Analytical solutions for one-phase seepage flows impeded by wellbore seals

Steady, one-phase, plane and axisymmetric, Darcian seepage in a homogeneous rock adjacent to a partly isolated wellbore with annular seals is analytically studied. Water flows from an isobaric feeding contour and a fracture, which is kept at the same pressure as the feeding contour, to a wellbore. Partial isolation of the wellbore makes its wall a composition of intermittently arrayed no-flow boundaries, which model the wellbore seals, and isobaric surfaces, which model the annular compartments between the seals and a wellbore tubular on which the seals are mounted. Pressure drops from the aquifer (fracture) to the compartments and further to the borehole that generates a hierarchy of flows mathematically equivalent to the Toth [Freeze, R.A., Cherry, J.A., 1979. Groundwater. Prentice Hall, Englewood Cliffs] hydrogeological patterns of regional, intermediate and local groundwater flows on the scale of catchments. Conformal mappings of complex potential domains onto physical planes, where water seepage takes place, are used to tackle the fragments of the full feeding contour-fracture–sealed wellbore system. Explicit rigorous solutions for the flow characteristics (pressure and stream function) enable calculating optimal wellbore isolation with a criterion of minimal water flow rate from the fracture.