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Worksheet Grade 7 Science

Sabine Bay's Desalination Pilot: Membrane Rejection and Flow Splits

A grade 7 worksheet on a fictional town's reverse osmosis pilot, calculating percent TDS removal, the permeate-reject flow split, and a gpm-to-gallons conversion.

Objectives

  1. Students will calculate the percent of dissolved solids a reverse osmosis membrane removes from feed water.
  2. Students will use a proportional permeate-to-reject split to scale a system's output to new flow rates.
  3. Students will convert a flow rate from gallons per minute to gallons per day.

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: membrane, permeate, reject

Teacher overview

The fictional coastal town of Sabine Bay is piloting a reverse osmosis (RO) system to turn brackish well water into drinking water. In an RO system, feed water is pushed under pressure through a membrane with pores small enough to block most dissolved solids; the water that passes through is called permeate, and the leftover, more concentrated stream is called reject. This worksheet uses measurements from Sabine Bay's fictional pilot unit to calculate how well the membrane performs and how its output splits between usable water and reject.

Sabine Bay's Desalination Pilot: Membrane Rejection and Flow Splits — Grade 7 Science
Name: ____________________________ Date: ______________

Student Worksheet

Use these facts about Sabine Bay's fictional pilot RO unit for every problem below.

  • Feed water entering the membrane measures 2,000 mg/L of total dissolved solids (TDS).
  • Treated water leaving the membrane (the permeate) measures 40 mg/L of TDS.
  • The reject stream that does not pass through the membrane measures 4,940 mg/L of TDS.
  • Sabine Bay's engineers set a project goal of keeping the finished water under 250 mg/L of TDS.
  • The pilot unit processes feed water at a rate of 15 gallons per minute (gpm).
  • Of that feed flow, 60 percent becomes usable permeate and the remaining 40 percent becomes reject.
  1. In your own words, what does a reverse osmosis membrane do to feed water, and what are the two streams that come out of it called?
  2. Using the removal efficiency formula, Removal % = (influent − effluent) ÷ influent × 100, calculate the percent of TDS the membrane removes from the feed water.
  3. Does the permeate meet Sabine Bay's project goal of under 250 mg/L of TDS? By how many mg/L does it clear the goal?
  4. The reject stream measures 4,940 mg/L of TDS, far higher than the feed water's original 2,000 mg/L. Explain in one or two sentences why the reject stream ends up more concentrated than the feed water.
  5. If 60 percent of the pilot unit's 15 gpm feed flow becomes permeate, how many gallons per minute of usable drinking water does the unit produce?
  6. How many gallons per minute of reject stream does the unit produce?
  7. Convert the unit's permeate production rate from gallons per minute to gallons per day.
  8. A second, larger pilot unit runs at 45 gpm, three times the feed flow of the first unit, and keeps the same 60/40 permeate-to-reject split. How many gallons per minute of permeate would it produce?
  9. Based on your answer to problem 2, is a membrane more effective at removing TDS when its removal percent is closer to 100 percent or closer to 0 percent? Explain your reasoning.
  10. Challenge. Sabine Bay wants to raise its permeate rate to 12 gpm by adjusting the feed flow, while keeping the same 60 percent recovery rate. What feed flow rate, in gpm, would be needed?

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: permeate and reject.
    A reverse osmosis membrane pushes feed water through pores small enough to block most dissolved solids. Water that passes through is called permeate; the leftover, more concentrated water that does not pass through is called reject.
  2. Answer: 98 percent.
    (2,000 − 40) ÷ 2,000 × 100 = 1,960 ÷ 2,000 × 100 = 98%.
  3. Answer: 210 mg/L.
    The permeate measures 40 mg/L, well under the 250 mg/L goal. 250 − 40 = 210 mg/L of margin below the goal.
  4. Answer: The dissolved solids concentrate in the reject stream.
    The membrane blocks most of the dissolved solids from passing through, so the solids that don't leave with the permeate stay behind and become concentrated into the smaller reject stream, raising its TDS well above the original feed water.
  5. Answer: 9 gpm.
    15 gpm × 0.60 = 9 gpm of permeate.
  6. Answer: 6 gpm.
    15 gpm × 0.40 = 6 gpm of reject (or 15 − 9 = 6).
  7. Answer: 12,960 gal/day.
    9 gpm × 1,440 minutes/day = 12,960 gallons per day.
  8. Answer: 27 gpm.
    45 gpm × 0.60 = 27 gpm of permeate.
  9. Answer: closer to 100 percent.
    A removal percent closer to 100% means almost all of the dissolved solids stayed out of the permeate, which is the goal of treatment; a removal percent closer to 0% would mean the membrane barely changed the water's TDS at all.
  10. Answer: 20 gpm.
    12 gpm ÷ 0.60 = 20 gpm of feed flow needed to produce 12 gpm of permeate at a 60% recovery rate.

Differentiation

Support (below grade level)

Provide the removal efficiency formula on a printed reference card, and work through problem 2 as a full class example before students attempt problems 3 and 9 independently. Give students a simple diagram of the membrane with feed, permeate, and reject arrows labeled to support problems 1 and 4.

Extension (above grade level)

Ask students to find what percent recovery (permeate ÷ feed) the pilot unit in problems 5 and 6 achieves, expressed as a fraction, a decimal, and a percent, and to explain why a utility might want to raise that recovery percentage over time.

ELL supports

Pre-teach "membrane," "permeate," "reject," and "dissolved solids" with a simple diagram showing water and particles approaching a barrier, with small water molecules passing through and larger particle dots blocked. Allow problems 1 and 4 to be answered with labeled diagrams and short phrases rather than full sentences.