# 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.

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