Reconciliation of material balance of a large petroleum refinery in conditions of incomplete data

Journal of Computer and Systems Sciences International (Impact Factor: 0.48). 04/2010; 49(2):295-305. DOI: 10.1134/S1064230710020140


The problem of reconciliation of material balance of a large petroleum refinery using measured mass flows of materials in
the conditions of incomplete data (not all mass flows were measured) is formalized in the form of the problem of minimization
of a degenerate quadratic function (sum of squared differences of measured and corrected mass flows of material weighted using
a priori values of relative measurement errors) in the presence of linear equalities-constraints, which represent material
balance equations of technological diagram nodes. For reducing the data uncertainty due to measurement errors and compensation
of data incompleteness, the system of balance equations is added by a priori percentage of losses of product flows at technological
diagram nodes and linear equations reflecting the proportions between mass flows of raw materials and products due to specific
features of technology determined by experts. For overcoming the consequences of possible degeneracy and incompatibility of
the united system of constraints, it is proposed to seek the normal pseudo-solution to the problem of material balance reconciliation.
Numerical formulas using operations of matrix pseudo-inversion are substantiated. Methods for analysis of unambiguity (or
ambiguity) of determination of reconciled values corresponding to missing measurements and finding contradictory constraints
are indicated. Illustrative numerical example is given.

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