## 3 Results and Discussion
### Characterization of the Salled Water-Based Fluid Formulations  
The regression equation that correlates the palygorskite (P) and PAC LV (C) contents with the filtrate volume, the relevant data for the analysis of variance (ANOVA), the  
Figure 2: Morphology of the palygorskite sample. response surface generated based on the model, and the values of this property for each formulation are presented in Equation (4), Table 5, and Figure 3a,b, respectively. \[\text{VF}=(14.51\pm 0.24)-(0.05\text{P}\pm 0.32)-(3.25\text{C}\pm 0.32)-(0.35 \text{P}\text{C}\pm 0.32) \tag{4}\]  
The mathematical model, obtained through the regression of the experimental data, presented a good fit, with a coefficient of determination of 97.18%. Furthermore, at a 95% confidence level, it can also be considered statistically significant and useful for predictive purposes, as the Fcalculated/Ftabulated ratio was greater than five [36]. Equation (1) and the response surface presented in Figure 3a indicate that only the PAC content exerts a significant influence on the filtrate volume, and the variation in the palygorskite content does not cause changes in this property. Polymers of the same nature as PAC LV have ionized carboxylic groups. Thus, the resulting electrostatic repulsion causes its molecular chains in solution to hydrate and assume an extended conformation, with repulsion also occurring between adjacent chains. Because of this hydration, the filtrate volume is reduced. This mechanism was explained by [PERSON] et al. [37]. Despite not having shown a statistically significant influence on the filtrate volume, palygorskite still plays an important role in this property. As can be seen in Figure 3b, formulation F0, prepared without the addition of clay and with 8 g of PAC LV, presented a filtrate volume of 15.2 mL. In contrast, formulation F3, for example, which has the same polymer content and 10 g of palygorskite, presented a filtrate volume of 12 mL, which represents a reduction of approximately 21%. When the clay content was increased to 20 g (F4), this reduction was even greater, approximately 26%. This result indicates that the action of clay together with the polymer is essential for filtrate control. The interaction mechanism between PAC LV and palygorskite can be explained through electrostatic interactions. When added to clay-containing suspensions, such as the formulations studied, PAC LV is adsorbed onto the surface of the clay particles, increasing the negative surface charge due to its polyanionic nature. This increase in charge intensifies the electrostatic repulsion  
Figure 3: Response surface (**a**) and values (**b**) of the HPHT filtrate volume of the salted water-based fluid with palygorskite. \begin{table}
\begin{tabular}{c c} \hline
**Coefficient of Determination (R2)** & **Fcalculated/Ftabulated** \\ \hline
97.18\% & 9.95 \\ \hline \end{tabular}
\end{table} 
Table 5: Analysis of variance for the HPHT filtrate volume of the salted water-based fluid with palygorskite. between the particles, preventing their aggregation and promoting the stabilization of the system by keeping them in suspension. As a result, the volume of free water available is reduced, which improves fluid properties that depend on this arrangement, such as filtrate control. The interaction of this polymer with clays was studied by [PERSON] et al. [38]. Although the results obtained from the factorial design have demonstrated the influence of additive content in minimizing the filtrate volume, the interpretation of these results is limited due to the absence of comparative parameters within the international standards in force that allow for the qualification, based on this property, of fluids used as a barrier element for well abandonment. Therefore, the analysis of the results presented in Figure 4 was conducted based on a comparison with aqueous palygorskite drilling fluids developed for applications in well drilling (Table 6).