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Single vertical fractures

This study investigates the effects of vertical fractures on unsteady-state drawdown in a well intersecting a single vertical fracture. It contrasts traditional Theis solutions with observed behaviors in fractured aquifer systems. Assumptions include homogeneity, isotropy, and infinite hydraulic conductivity within the fracture. Various methods, including Gringarten and Witherspoon (1972) and Ramey and Gringarten (1976), are employed to analyze drawdowns from different wells, highlighting the transition from 1D to pseudo-radial flow as pumping progresses.

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Single vertical fractures

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  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

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