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.