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 .