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Water Quality : Reservoir Water Quality : Utility Methods : Total Dissolved Gas Methodology
Total Dissolved Gas Methodology
Total Dissolved Gas modeling is a simulation method that does the following:
• Computes the TDG concentrations in the reservoir.
• Computes partial derivatives that are used in subsequent optimization runs. Within Optimization, constraints are generated and the user can write policy to limit the change in deltas.
This section describes the mathematical formulation and specifics of the methods used in this approach. It does not outline how to use the approach, however, which is beyond the scope of this document. Contact CADSWES for more information.
Note:  TDG concentration is typically reported as the TDG saturation percentage. So a TDG of 115 is 115% of saturation. Some literature uses a decimal, 1.15, some use a percentage 115%. As a result, in RiverWare, all TDG concentrations use the FRACTION unit type. Then the user can choose to see values in either of the two user units: decimal or percent.
* Outflow TDG using Tailwater Depth
This method is available only if one of the “Regulated...” spill methods is selected. It is not available for the None, Monthly Spill, or Unregulated Spill methods
Slots Specific to This Method
 Entrained Flow
Type: Series
Units: FLOW
Description: Entrained Flow is the portion of the Turbine Release that has air from the spillways entrained in it. In the tailrace, there are surface deflectors that attempt to move the spill horizontally and keep it from plunging into the tailrace. These deflectors attract water from the turbine release due to the increased velocity. This portion of the turbine release is then entrained with air from the spillways and has the TDG concentration of the spill. This value is nonnegative.
Information: This slot is computed based on the equation .
I/O: Output only.
 Inflow TDG Concentration
Type: Series
Units: Fraction
Description: This slot contains the inflow TDG concentration
I/O: Output or required input
 Outflow TDG Concentration
Type: Series
Units: Fraction
Description: This slot shows the resulting Outflow TDG Concentration. The values can then be compared to the values in the Outflow TDG Concentration Estimate. Once the TDG solution has converged the values in this slot should be equal to the values in the Outflow TDG Concentration Estimate slot at all time steps (within a tolerance)
 Spill TDG Concentration
Type: Series
Units: Fraction
Description: This slot shows the resulting Spill TDG Concentration.
 Tailwater Bottom Elevation
Type: Scalar
Units: Length
Description: Elevation at the bottom of the tailrace.
Information: The value in this slot is used in the TDGS computation to get the depth of tailwater.
I/O: Required input
 TDG c1
Type: Scalar
Units: Fraction
Description: Contains the constant in the TDG equation when Spill is zero.
I/O: Required input
 TDG Entrainment b1
Type: Scalar
Units: None
Description: Fraction of Spill that can be entrained. A portion of the Turbine Release up to this amount will have the same TDG concentration as the Spill.
I/O: Required input
 TDG Entrainment b3
Type: Scalar
Units: Flow
Description: Constant of Spill that can be entrained. A portion of the Turbine Release up to this amount will have the same TDG concentration as the Spill.
I/O: Required input
 TDG Spill b2
Type: Scalar
Units: PerLengthTime
Description: This scalar slot contains the coefficient in the Spill TDG Concentration equation.
Note:  This unit type may need to be added.
I/O: Required input
 Turbine Release TDG Concentration
Type: Series
Units: Fraction
Description: This slot shows the resulting Turbine TDG Concentration. This is sometimes called the forebay concentration or the reservoir concentration.
 Spill and Turbine Release Limit
Type: Scalar
Units: Flow
Description: Lower bound for which spill and turbine release will be treated the same as higher flows. Below this flow limit, the computations will be modified.
I/O: Required input
Method Details  
The method is executed by the two water quality dispatch methods.
First, some notation:
TDGS = Spill TDG Concentration
TDGT = Turbine Release TDG Concentration, concentration just above the dam.
TDGO = Outflow TDG Concentration
TDGI = Inflow TDG Concentration (linked to upstream reservoir’s TDGO
Qsm = Spill and Turbine Release Limit (calculations are changed for small flows)
Compute the TDGs:
TW is Tailwater Elevation.
TW0 is the elevation at the bottom of the tailrace, a project constant (scalar length).
is the density of water, a global constant. (internal, 999.7kg/m3)
g is the gravitation constant. (internal, 9.81m/s^2)
patm is the atmospheric pressure. (internal, 101325kg/(m*s)^2)
b2 is a project constant, TDG Entrainment b2, (1 / Length-Time).
Get the TDGT. This is the same as the TDGI which may be linked to an upstream reach that lags the TDG concentration by some number of timesteps.
Compute the Entrained Flow, QE:
QS = Spill
QT = Turbine Release
b1, TDG Entrainment b1, and b3, TDG Entrainment b3, are scalar constants for each project.
The final computation is to compute the TDGO. This is the mixed outflow concentration which could also be called the tailwater concentration.
If QT + QS = 0
c1 is a constant for each reservoir in fraction units.
Else
To provide continuity with the concentration when outflow is zero, the concentration is adjusted when outflow is small.
If c1 >= 0
    
Else If QS < Qsm
    
End If
Revised: 08/02/2021