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Lesson plan Grade 11 Careers & CTE

Writing Vardenmill's Discharge Permit for Ockridge Creek

A 60-minute grade 11 careers lesson in which students act as a state permit writer, converting effluent limits to loads and testing them against a creek at low flow.

Objectives

  1. Students will convert effluent concentrations into daily mass loads using the pounds formula.
  2. Students will calculate the mixed dissolved oxygen of a creek receiving a treated discharge at summer low flow.
  3. Students will evaluate whether post aeration is needed and explain why a permit carries both concentration and mass limits.

Vocabulary

Effluent
Effluent is the cleaned water that leaves a treatment plant at the end of the process. It is tested carefully before being released to a river, lake, or the ocean.
Dissolved oxygen
Dissolved oxygen is the oxygen gas mixed into water that fish and other underwater animals breathe. Cold, moving water holds more oxygen than warm, still water.

Also: mass load, low flow, post aeration

Teacher overview

A discharge permit runs only a few pages, yet it can take months to write, because every number in it has to hold up against challenges from the plant and from the communities downstream. The permit writer's job is to translate a stream's capacity into limits a plant can be held to. This lesson puts students in a state agency office reviewing an expansion request from the fictional town of Vardenmill, whose plant discharges to the fictional Ockridge Creek. The misconception the lesson corrects is the assumption that meeting a concentration limit is enough; a plant that doubles its flow while holding the same concentration doubles the pounds it sends downstream, which is why permits carry a mass limit alongside the concentration limit.

Procedure

Hook (5 min): Tell students the fictional Vardenmill plant currently meets every number in its permit and wants to expand from 1.8 to 2.6 million gallons per day at the same effluent quality. Ask whether the state should simply reissue the same permit. Record the split before any calculation, then tell the class they will settle it with the creek's own numbers.

Direct instruction (14 min): Introduce the pounds formula: pounds per day equals concentration in milligrams per liter times flow in million gallons per day times 8.34. Work one example on the board using a plant not on the handout, at 25 milligrams per liter and 1.0 million gallons per day, giving 208.5 pounds per day, and have students identify where the 8.34 comes from. Then introduce mixing. Explain that when a discharge enters a stream, the downstream concentration of a conservative parameter is the flow-weighted average of the two streams, and write that as the sum of each flow times its concentration, divided by the total flow. Note that summer low flow is the design condition because that is when the creek has the least water to dilute with and the least oxygen to spare.

Guided practice (14 min): Distribute the handout. Work items 1 through 4 together. Formative check: after item 3, ask for a show of hands on whether a removal efficiency above 90 percent guarantees the plant meets its permit. Do not move on until most of the class can say that removal efficiency describes the plant's performance while the permit limit is set on the effluent value itself, so a very dirty influent can produce high removal and still fail.

Independent work (20 min): Students complete items 5 through 10 in pairs. Circulate and watch for two errors. The first is averaging the two dissolved oxygen values without weighting by flow. The second is converting the plant's flow to cubic feet per second only after mixing rather than before, which leaves the two flows in different units.

Closure and exit ticket (7 min): Ask one pair to state the mixed oxygen with and without post aeration and to name which one clears the level most fish need. Then collect a one-sentence exit response: state one condition, other than plant flow, that would make the permit writer set a stricter limit. Expect answers naming lower creek flow, warmer water, an additional upstream discharge, or a drinking water intake below the outfall.

Writing Vardenmill's Discharge Permit for Ockridge Creek — Grade 11 Careers & CTE
Name: ____________________________ Date: ______________

Student Handout

The fictional town of Vardenmill operates a wastewater plant that discharges to the fictional Ockridge Creek. Use the pounds formula, which is pounds per day equals concentration in milligrams per liter times flow in million gallons per day times 8.34. Use the conversion that one million gallons per day equals 1.547 cubic feet per second. Federal secondary treatment standards set a monthly average effluent limit of 30 milligrams per liter for biochemical oxygen demand. Most fish need dissolved oxygen above 5 milligrams per liter.

Current plant conditions: flow 1.8 million gallons per day, influent BOD 240 milligrams per liter, effluent BOD 22 milligrams per liter. Proposed expansion: flow 2.6 million gallons per day at the same effluent quality.

Creek conditions used for the permit: summer low flow upstream is 2.5 cubic feet per second carrying dissolved oxygen of 8.6 milligrams per liter. The plant's effluent leaves the final clarifier at a dissolved oxygen of 2.0 milligrams per liter unless post aeration is added, which would raise it to 6.5 milligrams per liter.

  1. Find the influent BOD load at the current flow, in pounds per day.
  2. Find the effluent BOD load at the current flow, in pounds per day. Round to the nearest tenth.
  3. Find the plant's BOD removal efficiency as a percent, using removal equals influent minus effluent, divided by influent, times 100. Round to the nearest tenth.
  4. Find the mass limit the 30 milligrams per liter secondary standard implies at the current flow of 1.8 million gallons per day, in pounds per day. Round to the nearest tenth.
  5. Suppose the permit writer holds the mass limit from item 4 constant through the expansion to 2.6 million gallons per day. Find the effluent concentration limit, in milligrams per liter, that this mass limit would imply at the higher flow. Round to the nearest tenth.
  6. Convert the proposed plant flow of 2.6 million gallons per day to cubic feet per second. Round to the nearest hundredth.
  7. At summer low flow, find the dissolved oxygen of the mixed creek downstream of the outfall, using the upstream flow and oxygen, your effluent flow from item 6, and an effluent oxygen of 2.0 milligrams per liter. Round to the nearest hundredth.
  8. Repeat item 7 with post aeration raising the effluent oxygen to 6.5 milligrams per liter. Round to the nearest hundredth.
  9. Compare your answers from items 7 and 8 against the 5 milligrams per liter most fish need, and state which condition meets it.
  10. Explain in three or four sentences why the permit writer sets both a concentration limit and a mass limit, using the difference between item 4 and item 5 as your evidence.

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: 3,602.88 pounds per day.
    240 milligrams per liter times 1.8 million gallons per day times 8.34 equals 3,602.88 pounds per day. First 240 times 1.8 equals 432, then 432 times 8.34 equals 3,602.88.
  2. Answer: 330.3 pounds per day.
    22 times 1.8 equals 39.6, and 39.6 times 8.34 equals 330.264, which rounds to 330.3 pounds per day.
  3. Answer: 90.8 percent.
    Influent minus effluent is 240 minus 22, or 218. Then 218 divided by 240 equals 0.90833, which is 90.8 percent.
  4. Answer: 450.4 pounds per day.
    30 milligrams per liter times 1.8 million gallons per day times 8.34 equals 450.36 pounds per day, which rounds to 450.4.
  5. Answer: 20.8 milligrams per liter.
    At the expanded flow, one milligram per liter is worth 2.6 times 8.34, or 21.684 pounds per day. Dividing the 450.36 pound per day cap by 21.684 gives 20.77, which rounds to 20.8 milligrams per liter. Holding the mass cap forces a stricter concentration than the 30 milligrams per liter the plant is allowed today.
  6. Answer: 4.02 cubic feet per second.
    2.6 million gallons per day times 1.547 cubic feet per second per million gallons per day equals 4.0222, which rounds to 4.02 cubic feet per second.
  7. Answer: 4.53 milligrams per liter.
    The upstream contribution is 2.5 times 8.6, or 21.5. The effluent contribution is 4.02 times 2.0, or 8.04. The total flow is 2.5 plus 4.02, or 6.52 cubic feet per second. Then 21.5 plus 8.04 equals 29.54, and 29.54 divided by 6.52 equals 4.5307, which rounds to 4.53 milligrams per liter.
  8. Answer: 7.31 milligrams per liter.
    The effluent contribution becomes 4.02 times 6.5, or 26.13. Then 21.5 plus 26.13 equals 47.63, and 47.63 divided by 6.52 equals 7.3052, which rounds to 7.31 milligrams per liter.
  9. Answer: Only the post-aerated condition meets the 5 milligrams per liter level.
    Without post aeration the mixed creek sits at 4.53 milligrams per liter, which is 0.47 below what most fish need. With post aeration it rises to 7.31 milligrams per liter, comfortably above. Note that at low flow the plant is contributing more water to the creek than the creek carries on its own, which is why the effluent's oxygen dominates the mixed result.
  10. Answer: The concentration limit controls what leaves the plant, while the mass limit controls what the creek receives.
    Item 4 shows the current permit allowing 450.4 pounds per day at 30 milligrams per liter. Item 5 shows that holding that load at 2.6 million gallons per day requires 20.8 milligrams per liter; if the plant stayed at 30 milligrams per liter, it would send roughly 650 pounds per day to the same creek, because the flow grew by nearly half. A concentration limit alone would let a plant grow its load indefinitely by growing its flow, and a mass limit alone would let a plant discharge poorly treated, high-concentration effluent whenever its flow is low enough to stay under the pound cap. Together the two numbers hold both the treatment quality and the total pollutant delivered to the creek.

Differentiation

Support

Give students a completed pounds formula example for the fictional plant at a third concentration, and provide the two flow-weighted contributions for item 7 already set up as products so the calculation reduces to adding and dividing. Supply a labeled sketch of the fictional creek showing upstream flow, the outfall, and the mixed reach.

Extension

Ask students to find the effluent dissolved oxygen the fictional plant would need in order to hold the mixed creek at exactly 6.0 milligrams per liter at summer low flow, then judge whether that is achievable with post aeration alone.

ELL supports

Pre-teach "effluent," "load," "low flow," and "post aeration" with a labeled flow diagram of the fictional plant and creek, marking where each number in the handout is measured. Provide the sentence frame "The mixed oxygen is ___ because most of the flow at low flow comes from ___" for item 9.

Extensions

Have students draft the three sentences of permit language that would carry their recommended limits, then trade drafts and mark any wording a plant operator could reasonably read two ways.