Gringarten and Ramey Solution for Fractured Aquifers with a Single Horizontal Plane Fracture

Well-aquifer configuration for Gringarten and Ramey (1974) solution for a pumping test in a fractured aquifer with 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.

AQTESOLV provides visual and automatic methods for matching the Gringarten and Ramey solution to pumping test data. This easy-to-use and intuitive software promotes rapid and accurate determination of aquifer properties.


The following assumptions apply to the use of the Gringarten and Ramey horizontal fracture solution:

  • 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


provides the following options for the Gringarten and Ramey horizontal fracture solution:

  • variable pumping rates
  • multiple pumping wells
  • multiple observation wells


AQTESOLV benchmark for Gringarten and Ramey (1974) solution for a uniform-flux horizontal plane fracture
Comparison of AQTESOLV (blue line) and published uniform-flux horizontal plane fracture well function values (symbols) at the wellbore for hD=1 and zD=0.5 (Gringarten and Ramey 1974).


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.