Lesson plan Grade 12 Science

Desalination Recovery Rate and Salt Rejection at Talon Point

A grade 12 lesson where students calculate a fictional plant's permeate flow, salt rejection, and concentrate TDS, benchmarked against the real Carlsbad plant.

Grade: Grade 12
Subject: Science
Material: Lesson plan
Time: 55 min
Prep: Low prep
Materials: Calculator, Printed data handout

Standards

HS-ESS3-2 NGSS

Evaluate competing design solutions for developing, managing, and utilizing energy and mineral resources based on cost-benefit ratios.

How this material aligns: Students weigh the cost-benefit trade-offs of building Talon Point's desalination plant by comparing its recovery-rate math to the real Carlsbad facility's scale and output.

All materials for HS-ESS3-2 →

HSA-CED.A.1 Common Core Math

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

How this material aligns: Students set up and solve the one-variable mass-balance equation for concentrate TDS during guided practice, creating an equation from a real desalination context.

All materials for HSA-CED.A.1 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-16.

Objectives

Students will calculate a desalination plant's permeate and concentrate flow rates from a stated feed flow and recovery rate.
Students will calculate salt rejection percentage from feed and permeate TDS concentrations.
Students will evaluate desalination against other water-supply strategies using cost-benefit reasoning and a real case study.

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: recovery rate, salt rejection, concentrate

Teacher overview

Talon Point, a fictional coastal town, is studying whether to build a small seawater desalination plant to supplement its supply during dry years. The nation's largest seawater reverse osmosis plant, the Carlsbad facility in California, produces about 50 million gallons per day and supplies roughly 10 percent of San Diego County's water. This lesson uses Talon Point's much smaller proposed plant to teach two core desalination calculations, recovery rate and salt rejection, then asks students to weigh the technology's costs and benefits against the real Carlsbad case.

A common misconception in this math is assuming that a desalination plant converts all the seawater it takes in into drinking water. In reality, only a fraction of the feed becomes usable permeate, called the recovery rate, while the rest leaves as a concentrated brine, called the concentrate, a distinction the guided practice step is built to make concrete with numbers.

Procedure

Hook (5 min): Show students the real Carlsbad figure, 50 million gallons per day serving about 10 percent of San Diego County, and ask them to guess what percentage of the seawater entering that plant actually becomes drinking water. Record guesses without comment, then reveal that seawater reverse osmosis plants typically recover only about 40 to 50 percent of the seawater fed to the membranes.

Direct instruction (15 min): Introduce Talon Point's proposed plant, which would take in a feed flow of 4 MGD of seawater. Model the recovery-rate calculation: at a design recovery rate of 45 percent, Permeate flow = Feed flow x Recovery rate = 4 MGD x 0.45 = 1.8 MGD, and Concentrate flow = Feed flow - Permeate flow = 4 - 1.8 = 2.2 MGD. Then introduce salt rejection: assuming the incoming seawater carries 35,000 mg/L of total dissolved solids (TDS) and the finished permeate carries only 250 mg/L, Salt rejection (%) = (Feed TDS - Permeate TDS) / Feed TDS x 100 = (35,000 - 250) / 35,000 x 100 ≈ 99.3 percent.

Guided practice (15 min): In pairs, students use a mass-balance equation to find the TDS concentration of the concentrate stream leaving Talon Point's plant. Guide them to set up: (Feed flow x Feed TDS) = (Permeate flow x Permeate TDS) + (Concentrate flow x Concentrate TDS), substitute the known values, and solve the one-variable equation for the unknown Concentrate TDS: 4 x 35,000 = 1.8 x 250 + 2.2 x C, so 140,000 = 450 + 2.2C, and C = (140,000 - 450) / 2.2 ≈ 63,432 mg/L. Discuss why the concentrate is so much saltier than the original seawater.

Independent practice (15 min): Students solve two related problems on their own. (1) If Talon Point's feed flow rises to 6 MGD while the recovery rate stays at 45 percent, they find the new permeate flow. (2) They compare Talon Point's original 1.8 MGD permeate output to a fictional neighboring plant, Cove Ridge, which recovers 50 percent from the same 4 MGD feed, and calculate how much more permeate Cove Ridge produces per day.

Closure / exit ticket (5 min): Students answer one question on an index card: (3) if Talon Point's salt rejection holds at 99.3 percent but the feed TDS rises to 36,000 mg/L during a dry season, what would the new permeate TDS be? Collect and scan for the correct method (multiplying feed TDS by the fraction of salt that passes through, 1 minus the rejection rate) before dismissal.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

Answer: 2.7 MGD.
Permeate = Feed x Recovery rate = 6 MGD x 0.45 = 2.7 MGD.
Answer: 0.2 MGD more.
Cove Ridge's permeate = 4 MGD x 0.50 = 2.0 MGD. Talon Point's original permeate was 1.8 MGD. 2.0 - 1.8 = 0.2 MGD more from Cove Ridge.
Answer: 252 mg/L.
If rejection is 99.3 percent, then 100 - 99.3 = 0.7 percent of the feed TDS passes through into the permeate. 36,000 mg/L x 0.007 = 252 mg/L.

Differentiation

Support (below grade level)

Provide the recovery-rate and salt-rejection formulas already written out with labeled variables, and complete the first guided-practice substitution step together as a class before pairs finish solving for concentrate TDS on their own.

Extension (above grade level)

Ask students to calculate, using only the Carlsbad figures given in this lesson, what percentage of San Diego County's total water supply a plant matching Talon Point's original permeate output would represent if the county's total supply scaled proportionally with Carlsbad's 50 MGD serving 10 percent. Have them set up and solve the proportion.

ELL supports

Pre-teach "feed," "permeate," "concentrate," and "recovery rate" with a simple diagram showing one stream of seawater splitting into two output streams, labeled with arrows. Allow the exit ticket to be answered as a labeled calculation without a full written sentence.

Extensions

Have students research a real desalination plant beyond Carlsbad and identify its permeate flow rate versus feed flow rate if that information is publicly reported, then compute what recovery rate that implies, comparing it to Talon Point's 45 percent design value.