## 2 State of the Art and Theoretical Framework  
### Measurement of Clogging Potential in Wine  
To address the challenges associated with the variability in particle content and its impact on the entire bottling process, various methods are employed to measure clogging potential, replicating the operational conditions of industrial filtration [14]. The most common methods, such as the Laurenty Filtration Index (FI), the Modified Filtration Index (MFI), and the Maximum Filterable Volume (Vmax), are conducted under standardized conditions: constant pressure of 30 psi, a temperature of 20 \({}^{\circ}\)C, and the use of a 25 mm diameter membrane with a pore size of 0.65 \(\upmu\)m. Although these methods share these testing conditions, they differ in how they calculate the level of filter obstruction [15].  
The Laurenty Filtration Index (FI), represented in Equation (1), measures the time difference between filtering two known volumes of wine (200 mL and 400 mL). Meanwhile, the Modified Filtration Index (MFI), expressed in Equation (2), introduces an additional 300 mL volume to reduce variability in the results and provide more accurate measurements. Finally, the Maximum Filterable Volume (Vmax), represented in Equation (3), estimates the maximum volume that can be filtered before significant clogging occurs, providing a measure of filter performance under constant pressure [14].  
Figure 1 presents the function that describes the relationship between processing time and total volume filtered under these standardized testing conditions. Although the three methods share the same operational conditions, their differences in calculating clogging potential make them complementary tools for operational decision-making, enabling better planning and control of filtration processes [12].  
\[FI=T_{400}-2T_{200} \tag{1}\]  
\[MFI=\left(T_{300}-T_{100}\right)-2\left(T_{200}-T_{100}\right) \tag{2}\]  
\[\text{Vmax}=\frac{\left(T_{200}-T_{100}\right)}{\frac{T_{200}}{T_{200}}-\frac {T_{200}}{T_{200}}} \tag{3}\]  
Despite the standardization of conditions for clogging measurement methods, such as pressure, temperature, and membrane type, intrinsic variability persists due to factors such as sample heterogeneity, slight fluctuations in testing conditions, and result interpretation [14]. This variability poses challenges in assessing the reproducibility of the methods, as differences in initial conditions or operation can influence the outcomes. However, under strictly controlled conditions and with the use of statistical tools, it is possible to establish error margins that characterize the accuracy and reliability of each method, enhancing their utility for operational decision-making [22].  
While it is true that the clogging indices used in the wine industry share the same operational conditions for measurements, such as pressure, temperature, and membrane type, they differ both in their calculation methods and in their interpretability, which is often based on abstract numerical scales. Previous research has highlighted the limited ability of these indices to directly contribute to operational decision-making, as their interpretation in the industry is often discrete, focusing on establishing minimum or maximum values to determine whether a wine is suitable for bottling [23]. Furthermore, since these indices use volume as an independent variable, their precision and resolution can be affected by the hydraulic properties of the wine, such as viscosity, which influences each method differently. This can lead to variations in the evolution of measurement curves depending on the type of wine, further limiting their standardization and interpretability. Despite these limitations, there is a consensus that, regardless of scale or interpretation, these indices remain useful tools for operational decision-making. Their value lies in their ability to provide information based on historical behaviors specific to each company, as well as to allow comparisons with reference parameters established in the industry [24].