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)

Reference(s)

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