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Pennsylvania Water Science Center

Fractured Rock Hydrology Research


Dan Goode


Comparison of Stair-Step and Dipping-Layer Approaches for Simulation of Flow and Advective Transport in Fractured-Sedimentary Formations (Goode & Fan, 2007)

Daniel J. Goode
U.S. Geological Survey

Ying Fan
Rutgers University


Ground-water flow in fractured-sedimentary formations is often dominated by bed-oriented high-permeability fractures or fracture zones and alternating beds of high and low permeability. Where these beds are inclined, it is challenging to represent the hydrogeologic framework by an orthogonal three-dimensional finite-difference (FD) grid. One approach is to approximate a dipping bed of the formation by cells which form a stair-step structure through the grid. Accuracy is controlled by discretization, and many layers are needed to provide continuity of thin beds. An alternative approach is use of a non-orthogonal FD grid, with model layers representing beds oriented along dip. This approach ensures continuity of beds, which is important for resolution of advective transport, and allows coarser discretization. However, this approach is not formally consistent with derivation of FD equations for orthogonal grids because the geometric effects of dipping layers can only be resolved in models employing an integrated finite-difference or finite-element basis. The stair-step and dipping-layer approaches are compared for several different dipping structures and different degrees of permeability contrast. In tested cases with low to moderate dip (less than 27 degrees), the differences in flow and advective transport simulations are small in comparison to practical errors for field problems. When used in a calibration mode, adjustments in parameters estimated using the two approaches somewhat compensate for the differences in the numerical models. Incorporation of general non-orthogonal and full-tensor anisotropy formulations in practical FD flow models is suggested and would improve applications for fractured-sedimentary aquifers.

Citation: Goode, D.J., and Fan, Ying, 2007, Comparison of stair-step and dipping-layer approaches for simulation of flow and advective transport in fractured-sedimentary formations (abstract): in 2007 NGWA/U.S. EPA Fractured Rock Conference: State of the Science and Measuring Success in Remediation, September 24-26, 2007, Portland, Maine: National Ground-Water Association (CD-ROM), p. 517.

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