## 2 Materials and Methods
### Nanofluid Stability and Determination of NP Concentration  
The suspended NP in fluid have the tendency to aggregate due to the large surface area to volume ratio leading to high surface energy, hence they tend to aggregate to minimize the surface energy \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & **Conc (g/L)** & **Dispersing Phase** & **Zeta Potential (mV)** & **Particle Radius (nm)** & **Method** \\ \hline Silica & 1 & DIW & \(-\)51.45 & 161.2 & DLS \\ Sulfonated Silica & 1 & DIW & \(-\)44.8 & 182.9 & DLS \\ Silica & 1 & DIW + 1 g/100 mL MPTMS & \(-\)47.75 & 153.3 & DLS \\ Powdered Berea & 10 & DIW & \(-\)29.53 & NA & ESA \\ Quartz powder & 10 & DIW & \(-\)5.732 & NA & ESA \\ Kaolinite powder & 10 & DIW & \(-\)9.097 & NA & ESA \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Particle Size and Zeta potential measurements. DIW: Deionized water; MPTMS 3-Mercaptopropyl Trimethoxysilane; NA: Not Applicable; DLS: Dynamic Light Scattering; ESA: Electrostatic Attenuation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Experiment No.** & **NP Conc. (g/L)** & **Type of NP** & **Dispersing Phase** & **Comments** \\ \hline
1 & 1 & Silica & DIW & \\
2 & 2.5 & Silica & DIW & \\
3 & 1 & Silica & DIW & \\
4 & 1 & Silica & DIW + MPTMS (1 g/100 mL) & \\
5 & 2.5 & Silica & DIW + MPTMS (1 g/100 mL) & \\
6 & 4 & Silica & DIW + MPTMS (1 g/100 mL) & \\
7 & 1 & Silica & DIW + MPTMS (1 g/100 mL) & Repeated Experiment 4 \\
8 & 2.5 & Silica & DIW + MPTMS (1 g/100 mL) & Repeated Experiment 5 \\
9 & 1 & Sulfonated & DIW & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: List of injection experiments performed in this study. The stability of the nanofluids was investigated. Measurement of transmissivity of nanofluids at different points (along the vertical height) in a sample is a method that addresses the uniformity of dispersion of the NP in the fluid. The used instrument was TurbiScan Lab by Formulation Inc. The instrument measures, among other things, the % transmissivity with predetermined scanning time and duration. Uniform dispersion of the NP in a fluid, is indicated by stable transmissivity along the vertical length. The results for the prepared nanofluid showed that it was stable and uniformly dispersed for up to 24 h. In general, from this work it was found that the tested nanofluids were stable for about 24 h beyond which the settlement of particles could be visually observed. The nanofluid with sulfonated silica NP was the most stable. This nanofluid was stable for about one week. All the experiments were performed within 10 h to ensure that the experiments were within the stability period. The effluent was analyzed for the concentrations of the NP and the stabilizing fluid. Transmissivity calibration curve (Figure 2) was constructed by dispersing NP in a corresponding fluid. In this case was done with deionized water (DIW) with different concentrations of NP. For example, the transmissivity measurement of the 1 g/L dispersion of bare silica in DIW was performed along the turbiscan tubes with sample height of 35 mm. The maximum transmissivity measured was 35.67%, the minimum was 34.87% and the mean transmissivity was 35.14%. This indicates that the prepared nanofluid prepared was uniformly dispersed. Further, the nanofluid was diluted to 0.5 g/L and 0.33 g/L NP concentration and the samples were placed in an ultrasonic bath for 1 h after which the transmissivity was measured. These measurements along with the transmissivity of DIW (no NP) was used to make the calibration curve shown in Figure 2. The calibration curve was used to determine the concentration of NP in effluent samples. For each nanofluid prepared for particular experiment, a calibration curve was constructed following the above process. The transmissivity of the effluent samples is measured and compared against the calibration curve to determine the concentration of the NP in the effluent.