Total Dissolved Gas Methodology
Total Dissolved Gas Modeling consists of two components, A simulation method that computes the TDG concentrations in the reservoir. It also 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 the specifics of the methods, but does not outline how to use this approach. That 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.
The following sections describe these new methods.
Outflow TDG using Tailwater DepthThe method is only available if one of the “Regulated...” spill methods is selected. It is not available for the None method, 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.
Links: Not Linkable
Inflow TDG Concentration
Type: Series
Units: Fraction
Description: This slot contains the inflow TDG concentration
I/O: Output or required input
Links: Linkable to upstream object’s Outflow TDG Concentration
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.
Links: Not Linkable
Tailwater Bottom Elevation
Type: Scalar
Units: Length
Description: The 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
Links: Not linkable
TDG c1
Type: Scalar
Units: Fraction
Description: This scalar slot contains the constant in the TDG equation when Spill is zero.
I/O: Required Input
Links: Not Linkable
TDG Entrainment b1
Type: Scalar
Units: None
Description: The value in this scalar slot represents the fraction of Spill which 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: The value in this scalar slot represents the constant of Spill which 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
Links: Not Linkable
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.
Links: Not Linkable
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: 11/11/2019