Single vertical fractures

1. Single vertical fractures Adam Forsberg GEOL 8730 Spring 2014

2. 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

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

4. 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

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

6. Methods • Gringarten and Witherspoon (1972) • 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

7. 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

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

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

10. Gringarten and Ramey (1974) Early time (parallel flow) Uvf2(radial flow)

11. 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