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- 1. Civil Engineering Department Prof. Majed Abu-Zreig Hydraulics and Hydrology – CE 352 Chapter 7Groundwater Hydraulics 12/26/2012 1
- 2. Hydrologic cycle
- 3. Occurrence of Ground Water• Ground water occurs when water recharges aporous subsurface geological formation “calledaquifers” through cracks and pores in soil and rock• it is the water below the water table where all ofthe pore spaces are filled with water.• The area above the water table where the porespaces are only partially filled with water is called thecapillary fringe or unsaturated zone.• Shallow water level is called the water table
- 4. Groundwater Basics - Definitions
- 5. Recharge Natural Artificial• Precipitation • Recharge wells• Melting snow • Water spread over• Infiltration by streams land in pits, furrows, and lakes ditches • Small dams in stream channels to detain and deflect water
- 6. AquifersDefinition: A geological unit which can store andsupply significant quantities of water.Principal aquifers by rock type: Unconsolidated Sandstone Sandstone and Carbonate Semiconsolidated Carbonate-rock Volcanic Other rocks
- 7. Example Layered Aquifer SystemBedient et al., 1999.
- 8. Other Aquifer Features
- 9. Groundwater occurrence in confined and unconfined aquifer
- 10. Potentiometric Surfaces
- 11. Eastern Aquifer
- 12. Growndwater basins in Jordan
- 13. Unconfined Aquifers• GW occurring in aquifers: water fills partly an aquifer: upper surface free to rise and decline: UNCONFINED or water-table aquifer: unsaturated or vadose zone• Near surface material not saturated• Water table: at zero gage pressure: separates saturated and unsaturated zones: free surface rise of water in a well
- 14. Confined Aquifer• Artesian condition• Permeable material overlain by relatively impermeable material• Piezometric or potentiometric surface• Water level in the piezometer is a measure of water pressure in the aquifer
- 15. Groundwater Basics - Definitions• Aquifer Confining Layer or Aquitard – A layer of relatively impermeable material which restricts vertical water movement from an aquifer located above or below. – Typically clay or unfractured bedrock.
- 16. Aquifer Characteristics• Porosity – The ratio of pore/void volume to total volume, i.e. space available for occupation by air or water. – Measured by taking a known volume of material and adding water. – Usually expressed in units of percent. – Typical values for gravel are 25% to 45%.
- 17. Typical Values of PorosityBedient et al., 1999.,
- 18. Aquifer Properties• Porosity: maximum amount of water that a rock can contain when saturated.• Permeability: Ease with which water will flow through a porous material• Specific Yield: Portion of the GW: draining under influence of gravity:• Specific Retention: Portion of the GW: retained as a film on rock surfaces and in very small openings:• Storativity: Portion of the GW: draining when the piezometric head dropped a unit depth
- 19. Storage Terms hh bUnconfined aquifer Confined aquiferSpecific yield = Sy Storativity = S S=V/Ah S = Ss b Ss = specific storage Figures from Hornberger et al. (1998)
- 20. Aquifer Characteristics• Hydraulic Conductivity – Measure of the ease with which water can flow through an aquifer. – Higher conductivity means more water flows through an aquifer at the same hydraulic gradient. – Measured by well draw down or lab test. – Expressed in units of mm/day, ft/day or gpd/ft2. – Typical values for sand/gravel are 2.5 cm/day to 33 m/day m1 (1 to 100 ft/day). – Typical values for clay are 0.3 mm/day (0.001 ft/day). That is why is is an aquifer confining layer.• Transmissivity (T = Kb) is the rate of flow through a vertical strip of aquifer (thickness b) of unit width under a unit hydraulic gradient
- 21. Aquifer Characteristics• Hydraulic gradient – Steepness of the slope of the water table. – Groundwater flows from higher elevations to lower elevations (i.e. downgradient). – Measured by taking the difference in elevation between two wells and dividing by the distance separating them. – Expressed in units of ft/ft or ft/mi. – Typical values for groundwater are .0001 to .01 m/m.
- 22. Aquifer Characteristics• Groundwater Velocity – How fast groundwater is moving. – Calculated by conductivity multiplied by gradient divided by porosity. – Expressed in units of ft/day. – Typical values for gravel or sand are 0.15 to 16 m/day (1 to 50 ft/day).
- 23. The Water Table• Water table: the surface separating the vadose zone from the saturated zone.• Measured using water level in well Fig. 11.1
- 24. Ground-Water Flow• Precipitation• Infiltration• Ground-water recharge• Ground-water flow• Ground-water discharge to – Springs – Streams and – Wells
- 25. Ground-Water Flow• Velocity is proportional to – Permeability Fast (e.g., cm per day) – Slope of the water table• Inversely Proportional to – porosity Slow (e.g., mm per day)
- 26. Natural WaterTable Fluctuations• Infiltration – Recharges ground water – Raises water table – Provides water to springs, streams and wells• Reduction of infiltration causes water table to drop
- 27. Natural WaterTable Fluctuations• Reduction of infiltration causes water table to drop – Wells go dry – Springs go dry – Discharge of rivers drops• Artificial causes – Pavement – Drainage
- 28. Effects ofPumping Wells• Pumping wells – Accelerates flow near well – May reverse ground-water flow – Causes water table drawdown – Forms a cone of depression
- 29. Effects of Pumping Wells Gaining• Pumping wells Stream – Accelerate flow – Reverse flow Water Table Drawdown Low well – Cause water Cone of Dry Spring table drawdown Depression Gaining – Form cones of Stream Low well Low river depression Pumping well
- 30. Effects of Dry wellPumping Wells• Continued water- Losing Stream Dry well table drawdown – May dry up springs and wells – May reverse flow of rivers (and may contaminate Dry well aquifer) Dry river – May dry up rivers and wetlands
- 31. Ground-Water/Surface-Water Interactions• Gaining streams – Humid regions – Wet season• Loosing streams – Humid regions, smaller streams, dry season – Arid regions• Dry stream bed
- 32. Darcy column h h Q A Q K A x x h/L = grad h Q is proportional to grad h q = Q/AFigure taken from Hornberger et al. (1998)
- 33. Darcy’s LawHenry Darcy’s Experiment (Dijon, France 1856)Darcy investigated ground water flow under controlled conditions h1 h2 Q h, Q 1 x , Q AA h Q: Volumetric flow rate [L3/T]Q A: Cross Sectional Area (Perp. to flow) K: The proportionality constant is added to form the following equation: h h : Hydraulic Gradient h Slope = h/x x h h h1 ~ dh/dx Q A Q K A h2 h x x x K units [L/T] x1 x2 x
- 34. Calculating Velocity with Darcy’s Law• Q= Vw/t – Q: volumetric flow rate in m3/sec – Vw: Is the volume of water passing through area “a” during – t: the period of measurement (or unit time).• Q= Vw/t = H∙W∙D/t = a∙v v – a: the area available to flow – D: the distance traveled during t Vw – v : Average linear velocity• In a porous medium: a = A∙n – A: cross sectional area (perpendicular to flow) – n: porous For media of porosity K h• Q = A∙n∙v v n x• v = Q/(n∙A)=q/n
- 35. Darcy’s Law (cont.)• Other useful forms of Darcy’s Law Used for calculating dh Volumetric Flow Rate Q K A Volumes of groundwater dx flowing during period of time Volumetric Flux Q dh Used for calculating A= q K Q given A (a.k.a. Darcy Flux or dx Specific discharge) Ave. Linear Q q K dh Used for calculating Velocity A.n = n = v average velocity of n dx groundwater transport (e.g., contaminant Assumptions: Laminar, saturated flow transport
- 36. True flow paths Linear flow paths assumed in Darcy’s law Average linear velocitySpecific dischargeq = Q/A v = Q/An= q/n n = effective porosity Figure from Hornberger et al. (1998)
- 37. Steady Flow to Wells in Confined Aquifers• Radial flow towered wells• Aquifers are homogeneous (properties are uniform)• Aquifers are isotropic (permeability is independent of flow direction)• Drawdown is the vertical distance measured from the original to the lowered water table due to pumping• Cone of depression the axismmetric drawdown curve forms a conic geometry• Area of influence is the outer limit of the cone of depression• Radius of Influence (ro) for a well is the maximum horizontal extent of the cone of depression when the well is in equilibrium with inflows• Steady state is when the cone of depression does not change with time
- 38. Horizontal and Vertical Head GradientsFreeze and Cherry, 1979.
- 39. Flow to Wells
- 40. Steady Radial Flow to a Well- Confined Cone of Depression Q s = drawdown r h
- 41. Steady Radial Flow to a Well- Confined• In a confined aquifer, the drawdown curve or cone of depression varies with distance from a pumping well.• For horizontal flow, Q at any radius r equals, from Darcy’s law, Q = -2πrbK dh/dr for steady radial flow to a well where Q,b,K are const
- 42. Steady Radial Flow to a Well- Confined• Integrating after separation of variables, with h = hw at r = rw at the well, yields Thiem Eqn Q = 2πKb[(h-hw)/(ln(r/rw ))] Note, h increases indefinitely with increasing r, yet the maximum head is h0.
- 43. Steady Radial Flow to a Well- Confined• Near the well, transmissivity, T, may be estimated by observing heads h1 and h2 at two adjacent observation wells located at r1 and r2, respectively, from the pumping well T = Kb = Q ln(r2 / r1) 2π(h2 - h1)
- 44. Steady Radial Flow to a Well- Unconfined
- 45. Steady Radial Flow to a Well- Unconfined• Using Dupuit’s assumptions and applying Darcy’s law for radial flow in an unconfined, homogeneous, isotropic, and horizontal aquifer yields: Q = -2πKh dh/dr integrating, Q = πK[(h22 - h12)/ln(r2/ r1) solving for K, K = [Q/π(h22 - h12)]ln (r2/ r1) where heads h1 and h2 are observed at adjacent wells located distances r1 and r2 from the pumping well respectively.
- 46. Steady Flow to a Well in a Confined Aquifer Q Ground surface Pre-pumping head Pumping Drawdown curve well dh ObservationQ = Aq = (2prb)K wells dr Confining Layer dh Q h0r = r1 hw dr 2pT b h2 h1 Confined r2 Q aquifer Q r2 h2 = h1 + ln( ) Bedrock 2pT r1 2rw Theim Equation In terms of head (we can write it in terms of drawdown also)
- 47. Steady Flow to a Well in a Confined Aquifer Example - Theim Equation Q • Q = 400 m3/hr Ground surface • b = 40 m. • Two observation wells, Pumping well 1. r1 = 25 m; h1 = 85.3 m 2. r2 = 75 m; h2 = 89.6 m Confining Layer • Find: Transmissivity (T) h0 r1 hw b h 2 h1 Confine r2 Q d Q r aquifer h2 = h1 + ln( 2 ) 2pT r1 Bedrock 2rw Q æ r2 ö 400 m 3 /hr æ 75 m ö T= lnç ÷ = lnç ÷ = 16.3 m /hr 2 2p ( h2 - h1 ) è r1 ø 2p ( 89.6 m - 85.3m) è 25 m ø
- 48. Steady Flow to a Well in a Confined Aquifer Steady Radial Flow in a Confined Aquifer • Head Q ærö h( r ) = h0 + lnç ÷ 2pT è R ø • Drawdown s(r) = h0 - h( r ) Q æ Rö s( r ) = lnç ÷ 2pT è r ø Theim Equation In terms of drawdown (we can write it in terms of head also)
- 49. Steady Flow to a Well in a Confined Aquifer Example - Theim Equation Q • Ground surface 1-m diameter well • Q = 113 m3/hr Drawdown Pumping well • b = 30 m • h0= 40 m Confining Layer • h0 Two observation wells, b h h1 r1 hw 2 1. r1 = 15 m; h1 = 38.2 m Confine r2 Q d 2. r2 = 50 m; h2 = 39.5 m aquifer • Find: Head and Bedrock 2rw drawdown in the well Q æ Rö s( r ) = lnç ÷ 2pT èrø Q æ r2 ö 113m 3 /hr æ 50 m ö T= lnç ÷ = lnç ÷ = 16.66 m /hr 2 2p ( s1 - s2 ) è r1 ø 2p (1.8 m - 0.5 m) è 15 m ø Adapted from Todd and Mays, Groundwater Hydrology
- 50. Steady Flow to a Well in a Confined Aquifer Example - Theim Equation Q Ground surface Drawdown @ well Q r h2 = h1 + ln( 2 ) Confining Layer 2pT r1 h0 r1 hw b h 2 h1 Confine r2 Q d aquifer Bedrock 2rw Q rw 113m 3 /hr 0.5 m hw = h2 + ln( ) = 39.5 m + ln( ) = 34.5 m 2pT r2 2p *16.66 m /hr 50 m 2 sw = h0 - hw = 40 m - 34.5 m = 5.5 m Adapted from Todd and Mays, Groundwater Hydrology
- 51. Steady Flow to Wells in Unconfined Aquifers
- 52. Steady Flow to a Well in an Unconfined Aquifer dh QQ = Aq = (2prh)K Ground surface dr Pre-pumping Water level dh 2 Pumping = prK Water Table well dr Observation wells r ( )= Q d h2 h0 h r1 hw dr pK Unconfined 2 h1 Q r2 aquifer Q æ Röh0 - h 2 = 2 lnç ÷ pK è r ø Bedrock 2rw Q ærö Q rh 2 (r) = h0 2 + lnç ÷ h2 = h1 + ln( 2 ) pK è R ø 2pT r1 Unconfined aquifer Confined aquifer
- 53. Steady Flow to a Well in an Unconfined Aquifer Q ærö 2 (r) = h0 2 + Qh lnç ÷ pK è R ø Ground surface Prepumping Water level Pumping Water Table well2 observation wells: Observation wellsh1 m @ r1 mh2 m @ r2 m h0 r1 hw h 2 h1 Q æ r2 ö Unconfined r2 Q aquifer h2 = h1 + 2 2 lnç ÷ pK è r1 ø Bedrock 2rw æ r2 ö Q K= lnç ÷ ( p h2 - h1 è r1 ø 2 2 )
- 54. Steady Flow to a Well in an Unconfined Aquifer Example – Two Observation Wells in an Unconfined Aquifer Q • Given: Ground surface Prepumping Water level – Q = 300 m3/hr Pumping Water Table well – Unconfined aquifer Observation wells – 2 observation wells, • r1 = 50 m, h = 40 m h0 r1 hw • r2 = 100 m, h = 43 m h 2 h1 Unconfined r2 Q aquifer • Find: K Bedrock 2rw Q æ r2 ö 300 m 3 /hr / 3600 s /hr æ100 m ö K= lnç ÷ = lnç ÷ = 7.3x10 -5 m /sec ( ) [ p h2 - h1 è r1 ø p (43m)2 - (40 m)2 2 2 è 50 m ø ]
- 55. Pump Test in Confined Aquifers Jacob Method
- 56. Cooper-Jacob Method of Solution Cooper and Jacob noted that for small values of r and large values of t, the parameter u = r2S/4Tt becomes very small so that the infinite series can be approx. by: W(u) = – 0.5772 – ln(u) (neglect higher terms) Thus s = (Q/4πT) [– 0.5772 – ln(r2S/4Tt)] Further rearrangement and conversion to decimal logs
- 57. Cooper-Jacob Method of Solution A plot of drawdown s vs. Semi-log plot log of t forms a straight line as seen in adjacent figure. A projection of the line back to s = 0, where t = t0 yields the following relation: 0 = (2.3Q/4πT) log[(2.25Tt0)/ (r2S)]
- 58. Cooper-Jacob Method of Solution
- 59. Cooper-Jacob Method of Solution So, since log(1) = 0, rearrangement yields S = 2.25Tt0 /r2 Replacing s by s, where s is the drawdown difference per unit log cycle of t: T = 2.3Q/4πs The Cooper-Jacob method first solves for T and then for S and is only applicable for small values of u < 0.01
- 60. Cooper-Jacob ExampleFor the data given in the Fig.t0 = 1.6 min and s’ = 0.65 mQ = 0.2 m3/sec and r = 100 mThus:T = 2.3Q/4πs’ = 5.63 x 10-2 m2/sec T = 4864 m2/secFinally, S = 2.25Tt0 /r2 and S = 1.22 x 10-3Indicating a confined aquifer
- 61. Pump Test Analysis – Jacob Method Jacob Approximation Q r 2S • Drawdown, s s ( u) = W ( u) u= 4 pT 4Tt ¥ e -h u2 • Well Function, W(u) W ( u) = ò dh » -0.5772 - ln(u) + u - + u h 2! • Series W (u) » -0.5772 - ln(u) for small u < 0.01 approximation of W(u) Q é æ r 2 S öù s(r,t) » ê-0.5772 - lnç ÷ú 4 pT ê ë è 4Tt øú û • Approximation of s 2.3Q 2.25Tt s(r,t) = log10 ( 2 ) 4 pT r S
- 62. Pump Test Analysis – Jacob Method Jacob Approximation 2.3Q 2.25Tt s= log( 2 ) 4 pT r S 2.3Q 2.25Tt 0= log( 2 0 ) 4 pT r S 2.25Tt 0 1= r 2S 2.25Tt 0 S= r2 t0
- 63. Pump Test Analysis – Jacob Method Jacob Approximation 1 LOG CYCLE æ t2 ö æ10 *t1 ö logç ÷ = logç ÷ =1 è t1 ø è t1 ø s2 s s1 1 LOG CYCLE t1 t2 2.25Tt 0 S= r2 t0
- 64. Pump Test Analysis – Jacob Method Jacob Approximation t0 = 8 min s2 = 5 m s1 = 2.6 m s2 s = 2.4 m s s1 t1 t2 t0 2.25Tt 0 2.25(76.26 m 2 /hr)(8 min*1 hr /60 min) S= 2 = r (1000 m)2 = 2.29x10 -5
- 65. Multiple-Well Systems• For multiple wells with drawdowns that overlap, the principle of superposition may be used for governing flows:• drawdowns at any point in the area of influence of several pumping wells is equal to the sum of drawdowns from each well in a confined aquifer
- 66. Multiple-Well Systems
- 67. Injection-Pumping Pair of WellsPump Inject
- 68. Multiple-Well Systems• The previously mentioned principles also apply for well flow near a boundary• Image wells placed on the other side of the boundary at a distance xw can be used to represent the equivalent hydraulic condition – The use of image wells allows an aquifer of finite extent to be transformed into an infinite aquifer so that closed-form solution methods can be applied
- 69. Multiple-Well Systems •A flow net for a pumping well and a recharging image well -indicates a line of constant head between the two wells
- 70. Three-Wells PumpingTotal Drawdown at A is sum of drawdowns from each well Q2 Q1 A r Q3
- 71. Multiple-Well Systems The steady-state drawdown s at any point (x,y) is given by: (x + xw) + (y - yw)2 2 s’ = (Q/4πT)ln (x - xw)2 + (y - yw)2 where (±xw,yw) are the locations of the recharge and discharge wells. For this case, yw= 0.
- 72. Multiple-Well SystemsThe steady-state drawdown s at any point (x,y) is given bys’ = (Q/4πT)[ ln {(x + xw)2 + y2} – ln {(x – xw)2 + y2} ]where the positive term is for the pumping well and thenegative term is for the injection well. In terms of head,h = (Q/4πT)[ ln {(x – xw)2 + y2} – ln {(x + xw)2 + y2 }] + HWhere H is the background head value before pumping.Note how the signs reverse since s’ = H – h
- 73. 7.5 Aquifer BoundariesThe same principle applies for well flow near a boundary – Example: pumping near a fixed head stream
- 74. well near an impermeable boundary

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