ABSTRACTThe concepts of total stress, effective stress, and fluidpressure are important to understanding where watercomes from when producing water from a confinedaquifer system. However, the overall conceptual imageof pumping confined aquifers is difficult for manystudents to grasp, because pore space is not drained, butrather water is produced as a function of the water andaquifer compressibilities. I present a simple, inexpensivedemonstration, which can be used to help studentsvisualize the interplay between stresses and fluidpressure when pumping a confined aquifer, and can beincorporated into a standard class period of anintroductory hydrogeology class. This exercise uses ajuice container as a simple analog for a confined porespace, and demonstrates how a decrease in fluidpressure from pumping causes an increase in effectivestress assuming a constant total stress, potentiallyleading to subsidence.

INTRODUCTIONMacdonald et al. (2000) highlight the importance ofquantitative skills in the classroom. Many students arecomfortable "plugging and chugging" with equations;however, not developing an intuition for the processesdescribed by the mathematics can prevent students fromunderstanding their results. While the mathematicsdescribing the extraction of water from confined aquifers is not difficult, understanding how water is extractedfrom confined aquifers is a challenge for many students,who find the concepts of water expansion and aquifercontraction-the controlling phenomena in removingwater from confined systems-more difficult than thesimple draining of pore space that occurs in unconfinedaquifers. Providing students with a hands-on experiencehelps them to develop an intuitive understanding of therelationship between total stress, effective stress, andfluid pressure-the controlling components ofconfined-aquifer groundwater extraction. I describe ashort demonstration that is simple, inexpensive, andmemorable.

FLUID FLOW AND AQUIFERCHARACTERISTICSGroundwater in the subsurface moves according to itstotal energy, which is the sum of its kinetic energy,potential energy, and elastic energy (fluid pressure). Thetotal energy required to move a unit weight of water isdefined as the hydraulic head, h [L],

hvg z

Pgw

= + +2

2 ρ(1)

where v is the groundwater velocity [L/T], g is thegravitational acceleration [L/T2], z is the elevation of thefluid above the chosen datum [L], P is the fluid pressure[M/LT2] , and w is the density of water [M/L3]. Thevelocity component in groundwater is generally so smallthat the first term on the right-hand side, the kineticenergy term, is ignored. Groundwater moves fromlocations of higher hydraulic head to areas of lowerhydraulic head-not from high pressure to low pressure. Idigress briefly here to note that it is worthwhile andcommonly necessary to disabuse students of themisconception that water moves from areas of higherpressure to areas of lower pressure. Consider a glass ofwater. Although there is no movement of water insidethe glass, the pressure obviously increases with depthaccording to P = wgl, where l is depth from the watersurface. The increase in pressure head (P/ wg) withdepth is countered by the equivalent decrease inelevation head (z); hence the head is equal throughoutthe column and there is no movement of water.

To extract water from an aquifer for use, we canpump a well, which leads to a local decrease in thehydraulic head. The volume of water that can beremoved from any aquifer is dependent on thesubsurface material's ability to store water,

V SA h= ∆ (2)

where V is the volume of water removed [L3], S is thestorage coefficient of the aquifer [dimensionless], A is the surface area overlying the unconfined aquifer [L2], and his the decline in head.

In unconfined aquifers, which have no impermeablematerial overlying them, water is removed from theaquifer by a decrease in hydraulic head that occurs fromdraining the pore space. The storage coefficient for anunconfined aquifer is defined largely by the amount ofwater that is available to be drained, and is thereforesomewhat less than the porosity. If an aquifer is overlainby low-permeable material and the head in the aquifer isabove the top of the aquifer, it is termed a confinedaquifer. Because groundwater cannot easily move out ofor into many confined aquifers, the water is usuallyunder greater pressure than in an unconfined aquifer ofsimilar depth. When wells are drilled into confinedaquifers, the water level will rise above the top of theaquifer unit due to this pressure, which is known asartesian conditions. When extracting water from aconfined aquifer, pumping will lead to a decline in head,but the aquifer itself may remain saturated. Importantly,extraction of water from confined aquifers is notassociated with dewatering; i.e., no pore space isdrained, no rock or soil dries out. So where exactly doesthis water come from?

O.E. Meinzer, upon observing flowing artesianwells, where the pressure in the confined aquifer is highenough that the water level rises above land surface, wasthe first to predict that confined aquifers werecompressible, and storage in these aquifers wasdescribed by the elasticity of the subsurface material

Singha - Active Learning Exercise for Introducing Ground-Water Extraction 131

An Active Learning Exercise for Introducing Ground-WaterExtraction from Confined AquifersKamini Singha Department of Geosciences, The Pennsylvania State University, 311 Deike

Building, University Park PA 16802, ksingha@psu.edu

(Narasimhan, 2006). Elasticity describes how easily amaterial deforms under stress and returns to shape in the absence of that stress, and is important in groundwaterhydrology. When fluid pressure in the subsurfaceincreases, the skeleton of the aquifer expands;conversely, a decrease in fluid pressure, which wouldoccur during pumping, will lead to aquifer compression,and potentially subsidence, as described later. Meinzerproposed that the release of water in confined aquiferswas a function of the elasticity and compressibility of theaquifer, especially in "aquifers that have lowpermeability, slow recharge, and high head" (Meinzer,1928).

The storage coefficient in a confined aquifer isdefined by the compressibility of the aquifer skeletonand the expansion of the pore fluid as defined by Jacob(1940):

S gb nw= +ρ α β( ) (3)

where b is the aquifer thickness [L], α is thecompressibility of the aquifer [LT2/M], n is the porosity[L3/L3], and β is the compressibility of water [LT2/M].This elastic storage coefficient is much less than thestorage available in an unconfined aquifer.Compressibility describes a change in volume under anapplied stress. In the case of water, this stress is appliedthrough the fluid pressure, such that

β =−

∆

∆

VVP

ww (4)

where an increase in the volume of water Vw [L3] is afunction of a decrease in fluid pressure. Similarly, anincrease in the volume of an aquifer VT [L3] is a functionof a decrease in stress carried by the soil skeleton, calledthe effective stress σe [M/LT2], where

ασ

=−

∆

∆

VVT T

e(5)

As shown in equation 3, it is the combination of thesecompressibilities that contributes to the aquifer storageand consequently the volume of water that can beextracted. In highly compressive aquifers, like clays, can be quite large compared to β, and most of the watercomes from aquifer compression. Alternatively, βdominates in cases of very competent bedrock.

The effective stress and fluid pressure are simplyrelated to one another in the case of a saturated porousmedia under equilibrium stress conditions as

σ σT e P= + (6)

where the total stress on an aquifer, σT [M/LT2], isdefined by the weight of rock and water above theaquifer. The total stress pushing down on the aquifer isborne by both the aquifer skeleton (the effective stress)and water filling the pore space (the fluid pressure), asoriginally described by Terzaghi (1936). In the simplifiedcase of a confined aquifer where the weight of theoverlying rock and water is considered constant suchthat the total stress doesn't change, the effective stressmust increase as the fluid pressure drops from pumping.A reduction in fluid pressure causes 1) the fluid toexpand according to equation 4, and 2) an increase ineffective stress (equation 6) because the total stressremains constant. The increase in effective stress causesthe aquifer materials to compress (equation 5). Thecombination of these responses-the compression of theaquifer and the expansion of the fluids-leads to theproduction of water. Additionally, the increase ineffective stress that occurs during pumping tocompensate for the decrease in fluid pressure may lead

132 Journal of Geoscience Education, v. 56, n. 2, March , 2008, p. 131-135

Figure 1. (A) Schematic of a confined aquifer system, with the total stress, σT, from the weight of rock andfluid above acting on the aquifer, which is countered by the effective stress, σe, of the aquifer skeleton andthe fluid pressure, P, within the pore space; and (B) the analog confined pore.

to subsidence depending on the compressibility of theaquifer.

The interplay between total stress, effective stress,and fluid pressure define the extraction of water inconfined aquifers. The volume of water that can beremoved from these aquifers will be dependent on thematerial composition of the aquifer and the expansion ofwater. While these concepts are outlined fully inhydrogeologic textbooks (e.g., Freeze and Cherry, 1979,Domenico and Schwartz, 1990, Fetter, 1994),understanding the interplay between these stresses isdifficult for many students, who may not be able to 1)visualize the removal of water from the subsurfacewithout draining pore space, and 2) conceptualize theconnection between ground-water mining andsubsidence. Few hands-on exercise exist fordemonstrating the concepts, and the simple hands-ondemonstration described here has been found to helpstudents new to these concepts.

CONFINED AQUIFER DEMONSTRATIONThis demonstration has been used in a 40-studenthydrogeology class composed of upper-levelundergraduates and graduate students, and requiresonly a cardboard juice box or a compressible metallicjuice "bag")-the kind that can be purchased at thesupermarket and comes with a straw (Figure 1). Eachjuice container has its benefits: the box is lesscompressible and withstands a higher effective stress;however, one concern about the juice box is that withoutenough total stress applied, it has the possibility ofdewatering, which would be an inappropriate analog fora confined aquifer. The collapsible juice bag may preventsuch misconceptions, but is able to withstand lesseffective stress. Students are asked to select a partner (ortwo) and each student is given a juice container, which,for the purposes of this demonstration, is nowconsidered to be a single pore in a confined aquifer.Students are asked to answer a series of prescribedquestions in groups after an introduction to the conceptsof total stress, effective stress, and fluid pressure ashighlighted in the last section.

Before inserting the straw, students are asked toapply a downward force on the top of the juice containerby pushing it against a hard surface. It is important thatthe students maintain this force during the experiment so that they are not misled into thinking that they aredewatering the pore space during fluid removal. Theyare now providing the "total stress" on their aquifer, orthe weight of the overlying materials. In groups, thestudents are asked to discuss two concepts: 1) why thecontainer does not collapse with the application of thistotal stress, and 2) what will happen with the straw isinserted, depending on the amount of force that isapplied. After writing out their reasoning on a pre-madeworksheet, they "drill" their confined aquifer and inserttheir well (the straw). After inserting the well into theaquifer, they withdraw fluids via pumping (drinking),while still providing a force from above, which leads to adecrease in the volume of the aquifer (container) as thetotal stress is continuously applied. Students are asked to discuss what happens to their confined aquifer duringthe removal of fluid.

The goal is for the students to see that the containerdoes not collapse prior to pumping despite theapplication of the total stress because the effective stress(the container itself), and the fluid pressure in the pore

space (the juice) push back against weight of theoverburden (their hand); aquifers are similarlysupported by fluid pressure and aquifer strength fromthe weight of overlying rock. Many note that when thestraw is inserted, that fluid will spray out due to the totalstress. This provides an opportunity to discuss flowingartesian wells, which are under high enough pressurethat the height of fluid rises above the aquifer itself andcomment that if the applied force is not that high, juicemay rise in the straw above the height of the juicecontainer, but not flow freely.

After having had the opportunity to develop thevocabulary required to describe pumping in confinedaquifers, we can return to the mathematics describedearlier. All of the students recognize that the juicecontainer collapses as the fluid pressure is released,given a constant applied total stress. The relationshipbetween the total stress applied by their hand andincrease in effective stress is clear. We can return toequation 6, and note that because the total stress isremaining (approximately) constant, the change ineffective stress and fluid pressure must be equal andopposite. As the effective stress borne by the skeletonincreases, the fluid pressure must be decreasing, asexpected.

Subsidence can also be discussed here; the aquifercompression leads to subsidence (the eventual collapseof the container) given the highly compressible aquifermaterial and the increase in effective stress. Students canexplore equation 3, which describes the amount of waterthat can be released as a function of aquifer and fluidcompressibility. Assuming that we're dealing only withwater-filled aquifers and that fluid compressibilityremains constant, the group can discuss how storagewould change with a more or less compressible aquifer.Students understand that with a more compressible juice container, fluids would be easier to produce. Similarly,more water will be extracted from systems where theaquifer compressibility is higher than the watercompressibility. The problem, of course, is that clays andsilts compress easily, but may not easily return to theiroriginal shape. The idea of subsidence control wells mayalso be demonstrated by asking the students to discusswith one another what would happen if we could"re-inject" the removed fluids back into the pore space(e.g., Phien-wej et al., 1998). To re-inject fluids into theaquifer, all we need is to exceed the head in the aquifer; in the case of an artesian but non-flowing well, it would besufficient to just drop water down a well in order to havehigher head than in a deep aquifer-it is not, as mentionedearlier, a matter of exceeding in-situ pressure counter tosome students' intuition. Although pressure head maybe high in deep aquifers, elevation head is relatively low.The restoration of the aquifer toward its original shapewill depend on the geologic conditions of the aquifer,specifically how elastic (recoverable), as opposed toinelastic (permanently deformed) the subsurfacematerials are. Our juice container would likely return, inpart, to its original form; the juice bags are more elasticthan the juice boxes and recover more easily. In reality,recharging an aquifer may not result in a notablerecovery of the land-surface elevation.

Representative student feedback after the first examabout this demonstration was that "…the juice boxanalogy and flow through different mediums [sic,referring to Darcy tube experiments] really helped forthe test", "the [juice container] analogy was helpful for aphysical comparison…handling the juice box did help to

Singha - Active Learning Exercise for Introducing Ground-Water Extraction 133

remember the concept", and "Hi-C box = awesome. Iused it to study, to mentally review the concept!" Otherstudents, semesters later, have commented that they stillremember how fluids are removed from confinedaquifers. The most satisfying result was that almost all ofthe students in this class, after the demonstration, wereable to explain how water produced from an unconfinedaquifer differed from a confined aquifer on the exam, and could accurately describe the interplay between effective stress, total stress, and fluid pressure. Thisdemonstration has proven effective in classrooms withboth undergraduates and graduate students. It providedboth a conceptual tool and "hook" to engage students,and provided a platform to which more advancedconcepts could be related.

SUMMARYI provide an inexpensive and simple hands-on exerciseusing juice containers to allow students to betterconceptualize the relationships between fluid pressure,total and effective stress, and subsidence when pumpingconfined aquifers. After providing an overview ofconfined aquifers, stress, and storage, the students workthrough a short worksheet in groups of 2-3 to discusshow water is produced from an aquifer under confiningpressure given a physical analog. Students work in smallgroups to prompt discussion, which allows them to build a vocabulary regarding stress, pressure, and confinedaquifers as needed. By extracting the fluid (juice) fromtheir confined aquifer system (juice container), studentscan visualize the connections between the applied totalstress, the effective stress of the aquifer skeleton, and thefluid pressure. The juice container is a useful analogbecause students can see that the aquifer is notdewatered, but rather compressed due to the weight ofthe overlying material, and provides a memorabledemonstration that they may think about every timethey're handed a juice container.

ACKNOWLEDGMENTSI appreciate the thoughtful reviews of Gregory Hancock,Eric Peterson, and the associate editor Stephen Boss.Discussions with Fred Day-Lewis improved the in-classexercise.

REFERENCESDomenico, P. A., and Schwartz, F.W., 1990, Physical and

Chemical Hydrogeology, John Wiley and Sons.Fetter, C. W., 1994, Applied Hydrogeology,

Prentice-Hall.Freeze, R. A., and Cherry, A.J., 1979, Groundwater,

Prentice Hall.Jacob, C. E., 1940, On the flow of water in an elastic

artesian aquifer, EOS: Transactions of the AmericanGeophysical Union, p. 574-586.

Macdonald, R. H., Srogi, L., and Stracher, G., 2000,Building the Quantitative Skills of Students inGeoscience Courses, Journal of GeoscienceEducation, v. 48, p. 409-412.

Meinzer, O. E., 1928, Compressibility and elasticity ofartesian aquifers, Economic Geology, v. 23, p.263-291.

Narasimhan, T. N., 2006, On Storage Coefficient andVertical Strain, Ground Water, v. 44, p. 488-491.

Phien-wej, N., Giao, P.H., and Nutalaya, P., 1998, Fieldexperiment of artificial recharge through a well withreference to land subsidence control, EngineeringGeology, v. 50, p. 187-201.

Terzaghi, K., 1936, The shear resistance of saturated soils, Pages 54-56 in Proceedings of 1st InternationalConference on Soil Mechanics and FoundationEngineering, Boston.

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