Energy Balance Rule Methodology

Use the Energy Balance Analysis Rule to do reconciliation Cases for Models based on the Sigmafine templates. The Cases store the reconciled values for the measured flows and material storage inventories.

The calculations Sigmafine uses when performing a mass balance are a weighted least squares algorithm. In this calculation, these basic assumptions are made.

• There are no quantity losses from any balance point in the Model that leaves the point via a flow. Therefore the flowing condition defined by the following equation is met.
• The meter readings are approximately correct.
• A zero flow is defined to exist when no flow occurs between vessels.

Additionally, the Energy Balance provides an energy balance across nodes that specify it. All balance objects allow an energy balance, with the exception of inventory elements. The following are the basic assumptions for energy balance:

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

  Where, Hin and Hout are specific energy.

The energy 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.