Single vertical fractures Adam Forsberg GEOL 8730 Spring

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

Assumptions • Early-time – Flow is 1 D • 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 pseudoradial – Well discharge originates from areas further from fracture

Methods 1. Gringarten and Witherspoon (1972) Uses drawdown from observation wells – 2. Gringarten and Ramey (1974) Uses drawdown from pumped well only – • Neglects well losses and well-bore storage 3. 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

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)

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