ASBOG Hydrogeology 3 — Questions and Answers
Question 1: Which equation is the governing partial differential equation for transient groundwater flow in a confined, homogeneous, isotropic aquifer?
- Laplace equation: ∇²h = 0
- Poisson equation: ∇²h = W/T
- Diffusion equation: ∇²h = (S/T)(∂h/∂t) (Correct answer)
- Richards equation: ∂θ/∂t = ∇·[K(h)∇(h+z)]
Correct answer: Diffusion equation: ∇²h = (S/T)(∂h/∂t)
The diffusion (or heat) equation relates the Laplacian of head to storativity divided by transmissivity times the time derivative of head.
Question 2: What is the primary mechanism for dispersion in a heterogeneous porous medium at the field scale?
- Molecular diffusion along concentration gradients
- Mechanical mixing caused by velocity variations due to heterogeneity (Correct answer)
- Density differences between fresh and saline water
- Osmotic pressure across clay membranes
Correct answer: Mechanical mixing caused by velocity variations due to heterogeneity
Field-scale (macrodispersion) is dominated by spatial variations in hydraulic conductivity that create a range of groundwater velocities.
Question 3: During a slug test analyzed with the Bouwer and Rice method, what parameter is primarily being estimated?
- Storativity of the formation
- Hydraulic conductivity of the formation near the well (Correct answer)
- Dispersivity of the aquifer
- Specific yield of an unconfined aquifer
Correct answer: Hydraulic conductivity of the formation near the well
The Bouwer and Rice method estimates horizontal hydraulic conductivity from the rate of water-level recovery after a slug displacement.
Question 4: Which of the following is NOT typically an assumption of the Theis solution for pumping test analysis?
- The aquifer is homogeneous and isotropic
- The well is fully penetrating
- The aquifer has a free (unconfined) water table that drains under gravity (Correct answer)
- The aquifer is of infinite lateral extent
Correct answer: The aquifer has a free (unconfined) water table that drains under gravity
The Theis solution assumes a confined aquifer; drainage from the water table (specific yield) violates the elastic storage assumption.
Question 5: The concept of 'effective porosity' is most important for calculating:
- Total water storage in an aquifer
- Average linear groundwater velocity (Correct answer)
- Capillary rise in unsaturated soils
- Specific retention of fine-grained sediments
Correct answer: Average linear groundwater velocity
Average linear velocity equals hydraulic conductivity times gradient divided by effective (kinematic) porosity, so only interconnected pores that transmit flow matter.
Question 6: A potentiometric surface map shows closely spaced contours in one area and widely spaced contours in another. What does this pattern indicate?
- Higher transmissivity where contours are closely spaced
- Higher hydraulic gradient and slower groundwater flow where contours are closely spaced
- Higher transmissivity where contours are widely spaced (Correct answer)
- Lower hydraulic gradient where contours are closely spaced
Correct answer: Higher transmissivity where contours are widely spaced
Wide contour spacing means a low gradient; to maintain the same flux, transmissivity must be higher in that area (by Darcy's law).
Question 7: Which of the following best describes 'specific retention'?
- Water drained from an unconfined aquifer by gravity per unit volume
- Water held in an aquifer against gravity after drainage (Correct answer)
- Water released from elastic storage per unit decline in head
- Total volumetric porosity of a rock sample
Correct answer: Water held in an aquifer against gravity after drainage
Specific retention is the volume of water retained by capillary and adhesive forces after gravity drainage, equal to total porosity minus specific yield.
ASBOG Hydrogeology 3
Which equation is the governing partial differential equation for transient groundwater flow in a confined, homogeneous, isotropic aquifer?