## 2 Materials and Methods
### SiO\({}_{2}\) Nanofluid Preparation  
Sandstone rocks have a uniform pore system and are homogeneous, whereas carbonate rocks have a complex pore system consisting of macro- and micro-pores. When injecting nanoparticles of the same size into both reservoirs, the pores are easily plugged by nanoparticles, and this effect is further amplified by particle aggregation. Therefore, the particle-size sensitivity was compared between sandstone and carbonate reservoirs for the injection of nanofluids [17]. Additionally, preventing particle aggregation under reservoir conditions was important. Achieving colloidal stability under reservoir conditions is crucial for recovering residual oil from carbonate reservoirs, necessitating tiny nanoparticles. GPTMS-SiO\({}_{2}\) comprises surface-modified silica, which resists high-concentration electrolytes and elevated temperatures. Additionally, it has proven effective in altering the wettability of carbonates [11]. To prepare the GPTMS-SiO\({}_{2}\) nanofluid (as illustrated in Figure 1), we added 1.0 mmol/g of GPTMS to the SNPs in deionized water to achieve a pH range of 6-7, resulting in a 10 wt.% SNP concentration. Magnetic stirring facilitated the addition of GPTMS to the diluted SNPs, followed by stirring for 1 h and heating at 70 \({}^{\circ}\)  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**API Gravity,** & **Specific Gravity,** & **Viscosity at** & **Acid Number,** & **Base Number,** \\ \({}^{\circ}\)**API** & **Fraction** & **60 \({}^{\circ}\)C, mPa\(\cdot\)s** & **mg/g KOH** & **mg/g KOH** \\ \hline
32.7 & 0.861 & 5.75 & 0.1 & 1.1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Crude oil properties.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No.** & **Litho-Type** & **Diameter,** & **Length,** & **Permeability,** & **Porosity,** & **Pore Volume,** \\  & **cm** & **cm** & **md** & **\%** & **cc** \\ \hline \#01 & & 3.75 & 6.74 & 38.1 & 28.1 & 20.9 \\ \#02 & Low density, high phi carbonate & 3.78 & 6.51 & 9.0 & 27.3 & 19.9 \\ \#03 & & 3.77 & 6.53 & 37.0 & 30.3 & 22.1 \\ \#04 & & 3.75 & 6.71 & 10.0 & 26.7 & 19.8 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Carbonate rock properties for nanofluid injection performance.  
for 24 h. This process involved GPTMS hydrolysis and grafting onto the SNP surfaces, enhancing the colloidal stability of the nanofluid. The hydrolysis reaction is as follows [18]:  
\[RSI(OCH_{3})_{3}\overset{H_{2}O}{\rightarrow}RSI(OH)_{3}+3 CH_{3}OH. \tag{1}\]  
At 70 \({}^{\circ}\)C, OR\({}^{\prime}\) covalently bonds to free hydroxyl groups on SNP surfaces, modifying surface characteristics. Rather than reducing the electrostatic repulsion, this process enhances the repulsive forces and kinetically stabilizes the GPTMS-SiO\({}_{2}\) nanofluid under high electrolyte and temperature conditions [11]. Subsequently, the solution of modified SNPs was filtered using cellulose esters and purified via dialysis against deionized water to remove ungrafted SNPs. Following this process, the impact of the GPTMS on grafting was assessed via FTIR at Kangwon National University's central laboratory in Samcheok, Republic of Korea. Then, the grafted product was dispersed in simulated formation water.