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.