Nonconservative Point Source Discharge Effect on Water Quality
If we discharge a nonconservative substance (pollutant) into a river or stream, the
substance will decay with time. This is due to chemical reactions, bacterial degradation,
radioactive decay, or the settling of particulates out of the water column. Settling of
pollutants causes another problem, resuspension due to variation of velocities and mixing
conditions, but will no be discussed here. Some substances that are considered to be
nonconservative are;
- Oxidizable organic material
- Nutrients (P, K, C, N, S, Etc.)
- Volatile Chemicals
- Bacteria
The first assumption that must be made is that the substance decays according to a
first order reaction. This means that the rate of loss of the substance is proportional
to the concentration at any time. The mass balance equation, at steady state, is a
first-order linear differential equation (O'Conner, 1967):
where K id the decay rate of the substance
By assuming steady state (dQ/dx = 0) and a uniform cross sectional area (dA/dx = 0), then:
By setting the boundary conditions as s = so and x = 0, where So is the concentration determined
by a mass balance around the discharge. The solution then becomes:
where:
S = Substance concentration x feet downstream
So = Initial concentration at the discharge
K = Decay rate of substance
x = Downstream location of interest, ft
U = velocity, fps