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.
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 Presentation
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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.
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.
• 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)