Component Balance Analysis Rule Methodology

The Component Balance Analysis Rule is used to analyze Cases of mass and component balancing for Sigmafine models. The Cases store the reconciled values for the measured flows and material storage inventories, as well as reconciled values by component for these elements.

When doing a component balance, Sigmafine uses a weighted least squares algorithm and two types of constraints; 'linear' and 'non-linear'. The 'linear' restrictions are satisfied without iteration, while the 'non-linear' restrictions require iterations over the reconciled values to find the solution that satisfies this constraint. In these calculations, the following assumptions are made:

• There are no losses from any balance point in the model. Everything that leaves the balance point exits through a flow. Therefore, the flowing condition defined by the following equation is met.

  

  There are no component losses from any balance point also, which is defined by the following equation.

  

  Where:

  CxIn : Is each component fraction into the balance point.

  CxOut : Is each component fraction out of the balance point.

  CxI : Is the initial inventory component fraction

  Cxf : Is the ending inventory component fraction

  The meter readings are approximately correct.

• A zero flow is defined to exist when no flow occurs between vessels.

The component mass balance involves distributing all the errors in proportion to the confidences on the measurements. This is done in such a way that all the balances are satisfied precisely, yet the total sum of perturbations to each instrument is minimized. The sum is the squared deviation normalized by the confidence on that measurement, as given. Mathematically, this becomes a large "sum-of-error-squared" problem, with the addition of constraints. The constraints include those listed above, plus the assumption that there is sufficient measurement redundancy and solvability available to solve the model.