Our purpose of well studies

1. 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.

2. 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.

4. 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.

5. 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.

9. 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.

10. 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

12. 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)

13.  = 2/(t2-t1) • = ln[H(t1)/H(t2)]/ (t2 – t1)

14. 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)

15. Confined x = -y/tan(2Kbiy/Q) Q - pumping rate K - conductivity b – initial thickness i – initial h gradient x0 = -Q/tan(2Kbi) ymax =  Q/(2Kbi)

16. Capture Zone Analysis (unconfined aquifer) • x = -y / tan[K[h12-h22)y/QL] • x0 = -QL/[K(h12-h22)] • ymax =  QL/[K (h12-h22)]

17. Static fresh and slat water Ghyben-Herzberg principle

19. Total Dissolved Solids (TDS) • Total dissolved solids (TDS) is the total amount of solids, in milligrams per liter, that remain when a water sample is evaporated to dryness.

21. Solid Constituents • Major constituents: Calcium, magnesium, sodium, and potassium (cations); Chloride, sulfate, carbonate, and bicarbonate (anions). • Minor constituents: iron, manganese, fluoride, nitrate, strontium, and Boron. • Trace elements: arsenic, lead, cadmium, and Chromium.

22. Dissolved Gases • Oxygen. • Carbon dioxide. • Nitrogen. • Hydrogen sulfide • Methane.

23. Mass transport of solutes • Diffusion – both ionic and molecular species dissolved in water move from area of higher concentration (chemical activity) to areas of lower concentration. • Advection – moving water carries it dissolved solutes.

24. Diffusion – Fick’s laws • Fick’s first law F = -D dC/dx F = mass flux of solute per unit area per unit time. D = diffusion coefficient (area/time) C = solute concentration (mass/volume) dC/dx = concentration gradient (mass/volume/distance). • D ranges from 1 x 10-9 to 2 x 10-9 m2/s, for the major cations and anions.

25. Diffusion – Fick’s laws (cont.) • Fick’s second law C/t = D 2C/x2 D = diffusion coefficient (area/time) C = solute concentration (mass/volume) t = time

26. Effective diffusion coefficient • D* = wD. D* = effective diffusion coefficient. w = empirical coefficient.

27. Advection • Advecting contaminants travel at the same rate as the average linear velocity of ground water vx= -(K/ne) dh/dl vx= average linear velocity K = hydraulic conductivity ne = effective porosity dh/dl = hydraulic gradient

28. Mechanical Dispersion • Dispersion is a process that a contaminated fluid dilutes as it mixs with noncontaminated water when passing through a porous medium.

29. Mechanical Dispersion • Longitudinal dispersion: the mixing occurs along the pathway of fluid flow

30. Mechanical Dispersion • Longitudinal dispersion: if the mixing occurs along the pathway of fluid flow - it moves faster through the center of the pore; - some of the fluid will travel in longer pathways; - fluid travels faster through larger pore. • Transverse or lateral dispersion: if the mixing occurs normal to the pathway of fluid flow. - flow paths can split and branch out to the side.

32. Mechanical Dispersion • Mechanical dispersion = aLvx aL = dynamic dispersivity vx = average linear velocity

33. Hydrodynamic Dispersion • Hydrodynamic dispersion: DL = D* + aLvx DL = longitudinal coefficient of hydrodynamic dispersion D* = effective molecular diffusion coefficient aL = dynamic dispersivity vx = average linear ground-water velocity

35. Advection-dispersion Equation • DL2C/x2 – vxC/x = C/t DL2C/x2 – dispersion (diffusion + dispersivity). vxC/x – Advection

36. Solute Transport by Advection-Dispersion • C = C0/2{erfc[(L-vxt)/2(DLt)1/2] + exp(vxL/DL)erfc[(L-vxt)/2(DLt)1/2] } C = solute concentration (M/L3, mg/L) C0 = initial concentration (M/L3, mg/L) L = flow path length (L; ft/m) vx = average ground velocity (L/T) t = time since release of the solute (T) DL = longitudinal dispersion coefficient (L2/T)

40. Apparent longitudinal dynamic dispersivity • aL = 0.83(log L)2.414 • aL = apparent longitudinal dynamic dispersivity (L; ft/m) • L = length of the flow path (L; ft or m).

41. Ground water flow Continuous source

42. Ground water flow Continuous source

43. Retardation • Adsorption is a process for a negative (positive) charge to adsorbing a charged cation (ion).

44. Retardation – adsorption isotherm • A graphic plot of C as a function of C* • C = mass of solute adsorbed per bulk unit dry mass of soil C* = equilibrium solute concentration

45. Retardation - Freundlich equation • log C* = j log C + log Kf or C* = KfCj C = mass of solute adsorbed per bulk unit dry mass of soil C* = equilibrium solute concentration Kf, j = coefficients • If C vs C* is a straight line: Kd = dC*/dC (distribution coefficient)

46. C* mass adsorbed per unit weight of soil C equilibrium concentration of solute remaining in solution Adsorption isotherm

47. Langmuir Adsorption Isotherm • If C/C* vs. C is a straight line: C/C* = 1/(12) + C/2 C = equilibrium concentration of the ion in contact with the soil (mg/L) C* = amount of the ion adsorbed perl unit weight of soil (mg/g) 1 = an adsorption constant related to the binding energy 2 = an adsorption maximum for the soil.

49. Retardation Factor • Retardation factor = 1 + (b/)(Kd) b = dry bulk mass density of the soil (M/L3; gm/cm3)  = volumetric moisture content of the soil (dimensionless). Kd = distribution coefficient for solute with the soil (L3/M; mL/g)

50. Solute Movement with Retardation • vc = vx/[1+ (b/)(Kd)] vc = velocity of the solute front. In one-dimensional column the solute concentration is one-half of the original value (L/T; ft/day or m/day). vx = average linear velocity (L/T; ft/day or m/day).