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 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

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) 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

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)
Uvf ≥ 2 (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