General Constituent Simulation Module

The General Constituent Simulation Module (GCSM) computes the kinetics of a generalized constituent in the water column. It can be used to model conservative tracers, coliform bacteria, and reactive particles. The GCSM simulates four processes for any user-defined constituent:

zero-order decay,
first-order decay,
sediment release, and
settling loss.

In HEC-ResSim, users may define as many generalized constituents as needed (up to 100), each with unique rate coefficients. However, the GCSM does not consider interactions among constituents; each constituent is considered in isolation.

The differential constituent rate equation is expressed as:

$\begin{array}{l}\displaystyle \frac{dC}{dt} = \frac{k_{sed}(T_w)}{h} - k_0(T_w) - k_1(T_w) C + v_s \frac{\partial C}{\partial z}\end{array}$

where

$\begin{array}{l}C\end{array}$ is the concentration of the general constituent (mg/L),
$\begin{array}{l}k_{sed}\end{array}$ is a sediment release rate (g/m²/day),
$\begin{array}{l}k_0\end{array}$ is a zero-order decay rate coefficient (mg/L/day),
$\begin{array}{l}k_1\end{array}$ is a first-order decay rate coefficient (1/day),
$\begin{array}{l}v_s\end{array}$ is a settling rate (m/day),
$\begin{array}{l}h\end{array}$ is a water quality cell depth or layer thickness (m), and
$\begin{array}{l}T_w\end{array}$ is the water temperature (°C).

The zero- and first-order decay rates and the sediment release rates are temperature dependent. The rate coefficients are corrected for temperature using a modified Arrhenius Equation (Fogler, 2005):

$\begin{array}{l}\displaystyle k(T_w) = k(20)\theta^{T_w - 20}\end{array}$

where

$\begin{array}{l}k(T_w)\end{array}$ is the kinetic rate at the water temperature,
$\begin{array}{l}k(20)\end{array}$ is the kinetic rate at 20°C, and
$\begin{array}{l}\theta\end{array}$ is the temperature correction coefficient (unitless).

The temperature coefficient ( $\begin{array}{l}\theta\end{array}$ ) typically ranges between 1.01 and 1.10.

Constituent settling from the surface layer of the water column is dependent only on the concentration in that top layer ( $\begin{array}{l}i_{sfc}\end{array}$ ):

$\begin{array}{l}\displaystyle v_s \frac{\partial C}{\partial z} = -v_s \frac{C_{i_{sfc}}}{h_{i_{sfc}}}\end{array}$

For layers within the water column, settling fluxes depend on the vertical gradient of the constituent:

$\begin{array}{l}\displaystyle v_s \frac{\partial C}{\partial z} = v_s \frac{C_{i+1} - C_i}{h_i}\end{array}$

Sediment releases ( $\begin{array}{l}k_{sed}/h\end{array}$ ) are computed based on the area of water quality cell in contact with the sediment. For river reach cells, the area is equal to the wetted cell surface area. For reservoir water quality cells (layers), the area is the difference between the layer's surface area and the surface area of the layer immediately below it.