Water for Schools
Menu

Math problem set Grade 11 Careers & CTE

Sarrow Point Desalination: A Recovery and Energy Problem Set

A grade 11 careers problem set where students find recovery, permeate and concentrate flows, and energy use at a fictional seawater reverse osmosis plant.

Objectives

  1. Students will calculate recovery, permeate flow, and concentrate flow for a reverse osmosis plant.
  2. Students will compare the daily energy use of desalination and conventional treatment.

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.

Also: recovery, permeate, concentrate

Teacher overview

A seawater desalination plant takes in far more water than it delivers, and it uses a large amount of electricity. This problem set uses the fictional Sarrow Point seawater reverse osmosis plant so students can work recovery, flow, and energy calculations in one connected setting. The common misconception this set corrects is assuming the plant produces as much drinking water as it takes in; because recovery is well below 100 percent, the intake must be far larger than the output.

Sarrow Point Desalination: A Recovery and Energy Problem Set — Grade 11 Careers & CTE
Name: ____________________________ Date: ______________

Problems

The fictional Sarrow Point seawater reverse osmosis plant takes in seawater and pushes part of it through membranes as fresh permeate, leaving the rest as salty concentrate. Use these facts for every problem: one MGD equals 694 gpm; recovery (percent) equals permeate produced divided by feed taken in, times 100.

  1. The plant takes in a feed of 20 MGD of seawater and recovers 45 percent of it as fresh permeate. How many MGD of permeate does it produce?
  2. How many MGD of concentrate (the salty leftover) does the plant reject? Use your permeate answer from problem 1.
  3. Convert the permeate production from problem 1 to gallons per minute, using one MGD equals 694 gpm.
  4. The plant uses 12 kilowatt-hours of electricity for every 1,000 gallons of permeate. How many kilowatt-hours does it use to make 1,000,000 gallons of permeate?
  5. Using the permeate flow from problem 1 (9.0 MGD equals 9,000,000 gallons per day), how many kilowatt-hours does the plant use per day at 12 kilowatt-hours per 1,000 gallons?
  6. A conventional surface-water plant uses about 1.5 kilowatt-hours per 1,000 gallons. To produce the same 9,000,000 gallons per day, how many kilowatt-hours per day would it use?
  7. Using problems 5 and 6, how many times more energy per day does the desalination plant use than the conventional plant? Round to the nearest tenth.
  8. The plant's intake is 20 MGD but it delivers only 9 MGD of drinking water. Using the recovery percentage, explain why seawater desalination must take in far more water than it produces.

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: 9.0 MGD. 20 MGD × 0.45 = 9.0 MGD of permeate.
  2. Answer: 11 MGD. Feed minus permeate = 20 MGD − 9.0 MGD = 11 MGD of concentrate.
  3. Answer: 6,246 gpm. 9.0 MGD × 694 gpm per MGD = 6,246 gpm.
  4. Answer: 12,000 kWh. 1,000,000 gallons ÷ 1,000 = 1,000 units; 1,000 × 12 kWh = 12,000 kWh.
  5. Answer: 108,000 kWh/day. 9,000,000 gallons ÷ 1,000 = 9,000 units; 9,000 × 12 kWh = 108,000 kWh per day.
  6. Answer: 13,500 kWh/day. 9,000 units × 1.5 kWh = 13,500 kWh per day.
  7. Answer: About 8.0 times. 108,000 kWh ÷ 13,500 kWh = 8.0, or about 8.0 times as much energy.
  8. Answer: Recovery is only 45 percent, so fewer than half the gallons taken in leave as drinking water. The rest exits as concentrate, which is why the 20 MGD intake produces just 9 MGD of permeate, and the plant must take in more than twice what it delivers.

Differentiation

Support

Provide the recovery step already set up for problem 1 (feed times the recovery as a decimal) and a printed reminder that "of" means multiply, so students can start the chain of calculations without stalling on the first step.

Extension

Ask students to find what feed, in million gallons per day, the plant would need to take in to deliver 12 million gallons per day of permeate at the same 45 percent recovery, working backward from the recovery definition, and to show their rearranged equation.

ELL supports

Pre-teach "recovery," "permeate," "concentrate," and "reverse osmosis" with simple definitions and a labeled flow diagram showing feed splitting into permeate and concentrate. Allow problem 8 to be answered with the diagram plus a short phrase.