Unformatted text preview: HYDROGEOLOGY LECTURE NOTES Chapter 5 – Storage Parameters
(or Flow Equations part 2) Introduction
In the last chapter we discussed equations and introduced the main groundwater flow equation, which is: ∂q x ∂q y ∂q z ∂h + + = Ss ∂x ∂y ∂z ∂t
where… q = specific discharge (i.e., groundwater flow) in the x, y, or z direction [L/t] h = hydraulic head [L] t = time [t] x, y, z = lengths in the principal directions in our coordinate systems We also substituted Darcy’s law… (Equation 5-1) q=K
where… dh dl (Equation 5-2) K = hydraulic conductivity [L/t] dh/dl = hydraulic gradient, or change in head with length [-] …for q, and we got the following equation. ∂h ∂h ∂h ∂ K z ∂ K x ∂ K y ∂y ∂h ∂x ∂z + + = Ss ∂x ∂y ∂z ∂t (Equation 5-3) Now, the observant student will notice that, so far, we have not defined the variable Ss on the right side, nor have we specifically discussed what the right side of the equation means. However, we did establish that this equation is basically the continuity equation, where the left side represents I – O (what goes in minus what goes out), and the right side represents ∆S (change in storage). Ss is a storage parameter called the specific storage, and it basically is a coefficient that relates the changes in head in the aquifer to the change in the amount of water stored in the aquifer at a certain point. In other words, it is a quantity that tells us how much water we can get out of a unit volume of aquifer for a unit drop in head. We will discuss specific storage, and the other storage parameters, in this chapter. Aquifers
Before we discuss storage parameters, let’s review aquifers and the occurrence of groundwater in nature. An aquifer is a geologic unit that can store and transmit a sufficient amount of water to supply a well. The factors that determine if a geologic unit is an aquifer include: permeability – must be high enough that flow can be maintained aquifer dimensions – there must be a significant saturated thickness to supply water to the well If the aquifer unit is close to the Earth’s surface, and the sediments that comprise it are relatively permeable, the primary source of recharge to the aquifer will probably be infiltration of groundwater from precipitation that falls directly on the ground. In this case, a water table will form, and the aquifer is called a water-table aquifer or an unconfined aquifer (Figure 5-1).
HYDROGEOLOGYLECTURENOTES(SPRING2004).DOC PRINTED ON 8/2/2005 27 HYDROGEOLOGY LECTURE NOTES - The water table is defined as the point where the pore-water pressure and the atmospheric pressure are equal. Water in a well will basically rise to the point where it was encountered during drilling. Figure 5-1. Unconfined aquifer (© Uliana, 2001). If the regional geology consists of alternating layers of low- and high-permeability units (e.g., interbedded sand and clay), then the permeable layers that are overlain by the low-permeability units can form confined aquifers (Figure 5-2). Confined aquifers contain an additional component of pressure head that causes the water in a well to rise above the point where the well encounters the top of saturation. The low-permeability units are called confining layers. Figure 5-2. Interbedded sand and clay units creating both confined and unconfined aquifers (© Uliana, 2001). This additional component of pressure head is created by the difference in elevation between the recharge area and the point in the aquifer in which the well is completed. This is basically the same thing we see in the Darcy tube – the reservoir to the left represents the recharge area, and the change in head from one manometer to the other represents the potentiometric (or pieziometric) surface (Figure 5-3).
HYDROGEOLOGYLECTURENOTES(SPRING2004).DOC PRINTED ON 8/2/2005 28 HYDROGEOLOGY LECTURE NOTES Figure 5-3. Darcy tube experiment (© Uliana, 2001). In addition to unconfined and confined aquifers, we can also have perched aquifers, which are saturated zones developed above isolated low-permeability units (like clay lenses) (Figure 5-2). These are basically unconfined aquifers that are not laterally continuous. So… what we’ve established here is that we have two basic types of groundwater conditions. Unconfined conditions exist where the groundwater is not restricted by a confining layer and the pore fluid pressures at the top of saturation are equal to atmospheric pressure. Confined conditions exist where there is a confining layer and the water under the confining layer has an additional component of pressure that causes it to rise in a well to a point above the top of saturation. This point represents a point on the potentiometric (or pieziometric) surface of the aquifer. The reason we bring all of this up now is because the storage parameters that characterize an aquifer depend on the conditions we just outlined. So lets move on to a discussion of storage parameters, focusing first on storage of water in confined aquifer. Storage Parameters
Confined aquifers – a conceptual understanding
Let’s consider a confined aquifer that consists of a layer of sand overlain by a layer of clay that acts as a confining layer. If we stick a well into the aquifer and pump water out of it, we begin to lower the heads around the well in such a way that we create a cone of depression in the potentiometric surface (Figure 5-4). The more we pump from the well, the larger the cone of depression gets (both in terms of depth and areal extent). Now, if we look at the example in figure 5-4, we see that we have removed a volume of water (reflected by the volume in the barrel), and have lowered the water level in the well and in the surrounding aquifer. However, we have not changed the saturated thickness of the aquifer itself (i.e., the aquifer is still full up to the base of the confining layer). Where does the water come from? The conceptual answer deals with elastic deformation and compressibility of the aquifer materials and the water. The aquifer is made up of sand grains with pore spaces that are full of water. If there is no confining layer and the aquifer is simply recharged by water infiltrating from above, the pore spaces are full of water and the pore fluid pressure is equal to atmospheric pressure plus the overlying column of water. In this case, you can fit a volume of water into the pore space that is equal to the volume of the pore space. HYDROGEOLOGYLECTURENOTES(SPRING2004).DOC PRINTED ON 8/2/2005 29 ...
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- Fall '10
- Hydrogeology, Aquifer, Uliana