Unsteady Transient Storage and Flow

In a confined aquifer, the quantity corresponding to specific yield is called storativity, 5, and is typically much smaller than Sy. Storativity is a function of the compressibility of water and aquifer material and is proportional to aquifer thickness. A related term is specific storage, Ss, which is storativity divided by aquifer thickness. Storativity increases as thickness of the aquifer increases, whereas specific yield is not a function of aquifer thickness. Removal of large volumes of water from confined aquifers can result in measurable ground subsidence. 

Because qx is equal to — K dh/dx and qy is equal to — K dh/dy, mass conservation of water at the point also can be written as 

[3-10b] assumes that the aquifer is horizontally isotropic (i.e., K is the same in both x and y directions). Solutions to the preceding differential equations under appropriate boundary and initial conditions describe the time-varying hydraulic head, i, in two dimensions. Several solutions are given by Carslaw and Jaeger (1959). More complicated boundary and initial conditions are treated by Hantush (1964), Reed (1980), and Wang and Anderson (1982). Note that in Eq. [3-1 Ob] the quantity (Kb) could be replaced by T, the aquifer transmissivity. 

A common application of a solution to Eq. [3-10b] is the prediction of time-varying drawdown in the vicinity of a well that is pumped at a constant rate. The Theis equation (Theis, 1935) was derived for confined aquifers and applies to unconfined aquifers for some period of time after a well begins to be pumped. The Theis equation can be written as 

As shown by Cooper and Jacob (1946), Eq. [3-11] can be written for small values of u (less than 0.01) as 

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