Variable classification and reduced balance generation

The computational effort can be minimized if a reduced set of balance equations can be obtained from the set of potential balance points, such that reduced set involves no unmeasured flow but a maximum number of measured flows. The remaining measured flows are reconciled, and the unmeasured flows can then be derived from the solution of the material balance equations.

Matrix project method

AVEVA Production Accounting uses the matrix project method to get the reduced balance set containing only redundant flows. This method is based on the use of a projection matrix which can be directly constructed and which effectively blanks out the unmeasured flows in producing the reduced set of balances.

AVEVA Production Accounting bases its matrix on the set of balance envelopes which can be constructed. A balance envelope may correspond to a balance point or a set of balance points for which all input and output flows are known. The fact that the number of balance envelopes is smaller than the number of balance points is a key factor in reducing computational complexity.

The above diagram shows reduction to three balance envelopes. We may conceive of a balance envelope as a “reduced balance point” that potentially contains multiple balance points that may not be individually balanceable. “Reduced Balance Point 1” is the balance envelope combining points NO1, NO2 and NO4, and “Reduced Balance Point 3” is the balance envelope combining NO1, NO2, NO3 and NO4.

Using the reduced set of envelopes, you can determine the solvability of each flow and come up with these two lists, which are important for the DR algorithm:

• Nonsolvable flow list – reconciliation does not need to provide values for these flows.

• Nonredundant flow list – reconciliation will not try to reconcile these flows, but will use the measured values as input.