## 3 Results and Discussion
### Limestone Permeability Damage  
The pH within the limestone core was assumed to be the average of all the effluents' pH values. In all cases, the pH of the effluent was measured immediately after the injection of each pore volume to avoid equilibrium between the dissolved CO\({}_{2}\) and air. After conducting the core flooding experiments, cleaning the cores, and measuring the new permeability of each core, permeability damage was calculated as the permeability's reduction percentage. The permeability damage and pH results are presented in Table 3.  
Figure 4: (a) Zeta potential of \(\alpha\)-Al\({}_{2}\)O\({}_{3}\) nanoparticles at various pH values. (b) The dimensionless total energy of interaction between nanoparticles in relation to the distance between nanoparticles at various pH values. Figure 5: Sedimentation of nanoparticles after 24 h of nanofluid preparation at various pH conditions. (a) pH = 4.5, (b) pH = 6.7, and (c) pH = 7.5. The total interaction energy between the nanoparticles and the rock surface was calculated according to DLVO theory using Equations (1) and (4)-(7). In this case, the equations of \(V_{VDW}\) and \(V_{EDL}\) differ considerably because of the interaction being a sphere-plate interaction instead of a sphere-sphere interaction as in the case of the nanoparticles' interactions [20]. The results are presented in Figure 6.  
\[V_{VDW}=-\frac{A}{6}\left[\frac{2(1+H)}{H(2+H)}+ln\left(\frac{H}{2+H}\right)\right] \tag{5}\]  
\[H=\frac{h}{a_{p}} \tag{6}\]  
\[V_{EDL}=\left(\frac{\varepsilon_{F}\varepsilon_{0}a_{p}}{4}\right)\left[2 \zeta_{1}\zeta_{2}\ ln\left(\frac{1+exp(-\kappa h)}{1-exp(-\kappa h)}\right)+ \Big{(}\zeta_{1}^{2}+\zeta_{2}^{2}\Big{)}ln(1-exp(-2\kappa h))\right] \tag{7}\]  
where \(\zeta_{1}\) and \(\zeta_{2}\) are the zeta potentials of the nanoparticles and the rock surface, respectively (mV). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Experiment’s** & **Effluent’s** & **Original** & **Post Flooding** & **Permeability** & **Permeability** \\
**Description** & **Average pH** & **Permeability** & **Permeability** & **(MD)** & **Reduction** \\ \hline Nanofluid alternating & & & & & \\ CO2 injection & 6.5 & 229.444 & 176.14 & 23.23\% \\ Nanofluid injection & 7.6 & 212.025 & 111.23 & 47.54\% \\ Low-pH nanofluid & 7.2 & 208.178 & 143.61 & 31.02\% \\ injection & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Permeability damage to the limestone cores after each core flooding experiment. Figure 6: (**a**) Zeta potential of limestone powder in 0.1 wt% NaCl water and 0.03 wt% CTAB surfactant at various pH values. (**b**) The dimensionless total energy of interaction between \(\alpha\)-Al\({}_{2}\)O\({}_{3}\) nanoparticles and limestone rock surface in relation to the distance between them at various pH values. The results revealed that permeability reduction occurred in all cases. However, the nanofluid alternating CO\({}_{2}\) injection case resulted in the least permeability damage. As displayed in Figures 4-6, lower pH conditions resulted in stronger repulsion between the nanoparticles themselves, and between nanoparticles and the rock surface. The stronger repulsion in those cases resulted in less retention of nanoparticles because sedimentation and adsorption are two of the main nanoparticles' retention mechanisms. Therefore, the lower permeability damage when the nanofluid was alternately injected with the CO\({}_{2}\) was attributed to the lower pH condition within the core. Despite the lower pH condition in the nanofluid alternating CO\({}_{2}\) injection core flooding experiment (IDLS_1), it was not sufficient to completely prevent the continuous accumulation of nanoparticles after injection into each pore volume of the nanofluid. In all experiments, the differential pressure increased during the nanofluid injection step, as displayed in Figure 7. This increase proved that the pore-plugging effect occurred in all experiments. Nevertheless, in the nanofluid alternating CO\({}_{2}\) injection experiment, the plugging effect occurred at a slower rate.