treatment

Removal of pollutants from the flow streams entering any drainage system node is modeled by assigning a set of treatment functions to the node. A treatment function can be any well-formed mathematical expression involving:

·       The pollutant concentration of the mixture of all flow streams entering the node (use the pollutant name to represent a concentration)

·       The removals of other pollutants (user_ prefixed to the pollutant name to represent removal)

·       Any of the following process variables:

1.      FLOW for flow rate into node (in user-defined flow units)
2.      DEPTH for water depth above node invert (ft or m)
3.      AREA for node surface area (ft² or m²)
4.     DT for routing time step (sec)
5.     HRT for hydraulic residence time (hours)

·       Any of the following math functions (which are case sensitive) can be used in a treatment expression:

1.         abs(x) for absolute value of x
2.         sgn(x) which is +1 for x >=0 or -1 otherwise
3.         step(x) which is 0 for x <=0 and 1 otherwise
4.         sqrt(x) for the square root of x
5.         log(x) for logarithm base e of x
6.         log10(x) for logarithm base 10 of x
7.         exp(x) for e raised to the x power
8.         the standard trig functions (sin, cos, tan, and cot)
9.         the inverse trig function (asin, acos, atan, and acot)
10.         the hyperbolic trig functions (sinh, cosh, tanh, and coth) along with the standard operators +, -, *, /, ^ (for exponentiation) and any level of nested parentheses.

The result of the treatment function can be either a concentration (denoted by the letter C) or a fractional removal (denoted by R). For example, a first-order decay expression for BOD exiting from a storage node might be expressed as:

C = BOD x exp (-0.05 x HRT)

Or, the removal of some trace pollutant that is proportional to the removal of total suspended solids (TSS) could be expressed as:

R = 0.75 x R_TSS

Care must be taken to avoid circular references when specifying treatment functions. For example, the above expression would not be computable if it were used to compute fractional removal of TSS.