our purpose of well studies compute the decline in the water level, or drawdown, around a pumping...
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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.
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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.
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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.
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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.
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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.
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Cooper-Bredehoeft-Papadopulos Method (confined aquifer)
• H/H0 = F(,)• H – head at time t.• H0 – head at time t = 0. = T t/rc
2
= rs2S/rc
2
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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)
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= ln[H(t1)/H(t2)]/ (t2 – t1)
= 2/(t2-t1)
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Underdamped Response Slug Test (cont.)
• T = c + a ln T c = -a ln[0.79 rs
2S(g/L)1/2]
a = [rc2(g/L)1/2] / (8d)
d = /(g/L)1/2
L = g / (2 + 2)
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x = -y/tan(2Kbiy/Q)
Q - pumping rateK - conductivityb – initial thicknessi – initial h gradient
x0 = -Q/tan(2Kbi)
ymax = Q/(2Kbi)
Confined
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Capture Zone Analysis (unconfined aquifer)
• x = -y / tan[K[h12-h2
2)y/QL]
• x0 = -QL/[K(h12-h2
2)]
• ymax = QL/[K (h12-h2
2)]
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Static fresh and slat water
Ghyben-Herzberg principle
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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.
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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.
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Dissolved Gases
• Oxygen.• Carbon dioxide.• Nitrogen.• Hydrogen sulfide• Methane.
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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.
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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.
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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
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Effective diffusion coefficient
• D* = wD. D* = effective diffusion coefficient. w = empirical coefficient.
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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
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Mechanical Dispersion
• Dispersion is a process that a contaminated fluid dilutes as it mixs with noncontaminated water when passing through a porous medium.
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Mechanical Dispersion
• Longitudinal dispersion: the mixing occurs along the pathway of fluid flow
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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.
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Mechanical Dispersion
• Mechanical dispersion = aLvx
aL = dynamic dispersivity
vx = average linear velocity
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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
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Advection-dispersion Equation
• DL2C/x2 – vxC/x = C/t
DL2C/x2 – dispersion (diffusion + dispersivity).
vxC/x – Advection
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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)
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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).
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Ground water flow
Continuous source
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Ground water flow
Continuous source
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Retardation
• Adsorption is a process for a negative (positive) charge to adsorbing a charged cation (ion).
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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
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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)
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C* mass adsorbed per unit weight of soil
C equilibrium concentration of solute remaining in solution
Adsorption isotherm
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Langmuir Adsorption Isotherm
• If C/C* vs. C is a straight line: C/C* = 1/(12) + 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.
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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)
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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).
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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.
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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)