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.