Chapter 9: Problems

  1. A chemical analysis of groundwater yields the following results (mg/ℓ):
    K+ = 3, Na+ = 110, Ca2+ = 80, Mg2+ = 55, \ce{HCO^-3} = 420, Cl– = 220, SO42– = 35, N = 15, Fe(total) = 0.8, Mn(total) = 0.2, F– = 0.6, As = 0.03, Pb = 0.08, B = 0.9. Comment on the suitability of this water for H following uses:

    1. Municipal water supply.
    2. Irrigation of vegetable crops.
    3. Livestock.
    4. Brewing of beer.
  1. Would water with the composition indicated in Problem 1 normally be softener for household use? How would the process of water softening be expected to alter the composition?
  1. Using a cylindrical column (10 cm in diameter and 30 cm long) of relatively homogeneous sand, an experiment with a step-function input of a nonreactive tracer is conducted (see Figure 9.1). The porosity of the sand is 35%, the steady-state flow rate is 1 ℓ/h, and the hydraulic gradient is 0.1. The C/C0 = 0.5 point on the breakthrough curve arrived 0.8 h after the tracer initially entered the column. The C/C0 = 0.25 point arrived at 0.7 h and the C/C0 = 0.75 point at 0.9 h. Estimate the dispersivity of the sand.
  1. A contaminant zone is migrating through an aquifer composed of medium-grained sand. The average hydraulic gradient is 0.01. A representative value of the hydraulic conductivity of the sand is 1 × 10-5 m/s. Is the movement of nonreactive contaminants influenced primarily by advection and mechanical dispersion or by molecular diffusion? Explain.
  1. A sanitary landfill is located on a deposit of dense clay that is 5 m thick overlying an aquifer that provides drinking water to a small town. A zone of leachate-contaminated groundwater has accumulated at the base of the landfill on the clay surface. Observations in the aquifer indicate a steady piezometric level of 250.5 m above mean sea level. The surface of the water table in the landfill is at about 251.3 m. The hydraulic conductivity of the clay is approximately 2 × 10-11 m/s, and the porosity is 19%. Estimate how long it will take for nonreactive contaminants to move through the clay into the aquifer. Express your answer as a range of values that you consider to be reasonable in light of the available data.
  1. As a result of the rupture of a storage tank, 10 m3 of liquid waste containing 100 kg of dissolved arsenic rapidly infiltrated into a shallow, unconfined, sandy aquifer in which the flow is horizontal. The average groundwater velocity in the aquifer is 0.5 m/day, the dispersivity is 0.1 m, and the coefficient of molecular diffusion is 2 × 10–10 m2/s. As the contaminated zone moves through the aquifer, the arsenic does not undergo significant adsorption or precipitation. Estimate the maximum arsenic concentration after the contaminant cloud has moved a distance of 500 m. What will be the approximate dimensions of the cloud? Assume that the leakage from the storage tank can be approximated as a point source and that the aquifer can be treated as a homogeneous medium with uniform flow.
  1. High-level radioactive waste is buried in a cavern in unfractured shale at a depth of 1000 m below ground surface. The burial zone is separated from the nearest overlying aquifer by a vertical thickness of 100 m of shale. The shale has a hydraulic conductivity of the order of 10–12 m/s and vertical hydraulic gradient of about 10-2 directed upward. In the shale, nonreactive radionuclides have effective diffusion coefficients in the order of 10–10 m2/s. It is expected that the wastes will become wet at some time during the next 1000 years and will then move slowly out into the shale. Is it reasonable to expect that radionuclides will remain entirely within the shale during the next 100,000 years? Ignore the potential effects of faulting, glaciation, and so on, as a cause of radionuclide transfer through the shale. Consider only the influence of How, mechanical dispersion, and molecular diffusion.
  1. Field observations in a granitic area indicate bulk hydraulic conductivities on the order of 10–6 cm/s. The granite has a cubic array of joints with a representative spacing of 10 cm between joint planes. Estimate the average groundwater velocity for a zone in which the flow is horizontal and the hydraulic gradient is 10–2.
  1. In laboratory experiments using a pesticide and samples from a sandy aquifer, it is observed that when water with the pesticide is equilibrated at various concentrations with the sand samples, the partitioning of the pesticide between the liquid and solid phases is as follows: test 1, 100 μg/g adsorbed at 10 mg/mℓ in solution; test 2, 300 μg/g adsorbed at 220 mg/mℓ in solution; test 3, 600 μg/g adsorbed at 560 μg/mℓ in solution; test 4, 1000 μg/g adsorbed at 1000 mg/mℓ in solution. What distribution coefficient is indicated by these data? Express your answer in milliliters per gram. In sand (porosity = 35%) below the water table, estimate the relative velocity at which the pesticide would migrate in an advection-controlled system.
  1. Studies of the behavior of a toxic chemical compound in a sandstone aquifer indicate the following parameter values: porosity 10 %, average linear velocity 0.1 cm/day, and distribution coefficient 75 mℓ/g. Estimate the velocity at which the center of mass of a zone contaminated with the compound would travel.
  1. Hydrogeological studies of a site for a proposed lagoon for storage of toxic liquid wastes indicate that the hydraulic gradient at the site is downward. The Water table is located at a depth of 4 m below the ground surface. Samples from piezometers at depths of 5, 10, 15, 20, 25, 30, 40, and 50 m below ground surface have tritium concentrations of 75, 81, 79, 250, 510, 301, 50, and 10 tritium units. The site is located in the interior of North America. The piezometers are situated in a thick deposit of shale. Provide an interpretation of the tritium data. What is the nature of the permeability of the shale?
  1. Groundwater in a sandstone aquifer at a temperature of 25°C has the following composition (mg/ℓ): K+ = 12, Na+ = 230, Ca2+ = 350, Mg2+ = 45, \ce{HCO^-3} = 320, Cl– = 390, and SO42- = 782; pH 7.6. If F– is supplied to the water from minerals in the aquifer and if the F– concentration is not limited by availability, will solubility constraints be expected to maintain the F– concentration at a level below the limit specified for drinking water? Explain.
  1. Effluent from a septic (sewage disposal) system infiltrates into an unconfined gravel aquifer. Upon mixing with the groundwater, the contaminated part of the aquifer has the following content of inorganic constituents (mg/ℓ): K+ = 3.1, Na+ = 106, Ca2+ = 4.2, Mg2+ = 31, \ce{HCO^-3} = 81, Cl– = 146, and SO42- = 48; pH 6.3, Eh = -0.1 V, DO = 0, temperature 23°C. Assuming that equilibrium occurs and that mineral precipitation-dissolution reactions control the concentration of dissolved inorganic phosphorus, indicate (a) the mineral that would provide the solubility constraint on the phosphorus concentration; (b) the dominant dissolved species of inorganic phosphorus; (c) the equilibrium concentration of dissolved phosphorus.
  1. A borehole-dilution test is conducted in a well with an inside diameter of 10 cm. The packer-isolated interval in which the tracer is introduced is 100 cm long. After 2 h the tracer concentration declines to one-half of its initial value. The flow in the formation is horizontal, the well has no sand or gravel pack, and the tracer is nonradioactive and nonreactive. Estimate the average linear velocity in the formation.
  1. A disposal well for liquid industrial waste commences operation in a horizontal isotropic confined limestone aquifer that has the following characteristics: thickness = 10 m, secondary porosity = 0.1%, bulk hydraulic conductivity = 5 × 10–5 m/s, specific storage = 10–6 cm–1. The injection rate is 100 ℓ/min.
    1. To what distance from the injection well will the front of the potentiometric mound have extended after 1 month?
    2. To what distance from the injection well will the front of contamination have moved after 1 month? Neglect the effects of regional groundwater flow and dispersion. Assume that the aquifer is homogeneous and that the primary permeability of the limestone matrix is negligible.
  1. Studies of an unconfined aquifer indicate a shallow zone that contains dissolved oxygen in the range 2–6 mg/ℓ and \ce{NO^-3} in the range 30–50 mg/ℓ. The source of the \ce{NO^-3} is fertilizer. Below this zone there is no detectable dissolved oxygen and no detectable \ce{NO^-3}. Hydraulic-head data indicate that groundwater flows from the upper zone to the lower zone. All the water in the aquifer is very young. Suggest a hydrochemical hypothesis to account for the large decrease in \ce{NO^-3} as the water moves downward in the aquifer. What additional data would be desirable as a basis for testing your hypothesis?
  1. Salt (as NaCl only) applied to a highway during the winter for prevention of icing problems has caused contamination of a shallow unconfined aquifer near the highway. It has been observed that the Cl– content of water from many domestic wells, which was formerly soft, has become hard as the Cl– has risen. The large increase in hardness can be attributed to the effect of road-salt contamination. Outline a geochemical hypothesis to explain the hardness increase.
  1. Natural water in a deep sandstone aquifer composed of quartz, feldspar, and a small amount of clay has the following composition (mg/ℓ): K+ = 18, Na+ = 850, Ca2+ = 41, Mg2+ = 120, \ce{HCO^-3} = 820, Cl– = 470, and SO42– = 1150; pH 8.1. Wastewater that contains abundant dissolved organic matter is put into the aquifer through a disposal well. After injection commences, observation wells in the aquifer near the disposal well yield water in which abundant H2S and CH4 are detected. Prior to waste injection, the observation wells showed no detectable H2S and CH4. The wastewater injected into the aquifer did not contain these gases. Outline a geochemical hypothesis to account for the occurrence of H2S and CH4 in the observation wells. Would you expect the pH of the water to increase or decrease? Explain, with the aid of appropriate chemical equations.
  1. An unlined lagoon is used intermittently for recharge of water from a secondary sewage treatment plant. The water has moderate concentrations of major ions (K+, Na+, Ca2+, Mg2+, Cl–, SO42–, and \ce{HCO^-3}) and an appreciable content of \ce{NH^+_4}, bacteria, and organic matter. The treated sewage infiltrates from the lagoon downward into a sandy aquifer. Observation wells used to monitor the change in groundwater chemistry caused by the artificial discharge system indicate that the aquifer water in the zone of influence has total hardness, nitrate, and dissolved inorganic carbon concentrations that are considerably above the natural levels in the aquifer. No bacteria are detected in the aquifer. The N concentrations are very low. Account for these chemical characteristics of the water. Include appropriate chemical equations as part of your explanation.
  1. In an area of strip mining for coal, the noncoal geologic materials removed during mining (referred to as cast overburden) are returned to the stripped areas as part of a land reclamation program. The average porosity of the cast overburden is 30%. The average degree of saturation of the material is 40%. Assuming that the water and entrapped air in the voids do not migrate, and assuming that all the oxygen in the air and water in the voids is consumed by oxidation of pyrite, estimate the following:
    1. The SO42– content of the pore water.
    2. The pH of the pore water (assume that no carbonate-mineral buffering occurs).
    3. The amount (weight percent) of calcite that would be necessary in the cast overburden to neutralize the acid product by pyrite oxidation.
    4. The amount of pyrite necessary for consumption of all the oxygen by the oxidation reaction.
    5. Would the amounts of calcite and pyrite obtained in parts (c) and (d) be noticeable by normal means of examination of the geologic materials?