The overreaching purpose of this study is to evaluate new approaches for determining the optimal operational and column conditions in chromatography laboratories, i.e., how best to select a packing material of proper particle size and how to determine the proper length of the column bed after selecting particle size. As model compounds, we chose two chiral drugs for preparative separation: omeprazole and etiracetam. In each case, two maximum allowed pressure drops were assumed: 80 and 200 bar. The processes were numerically optimized (mechanistic modeling) with a general rate model using a global optimization method. The numerical predictions were experimentally verified at both analytical and pilot scales. The lower allowed pressure drop represents the use of standard equipment, while the higher allowed drop represents more modern equipment. For both compounds, maximum productivity was achieved using short columns packed with small-particle size packing materials. Increasing the allowed backpressure in the separation leads to an increased productivity and reduced solvent consumption. As advanced numerical calculations might not be available in the laboratory, we also investigated a statistically based approach, i.e., the Taguchi method (empirical modeling), for finding the optimal decision variables and compared it with advanced mechanistic modeling. The Taguchi method predicted that shorter columns packed with smaller particles would be preferred over longer columns packed with larger particles. We conclude that the simpler optimization tool, i.e., the Taguchi method, can be used to obtain “good enough” preparative separations, though for accurate processes, optimization, and to determine optimal operational conditions, classical numerical optimization is still necessary. Keywords Preparative chromatography · Omeprazole · Etiracetam · Optimization of productivity · Taguchi optimization · Equilibrium–dispersive model Electronic supplementary material The online version of this Introduction article (https ://doi.org/10.1007/s1033 7-018-3519-z) contains supplementary material, which is available to authorized users. Preparative chromatography is extensively used for peptides, bio separations, chiral separations, as well as the new bio- * Jörgen Samuelsson firstname.lastname@example.org similar drugs such as mRNA and oligonucleotides [1–7]. Batch-mode process chromatography is the best generic * Krzysztof Kaczmarski email@example.com method to obtain pure drug/drug candidate components in amounts under 10 kg in the discovery stage of pharmaceuti- Department of Engineering and Chemical Sciences, Karlstad cal development. The process is mainly carried out using University, 651 88 Karlstad, Sweden empirical optimization methods, such as touching-band Department of Chemical Engineering, Rzeszow University separation, but also using numerical optimization based on of Technology, 35 959 Rzeszow, Poland chromatographic models of varying complexity [6, 8–14]. Akzo Nobel Pulp and Performance Chemicals AB, It is of highest importance for both preparative and ana- 445 80 Bohus, Sweden lytical chromatography to take a scientific step from using AstraZeneca R&D, 431 83 Mölndal, Sweden Vol.:(0123456789) 1 3 852 J. Samuelsson et al. empirical data and instead use powerful modeling to secure column diameter is x fi ed [ 21]. The process is r fi st optimized generation of scientific and mechanistic understanding (pre- using numerical modeling, but, since numerical optimization dictive science). This is well in line with the upcoming and is tedious from a practical perspective, a simpler statistical for the pharmaceutical industry important ICHQ12 guideline optimization approach, i.e., the Taguchi method, is evaluated . There are still no strict criteria for successful prepara- as an alternative. The Taguchi method exploits special stand- tive separation, despite some longstanding rules of thumb, ard orthogonal arrays, which has been successfully applied such as having a retention factor as small as possible for the in many manufacturing industries and experimental designs first-eluted component collected and dissolving the sample , and it is well suited for discrete variables. Experimen- in a concentration close to its solubility in a particular elu- tally, the two separation processes were performed at maxi- ent [6, 16]. mum allowed backpressures of 80 and 200 bar to determine One recent numerical study based on the chiral resolu- whether pressure affected the optimal column length and tion of racemic omeprazole on an amylose tris (3,5-dime- stationary-phase particle size in these cases. thyl phenyl carbamate)-coated macroporous silica column investigated how maximum productivity depends on the maximum allowed pressure drop and on the packing mate- Theory rial particle size for fixed-size analytical columns . It was found that the optimum particle size was large for Column Model separations conducted at low pressures, but that at higher pressures, 10- and 5-µm particles were more productive. A This study used the equilibrium–dispersive model equivalent later study used Monte Carlo simulations of 1000 randomly to general rate (EDEG) model, which is based on the equi- selected separation systems to draw more general conclu- librium–dispersive (ED) model [5, 9], described as follows: sions . It was found that it is almost always beneficial to c (1 − ) q c c i t i i i use shorter columns with higher pressure drops. Moreover, + + = D , (1) a,z t t z z z t t the dependence of productivity on packing particle size, as mentioned above, was verified and can be summarized as where c and q are the concentrations of the mobile and i i follows: (1) if the pump’s maximum flow rate is the limit - stationary phases, respectively, u is the superficial veloc- ing factor, use smaller particle-size packing; but (2) if the ity, ε is the total external porosity, t is time, and D is an t a,z system pressure is the limiting factor, use larger-particle-size apparent dispersion coefficient whose value can be deter - (≤ 40 µm) packing [16–18]. mined from the measured height equivalent to the theoretical The model compounds in this study are the proton-pump plate (HETP). For preparative chromatography, the column inhibitor omeprazole and the antiepileptic levetiracetam (an works in the nonlinear part of the isotherm curve and D a,z enantiomer of etiracetam). Racemic omeprazole and its bio- depends indirectly on the sample concentration . When logically more potent S-enantiomer (esomeprazole) are syn- the transport-dispersive model is to be used, one must cor- thesized without using chromatography . Omeprazole rectly calculate the effective mass transfer coefficient, which was selected, because it has previously been studied from the also depends on concentration . In the present work, we perspective of chromatographic separation and optimization analyzed a preparative process for species separation and [3, 8, 17]. Levetiracetam was selected, because it is currently decided to apply a version of the EDEG model proposed by produced using large-scale continuous chromatography  Antos et al.  and Kaczmarski et al. [23, 24]. and it was the first active pharmaceutical ingredient (API) In solving Eq. (1), the apparent dispersion coefficient is produced this way . An integrated synthesis and chro- calculated from the following relationship, for the first and matographic process for resolving levetiracetam from eti- second components: racetam was designed by UCB in the 1990s and 2000s , 2 2 and chromatography was found to be the most economic u d d D k p p L e 1 method. Smaller particles were deemed uneconomic due to D = + + , (2) a,z 1 + k F 6 10D k t 1 t e e eﬀ ext the higher cost of the material and higher required pressures in the chromatographic system . where ε is external porosity, D is an axial dispersion coef- e L The aim of this investigation is to determine how the ficient, and k , F , and D can be expressed as: 1 e eff Dynamic Axial Compression (DAC) column should be 1 − q p m packed (i.e., determine the appropriate column length and e k = F + 1 − , F = , and D = , 1 e p p e eﬀ stationary-phase particle size) to achieve optimal productiv- (3) ity. For over 20 years, preparative batch LC has been domi- nated by the DAC mode, in which a hydraulically actuated respectively, where D is diffusivity, k is a mass transfer m ext piston allows any column length to be selected, while the coefficient, d is particle diameter, τ is tortuosity, ε is pore p p 1 3 Optimizing Column Length and Particle Size in Preparative Batch Chromatography Using… 853 porosity, and ∂q/∂c is approximated using the slope at C = 0. k d ud ext p p Sh = , Re = and Sc = . When calculating D , it is assumed that the surface diffu- (9) eff D D m m sion can be ignored. The external porosity, ε , is assumed 2 −1 to be 0.4. The tortuosity coefficient was obtained from the The diffusivity, D (m s ), was calculated from the following relationship: Wilke–Chang model : 0.5 (2 − ) p ( ⋅ M ) −16 = . (4) D = 1.17 × 10 T , (10) 0.6 ⋅ V In this study, a bi-Langmuir-like adsorption–desorption where T is temperature (K), M is the solute molar mass −1 kinetic model was used for the enantiomeric separation of (kg mol ), η is viscosity (Pa × s), α = 1.9 for methanol and omeprazole; it can be described as: 1 for 60/40 ethanol/heptane, V is the molar volume in the 3 −1 −3 3 −1 mobile phase (m mol ), and V = 368.5 × 10 (m kmol ) −3 3 −1 for omeprazole and 194.5 × 10 (m mol ) for etiracetam. i j j j j j j (5) = k C q − q − q − k q , a,i s,i 1 2 d,i i Finally, the axial dispersion coefficient is obtained from the following relationship: where k and k are the rate constants for adsorption and des- a d D = 0.7D + 0.5ud . L m p (11) orption, respectively, q is the monolayer saturation capacity, and q is the amount of component i adsorbed on site j. The In this study, the adsorption isotherm was estimated using the inverse method [28, 29], solved using orthogonal collo- total amount of adsorbed compound is: cation on finite elements . The chosen base experimental 1 2 q = q + q , (6) i i concentration profiles were estimated by minimizing the sum where q is the adsorbed amount of component i and the of squared differences between the experimental and calcu- superscript indicates the first site or second site. lated elution profiles. For the enantiomeric separation of etiracetam, the follow- ing competitive bi-Langmuir isotherm model was applied: Optimization q K C q K C ns ns i es es i As objective function in the optimization, the productivity q = + , i (7) 1 + K C + K C 1 + K C + C es,1 1 es,2 2 ns 1 2 (Pr) (defined as gram product collected per minute), was used. In this study, the optimization problem comes down where q and q are the saturation capacities and K and ns es ns to the following expression: K are the association equilibrium constants of the non- es Max(Pr )= f (u, t , d , L). i inj p (12) selective and selective adsorption sites, respectively. This isotherm model assumes two types of adsorption sites: the As the optimization problem expressed by Eq. (12) was first type (first term) behaves identically toward the two quite complex, the hybrid method of simulated annealing enantiomers, while the second type (second term) is enanti- coupled with a simplex algorithm was applied . This oselective and responsible for chiral separation. The model hybrid optimization tool, which combines the stochastic has been widely and successfully applied to describe adsorp- method of simulated annealing with a deterministic simplex tion isotherms of chiral solutes; for example, the 1-indanol algorithm, is suitable for solving difficult optimization prob- enantiomers . The benet fi s of using bi-Langmuir adsorp - lems in which the desired global optimum is hidden among tion model are that it has a foundation in the physiochemical many local optima. The detailed algorithm and a study of adsorption process, but a drawback is that it contains more the effectiveness of the applied optimization method were parameters, thus making the numerical determination more presented by Kaczmarski and Antos . However, this complex. numerical optimization of the chromatographic separation The discussed model was solved with typical initial and is time-consuming; therefore, a faster algorithm based on boundary conditions and the kinetic parameters were cal- design of experiments (DoE) was also investigated. culated as follows. The mass transfer coefficient, k , was The DoE method allows one to conduct just a few experi- ext evaluated from the Wilson–Geankoplis correlation : ments to describe the system variance. In DoE, all factors (in this case, superficial fluid velocity, injection time, col- 1.09 1∕3 1∕3 Sh = Re Sc , (8) umn length, and particle diameter) are studied at different levels (i.e., low, medium, and high). As the total number of where Sh is the Sherwood number, Re the Reynolds number, required experiments increases rapidly with the number of factors, reduced design schemas are often employed. The and Sc the Schmidt number: 1 3 854 J. Samuelsson et al. Taguchi model is a special orthogonal array approach that (97%) from Sigma-Aldrich (Steinheim, Germany) was used drastically reduces the number of needed experiments . to estimate the void volume. The analytical scale experi- In this study, four factors were considered at three levels. ments were performed on Agilent 1100 and 1200 HPLC For such cases, Taguchi proposes the L orthogonal array, systems (Palo Alto, CA, USA) consisting of a binary pump, which reduces a full-factor design of 81 (3 ) experiments to a preparative auto-sampler (900 µL, max. 200 bar) and a only nine (see Tables S1–S4 in Electronic Supplementary diode array UV detector. At analytical scale, 0.46-cm-i.d. Material). Kromasil AmyCoat columns from Akzo Nobel Pulp and Per- The Taguchi optimum can be calculated as: formance Chemicals AB (Bohus, Sweden), 10-, 15-, and 25-cm long and packed with 10- and 25-µm particles, were (Pr∕L) = T + A − T + B − T + C − T + D − T , used. An additional 10 × 0.46-cm AmyCoat column packed opt max max max max with 5-µm particles was used in the validation experiments. (13) The column temperature was kept at 23.0 °C by immers- where A , B , C and D are the highest average max max max max ing the columns in a temperature-controlled water bath. effects of the factors corresponding to the optimal values The pilot-scale experiments were performed using a Packer of the factors; and T is the grand average of productivity, LC50.340 VE100 PS TH column (Novasep, Boothwyn, PA, obtained by averaging the results of all trial combinations USA), 50-mm i.d., packed to a bed height of 105 mm with of factors and levels: AmyCoat 5-µm particles (same batch as used in the analyti- cal columns), together with two K-1800 preparative pumps T = (Pr ∕L), (14) i and a K-2600 UV detector (Knauer, Berlin, Germany). i=1 Procedures where Pr is the productivity of individual trials. The average effect of a factor at a given level is calculated by averaging The holdup volumes were estimated on all columns for both all productivities containing the factor level of interest: eluents by injecting 5 µL of diluted 1,3,5-tri-tert-butylben- −1 3 3 zene three times at a flow rate of 2 mL min (except at 1 1 −1 A = (Pr ∕L), B = (Pr ∕L), pilot scale, at which the flow rate was 205 mL min ) when i i,j i i,j 3 3 j=1 j=1 detecting at 220 nm. The average elution volume was consid- (15) 3 3 ered to be the void volume of the column. Analytical injec- 1 1 −1 C = (Pr ∕L) and D = (Pr ∕L), i i,j i i,j tions of 5 µL of 1 g L omeprazole dissolved in MeOH and 3 3 j=1 j=1 −1 of 0.35 g L etiracetam dissolved in 60/40% (v/v) ethanol/ heptane were performed and recorded at 220 nm. The pres- −1 sure/flow rate dependence was determined at 1–5 mL min where A , B , C and D are the average effects (i.e., produc- i i i i for all column lengths and packing material particle sizes tivity) of the considered factors at the ith level; and Pr is i,j using pure methanol as well as 60/40% (v/v) ethanol/hep- the productivity calculated for the considered factor at the tane as the eluent. The system pressure contributions of the ith level in accordance with the L array (see Tables S1–S4). Agilent 1100 and 1200 systems were also measured without −1 columns at 1–5 mL min using both eluents. Overloaded duplicate samples of 50, 100, 200, 400, 600, and 900 µL −1 of 30 g L omeprazole and triplicate samples of 50, 75, Experimental −1 100, 150, 200, 250, 300, and 350 µL of 60 g L etiracetam −1 were injected into each column. A flow rate of 2 mL min Apparatus and Chemicals was maintained for both substances. Chromatograms were recorded at 345 nm for omeprazole and 260 nm for The solutes used in this study were R/S-omeprazole and R/S- etiracetam obtained from AstraZeneca (Mölndal, Sweden) etiracetam. and UCB Pharma (Bruxelles, Belgium), respectively. As eluent, HPLC-grade (99.99%) methanol from Fisher Sci- Calculations entific (Loughborough, UK) was used for omeprazole  and 60/40% (v/v) ethanol/heptane was used for etiracetam The adsorption parameters needed to solve Eq. (1) were estimated from the experimental overloaded elution profiles . The ethanol was analytical grade (99.90%) from VWR International (Fontenay-sous-Bois, France) and the heptane using the inverse method. Before calculating the adsorption parameters using the inverse method, the UV absorbance was HPLC grade (99%) from Fisher Scientific (Loughbor - ough, UK). In all experiments, 1,3,5-tri-tert-butylbenzene was converted to concentration. This was done by fitting 1 3 Optimizing Column Length and Particle Size in Preparative Batch Chromatography Using… 855 the UV response to the elution profile and requiring that the dependent on the eluent and the maximum allowed pressure mass balance equation be fulfilled . drop (80 or 200 bar) in the separation. The optimum productivity was calculated as a function of the flow rate, column length, packing material diameter, and injection time. As constraints, the maximum allowed Results and Discussion backpressure was set to 80 or 200 bar, and the purity of the products to 99%. Numerical Model Validation In the calculations, the particle size was varied between 5 −1 and 25 µm, the flow rate was set to 5 mL min , the pressure Previously, the equilibrium–dispersive (ED) column model constraint was as calculated from the experimental meas- has been used to describe the enantiomeric separation of urements, the column length was varied between 100 and omeprazole . However, the analytical peaks for ome- 250 mm, and the injection volume was limited to a maxi- prazole were tailing. To deduce whether this peak tailing is mum of 900 µL. All calculations were conducted assuming due to thermodynamic (overloading) reasons, the column the column to have an inner diameter of 4.6 mm. The par- load of omeprazole was reduced from 25 µg to 1.25 µg ticle diameter, superficial fluid velocity, and column length on a 250 × 4.6 mm column without any reduction in peak were limited by the pressure drop, which is the sum of the tailing, see Fig. S1 in the Electronic Supplementary Mate- column pressure drop and the pressure drop contributed by rial. We also noted that increasing the flow rate from 0.25 −1 the system. The pressure drop of the Agilent system was to 2 mL min resulted in increased tailing, see Fig. S2 approximated by a polynomial relationship based on experi- in the Electronic Supplementary Material. We, therefore, mental data and the column pressure drop was calculated conclude that the peak tailing occurs due to kinetic rea- using the Blake–Kozeny equation. sons, namely, a slow adsorption–desorption process. From In the numerical optimization, the particle diameter and a model perspective, the kinetic tailing is handled using column length were considered continuous variables in the a kinetic representation of the adsorption isotherm, see optimization, so they were rounded to the nearest real value Eq. (5). after optimization. To calculate the elution profiles more accurately, the In the Taguchi approach, four variables (factors) were EDEG model was used (see subsection “Column Model” considered at three levels, as follows: superficial velocity in the “Theory” section). The inverse method was used of the mobile phase (u , 2/3 u , and 1/3 u ), injection to estimate the adsorption isotherm parameters for the max max max volume (0.9, 0.6, and 0.3 cm ), column length (25, 15, and enantiomeric separation of omeprazole and etiracetam 10 cm), and particle diameter (25, 10, and 5 µm). The u is at different column lengths and particle sizes. Figure 1 max Fig. 1 Experimental chroma- ab tograms (blue lines) and model predictions (red lines) of the enantiomeric separation of ome- −1 prazole. Flow rate, 2 mL min ; injection volume, 200 μL. Col- umns: a 10 μm, 4.6 × 100 mm; b 10 μm, 4.6 × 150 mm; c 10 μm, 4.6 × 250 mm; d cd 25 μm, 4.6 × 100 mm; e 25 μm, 4.6 × 150 mm; and f 25 μm, 4.6 × 250 mm ef 1 3 856 J. Samuelsson et al. corresponding to a 118-times scale-up (see Fig. 3). Both columns, approximately 100-mm long, were packed with 5-µm AmyCoat packing. In Fig. 3a, the separation on the 4.6-mm-i.d. column is plotted; this separation was −1 performed with an 85-µL injection of 30 g L omepra- b −1 zole at a flow rate of 1.7 mL min . Figure 3b shows the corresponding pilot-scale separation, performed with a −1 10-mL injection of 30 g L omeprazole at a flow rate of −1 205 mL min . As it can be seen, the experiments con- ducted at analytical scale and pilot scale differed only slightly in their results, so it can be concluded that this process is likely scalable and that our model could be used to predict elution profiles. Optimal Column Length and Particle Size Fig. 2 Experimental chromatograms (blue lines) and model predic- tions (red lines) of the enantiomeric separation of etiracetam. Flow −1 rate, 2 mL min ; injection volume, 150 μL. Columns: a 5 μm, Based on the model validation results, the enantiomeric 4.6 × 100 mm; b 10 μm, 4.6 × 150 mm; and c 25 μm, 4.6 × 150 mm separation of omeprazole and etiracetam was numeri- cally optimized and experimentally confirmed. Table 1 presents the optimal experimental settings as well as the calculated productivity. Figures 4, 5 present the calcu- lated optimal conditions for the enantiomeric separa- tion of omeprazole and etiracetam at 80 and 200 bars, respectively, for the R and S enantiomers with overlaid experimental verification. In both cases, relatively good agreement was obtained. The optimum particle size for omeprazole at 80 and 200 bar is 5 µm, and the maximum productivity was found at the minimum allowed column length of 10 cm. When the maximum allowed pressure was increased from 80 to 200 bar, this resulted in an approximately 1.5 times higher productivity, while the solvent consumption decreased 0.6 times. The reduced solvent consumption with increased pressure is in line with the previous findings . For etiracetam, the optimum packing at 80 and 200 bar Fig. 3 Enantiomeric separation of omeprazole on AmyCoat col- is 10 µm and, as in the case of omeprazole, the short- umns at analytical scale (top, blue line) and pilot scale (bottom, green line). Analytical separation on a 100 × 4.6 mm column using a est column of 10 cm should be used at both pressures. −1 85-µL sample of 30 g L racemic omeprazole injected at a flow rate Increasing the maximum allowed pressure from 80 to −1 of 1.7 mL min ; pilot separation on a 105 × 50 mm column using a 200 bar led to approximately 1.4 times higher productiv- −1 10-mL sample of 30 g L racemic omeprazole injected at a flow rate −1 ity, while the solvent consumption decreased by 0.6 times. of 205 mL min This clearly indicates that pressure is the most important factor in increasing the productivity, because it allows presents the experimental chromatograms and the model the operational flow rate to increase. This also suggests predictions for the enantiomeric separation of omeprazole, that using smaller particles will result in more productive while Fig. 2 presents the corresponding experimental and processes. predicted results for etiracetam. Inspecting Figs. 1 and 2, From Table 1, we also see, as suspected, that the pro- we can conclude that the numerical models describe the ductivity is always higher for the first-eluted compound experimental data well. (i.e., S-omeprazole and R-etiracetam), for both sys- To investigate potential scale-up issues, the enantio- tems. However, the etiracetam process is approximately meric separation of omeprazole conducted on a 4.6-mm- 4–5 times more productive than the omeprazole pro- i.d. column was compared with separation experi- cess, mainly because the cycle time is much shorter for ments conducted on a 50-mm-i.d. pilot-scale column, 1 3 Optimizing Column Length and Particle Size in Preparative Batch Chromatography Using… 857 Table 1 Optimum conditions for first- and second-eluted enantiomers of omeprazole and etiracetam, respectively −1 2 a 2 b 3 Compound Target ΔP (bar) Method L (cm) d (µm) u (cm min ) t (min) Pr × 10 Pr × 10 SP × 10 max p inj −1 −1 −1 (g min ) (g min ) (g cm ) Omeprazole S (1) 80 T 10 25 8.32 0.651 0.8336 0.9376 0.7642 SS 10 5 12.20 0.342 1.337 – 0.8363 200 T 10 5 30.08 0.180 1.678 1.616 0.4260 SS 10 5 29.55 0.119 1.995 – 0.5150 R (2) 80 T 10 5 8.32 0.651 0.5940 0.5762 0.5445 SS 10 5 12.40 0.186 0.8417 – 0.5177 200 T 10 5 30.08 0.180 1.296 0.9800 0.3291 SS 10 5 29.59 0.1027 1.345 – 0.3469 Etiracetam S (2) 80 T 15 5 4.80 1.128 2.535 2.526 3.792 SS 10 10 12.32 0.087 4.659 – 2.695 200 T 10 5 25.0 0.217 4.178 3.793 1.199 SS 10 10 29.47 0.040 6.542 – 1.582 R (1) 80 T 15 5 4.80 0.376 3.392 2.576 5.073 SS 10 10 12.35 0.140 6.270 – 3.618 200 T 15 5 16.7 0.324 6.868 8.931 1.969 SS 10 10 23.60 0.062 7.463 – 2.254 Two optimization methods were used: T Taguchi and SS simulated annealing + simplex. The numbers 1 and 2 under “Target” indicate the first- and second-eluting enantiomers In the Taguchi method, the productivity is calculated using the column model with optimum run conditions predicted using the Taguchi method Productivity is estimated using the Taguchi method, Eq. (13) Fig. 4 Experimental (blue lines) ab and calculated (red lines) opti- mal conditions for the enantio- meric separation of omeprazole and etiracetam at 80 bar for the first- and second-eluted enan- tiomers. Optimal conditions for: a first-eluted enantiomer of omeprazole, b second-eluted enantiomer of omeprazole, c first-eluted enantiomer of etiracetam, and d second-eluted enantiomer of etiracetam cd etiracetam than for omeprazole. Other factors that increase Taguchi vs. Classical Numerical Optimization the productivity for etiracetam are that the separation sys- tem is more efficient and that the sample concentration of The Taguchi approach was investigated to see whether it etiracetam is double that of omeprazole due to solubility could speed up the optimization process. From a practical reasons. perspective, the Taguchi method could be interesting as 1 3 858 J. Samuelsson et al. an alternative/complement to touching-band optimization, (see Tables S1–S4 in Electronic Supplementary Material because it could simplify the selection of column length, for more information). The optimal decision variables and packing material, packing material particle size, etc. productivity estimated using Taguchi optimization are pre- Here, the Taguchi method required only nine experiments sented in Table 1. In Fig. 6, the normalized average effects to optimize the column length, stationary-phase packing of all decision variables are plotted for the optimization of material particle size, injection volume, as well as flow rate S-omeprazole and R-etiracetam at 200 and 80 bar. Fig. 5 Experimental (blue lines) ab and calculated (red lines) opti- mal conditions for the enantio- meric separation of omeprazole and etiracetam at 200 bar for the first- and second-eluted enan- tiomers. Optimal conditions for: a first-eluted enantiomer of omeprazole, b second-eluted enantiomer of omeprazole, c first-eluted enantiomer of etiracetam, and d second-eluted enantiomer of etiracetam cd Fig. 6 Plot of factor average effect minus the grand aver - ab age in Taguchi optimization, optimized system: a omeprazole (S), pressure restriction 200 bar; b etiracetam (R), pressure restriction 200 bar; c omepra- zole (S), pressure restriction 80 bar; d etiracetam (R), pres- sure restriction 80 bar. The gray line is the grand average cd 1 3 Optimizing Column Length and Particle Size in Preparative Batch Chromatography Using… 859 In the omeprazole case, roughly the same optimal condi- achieve maximum productivity. We also compared advanced tions were predicted using both the numerical and Taguchi numerical optimization based on a mechanistic model with methods. At 80 bar, the Taguchi method suggested using empirical optimization, i.e., the Taguchi method, with the lat- smaller packing than did the numerical method. How- ter being more readily available in the laboratory to the general ever, the average effects of stationary-phase packing par - chromatographer. ticle diameter calculated using the Taguchi method were Both separation systems were numerically optimized to only slightly worse for 5-µm than for 25-µm particles (see derive the optimal packing material particle size, column Fig. 6c). Inspecting the productivity, in Table 1, the classi- length, and flow rate. Maximum allowed backpressures of 80 cal numerical method predicted much higher productivity and 200 bar were investigated. Preparative chromatography is for the 80 bar omeprazole separation for both enantiomers often conducted using large-particle-diameter packing mate- than did the Taguchi method. This is because Taguchi opti- rial and a column length of 25 cm. Here, we demonstrated mization was flow limited, i.e., operating at the maximum that, in the studied batch chromatography cases, shorter col- allowed flow rate. The maximum allowed flow rate in the umns were more suitable when using packing materials with Taguchi method was set to the maximum allowed flow rate smaller stationary-phase particle sizes. In both investigated for the longest column (25 cm) packed with the smallest cases, a column length of 10 cm was found to be optimal. We stationary-phase packing particles (5 µm). When the Taguchi also demonstrated that increasing the maximum allowed back- method was flow limited, the maximum allowed flow rate pressure 2.5 times resulted in approximately 1.5 times greater could not be increased by decreasing the column length or productivity and a 0.6 times reduction in solvent consumption. increasing the packing material particle size, as can be done In this study, we also used the Taguchi method, a chemo- in classical numerical optimization. Therefore, the velocities metric method that can work strictly from experimental data. obtained from Taguchi and from classical numerical optimi- The Taguchi method is easy to learn and use for the practical zation differed from each other. chromatographer. It is very suitable for quickly determining In the etiracetam case, larger differences in optimal sepa- optimal discrete parameters or pre-estimating an objective ration systems were found between the classical numerical function, as exemplified in this study by determining what and Taguchi methods than in the omeprazole case (Table 1). column length and particle diameter should be used to achieve In this case, the Taguchi method suggested that longer col- the highest productivity. In this study, we noted that short col- umns packed with smaller packing particles should be used umns packed with smaller particles were preferable to longer than did the numerical method. To explain these differences, columns packed with larger particles. The optimum process first, we note that the separation was flow limited (except conditions were not exactly found, this is why we still recom- for R-etiracetam at 200 bar) in the Taguchi optimization. As mend classical numerical optimization for the most accurate a consequence, longer columns and smaller packing were process optimization. However, this study clearly demonstrates found as optimum by the Taguchi method (see Fig. 6b, d). that quite acceptable predictions can be achieved with less In the 200 bar case, the column length had very small impact numerical effort. on the optimum; see Fig. 6b. Acknowledgements This work was supported by the Swedish Knowl- The Taguchi approach is very useful and successful, edge Foundation as part of the KKS SYNERGY project 2016 “BIO- mainly in areas where optimal values of discrete decision QC: Quality Control and Purification for New Biological Drugs” (grant variables, such as packing particle diameter and column number 20170059) and by the Swedish Research Council (VR) as part of the project “Fundamental Studies on Molecular Interactions aimed at length, are to be determined. The Taguchi method is easy Preparative Separations and Biospecific Measurements” (Grant number to apply in such cases, but it may be difficult to establish 2015-04627). We also thank the National Science Centre, Poland for appropriate Taguchi design spaces in more complex optimi- support via Grant number 2015/18/M/ST8/00349. We are grateful to zations such as those presented here. To conclude, the Tagu- AstraZeneca and UCB Pharma for kindly giving us omeprazole and etiracetam, respectively, and to Kromasil/Akzo Nobel Pulp and Perfor- chi approach could be recommended for relatively simple mance Chemicals AB for giving us the AmyCoat columns. optimization or pre-optimization to help in selecting column packing, etc. For accurate and complicated optimizations, Compliance with Ethical Standards however, classical numerical methods are still preferred. Conflict of interest All authors declare that they have no conflict of interest. Conclusion Ethical approval This article does not contain any studies with human participants or animal performed by any of the authors. In this study, we have considered, given a column of a cer- Open Access This article is distributed under the terms of the Crea- tain diameter, what column length should be selected and tive Commons Attribution 4.0 International License (http://creat iveco what sized particles that the column should be packed with to 1 3 860 J. Samuelsson et al. mmons.or g/licenses/b y/4.0/), which permits unrestricted use, distribu- 18. Forssén P, Samuelsson J, Fornstedt T (2013) Relative impor- tion, and reproduction in any medium, provided you give appropriate tance of column and adsorption parameters on the productivity credit to the original author(s) and the source, provide a link to the in preparative liquid chromatography. I: investigation of a chi- Creative Commons license, and indicate if changes were made. ral separation system. 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