Calculate Statistics - Balance Variance
The Balance Variance, or uncertainty around a balance point (Process, Node or Inventory element) within a Model is used in the calculations of the test factors Test3 and Test4. This variance can be used to determine the confidence on the values shown in any area in the model. The variance is defined by the following equations. These equations are the same, regardless of the type of analysis.
Where:
n = number of measurements
Qi \= inlet flow
Ti = inlet absolute tolerance
Qo \= outlet flow
To = outlet absolute tolerance
Eit \= overall uncertainty on inlet flow as %
Eot \= overall uncertainty on outlet flow as %
Ei \= uncertainty on inlet flow as % - relative tolerance
Eo \= uncertainty on outlet flow as % - relative tolerance
Eu \= overall node uncertainty as %.
The solver uses terms of absolute tolerances, and reports an absolute uncertainty around the balance point rather than a relative one. Consider the following equation.
Where:
E = any relative tolerance
T = any absolute tolerance
Q = any flow
You can rearrange the equations listed on the previous page to derive the form actually used by the reconciliation solver. For example, consider these equations, with the same terms used previously.
This rearrangement is made for computational reasons only, and does not change the value of Eu. The absolute uncertainty Euabs is reported and defined by the following equation.
Variance for Component Balances ONLY
This section applies only to the Component Mass Balance Analysis.
Component variance is based on the definition of mass balance variance and is derived by substituting the component material masses Qifk and Qofk for the direct total mass flows. The tolerance term used is then defined in terms of the absolute tolerances of the mass flow and fraction terms as shown below.
Where:
Ec \= uncertainty on component flow in % relative tolerance
Tmf \= absolute tolerance on mass flow
Qmf \= mass flow
Tk \= absolute tolerance on component fraction k
Fk \= fraction of component k.