#
Monitoring of Biopolymer Production Process Using Soft Sensors Based on Off-Gas Composition Analysis and Capacitance Measurement^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

- “gray box” type of soft sensor, alternatively referred to as “model-driven”—using a first-principle mathematical model of the monitored process based on physical, chemical, or biological relationships with experimental identification of unknown parameters from historical process data;
- “black box” type of soft sensor, alternatively referred to as a “data-driven”—where the mathematical model describing the relationship between the inputs and outputs of the soft sensor is not known in advance, and hence the mathematical description of this relationship must be designed on the basis of historical process data using suitable computational tools, e.g., regression analysis, neural networks, etc.

- high sensitivity of the production microbial culture to changes in cultivation conditions such as pH, temperature, etc.;
- during the cultivation itself, the microbial culture passes through various physiological states, which usually result in different types of culture behavior;
- key parameters of bioprocess models typically change during cultivation, whereas on-line measurement, or at least estimation, of these changes is rather complicated.

_{2}production rate (CPR), respiratory quotient (RQ), or oxygen transfer coefficient from gaseous to liquid phase in a bioreactor (k

_{L}a). More advanced soft sensors can be used for the on-line estimation of key bioprocess indicators, such as biomass concentration, biomass growth rate, or concentrations and rates of production of the main products (see, e.g., [10,11,12,13,14]).

## 2. Materials and Methods

#### 2.1. Process Description

#### 2.2. Process Data Measurement and Analytical Methods

_{2}) and 1400B (CO

_{2}) process analyzers (Spectris plc, Egham, UK) and these measurements were stored with a 1 min sampling period. The resulting off-gas composition measurement data were then used for on-line calculation of the OUR and CPR rates, as well as their corresponding cumulative values—cumulative oxygen consumption (COC) and cumulative carbon dioxide production (CCP), using Equations (1)–(4):

^{3}/s) is the volumetric air flow rate on the inlet to the bioreactor, V

_{L}(m

^{3}) is the broth volume in the bioreactor, ρ

_{A}(kg/m

^{3}) is the air density, M

_{A}(kg/mol) is the molecular weight of air, ΔO

_{2}(% vol.) is the difference between oxygen concentrations in the inlet air and the off-gas, ΔCO

_{2}(% vol.) is the difference between carbon dioxide concentrations in the inlet air and the off-gas, O

_{2}(% vol.) is the oxygen concentration in the off-gas, CO

_{2}(% vol.) is the carbon dioxide concentration in the off-gas, N

_{2}(% vol.) is the nitrogen concentration in the air (assumed to be constant at 79.07%), M

_{O2}(kg/mol) is the molecular weight of oxygen, M

_{CO2}(kg/mol) is the molecular weight of carbon dioxide, k

_{c}is the coefficient for the conversion of concentration values from volume percent into dimensionless volume fraction (k

_{conv}= 1/100 = 0.01), t (min) is the current cultivation time, and τ (min) is the variable of integration (takes on values from time 0 to the current t).

#### 2.3. Soft Sensors Based on Off-Gas Analysis

_{O/X}(kg oxygen consumed per 1 kg biomass produced) is the yield coefficient relating oxygen consumption to biomass production, c

_{X}(kg/m

^{3}) is the microbial cell concentration in the bioreactor, t (min) is the cultivation time, m

_{O}(kg oxygen consumed per 1 kg biomass per 1 min) is the oxygen consumption coefficient related to maintenance, Y

_{C/X}(kg carbon dioxide produced per 1 kg biomass produced) is the yield coefficient relating carbon dioxide production to biomass production, and m

_{C}(kg carbon dioxide produced per 1 kg biomass per 1 min) is the carbon dioxide coefficient related to maintenance. If the yield coefficients can be assumed to be constant, and the contribution of the maintenance part of Equations (5) and (6) is low enough to be neglected, then the relationship between the cumulative (integral) values of O

_{2}consumption (COC) and CO

_{2}production (CCP), and the biomass concentration can be considered to be linear [20,22].

#### 2.4. Soft Sensors Based on Capacitance Measurement

_{L}) is capacitance measurement at low frequency, which reflects the concentration of living cells in the bioreactor, and C(f

_{H}) is background capacitance measurement at high frequency corresponding to high frequency capacitance contributions from non-cell components, such as air bubbles, etc. While f

_{H}is typically chosen as the highest available frequency within the measured capacitance spectrum (e.g., 19.49 MHz in the case of Aber Biomass Monitor 210), the main frequency f

_{L}is chosen so that the capacitance measurement at this particular frequency is best correlated with the live cell concentration (compared to capacitance measurement at other frequencies).

## 3. Results and Discussion

#### 3.1. Regression Analysis of the Relationship between the On-Line Process Data and Off-Line Concentrations Measurements

- Case 1: biomass and biopolymer concentrations, respectively, are assumed to be linearly dependent on oxygen uptake rate OUR;
- Case 2: biomass and biopolymer concentrations, respectively, are assumed to be linearly dependent on carbon dioxide production rate CPR;
- Case 3: biomass and biopolymer concentrations, respectively, are assumed to be linearly dependent on cumulative oxygen consumption COC;
- Case 4: biomass and biopolymer concentrations, respectively, are assumed to be linearly dependent on cumulative carbon dioxide production CCP.

^{2}) for individual variants are summarized in Table 1. The overall statistical significance of the so obtained regression models has been tested and successfully verified using the standard F-test (at the 0.05 level).

_{H}) was chosen, in line with the goal of removing high frequency capacitance contributions from non-cell components, such as air bubbles etc., as the capacitance measurement at the highest available frequency within the measured capacitance spectrum, i.e., f

_{H}= 19.49 MHz. The main frequency f

_{L}was variable and corresponded to the remaining 24 measuring frequencies (0.1, 0.12, … 15.65 MHz). Hence, a total of 24 capacitance measurement differences ΔC

_{f}(where f = 0.1, 0.12, … 15.65 MHz) were obtained. Each of the ΔC

_{f}calculated in this way was then subjected to regression analysis as an independent variable in relation to both off-line concentrations CDW and PHA, respectively. The overall statistical significance of the so-obtained regression models has been tested and successfully verified using the standard F-test (at the 0.05 level). The resulting coefficients of determination (R

^{2}) for individual variants are shown in the bar graphs in Figure 2 and Figure 3.

^{2}was reached at the capacitance measurement difference ΔC

_{0.24}, i.e., for the main frequency value f

_{L}= 0.24 MHz. However, this maximum is not very distinct (see Figure 2); slightly lower values were achieved for other capacitance measurement differences, approximately in the range of main frequencies f

_{L}from 0.12 to 0.58 MHz. In the case of biomass concentration, the highest value of R

^{2}was reached at the capacitance measurement difference ΔC

_{0.58}, i.e., for the main frequency value f

_{L}= 0.58 MHz. Here, the maximum is more distinct than in the case of biopolymer concentration. However, even in this case the range of high values of R

^{2}corresponds approximately to the range of main frequencies f

_{L}from 0.12 to 1.40 MHz, see Figure 3.

#### 3.2. Design of Soft Sensors for Biomass and Biopolymer Concentration Estimation

- Type 1: simply structured soft sensors based on simple linear regression, where biomass and biopolymer concentrations are estimated using only single input on-line process variable—COC or CCP or single ΔC
_{f}, see Equation (8) and Figure 4a.

_{f}(specifically ΔC

_{0.24}for biopolymer and ΔC

_{0.58}for biomass concentration in accordance with the above results of the regression analysis), and k

_{1}, k

_{0}are calibration constants of the specific soft sensor. This simple structure of the soft sensor (with only one independent variable at the sensor input) based on linear regression was chosen for two reasons—practical and statistical. The practical reason was that, in practice, both sets of on-line measurements (off-gas composition and capacitance measurements) are often not available at the same time, and even when only the off-gas composition is measured (in practice more widespread than the capacitance measurement), sometimes only one of the O

_{2}or CO

_{2}concentration measurements is available. The second, statistical reason why a soft sensor with multiple independent variables on the input based on multiple linear regression was not considered, was the fact that all considered variables (OUR, CPR, COC, CCP, ΔC

_{f}) are mutually correlated and therefore the condition of real independence of input variables was not met. For this reason, multivariate regression methods based on partial least squares regression and principal component regression were used for a complex type of soft sensor with multiple inputs, see the following type 2.

- Type 2: comprehensively structured soft sensors based on multivariate statistical methods—partial least squares regression (PLS) or principal component regression (PCR), respectively, see Figure 4b. For a detailed description of both well-known methods, see, e.g., [25,26]. In both of these cases, the input of the soft sensors consisted of both mutually correlated cumulative quantities based on off-gas composition measurement (COC, CCP) combined with a selected set of ΔC
_{f}. The output of the sensors included both estimated concentrations (biomass and biopolymer). Specifically, the selected set of ΔC_{f}comprised 12 capacitance measurement differences (ΔC_{0.12}, ΔC_{0.16}, ΔC_{0.19},…, ΔC_{1.40}), i.e., capacitance measurement differences corresponding to the range of main frequencies f_{L}from 0.12 to 1.40 MHz, for which high values of R^{2}were attained in relation to off-line concentrations in the regression analyzes described in Section 3.1. Thus, there were a total of 14 on-line variables at the input of these type 2 soft sensors–COC, CCP, and 12 ΔC_{f}.

_{f}as their input are more complicated in that the capacitance measurement is usually marked by considerable noise (e.g., as a result of bioreactor aeration and other factors). The measured data must therefore be filtered by a combination of several digital filters before use in a soft sensor (see Section 2.2). However, sensors based on capacitance measurement differences are better able to capture the end of the biopolymer production phase at the end of cultivation, which is a key feature in terms of production monitoring (see Figure 5 and Figure 6).

_{0.58}as input; and two for biopolymer with COC or ΔC

_{0.24}as input) and one complex soft sensor of the type 2 (PLS-based). On-line measured data from a typical biopolymer production cultivation with characteristic time course were used for testing (see Figure 5, Figure 6 and Figure 7). From the output data obtained for the tested examples of soft sensors (Figure 6 and Figure 7), it is clear that the differences between the tested sensors are minimal for most of the cultivation time. Larger differences are apparent towards the end phase of the production cultivation, when there is a significant slowing down of the cell culture growth and biopolymer production. In the case of both monitored concentrations (biomass and biopolymer), the final stagnation of growth, or even a decrease, is most evident from the outputs of the simple type 1 soft sensors, which have capacitance measurement differences at their input. It is therefore apparent also from this model example that soft sensors based on capacitance measurement can be very useful for early detection of the end of the production phase.

## 4. Conclusions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Coefficients of determination (R

^{2}) of simple linear regressions-biopolymer concentration PHA as dependent variable, individual capacitance measurement differences ΔC

_{f}as independent variables, respectively.

**Figure 3.**Coefficients of determination (R

^{2}) of simple linear regressions-biomass concentration CDW as dependent variable, individual capacitance measurement differences ΔC

_{f}as independent variables, respectively.

**Figure 6.**Model test cultivation-biopolymer concentration-comparison of off-line measurements and estimates using selected variants of soft sensors.

**Figure 7.**Model test cultivation-biomass concentration-comparison of off-line measurements and estimates using selected variants of soft sensors.

**Table 1.**Results of regression analysis (on-line variables based on off-gas composition data vs. CDW, PHA).

Variants | Coefficients of Determination (R^{2}) | |
---|---|---|

Biomass Concentration (CDW) | Biopolymer Concentration (PHA) | |

Case 1 | 0.46 | 0.40 |

Case 2 | 0.59 | 0.53 |

Case 3 | 0.98 | 0.98 |

Case 4 | 0.97 | 0.98 |

Sensor Types | RMSE-CV (% of Measurement Range) | |
---|---|---|

Biomass Concentration Estimation | Biopolymer Concentration Estimation | |

Type 1 (COC as input) | 3.64% | 4.63% |

Type 1 (CCP as input) | 4.15% | 4.64% |

Type 1 (ΔC_{0.24} as input) | – | 5.53% |

Type 1 (ΔC_{0.58} as input) | 3.42% | – |

Type 2 (PLS-based) | 2.78% | 4.46% |

Type 2 (PCR-based) | 2.85% | 4.47% |

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**MDPI and ACS Style**

Hrnčiřík, P.
Monitoring of Biopolymer Production Process Using Soft Sensors Based on Off-Gas Composition Analysis and Capacitance Measurement. *Fermentation* **2021**, *7*, 318.
https://doi.org/10.3390/fermentation7040318

**AMA Style**

Hrnčiřík P.
Monitoring of Biopolymer Production Process Using Soft Sensors Based on Off-Gas Composition Analysis and Capacitance Measurement. *Fermentation*. 2021; 7(4):318.
https://doi.org/10.3390/fermentation7040318

**Chicago/Turabian Style**

Hrnčiřík, Pavel.
2021. "Monitoring of Biopolymer Production Process Using Soft Sensors Based on Off-Gas Composition Analysis and Capacitance Measurement" *Fermentation* 7, no. 4: 318.
https://doi.org/10.3390/fermentation7040318