Gringarten and Ramey Solution for Fractured Aquifers with a Single Horizontal Plane Fracture
A mathematical solution by Gringarten and Ramey (1974) is useful for determining the hydraulic properties (hydraulic conductivity, specific storage, hydraulic conductivity anisotropy and fracture radius) of fractured aquifers with a single horizontal plane fracture intersecting the control well. Analysis involves matching the solution to drawdown data collected during a pumping test. The solution estimates hydraulic conductivity anisotropy in a vertical (x-z) plane.
You are not restricted to constant-rate tests with the Gringarten and Ramey solution. AQTESOLV incorporates the principle of superposition in time to simulate variable-rate and recovery tests with this method.
The early-time response of a pumped well intersecting a horizontal fracture has a distinct signature that you can diagnose with a linear flow plot.
- aquifer has infinite areal extent
- aquifer has uniform thickness
- aquifer potentiometric surface is initially horizontal
- fractured aquifer represented by anisotropic nonleaky confined system with a single plane horizontal fracture
- flow is unsteady
- water is released instantaneously from storage with decline of hydraulic head
- diameter of control well is very small so that storage in the well can be neglected
The following equation by Gringarten and Ramey (1974) predicts drawdown at a fixed point (piezometer) in an anisotropic confined aquifer with a uniform-flux horizontal fracture:
- is aquifer saturated thickness [L]
- is modified Bessel function of first kind, zero order
- is radial hydraulic conductivity [L/T]
- is vertical hydraulic conductivity [L/T]
- is pumping rate [L³/T]
- is radial distance from pumping well to observation well [L]
- is radius of horizontal fracture [L]
- is drawdown [L]
- is specific storage [L-1]
- is elapsed time since start of pumping [T]
- and are variables of integration
- is distance in z direction [L]
- pumping and observation well locations
- pumping rate(s)
- observation well measurements (time and displacement)
- saturated thickness
- radius and depth of horizontal fracture
- variable pumping rates
- multiple pumping wells
- multiple observation wells
- (radial hydraulic conductivity)
- (specific storage)
- (hydraulic conductivity anisotropy ratio)
- (radius of fracture)
Curve Matching Tips
- Use linear flow plots to help diagnose linear flow.
- Match the Cooper and Jacob (1946) solution to late-time data to obtain preliminary estimates of aquifer properties.
- Choose Match>Visual to perform visual curve matching using the procedure for type curve solutions.
- Use active type curves for more effective visual matching with variable-rate pumping tests.
- Select values of from the Family and Curve drop-down lists on the toolbar.
- Use parameter tweaking to perform visual curve matching and sensitivity analysis.
- Perform visual curve matching prior to automatic estimation to obtain reasonable starting values for the aquifer properties.
Gringarten, A.C. and H.J. Ramey, 1974. Unsteady state pressure distributions created by a well with a single horizontal fracture, partial penetration or restricted entry, SPE Journal, pp. 413-426.