# Experimental Study and Modeling of Beer Dealcoholization via Reverse Osmosis

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## Abstract

**:**

^{2}surface was used. The flux values were measured during the separations. The ethanol content, extract content, bitterness, color, pH, turbidity, and dynamic viscosity of beer and permeate samples were measured. The initial flux values were determined using linear regression. The initial ethanol flux (${J}_{EtOH0}$) values were calculated from the initial flux values and the ethanol content values. A 2

^{P}full factorial experimental design was applied, and the factors were as follows: transmembrane pressure (TMP): 10, 20, 30 bar; retentate flow rate (Q): 120, 180, 240 L/h; ${J}_{EtOH0}$ was considered as the response. The effect sizes of the significant parameters were calculated. The global maximum of the objective function was found using a self-developed Grid Search code. The changes in the analytical parameters were appropriate. The TMP had a significant effect, while the Q had no significant effect on the ${J}_{EtOH0}$. The effect size of the TMP was 1.20. The optimal value of the factor amounted to TMP = 30 bar. The predicted ${J}_{EtOH0}$ under the above conditions was 121.965 g/m

^{2}h.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Beers

#### 2.2. Beer Dealcoholization via Reverse Osmosis

^{2}active surface was used for the dealcoholization processes. Dealcoholization experiments were performed according to the experimental design (Table 3) discussed in Section 2.9. The two factors were the transmembrane pressure (TMP) and the retentate flow rate (Q). Generally, in the case of RO processes, the retentate flow rate (Q) is lower than the feed flow rate by the permeate flow rate (flow drop) [23]. In this study, the permeate flow rates were less than 0.4% of the feed flow rates, and thus, the flow drops were negligible.

#### 2.3. Membrane Cleaning

#### 2.4. Analytical Parameters

#### 2.5. Separation Characteristics Parameters

_{i}is the retention (%) of the component i, ${C}_{{p}_{i}}$ (g/L) is the permeate concentration of the component i, and ${C}_{{b}_{i}}$ (g/L) is the bulk concentration of the component i.

#### 2.6. Hydrodynamic Parameters

^{2}h) is the flux, $V$ (L) is the permeate volume, ${A}_{m}$ (m

^{2}) is the membrane active surface area, and ${t}_{i}$ (h) is the time interval.

^{2}h) is the mass flux, and $m$ (g) is the permeate mass.

^{2}h) is the ethanol flux, ${m}_{EtOH}$ (g) is the mass of the ethanol in the permeate, ${c}_{EtOH}$ (% (w/w)) is the ethanol content in the permeate, and ${\rho}_{EtOH}$ (g/L) is the ethanol density at the given temperature.

^{2}h) is the flux at any time (BDA permeate), ${J}_{0}$ (L/m

^{2}h) is the initial flux (BDA permeate), $K$ (1/h) is the flux decline coefficient (BDA permeate), and $t$ (h) is the time.

^{2}h) is the water flux before separation, ${\mu}_{w}$ (Pas) is the dynamic viscosity of the water at the given temperature, and ${R}_{m}$ (1/m) is the intrinsic resistance of the clean membrane.

#### 2.7. Evaluation of Cleaning Efficiency

^{2}h) is the water flux after the membrane cleaning, and ${R}_{n}$ (1/m) is the intrinsic resistance of the membrane after the membrane cleaning.

#### 2.8. Linear Regression

#### 2.9. Modeling

#### 2.10. Assumptions

## 3. Results and Discussion

**Analytical parameters**of beer and permeate samples,**Separation characteristic parameters**of BDA processes,**Hydrodynamic parameters**of BDA processes,- Results of the
**linear regression**of BDA processes, - Results of
**modeling,** - Results of
**membrane cleaning efficiency,** - Research
**limitations.**

#### 3.1. Analytical Parameters

^{−3}Pas).

#### 3.2. Separation Characteristics Parameters

#### 3.3. Hydrodynamic Parameters

#### 3.4. Linear Regression

#### 3.5. Modeling

^{2}h. Therefore, the highest ${J}_{EtOH0}$ could be achieved with the highest TMP.

#### 3.6. Membrane Cleaning Efficiency

#### 3.7. Limitations

## 4. Conclusions

^{2}h in our experiments) could be achieved with the highest TMP (TMP = 30 bar in our experiments). Thus, commercial breweries should set the TMP at the highest possible level, considering the energy consumption.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Schematic flow diagram of crossflow reverse osmosis (CFRO) equipment. 1—feed tank, 2—pump, 3—reverse osmosis membrane module, 4—valve, 5—heat exchanger (cooler/heater), 6—manometer, 7—measuring cylinder, 8—flowmeter, 9—thermometer.

**Figure 3.**Hydrodynamic parameters of the separations: (

**a**) initial flux (log); (

**b**) initial ethanol flux (log).

**Figure 4.**Two-dimensional response plot of the effect of significant parameter (transmembrane pressure–${x}_{TMP}$) for initial ethanol flux (${J}_{EtOH0}$).

**Table 1.**Comparison of installation cost, operating cost, and quality of final beer of low-alcohol beer (LAB) and alcohol-free beer (AFB) production methods (based on [10]).

Method | Installation Cost | Operating Cost | Beer Quality |
---|---|---|---|

Evaporation | ** | * | * |

Rectification | ** | * | ** |

Stripping | ** | ** | ** |

Dialysis | *** | * | * |

Nanofiltration | ** | ** | *** |

Osmotic distillation | ** | *** | ** |

Pervaporation | * | ** | *** |

Reverse osmosis | ** | * | ** |

Changed mashing | * | *** | * |

Arrested/limited fermentation | * | *** | * |

Cold contact process | ** | ** | * |

Special yeast | ** | ** | * |

Continuous fermentation | * | ** | * |

Factor | Abbreviation | Code | Unit | Factor Levels | ||
---|---|---|---|---|---|---|

Low (−1) | Central (0) | High (+1) | ||||

Transmembrane pressure | TMP | x_{TMP} | bar | 10 | 20 | 30 |

Retentate flow rate | Q | x_{Q} | L/h | 120 | 180 | 240 |

**Table 3.**The design matrix of the ${2}^{p}$ full factorial experimental design of BDA via RO experiments.

Standard Order Number | Actual Value | Coded Value | ||
---|---|---|---|---|

TMP (bar) | Q (L/h) | x_{TMP} | x_{Q} | |

1 | 10 | 120 | −1 | −1 |

2 | 10 | 240 | −1 | +1 |

3 | 30 | 240 | +1 | +1 |

4 | 30 | 120 | +1 | −1 |

5 (C) | 20 | 180 | 0 | 0 |

6 (C) | 20 | 180 | 0 | 0 |

7 (C) | 20 | 180 | 0 | 0 |

**Table 4.**Aspects and comments on Grid Search optimization method applied for response objective function.

Method | Comments | Conclusion |
---|---|---|

Response method | The objective function is continuous. | Using Grid Search optimization for the response objective function can provide an optimal parameter set that can be directly applied in the membrane separation process. |

Analytical optimization of the objective function results in a parameter set that does not necessarily fit to the parameter settings available for membrane separation process. | ||

Grid Search optimization method | It is a numerical method with brute force (exhaustive) search (global optimization method on a grid). | |

It does not become stuck at a local optimum. | ||

The set of optimization grid points can be adjusted to the resolution of the parameter ranges available for the membrane process. |

Name of Parameter | Beer (Feed) |
---|---|

Alcohol content (v/v%) | 4.34 |

Original real extract (w/w%) | 10.28 |

Final real extract (w/w%) | 3.63 |

Final apparent extract (w/w%) | 2.04 |

Bitterness (IBU) | 12 |

Color (EBC) | 8.89 |

pH | 4.23 |

Turbidity at 20 °C (EBC) | 0.5 |

Dynamic viscosity at 20 °C (mPas) | 5.48 |

Sample | Dynamic Viscosity at 15 °C (mPas) | |
---|---|---|

Beer (feed) | 5.85 ± 0.03 | |

Standard order number (permeate) | 1 | 5.50 ± 0.03 |

2 | 5.43 ± 0.01 | |

3 | 5.07 ± 0.04 | |

4 | 5.04 ± 0.03 | |

5 | 5.37 ± 0.03 | |

6 | 5.14 ± 0.02 | |

7 | 5.13 ± 0.02 |

Sample | Ethanol Content at 20 °C (% (v/v)) | |
---|---|---|

Beer (feed) | 4.34 ± 0.02 | |

Standard order number (permeate) | 1 | 2.56 ± 0.02 |

2 | 2.75 ± 0.01 | |

3 | 1.45 ± 0.01 | |

4 | 1.82 ± 0.01 | |

5 | 1.92 ± 0.01 | |

6 | 2.10 ± 0.01 | |

7 | 2.07 ± 0.05 |

**Table 8.**Parameter estimates of the significant parameters, and effect size estimate of the significant parameter of the objective function.

Coefficient | Effect Size | ||||||||
---|---|---|---|---|---|---|---|---|---|

Term | Estimate | Standard Error | $\mathit{t}$ | $\mathit{P}\mathit{r}(>\left|\mathit{t}\right|)$ | Parameter | Estimate | Standard Error | $\mathit{t}$ | $\mathit{P}\mathit{r}(>\left|\mathit{t}\right|)$ |

${b}_{0}$ | 80.871 | 2.597 | 31.14 | *** | - | - | - | - | - |

${b}_{TMP}$ | 41.094 | 3.435 | 11.96 | *** | TMP | 1.20389 | 0.09187 | 13.1 | *** |

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## Share and Cite

**MDPI and ACS Style**

Varga, Á.; Bihari-Lucena, E.; Ladányi, M.; Szabó-Nótin, B.; Galambos, I.; Koris, A.
Experimental Study and Modeling of Beer Dealcoholization via Reverse Osmosis. *Membranes* **2023**, *13*, 329.
https://doi.org/10.3390/membranes13030329

**AMA Style**

Varga Á, Bihari-Lucena E, Ladányi M, Szabó-Nótin B, Galambos I, Koris A.
Experimental Study and Modeling of Beer Dealcoholization via Reverse Osmosis. *Membranes*. 2023; 13(3):329.
https://doi.org/10.3390/membranes13030329

**Chicago/Turabian Style**

Varga, Áron, Eszter Bihari-Lucena, Márta Ladányi, Beatrix Szabó-Nótin, Ildikó Galambos, and András Koris.
2023. "Experimental Study and Modeling of Beer Dealcoholization via Reverse Osmosis" *Membranes* 13, no. 3: 329.
https://doi.org/10.3390/membranes13030329