Single vertical fractures Adam Forsberg GEOL 8730 Spring 2014

The Problem A well intersects a single vertical fracture The unsteady-state drawdown will differ significantly from the Theis solution Some methods were developed for knowledge of hydraulically fractured geologic formations

Assumptions Aquifer Fracture Homogeneous Isotropic Large lateral extent Bounded by aquacludes The well intersects the fracture midway A plane Relatively short length Infinite (very large) hydraulic conductivity No hydraulic gradient in fracture Drawdown is uniform

Assumptions Early-time Flow is 1D Horizontal Parallel Perpendicular Water from the aquifer enters the fracture at an equal rate per unit area Uniform flux

Assumptions As pumping continues Flow becomes pseudo-radial Well discharge originates from areas further from fracture

Methods Gringarten and Witherspoon (1972) Gringarten and Ramey (1974) Uses drawdown from observation wells Gringarten and Ramey (1974) Uses drawdown from pumped well only Neglects well losses and well-bore storage Ramey and Gringarten (1976) Allows for well-bore storage in the pumped well

Gringarten and Witherspoon (1972) General solution for drawdown in an observation well along the x-axis, y-axis, or at a 45 degree angle For r’ ≥ 5, use the Theis method for T and S

Drawdown function(s) Observation well located along the x-axis

Gringarten and Ramey (1974) General solution for the drawdown in the pumped well Reduced form of drawdown function for r’ = 0

Gringarten and Ramey (1974) Early time (parallel flow) Uvf ≥ 2 (radial flow)

Ramey and Gringarten (1976) For a well intersecting a non-plane vertical fracture that accounts for storage of the fracture Assumes a large-diameter well and a plane vertical fracture of infinite conductivity