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Worksheet Grade 9 Science

Piloting Reverse Osmosis for Salt Fork's Brackish Well Water

A grade 9 worksheet in which students size a reverse osmosis pilot skid for a fictional town's brackish well, calculating recovery rate and concentrate salinity.

Objectives

  1. Students will calculate the recovery rate of a reverse osmosis system from feed, permeate, and concentrate flows.
  2. Students will use a mass balance to find the salt concentration in a reverse osmosis reject stream.
  3. Students will evaluate a reverse osmosis pilot against cost and disposal trade-offs.

Vocabulary

Reverse osmosis
Reverse osmosis cleans water by pushing it through a membrane with holes so tiny that salt and most other dissolved things cannot fit through. It can even turn seawater into fresh water.
Total dissolved solids (TDS)
Total dissolved solids is a measure of everything dissolved in water that you cannot see or filter out, like minerals and salts. Water with very high TDS can taste salty or bitter, even though it might look perfectly clear.

Also: permeate, concentrate, recovery rate

Teacher overview

The fictional town of Salt Fork sits over a groundwater aquifer that has grown saltier as nearby irrigation wells have pulled down the water table over several decades. Rather than drill a new well, the town's water department is testing a small reverse osmosis (RO) unit that would treat the brackish well before blending it into the regular supply. This worksheet uses that pilot to give students a full membrane mass balance: a feed stream splits into a cleaned permeate stream and a smaller, saltier concentrate stream, and both must add back up to the original feed.

A common misconception in this math is assuming that reverse osmosis destroys the salt it removes. It does not. Every milligram of dissolved solids that is kept out of the permeate stream has to show up somewhere, and that somewhere is the concentrate stream at a higher concentration. Watch for students who calculate a recovery rate correctly but then assume the concentrate is simply "waste" with no measurable salt content of its own.

Piloting Reverse Osmosis for Salt Fork's Brackish Well Water — Grade 9 Science
Name: ____________________________ Date: ______________

Student Worksheet

The pilot skid at the town of Salt Fork's well site processes water at a feed flow of 40,000 gallons per day (gpd). All figures in this worksheet describe Salt Fork's fictional pilot skid. Use these facts for all items:

  • The skid is designed to recover 75 percent of the feed water as permeate; the rest becomes concentrate.
  • The feed water entering the skid measures 2,800 mg/L of total dissolved solids (TDS).
  • The membrane rejects 98 percent of the dissolved solids from the feed, meaning only 2 percent of the original TDS mass passes through into the permeate.
  • The town's water department wants finished (permeate) water below 500 mg/L TDS before blending.
  1. How many gallons per day of permeate does the skid produce, based on the 75 percent recovery rate?
  2. How many gallons per day of concentrate does the skid produce?
  3. What is the total mass of dissolved solids entering the skid each day, in pounds? (Use the pounds formula: pounds/day = concentration in mg/L × flow in MGD × 8.34. Convert 40,000 gpd to MGD first.)
  4. If the membrane rejects 98 percent of the feed's dissolved solids, what mass of dissolved solids (in pounds per day) passes through into the permeate stream?
  5. Using your answer from item 4 and the permeate flow from item 1, calculate the TDS concentration of the permeate in mg/L. (Rearrange the pounds formula: concentration = pounds/day ÷ (flow in MGD × 8.34).) Does the permeate meet the town's 500 mg/L target?
  6. The concentrate stream carries the dissolved solids mass that did not pass through the membrane. Calculate that mass in pounds per day, then use the concentrate flow from item 2 to find the concentrate's TDS concentration in mg/L.
  7. The town must truck the concentrate to a disposal site because Salt Fork has no wastewater outfall large enough to accept it. Based on your answer to item 2, explain in two or three sentences why a higher recovery rate (say, 90 percent instead of 75 percent) would reduce the town's disposal costs.
  8. Trade-off item. A higher recovery rate reduces concentrate volume, yet real RO systems lose efficiency and can foul membranes faster at very high recovery on brackish groundwater. Using this trade-off and your answers above, write a two-to-three sentence recommendation for whether Salt Fork should target 75 percent or push for a higher recovery rate.

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: 30,000 gpd.
    40,000 gpd × 0.75 = 30,000 gallons per day of permeate.

  2. Answer: 10,000 gpd.
    40,000 gpd − 30,000 gpd = 10,000 gallons per day of concentrate (or 40,000 × 0.25 = 10,000).

  3. Answer: 934.08 lb.
    40,000 gpd = 0.04 MGD. Pounds/day = 2,800 mg/L × 0.04 MGD × 8.34 = 934.08 pounds of dissolved solids entering the skid each day.

  4. Answer: 18.68 lb.
    2 percent of the feed's dissolved solids passes through: 934.08 × 0.02 = 18.68 pounds per day in the permeate.

  5. Answer: about 75 mg/L.
    Permeate flow is 30,000 gpd = 0.03 MGD. Concentration = 18.68 ÷ (0.03 × 8.34) = 18.68 ÷ 0.2502 ≈ 74.7 mg/L, which rounds to about 75 mg/L. This is well below the 500 mg/L target, so the permeate meets the town's goal by a wide margin.

  6. Answer: about 10,976 mg/L.
    The concentrate carries the remaining 98 percent of the dissolved solids mass: 934.08 − 18.68 = 915.4 pounds per day. Concentrate flow is 10,000 gpd = 0.01 MGD. Concentration = 915.4 ÷ (0.01 × 8.34) = 915.4 ÷ 0.0834 ≈ 10,976 mg/L. Note for discussion: this concentrate is nearly four times saltier than the original feed water, which is why it cannot simply be released to a creek or storm drain.

  7. Answer: Explanation, not a single number. At 90 percent recovery, the same 40,000 gpd feed would produce only 4,000 gpd of concentrate instead of 10,000 gpd, a much smaller volume to truck and dispose of, which lowers hauling costs and the number of loads needed each week.

  8. Answer: Recommendation, not a single number. A strong response weighs the lower disposal cost and volume at higher recovery against the real risk of membrane fouling and reduced water quality at brackish-groundwater sites, and states a clear recommendation, such as starting the pilot at 75 percent recovery and testing whether the membrane performs well enough to raise that target later.

Differentiation

Support (below grade level)

Provide a labeled diagram showing the feed stream splitting into permeate and concentrate arrows, with the recovery percentage written on each arrow, before students attempt items 1 and 2. Give the pounds formula already written out with blanks for students to fill in the three values (concentration, flow, and 8.34) for items 3 through 6.

Extension (above grade level)

Ask students to calculate what recovery rate the skid would need to reduce Salt Fork's concentrate volume to 2,000 gallons per day, working backward from the 40,000 gpd feed flow, and to recompute the concentrate's TDS concentration at that new recovery rate.

ELL supports

Pre-teach "feed," "permeate," and "concentrate" with a simple diagram showing water entering a membrane and splitting into a clean stream and a salty stream, labeled in English and students' home languages where possible. Allow items 7 and 8 to be answered with a labeled sketch plus one sentence rather than a full paragraph.