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Math problem set Grade 10 Science

Wickstead Wells: Oxidizing Iron and Manganese Before Filtration

Grade 10 problems that size a chlorine feed for iron and manganese oxidation at a well field plant, then check filter loading rates and backwash volumes.

Objectives

  1. Students will calculate the chlorine demand created by dissolved iron and manganese in a raw groundwater.
  2. Students will convert a chemical dose in pounds per day into gallons per day of hypochlorite solution.
  3. Students will calculate filter loading rates and judge them against normal operating ranges.

Vocabulary

Backwash
Backwash is when a treatment plant reverses the flow of water through a filter to flush out the dirt and particles it has trapped. It is like rinsing out a dirty sponge so the filter can keep working well.

Also: oxidation, chlorine demand, hypochlorite, percent strength, filter loading rate

Teacher overview

Groundwater that has sat in a reducing aquifer often carries iron and manganese in dissolved form, where neither one is a particle and neither one can be strained out. A plant has to oxidize them first, converting dissolved iron and manganese into solid oxides that a sand filter can capture. The filter is easy to mistake for the step that does the removing, and a plant sized on that assumption would send water to the clearwell that looks clear leaving the plant and turns brown in a customer's glass an hour later. The second error to watch for is treating percent strength as though it were a concentration in milligrams per liter rather than a mass fraction of the solution.

Wickstead Wells: Oxidizing Iron and Manganese Before Filtration — Grade 10 Science
Name: ____________________________ Date: ______________

Problems

Suppose the fictional Wickstead well field supplies a town of 26,000 people, and the treatment plant runs at 3.5 MGD. Raw water from the wells carries 2.4 mg/L of dissolved iron and 0.6 mg/L of dissolved manganese. The plant's design manual uses 0.62 milligrams of chlorine per milligram of iron and 1.30 milligrams of chlorine per milligram of manganese. Use these constants: pounds per day equals mg/L times MGD times 8.34, one million gallons per day equals 694 gallons per minute, a one percent solution equals 10,000 mg/L, and filter loading rate equals flow in gallons per minute divided by filter surface area in square feet.

  1. The raw water carries 2.4 mg/L of dissolved iron, and oxidizing it takes 0.62 milligrams of chlorine per milligram of iron. Calculate the chlorine dose in mg/L that the iron alone demands.
  2. The raw water also carries 0.6 mg/L of dissolved manganese, and oxidizing it takes 1.30 milligrams of chlorine per milligram of manganese. Calculate the chlorine dose in mg/L that the manganese alone demands.
  3. The plant must satisfy an iron demand of 1.49 mg/L and a manganese demand of 0.78 mg/L and still leave a residual of 0.50 mg/L entering the clearwell. Calculate the total chlorine dose in mg/L.
  4. Using a total dose of 2.77 mg/L, a flow of 3.5 MGD, and the pounds formula, calculate the pounds of chlorine the plant must feed each day.
  5. The plant feeds sodium hypochlorite at 12.5 percent strength, and gallons per day equals pounds per day divided by the product of the decimal strength and 8.34. Using a requirement of 80.86 pounds per day, calculate the gallons of hypochlorite solution the plant uses each day.
  6. Convert the plant flow of 3.5 MGD to gallons per minute, using 694 gallons per minute per MGD.
  7. The plant has four filters, each 12 feet by 16 feet. Using a plant flow of 2,429 gallons per minute divided evenly among all four, calculate the filter loading rate in gallons per minute per square foot.
  8. One filter is taken out of service for backwashing while the plant keeps producing 2,429 gallons per minute through the remaining three filters. Calculate the new loading rate in gallons per minute per square foot, and state whether it stays within the usual range of 2 to 6 gallons per minute per square foot.
  9. A backwash runs at 12 gallons per minute per square foot for 8 minutes across one 192 square foot filter. Calculate the gallons of water used in a single backwash.
  10. Explain in three or four sentences why the plant adds chlorine ahead of the filters rather than after them, and describe what customers would see if raw well water went straight to the filters with no oxidation step.

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: 1.49 mg/L.
    Multiply the iron concentration by the demand factor: 2.4 mg/L x 0.62 = 1.488 mg/L, which rounds to 1.49 mg/L of chlorine.
  2. Answer: 0.78 mg/L.
    Multiply the manganese concentration by its demand factor: 0.6 mg/L x 1.30 = 0.78 mg/L of chlorine. Manganese takes more chlorine per milligram than iron does, which is why a small manganese number still matters.
  3. Answer: 2.77 mg/L.
    Add the two demands and the residual: 1.49 + 0.78 + 0.50 = 2.77 mg/L. Dose equals demand plus residual, so a student who reports 2.27 has left out the residual the plant intends to keep.
  4. Answer: 80.9 lb/day.
    Apply the pounds formula: 2.77 mg/L x 3.5 MGD x 8.34 = 80.86 pounds per day, or about 80.9 pounds of chlorine per day.
  5. Answer: 77.6 gal/day.
    Divide the pounds required by the pounds of chlorine each gallon of solution carries: 0.125 x 8.34 = 1.0425 pounds of available chlorine per gallon, and 80.86 / 1.0425 = 77.56 gallons per day, or about 77.6 gallons. Students may check the strength another way, since 12.5 percent equals 125,000 mg/L.
  6. Answer: 2,429 gpm.
    Multiply by the conversion factor: 3.5 MGD x 694 gallons per minute per MGD = 2,429 gallons per minute.
  7. Answer: 3.16 gpm/sq ft.
    Find the total area first: each filter is 12 x 16 = 192 square feet, and four filters give 768 square feet. Then divide flow by area: 2,429 / 768 = 3.16 gallons per minute per square foot, comfortably inside the usual range.
  8. Answer: 4.22 gpm/sq ft.
    Three filters give 3 x 192 = 576 square feet. Dividing the same flow by the smaller area gives 2,429 / 576 = 4.22 gallons per minute per square foot, which is higher but still within the usual range of 2 to 6, so the plant can keep producing during a backwash.
  9. Answer: 18,432 gallons.
    Find the backwash flow first: 12 gallons per minute per square foot x 192 square feet = 2,304 gallons per minute. Then multiply by the duration: 2,304 x 8 minutes = 18,432 gallons for one backwash event.
  10. Answer: Chlorine must convert dissolved metals into filterable solids first.
    Iron and manganese arrive dissolved, spread evenly through the water as ions, and a sand filter can only capture particles. Chlorine oxidizes them into iron and manganese oxides, which are solids the filter media can trap. Adding chlorine after the filters would leave the metals dissolved right through the plant, so they would oxidize slowly in the distribution system instead, staining fixtures and laundry and producing brown or black water at the tap. Customers would also report a metallic taste, and the plant would find the filters clean while complaints climbed.

Differentiation

Support

Provide a completed example for problems 1 through 4 using a different well with 1.0 mg/L of iron and 0.2 mg/L of manganese, worked all the way to pounds per day, and let students keep it beside them. Give a formula strip with the pounds formula, the loading rate formula, and the gallons per day form written in the order the problems need them.

Extension

Have students determine the highest flow the fictional Wickstead plant could run with only three filters in service while staying at or below 6 gallons per minute per square foot, then convert that flow to MGD and calculate the chlorine feed rate it would require at the same 2.77 mg/L dose.

ELL supports

Post a labeled diagram of the treatment path with the words "dissolved" and "particle" attached to the correct points, so the reason for oxidation is visible before the arithmetic starts. Pair "demand," "dose," and "residual" with a simple bar showing the three parts stacked, and give the sentence frame "The plant adds chlorine before the filters because ___" for problem 10.

Extensions

Ask students to build a one-page operating sheet for the fictional Wickstead plant that an operator could post in the chemical room. It should list the design dose in mg/L, the daily hypochlorite volume in gallons, the loading rate with all four filters and with three, and one line naming the reading that would tell the operator the oxidation step has stopped working.