Finite-Difference Grid for a Doublet Well in an Anisotropic Aquifer


  • Robert T. Miller is a Hydrologist with the U.S. Geological Survey, Water Resources Division, He is a graduate of the University of Connecticut with a B.S. degree in Geology, He has worked on areal studies to determine both the movement and quality of ground waters in Minnesota, He is currently involved in projects to determine the movement of both energy and solute transport in confined and unconfined aquifer systems.

  • Clifford L. Voss is Chief of the U.S. Geological Survey research project “Subsurface Transport Phenomena,” in Reston, Virginia, He received his B.S. in Physics from Bucknell University in 1971. He undertook M.S. studies in the Geology and Geophysics Department at Boston College, Massachusetts, until 1973, and received his M.A., M.S.E, and Ph.D. in Civil Engineering and Hydrology from Princeton University, New Jersey, by 1978. He was a visiting researcher at The Royal Institute of Technology in Stockholm, Sweden, from 1978 to 1981, and in 1985 was a Visiting Associate Professor at the Department of Geology and Geophysics at the University of Hawaii in Honolulu. His research interests relate to analysis of subsurface flow and transport in heterogeneous geologic environments.


The U.S. Geological Survey is modeling hydraulic flow and thermal-energy transport at a two-well injection/ withdrawal system in St. Paul, Minnesota. The design of the finite-difference model grid for the doublet-well system is complicated because the aquifer is anisotropic and the principal axes of transmissivity are not aligned with the axis between the two wells.

An analytical solution for flow in a doublet-well system in an infinite anisotropic aquifer was employed in the design of a grid with artificial boundaries placed in the midst of the flow field. Flow-net analysis was used to determine water flux across an cquipotential boundary and to assign approximate flux values at model boundaries. This enabled the simulation of the effects of the entire flow field, although only a small part was modeled.

The validity of the flux values at the model boundaries for the isothermal case was tested by simulation of an eight-day injection test of ambient-temperature water. Model-computed pressures compared very favorably with field-observed pressures. The validity of boundary-flux values also was tested for nonisothermal conditions by simulation of injection of 300o F water at 300 gallons per minute for eight days.