# Residence Time Section Evaluation and Feasibility Studies for One-Column Simulated Moving Bed Processes (1-SMB)

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Chromatography Columns, Buffers and Feed

^{®}SI 60 material (15–25 µm, Merck KGaA, Darmstadt, Germany) using Superformance

^{®}600-16 columns (Götec-Labortechnik GmbH, Bickenbach, Germany) with a 12.5 cm bed length. All the chromatography runs were isocratic, with 85% (v/v) hexane (LiChrosolv

^{®}, Merck KGaA) and 15% (v/v) ethyl acetate (LiChrosolv

^{®}, Merck KGaA). A mixture of cyclopentanone (purity 99%) and cycloheptanone (purity 98%) from Alfa Aesar (Haverhill, MA, USA) was used as a test substance. For the overloaded conditions, a selectivity α of 1.29 and a resolution R

_{s}of 0.46 were found, which were calculated with Equations (1) and (2):

#### 2.2. Chromatography Modeling

#### 2.2.1. General Rate Model

#### 2.2.2. Mass Balance of Mobile Phase

#### 2.2.3. Mass Balance of Stationary Phase

_{p,I}, and surface diffusion, D

_{S,i}[23,26]:

_{eff}[26,27]:

#### 2.2.4. Adsorption Equilibrium

_{i}. However, it is possible to convert between these different notations using the following equation:

#### 2.3. Model Parameter Determination

#### 2.3.1. Fluid Dynamics

#### 2.3.2. Adsorption Equilibrium

^{®}SI 60 material to determine the isotherms of the cyclopentanone/cycloheptanone mixture. A mixture of 85 vol.-% hexane and 15 vol.-% ethyl acetate was used as the eluent at a flow rate of 12.5 mL/min. The adsorbent was packed in Götec glass columns with an inner diameter of 1.6 cm and a length of 10 cm.

#### 2.3.3. Mass Transport

#### 2.3.4. Model Validation

#### 2.4. Triangle Theory

#### 2.5. Axial Dispersion Coefficient for Residence Time Sections

## 3. Results and Discussion

#### 3.1. Simulated Moving Bed Design

#### 3.2. Simulation Studies

^{−4}cm

^{2}/s to 100 cm

^{2}/s.

^{−4}cm

^{2}/s and 1 cm

^{2}/s. Higher axial dispersion coefficients result in a significant mass loss in the retention sections because the concentration profiles spread too much. The front of the profiles does not remain in the retention section but is pushed beyond it into the waste. This mass loss results in lower concentrations and, therefore, accounts for the differences in the concentration profiles, as can be seen in Figure 5A. This mass loss also takes place for the lower dispersion coefficients, hence the deviation in the concentrations there but to a much smaller extent.

_{ax}values < 1 and then decreases gradually to 99.7. The column yield is calculated as the amount of product leaving the column divided by the amount of product entering the column.

_{ax}= 10

^{−4}cm

^{2}/s and decreases to 20% for the highest axial dispersion, compared to 100% for the 4-SMB. The overall yield is calculated as the amount of product gained entirely divided by the amount of product entering the whole setup.

_{ax}of 1 m

^{2}/s. The process yield, however, is roughly 10% less and decreases with increasing axial dispersion.

^{2}/s. Thus, a brief evaluation of different residence time devices is needed.

#### 3.3. Retention Time Device Concepts

#### 3.3.1. Coiled Flow Inverter (CFI)

^{2}/s, and the simulation-based estimation provided 42 cm

^{2}/s. Saxena and Nigam found a correlation in 1984 [51]:

#### 3.3.2. Packed Bed Columns

_{ax}= 10

^{−4}cm

^{2}/s. Additionally, columns packed with 0.5 mm glass beads were tested. These had a measured D

_{ax}of 0.016 cm

^{2}/s. The model estimate was 0.022 cm

^{2}/s and a correlation of Chung and Wen ([53], Equation (24)) would yield 0.077 cm

^{2}/s.

#### 3.3.3. Tank Cascades or Sequential Setups

^{2}/s.

#### 3.3.4. Eluate Recycling Device

## 4. Conclusions

^{2}/s. No changes in performance data were observed between D

_{ax}= 10

^{−4}cm

^{2}/s and 10

^{−1}. At a D

_{ax}of 1 cm

^{2}/s, the yield and productivity decrease slightly. With a further increase, the trend intensifies significantly.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

α | Selectivity | |

${c}_{i}$ | (g/L) | Concentration of component i |

${c}_{p,i}$ | (g/L) | Concentration of component i inside the pores |

${D}_{ax}$ | (cm^{2}/s) | Axial dispersion coefficient |

D_{eff} | (cm^{2}/s) | Effective diffusion coefficient |

${d}_{p}$ | (cm) | Particle diameter |

D_{p,i} | (cm^{2}/s) | Pore diffusion coefficient |

D_{S,i} | (cm^{2}/s) | Surface diffusion coefficient |

${\epsilon}_{p,i}$ | (-) | Porosity |

${\epsilon}_{s}$ | (-) | Voidage |

${\epsilon}_{t}$ | (-) | Total porosity |

H_{i} | (-) | Henry coefficient of component i |

K_{i} | (L/g) | Langmuir coefficient of component i |

${k}_{eff}$ | (cm/s) | Effective mass transport coefficient |

k_{f} | (cm/s) | Mass transport coefficient |

l | (cm) | Length |

m_{j} | Mass flow ratio of zone j | |

n | Number of bends | |

PAT | Process analytical technology | |

q_{i} | (g/L) | Loading of component i |

q_{max,i} | (g/L) | Maximum loading capacity of component i |

r | (cm) | Radius |

Re | (-) | Reynolds number |

${R}_{p}$ | (cm) | Particle radius |

R_{s} | Resolution | |

t | (s); (min) | Time |

t_{0} | (s); (min) | Dead time |

t_{R}_{1} | (s); (min) | Retention time peak 1 |

t_{R}_{2} | (s); (min) | Retention time peak 2 |

$\overline{{t}_{i}}$ | (s); (min) | Mean residence time |

${u}_{int}$ | (cm/s) | Interstitial velocity |

v | (cm/s) | Velocity |

$\dot{V}$ | (mL/min) | Volumetric flow |

${V}_{column}$ | (mL) | Volume of column |

$\eta $ | (mg/cm*s) | Dynamic viscosity |

$\rho $ | (g/L) | Density |

${\sigma}^{2}$ | (s^{2}) | Variance |

${\omega}_{i}$ | Mass fraction of component i | |

w_{b}_{1} | (s); (min) | Peak width peak 1 |

w_{b}_{2} | (s); (min) | Peak width peak 1 |

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**Figure 1.**(

**A**) Simplified process flow diagram of a 4-SMB with 5 pumps. (

**B**) Simplified process flow diagram of a 1-SMB with 2 pumps.

**Figure 2.**Process flow charts of one cycle of a 1-SMB. Depicted is the end of the cycle just before switching to the next zone.

**Figure 3.**Triangle diagram for cyclopentanone/cycloheptanone. The dark blue triangle is valid for low concentrations representing the linear region of the Langmuir isotherm. For higher concentrations, the triangle shifts to the right, as depicted with the light blue lines. The orange triangle represents the working condition for Zones I and IV.

**Figure 4.**Working diagram for the test mixture cyclopentanone/cycloheptanone with 5 g/L feed concentration.

**Figure 5.**SMB chromatograms for working point 1. The signal is measured at the column outlet. The red lines indicate the extract, the blue lines indicate raffinate. (

**A**): 1-SMB with plug flow with varying axial dispersion. The solid lines represent the classical 4-column SMB, the dashed lines represent 1-SMB with pipes. (

**B**) 1-SMB with tanks (double lines).

**Figure 6.**Process metrics for working point 1. (

**A**) for raffinate/cycloheptanone (C7) and (

**B**) for extract/cyclopentanone (C5). On the primary axis: purity (%, blue), yield (%, red for column yield, green for process yield) and productivity (g/L/d, purple). On the secondary axis: eluent consumption (L/g, turquoise).

**Figure 7.**SMB Chromatograms for working point 2. The signal is measured at the column outlet. The red lines indicate the extract, the blue lines indicate raffinate. (

**A**) 1-SMB with plug flow with varying axial dispersion. The solid lines represent the classical 4-column SMB, the dashed lines represent 1-SMB with pipes. (

**B**) 1-SMB with tanks (double lines).

**Figure 8.**Process metrics for working point 2. (

**A**) for raffinate/cycloheptanone (C7) and (

**B**) for extract/cyclopentanone (C5). On the primary axis: purity (%, blue), yield (%, red for column yield, green for process yield) and productivity (g/L/d, purple). On the secondary axis: eluent consumption (L/g, turquoise).

Point | m2 | m3 |
---|---|---|

a | ${H}_{2}$ | ${H}_{2}$ |

b | ${H}_{1}$ | ${H}_{1}$ |

r | $\frac{{\omega}_{2}{}^{2}}{{H}_{2}}$ | $\frac{{\omega}_{2}\xb7\left[{\omega}_{2}\xb7\left({H}_{1}-{\omega}_{1}\right)+{\omega}_{1}\xb7\left({H}_{2}-{H}_{1}\right)\right]}{{H}_{1}\xb7\left({H}_{2}-{\omega}_{1}\right)}$ |

w | $\frac{{\omega}_{2}\xb7{H}_{1}}{{H}_{2}}$ | $\frac{{\omega}_{2}\xb7\left[{H}_{1}\xb7\left({H}_{1}-{\omega}_{1}\right)+{\omega}_{1}\xb7\left({H}_{2}-{H}_{1}\right)\right]}{{H}_{1}\xb7\left({H}_{2}-{\omega}_{1}\right)}$ |

Working Point 1 | Working Point 2 | |
---|---|---|

m1 | 9.4 | 10.1 |

m2 | 6.4 | 6.9 |

m3 | 6.9 | 7.3 |

m4 | 5.9 | 4.9 |

Purity | Yield Column | Yield Process | Productivity | Eluent Consumption | ||||||
---|---|---|---|---|---|---|---|---|---|---|

C5 | C7 | C5 | C7 | C5 | C7 | C5 | C7 | C5 | C7 | |

4-SMB | 100 | 100 | 100 | 100 | 100 | 100 | 89.5 | 89.5 | 1.4 | 1.4 |

D_{ax} 0.0001 | 99.9 | 100.0 | 100.0 | 100.0 | 93.9 | 87.1 | 84.0 | 78.0 | 1.5 | 1.6 |

D_{ax} 0.001 | 99.9 | 100.0 | 100.0 | 100.0 | 93.9 | 87.1 | 84.0 | 78.0 | 1.5 | 1.6 |

D_{ax} 0.01 | 99.9 | 100.0 | 100.0 | 100.0 | 93.8 | 87.0 | 84.0 | 77.9 | 1.5 | 1.6 |

D_{ax} 0.1 | 99.9 | 100.0 | 100.0 | 100.0 | 93.6 | 86.5 | 83.8 | 77.4 | 1.5 | 1.6 |

D_{ax} 1 | 99.9 | 100.0 | 100.0 | 100.0 | 91.5 | 82.0 | 81.9 | 73.4 | 1.5 | 1.7 |

D_{ax} 10 | 99.9 | 100.0 | 100.0 | 99.9 | 79.4 | 58.7 | 71.1 | 52.5 | 1.8 | 2.4 |

D_{ax} 40 | 99.9 | 100.0 | 100.0 | 99.9 | 55.5 | 38.7 | 49.7 | 34.7 | 2.5 | 3.6 |

D_{ax} 100 | 99.1 | 100.0 | 100.0 | 99.7 | 50.0 | 20.0 | 44.7 | 17.9 | 2.8 | 7.0 |

Tank | 92.1 | 99.4 | 99.8 | 97.4 | 99.3 | 86.5 | 88.9 | 77.5 | 1.4 | 1.6 |

Tank—10 sec cut | 99.9 | 98.9 | 99.6 | 100 | 13.5 | 3.1 | 12.1 | 2.7 | 10.4 | 45.7 |

Purity | Yield Column | Yield Process | Productivity | Eluent Consumption | ||||||
---|---|---|---|---|---|---|---|---|---|---|

C5 | C7 | C5 | C7 | C5 | C7 | C5 | C7 | C5 | C7 | |

4-SMB | 100 | 100 | 100 | 100 | 100 | 100 | 89.5 | 89.5 | 2.6 | 2.6 |

D_{ax} 0.0001 | 100 | 100 | 100 | 100 | 90.9 | 91.8 | 81.4 | 82.2 | 2.9 | 2.8 |

D_{ax} 0.001 | 100 | 100 | 100 | 100 | 90.9 | 91.8 | 81.4 | 82.2 | 2.9 | 2.8 |

D_{ax} 0.01 | 100 | 100 | 100 | 100 | 90.9 | 91.8 | 81.4 | 82.2 | 2.9 | 2.8 |

D_{ax} 0.1 | 100 | 100 | 100 | 100 | 90.6 | 91.5 | 81.1 | 81.9 | 2.9 | 2.8 |

D_{ax} 1 | 100 | 100 | 100 | 100 | 88.4 | 88.8 | 79.2 | 79.5 | 2.9 | 2.9 |

D_{ax} 10 | 100 | 99.9 | 100 | 100 | 75.5 | 73.1 | 67.6 | 65.5 | 3.4 | 3.6 |

D_{ax} 40 | 99.9 | 99.9 | 99.9 | 99.9 | 59.3 | 53.6 | 53.1 | 48 | 4.4 | 4.8 |

D_{ax} 100 | 99.8 | 99.8 | 99.9 | 99.8 | 46.1 | 39.2 | 41.3 | 35.1 | 5.6 | 6.6 |

Tank | 99.4 | 96.8 | 97.6 | 99.5 | 96.6 | 99.8 | 86.5 | 89.4 | 2.7 | 2.6 |

Tank—10 sec cut | 99.8 | 99.4 | 99.6 | 99.9 | 5 | 6.8 | 4.4 | 6.1 | 52.4 | 38 |

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**MDPI and ACS Style**

Zobel-Roos, S.; Vetter, F.; Strube, J.
Residence Time Section Evaluation and Feasibility Studies for One-Column Simulated Moving Bed Processes (1-SMB). *Processes* **2023**, *11*, 1634.
https://doi.org/10.3390/pr11061634

**AMA Style**

Zobel-Roos S, Vetter F, Strube J.
Residence Time Section Evaluation and Feasibility Studies for One-Column Simulated Moving Bed Processes (1-SMB). *Processes*. 2023; 11(6):1634.
https://doi.org/10.3390/pr11061634

**Chicago/Turabian Style**

Zobel-Roos, Steffen, Florian Vetter, and Jochen Strube.
2023. "Residence Time Section Evaluation and Feasibility Studies for One-Column Simulated Moving Bed Processes (1-SMB)" *Processes* 11, no. 6: 1634.
https://doi.org/10.3390/pr11061634