Final Exam

1. Final Exam • May 10, 5 – 7:30 pm, ESS 081

2. Energy Transformation • 1 Caloria of heat = energy necessary to raise the temperature of one gram of pure water from 14.5 – 15.5oC • Latent Heat of vaporization Hv = 597.3 – 0.564T (Cal./g) • Latent Heat of condensation

3. Energy Transformation, Cont. • Latent heat of fusion – Hf – 1 g of ice at 0oC => ~80 cal of heat must be added to melt ice. Resulting water has same temperature. • Sublimation – Water passes directly from a solid state to a vapor state. Energy = Hf + Hv => 677 cal/g at 0oC. • Hv > 6Hf > 5 x amt. to warm water from 0oC -> 100oC

4. Hydrologic Equation • Inflow = outflow +/- Changes in storage • Equation is simple statement of mass conservation

6. Condensation • Condensation occurs when air mass can no longer hold all of its humidity. • Temperature drops => saturation humidity drops. • If absolute humidity remains constant => relative humidity rises. • Relative humidity reaches 100% => condensation => Dew point temperature.

7. Limited soil-moisture storage Cool, moist Cool, moist Warm, dry

8. All infiltrate some water always on the surface All infiltrate Puddles and overland flow

9. Q0

10. Determining ground water recharge from baseflow (1) • Meyboom method (Seasonal recession method): utilizes stream hydrographs from two or more consecutive years. • Assumptions: the catchment area has no dams or other method of streamflow regulation; snowmelt contributes little to the runoff.

11. Determining ground water recharge from baseflow (2) • Rorabaugh method (Recession curve displacement method): utilizes stream hydrograph during one season.

12. Aquifer • Properties: Porosity, specific yield, specific retention. • Potential: Transmissivity, storativity. • Types: confined, unconfined. • Hydraulic conductivity, Physical Laws controlling water transport.

14. d60 d10 d60 d10

15. Sediment Classification • Sediments are classified on basis of size of individual grains • Grain size distribution curve • Uniformity coefficient Cu = d60/d10 • d60 = grain size that is 60% finer by weight. • d10 = grain size that is 10% finer by weight. • Cu = 4 => well sorted; Cu > 6 => poorly sorted.

16. Specific Yield and Retention • Specific yield – Sy: ratio of volume of water that drains from a saturated rock owing to the attraction of gravity to the total volume of the rock. • Specific retention – Sr: ratio of the volume of water in a rock can retain against gravity drainage to the total volume of the rock. • n = Sy + Sr. • Sr increases with decreasing grain size.

17. Darcy’s Law • Q = -KA(dh/dl). • dh/dl = Hydraulic gradient. • dh = change in head between two points separated by small distance dl.

18. Darcy’s Law: Yes Laminar flow (Small R < 10) Flow lines Darcy’s Law: No Flow lines Turbulent flow (Large R)

19. Hydraulic conductivity • K = hydraulic conductivity (L/T). • K is also referred to as the coefficient of permeability. • K = -Q[A(dh/dl)] [ L3/T/[L2(L/L)] = L/T] • V = Q/A = -K(dh/dl) = specific discharge or Darcian velocity.

20. Intrinsic Permeability • Intrinsic permeability Ki = Cd2 (L2). • K = Ki(γ/μ) or K = Ki(ρg/ μ) • Petroleum industry 1 Darcy = unit of intrinsic permeability Ki • 1 darcy = 1 cP x 1 cm3/s / (1 atm/ 1 cm). cP – centipoise - 0.01 dyn s/cm2 atm – atmospheric pressure – 1.0132 x 1016 dyn/cm2 • 1 darcy = 9.87 x 10-9 cm2 ~ 10-8 cm2

21. Aquifer • Aquifer – geologic unit that can store and transmit water at rates fast enough to supply amounts to wells. Usually, intrinsic permeability > 10-2 Darcy. • Confining layer – unit with little or no permeability … < 10-2 Darcy. aquifuge – absolutely impermeable unit. aquitard - a unit can store and transmit water slowly. Also called leaky confining layer. Raritan formation on Long Island. -- all these definitions are in a relative sense.

23. Transmissivity • The amount of water that can be transmitted horizontally through a unit width by the full saturated thickness of the aquifer under a hydraulic gradient of 1. • T = bK • T = transmissivity. • b = saturated thickness. • K = hydraulic conductivity. • Multilayer => T1 + T2 + … + Tn

24. Specific Storage • Specific storage Ss = amount of water per unit volume stored or expelled owing to compressibility of mineral skeleton and pore water per unit change in head (1/L). • Ss = ρwg(α+nβ) • α = compressibiliy of aquifer skeleton. • n = porosity. • β = compressibility of water.

25. Storativity of confined Unit S = b Ss • Ss = specific storage. • b = aquifer thickness. • All water released in confined, saturated aquifer comes from compressibility of mineral skeleton and pore water.

26. Storativity in Unconfined Unit • Changes in saturation associated with changes in storage. • Storage or release depends on specific yield Sy and specific storage Ss. • S = Sy + b Ss

27. Volume of water drained from aquifer • Vw = SAdh • Vw = volume of water drained. • S = storativity (dimensionless). • A = area overlying drained aquifer. • dh = average decline in head.

28. Hydraulic head, h • Hydraulic head is energy per unit weight. • h = v2/2g + z + P/gρ. [L]. • Unit: (L; ft or m). • v ~ 10-6 m/s or 30 m/y for ground water flows. • v2/2g ~ 10-12 m2/s2 / (2 x 9.8 m/s2) ~ 10-13 m. • h = z + P/gρ. [L].

30. Flow lines and flow nets • A flow line is an imaginary line that traces the path that a particle of ground water would flow as it flows through an aquifer. • A flow net is a network of equipotential lines and associated flow lines.

31. Boundary conditions • No-flow boundary – flow line – parallel to the boundary. Equipotential line - intersect at right angle. • Constant-head boundary – flow line – intersect at right angle. Equipotential line - parallel to the boundary. • Water-table boundary – flow line – depends. Equipotential line - depends.

32. Estimate the quantity of water from flow net • q’ = Kph/f. • q’ – total volume discharge per unit width of aquifer (L3/T; ft3/d or m3/d). • K – hydraulic conductivity (L/T; ft/d or m/d). • p – number of flowtubes bounded by adjacent pairs of flow lines. • h – total head loss over the length of flow lines (L; ft or m). • f - number of squares bounded by any two adjacent flow lines and covering the entire length of flow.

36. Water table • Water table = undulating surface at which pressure in fluid in pores = atmospheric pressure. Water table

37. Our purpose of well studies • Compute the decline in the water level, or drawdown, around a pumping well whose hydraulic properties are known. • Determine the hydraulic properties of an aquifer by performing an aquifer test in which a well is pumped at a constant rate and either the stabilized drawdown or the change in drawdown over time is measured.

38. Drawdown • T = Q/ 4(h0-h)G(u) • G(u) = W(u) - completely confined. W(u,r/B) – leaky, confined, no storage. H(u,) – leaky, confined, with storage. W(uA,uB,) - unconfined.

40. Aquifer test • Steady-state conditions. Cone of depression stabilizes. • Nonequilibrium flow conditions. Cone of depression changes. Needs a pumping well and at least one observational well.

41. Aquifer tests • T = Q/ 4(h0-h)G(u) • G(u) = W(u) - completely confined. W(u,r/B) – leaky, confined, no storage. H(u,) – leaky, confined, with storage. W(uA,uB,) - unconfined.

45. Slug test • Overdamped – water level recovers to the initial static level in a smooth manner that is approximately exponential. • Underdamped – water level oscillates about the static water level with the magnitude of oscillation decreasing with time until the oscillations cease.

46. Cooper-Bredehoeft-Papadopulos Method (confined aquifer) • H/H0 = F(,) • H – head at time t. • H0 – head at time t = 0. •  = T t/rc2 •  = rs2S/rc2

48. Underdamped Response Slug Test • Van der Kamp Method – confined aquifer and well fully penetrating. • H(t) = H0 e-t cos t H(t) - hydraulic head (L) at time t (T) H0 - the instantaneous change in head (L)  - damping constant (T-1)  - an angular frequency (T-1)

49.  = 2/(t2-t1) • = ln[H(t1)/H(t2)]/ (t2 – t1)

50. Underdamped Response Slug Test (cont.) • T = c + a ln T c = -a ln[0.79 rs2S(g/L)1/2] a = [rc2(g/L)1/2] / (8d) d = /(g/L)1/2 L = g / (2 + 2)