I. Aquifers and confining units revisited, with some additional definitions
Figure 4.1 illustrates a "perched" aquifer, which is bounded by upper and lower surfaces along which h=z (or p = 0), the "regional water table" and the "piezometric" (equivalent to "potentiometric") surface of a confined aquifer. Note that the confined aquifer in this figure has both a flowing well and a non-flowing well. The term "artesian" is sometimes used to mean flowing well, but the correct definition of this term is equivalent to "confined". Thus, both wells open to the confined aquifer are "artesian wells". It is also possible to have flowing wells that tap an unconfined aquifer (for example adjacent to a stream). These would be flowing wells, but they are not artesian.
II. Because flow in aquifers is often dominantly horizontal, we can often make a 2D "aquifer flow" assumption in which all flow is assumed to be horizontal. In that case, we can write a version of Darcy's law in terms of flow per unit width of aquifer (see opening B in figure 4.3).
Q' (flow per unit width) = - Kb 3h where b is the aquifer thickness
The product Kb is the aquifer property "transmissivity" represented by the letter T.
Total flow through the aquifer is the
Q = -TW 3h where W is the aquifer width
Note that 3h is a 2D vector, since we assume no vertical gradient, and T is a tensor in only two principle directions (Tx and Ty). Note that T can vary with location (x,y) not only as a function of K(x,y) but also as a function of variations in aquifer thickness b.
III. Storage properties
A second important aquifer property is the aquifer storativity, S. This is defined as the volume of water added to storage per unit area of aquifer (i.e. the column of aquifer beneath a unit area, see figure 4.4) per unit increase in head. Equivalently it is the volume of water removed from a unit area of aquifer per unit decrease in head. Storativity is dimensionless.
A. Unconfined aquifer storativity
For an unconfined aquifer, the water removed as head decreases comes predominantly from draining pores at the water table. If the pores drained completely, S would equal porosity (n). However, pores don't drain completely, as some water is held against gravity drainage by capillary forces. Far above the water table, the fraction of the porous medium that contains water held by these forces is the specific retention, Sr. A moisture profile, similar to that illustrated in Figure 6.6 of the text ,was used to demonstrate that the volume of water drained by gravity during a unit drop in head is equal to n-Sr = Sy, the specific yield. The aquifer storativity of an unconfined aquifer is essentially equal to the specific yield.
B. Confined aquifer storage
When water is removed from a confined aquifer, the head declines (pressure drops) but the pores remain filled. A bicycle tire analog was demonstrated. When air is removed from the tire, the remaining air expands to fill the tube but the pressure is lower. When air is pumped into the tire, the air pressure increases but the tire volume remains about the same. This is a type of "elastic" storage. The elastic compression and expansion of water associated with pressure changes is one source of storage in a confined aquifer.
The specific "elastic" storage Ss is defined as the volume water that is removed from a unit cube of aquifer per unit decline in head. Note that Ss has units of 1/L.
The specific storage due to water compressibility can be quantified as
where the compressibility of water is
A second source of elastic storage is that due to compressibility of the aquifer matrix (actually compressibility of the pores in the aquifer). The matrix responds to changes in effective vertical stress that are the result of changes in pressure.
The total vertical stress at a point in an aquifer is balanced by effective stress on the matrix and by the pore pressure such that
For fixed vertical stress
The specific storage due to matrix compressibility can be quantified as
where the vertical matrix (or pore) compressibility is
and b is the aquifer thickness. Total specific elastic storage is equal to the sum of these two
An example of water level changes in a well near a train station was used to illustrate the response to loading that results from compression of water and subsequent transfer of the load to the matrix as water flows away from the site of loading.