# Process Monitoring of Antisolvent Based Crystallization in Low Conductivity Solutions Using Electrical Impedance Spectroscopy and 2-D Electrical Resistance Tomography

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{12}H

_{22}O

_{11}) production has a significant importance, and crystallization plays a fundamental role in its manufacturing process. Applications of process monitoring techniques in sucrose crystallization and manufacturing have been seldom reported in the literature and works have been limited to cooling and evaporative crystallization and concentration measurements [30]. For instance, applications of EIS [31] and image acquisition by high-speed camera [32] have been successfully demonstrated during cooling crystallization of sucrose. Moreover, ultrasound computed tomography [7] systems have been used to evaluate concentration change in different sucrose solutions. Therefore, advancement in innovative monitoring methods and new crystallization techniques are critical to ensuring the improvement in final particle quality as well as intensifying the overall process in terms of energy and sustainability.

## 2. Application of 1-D EIS and 2-D ERT as a PAT in Crystallization Processes

#### 2.1. Application of Electrical Impedance Spectroscopy to the Crystallization Process

_{2}CO

_{3}have been performed [30]. The study of impedance signatures as a PAT tool for sucrose crystallization was recently done by [31]. During the crystallization of sugar using ethanol as an antisolvent, there is a mixture of three components in the solution. The impedances of all these three individual components are different. The study of the impedance signatures of sucrose solutions at various concentrations and at various ethanol to water ratios, and to model them into a transfer function is our interest of study in this module. Figure 1a shows the schematic of the setup made for the antisolvent crystallization. Figure 1b shows the sucrose–water phase equilibrium.

#### 2.2. Application of a Voltage Injected–Current Detected (V–C) Based Low Conductivity Sensitive Electrical Resistance Tomography (ERT)

_{n}is the characteristic function, and X

_{n}= 1 in the n

^{th}element, and Ω

_{n}and X

_{n}= 0 otherwise.

_{1},…x

_{N})

^{T}is p(x). The joint density of the components of two random vectors x and y are denoted by p(x,y). The cross-covariance of x and y is defined as [54];

## 3. Experimental Setup, Materials, and Procedure

#### 3.1. Experimental Apparatus Setup for EIS (Electrical Impedance Spectroscopy)

#### 3.2. Experimental Apparatus Setup for ERT (Electrical Resistance Tomography)

^{2}. The signal processing unit containing the amplifier and the noise removal electronics was mounted directly on the sensor tail. Using the MCX type of insulating co-axial cable, lossless transmission was achieved. The data acquisition system from Rocsole Inc. was utilized to acquire the ERT data. The Roc-GUI software interface was used to communicate between the ERT machine and the computer. The Bayesian reconstruction method was used to reconstruct the images [51].

## 4. Results and Discussion

#### 4.1. Results for EIS

#### 4.1.1. EIS of the Solutions before Adding Ethanol

#### 4.1.2. EIS of Solutions after Addition of Ethanol

#### 4.1.3. Creating Transfer Function Models from EIS Data and Comparative Analysis

`deg2rad`. The impedance magnitude and phase in radians was converted into a rectangular complex number format. This complex variable was created using Magnitude–Angle to complex block using the Simulink® software. Figure 7 shows the Simulink program to autogenerate the complex variables for the recorded impedance spectra. This complex variable was further used to create a frequency response data (frd) model object in MATLAB.

_{0}to a

_{n}gives the coefficients of the numerator polynomial and b

_{0}to b

_{m}gives the coefficients of the denominator polynomial. m is the number of zeroes, and n is the number of poles in the system. The equivalent factorized form of the transfer function is given as

_{1}, z

_{2}…, z

_{m}are zeroes of the system and p

_{1,}p

_{2}…, p

_{n}are poles of the system.

_{1}, A

_{0}, B

_{1}, and B

_{0}of the Model 3, and B

_{2}= 1. The increase in A

_{1}was observed as the ethanol to water ratio is increased, whereas a decrease was observed in the coefficients A

_{0}, B

_{0}, and B

_{1}. The decrease in coefficients was greater for the lower concentration of ternary solutions of 33% w/w and 44% w/w as compared to the solutions with higher concentrations. The analysis of the model parameters shows a clear dependence between the concentration of the sucrose constituent component with EIS measurements. Accordingly, at a given sucrose concentration, the model parameters can be utilised to correspond to specific ethanol to water ratio present in the crystallizer. The variable domain obtained through the estimated transfer function model provides a framework to evaluate the concentration variation at a given operating condition during the antisolvent crystallization. This is an essential task that could lead to the design of a process control unit.

#### 4.2. Results for Electrical Resistance Tomography Experiments

_{i}is the dataset of all currents (i1-i15) for sensor excited with voltage V.

_{Normalized}from 0 to 1. Similar results were obtained using ERT techniques in gas hold up applications within stirred vessel [61].

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

PAT | Process analytical technology |

ERT | Electrical resistance tomography |

ECT | Electrical capacitance tomography |

EIS | Electrical impedance spectroscopy |

FEM | Finite element method |

Hz | Hertz (measure of frequency) |

w/w % | Weight to weight ratio in percentage |

K | Steady-state gain constant |

$\tau $ | Time constant |

V–C based ERT | Voltage injected and current detected ERT |

C–V based ERT | Current injected and voltage detected ERT |

V | Voltage |

I | Current |

A | Amperes |

1-D | One dimensional |

2-D | Two dimensional |

3-D | Three dimensional |

g | Grams |

g/s | Grams per second |

L | Litres |

$\mathrm{Z}\left(\omega \right)$ | Impedance in phasor form with ω as the angular frequency |

z_{1}, z_{2} …, z_{m} | Zeroes |

p_{1,} p_{2}…, p_{n} | Poles |

$E\{x{x}^{T}\}$ | Correlation Matrix of random vector x |

${\eta}_{x}$ | Mean or Expected value |

${C}_{xy}$ | Cross covariance of x and y |

Δσ_{Normalized} | Normalized changes in conductivity |

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**Figure 1.**(

**a**) Schematic showing antisolvent crystallization; (

**b**) sucrose–water phase equilibrium diagram, Reproduced with permission from [50], Elsevier, 2016.

**Figure 2.**(

**a**) Voltage injected-current detected based electrical resistance tomography (ERT) system schematic; (

**b**) finite element method (FEM) mesh created using EIDORS.

**Figure 3.**(

**a**) Experimental setup for the impedance spectroscopy testing unit with reactor placed over magnetic stirrer and syringe pump; (

**b**) impedance spectrometer.

**Figure 4.**(

**a**) Sensor mounted with the low conductivity signal processing unit; (

**b**) ERT data acquisition flow and reconstruction system.

**Figure 5.**Impedance magnitude and phase response for sucrose solution before ethanol addition from 1 kHz to 1 MHz (

**a**,

**b**) from 50 kHz to 300 kHz (

**c**,

**d**).

**Figure 6.**Impedance magnitude and phase response of the solutions at ethanol to water ratio; 0.33 (

**a**,

**b**), 0.66 (

**c**,

**d**), and 0.99 (

**e**,

**f**) for the frequency range from 50 kHz to 300 kHz. Table 1 lists all the solutions.

**Figure 7.**Simulink program used to convert from rectangular coordinates to complex coordinates. The output data was used to create an frd model object.

**Figure 8.**Bode plot comparisons of acquired data with transfer function models for sucrose 33% w/w and (

**a**) 0% ethanol, (

**b**) sucrose to Ethanol ratio 1, (

**c**) sucrose to Ethanol ratio 0.5, (

**d**) sucrose to ethanol ratio 0.33. Table 3 shows effective sucrose to ethanol ratios for all the solutions.

**Figure 9.**Changes of Model 1 parameters. (

**a**) Gain constant K; (

**b**) system time constant $\tau $, for different working conditions.

**Figure 10.**Parameters of Model 3 for various working conditions, where: coefficients in numerator (

**a**) A

_{1}, (

**b**) A

_{0}and denominator (

**c**) B

_{1}, (

**d**) B

_{0}, and B

_{2}= 1.

**Figure 11.**(

**a**) Voltage injections at the sensor for a frame, (

**b**) Current detections through the sensors.

**Figure 12.**Tomographic reconstructions indicating conductivity changes Δσ

_{Normalized}(

**a**) A 10 mm phantom inside demineralized water (

**b**) density distribution of the sucrose crystals within industrial food grade saturated sucrose solution.

Solution Index | Effective Ethanol to Water Ratio | Different Concentrations of Sucrose Solutions (% w/w) | Sucrose Weight Percentage in 100 mL | Effective Sucrose/Ethanol Ratio in 100 mL Solution |
---|---|---|---|---|

1 | 0 | 33 | 33 | - |

2 | 44 | 44 | - | |

3 | 55 | 55 | - | |

4 | 66.67 | 66.67 | - | |

5 | 0.33 | 33 | 19.87 | 1 |

6 | 4 | 24.85 | 1.33 | |

7 | 55 | 29.25 | 1.66 | |

8 | 66.67 | 33.16 | 2 | |

9 | 0.66 | 33 | 16.58 | 0.5 |

10 | 44 | 20.95 | 0.66 | |

11 | 55 | 24.88 | 0.83 | |

12 | 66.67 | 28.44 | 1 | |

13 | 0.99 | 33 | 14.22 | 0.33 |

14 | 44 | 18.10 | 0.44 | |

15 | 55 | 21.65 | 0.55 | |

16 | 66.67 | 24.90 | 0.66 |

Model | Number of Poles | Number of Zeroes | Order of the Model |
---|---|---|---|

Model 1 | 1 | 0 | First-order |

Model 2 | 2 | 0 | Second-order |

Model 3 | 2 | 1 | Second-order with a zero |

Solution Index | Effective Ethanol to Water Ratio | Different Concentrations of Sucrose Solutions (% w/w) | Effective Sucrose/Ethanol Ratio in 100 mL Solution | Tfest Fit % | ||
---|---|---|---|---|---|---|

Model 1 | Model 2 | Model 3 | ||||

1 | 0 | 33 | - | 55.2 | 67.8 | 96.43 |

2 | 44 | - | 55.56 | 68.48 | 95.84 | |

3 | 55 | - | 62.31 | 76.26 | 93.42 | |

4 | 66.67 | - | 88.98 | 80.12 | 91.75 | |

5 | 0.33 | 33 | 1 | 64.87 | 63.73 | 95.12 |

6 | 44 | 1.33 | 71.26 | 72.85 | 94.95 | |

7 | 55 | 1.66 | 78.31 | 76.86 | 92.33 | |

8 | 66.67 | 2 | 89.94 | 80.51 | 90.9 | |

9 | 0.66 | 33 | 0.5 | 74.3 | 65.82 | 94.74 |

10 | 44 | 0.66 | 75.82 | 79.5 | 94.88 | |

11 | 55 | 0.83 | 80.38 | 81.39 | 92.03 | |

12 | 66.67 | 1 | 91.5 | 83.07 | 92.92 | |

13 | 0.99 | 33 | 0.33 | 79.22 | 89.45 | 93.29 |

14 | 44 | 0.44 | 79.1 | 90.27 | 94.13 | |

15 | 55 | 0.55 | 83 | 91.61 | 92.07 | |

16 | 66.67 | 0.66 | 92.11 | 92.2 | 93.74 |

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## Share and Cite

**MDPI and ACS Style**

Rao, G.; Aghajanian, S.; Koiranen, T.; Wajman, R.; Jackowska-Strumiłło, L.
Process Monitoring of Antisolvent Based Crystallization in Low Conductivity Solutions Using Electrical Impedance Spectroscopy and 2-D Electrical Resistance Tomography. *Appl. Sci.* **2020**, *10*, 3903.
https://doi.org/10.3390/app10113903

**AMA Style**

Rao G, Aghajanian S, Koiranen T, Wajman R, Jackowska-Strumiłło L.
Process Monitoring of Antisolvent Based Crystallization in Low Conductivity Solutions Using Electrical Impedance Spectroscopy and 2-D Electrical Resistance Tomography. *Applied Sciences*. 2020; 10(11):3903.
https://doi.org/10.3390/app10113903

**Chicago/Turabian Style**

Rao, Guruprasad, Soheil Aghajanian, Tuomas Koiranen, Radosław Wajman, and Lidia Jackowska-Strumiłło.
2020. "Process Monitoring of Antisolvent Based Crystallization in Low Conductivity Solutions Using Electrical Impedance Spectroscopy and 2-D Electrical Resistance Tomography" *Applied Sciences* 10, no. 11: 3903.
https://doi.org/10.3390/app10113903