Test3

Use Test3 to identify significant quantity imbalances for a Balance Analysis, and mass imbalances for a Mass Balance Analysis. It applies to all balance point elements (inventory, nodes, and processes). In the Test3 equation, shown below, any imbalances in the measured data are deduced by dividing the balance error by the balance variance. If the result exceeds the absolute value of 1.0, then the imbalance condition is greater than expected, at the 95% confidence level (Section "Measurement Confidence Interval").

A process balance constraint is represented by this equation.

Where:

x1r and x2r = values of reconciled measured variables

x3u \= an unmeasured variable.

Where:

balerr = imbalance in measured data.

balvar = balance variance, calculated using the equations described earlier.

T = number of standard deviations for the instrument tolerance. You set this value in the Tolerance box in the Sigmafine Balance Configuration window.

ArcErf = inverse normal error distribution function.

ZT \= the number of standard deviations corresponding to the required level of confidence. You set this value in the Confidence box in the Sigmafine Balance Configuration window. For 95% level of confidence, ZT = 2.0.

The following equation is an approximation for Test3.

Note:

Imbalance is expressed by the following equation

0 = Sum flows in - Sum flows out - delta inventory

• When the total flows entering the balance point are greater than the total leaving, the imbalance and the Test3 value are positive.
• When the total flows entering the balance point are less than the total leaving, the imbalance and the Test3 value are negative.