Additive crystalline salt and water amount to increase the density - Method I (two-salt systems)

Input(s)

$V_{i}$ : Volume of Initial Brine (bbl)

$V_{w}$ : Total Water Volume to add to achieve the Final Brine Density (bbl)

$C_{m s f}$ : Concentration of More Soluble Salt in Final Brine Formulation (%) $(\mathrm{lbm} / \mathrm{bbl})$

$C_{l s f}$ : Concentration of Less Soluble Salt in Final Brine Formulation $(\mathrm{lbm} / \mathrm{bbl})$

$C_{m s i}$ : Concentration of More Soluble Salt in Initial Brine Formulation (lbm/bbl)

$C_{l s i}$ : Concentration of Less Soluble Salt in Initial Brine Formulation (lbm/bbl)

$W_{i}$ : Water Fraction in Initial Brine Formulation (fraction)

$W_{f}$ : Water Fraction in Final Brine Formulation (fraction)

$V_{f}$ : Final Volume of Brine after Adjustment (bbl)

$m_{m s}$ : Additional More Soluble Salt need to raise the Brine Density (lbm)

\begin{gathered} m_{m s}=\left(V_{i}\right) \frac{C_{l s i} C_{m s f}}{C_{l s f}}-C_{m s i} \\ V_{w}=\left(V_{i}\right) \frac{C_{l s i} W_{f}}{C_{l s f}}-W_{i} \\ V_{f}=\frac{C_{l s i} V_{i}}{C_{l s f}} \end{gathered}

Bridges, K. L. (2000). Completion and Workover Fluids (Vol. 19). Society of Petroleum Engineers, Page: 56.