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Lesson plan Grade 10 Science

Aldenbury's Aquifer Storage and Recovery Wells

A 55-minute grade 10 lesson on storing treated water underground, where students calculate injected volume, recovery efficiency, and chloride in the recovered blend.

Objectives

  1. Students will calculate the volume of water an aquifer storage and recovery well injects and later recovers.
  2. Students will compute recovery efficiency and explain why part of the injected water cannot be pumped back.
  3. Students will predict the chloride concentration of recovered water using a blend of two sources.

Vocabulary

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: aquifer storage and recovery, recovery efficiency, native groundwater, chloride

Teacher overview

Some utilities treat more water than they need in wet months and push the surplus down a well into an aquifer, then pump it back when demand rises. The practice is called aquifer storage and recovery, and it turns an aquifer into a seasonal storage tank that loses far less water to evaporation than a surface reservoir. This lesson uses the fictional Aldenbury Water District and its invented well-field records to teach the volume, efficiency, and mixing calculations behind the practice. A common misconception this lesson corrects is that injected water sits underground as a clean bubble and can be recovered in full; in practice it mixes with native groundwater and part of it drifts beyond the reach of the well.

Procedure

Hook (5 min): Ask students where a town could store a hundred million gallons of drinking water without building a reservoir. Collect three or four answers, then show a simple cross-section of the fictional Aldenbury well, drawn on the board, with an arrow pointing down in winter and up in summer.

Direct instruction (12 min): Define injection, storage, and recovery, and define recovery efficiency as the volume recovered divided by the volume injected, times 100. Explain porosity as the fraction of an aquifer's bulk volume that is open pore space, and state that stored water fills those pores rather than an open cavern. Name the two reasons recovery efficiency falls below 100 percent: the injected water mixes with native groundwater, and some of it moves away with the regional flow of the aquifer.

Worked example, teacher-modeled (8 min): Using values that do not appear on the handout, model a volume calculation for the fictional district: an injection rate of 0.5 MGD held for 60 days stores 0.5 million gallons per day times 60 days, or 30,000,000 gallons. Then model the unit conversion 1 MGD = 694 gpm, so 0.5 MGD is 347 gpm. Emphasize writing the units beside every number.

Guided practice (10 min): In pairs, students explain in writing why an aquifer with a porosity of 25 percent can hold only a quarter of its bulk volume as water. Circulate and check that pairs describe pore space rather than an underground lake, which is the misconception named above.

Independent practice (15 min): Students complete the numbered handout below on their own.

Closure and exit ticket (5 min): On an index card, students answer one question: a district injects 60,000,000 gallons and recovers 45,000,000 gallons, so what is the recovery efficiency? Confirm that students divided to get 75 percent, and reteach the efficiency formula the next day if more than a quarter of the class misses it.

Aldenbury's Aquifer Storage and Recovery Wells — Grade 10 Science
Name: ____________________________ Date: ______________

Student Handout

Suppose the fictional Aldenbury Water District runs one aquifer storage and recovery well in a sand aquifer. Every figure below is invented for this scenario. Use 1 MGD = 694 gpm, 7.48 gallons per cubic foot, and cylinder volume = 0.785 x diameter squared x thickness.

  1. The district injects treated water at a steady rate of 1.2 MGD for 100 days. Calculate the total volume injected, in gallons.
  2. Convert the injection rate of 1.2 MGD to gallons per minute.
  3. The next summer the district recovers 84,000,000 gallons of the 120,000,000 gallons it injected. Calculate the recovery efficiency as a percent.
  4. The district recovers water at a steady rate of 2.0 MGD. Calculate how many days it takes to recover 84,000,000 gallons.
  5. A sample of recovered water is 60 percent injected water and 40 percent native groundwater. The injected water holds 20 mg/L of chloride and the native groundwater holds 250 mg/L of chloride. Calculate the chloride concentration of the blended sample.
  6. The storage zone is modeled as a cylinder 3,000 feet in diameter and 40 feet thick, with a porosity of 25 percent. Calculate the pore volume of that storage zone in gallons.
  7. Explain why the recovery efficiency you found in question 3 is below 100 percent even though no water leaked at the surface.

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: 120,000,000 gallons. An injection rate of 1.2 MGD is 1,200,000 gallons per day, and 1,200,000 x 100 days = 120,000,000 gallons.
  2. Answer: 832.8 gpm. Multiply 1.2 MGD by 694 gpm per MGD to get 832.8 gpm.
  3. Answer: 70 percent. Recovery efficiency = 84,000,000 / 120,000,000 x 100 = 70 percent.
  4. Answer: 42 days. A recovery rate of 2.0 MGD is 2,000,000 gallons per day, and 84,000,000 / 2,000,000 = 42 days.
  5. Answer: 112 mg/L. The blend contributes 0.60 x 20 = 12 from the injected water and 0.40 x 250 = 100 from the native groundwater, and 12 + 100 = 112 mg/L of chloride.
  6. Answer: 528,462,000 gallons. Bulk volume = 0.785 x 3,000 x 3,000 x 40 = 282,600,000 cubic feet. Pore volume = 0.25 x 282,600,000 = 70,650,000 cubic feet, and 70,650,000 x 7.48 = 528,462,000 gallons.
  7. Answer: Part of the injected water mixes with native groundwater or drifts away from the well with the regional flow of the aquifer, so it is no longer close enough or clean enough to pump back. Recovery efficiency measures how much of the stored water the district can actually reach, not how much water survived underground.

Differentiation

Support

Give students a formula card listing recovery efficiency, the cylinder volume formula, and the two conversions used on the handout, with question 1 already worked as a model. Allow calculators throughout and let students answer question 7 in two sentences rather than a paragraph.

Extension

Ask students to predict how the recovery efficiency would change if the aquifer's regional flow were twice as fast, and to justify the prediction in writing using the mixing idea from question 5. Then ask them to describe one measurement the district could take to test that prediction.

ELL supports

Pre-teach "inject," "recover," "porosity," and "blend" with a labeled cross-section showing water moving down the well in winter and up in summer. Provide the sentence frame "The recovery efficiency is ___ percent because the district recovered ___ gallons of the ___ gallons it injected."