In the hydrologic cycle, groundwater occurs whenever surface water occupies and saturates the pores or interstices of the rocks and soils beneath Earth's surface. The geologic formations that store and transmit the subsurface water are known as aquifers. Aquifers, aquitards (semipermeable formations), or aquicludes (nonperme-able formations) may underlie a geographic area, watershed, or drainage basin, and all may hold water. But drawing water from aquitards and aquicludes is impractical and economically prohibitive, whereas groundwater stored in aquifers can be removed economically and is often a dependable source of water supply (Todd, 1980). Most aquifers can be considered as underground storage reservoirs that receive recharge from both natural and artificial sources.
Depending on local geological formation and boundary conditions, groundwater may flow out of the aquifer, contributing to surface runoff. In most cases, each aquifer formation has spatially varying properties, such as transmissivity and stor-ativity, which affect the basin's response to pumping and artificial recharge. These formations are collectively referred to as a groundwater reservoir or groundwater system (Willis and Yeh, 1987). Groundwater aquifers can be classified as confined or unconfined, depending on the existence of a water table. A leaky confined aquifer represents a geological formation that leaks and allows water to flow through the confining layer.
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The fundamental law that governs groundwater flow in a laminar flow regime is Darcy's law. If we assume the porous medium is homogeneous and isotropic, Darcy's law states that the specific discharge is proportional to the gradient of hydraulic head:
where q is the specific discharge vector (volume flow rate per unit cross-sectional area normal to the direction of flow), K is the hydraulic conductivity, h is the head, and Vh is the gradient vector of the head, where i,j, and k are unit vectors in the x,y, and z coordinate directions, respectively. The hydraulic conductivity (K) is a function of both fluid and medium properties. As can be shown by dimensional analysis using the basic units of length (L), mass (M), and time (T), K can be expressed as (see, e.g., DeWiest, 1965):
where d(L) is some characteristic length of the medium, e.g., the average pore size or mean grain diameter of the granular material, p M/(LT) is the dynamic viscosity, y M/(L2T2) is the specific weight of the fluid (water), and C is a constant or shape factor, which accounts for the effects of stratification, packing, arrangement of grains, size distribution, and porosity. Parameter k is referred to as the intrinsic permeability and is solely dependent on the medium properties (k = Cd2).
The porous medium is said to be homogeneous if the hydraulic conductivity is independent of the position (x, y, z) within the aquifer. If not, the aquifer is inho-mogeneous, i.e., K = K(x,y, z). The isotropy or anisotropy of the aquifer reflects the directional variability of the hydraulic conductivity. If the hydraulic conductivity varies with the direction of flow, the aquifer is anisotropic. On the other hand, if the hydraulic conductivity is independent of the direction of flow, the aquifer is isotropic. The conditions of inhomogeneity and anisotropy are common occurrences in the soils and geologic formations of aquifers.
Because the specific discharge may not be collinear with the gradient of the hydraulic head, nor have equal specific discharge components in the x,y, and z q = -KVh
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