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Classroom activity Grade 12 Engineering & Design

Pinderloe GAC Contactor Sizing Relay for PFAS Removal

Grade 12 teams pass one spec sheet through four desks, size carbon vessels for a fictional plant, find the contact time falls short, and redesign the bed depth.

Objectives

  1. Students will convert plant design flow into gallons per minute per treatment vessel.
  2. Students will calculate empty bed contact time from carbon bed volume and vessel flow.
  3. Students will resize a carbon bed depth so the contactor meets a stated contact time.

Vocabulary

Granular activated carbon
Small black grains of specially treated carbon that grab contaminants as water flows through them. Utilities use big tanks of it to remove PFAS, bad tastes, and odors.

Also: contactor, empty bed contact time, loading rate, bed depth, changeout

Teacher overview

This is a four-desk relay for teams of three or four, run as a single pass with one spec sheet that travels with the team. Teams design granular activated carbon contactors for the fictional Pinderloe Water Works, which detected PFOA above the drinking water limit and must add carbon treatment. Each desk completes one stage of the design and hands the sheet on, so no team can skip to the answer. The relay is built around a design failure the teams discover for themselves at the third desk, where the first bed depth turns out to give too little contact time. One misconception worth naming beforehand is that contact time depends on bed depth alone. Contact time is the volume of carbon, cross-sectional area times bed depth, divided by the flow, so either a wider vessel or a deeper bed raises it; because the diameter here is fixed at 12.0 feet, the fix is a deeper bed.

Activity Directions

  1. Before class, print one spec sheet per team and set up four desks labeled Flow, Vessel, Contact Time, and Changeout. Each desk card states only the criterion that desk enforces, drawn from the fictional Pinderloe design data on the student handout.
  2. Form teams of three or four. Give each team one spec sheet, one calculator, and a starting position at the Flow desk. Stagger team start times by two minutes so the desks do not jam.
  3. At the Flow desk, teams complete handout items 1 and 2, converting the plant's design flow into gallons per minute and dividing it among the four vessels. A team may not advance until both figures appear on the sheet.
  4. At the Vessel desk, teams complete items 3 and 4, finding the cross-sectional area of one vessel and the loading rate. The desk card states the accepted design range of 2 to 6 gallons per minute per square foot, and teams must write whether their loading rate falls inside it.
  5. At the Contact Time desk, teams complete items 5, 6, and 7. This is where the first design fails, because the six-foot bed does not hold enough carbon to meet the ten-minute minimum. Teams write the word "fails" on the sheet before moving on.
  6. At the Changeout desk, teams complete items 8 through 12. They resize the bed depth to meet the ten-minute criterion, find the carbon mass and fill cost, and state how much PFOA removal the plant needs.
  7. End the relay when every team has a completed spec sheet with a revised bed depth on it, or at the forty-five minute mark, whichever comes first. Post each team's revised depth so the class can compare.
  8. Debrief with two specific questions. First, the diameter never changed, so what physically changed in the vessel to raise contact time from the failing value to ten minutes? Second, a deeper bed costs more carbon per fill, so how would a team argue for adding a fifth vessel instead of deepening the four the plant already has?
Pinderloe GAC Contactor Sizing Relay for PFAS Removal — Grade 12 Engineering & Design
Name: ____________________________ Date: ______________

Student Handout

The fictional Pinderloe Water Works has a design flow of 3.6 MGD and is adding four granular activated carbon vessels operating in parallel. Each vessel is a vertical cylinder 12.0 feet in diameter. The first design uses a carbon bed 6.0 feet deep. The carbon vendor requires a minimum empty bed contact time of 10.0 minutes and supplies carbon with a bulk density of 30.0 pounds per cubic foot at $2.15 per pound. Raw water at the fictional plant carries 18 ppt of PFOA, and the drinking water limit for PFOA is 4.0 ppt.

Use these relationships: 1 MGD equals 694 gpm; the area of a cylinder equals 0.785 times the diameter squared; 1 cubic foot holds 7.48 gallons; loading rate equals flow in gallons per minute divided by surface area in square feet; and empty bed contact time in minutes equals the carbon bed volume in gallons divided by the vessel flow in gallons per minute.

  1. The plant's design flow is 3.6 MGD, and 1 MGD equals 694 gpm. Find the design flow in gallons per minute.
  2. Using a plant flow of 2,498.4 gpm split evenly among 4 vessels, find the flow through one vessel.
  3. Each vessel is 12.0 feet in diameter. Using area equals 0.785 times diameter squared, find the cross-sectional area of one vessel.
  4. Using a vessel flow of 624.6 gpm and a vessel area of 113.04 square feet, find the loading rate in gallons per minute per square foot.
  5. The first design uses a bed 6.0 feet deep in a vessel of 113.04 square feet, and 1 cubic foot holds 7.48 gallons. Find the carbon bed volume in gallons.
  6. Using a bed volume of 5,073.2 gallons and a vessel flow of 624.6 gpm, find the empty bed contact time in minutes.
  7. The vendor requires at least 10.0 minutes of contact time. Using a calculated contact time of 8.12 minutes, find how many minutes short of the requirement the first design falls.
  8. The vendor requires 10.0 minutes of contact time at a vessel flow of 624.6 gpm. Find the carbon bed volume in gallons that this requires.
  9. Using a required bed volume of 6,246 gallons, a vessel area of 113.04 square feet, and 7.48 gallons per cubic foot, find the bed depth in feet the revised design needs.
  10. Carbon has a bulk density of 30.0 pounds per cubic foot. Using a vessel area of 113.04 square feet and a revised bed depth of 7.39 feet, find the pounds of carbon in one vessel.
  11. Carbon costs $2.15 per pound. Using 25,061 pounds per vessel and 4 vessels, find the cost of a complete carbon fill for the plant.
  12. Raw water carries 18 ppt of PFOA and the limit is 4.0 ppt. Find the percent removal the carbon must achieve.

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: 2,498.4 gpm. At the fictional plant, 3.6 MGD times 694 gpm per MGD equals 2,498.4 gallons per minute.
  2. Answer: 624.6 gpm. 2,498.4 gpm divided by 4 vessels equals 624.6 gallons per minute through each vessel.
  3. Answer: 113.04 sq ft. 0.785 times 12.0 squared equals 0.785 times 144, which is 113.04 square feet.
  4. Answer: 5.53 gpm per square foot. 624.6 divided by 113.04 equals 5.526, which rounds to 5.53 and falls inside the accepted range of 2 to 6.
  5. Answer: 5,073.2 gallons. 113.04 square feet times 6.0 feet equals 678.24 cubic feet, and 678.24 times 7.48 equals 5,073.24 gallons.
  6. Answer: 8.12 minutes. 5,073.2 gallons divided by 624.6 gallons per minute equals 8.122 minutes, which rounds to 8.12.
  7. Answer: 1.88 minutes. 10.0 minutes minus 8.12 minutes equals 1.88 minutes short of the vendor requirement.
  8. Answer: 6,246 gallons. 10.0 minutes times 624.6 gallons per minute equals 6,246 gallons of carbon bed volume.
  9. Answer: 7.39 feet. 6,246 gallons divided by 7.48 equals 835.03 cubic feet, and 835.03 divided by 113.04 square feet equals 7.387 feet, which rounds to 7.39 feet.
  10. Answer: 25,061 pounds. 113.04 square feet times 7.39 feet equals 835.37 cubic feet, and 835.37 times 30.0 pounds per cubic foot equals 25,061 pounds.
  11. Answer: $215,524.60. 25,061 pounds times 4 vessels equals 100,244 pounds, and 100,244 times $2.15 per pound equals $215,524.60.
  12. Answer: 77.8 percent. 18 minus 4.0 equals 14, and 14 divided by 18 equals 0.7778, which is 77.8 percent removal.

Differentiation

Support

Give these teams a spec sheet with the unit labels already printed beside every blank, so gallons per minute, square feet, and cubic feet cannot be confused mid-relay. Provide a worked contact-time model on a different fictional vessel, such as a 10.0-foot diameter vessel at 400 gpm with a 5.0-foot bed, before the relay begins.

Extension

Ask these teams to price the alternative the debrief raises. Have them size a fifth vessel of the same 12.0-foot diameter at the fictional plant, recompute the flow per vessel and the bed depth needed for 10.0 minutes of contact, and compare the total carbon fill cost against the four-vessel revised design.

ELL supports

Provide a cutaway sketch of a carbon vessel with the diameter, bed depth, and flow path labeled, so "bed volume" and "surface area" are visibly different quantities. Offer sentence frames for the desk handoffs: "The flow through one vessel is ___ gpm," and "The contact time is ___ minutes, which is ___ than the required 10.0 minutes."

Extensions

Suppose the fictional Pinderloe plant learns that its carbon will need changing every 18 months at design flow. Ask students to find how many vessel changeouts the plant averages per year across four vessels, then to argue whether the plant should stagger the changeouts or replace all four at once, naming one water quality risk and one cost effect for each choice.