The Effective Vertical Anisotropy of Layered Aquifers

Many sedimentary aquifers consist of small layers of coarser and finer material. When groundwater flow in these aquifers is modeled, the hydraulic conductivity may be simulated as homogeneous but anisotropic throughout the aquifer. In practice, the anisotropy factor, the ratio of the horizontal divided by the vertical hydraulic conductivity, is often set to 10. Here, numerical experiments are conducted to determine the effective anisotropy of an aquifer consisting of 400 horizontal layers of which the homogeneous and isotropic hydraulic conductivity varies over two orders of magnitude. Groundwater flow is simulated to a partially penetrating canal and a partially penetrating well. Numerical experiments are conducted for 1000 random realizations of the 400 layers, by varying the sequence of the layers, not their conductivity. It is demonstrated that the effective anisotropy of the homogeneous model is a model parameter that depends on the flow field. For example, the effective anisotropy for flow to a partially penetrating canal differs from the effective anisotropy for flow to a partially penetrating well in an aquifer consisting of the exact same 400 layers. The effective anisotropy also depends on the sequence of the layers. The effective anisotropy values of the 1000 realizations range from roughly 5 to 50 for the considered situations. A factor of 10 represents a median value (a reasonable value to start model calibration for the conductivity variations considered here). The median is similar to the equivalent anisotropy, defined as the arithmetic mean of the hydraulic conductivities divided by the harmonic mean.