## 5 Parametric Sensitivity Analysis
### Dimeter Ratio and Eccentricity Effect on the Pressure Loss in Power-Law and Yield Power-Law Fluids  
The drilling fluids and the well geometries used for the parametric sensitivity study are provided in Table 5. Figure 6 shows the simulated effect of diameter ratio on the pressure loss for the power-law fluids (1 and 2) filled in two eccentric wells. As the flow annular spacing reduces, the pressure loss increases. Since both fluids have the same consistency index, the difference in pressure loss is due to the flow index value. The impact is higher when the annulus is narrower. When the \(d_{p}/d_{h}\) is lower, the effect is insignificant.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Fluid**} & \multirow{2}{*}{
\begin{tabular}{c} **Rheology** \\ **Models** \\ \end{tabular} } & \multicolumn{3}{c}{**Rheological Parameters**} & \multicolumn{3}{c}{**Drill Pipe/Well Geometry**} \\ \cline{3-7}  & & \(n\) [ ] & \(k\) (lbf.s\({}^{\text{n}}\)/100 ft\({}^{\text{2}}\)) & \(\tau_{y}\) (lbf/100 ft\({}^{\text{2}}\)) & \(d_{p}\) (in) & \(d_{h}\) (in) & \(d_{p}\)/\(d_{h}\) \\ \hline Fluid 5 & Power Law & 0.43 & 2.78 & 0 & & 6.6 & 0.2 \\ Fluid 6 & & 0.73 & 2.78 & 0 & & 3.3 & 0.4 \\ \hline Fluid 7 & \multirow{2}{*}{Yield Power Law} & 0.43 & 2.78 & 6.20 & & 1.65 & 0.8 \\ Fluid 8 & & 0.73 & 2.78 & 6.20 & & 1.466 & 0.9 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Power law and modified power law fluids used to simulate the effect of flow index (\(n\)), diameter ratio and eccentricity.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Figure**} & \multirow{2}{*}{**Fluid**} & \multirow{2}{*}{\begin{tabular}{c} **Model** \\ **(This Work Equation (11))** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Model** \\ **([PERSON] et al., 2017) [12]** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} \(\beta^{*}\) \\ **This Model** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **This Work** \\ **R-Factor** \\ \end{tabular} } \\ \cline{3-3} \cline{5-5}  & & & & **Absolute Mean Error \%** & & \\ \hline Figure 4 & Fluid 3 & 5.2 & 8.7 & 10 & Equation (15) \\ Figure 5 & Fluid 4 & 6.9 & 11.7 & 10 & Equation (15) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Model performance accuracy analysis for the yield-power-law fluids using this work R-factor.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Fluid**} & \multirow{2}{*}{
\begin{tabular}{c} **Rheology** \\ **Models** \\ \end{tabular} } & \multicolumn{3}{c}{**Rheological Parameters ([PERSON] et al.’s (2017)) [12]**} & \multicolumn{3}{c}{**Drill Pipe/Well Geometry**} \\ \cline{3-7}  & & \(n\) [ ] & \(k\) (lbf.s\({}^{\text{n}}\)/100 ft\({}^{\text{2}}\)) & \(\tau_{y}\) (lbf/100 ft\({}^{\text{2}}\)) & \(d_{p}\) (in) & \(d_{h}\) (in) & \(d_{p}\)/\(d_{h}\) \\ \hline Fluid 1 & \multirow{2}{*}{Power Law} & 0.43 & 2.78 & 0 & & 6.6 & 0.2 \\ Fluid 2 & & 0.73 & 2.78 & 0 & & 3.3 & 0.4 \\ Fluid 3 & & 0.3255 & 6.40 & 20.9 & & 1.65 & 0.8 \\ Fluid 4 & & 0.3428 & 2.52 & 6.20 & & 1.466 & 0.9 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Power law and modified power law fluids used to simulate the effect of diameter ratio in eccentric drill strings.  
Similarly, Figure 7 illustrates the impact of the pipe-well diameter ratio and eccentricity on the behavior of yield-power-law fluids.