315 C HAPTER 13 Groundwater Once polluted, groundwater is difficult, if not impossible, to clean up, since it contains few decom- posing microbes and is not exposed to sunlight, strong water flow, or any of the other natural purification processes that cleanse surface water. Eugene P. Odum; Ecology and Our Endangered Life Support Systems 13.1 GROUNDWATER AND AQUIFERS Part of the precipitation that falls on land may infiltrate the surface, percolate downward through the soil under the force of gravity, and become what is known as groundwater . Like surface water, groundwater is an extremely important part of the hydrologic cycle. Almost half of the people in the U.S. obtain their public water supply from groundwater. Overall, the U.S. has more groundwater than surface water, including the water in the Great Lakes. Unfortunately, pumping it to the surface for use is sometimes uneconomical and, in recent years, the pollution of groundwater supplies from improper disposal has become a significant problem (Spellman, 1996). Groundwater is found in saturated layers called aquifers that lie under the Earth’s surface. Aquifers are made up of a combination of solid material such as rock and gravel, and open spaces called pores . Regardless of the type of aquifer, the groundwater in the aquifer is always in motion. Aquifers that lie just under the Earth’s surface are in the zone of saturation and are called unconfined aquifers (see Figure 13.1). The top of the zone of saturation is the water table. An unconfined aquifer is only contained on the bottom and is dependent on local precipitation for recharge. This type of aquifer is often referred to as a water table aquifer . The actual amount of water in an aquifer is dependent upon the amount of space available between the various grains of material that make up the aquifer. The amount of space available is called porosity . The ease of movement through an aquifer depends upon how well the pores are connected. The ability of an aquifer to pass water is called permeability . Types of aquifers include: • Unconfined aquifers: a primary source of shallow well water (see Figure 13.1). Because these wells are shallow, they are subject to local contamination from hazardous and toxic materials that provide increased levels of nitrates and microorganisms, including fuel and oil; agricultural runoff containing nitrates and microorganisms; and septic tanks. (Note that this type of well may be classified as groundwater under the direct influence of surface water [GUDISW] and therefore require treatment for control of microorganisms [disinfection]). • Confined aquifers: aquifers sandwiched between two impermeable layers that block the flow of water. The water in a confined aquifer is under hydrostatic pressure. It does not have a free water table (see Figure 13.2). L1681_book.fm Page 315 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC 316 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK Confined aquifers are artesian aquifers. A well drilled in an artesian aquifer is called an artesian well and commonly yields large quantities of high-quality water. A well in a confined aquifer is normally referred to as a deep well and is not generally affected by local hydrological events. A confined aquifer is recharged by rain or snow in the mountains, where it is close to the surface of Figure 13.1 Unconfined aquifer. (From Spellman, F.R., 1996, Stream Ecology & Self-Purification . Lancaster, PA: Technomic Publishing Company.) Figure 13.2 Confined aquifer. (From Spellman, F.R., 1996, Stream Ecology & Self-Purification . Lancaster, PA: Technomic Publishing Company.) Ground surface Water table well Water table Rain Infiltration Percolation Unconfined aquifer Recharge area Rain Ground Artesian well Confining layer Confined aquifer Clay Flow Clay Bedrock L1681_book.fm Page 316 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC GROUNDWATER 317 the Earth. Because the recharge area is some distance from areas of possible contamination of the confined aquifer, the possibility of contamination is usually very low. However, once contaminated, such aquifers may take centuries to recover. When groundwater exits the Earth’s crust, it is called a spring . The water in a spring can originate from a water table aquifer or from a confined aquifer. Only water from a confined aquifer spring is considered desirable for a public water system. 13.1.1 Groundwater Quality Generally, groundwater possesses high chemical, bacteriological, and physical quality. When pumped from an aquifer composed of a mixture of sand and gravel, groundwater is often used without filtration (if not directly influenced by surface water). It can also be used without disinfection if it has a low coliform count. However (as pointed out earlier), groundwater can become contam- inated. For example , when septic systems fail; saltwater intrudes; improper disposal of wastes occurs;, chemicals are improperly stock-piled; underground storage tanks leak; hazardous materials are spilled; fertilizers and pesticides are misapplied; and mines are improperly abandoned, ground- water can become contaminated. When groundwater is removed from its underground water-bearing stratum via a well, water flows toward the center of the well. In a water table aquifer, this movement causes the water table to sag toward the well. This sag is called the cone of depression . The shape and size of the cone is dependent on the relationship between the pumping rate and the rate at which water can move toward the well. If the movement rate is high, the cone is shallow and its growth stable. The area included in the cone of depression is called the zone of influence ; any contamination in this zone will be drawn into the well. 13.1.2 GUDISW Groundwater under the direct influence of surface water (GUDISW) is not classified as a ground- water supply. When a supply is designated as GUDISW, the state’s surface water rules apply to the source rather than the groundwater rules. The Surface Water Treatment Rule of the Safe Drinking Water Act requires each site to determine which groundwater supplies are influenced by surface water (when surface water can infiltrate a groundwater supply and could contaminate it with Giardia , viruses, turbidity, or organic material from the surface water source). To determine whether a groundwater supply is under the direct influence of surface water, USEPA has developed proce- dures that focus on significant and relatively rapid shifts in water quality characteristics, including turbidity, temperature, and pH. When these shifts can be closely correlated with rainfall or other surface water conditions or when certain indicator organisms associated with surface water are found, the source is said to be under the direct influence of surface water. 13.2 AQUIFER PARAMETERS Certain aquifer parameters are relevant to determining the available volume of water and the ease of its withdrawal. We identify and define these relevant parameters in this section. 13.2.1 Aquifer Porosity Aquifer porosity is defined as the ratio of the volume of voids (open spaces) in the soil to the total volume. Simply stated, porosity is the volume of open space and is often determined using the equation: L1681_book.fm Page 317 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC 318 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK (13.1) Two basic types of porosity are common: primary , formed at the time the rock was deposited, and secondary , formed later (by dissolution of carbonate in caverns). Well-sorted materials tend to have higher porosities than poorly sorted ones. Fine-grained sediments tend to have higher porosities than coarse-grained sediments, although they are often poorly connected. Some typical values of porosity are clay, 55%; fine sand, 45%; sand and gravel, 20%; sandstone, 15%; and limestone, 15%. The interconnected or effective porosity ( φ e ) is the most important in hydrology, and ≤φ . 13.2.2 Specific Yield (Storage Coefficient) Specific yield is the percentage of water that is free to drain from the aquifer under the influence of gravity. It is not equal to porosity because the molecular and surface tension forces in the pore spaces keep some of the water in the voids. Specific yield reflects the amount of water available for development (Davis and Cornwell, 1991). Specific yield and storage coefficient may be used interchangeably for unconfined aquifers. 13.2.3 Permeability ( K ) Permeability describes the measure of an aquifer’s ability to transmit water under a sloping piezometric surface. It is defined as the discharge that occurs through a unit cross-section of aquifer. 13.2.4 Transmissivity ( T ) Transmissivity describes the capacity of an aquifer to transmit water. It is the product of hydraulic conductivity (permeability) and the aquifer’s saturated thickness: (13.2) where T = transmissivity of an aquifer, gallons per day per foot or cubic meters per day-meter K = permeability, gallons per day per square foot (per day-square meter) b = thickness of aquifer, feet or meters A rough estimation of T is found by multiplying specific capacity by 2000 (USEPA, 1994). Example 13.1 Problem : If an aquifer’s thickness is 60 ft, estimate the permeability of the aquifer with transmissibility of 30,000 gpm/ft. Solution : Rearranging Equation 13.2: ϕ = V V void total TKb= KT/b (30,000 gpm/ft)/60 ft== = 500 gpm/ft 2 L1681_book.fm Page 318 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC GROUNDWATER 319 13.2.5 Hydraulic Gradient and Head The height of the potentiometric surface at any point in an aquifer is the hydraulic gradient. Stated differently, the hydraulic gradient is the slope of the piezometric surface. The difference in elevation from one point to another along the hydraulic gradient is a measure of pressure. This elevation difference is called pressure head . We usually express the amount of mechanical energy that groundwater contains in terms of the hydraulic head ( h ), the total mechanical energy per unit weight. The hydraulic head is conveniently measured as the elevation to which water will rise in an open pipe, relative to some reference level. Therefore, the hydraulic head has units of length — for example, the elevation to which water will rise. Two main components contribute to the mechanical energy or the hydraulic head of ground- water: potential energy due to gravity and pressure exerted on the water. Kinetic energy, a third energy, is caused by movement of water and is very small compared to the other two energies because groundwater flows very slowly and the energy can therefore be neglected. In terms of hydraulic head, the potential energy is expressed as the elevation head ( z ) or simply the elevation of the point of interest relative to some reference level. The energy of fluid pressure is expressed as the pressure head ( h p ). The pressure head is equivalent to the height of the water column overlying the point of interest. The total hydraulic head is then given by: (13.3) According to Baron (2003), groundwater will move from areas of high mechanical energy to areas with low mechanical energy. The hydraulic gradient of a flow system of interest is defined as the difference in hydraulic head between two points of interest ( dh ) and the flow distance between these two points ( dl ) or, in mathematical terms: (13.4) 13.2.6 Flow Lines and Flow Nets A flow line is an imaginary line that follows the path that a parcel of groundwater would follow as it flowed through an aquifer. These lines are useful tools for visualizing the flow of groundwater. Flow lines can be constructed from equipotential lines or lines of equal hydraulic head. The combination of equipotential lines and flow lines results in a flow net — basically, a graphical solution of the two-dimensional Laplace equation (Fetter, 1994). 13.3 GROUNDWATER FLOW Groundwater flow for a steady-state condition in which the water table or piezometric head does not change within a specified time is expressed by the following equations (Gupta, 1997): (13.5) where pore area of flow, A v = nA . Because Q = Av , combining the two gives us Darcy’s law: (13.6) hzh p =+ gradient h dh/dl= Pore velocity or advection, v K(h h ) 12 = − nnL Rate of groundwater flow, Q K(h h ) L 12 = − A L1681_book.fm Page 319 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC 320 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK where Q = rate of groundwater flow v = pore velocity or advection K = hydraulic conductivity A = aquifer cross-section area through which flow takes place h 1 = water head at upstream end h 2 = water head at downstream end L = distance between h 1 and h 2 n = porosity Note : The term ( h 1 – h 2 )/ L is the hydraulic gradient. Example 13.2 Problem : An irrigation ditch runs parallel to a pond; they are 2200 ft apart. A pervious formation of 40- ft average thickness connects them. Hydraulic conductivity and porosity of the pervious formation are 12 ft/day and 0.55, respectively. The water level in the ditch is at an elevation of 120 ft and 110 ft in the pond. Determine the rate of seepage from the channel to the pond. Solution : For each 1 ft width: From Equation 13.6: From Equation 13.5: 13.4 GENERAL EQUATIONS OF GROUNDWATER FLOW The combination of Darcy’s law and a statement of mass conservation results in general equations describing the flow of groundwater through a porous medium. These general equations are partial differential equations in which the spatial coordinates in all three dimensions ( x , y , and z ) and the time are all independent variables. To derive the general equations, Darcy’s law and the law of mass conservation are applied to a small volume of aquifer, the control volume . The law of mass conservation is basically an account Hydraulic gradient, I hh L 12 = − = −120 110 220 00 0 0045= . A14040 ft 2 =× = Q(12 ft/day)(0.0045)(40 ft ) 2.16 ft / 23 ==dday/ft width Seepage velocity, v K(h h nL 12 = − = )()(.12 0 00045 055 0 098 ) . .= ft/day L1681_book.fm Page 320 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC GROUNDWATER 321 of all the water that goes into and out of the control volume. That is, all the water that goes into the control volume must come out, or a change must occur in water storage in the control volume. Applying these two laws to a confined aquifer results in Laplace’s equation, a famous partial differential equation that can also be used to describe many other physical phenomena (for example, the flow of heat through a solid) (Baron, 2003): Applying Darcy’s law and the law of mass conservation to two-dimensional flow in an uncon- fined aquifer results in the Boussinesq equation: where S y is the specific yield of the aquifer. If the drawdown in the aquifer is very small compared with the saturated thickness, the variable thickness, h , can be replaced with an average thickness that is assumed to be constant over the aquifer. The Boussinesq equation can then be simplified to: Describing groundwater flow in confined and unconfined aquifers by using these general partial differential equations is difficult to solve directly. However, these differential equations can be simplified to algebraic equations for the solution of simple cases (for example, one-dimensional flow in a homogenous porous medium). Another approach is to use a flow net (described earlier) to solve Laplace’s equation graphically for relatively simple cases. More complex cases, however, must be solved mathematically, most commonly with computerized groundwater modeling pro- grams. The most popular of these programs is MODFLOW-2000, published by the United States Geological Society (USGS). 13.4.1 Steady Flow in a Confined Aquifer If steady movement of groundwater occurs in a confined aquifer and the hydraulic heads do not change over time, we can use another derivation of Darcy’s law directly to determine how much water is flowing through a unit width of aquifer, using the following equation: (13.7) where q ′ = flow per unit width ( L 2 / T ) K = hydraulic conductivity ( L / T ) b = aquifer thickness ( L ) dh / dl = hydraulic gradient (dimensionless) 13.4.2 Steady Flow in an Unconfined Aquifer Steady flow of water through an unconfined aquifer can be described by Dupuit’s equation: dh/dx dh/dy d /dz 0 222222 ++= d/dx (h dh/ds) d/dx (h dh/dy) S /K dh/d y +=tt dh/dx dh/dy S /(Kb) dh/dt 22 22 y += ′ =q–Kbdh/dl L1681_book.fm Page 321 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC 322 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK (13.8) where h 1 and h 2 = the water level at two points of interest L = the distance between these two points Based on Dupuit’s assumptions, this equation states that the hydraulic gradient is equal to the slope of the water table; the streamlines are horizontal; and equipotentials are vertical. This equation is useful, particularly in field evaluations of the hydraulic characteristics of aquifer materials. REFERENCES Baron, D. (2003). Water: California’s Precious Resource. Accessed at http://www.cs.Csubak.edu/Geology/Fac- ulty/Baron/SuppGWNotes-2.htm. Davis, M.L. and Cornwell, D.A. (1985). Introduction to Environmental Engineering , 2nd ed. New York: McGraw-Hill, Inc. Fetter, C.W. (1994). Applied Hydrology , 3rd ed. New York: Prentice Hall. Gupta, R.S. (1997). Environmental Engineering and Science: An Introduction . Rockville, MD: Government Institutes. Odum, E.P. (1997). Ecology and Our Endangered Life-Support Systems. New York: Sinauer Associates. Spellman, F.R. (1996). Stream Ecology & Self-Purification . Lancaster, PA: Technomic Publishing Company. USEPA. (1994). Handbook: Ground Water and Wellhead Protection , EPA/625/R-94/001. Washington, D.C.: United States Environmental Protection Agency. ′ = −q–K((h h )/L) 1 2 1 2 2 2 L1681_book.fm Page 322 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC . free water table (see Figure 13. 2). L1681_book.fm Page 315 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC 316 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK Confined aquifers are. Page 317 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC 318 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK (13. 1) Two basic types of porosity are common: primary , formed at. LLC 320 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK where Q = rate of groundwater flow v = pore velocity or advection K = hydraulic conductivity A = aquifer cross-section