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)