## 3 Results and Discussion
### Interaction between Fines and Porous Media  
The surface charge of berea in DIW was determined to be \(-29.53\) mV (Table 2). To investigate the surface charge modification caused by NP, powdered berea at 10 g/L concentration was added to nanofluids of silica and sulfonated silica prepared in DIW at 1 g/L concentration. This mixture was left under stirring for 12 h. Thereafter, the surface charge of the berea powder treated with unmodified and sulfonated silica was measured using Acousustisizer II S/M Flow-through System. It was found that the surface charge of treated berea was reduced to \(-11.4\) mV and \(-20.36\) mV in the case of unmodified and sulfonated silica respectively. The fines produced were analysed for the size and zeta potential. Specifically, effluent sample from effluent bank collected during DIW injection was collected and analysed in the Zetasizer Nano ZSP (Malvern instruments). It was found that the zeta potential of the fine particles was \(-22.9\) mV. The measured zeta potential of fines is in close agreement with previous measurements of fines eluted from berea sandstone [32]. In addition, the fines produced were in there different size classes (Table 4).  
The interaction potential between the fine particles and the porous media was calculated based on the sphere plate collector model presented in Section 2.8. Since the fines have separate size classes, the interaction potential was calculated for each size class and summed on a weighted basis:  
\[V_{t}(h)=\sum_{i=1}^{n}\{V_{t,i}(h)\times w_{i}\} \tag{7}\]  
\begin{table}
\begin{tabular}{c c} \hline
**Radius of Fine Particles (nm)** & **Intensity (\%)** \\ \hline
233.8 & 73.0 \\
68.57 & 24.2 \\
2687 & 2.8 \\ \hline \end{tabular}
\end{table}
Table 4: Size classes of the fine particles.  
Figure 12: Interaction potential between the mineral and (**a**) unmodified silica; (**b**) sulfonated silica; and (**c**) unmodified silica + MPTMS.  
where \(w_{i}\) is the weight intensity of each size class and \(V_{t,i}(h)\) is the interaction potential calculated for the specific size class and finite distance of separation (\(h\)). Thereafter, the non-dimensional interaction energy was determined using Equation (2). The interaction potentials between berea mineral and fines calculated for the reference case (no NP) and berea treated with silica and sulfonated silica is shown in Figure 13.  
In Figure 13, it may be observed that in the reference case, there is a net repulsive potential (energy barrier) between the fines and the mineral surface. However, for mineral treated with silica, there is a net attractive potential (no energy barrier) between the fines and the mineral. This could possibly cause the mineral to act as collectors for capturing fine particles thereby reducing fine migration. This may explain the improvement in water injectivity post application of silica nanofluid as observed in Figures 4 and 5. In the case where berea was treated with sulfonated NP, there a reduction in the energy barrier (Figure 13), however the net potential is still repulsive and close to the reference case. This may explain the similarity in pressure drops observed during initial DIW injection and post flush after saturating the core with sulfonated NP in Figure 10. Thus, it maybe concluded that the surface modification caused silica is much more effective at reducing fine migration and thereby improving the water injectivity in berea cores. [PERSON] and [PERSON] [PERSON] and [PERSON] (2016) observed that the injection of colloidal NP into berea sandstone did not lead to permeability impairment. They stated that adsorption of NP on the pore wall act like lubrication reducing the friction between the water and pore walls. However as discussed earlier, this effect may be explained based on reduction of the fine migration rather than direct influence on flow. Reduction of fine production may overcome the problem of formation damage induced during low salinity flooding in sandstones.