the period to ensure that the initial position of this line in the next period is a column downstream. Therefore, the simplest shifting schemes contain only a downstream movement of one column for all ports. It has been found that, among the possible shifting schemes with the same average column configurations, the simplest shifting scheme presents the best separation performance [55]. Though more than one simplest shifting scheme corresponds to a specific average column configuration, they are actually equivalent because they give the same product purities [55,56]. Thus, only the VARICOL process with the simplest shifting scheme is studied in this work, and the average column numbers in each zone can be used as decision variables for shifting scheme operation [56,57]. In this research, only symmetric average column configurations are considered. In other words, the average column number of Zone I and Zone IV is set to the same value, and the average column number of Zone II and Zone III is set to the same value as well in the VARICOL process.

Flow rate ratio $m_j$ is a dimensionless parameter [58], defined as

$$m_j={\displaystyle \frac{Q_j^{\mathrm{TMB}}}{Q_{\mathrm{s}}}}$$

(29)

The relationship between the SMB process and the corresponding TMB process is shown in the following:

$$Q_j=Q_j^{\mathrm{TMB}}+{\displaystyle \frac{\epsilon }{1-\epsilon }}{Q}_{\mathrm{s}}$$

(30)

$$Q_{\mathrm{s}}={\displaystyle \frac{\left(1-\epsilon \right)V_{\mathrm{C}}}{t_{\mathrm{s}}}}$$

(31)

where $Q_j^{\mathrm{TMB}}$ and $Q_{\mathrm{s}}$ are the flow rates of fluid and adsorbent particles in the corresponding TMB process, respectively. $t_{\mathrm{s}}$ is the period time of the SMB process.

To ensure the complete regeneration of the chiral stationary phase in Zone I and the eluent in Zone IV, the values of $m_{\mathrm{I}}$ and $m_{\mathrm{I}\mathrm{V}}$ were chosen by

$$m_{\mathrm{I}}=\beta \left(H_2+Q_{\max }{b}_2\right)$$

(32)

$$m_{\mathrm{I}\mathrm{V}}={\displaystyle \frac{H_1+Q_{\max }{b}_1}{\beta }}$$

(33)

where $H_1$, $H_2$, $Q_{\max }$, $b_1$, and $b_2$ are the adsorption isotherm parameters in the modified linear + Langmuir model, and $\beta$ is the safety margin. Herein, the value of $\beta$ is set at 1.25 to fix the flow rate of Zone I and Zone IV, and thereby, the eluent flow rate is fixed [48,59]. From the definition of productivity and solvent consumption shown in Equations (27) and (28), in an SMB unit with fixed column numbers, with a higher flow rate of the feed stream, the productivity rises and solvent consumption drops. The multi-objective optimization containing productivity and solvent consumption as objective functions can thus be transformed to a single-objective optimization for maximizing the feed flow rate of the VARICOL unit. In our future research for optimizing the operation conditions of the VARICOL process, the effect of the value for m_I and m_IV on the productivity and solvent consumption should be further investigated.

The parameters related to adsorption equilibrium and kinetics at 25 °C were measured in our previous work [47], as listed in

Table 1. Parameters related to adsorption equilibrium and kinetics.

Parameters		Value
Adsorption isotherm	H1	0.504
	H2	0
	Qmax (g/L)	265.94
	b1 (L/g)	3.83 × 10−3
	b2 (L/g)	7.35 × 10−3
Mass transfer coefficient	K (cm/s)	1.3 × 10−4

. Structure and operation designs are summarized in

Table 2. Design conditions for device structure and operation.

Design Conditions		Value
Structure parameter	LC (cm)	15
	dC (cm)	1
	dp (cm)	2 × 10−3
	ε	0.40
	Pe	3.4 × 103
Operation parameter	T (℃)	25
	c1,F (g/L)	10
	c2,F (g/L)	10
	ts (min)	2
	mI	2.44
	mIV	1.22
	PUX	≥0.95
	PUR	≥0.95

. The switching period and feed concentrations were set according to our previous work [47]. The purity requirement of both extract and raffinate was set at 95.0%. Separation regions for different average column configurations were obtained after simulating the VARICOL process with different pairs of ($m_{\mathrm{I}\mathrm{I}} \times m_{\mathrm{I}\mathrm{I}\mathrm{I}}$).

2.5. Definitions of the Ports Shifting

To better describe the shifting of the four inlet and outlet ports in a simplest shifting scheme, a series of parameters is defined [55,56,60].

The shifting time of the ports can be normalized by the switching period,

$$\mathrm{\delta }{t}_l={\displaystyle \frac{t_l}{t_{\mathrm{s}}}}$$

(34)

where $l$ ($l$ = D, X, F, R) refers to the inlet and outlet lines, with D, X, F, and R representing the desorbent, extract, feed, and raffinate, respectively. $t_l$ is the switching time of the ports within a period, and $\mathrm{\delta }{t}_l$ is the normalized switching time.

Constraints of the normalized switching time are as follows:

$$0<\mathrm{\delta }{t}_l\le 1$$

(35)

It should be noted that at least one of the four normalized switching times must be 1, which symbolizes the finish of the period. When all the normalized switching times of the inlet and outlet lines are 1, the process becomes a conventional SMB process. Therefore, the conventional SMB process can be regarded as a special case of the VARICOL process.

The differences in the normalized switching time for two neighboring lines are given as

$$\mathrm{\delta }\mathrm{x}=\mathrm{\delta }{t}_{\mathrm{X}}-\mathrm{\delta }{t}_{\mathrm{D}}$$

(36)

$$\mathrm{\delta }\mathrm{y}=\mathrm{\delta }{t}_{\mathrm{F}}-\mathrm{\delta }{t}_{\mathrm{X}}$$

(37)

$$\mathrm{\delta }\mathrm{z}=\mathrm{\delta }{t}_{\mathrm{R}}-\mathrm{\delta }{t}_{\mathrm{F}}$$

(38)

With these definitions, the difference between the normalized switching time of any two ports can be described:

$$\mathrm{\delta }{t}_{\mathrm{F}}-\mathrm{\delta }{t}_{\mathrm{D}}=\mathrm{\delta }\mathrm{x}\mathrm{x}+\mathrm{\delta }\mathrm{y}$$

(39)

$$\mathrm{\delta }{t}_{\mathrm{R}}-\mathrm{\delta }{t}_{\mathrm{X}}=\mathrm{\delta }\mathrm{y}+\mathrm{\delta }\mathrm{z}$$

(40)

$$\mathrm{\delta }{t}_{\mathrm{R}}-\mathrm{\delta }{t}_{\mathrm{D}}=\mathrm{\delta }\mathrm{x}+\mathrm{\delta }\mathrm{y}+\mathrm{\delta }\mathrm{z}$$

(41)

The constraints for these parameters can be inferred from Inequality (35):

$$-1<\mathrm{\delta }\mathrm{x}<1$$

(42)

$$-1<\mathrm{\delta }\mathrm{y}<1$$

(43)

$$-1<\mathrm{\delta }\mathrm{z}<1$$

(44)

$$-1<\mathrm{\delta }\mathrm{x}+\mathrm{\delta }\mathrm{y}<1$$

(45)

$$-1<\mathrm{\delta }\mathrm{y}+\mathrm{\delta }\mathrm{z}<1$$

(46)

$$-1<\mathrm{\delta }\mathrm{x}+\mathrm{\delta }\mathrm{y}+\mathrm{\delta }\mathrm{z}<1$$

(47)

The relationship between the initial column configuration and the average column configuration can be given by

$$\overline{N_{\mathrm{I}}}=N_{\mathrm{I}}^0-\mathrm{\delta }\mathrm{x}$$

(48)

$$\overline{N_{\mathrm{I}\mathrm{I}}}=N_{\mathrm{I}\mathrm{I}}^0-\mathrm{\delta }\mathrm{y}$$

(49)

$$\overline{N_{\mathrm{I}\mathrm{I}\mathrm{I}}}=N_{\mathrm{I}\mathrm{I}\mathrm{I}}^0-\mathrm{\delta }\mathrm{z}$$

(50)

$$\overline{N_{\mathrm{I}\mathrm{V}}}=N_{\mathrm{I}\mathrm{V}}^0+\mathrm{\delta }\mathrm{x}+\mathrm{\delta }\mathrm{y}+\mathrm{\delta }\mathrm{z}$$

(51)

where $\overline{N_j}$ is the average column number over a period, and $N_j^0$ is the initial column number at the beginning of a period.

In both the initial column configuration and average column configuration, the sum of the column numbers in all zones should be the total column numbers.

$${\displaystyle \sum _{j=\mathrm{I}}^{\mathrm{I}\mathrm{V}}{N}_j^0=N_{\mathrm{C}}}$$

(52)

$${\displaystyle \sum _{j=\mathrm{I}}^{\mathrm{I}\mathrm{V}}\overline{N_j}=N_{\mathrm{C}}}$$

(53)

2.6. Derivation of the Shifting Scheme

To simulate or operate a VARICOL unit, the shifting scheme, including the initial column numbers in each zone and the shifting time for each port, should be derived from the average column configurations.

From Equations (48)–(51) and Inequalities (42)–(44) and (47), it can be inferred that, for the zones possessing integer average column numbers, their initial column numbers at the beginning of a period must be equal to their average column number. Moreover, for the zones that have rational average column numbers, which are fraction numbers, their initial column numbers are the nearest lower integer or nearest upper integer of the average column numbers, $\left[\overline{N_j}\right]$ or $\left[\overline{N_j}\right]+1$, respectively. Meanwhile, the constraints for the initial column numbers in all zones, shown as Equation (52), must be fulfilled when the total column number is fixed. Thus, among the $N_Z$ zones with rational average column numbers, the initial column numbers in $N_{\mathrm{Z}}-N_{\mathrm{C}}+{\displaystyle \sum _{j=\mathrm{I}}^{\mathrm{I}\mathrm{V}}\left[\overline{N_j}\right]}$ zones should be assigned as $\left[\overline{N_j}\right]$, and the initial column numbers in $N_{\mathrm{C}}-{\displaystyle \sum _{\mathrm{j}=\mathrm{I}}^{\mathrm{I}\mathrm{V}}\left[\overline{N_j}\right]}$ zones should be assigned as $\left[\overline{N_j}\right]+1$. This leads to an option number for the nearest integer combinations of

$$N_{\mathrm{C}\mathrm{C}}={\mathrm{C}}_{N_{\mathrm{Z}}}^{N_{\mathrm{C}}-{\displaystyle \sum _{j=\mathrm{I}}^{\mathrm{I}\mathrm{V}}\left[\overline{N_j}\right]}}$$

(54)

The option quantity of the nearest integer combinations for different zone numbers with rational average column numbers and the difference between the total column number and the sum of the nearest lower integer of the average column numbers are summarized in

Table 3. Option number of the nearest integer combinations for different cases.

NZ	4-NZ	${\mathit{N}}_{\mathbf{C}}-{\displaystyle \sum _{\mathit{j}=\mathbf{I}}^{\mathbf{I}\mathbf{V}}\left[\overline{{\mathit{N}}_{\mathbf{j}}}\right]}$	NCC
4	0	1	4
4	0	2	6
4	0	3	4
3	1	1	3
3	1	2	3
2	2	1	2

.

However, among these nearest integer combinations, some may not make physical sense when used as an initial column configuration, because they may not fulfill the Inequalities (45) and (46).

For all the obtained nearest integer combinations, the difference of the normalized switching time for two neighboring lines, $\mathrm{\delta }\mathrm{x}$, $\mathrm{\delta }\mathrm{y}$ and $\mathrm{\delta }\mathrm{z}$, can be determined by Equations (48)–(50). The value of $\mathrm{\delta }\mathrm{x}+\mathrm{\delta }\mathrm{y}$ and $\mathrm{\delta }\mathrm{y}+\mathrm{\delta }\mathrm{z}$ can be further calculated, and the integer combinations that do not fulfill Inequalities (45) and (46) can be excluded.

For all the remaining possible initial column configuration options, the switching time of the four inlet and outlet lines giving the desired average column configuration should also be determined.

As explained before, the maximum value of the normalized switching time for the four ports must be 1. From Equations (36), (39), and (41), the normalized switching time of the eluent port can be determined by

$$\mathrm{\delta }{t}_{\mathrm{D}}=1-max\left\{0,\mathrm{\delta }\mathrm{x},\mathrm{\delta }\mathrm{x}+\mathrm{\delta }\mathrm{y},\mathrm{\delta }\mathrm{x}+\mathrm{\delta }\mathrm{y}+\mathrm{\delta }\mathrm{z}\right\}$$

(55)

The normalized switching time for other inlet and outlet ports can be determined by Equations (36)–(38) [56].

3. Experiments

3.1. Materials and Equipment

Racemic menthol, GC grade with a purity above 98%, was purchased from Tokyo Chemical Industry (Tokyo, Japan). n-hexane and 2-propanol, both HPLC grade with purities above 99.9%, were purchased from Fischer Scientific (Waltham, MA, USA). The preparative chiral stationary phase and analytical HPLC column Chiralpak AD-H (4.6 mm ID × 150 mm L) packed with analytical chiral stationary phase were purchased from Tokyo Daicel Chemical Industry (Tokyo, Japan). Both the preparative and analytical chiral stationary phases are amylose 3,5-dimethylphenylcarbamate coated on silica gel, commercially named Chiralpak AD, but they have different particle sizes of 20 μm and 5 μm, respectively. The preparative chiral stationary phase was packed in six stainless steel chromatographic columns (10 mm ID × 150 mm L) by the slurry method, which were used in the SMB separation. The hydrodynamic characteristics of these SMB columns, including bulk porosity and Peclet number, were measured in our previous study [47]. The relative errors of bulk porosity for these columns are less than 3.0%, showing good packing symmetry. The analytical column was used for the analysis of enantiomer concentrations.

VARICOL-micro is an SMB unit assembled by NOVASEP (Pompey, France). The device is equipped with five double piston pumps for the delivery of eluent, extract, feed, raffinate and recycling stream, respectively. An insulated chamber with air circulation and a heat exchanger is installed to control the operation temperature of the SMB columns, which can accommodate up to 8 columns. Another heat exchanger is installed to control the temperature of the two inlet streams, feed and eluent. The two heat exchangers are connected to a thermostatic bath. UV detector and polar detector are connected in the recycling line to online monitor the enantiomer concentrations. A six-port valve with a 250 μL loop is also installed in the recycling lines to facilitate the sample collections and obtain the internal concentration profiles. Two inlet lines and two outlet lines with individual valves are connected between every two neighboring columns for the purpose of VARICOL operation. The asynchronous port shifting can be realized by the opening and closing of these valves. Considering the case for temporarily superposition of two ports, the outlet lines are connected to the circulating lines in front of the inlet lines in the direction of the fluid flow [32], as shown in Figure 3. When Zone II or Zone III contains no column, the feed solution will not pollute the outlet product, and when Zone I or Zone IV contains no column, the eluent solution will not dilute the outlet product. The device configurations of the 6-column SMB unit and 5-column VARICOL unit are illustrated in Figure 4.

Ultimate 3000 is an analytical HPLC device purchased from Thermo Fischer Scientific (Waltham, MA, USA). It consists of a quaternary pump, autosampler, column oven and refractive index (RI) detector, and was used for the concentration determinations of menthol enantiomers.

3.2. SMB Operation

The eluent, n-hexane/2-propanol (95/5, v/v), was prepared by mixing 950 mL of n-hexane and 50 mL of 2-propanol, and the feed with a total concentration of 20 g/L was prepared by dissolving racemic menthol into the eluent. Both inlet solutions were filtered with 0.22 μm nylon filtration membranes and degassed in an ultrasonic bath after being freshly prepared. The flow rates of the five double piston pumps were corrected, and the SMB columns initially saturated with eluent were installed in the insulated chamber and then connected in series. The operation temperature was maintained by setting the temperature of the thermostatic bath. The designed operating conditions, including average column numbers in each zone, switching period and flow rates of eluent, feed, raffinate and recycling streams, were set on the control software (iFIX 4.5). The cyclic steady state was identified through the signals of the polar monitor. After reaching cyclic steady state, the outlet solution of extract and raffinate in an entire cycle was collected in order to evaluate the separation performance, and the solution at the recycling line was collected at 25%, 50%, 75% and 100% of each switching period using the six-port valve to obtain the internal concentration profiles.

It is worth noting that the recycling pump introduces an extra-column dead volume of 4 mL, as measured and recommended by the equipment producer. Two strategies were frequently used to design process conditions for SMB units with extra-column dead volume. The first strategy is applying an SMB model without considering extra-column dead volume, followed by operating the unit with compensation methods, while the second strategy includes the back-mixing occurred in the connecting lines into the mathematical model. It was found that the switching time compensation method, which belongs to the first strategy, and the second strategy predict almost overlapped separation regions for a micro-scale SMB unit [51]. The switching time compensation method was adopted in the present study because its mathematical model is simpler and requires less computational effort. The dead time caused by the recycling pump can be estimated by

$$t_{\mathrm{E}\mathrm{D}}={\displaystyle \frac{V_{\mathrm{E}\mathrm{D}}}{\overline{Q_j}}}$$

(56)

where $t_{\mathrm{E}\mathrm{D}}$ is the dead time caused by the extra-column dead volume. $V_{\mathrm{E}\mathrm{D}}$ is the extra-column dead volume. $\overline{Q_j}$ is the average flow rate of each section in the SMB process. To compensate for the time delay, the dead time is added to the switching time of all the inlet and outlet ports passing through the last column and the recycling lines in the SMB process [32,48].

3.3. Assay

The concentrations of menthol enantiomers in samples were determined by the HPLC-RI method, which was adapted from the literature [61]. The Chiralpak AD-H analytical column was used, with n-hexane/2-propanol (99/1, v/v) as the mobile phase in order to achieve a higher resolution. The temperature of the column oven and refractive index detector were set at 25 °C and 35 °C, respectively. The flow rate of the mobile phase was 1 mL/min, and the sample injection volume was 10 μL. The retention times of d-menthol and l-menthol were 8.38 min and 9.91 min, respectively, and the resolution was 2.62. External standard calibration curves with a single enantiomer concentration range of 0.040 g/L–2 g/L were used for quantitative analysis. The calibration curves of d-menthol and l-menthol were Y = 1.2422X + 0.0107 and Y = 1.2215X + 0.0094, respectively, where Y represents the peak area with unit of μRIU∙min, and X represents enantiomer concentration with unit of g/L.

4. Results and Discussion

4.1. VARICOL Process Optimization

The possible shifting schemes, including the initial column numbers in each zone and shifting time for each port in the six-column VARICOL process with average column configuration of θ/(3−θ)/(3−θ)/θ (0.5 < θ < 1), are listed in

Table 4. Possible initial column configurations and individual switching times of the inlet and outlet ports for the 6-column VARICOL process with an average column configuration of θ/(3−θ)/(3−θ)/θ (0.5 < θ < 1).

Parameters	Option 1	Option 2	Option 3
NI0	0	1	1
NII0	3	2	2
NIII0	2	2	3
NIV0	1	1	0
δtD	1	θ	1−θ
δtX	1−θ	1	2−2θ
δtF	1	θ	1−θ
δtR	θ	2θ−1	1

.

A possible shifting scheme, option 1 in Table 4, was used for the simulation of separation performance, as illustrated in Figure S1 of the Supplementary Materials. The initial column configuration in a period is 0/3/2/1, where the eluent line and extract line meet at the same port, because Zone I has no column. The extract stream is withdrawn from the outlet stream of the column in Zone IV before the remaining stream mixes with the inlet eluent stream because of the special design of the ports. After (1−θ)t_s, the extract line shifts downstream for a column, and the column configuration changes to 1/2/2/1. After (2θ−1)t_s, the raffinate line shifts downstream for a column, and the column configuration changes to 1/2/3/0, where the raffinate line and eluent line meet at the same port, because Zone IV has no column. The raffinate stream is withdrawn from the outlet stream of the column in Zone III before the remaining stream mixes with the inlet eluent stream. After (1−θ)t_s, the eluent and feed lines shift downstream for a column simultaneously, and the column configuration changes to 0/3/2/1 for the next period.

The separation regions of VARICOL processes with average column configuration of θ/(3−θ)/(3−θ)/θ (0.5 < θ < 1) and conventional SMB with column configuration of 1/2/2/1 were estimated by simulations, as shown in Figure 5.

For each average column configuration, the vertex points in the separation regions possess the highest feed flow rate, and thereby the highest productivity and lowest solvent consumption, so it is recognized as the optimal operation point. The separation performance of the optimal operation points for 6-column VARICOL and conventional SMB processes with different average column configuration are compared, as listed in

Table 5. Separation performance of the optimal operation points for the 6-column VARICOL and conventional SMB process with different average column configurations. Purity requirements, 95.0% for both extract and raffinate. Period time, 2 min. Flow rate ratios in Zone I and Zone IV, 2.44 and 1.22, respectively. Racemic menthol feed concentration, 20 g/L.

Average Column Configurations	QF,max (mL/min)	PRmax (gracemate/(LCSP∙min))	SCmin (L/gracemate)
0.7/2.3/2.3/0.7	1.159	0.547	0.236
0.8/2.2/2.2/0.8	1.184	0.558	0.232
0.9/2.1/2.1/0.9	1.184	0.558	0.232
1/2/2/1	1.177	0.555	0.233

. At optimized operation conditions, the VARICOL process with average column configuration of 0.9/2.1/2.1/0.9 and 0.8/2.2/2.2/0.8 has a greater feed flow rate and productivity, less solvent consumption compared with the process of 1/2/2/1. This can be partly explained by the increased column number of Zone II and Zone III in the VARICOL process, which is mainly responsible for the separation of the enantiomers. However, as the value of θ further decreases from 0.8, the feed flow rate and productivity seem to show a decreasing trend, and solvent consumption increases at the optimal point, which may be related to the poorer regeneration of the stationary phase and mobile phase with shorter average column length in Zone I and Zone IV.

The possible shifting scheme, including the initial column numbers in each zone and shifting time for each port in the five-column VARICOL process, with an average column configuration of θ/(2.5−θ)/(2.5−θ)/θ (0.5 < θ < 1) and 1/1.5/1.5/1, is listed in

Table 6. Possible initial column configurations and individual switching times of the inlet and outlet ports for a 5-column VARICOL process with an average column configuration of θ/(2.5−θ)/(2.5−θ)/θ (0.5 < θ < 1).

Parameters	Option 1	Option 2	Option 3	Option 4
NI0	0	1	1	1
NII0	2	1	2	2
NIII0	2	2	1	2
NIV0	1	1	1	0
δtD	1	θ	0.5	1−θ
δtX	1−θ	1	1.5−θ	2−2θ
δtF	0.5	θ−0.5	1	1.5−θ
δtR	θ	2θ−1	θ−0.5	1

and

Table 7. Possible initial column configurations and individual switching times of the inlet and outlet ports for a 5-column VARICOL process with an average column configuration of 1/1.5/1.5/1.

Parameters	Option 1	Option 2
NI0	1	1
NII0	1	2
NIII0	2	1
NIV0	1	1
δtD	1	0.5
δtX	1	0.5
δtF	0.5	1
δtR	1	0.5

, respectively.

Possible shifting schemes, Option 1 in Table 6 and Option 1 in Table 7, were used for the simulation of separation performance, as illustrated in Figure S2 and Figure S3 of the Supplementary Materials, respectively. The separation region of the VARICOL process with average column configuration of θ/(2.5−θ)/(2.5−θ)/θ (0.5 < θ ≤ 1) and conventional SMB with column configuration of 1/1/2/1 and 1/2/1/1 were estimated by simulations, as shown in Figure 6.

The separation performance of the optimal operation points for the five-column VARICOL and conventional SMB processes with different average column configuration are compared, as listed in

Table 8. Separation performance of the optimal operation points for the 5-column conventional SMB and VARICOL process with different average column configurations. Purity requirements, 95.0% for both extract and raffinate. Period time, 2 min. Flow rate ratios in Zone I and Zone IV, 2.44 and 1.22, respectively. Racemic menthol feed concentration, 20 g/L.

Average Column Configurations	QF,max (mL/min)	PRmax (gracemate/(LCSP∙min))	SCmin (L/gracemate)
0.7/1.8/1.8/0.7	1.074	0.608	0.251
0.8/1.7/1.7/0.8	1.085	0.614	0.249
0.9/1.6/1.6/0.9	1.064	0.602	0.253
1/1.5/1.5/1	1.025	0.58	0.260
1/2/1/1	0.763	0.432	0.332
1/1/2/1	0.710	0.402	0.353

. Similarly to the case with six columns, with a decreasing value of θ, a peak of feed flow rate, productivity and solvent consumption can also be found.

Figure 7 compares the feed flow rate, productivity and solvent consumption under the optimized operation point of both VARICOL and conventional SMB with optimal average column configurations for a total column number of five or six. For both cases with a fixed total column number of five or six, the VARICOL process can achieve a greater feed flow rate, and thereby, higher productivity and lower solvent consumption than the conventional SMB process, indicating a lower operation cost of the VARICOL process. This verified the universal superiority of the VARICOL process against conventional SMB in terms of separation performance, regardless of the outlet purity setpoint, thanks to the additional degree of freedom in operation offered by the asynchronous shifting mode. Whereas the separation performance is slightly improved by using the VARICOL process in a six-column unit, the productivity of the VARICOL process is 42.2% higher than the conventional SMB process in a five-column unit. It seems that the superiority is more pronounced when the total column number is five, which may be related to the very limited choice of column configurations with low total column numbers. As can be seen in Figure 7, the productivity of the five-column conventional SMB process under optimized operation conditions is low in comparison with the six-column conventional SMB process. In contrast, the five-column VARICOL process presents a productivity higher than that of the six-column conventional SMB process under optimized operating conditions, reflecting that the superiority of the former process over the latter process is derived from the asynchronous switching manner instead of solely the reduction of column numbers. It is also worth noting that the five-column VARICOL unit with an average column configuration of 0.8/1.7/1.7/0.8 presents a comparable feed flow rate, and thereby, higher productivity and comparable solvent consumption with the six-column 1/2/2/1 conventional SMB. This implies the lower fixed cost, containing device and stationary phase cost in the VARICOL process with a column removed from the separation unit. Figure 8 illustrates the estimated separation region of 0.8/1.7/1.7/0.8 and 1/2/2/1 under a product purity target of 95.0%, demonstrating comparable operation regions.

It must be pointed out that a VARICOL unit with fewer total column numbers can be inferior to a conventional SMB unit in terms of separation performance under optimized operation conditions, particularly when the product purity target is high [56]. Figure 9 compares the simulated maximum productivity of the five-column 0.8/1.7/1.7/0.8 VARICOL unit and the six-column 1/2/2/1 conventional SMB unit under different outlet purity requirements. At an outlet purity requirement below approximately 98.0%, a 0.8/1.7/1.7/0.8 VARICOL unit can achieve productivity higher than a 1/2/2/1 conventional SMB unit. In contrast, conventional SMB with a 1/2/2/1 configuration is beneficial with a purity setpoint higher than 98.0%. This is because with a stringent outlet purity requirement, the separation efficiency dropped due to reduced column numbers, which is more prominent, and therefore can not be fully compensated for by optimizing the column number distribution.

4.2. SMB Experiment

To demonstrate the superiority of the VARICOL process in terms of separation performance, a five-column VARICOL with an average column configuration of 0.8/1.7/1.7/0.8 and a six-column conventional SMB process with a column configuration of 1/2/2/1 were chosen for the resolution of menthol racemate under an outlet purity target of 95.0%, since they present the highest predicted productivity under optimized operation conditions among the VARICOL processes and conventional SMB process compared in the previous section, respectively. A pair of ($m_{\mathrm{I}\mathrm{I}} \times m_{\mathrm{I}\mathrm{I}\mathrm{I}}$) was selected inside the separation region for both of the two processes in order to compare them more conveniently, as shown in Figure 8, and the corresponding operation conditions are listed in

Table 9. Operation conditions of VARICOL and conventional SMB process [47].

Operation Conditions	Conventional SMB	VARICOL
Temperature (°C)	25
Total feed concentration (g/L)	20
Average column configuration	1/2/2/1	0.8/1.7/1.7/0.8
Packing amount of chiral stationary phase (mL)	42.41	35.34
ts (min)	2
QF (mL/min)	0.71
QX (mL/min)	3.11
QR (mL/min)	1.91
QD (mL/min)	4.31
QI (mL/min)	10.98
QII (mL/min)	7.87
QIII (mL/min)	8.58
QIV (mL/min)	6.67

. For both operation modes, a cyclic steady state was reached after operating 15 cycles. Samples were taken at the six-way valve located at the circulating line and subsequently analyzed to obtain the internal concentration profile at half of the switching period during cyclic steady state, which is compared with the predicted curve in Figure 10.

Table 10. Experimental and simulated separation performance of VARICOL and conventional SMB process.

Separation Performance		Conventional SMB	VARICOL
$\overline{c_{1,\mathrm{R}}}$ (g/L)	Experimental	3.62	3.56
	Simulated	3.69	3.66
$\overline{c_{2,\mathrm{R}}}$ (g/L)	Experimental	0.0739	0.133
	Simulated	0.0156	0.0472
$\overline{c_{1,\mathrm{X}}}$ (g/L)	Experimental	0.0574	0.0989
	Simulated	0.0123	0.0338
$\overline{c_{2,\mathrm{X}}}$ (g/L)	Experimental	2.24	2.20
	Simulated	2.24	2.22
PUR (%)	Experimental	98.0	96.4
	Simulated	99.6	98.7
PUX (%)	Experimental	97.5	95.7
	Simulated	99.5	98.5
PR (gracemate/(LCSP∙min))		0.333	0.400
SC (L/gracemate)		0.355	0.355

lists the experimental and simulated separation performances in cyclic steady state, and the analytic HPLC chromatograms of the outlet product in the VARICOL unit are displayed in Figure S4 of the Supplementary Materials. Good agreements can be found between the simulated results and the experimental results, though discrepancies may be derived from uncertainty in the estimation of model parameters, packing and tubing asymmetries, back-mixing in connecting lines, and flow rate fluctuations in recycling and external streams. In both conventional SMB and VARICOL processes, purities of both outlet products were above 95.0%, and solvent consumptions of 0.355 L/g_racemate were achieved. The productivity of the VARICOL process was 0.400 g_racemate/(L_CSP∙min), which was 20% higher than the conventional SMB process because of the reduced columns, despite the 1.6% and 1.8% lower purities for raffinate and extract in the VARICOL process, respectively. The sensitivity of the isotherm parameter H_i on internal concentration profiles is also analyzed, as shown in Figure 11. 0.9H_i shows a slightly higher product purity, while 1.1H_i presents lower predicted purities in both outlet streams, reflecting the importance of estimation accuracy for VARICOL unit design.

5. Conclusions

This work intends to develop the chiral separation process of racemic menthol on Chiralpak AD chiral stationary phase by the VARICOL process to enhance the productivity. A mathematical model was developed for the design and optimization of the VARICOL process. Prediction results show that, when the total column number is five or six, asynchronous shifting of the inlet and outlet ports can provide higher productivity and lower solvent consumption than the conventional SMB process. Moreover, the five-column VARICOL process is found to possess a comparable separation region, and thereby, comparable feed and eluent flow rates with the six-column conventional SMB process under a product purity setpoint of 95.0%. 0.8/1.7/1.7/0.8 VARICOL process and 1/2/2/1 conventional SMB process with the same switching period and flow rate in all zones were carried out for the resolution of racemic menthol. In the VARICOL process, purities for both the extract and raffinate were above 95.0%, and a productivity of 0.400 g_racemate/(L_CSP∙min) and a solvent consumption of 0.355 L/g_racemate were achieved. The productivity was 20% higher than the conventional SMB process with the same solvent consumption at the price of slightly decreased product purities.