# Water breakthrough correlations in vertical wells - Sobocinski and Cornelius

## Input(s)

h: Oil Column Thickness (ft)

$$h_{t}$$: Height of the Apex of the Water Cone above the Average Water-Oil Contact (ft)

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

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

$$\rho_{w}$$: Water Density $$(\mathrm{g} / \mathrm{cc})$$

$$\mu_{o}$$: Oil Viscosity $$(\mathrm{cP})$$

$$\rho_{o}$$: Oil Density $$(\mathrm{g} / \mathrm{cc})$$

$$q_{o}$$: Oil Production Rate (STB/D)

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

$$\alpha$$: Constant Value of 0.5 for $$\mathrm{M}<1$$ and 0.6 for $$\mathrm{M}$$ between 1 and 10 (RB/STB)

M: Water Oil Mobility Ratio (fraction)

$$\mathrm{t}$$: Breakthrough Time (days)

$$\varnothing$$: Porosity (fraction)

## Output(s)

Z: Dimensionless Cone Height (feet)

$$t_{D}$$: Dimensionless Breakthrough Time (days)

## Formula(s)

$\begin{gathered} Z=\frac{0.00307 *\left(\rho_{w}-\rho_{o}\right) * k_{h} * h * h_{t}}{\mu_{o} * q_{o} * B_{o}} \\ t_{D}=\frac{0.00137 *\left(\rho_{w}-\rho_{o}\right) * k_{h} *\left(1+M^{\alpha}\right) * t}{\mu_{o} * \emptyset * h *\left(\frac{k_{h}}{k_{v}}\right)} \end{gathered}$

## Reference(s)

Sobocinski, D.P., Cornelius, A.J. 1965. A Correlation for Predicting Water Coning Time. SPE ATCE, Houston, Texas.

## Related

### Water breakthrough correlation in vertical wells - Bournazel and Jeanson

An unhandled error has occurred. Reload 🗙