## 5 Conclusions  
This study analyzed the impact of surface-modified nanoparticles on wettability improvement and oil recovery rates in carbonate reservoirs. Flotation tests were conducted based on the nanoparticle concentration, reaction time, and treatment temperature. In addition, core flow experiments were conducted on field samples obtained from the oil field to investigate the impact of reaction time. The following results were obtained:  
1. The flotation test results showed that the hydrophilic sample ratio increased to 97.75%, confirming successful wettability improvement in the limestone and dolomite reservoirs. In the case of limestone, the results were consistent regardless of the particle concentration, whereas for dolomite, the degree of improvement increased with higher concentrations. Therefore, the composition of the reservoir rock must be considered when determining the concentration for nanofluid applications.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample No.** & **\#01** & **\#02** & **\#03** & **\#04** \\ \hline Incremental oil recovery & 7.2\% & 26.1\% & 12.6\% & 7.1\% \\ Permeability ratio & 0.78 & 0.64 & 0.48 & 0.11 \\ Contact angle & 9.7\({}^{\circ}\) & 123.1\({}^{\circ}\) & 103.0\({}^{\circ}\) & 107.1\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Experimental results with different reaction times.  
2. The core flow experimental results indicated that the additional oil recovery through nanofluid injection and subsequent waterflooding reached a maximum of 26.1%. Adjusting the reaction time resulted in an incremental oil recovery ranging from 7.2% to 26.1%. The contact-angle differences ranged from 9.7\({}^{\circ}\) to 123.1\({}^{\circ}\) with nanofluid treatment, and wettability improvement was observed in all samples with reaction times exceeding 12 h. Permeability exhibited a decrease with an increase in reaction time. Specifically, the permeability ratio was 0.78 for a 12-h reaction time and 0.11 for a 72-h reaction time.
3. With increasing reaction time, wettability improved, and nanoparticle aggregation also occurred, leading to reduced permeability and decreased oil recovery. In our case, the critical reaction time was 24 h to maximize oil recovery while minimizing permeability reduction. Below this limit, the wettability improvement did not facilitate oil recovery enhancement. In contrast, additional adsorption owing to particle aggregation decreased permeability beyond this limit, thereby reducing oil recovery.
4. To maximize the efficiency of the EOR method using GPTMS-SiO\({}_{2}\) nanofluid, it is crucial to control the reactivity between the rocks and nanofluids by adjusting the rock composition, nanoparticle concentration, and reaction time.  
H.J.: conceptualization, methodology, writing--original draft preparation, visualization, and validation. J.L.: supervision, writing--review and editing, and validation. All authors have read and agreed to the published version of the manuscript.  
This work was supported by (1) the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2020R1F1A1048182), (2) the Energy and Mineral Resources Development Association of Korea (EMRD) grant funded by the Korean government (MOTIE) (2021060001, Data science-based oil/gas exploration consortium) and (3) the \"Regional Innovation Strategy (RIS)\" through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (MOE) (2022 RIS-005).  
Not applicable.  
Data Availability Statement:Data will be made available on request.