Lecture Support for Lab 2. Loads
Mass Balance for Total Phosphorus in a Completely-MixedLake
Let’s begin with the basic mass balance for A CMFR,
First, let’s make this equation specific to phosphorus,
and then replace the inflow term with a more generic loading term,
What about kinetics? For total phosphorus, there is only loss to settling. It is parameterized by replacing the V∙k∙P term by the dimensionally identical,
where v is the settling velocity (m∙d-1) and As is the lake surface area. Setting the two terms equal to each shows the relationship between settling velocity and a first order loss coefficient due to settling,
which reduces to
Thus, we end up with a mass balance expression,
Thus, given the appropriate inputs and coefficients, this equation can be solved numerically to yield P = f(t).
Types of Loads
Point source: inputs that can be traced back to a single origin or source such as a wastewater treatment plant discharge. Because such discharges are typically operated under permit, point source loads are often well characterized. The load is quantified as the product of measured effluent flow and concentration with the load expressed as mass per time.
Nonpoint source: inputs originating from diffuse sources such as agricultural runoff. These loads are difficult to quantify due to their non-specific origin. Nonpoint loads (mass per time) are often estimated as the product of unit area loads (UALs; g∙ha-1∙d-1) and the land area associated with a particular land use and soil type or texture (hectares of high till cropland on fine, steeply sloped soils).
Atmosphere: this is an important source for some pollutants, especially synthetic organic chemicals. Atmospheric loads (mass per time) are calculated as the product of a measured flux (g∙m-2∙d-1) and the surface area of the lake (m2).
Sediments: a wide variety of pollutants (organic matter, nutrients, metals, synthetic organic chemicals) accumulate in lake sediments. They can be released back into the water creating an ‘internal’ load. The sediment contribution is typically measured directly (experiments with intact cores) or inferred from hypolimnetic accumulation rates. The sediment load (mass per time) is calculated as the product of sediment release rates (g∙m-2∙d-1) and the surface area of the lake (m2).
Characterizing Tributary Loads – The C/Q Relationship
Where a tributary load is calculated as the product of the concentration (C) and flow (Q), it is typically the case that we have much more detailed information on flow than we do on concentration. Missing “C” values can be determined through a C/Q plot, developed based on existing data or that collected through a special study.
[.ppt] Example C/Q plots.