Optimal placement of a wellbore seal impeding seepage from a tilted fracture

Abstract

Steady, one-phase, 2D Darcian seepage in a homogeneous pay from one horizontal isobar to another with a tilted fracture intersecting the two isobars is studied by the methods of complex analysis. The shortcut through the fracture is foiled by an impermeable seal of a constant length which is placed at the fracture-isobar intersection with an objective to minimise either the total flow rate from the fracture or the travel time of marked particles moving along the seal. Conformal mappings of the slanted-face half-strip in the physical domain onto a half-strip in the complex potential domain give explicit expressions of the seepage rate and travel time through hypergeometric functions. The optimal seal position is found by computer algebra routines for any given distance between isobaric horizons, tilt angle, pressure drop between isobars and hydraulic conductivity of the rock.