Axisymmetric flow in an oil reservoir of finite depth caused by a point sink above an oil-water interface (Q1392586)

The authors investigate the shape of an oil-water interface caused by flow into a point sink in an oil reservoir confined above by an impermeable rock strata and below by a water zone and a rock strata. The corresponding axisymmetric flow problem governed by Laplace's equation is solved numerically by the boundary integral equation method. It is observed that there is a critical flow rate at which the interface has a vertical cusp shape. For small flow rates, the authors derive a small parameter expansion and compare the results with numerical solutions.