Horizontal well breakthrough time-With gas cap or bottom water
Input(s)
\(\rho_{o}\): Oil Density \((\mathrm{g} / \mathrm{cc})\)
\(\rho_{q}\): Gas Density \((\mathrm{g} / \mathrm{cc})\)
\(t_{b t}\): Breakthrough Time (days)
\(\phi\): Porosity (fraction)
\(\mathrm{h}\): Oil Column Thickness (ft)
\(\mu_{o}\): Oil Viscosity \((\mathrm{cP})\)
\(q_{o}\): Flow Rate \((\mathrm{cP})\)
\(B_{o}\): Oil Formation Volume Factor \((\mathrm{rb} / \mathrm{STB})\)
\(k_{h}\): Vertical Permeability \((\mathrm{mD})\)
\(k_{v}\): Horizontal Permeability (mD)
Output(s)
\(t_{d b t}\): Breakthrough Time if breakthrough time is given (days)
\(q_{d}\): Dimensionless Flow Rate (dimensionless)
Formula(s)
\[
\begin{gathered}
t_{d b t}=k_{v} *\left(\rho_{o}-\rho_{g}\right) * \frac{t_{b t}}{364.72 * h * \emptyset * \mu_{o}} \\
q_{d}=325.86 * \mu_{o} * q_{o} * \frac{B_{o}}{\left(k_{v} * k_{h}\right)^{0.5} * h *\left(\rho_{o}-\rho_{g}\right)}
\end{gathered}
\]
Reference(s)
Horizontal Well Technology, Joshi, Page: 301.