Question

Explain why removal rates of both conservative and non-conservative substances in natural water bodies is assumed to follow first-order decay rate kinetics. Indicate the risks posed by the over-reliance on the first-order kinetic model in a broad range of scenarios.

Answer 1

Pollutants are classified into various categories. Two pollutant categories are conservative and non-conservative reflecting the rate they are transformed or degraded within the environment.

• Conservative Pollutants – Pollutants that are not normally physically or chemically transformed to non-toxic substances in the receiving water. These include, but are not limited to, salts and metals.
• Non-Conservative Pollutants – Pollutants that are transformed to non-toxic substances through physical, chemical, or biological processes in the receiving water. These include biochemical oxygen demand, ammonia, and certain other organic compounds.

Conservative pollutants tend to be stable, long-lived compounds that persist within the environment. Non-conservative pollutants can transform or degrade into other compounds, but the rate of transformation depends on the physical, chemical, and biological conditions occurring within the receiving water environment. Now these reaction are assumed to be first order because experimentally it has been observed that concentration of these substance in water bodies decrease exponentially .

Often the reaction rate is due to biological degradation also known as a decay rate. The decay rate is often modeled as a first order reaction, which means that the amount that decays is proportional to the amount present at any time. In other words:

                C_t = [C₀]*e^-[k*t]

Therefore for a steady state non-conservative pollutant, the equation needs and additional term to account for the decay as follows:

                Decay rate = -[k*C*V]

                k = reaction rate
                C = concentration at time
                V = volume of the system modeled