# Mathematical Modelling of Bioethanol Production from Raw Sugar Beet Cossettes in a Horizontal Rotating Tubular Bioreactor

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}), sugarcane 30% (ca. 30 millions m

^{3}), sugar beet and manioc 7% (ca. 7 millions m

^{3}) and all other raw materials 1% (ca. 1 million m

^{3}) [5]. For industrial bioethanol production, the most often used bioprocess conduction modes are fed batch, repeated batch or continuous mode. Semi-solid or solid state bioethanol production systems are related to the bioprocess with very high gravity fermentation media [6,7]. These bioethanol production systems are not often present at industrial scale due to their substrate or ethanol inhibitions, which have to be overcome to establish a stable bioethanol production system [8]. In Brazil, bioethanol production is based on the sugar cane and in North America on corn as raw materials [9]. In Europe, the sugar [10,11,12] and starch [8] containing raw materials are still the main raw materials for industrial bioethanol production. Sugar factories often redirect surplus of sugar beet into bioethanol production to achieve the sustainability of sugar production. The major cost of sugar production is related to the transport and availability of sugar beet in the surrounding of sugar factories. The current equipment of sugar factories produces different intermediates of sugar beet processing (e.g., thin (15–18% sugar) or thick (65–67% sugar) sugar beet juice as well as by-products (e.g., molasses ≈ 50% sugar)) that can be used for bioethanol production [13]. However, production of these intermediates in a classic bioethanol production system is related to the main energy and water consuming operations such as sugar extraction from sugar beet cossettes, sugar juice concentration by evaporation, ethanol distillation, and distillers mash concentration and drying. These processes significantly affect the energy input/output ratio as well as water consumption, and therefore they have direct impact on the ecological sustainability of bioethanol production. In the semi-solid bioethanol production system, sugar extraction by hot water and sugar juice concentration by evaporation can be avoided, and therefore considerable reduction in energy and water consumption can be achieved. Furthermore, reduced consumption of cooling water and energy for ethanol distillation, as well as decreased volume of fermentation stillage due to the reduced volume of fermentation broth, can be obtained [14,15]. Additionally, it is even possible to use non sterilized sugar beet cossettes to additionally reduce energy demand at the beginning of bioethanol production. However, this can have a dual effect due to the fact that sugar beet naturally contains many different naturally occurring microorganisms [16,17]. Some of them, due to improper storage or higher temperature during harvest, can contribute to spoilage and loss of the sugar, which can lead to lower ethanol yields and productivity [18]. Sugar losses vary, and in literature it is reported that these losses can be in the range of 0.02–0.66% w/w, respectively [19,20]. The quality of bioethanol produced from sugar beet is characterized by the lower content of fermentation by-products (e.g., higher alcohols) compared with the fermentation of starch containing raw materials. Higher concentration of by-products in unpurified ethanol reduces its price and can cause fast deterioration of molecular sieves for ethanol dehydration [15,21]. Mathematical models are very useful tool for the prediction of bioprocess performance under new experimental conditions and also additional bioprocess optimization.

## 2. Materials and Methods

#### 2.1. Bioethanol Production in the HRTB

^{−1}of sugar) with the addition of 1 g L

^{−1}of NH

_{4}H

_{2}PO

_{4}(Sigma Aldrich, St. Louis, MO, USA), as an additional source of phosphate and nitrogen, in order to support yeast growth and its physiological activity [16]. The flasks were cultivated on a rotary shaker (rotation speed of 100 min

^{−1}) for 18 h at 28 °C. The study of bioethanol production in the HRTB was also characterized by NH

_{4}H

_{2}PO

_{4}addition (1 g kg

^{−1}of raw sugar beet cossettes). Prior to the addition of raw sugar beet cossettes and yeast inoculation, the bioreactor was sterilized at 121 °C for 20 min. In this research, bioethanol production was studied by different HRTB operational conditions (Table 1). In the first part of the investigation, the impact of constant HRTB rotation on the bioethanol production was examined by varying the speed from 5 to 15 min

^{−1}. In the second part of the investigation, bioethanol production was studied by interval HRTB rotation (3–15 min per hour; rotation speed 5–15 min

^{−1}). In the first two sets of experiments, the HRTB was filled with 5 kg of unsterile raw sugar beet cossettes and inoculated with 1 L of yeast suspension (16.67% v/w raw sugar beet cossettes). In the third part of investigation, the effect of different working volume (ratio between the working (V

_{w}) and total (V

_{T}) bioreactor volume) of HRTB on bioethanol production was studied. In these experiments, the mass of raw sugar beet cossettes in the HRTB was changed in the range of 5–17.5 kg. Depending on the mass of initial sugar beet cossettes, the volume of yeast inoculum varied but always remained 16.67% v/w. The study of bioethanol production in the HRTB was performed at room temperature without pH value correction. Bioethanol production in the HRTB was conducted by all combinations of operational parameters until ethanol concentration reached approximately constant level in the period of at least 48 h. During the bioprocess, broth samples were taken, and their constituents were determined by HPLC (Shimadzu, Kyoto, Japan). All experiments in the HRTB were at least repeated, and the standard deviation of all measurements was in the range of experimental error (below 4.8%) [16].

#### 2.2. Mathematical Modelling of Bioethanol Production in the HRTB

#### 2.2.1. Yeast Growth during Bioethanol Production

_{d}), which is presented in Equation (1). The specific growth rate of yeast cells (µ) is defined using the Andrews model, which incorporates the negative impact of high substrate concentration on biomass growth [24] (Equation (2)). Both µ

_{max}and k

_{d}are adjustable parameters, and their values were predicted by mathematical model.

#### 2.2.2. Products Formation during Bioethanol Production

_{EtOH}is a specific rate of ethanol production (g

_{EtOH}/g

_{x}h). This parameter is also adjustable (q

_{EtOH}), and it is predicted by a model for each specific experimental setup.

_{GlY}is an adjustable model parameter in Equation (4) and is predicted by the model. During bioethanol production in the HRTB, lower concentrations of acetic acid were also detected. Production of acetic acid has also been observed with many different strains of S. cerevisiae that can be used in wine production [30]. One of the possible reasons for acetate production may be an inability for yeast cells to synthesize lipids, which are important for cell membrane integrity, for which pyruvate is the precursor. The yeast cell actually may try to synthesize acetyl CoA as the precursor for lipid synthesis, but this is only possible under aerobic conditions because of lack of oxygen yeast cells can accumulate acetyl CoA, which can be very easily hydrolyzed to acetic acid [31]. It has also been seen that some strains of S. cerevisiae are able to synthesize glycerol and larger quantities of acetic acid. The reason for this are changes in carbon and NADH usage [32]. The change in acetic acid concentration during fermentation in HRTB is given by the following equation:

#### 2.2.3. Substrate Utilization during Bioethanol Production

#### 2.2.4. Mathematical Model and Bioprocess Evaluation Criteria

^{2}

_{0}, EtOH

_{0}—initial concentration of substrate or ethanol (g L

^{−1}); S, EtOH—final concentration of substrate or ethanol (g L

^{−1}); Y

_{S}—total consumption of substrates (g L

^{−1}); Y

_{EtOH}—total ethanol yield (g L

^{−1}); Y

_{EtOH/S}—conversion coefficient of substrate into ethanol (g g

^{−1}); Y

_{EtOH/ST}—theoretical conversion coefficient of substrate into ethanol (g g

^{−1}); E—bioprocess efficiency (%), Pr—bioprocess productivity (g L

^{−1}h

^{−1}) and t—time (h).

## 3. Results

#### 3.1. Bioethanol Production in the HRTB

_{EtOH/S}), efficiencies (E), and productivities (Pr) are given in Table 1.

#### 3.2. Mathematical Model

_{max}, q

_{EtOH}, q

_{Gly}, q

_{Acet}and yeast cell death rate (k

_{d}). All values for adjustable parameters are given in Table 3.

## 4. Discussion

^{−1}h) in these experiments were obtained by bioethanol production in the HRTB with 10 kg of raw sugar beet cossettes (Table 1). The impact of bioreactor operational parameters on the bioethanol production in the HRTB was discussed in more detail earlier [16].

_{max}= 0.03 h

^{−1}) was obtained in the experiment with the lowest rotation speed. With an increase in HRTB rotation speed, the maximum specific growth rate was raised, and it was 0.07 h

^{−1}and 0.08 h

^{−1}in experiments with 10 and 15 rpm, respectively. The results for highest specific product formation rates were mixed. When the bioreactor rotation speed was the lowest, it benefited faster ethanol and glycerol production (q

_{ETOH}= 0.88 g g

_{x}

^{−1}h

^{−1}, q

_{GLY}= 0.10 g g

_{x}

^{−1}h

^{−1}). The slowest acetate production rate was observed at 5 rpm (q

_{ACET}= 0.03 g g

_{x}

^{−1}h

^{−1}), where at 10 and 15 rpm this parameter was almost the same (q

_{ACET}= 0.05 g g

_{x}

^{−1}h

^{−1}). Increasing the duration of mixing (6 min rotation and 54 min resting) did influence the correlation between experimental and model data. The smallest discrepancy was observed in the experiment where bioreactor speed was set to 10 rpm. The bioprocess model predicted the highest specific growth rate for the working microorganism in this case (µ

_{max}= 0.09 h

^{−1}). Additionally, predicted values for initial biomass concentration in all three experiments were around 1 g L

^{−1}. The weakest correlation between experimental and modelled data was observed in the case of glycerol and acetate concentrations in all three experiments (Table 4). Further increase in the duration of bioreactor rotation (9 min rotation, 51 min stationary) gave similar results as the previous HRTB operational setup. Slightly lower bioprocess model prediction was observed when bioreactor rotation speed was set to 5 and 10 rpm. The best bioprocess model fitting was observed in the case where rotation was set to 15 rpm (data not shown). The highest modelled specific growth rate was 0.11 h

^{−1}. This result was achieved at the lowest bioreactor rotation speed, and this shows that multiple factors influence the bioprocess dynamics and yeast activity. The initial biomass concentration predicted in all three models was similar and was around 1.6 g L

^{−1}. In the next series of experiments, HRTB rotation time was further prolonged to 12 min in a one-hour period. In all three cases, it was observed that the modelled specific growth rate was higher in comparison with experiments with lower bioreactor rotation times (µ

_{max}= 0.07 h

^{−1}). This can be explained by better homogenization in the HRTB and better mass transfer due to better mixing. The best results for model approximation of experimental data were obtained in the case where the bioreactor rotation speed was set to 10 rpm. The bioprocess model relatively well describes the experimental data. The mean square error calculated for this case is given in Table 4. In cases of lower and higher rotation speed (5 and 15 rpm) with the same rotation/stationary phase times, there was a noticeable discrepancy, probably due to the fact that lower bioreactor rotation speed contributed to poorer homogenization. In the case of 15 rpm, it seems that a higher rotation speed caused higher liquid phase dispersion within cossettes, which also influenced the sample homogeneity. It should be noted that in the case where the bioreactor rotation speed was set to 10 rpm, our developed model most accurately described the experimental data in comparison with all fermentations. The last bioreactor operational setting was 15 min rotation and 45 min stationary phase. Additionally, three experiments were done using three different HRTB rotation speeds. The bioprocess model described relatively well the obtained experimental data. In all three experiments (5 rpm, 10 rpm and 15 rpm) there was a similar discrepancy with obtained experimental data (Table 4). The highest maximum specific growth rate was observed at 15 rpm (µ

_{max}= 0.07 h

^{−1}). In addition, all three specific product synthesis rates were observed with the highest bioreactor rotation speed. Modelled values of these parameters were as follows; q

_{EtOH}= 0.82 g g

_{x}

^{−1}h

^{−1}, q

_{Gly}= 0.26 g g

_{x}

^{−1}h

^{−1}, q

_{Acet}= 0.17 g g

_{x}

^{−1}h

^{−1}, respectively. In conclusion to this part of the investigation, it seems that even lower rotation speed, when the bioreactor is rotating long enough, can ensure proper and good homogenization of the fermentation broth. It can also be concluded that 15 rpm is the optimal bioreactor rotation speed through all different combinations of rotation/stationary phases.

_{EtOH}= 0.80 g g

_{x}

^{−1}h

^{−1}, q

_{Gly}= 0.18 g g

_{x}

^{−1}h

^{−1}, q

_{Acet}= 0.07 g g

_{x}

^{−1}h

^{−1}, respectively (Table 3).

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Comparison between experimental (no line) and model values (dashed line) for (

**A**) substrate (●) and ethanol (▲) concentration and (

**B**) glycerol (■) and acetic acid (●) concentration obtained for experiment with constant HRTB rotation mode (10 rpm). Discrepancies between experimental data are presented as error bars.

**Figure 2.**Comparison between experimental (no line) and model values (dashed line) for (

**A**) substrate (●) and ethanol (▲) concentration and (

**B**) glycerol (■) and acetic acid (●) concentration obtained for experiment with interval HRTB rotation mode (12 min; 10 rpm). Discrepancies between experimental data are presented as error bars.

**Figure 3.**Comparison between experimental (no line) and model values (dashed line) for (

**A**) substrate (●) and ethanol (▲) concentration and (

**B**) glycerol (■) and acetic acid (●) concentration obtained for experiment with interval HRTB rotation mode (12 min; 15 rpm) and 17.5 kg of initial mass of sugar beet cossettes. Discrepancies between experimental data are presented as error bars.

**Table 1.**Bioprocess efficiency parameters obtained during bioethanol production in the HRTB under different operational conditions.

HRTB Operational Conditions | Bioprocess Efficiency Parameters | ||
---|---|---|---|

Y_{EtOH/S}(g g ^{−1}) | E (%) | Pr (g L ^{−1} h^{−1}) | |

Constant HRTB rotation mode | |||

5 rpm | 0.27 | 50.20 | 0.247 |

10 rpm | 0.19 | 35.20 | 0.185 |

15 rpm | 0.26 | 49.30 | 0.196 |

Interval HRTB rotation mode | |||

3 min; 5 rpm | 0.36 | 66.90 | 0.832 |

6 min; 5 rpm | 0.44 | 81.80 | 0.682 |

9 min; 5 rpm | 0.35 | 65.00 | 0.613 |

12 min; 5 rpm | 0.43 | 79.90 | 0.769 |

15 min; 5 rpm | 0.26 | 48.30 | 0.497 |

3 min; 10 rpm | 0.40 | 74.30 | 0.552 |

6 min; 10 rpm | 0.23 | 42.70 | 0.357 |

9 min; 10 rpm | 0.35 | 65.00 | 0.812 |

12 min; 10 rpm | 0.25 | 46.50 | 0.665 |

15 min; 10 rpm | 0.33 | 60.70 | 0.583 |

3 min;15 rpm | 0.35 | 64.30 | 0.934 |

6 min;15 rpm | 0.31 | 57.60 | 0.327 |

9 min;15 rpm | 0.32 | 58.70 | 0.606 |

12 min; 15 rpm | 0.47 | 87.36 | 0.618 |

15 min; 15 rpm | 0.22 | 40.90 | 0.332 |

Interval HRTB rotation mode (12 min; 15 rpm)—different initial mass of sugar beet cossettes | |||

10.0 kg | 0.45 | 83.64 | 0.560 |

12.5 kg | 0.38 | 70.63 | 0.312 |

15.0 kg | 0.37 | 68.77 | 0.548 |

17.5 kg | 0.37 | 68.77 | 0.552 |

Parameter | Y_{X/S}(g g ^{−1}) | Y_{EtOH/S}(g g ^{−1}) | Y_{GLY/S}(g g ^{−1}) | Y_{ACET/S}(g g ^{−1}) | Ks (g L ^{−1}) | Ki (g L ^{−1}) |
---|---|---|---|---|---|---|

Value | 0.02 | 0.50 | 0.18 | 0.28 | 6.07 | 20.00 |

**Table 3.**Adjustable model parameters obtained during simulation of bioethanol production in the HRTB under different operational conditions.

HRTB Operational Conditions | Adjustable Model Parameters | |||||
---|---|---|---|---|---|---|

X_{k}(g L ^{−1}) | µ_{max}(h ^{−1}) | q_{EtOH}(g g _{x}^{−1} h^{−1}) | q_{Gly}(g g _{x}^{−1} h^{−1}) | q_{Acet}(g g _{x}^{−1} h^{−1}) | k_{d}(h ^{−1}) | |

Constant HRTB rotation mode | ||||||

5 rpm | 1.36 | 0.05 | 0.79 | 0.10 | 0.16 | 0.04 |

10 rpm | 0.71 | 0.07 | 1.10 | 0.40 | 0.29 | 0.04 |

15 rpm | 1.03 | 0.01 | 0.27 | 0.63 | 0.10 | 0.04 |

Interval HRTB rotation mode | ||||||

3 min; 5 rpm | 2.82 | 0.03 | 0.88 | 0.10 | 0.03 | 0.04 |

6 min; 5 rpm | 1.49 | 0.05 | 0.80 | 0.01 | 0.08 | 0.04 |

9 min; 5 rpm | 1.60 | 0.11 | 0.80 | 0.05 | 0.01 | 0.04 |

12 min; 5 rpm | 1.66 | 0.06 | 0.90 | 0.14 | 0.06 | 0.04 |

15 min; 5 rpm | 0.70 | 0.04 | 0.78 | 0.20 | 0.15 | 0.01 |

3 min; 10 rpm | 1.13 | 0.08 | 0.65 | 0.08 | 0.08 | 0.01 |

6 min; 10 rpm | 1.00 | 0.09 | 0.80 | 0.27 | 0.15 | 0.04 |

9 min; 10 rpm | 1.70 | 0.10 | 0.68 | 0.06 | 0.003 | 0.02 |

12 min; 10 rpm | 2.63 | 0.07 | 0.57 | 0.09 | 0.04 | 0.03 |

15 min; 10 rpm | 1.35 | 0.02 | 0.61 | 0.13 | 0.07 | 0.01 |

3 min;15 rpm | 2.10 | 0.07 | 0.75 | 0.07 | 0.05 | 0.02 |

6 min;15 rpm | 1.00 | 0.07 | 0.30 | 0.10 | 0.06 | 0.01 |

9 min;15 rpm | 1.60 | 0.09 | 0.48 | 0.09 | 0.02 | 0.02 |

12 min; 15 rpm | 0.75 | 0.07 | 0.80 | 0.03 | 0.02 | 0.005 |

15 min; 15 rpm | 0.80 | 0.07 | 0.82 | 0.26 | 0.17 | 0.03 |

Interval HRTB rotation mode (12 min; 15 rpm)—different initial mass of sugar beet cossettes | ||||||

10.0 kg | 0.58 | 0.07 | 0.80 | 0.18 | 0.07 | 0.007 |

12.5 kg | 0.50 | 0.07 | 0.25 | 0.05 | 0.05 | 0.010 |

15.0 kg | 2.00 | 0.07 | 0.13 | 0.04 | 0.01 | 0.001 |

17.5 kg | 1.12 | 0.07 | 0.80 | 0.16 | 0.06 | 0.010 |

**Table 4.**Mean square errors for bioethanol production in the HRTB under different bioreactor operational conditions.

HRTB Operational Conditions | MSE | |||
---|---|---|---|---|

Substrate | Ethanol | Glycerol | Acetic Acid | |

Constant HRTB rotation mode | ||||

5 rpm | 480.60 | 53.05 | 42.70 | 0.26 |

10 rpm | 273.79 | 30.38 | 3.84 | 2.02 |

15 rpm | 629.86 | 18.83 | 15.79 | 11.83 |

Interval HRTB rotation mode | ||||

3 min; 5 rpm | 265.64 | 29.35 | 3.56 | 1.22 |

6 min; 5 rpm | 334.17 | 278.58 | 59.70 | 0.14 |

9 min; 5 rpm | 75.38 | 173.65 | 14.24 | 0.54 |

12 min; 5 rpm | 1468.88 | 265.26 | 3.18 | 0.49 |

15 min; 5 rpm | 524.14 | 20.09 | 3.24 | 0.80 |

3 min; 10 rpm | 144.53 | 1276.16 | 17.11 | 4.67 |

6 min; 10 rpm | 649.08 | 505.06 | 8667.72 | 345.15 |

9 min; 10 rpm | 690.02 | 4.52 | 3.15 | 0.04 |

12 min; 10 rpm | 282.46 | 36.75 | 1.72 | 0.30 |

15 min; 10 rpm | 171.00 | 40.83 | 2.97 | 1.94 |

3 min;15 rpm | 336.39 | 53.30 | 1.04 | 2.09 |

6 min;15 rpm | 365.11 | 27.05 | 7.42 | 4.70 |

9 min;15 rpm | 601.61 | 250.88 | 8.05 | 0.59 |

12 min; 15 rpm | 562.54 | 299.83 | 27.01 | 0.30 |

15 min; 15 rpm | 279.14 | 57.95 | 4.14 | 1.92 |

Interval HRTB rotation mode (12 min; 15 rpm)—different initial mass of sugar beet cossettes | ||||

10.0 kg | 377.57 | 81.06 | 8.51 | 1.69 |

12.5 kg | 460.67 | 18.69 | 27.54 | 3.60 |

15.0 kg | 401.92 | 528.26 | 14.28 | 3.79 |

17.5 kg | 383.48 | 374.22 | 6.20 | 1.05 |

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## Share and Cite

**MDPI and ACS Style**

Pavlečić, M.; Novak, M.; Trontel, A.; Marđetko, N.; Grubišić, M.; Ljubas, B.D.; Tominac, V.P.; Rakovac, R.Č.; Šantek, B.
Mathematical Modelling of Bioethanol Production from Raw Sugar Beet Cossettes in a Horizontal Rotating Tubular Bioreactor. *Fermentation* **2022**, *8*, 13.
https://doi.org/10.3390/fermentation8010013

**AMA Style**

Pavlečić M, Novak M, Trontel A, Marđetko N, Grubišić M, Ljubas BD, Tominac VP, Rakovac RČ, Šantek B.
Mathematical Modelling of Bioethanol Production from Raw Sugar Beet Cossettes in a Horizontal Rotating Tubular Bioreactor. *Fermentation*. 2022; 8(1):13.
https://doi.org/10.3390/fermentation8010013

**Chicago/Turabian Style**

Pavlečić, Mladen, Mario Novak, Antonija Trontel, Nenad Marđetko, Marina Grubišić, Blanka Didak Ljubas, Vlatka Petravić Tominac, Rozelindra Čož Rakovac, and Božidar Šantek.
2022. "Mathematical Modelling of Bioethanol Production from Raw Sugar Beet Cossettes in a Horizontal Rotating Tubular Bioreactor" *Fermentation* 8, no. 1: 13.
https://doi.org/10.3390/fermentation8010013