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.
• 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/rc2
• ? rs2S/rc2

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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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? 2?/(t2-t1)

• lnH(t1)/H(t2)/ (t2 t1)

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Underdamped Response Slug Test (cont.)

• T c a ln T
• c -a ln0.79 rs2S(g/L)1/2
• a rc2(g/L)1/2 / (8d)
• d ?/(g/L)1/2
• L g / (?2 ?2)

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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)
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Capture Zone Analysis (unconfined aquifer)

• x -y / tan?Kh12-h22)y/QL
• x0 -QL/?K(h12-h22)
• ymax ? QL/K (h12-h22)

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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 Ficks laws

• Ficks 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 Ficks laws (cont.)

• Ficks 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

• DL?2C/?x2 vx?C/?x ?C/?t
• DL?2C/?x2 dispersion (diffusion
  dispersivity).
• vx?C/?x Advection

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Solute Transport by Advection-Dispersion

• C C0/2erfc(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/(?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.

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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)