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Worksheet Grade 10 Science

Quarnwood Landfill Plume: Travel Time in the Dellwick Aquifer

Grade 10 students use monitoring well data to find a hydraulic gradient, calculate seepage velocity, and estimate how long a landfill plume needs to reach a well field.

Objectives

  1. Students will calculate a hydraulic gradient from water levels in two monitoring wells.
  2. Students will apply Darcy's law and porosity to find seepage velocity and plume travel time.
  3. Students will explain how a moving plume constrains a town's choices about its water supply.

Vocabulary

Hydraulic conductivity
Hydraulic conductivity is a number that tells you how easily water can flow through a particular soil or rock. Gravel has high hydraulic conductivity because water flows through it easily, while dense clay has very low hydraulic conductivity.
Porosity
Porosity measures how much empty space a rock or soil has between its grains, which tells you how much water it can hold. A sponge has high porosity, while a piece of glass has almost none.

Also: hydraulic gradient, seepage velocity, plume

Teacher overview

Groundwater moves slowly, and the two speeds involved are easy to confuse. Darcy's law gives the specific discharge, which is the volume of water crossing a unit area of aquifer per unit of time, while the water itself threads through the pore spaces at a faster rate called seepage velocity. The Darcy result is the one most often reported by mistake as the speed of the contamination, so this worksheet requires the division by porosity every time. The setting is the fictional town of Dellwick, whose closed Quarnwood landfill sits upgradient of the municipal well field.

Quarnwood Landfill Plume: Travel Time in the Dellwick Aquifer — Grade 10 Science
Name: ____________________________ Date: ______________

Student Worksheet

Suppose Dellwick is a town of 14,000 people that closed the Quarnwood landfill twenty years ago. Two monitoring wells sit along the groundwater flow path between the landfill and the town well field. Well MW-1 is nearer the landfill; well MW-2 is 1,200 feet away in the downgradient direction. Use these definitions throughout: hydraulic gradient i equals the change in water level divided by the distance between wells; Darcy's law gives specific discharge q equals hydraulic conductivity K times i; and seepage velocity v equals q divided by porosity. Porosity as a percent equals void volume divided by total volume times 100.

  1. A core taken from the sand and gravel aquifer has a total volume of 550 mL. The void space in that core measures 165 mL. Calculate the porosity of the aquifer material as a percent.
  2. The water level in MW-1 stands 42.0 feet above the datum, and the water level in MW-2 stands 33.6 feet above the same datum. The two wells are 1,200 feet apart. Calculate the hydraulic gradient between them.
  3. Using the two water levels in item 2, state which well is upgradient and explain in one sentence how the water levels tell you the direction of flow.
  4. The sand and gravel between the wells has a hydraulic conductivity of 45 feet per day. Using the gradient you found in item 2, calculate the specific discharge q from Darcy's law.
  5. Using your specific discharge from item 4 and a porosity of 0.30, calculate the seepage velocity of the groundwater in feet per day.
  6. The leading edge of the plume now sits at MW-2. The town well field is 2,100 feet downgradient of MW-2. Using a seepage velocity of 1.05 feet per day, calculate how many days the plume needs to travel that distance.
  7. Convert your answer from item 6 to years, using 365 days per year. Round to the nearest tenth.
  8. A clay layer along part of the path has a hydraulic conductivity of only 0.05 feet per day. Using the same gradient of 0.007 and the same porosity of 0.30, calculate the seepage velocity through the clay in feet per year.
  9. When the town runs its wells hard in August, the gradient between the landfill and the well field doubles to 0.014. Using a hydraulic conductivity of 45 feet per day and a porosity of 0.30, calculate the new travel time in days for the plume to cover 2,100 feet.
  10. Chloride in the plume measures 1.8 mg/L at MW-1 and 0.45 mg/L at MW-2. Calculate the percent reduction in concentration between the two wells.
  11. Explain the difference between the specific discharge you found in item 4 and the seepage velocity you found in item 5, and state which one describes how fast the contamination is moving.
  12. The town wants to add two new wells. Using your travel-time results from items 7 and 9, explain how the plume limits where those wells can go and how the pumping schedule itself changes the risk.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 30 percent.
    Divide void volume by total volume and multiply by 100: 165 mL / 550 mL = 0.30, so the porosity is 30 percent, which is 0.30 as a decimal for use in later items.
  2. Answer: 0.007.
    Subtract the water levels and divide by the distance: 42.0 feet minus 33.6 feet = 8.4 feet of drop across 1,200 feet, so i = 8.4 / 1,200 = 0.007. The gradient has no units because feet divide out.
  3. Answer: MW-1 is upgradient.
    Groundwater flows from higher head to lower head. MW-1 stands at 42.0 feet and MW-2 at 33.6 feet, so water moves from MW-1 toward MW-2, which is the direction of the town well field.
  4. Answer: 0.315 ft/day.
    Apply Darcy's law: q = K x i = 45 feet per day x 0.007 = 0.315 feet per day. This is the specific discharge, not the speed of a water particle.
  5. Answer: 1.05 ft/day.
    Divide specific discharge by porosity: 0.315 / 0.30 = 1.05 feet per day. Water threads through only the pore space, so it must move faster than the bulk figure suggests.
  6. Answer: 2,000 days.
    Divide distance by seepage velocity: 2,100 feet / 1.05 feet per day = 2,000 days.
  7. Answer: 5.5 years.
    Divide days by 365: 2,000 / 365 = 5.48 years, which rounds to 5.5 years. Accept 5.5 years, and accept 5.48 years from students who keep an extra digit.
  8. Answer: 0.43 ft/year.
    Work in the same order as before. Specific discharge is 0.05 x 0.007 = 0.00035 feet per day. Seepage velocity is 0.00035 / 0.30 = 0.001167 feet per day. Multiply by 365 days: 0.001167 x 365 = 0.426, or about 0.43 feet per year. A clay layer is roughly nine hundred times slower than the sand and gravel.
  9. Answer: 1,000 days.
    With the gradient doubled, q = 45 x 0.014 = 0.63 feet per day and v = 0.63 / 0.30 = 2.1 feet per day. Travel time is 2,100 / 2.1 = 1,000 days, which is half the original estimate.
  10. Answer: 75 percent.
    Use the removal form: (1.8 minus 0.45) / 1.8 x 100. That is 1.35 / 1.8 = 0.75, so the concentration falls by 75 percent between the wells. Dilution and dispersion account for the drop, since chloride is not broken down underground.
  11. Answer: Seepage velocity describes the contamination.
    Specific discharge treats the whole cross-section of aquifer as if it were open, so 0.315 feet per day is a flow rate per unit area rather than a particle speed. Water can only move through the connected pore space, which is 30 percent of the volume here, so the actual water and the dissolved contamination move at 1.05 feet per day. Reporting 0.315 would stretch the predicted travel time to the well field by a factor of about three.
  12. Answer: New wells belong outside the flow path, and hard pumping shortens the warning time.
    Students should note that at the ordinary gradient the plume needs roughly 5.5 years to reach the current well field, but summer pumping doubles the gradient and cuts that to about 1,000 days. A well placed directly downgradient of the landfill therefore inherits both problems. Strong answers recommend siting new wells off the flow path or upgradient, keeping monitoring wells between the landfill and the field, and spreading summer demand across more wells so no single well steepens the gradient.

Differentiation

Support

Provide a labeled cross-section of the fictional Dellwick aquifer showing the landfill, MW-1, MW-2, and the well field with the distances marked, and hand out a formula strip with i, q, and v written in order. Work item 4 and item 5 as a pair on the board with different numbers, such as a conductivity of 30 feet per day, so students see the division by porosity as the second half of one routine.

Extension

Have students recalculate items 5 through 7 for a porosity of 0.20 and again for 0.40, then write a short paragraph explaining why a lower porosity produces a faster arrival even though nothing about the gradient changed. Ask them to predict what a fractured rock aquifer with a porosity near 0.02 would mean for the town of Dellwick.

ELL supports

Post a visual glossary card for "upgradient," "downgradient," "plume," and "pore space," each with a simple sketch. Give sentence frames for items 3, 11, and 12, such as "Water flows from ___ to ___ because ___," and allow students to annotate the cross-section instead of writing full paragraphs on the first pass.

Extensions

Ask students to sketch a monitoring plan for the town of Dellwick that shows where they would place two additional monitoring wells and how often they would sample them. Require the plan to justify the spacing using the 1.05 feet per day seepage velocity, so that a sample taken on a stated schedule would detect the plume before it reaches the well field.