Field Investigations

Question 1

Scale of aerial photographs

Answer 1

f / H
where:
f = focal length
H = height during acquisition
where both variables are in uniform length units

Question 2

Spontaneous Potential Logging - positive vs negative conditions

Answer 2

SP is based on potential developed between borehole fluid and formation water/surrounding rock material

(+) SP =
- shale and limestone (higher salt mineral content)
- formation water is saline
(-) SP
- sand/sandstone (mostly silicate mineral, little salt mineral content)
- formation water is fresh

Question 3

SP Log standard setup

Answer 3

Left - negative
Right - positive

Question 4

Resistivity Logging - high R vs low R conditions

Answer 4

R is based on the ability of the material to resist flow of electric current. Most closely tied to porosity and salinity of porewater.

High R = limestone and coal (low n), fresh water (low salinity)
Low R = shale, sandstone (high n), saline water (high salinity)

Question 5

Gamma Ray Logging - High counts vs low counts - material ranks

Answer 5

GR is tied to presence of radionuclides, ranked as follows:
Granite/volcanic ash (felsic rock)
Shale (high potassium)
Sandstone
Carbonates
Coal
Gabbro/basalt (mafic rock)
Evaporites

Question 6

Neutron Logging - what does it measure

Answer 6

Measures moisture content in unsaturated soil (small source/short spacing) and porosity in saturated materials (large source/long spacing).

Question 7

Blowout

Answer 7

Uncontrolled flow of gas or fluids from a well

Question 8

Available Drawdown

Answer 8

The amount of drawdown from the static water level that may occur before a well ceases to function

Question 9

Safe Additional Available Drawdown

Answer 9

The difference between the drawdown at the average well pumping rate and the available drawdown, decreased by some safety factor (a percentage of the drawdown set aside for long term water declines or increases in peak drawdown)

Question 10

Specific capacity

Answer 10

SC = Q/s
Where
Q = well pumping rate
s = static drawdown at that pumping rate

Question 11

Zone of contribution

Answer 11

The area that receives recharge water that may may eventually reach a well

Question 12

Zone of influence

Answer 12

The area within the cone of depression of a well

Question 13

Calculated fixed rate model equation

Answer 13

Wellhead protection area radius determination equation that may be used in lieu of models or other methods:

r = sqrt(Q ⋅ t / π ⋅ n ⋅ H)

Q = pumping rate (ft³/yr)
t = travel time (yr)
n_e = effective porosity
H = screened interval

Question 14

Theis well equations for T, S
General form

Answer 14

T = Q ⋅ W(u) / 4 ⋅ π ⋅ s
S = 4 ⋅ T ⋅ t ⋅ u / r²
Q is pumping rate
All parameters are taken from the curve match

Question 15

Theis well equations for T, S
ft²/day units of T

Answer 15

T = 15.3 Q W(u) / s
S = T t u / 360 r²
Where
u = well parameter (unitless) from curve match
W(u) = well function of u (unitless) from curve match
r = distance from observation well to pumping well (feet)
S = storativity (unitless)
T = transmissivity (ft²/day)
Q = pumping rate (gal/min)
t = pumping duration (min)

Question 16

Cooper-Jacob
Distance-Drawdown
When is it valid?
Equations for T, S

Answer 16

Cooper-Jacob requires all Theis assumptions plus, u is <0.05 meaning r is small (obs well is close to pumping well) and t is long (system has come to steady state)
T = 2.303 ⋅ Q / 2 ⋅ π ⋅ ΔS
S = 2.25 ⋅ T ⋅ t / r₀²

Question 17

Cooper-Jacob
Time-Drawdown
Equations for T, S

Answer 17

T = 2.303 ⋅ Q / 4 ⋅ π ⋅ ΔS
S = 2.25 ⋅ T ⋅ t₀ / r²

Question 18

Theis equation for transient radius of influence

Answer 18

R = 1.5 ⋅ sqrt(t ⋅ K ⋅ D / S)
where
t = time since pumping began
K = hydraulic conductivity
D = saturated thickness of aquifer (initial saturated thickness for unconfined)
S = storativity (substitute with S_y for unconfined)

Question 19

Sichardt equation for steady state radius of influence

Answer 19

R = 3000 ⋅ s_w ⋅ sqrt(K)
where
s_w is drawdown at well radius (immediately outside of well)
K = hydraulic conductivity

Question 20

Constant head infiltration test equation for Ksat

Answer 20

Flow rate required to keep water
level steady (stabilized over 1 hour)
_____________________________________
Area of bottom of pit or infiltration pipe

Question 21

Vertical gradient equation for infiltration testing

Answer 21

i_z = (Dwc + Dpond) / 138.62 (Ksat^0.1) ⋅ CFsize

units of feet, feet/day, area in acres

where
Dwc = depth to water table or confining layer, feet
Dpond = 1/4 max depth of the water in the pond, feet
Ksat = saturated K, feet/day
CFsize = 0.73 ⋅ (Pond bottom area in ACRES)^-0.76

Question 22

Infiltration rate equation

Answer 22

f = Ksat ⋅ i_z ⋅ (0.02 ⋅ aspect ratio + 0.98)

Question 23

Hvorslev slug test equation
Where does it apply?

Answer 23

Applies in unconfined aquifers, partially/fully penetrating. Can also be used in unconfined aquifers.
Plot H/H₀ on log y-axis vs time on standard x-axis
K = r_w² ⋅ ln(L_s/r_s) / 2 ⋅ L_s ⋅ t₃₇
where
r_w = casing radius
r_s = screen radius
L_s = screen length
t₃₇ = time elapsed from slug insert/removal at which normalized head = 0.37

Question 24

Maximum pumping well capture width (Ymax) and pumping well capture width at well (Ywell)

Answer 24

Ymax = Q/2Ti
Ywell = Q/4Ti

Question 25

Downgradient capture width (x₀)

Answer 25

x₀ = Q/2πTi

Question 26

1-D advection-dispersion equation
for pulse introduction of a mass of contaminant at x = 0, t = 0
Also, what is the peak height (max concentration within the plume)
What is the plume width?

Answer 26

C(x,t) = M / sqrt(4πDt) ⋅ e^[-(x-vt)²/4Dt]

where
D = mechanical dispersion coefficient
x = distance from pulse input
t = time elapsed from pulse input
v = advective velocity of GW (v = Ki/n_e

Peak height = M / sqrt(4πDt)
Plume width ≈ 4 ⋅ sqrt(2Dt)

Question 27

Retardation coefficient (R)
How is it applied in estimate of transport times and concentrations

Answer 27

R = 1 + K_d ⋅ (ρ_b / n)
where
K_d = distribution coefficient (L³/M)
ρ_b = bulk density (M/L³)
n = porosity
Applied by dividing dispersion coefficients and seepage velocities by R

Question 28

Longitudinal dispersion coefficient estimation

Answer 28

D = 0.83(log₁₀(L))^2.414 ⋅ v
Where
D = longitudinal dispersion coefficient
L = Distance plume has traveled from origin (v ⋅ time elapsed since release)
v = linear velocity (seepage velocity) in aquifer

Question 29

1-D advection-dispersion equation
for continuous introduction of contaminant at x = 0, t = 0
Also, what is the peak height (max concentration within the plume)
What is the plume width?

Answer 29

C = C₀/2 ⋅ (erfc[x-vt/2sqrt(Dt)] + e^((vx/D) ⋅ erfc[x+vt/2sqrt(Dt)])
Where
C₀ = concentration of contaminant at source
C = concentration at x, t
v = seepage velocity
D = dispersion coefficient = dispersivity ⋅ v
erfc[x] = the error function compliment of the value within the brackets. For 0-1, it is about equal to 1-the value within the brackets

Question 30

Estimate flow rate from water flowing out of a horizontal pipe

Answer 30

Q = 3.61 ⋅ A ⋅ X / sqrt(Y)
Where
Q = flow rate in gpm
A = cross-sectional area of pipe in square inches
X = lateral distance at which drop Y occurs in inches
Y = drop in inches
Pipe must be flowing full