## 2 Materials and Methods
### Sag Behavior  
The sag-resistant influence of fly ash on the drilling fluid's sag susceptibility was investigated both statically and dynamically. Figure 7a shows the static sag testing apparatus, which consists of an HPHT Single-Cell Filter Press, OFI Testing Equipment Inc., Houston, TX, USA. It was redesigned for this purpose by mounting an inclinometer to measure the trajectories. The Base Fluid (0 lb/bbl of fly ash), fluids 3, and 4 were evaluated by conducting a static sag test at various temperatures (250 \({}^{\circ}\)F, 300 \({}^{\circ}\)F, 350 \({}^{\circ}\)F, and 400 \({}^{\circ}\)F) and deviations (30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), 70\({}^{\circ}\), 80\({}^{\circ}\), and 90\({}^{\circ}\)). Various inclinations of the cell were used to represent deviated wells. The sample (140 cm\({}^{3}\)) was emptied into a stainless steel cup while on the metal stand and capped (Figure 7b). Afterward, it was transferred to the HPHT Single-Cell Filter Press. It was then pressurized with nitrogen gas at 500 psi to prevent fluid vaporization. The temperature switch was turned on. The inclinometer holds the ceramic cell in place at a desired trajectory. The trajectory can be adjusted by loosening and locking the black screw. The trajectory may be determined with the aid of a protractor placed between the inclinometer, as shown by the red lines. When the drilling fluid was left to age for 24 h at the desired deviations and temperatures, 10 cm\({}^{3}\) of fluid was obtained from the cell's top through the cannula into a transparent graduated syringe. For the top density, the mass was obtained using a digital weighing balance and divided by volume. The procedure was repeated, but this time, the material was drawn from the lower section of the cell. The results were then applied to the following equations:  
\[\rho_{bottom} =\frac{Mass\;of\;fluid\;drawn\;from\;the\;bottom}{Volume\;of\;fluid\;drawn\;from\;the\;bottom} \tag{1}\]  
\[\rho_{top} =\frac{Mass\;of\;fluid\;obtained\;at\;the\;top}{Volume\;of\;sample\;obtained\;at\;the\;top} \tag{2}\]  
\[\text{Sag\;Factor\;(SF)}=\frac{\rho_{bottom}}{\rho_{bottom}+\rho_{top}} \tag{3}\]  
\[\rho_{bottom} =\text{Density\;of\;mud\;at\;the\;bottom\;of\;the\;cup}\]  
\[\rho_{top} =\text{Density\;of\;mud\;at\;the\;top\;of\;the\;cup}\]  
The tendency of the weight material in the drilling fluid to precipitate out either by hindered or free settling is an indication of the sag factor (SF) of the fluid. Higher SF values imply a more pronounced tendency to sag. The acceptable range for the sag factor's safe zone lies between 0.5 and 0.53 ([PERSON] et al., 2018).  
A dynamic sagging apparatus (Figure 7c) was employed to perform the VSST test. It consists of an 8-Speed Ofite Viscosimeter, OFI Testing Equipment Inc., Houston, TX, USA. a thermo-cup, a sag shoe, and a syringe. The sag shoe was placed inside the thermo-cup before filling it up with a 140 cm\({}^{3}\) volume of sample. Following this, the sample was agitated by the viscosimeter at 100 rpm for 30 min while applying a temperature of 120 \({}^{\circ}\)F to the fluid. Afterward, a fluid volume of 10 cm\({}^{3}\) was drawn into a transparent graduated syringe from the lowermost part of the sag shoe and weighed. The mass was obtained before and after agitation. The following equation was applied to obtain the VSST:  
\[\text{VSST}=0.833\;\times\;\left(W_{after}-W_{before}\right)\]  
\[W_{after}=\text{Mass\;of\;fluid\;drawn\;into\;the\;syring\;after\;30\;min\;of\; agitation} \tag{4}\]  
\[W_{before}=\text{Mass\;of\;fluid\;drawn\;into\;the\;syring\;before\; agitation}\]  
A stable fluid is identified with a VSST of 1 ppg and below (uniform mixture), while an unstable fluid typically has a value of above 1.6 ppg (non-uniform mixture), which may be the beginning of sagging ([PERSON] et al., 2018; [PERSON] et al., 2018). The envelope that lies between 1-1.6 ppg may be regarded as the transition boundary.