## 2 Materials and Methods
### Preparation of Drilling Fluid Samples  
A Hamilton Beach multimixer was adopted to homogeneously mix 350 cm\({}^{3}\) of drilling fluid formulated from the combination of the additives shown in Table 1 at ambient temperature. The formulation of the Base Fluid and other fluid samples comprised the additives indicated in each column. The additives were selected based on low cost, efficiency, and in line with the industry-standardized composition. Following the table, six laboratory barrels of drilling fluids with various ratios of fly ash (0, 1, 2, 3, and 4 lb/bbl) were prepared, and their effects on barite and ilmenite sagging mitigation were investigated. The Base Fluid and fluids 1 through 4, densified with barite, weighed 15.8 ppg, while the sixth sample (Fluid 5), densified with ilmenite, weighed 16.2 ppg. The addition of a partially hydrolyzed polyacrylamide (PHPA) copolymer to the fluid samples augmented their thermal stability, shale inhibition, and flow deficiencies. As supplied by Newpark Resources, the weighting agent barite is of an acceptable oil and gas standard. The results of the X-ray fluorescence (XRF) analysis of the elemental composition of barite, as displayed in Figure 1, usually have barium (Ba) present at 77.5 wt%, sulfur (S) at 17.7 wt%, and a minor trace of potassium, silicon, and iron [8]. While the obtained outcome of XRF analysis of Beulah fly ash as reported by [PERSON] et al. [9] revealed that it is made up of silicon oxide (SiO\({}_{2}\)) at 24.5%, calcium oxide (CaO) at 17.7 wt%, sodium oxide (Na\({}_{2}\)O) at 15.8 wt%, iron (III) oxide (Fe\({}_{2}\)O\({}_{3}\)) present at 11.2 wt%, aluminum oxide (Al\({}_{2}\)O\({}_{3}\)) at 10.9 wt%, sulfur trioxide (SO\({}_{3}\)) at 10.7 wt%, magnesium oxide (MgO) present at 5.1 wt%, and potassium oxide (K\({}_{2}\)O) at 1.9 wt% as shown by Figure 2. The elemental composition of ilmenite was measured utilizing the RIGAKU Benchtop Spectrometer and was found to contain 54.7% iron (Fe), 38.4% titanium (Ti), 1.8% magnesium (Mg), 1.4% silicon (Si), 1.3% manganese (Mn), 1.0% aluminum (Al), 0.4% calcium (Ca), 0.3% phosphorus (P), 0.2% zirconium (Zr), 0.1% sulfur (S), 0.1% niobium (Nb), 0.08% potassium (K), 0.07% zinc (Zn), 0.04% copper (Cu), 0.03% nickel (Ni), and 0.01% chlorine (Cl), as presented in Figure 3.  
A sieve analysis test was carried out to determine the weight of the material particle size and size distribution. The test was performed following the American Society for Testing Materials (ASTM) C136 [10] standard test procedure. The sample (Illemite rock) was crushed and pulverized, and a representative quantity was obtained for analysis. The weight of the empty sieves was recorded (Sieve weight). The sieves were stacked, and the sample was emptied on the topmost sieve. The stack was placed in a mechanical sieve shaker and turned on for 5 min. The weight of the retained sample was recorded (Sample retained). The percentage of retained, percentage of cumulative retained, and percentage of finer (\(\mu\)m) particles were calculated. Thereafter, the cumulative weight percentage was plotted against size (\(\mu\)m). The same procedure was repeated for barite, except for crushing and milling. The result presented in Figure 4 shows that barite and ilmenite were made up of 6.5 \(\mu\)m and 22 \(\mu\)m at D50 (median particle size), respectively, and were utilized in