our purpose of well studies
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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. - PowerPoint PPT PresentationTRANSCRIPT
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.
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.
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.
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.
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.
Cooper-Bredehoeft-Papadopulos Method (confined aquifer)
• H/H0 = F(,)
• H – head at time t.
• H0 – head at time t = 0.
= T t/rc2
= rs2S/rc
2
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)
= ln[H(t1)/H(t2)]/ (t2 – t1)
= 2/(t2-t1)
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)
x = -y/tan(2Kbiy/Q)
Q - pumping rateK - conductivityb – initial thicknessi – initial h gradient
x0 = -Q/tan(2Kbi)
ymax = Q/(2Kbi)
Confined
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)]
Static fresh and slat water
Ghyben-Herzberg principle
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.
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.
Dissolved Gases
• Oxygen.
• Carbon dioxide.
• Nitrogen.
• Hydrogen sulfide
• Methane.
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.
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.
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
Effective diffusion coefficient
• D* = wD.
D* = effective diffusion coefficient.
w = empirical coefficient.
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
Mechanical Dispersion
• Dispersion is a process that a contaminated fluid dilutes as it mixs with noncontaminated water when passing through a porous medium.
Mechanical Dispersion
• Longitudinal dispersion: the mixing occurs along the pathway of fluid flow
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.
Mechanical Dispersion
• Mechanical dispersion = aLvx
aL = dynamic dispersivity
vx = average linear velocity
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
Advection-dispersion Equation
• DL2C/x2 – vxC/x = C/t
DL2C/x2 – dispersion (diffusion + dispersivity).
vxC/x – Advection
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)
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).
Ground water flow
Continuous source
Ground water flow
Continuous source
Retardation
• Adsorption is a process for a negative (positive) charge to adsorbing a charged cation (ion).
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
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)
C* mass adsorbed per unit weight of soil
C equilibrium concentration of solute remaining in solution
Adsorption isotherm
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.
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)
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).
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.
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)