## Flow Equation For A Confined Or Leaky Aquifer

In a confined aquifer, the amount of water released from groundwater storage is dependent on the compressibility of the water and of the porous medium. Confined aquifers are bounded above and below by confining layers. In contrast, leaky or semiconfined aquifers have semipermeable confining layers that are capable of leakage and storage. A multilayered aquifer system is a system in which the aquifers are hydraulically interdependent as changes in head in one layer, caused by pumping, or recharge, can induce flow to and from adjacent layers. If we assume that the leakage or flow between layers and aquitards occurs only in the vertical direction and that any storage effects in the aquitards are negligible, the governing equation characterizing two-dimensional horizontal flow in a semiconfined or leaky aquifer can be expressed by where Txx, 7' = components of transmissivity along the x and y coordinate axes, the product of the hydraulic conductivity and the aquifer's thickness (L2/T)

S = storage coefficient (dimensionless) h — head in the main aquifer (L) t — time (L)

L — leakage from the overlying semiconfining stratum (L/T) Q = sink/source term (L/T)

The leakage term can be calculated by Darcy's law:

where Kz = vertical hydraulic conductivity of the overlaying semiconfining stratum

b' = thickness of the overlying semiconfining stratum (L) H = external head in the overlying semiconfining stratum (L)

The effect of pumping and injection wells in the main aquifer can be simulated by representing the wells as point sources or point sinks under the assumption that the wells fully penetrate the thickness of the aquifer. If we let the index set Q be the locations of all the pumping and injection wells, then the point sources/sinks can be expressed as:

where +QW is the pumping {—Qw recharge) from the wth pumping (injection) well located at (xw, yw) and d(x — xw, y — y„.) is the Dirac delta function, where

Equation (8) applies to a leaky aquifer system in which the main aquifer is overlain by a semiconfining stratum that leaks water into the main aquifer through the semiconfining stratum. If the term L goes to zero, Eq. (8) applies to a strictly confined system.