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Math problem set Grade 12 Careers & CTE

Brayfield Ridge UV Disinfection: An Operator's Dose Math

Grade 12 problem set on ultraviolet disinfection operations: reactor loading, exposure time, derated delivered dose, and putting a standby reactor in service.

Objectives

  1. Students will calculate flow per reactor and convert it from million gallons per day to gallons per minute.
  2. Students will find exposure time from a reactor chamber volume and a flow rate.
  3. Students will apply lamp aging and sleeve fouling factors to calculate the dose a reactor actually delivers.

Vocabulary

Ultraviolet (UV) disinfection
Ultraviolet disinfection uses a special kind of light to damage the DNA of germs in water so they cannot multiply and make anyone sick. It works fast and does not add any chemicals to the water.

Also: reactor, exposure time, delivered dose, lamp aging factor, sleeve fouling, standby unit

Teacher overview

Ultraviolet disinfection leaves no residual for an operator to measure at a customer's tap, so proving the process worked depends on calculations performed at the reactor itself. This set places students in the operator's role at the fictional Brayfield Ridge Water Treatment Plant, calculating how much flow each reactor carries, how long a drop of water stays in the irradiated chamber, and what dose that adds up to once the lamps have aged and the quartz sleeves have fouled. The misconception the set corrects is the belief that delivered dose is a fixed property of the equipment, when dose falls as flow rises because exposure time is inversely proportional to flow, and the number a control panel shows before derating is not what the water actually received. Problems 5 and 6 separate those two quantities deliberately.

Brayfield Ridge UV Disinfection: An Operator's Dose Math — Grade 12 Careers & CTE
Name: ____________________________ Date: ______________

Problems

Use the following operating data from the fictional Brayfield Ridge Water Treatment Plant, which serves the town of Brayfield. The plant is treating 6.0 MGD through a bank of three ultraviolet reactors, two of which are in service while the third is held as a standby unit. Each reactor's irradiated chamber holds 46 cubic feet. The intensity sensor on each reactor reads an average of 4.2 milliwatts per square centimeter. The plant applies a lamp aging factor of 0.85 and a sleeve fouling factor of 0.95 to every calculated dose. Dose in millijoules per square centimeter equals intensity in milliwatts per square centimeter times exposure time in seconds. The state has validated this installation for a delivered dose of 40 millijoules per square centimeter. Use 694 gallons per minute per MGD and 7.48 gallons per cubic foot.

  1. With two reactors in service, calculate the flow through each reactor in million gallons per day.
  2. Convert the flow through one reactor to gallons per minute.
  3. Calculate the volume of one reactor's irradiated chamber in gallons. Round to one decimal place.
  4. Calculate the exposure time in one reactor, in seconds, by dividing the chamber volume by the flow through the reactor and converting minutes to seconds. Round to one decimal place.
  5. Calculate the uncorrected dose in millijoules per square centimeter, using the sensor intensity and the exposure time from problem 4. Round to one decimal place.
  6. Apply the lamp aging factor and the sleeve fouling factor to the dose from problem 5 to find the delivered dose. Round to one decimal place.
  7. Does the two-reactor configuration meet the validated dose of 40 millijoules per square centimeter? Answer yes or no.
  8. The operator starts the standby unit so that all three reactors carry flow. Calculate the flow through each reactor in gallons per minute.
  9. Calculate the exposure time in one reactor at the three-reactor flow, in seconds. Round to one decimal place.
  10. Calculate the delivered dose with all three reactors in service, applying both derating factors to the exposure time from problem 9. Round to one decimal place.

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: 3.0 MGD. Flow per reactor = 6.0 MGD / 2 reactors in service = 3.0 million gallons per day through each unit.
  2. Answer: 2,082 gpm. Flow = 3.0 MGD x 694 gpm per MGD = 2,082 gallons per minute.
  3. Answer: 344.1 gallons. Volume = 46 cubic feet x 7.48 gallons per cubic foot = 344.08, which rounds to 344.1 gallons.
  4. Answer: 9.9 seconds. Exposure time in minutes = 344.1 gallons / 2,082 gallons per minute = 0.16527 minute. Converting, 0.16527 x 60 seconds per minute = 9.92, which rounds to 9.9 seconds.
  5. Answer: 41.6 mJ per square centimeter. Dose = 4.2 milliwatts per square centimeter x 9.9 seconds = 41.58, which rounds to 41.6 millijoules per square centimeter.
  6. Answer: 33.6 mJ per square centimeter. Delivered dose = 41.6 x 0.85 x 0.95. First, 41.6 x 0.85 = 35.36. Then 35.36 x 0.95 = 33.59, which rounds to 33.6 millijoules per square centimeter. The two factors together keep only about 81 percent of the uncorrected figure.
  7. Answer: No. The delivered dose of 33.6 is below the validated requirement of 40 millijoules per square centimeter, so the reactors are not achieving the disinfection the installation was validated for and the operator has to reduce flow per reactor.
  8. Answer: 1,388 gpm. Flow per reactor = 6.0 MGD / 3 reactors = 2.0 MGD, and 2.0 x 694 = 1,388 gallons per minute.
  9. Answer: 14.9 seconds. Exposure time in minutes = 344.1 gallons / 1,388 gallons per minute = 0.24791 minute. Converting, 0.24791 x 60 = 14.87, which rounds to 14.9 seconds. Cutting the flow by a third raised the exposure time by half, which is the inverse relationship the whole problem turns on.
  10. Answer: 50.5 mJ per square centimeter. Uncorrected dose = 4.2 x 14.9 = 62.58. Applying the factors, 62.58 x 0.85 = 53.19, and 53.19 x 0.95 = 50.53, which rounds to 50.5 millijoules per square centimeter. That figure clears the validated dose, so bringing the standby unit online returns the plant to compliance.

Differentiation

Support

Give students the two derating factors already multiplied together as a single combined factor of 0.8075, so problems 6 and 10 become one multiplication rather than two. Provide the chamber volume conversion in problem 3 as a worked example, and supply a unit checklist showing that gallons divided by gallons per minute yields minutes. Students who complete problems 1 through 7 have met all three objectives at the two-reactor configuration.

Extension

Ask students to determine the highest plant flow the two-reactor configuration could carry and still deliver the validated dose, working backward from 40 millijoules per square centimeter. Students can also calculate what the delivered dose would be at the end of a lamp's service life if the aging factor dropped further, and explain why an operator replaces lamps on a schedule rather than waiting for an alarm.

ELL supports

Pre-teach reactor, chamber, intensity, exposure time, dose, derating, and standby with a labeled diagram showing water entering a reactor, passing the lamps, and leaving. Post the dose relationship as a word equation with units written under each term, and allow students to answer problem 7 with a single word plus the two numbers being compared.

Extensions

Have students obtain the validation report summary a manufacturer publishes for a UV reactor and identify which operating conditions the validated dose depends on. Students can also compare what an operator must monitor for ultraviolet disinfection against what the same operator monitors for chlorine, and write a short shift checklist for each process.