Sand weight needed to refill a hydraulically fractured reservoir volume

Input(s)

$V$: Volume of Unit Area of the Fracture $\left(\mathrm{ft}^{3} / \mathrm{ft}^{2}\right)$

Ø: Porosity (fraction)

$\rho_{\text {sand }}$ : Density of the Sand $\left(\mathrm{lb} / \mathrm{ft}^{3}\right)$

Output(s)

$S$: Sand Weight needed to Refill the Hydraulically Fractured Reservoir Volume $\left(\mathrm{lb} / \mathrm{ft}^{2}\right)$

Formula(s)

$$ S=V \cdot(1-\varnothing) \cdot \rho_{\text {sand }} $$

Reference(s)

Saydam, T., (1967). Principles of Hydraulic Fracturing, ARI Publishing Co., Page: 98.