Horizontal well breakthrough time in a bottom-water-drive reservoir

Input(s)

$\emptyset$: Porosity (fraction)

$S_{w c}$: Connate Water Saturation (fraction)

$S_{\text {oir }}$: Residual Oil Saturation (fraction)

$E_{s}$: Sweep Efficiency (dimensionless)

$k_{h}$: Horizontal Permeability $(\mathrm{mD})$

$k_{v}$: Vertical Permeability $(\mathrm{mD})$

$\mathrm{h}$: Oil Column Thickness (ft)

$q_{o}$: Flow Rate $(\mathrm{STB} / \mathrm{d})$

$B_{o}$: Oil Formation Volume Factor (RB/STB)

Output(s)

$f_{d}$: Saturation Constant (dimensionless)

$t_{B T}$: Water Breakthrough Time (d)

Formula(s)

$$ \begin{gathered} \mathrm{f}_{\mathrm{d}}=\varnothing *\left(1-\mathrm{S}_{\mathrm{wc}}-\mathrm{S}_{\mathrm{oir}}\right) \\ \mathrm{t}_{\mathrm{BT}}=\left(\mathrm{f}_{\mathrm{d}} * \mathrm{~h}^{3} * \frac{\mathrm{E}_{\mathrm{s}}}{5.615 * \mathrm{q}_{\mathrm{o}} * \mathrm{~B}_{\mathrm{o}}}\right) * \frac{\mathrm{k}_{\mathrm{h}}}{\mathrm{k}_{\mathrm{v}}} \end{gathered} $$

Reference(s)

Joshi, S. D. 1991, Horizontal Well Technology. Tulsa, Oklahoma: PennWell Publishing Company. Chapter: 8, Page: 295 .