What is the Streeter-Phelps Oxygen Sag Model?

The Streeter-Phelps equation is a fundamental mathematical model used in environmental engineering and water quality management to describe the dissolved oxygen (DO) profile in a river or stream. Originally developed by Harold Warner Streeter and Earle Bernard Phelps in 1925, the model predicts how the concentration of dissolved oxygen changes over time or distance after a point source of organic pollution (like sewage effluent) is introduced into a water body.

When organic waste enters a stream, aerobic bacteria begin to decompose it, consuming oxygen in the process. This is known as deoxygenation. Simultaneously, the stream absorbs oxygen from the atmosphere to replenish what is lost, a process called reaeration. The Streeter-Phelps equation calculates the net effect of these two competing processes, resulting in the characteristic "Oxygen Sag Curve."

How to Use This Calculator

To use the Streeter-Phelps Oxygen Sag Calculator, you need to input several key parameters describing the state of the river and the waste load:

• Saturation DO (Cs): The maximum amount of oxygen the water can hold at its current temperature.
• Initial DO (C₀): The actual dissolved oxygen concentration in the water immediately after mixing with the waste.
• Initial BOD (L₀): The ultimate Biochemical Oxygen Demand of the river water after mixing.
• Deoxygenation Rate (k₁): The rate constant at which bacteria consume oxygen.
• Reaeration Rate (k₂): The rate constant at which oxygen is transferred from the air into the water.
• Time (t): The travel time downstream from the point of discharge.

Understanding the Oxygen Sag Curve

The oxygen sag curve represents the health of an aquatic ecosystem. If the "sag" or the minimum point of dissolved oxygen (the critical point) drops too low, aquatic life such as fish and insects can suffer from hypoxia or death. Environmental engineers use this model to determine the "assimilative capacity" of a river—how much waste it can handle without violating water quality standards.

Frequently Asked Questions (FAQs)

Q: Why does the reaeration rate change?
A: Reaeration rates depend on the turbulence, surface area, and velocity of the river. Fast-moving, shallow, rocky streams have much higher k₂ values than slow-moving, deep rivers.

Q: What is the Critical Point?
A: The critical point is the location (or time) where the dissolved oxygen concentration reaches its absolute minimum. This is the most dangerous zone for fish survival.

Q: Does temperature affect the calculation?
A: Yes. Both k₁ and k₂ are temperature-dependent. Higher temperatures generally increase the deoxygenation rate and decrease oxygen saturation levels, making the sag more severe in summer.