Water Quality Engineering: BOD Kinetics and Streeter–Phelps DO Sag

What does BOD stand for?

Biochemical Oxygen Demand.

Define biochemical oxygen demand (BOD).

The amount of oxygen consumed by bacteria and other microorganisms as they decompose organic matter under aerobic conditions at a specified temperature.

Why is dissolved oxygen (DO) important?

It is critical to aquatic life and water quality.

What does a high BOD indicate?

More oxygen-demanding material in the water, which can lower dissolved oxygen and indicate poorer water quality.

What BOD level is preferable for healthy water?

Low BOD.

What is ultimate BOD (L₀)?

The maximum oxygen consumption possible to completely degrade the waste; initial BOD remaining at time zero.

What does Lₜ represent?

BOD (oxygen demand) remaining at time t, in mg/L.

What does yₜ or BODₜ represent?

Oxygen consumed or BOD exerted by time t, in mg/L.

How do you calculate BOD remaining using base e?

Lₜ = L₀ e^(−kt), with k in day⁻¹ and t in days.

How do you calculate oxygen consumed from remaining BOD?

yₜ = L₀ − Lₜ.

How do you calculate BOD exerted using base e?

BODₜ = L₀[1 − e^(−kt)].

How do you calculate BOD exerted using base 10?

BODₜ = L₀[1 − 10^(−Kt)].

How are the base-e and base-10 rate constants related?

k (base e) = 2.303 × K (base 10).

What are the units for L₀, Lₜ, and BODₜ?

mg/L.

What are the units for time and the BOD rate constant?

Time t: days. Rate constants k or K: day⁻¹.

As time increases, what happens to Lₜ?

Lₜ (BOD remaining) decreases.

As time increases, what happens to BOD exerted?

BOD exerted increases toward ultimate BOD L₀.

What does BOD₅ mean?

The BOD exerted over a standard 5-day incubation at 20°C; it is a portion of ultimate BOD.

What duration and temperature are used for the standard BOD test?

5 days at 20°C.

According to the lecture, approximately when is biochemical oxidation complete?

After about 20 days (as stated in the slides).

What three factors does BOD depend on?

Nature of the waste; ability of microorganisms to utilize the waste; temperature.

How does the nature of the waste influence BOD decay?

Different organic compounds degrade at different rates, represented by the BOD rate constant.

Why does the microbial population matter for BOD?

Some organic compounds can be degraded by only a small group of microorganisms.

How does increasing temperature affect biological activity?

Biological processes generally speed up as temperature increases.

Why are BOD rate constants commonly standardized to 20°C?

Testing at every receiving-water temperature is impractical; use a 20°C standard and adjust the rate constant.

What equation adjusts the BOD rate constant for temperature?

k_T = k₂₀ θ^(T − 20).

What does k₂₀ mean?

BOD rate constant at 20°C.

What does θ represent?

Temperature coefficient used to adjust the BOD rate constant.

What θ value is used for 4°C < T < 20°C?

θ = 1.135.

What θ value is used for 20°C < T < 30°C?

θ = 1.056.

What is the DO sag curve?

A downstream pattern where dissolved oxygen falls near a waste discharge and then rises as the stream recovers.

What is another name associated with the DO sag curve?

Streeter-Phelps DO sag curve/equation.

What is a stream DO sag curve used to assess?

The stream's ability to absorb a waste load and the associated DO response.

What is the critical point on a DO sag curve?

The time/location of minimum dissolved oxygen (maximum DO deficit).

What is dissolved oxygen deficit D?

D = DO_sat − DO, where DO_sat is the saturation concentration.

How can actual dissolved oxygen be calculated from deficit?

DO = DO_sat − D.

What are k₁ and k₂ in Streeter-Phelps modeling?

k₁ is the deoxygenation rate constant, and k₂ is the reaeration rate constant (base e, day⁻¹).

What does D₀ represent in the Streeter-Phelps equation?

Initial dissolved oxygen deficit in the mixing zone (mg/L).

What does Lₐ represent in the Streeter-Phelps equation?

Initial ultimate BOD in the mixing zone (mg/L).

What does t_c represent in Streeter-Phelps modeling?

Time at which minimum dissolved oxygen occurs (days).

How is the mixed DO concentration calculated from two flows?

DO_mix = (Q_w DO_w + Q_r DO_r)/(Q_w + Q_r).

How is mixed ultimate BOD calculated from two flows?

L_mix = (Q_w L_w + Q_r L_r)/(Q_w + Q_r).

Convert 17,360 m³/day into m³/s.

17,360 ÷ 86,400 ≈ 0.20 m³/s.

For the slide example, what is DO after mixing 0.20 m³/s at 1.0 mg/L with 0.43 m³/s at 6.5 mg/L?

(0.20×1.0 + 0.43×6.5)/(0.20+0.43) ≈ 4.75 mg/L.

For the slide example, what is k at 10°C if k₂₀ = 0.12 day⁻¹?

k₁₀ = 0.12(1.135)^(10−20) ≈ 0.0338 day⁻¹.

For the slide example, if BOD₅ = 12 mg/L at 10°C and k₁₀ ≈ 0.0338 day⁻¹, what is ultimate BOD?

L₀ = 12/[1 − e^(−0.0338×5)] ≈ 77.12 mg/L.

For the slide example, what is the mixed ultimate BOD using L_w = 77.12 mg/L and L_r = 5 mg/L?

(0.20×77.12 + 0.43×5)/0.63 ≈ 27.90 mg/L (about 28 mg/L).

For the 10°C river example, what fraction of ultimate BOD is exerted after 4 days if k₂₀ = 0.115 day⁻¹?

k₁₀ ≈ 0.032 day⁻¹; BOD₄/L₀ = 1 − e^(−0.032×4) ≈ 0.12 (12%).

What inconsistency appears in the slides' early ultimate-BOD example?

The question slide gives BOD₃ = 70 mg/L, but the solution slide uses 75 mg/L; the stated 116 mg/L result corresponds to 75 mg/L.