Drilling mud density (solid content analysis of drilling muds)
Input(s)
\(\rho_{w}\): Density of used Water (lb/gal)
\(f_{w}\): Water Content Ratio of Drilling Mud (fraction)
\(\rho_{l g}\): Density of Clay and Cuttings (lb/gal)
\(f_{l g}\): Content Ratio of Clay and Cuttings in Drilling Mud (fraction)
\(\rho_{B}\): Density of Barite (lb/gal)
\(f_{B}\): Content Ratio of Barite (fraction)
\(\rho_{o}\): Density of Oil that is used in Oil-based Muds (lb/gal)
\(f_{o}\): Oil Content Ratio in Drilling Mud (fraction)
Output(s)
\(\rho_{m}\): Drilling Mud Density (lb/gal)
\(f_{s}\): Total Solid Content Ratio in a Drilling Mud (fraction)
Formula(s)
\[
\rho_{\mathrm{m}}=\rho_{\mathrm{w}} \mathrm{f}_{\mathrm{w}}+\rho_{\mathrm{lg}} \mathrm{f}_{\mathrm{lg}}+\rho_{\mathrm{B}} \mathrm{f}_{\mathrm{B}}+\rho_{\mathrm{o}} \mathrm{f}_{\mathrm{o}}
\]
For water-based muds
\[
\begin{gathered}
\mathrm{f}_{\mathrm{w}}+\mathrm{f}_{\mathrm{lg}}+\mathrm{f}_{\mathrm{B}}=1 \\
\mathrm{f}_{\mathrm{s}}=\mathrm{f}_{\mathrm{lg}}+\mathrm{f}_{\mathrm{B}} \\
\mathrm{f}_{\mathrm{w}}=1-\mathrm{f}_{\mathrm{s}} \\
\mathrm{f}_{\mathrm{s}}=0.3125\left[\frac{\rho_{\mathrm{m}}}{8.33}-1\right]+0.5 \mathrm{f}_{\mathrm{lg}}
\end{gathered}
\]
Reference(s)
Altun, G., Drilling Fluids Lab, Course Notes, ITU Petroleum and Natural Gas Engineering, Istanbul, Turkey, 2013-2014. Experiment 3, Page: 1.