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  (h 0 -h)G(u) G(u) = W(u) - completely confined. W(u,r/B) – leaky, confined, no storage. H(u,  ) – leaky, confined, with storage. W(u A,u B,  ) - 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  (h 0 -h)G(u) G(u) = W(u) - completely confined. W(u,r/B) – leaky, confined, no storage. H(u,  ) – leaky, confined, with storage. W(u A,u B,  ) - 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/H 0 = F( ,  ) H – head at time t. H 0 – head at time t = 0.  = T t/r c 2  = r s 2 S/r c 2

Underdamped Response Slug Test Van der Kamp Method – confined aquifer and well fully penetrating. H(t) = H 0 e -  t cos  t H(t) - hydraulic head (L) at time t (T) H 0 - the instantaneous change in head (L)  - damping constant (T -1 )  - an angular frequency (T -1 )

 = ln[H(t 1 )/H(t 2 )]/ (t 2 – t 1 )  = 2  /(t 2 -t 1 )

Underdamped Response Slug Test (cont.) T = c + a ln T c = -a ln[0.79 r s 2 S(g/L) 1/2 ] a = [r c 2 (g/L) 1/2 ] / (8d) d =  /(g/L) 1/2 L = g / (  2 +  2 )

x = -y/tan(2  Kbiy/Q) Q - pumping rate K - conductivity b – initial thickness i – initial h gradient x 0 = -Q/tan(2  Kbi) y max =  Q/(2Kbi) Confined

Capture Zone Analysis (unconfined aquifer) x = -y / tan[  K[h 1 2 -h 2 2 )y/QL] x 0 = -QL/[  K(h 1 2 -h 2 2 )] y max =  QL/[K (h 1 2 -h 2 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 to 2 x m 2 /s, for the major cations and anions.

Diffusion – Fick’s laws (cont.) Fick’s second law  C/  t = D  2 C/  x 2 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 v x = -(K/n e ) dh/dl v x = average linear velocity K = hydraulic conductivity n e = 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 = a L v x a L = dynamic dispersivity v x = average linear velocity

Hydrodynamic Dispersion Hydrodynamic dispersion: D L = D* + a L v x D L = longitudinal coefficient of hydrodynamic dispersion D* = effective molecular diffusion coefficient a L = dynamic dispersivity v x = average linear ground-water velocity

Advection-dispersion Equation D L  2 C/  x 2 – v x  C/  x =  C/  t D L  2 C/  x 2 – dispersion (diffusion + dispersivity). v x  C/  x – Advection

Solute Transport by Advection- Dispersion C = C 0 /2{erfc[(L-v x t)/2(D L t) 1/2 ] + exp(v x L/D L )erfc[(L-v x t)/2(D L t) 1/2 ] } C = solute concentration (M/L 3, mg/L) C 0 = initial concentration (M/L 3, mg/L) L = flow path length (L; ft/m) v x = average ground velocity (L/T) t = time since release of the solute (T) D L = longitudinal dispersion coefficient (L 2 /T)

Apparent longitudinal dynamic dispersivity a L = 0.83(log L) a L = 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 K f or C* = K f C j C = mass of solute adsorbed per bulk unit dry mass of soil C* = equilibrium solute concentration K f, j = coefficients If C vs C* is a straight line: K d = 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/(  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.

Retardation Factor Retardation factor = 1 + (  b /  )(K d )  b = dry bulk mass density of the soil (M/L 3 ; gm/cm 3 )  = volumetric moisture content of the soil (dimensionless). K d = distribution coefficient for solute with the soil (L 3 /M; mL/g)

Solute Movement with Retardation v c = v x /[1+ (  b /  )(K d )] v c = 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). v x = 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 /  )(K d )  b = dry bulk mass density of the soil (M/L 3 ; gm/cm 3 )  = volumetric moisture content of the soil (dimensionless). K d = distribution coefficient for solute with the soil (L 3 /M; mL/g)