Article

# 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

**ABSTRACT**

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.

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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- 01/1974; Prentice-Hall, Inc., London.
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**ABSTRACT:**Flow rate measurements in a steady-state process are reconciled by weighted least squares so that the conservation laws are obeyed. A projection matrix is constructed which can be used to decompose the linear problem into the solution of two subproblems, by first removing each balance around process units with an unmeasured component flow rate. The remaining measured flow rates are reconciled, and the unmeasured flow rates can then be obtained from the solution of the conservation equations. The basic case contains constraints which are linear in the component and the total flow rates. The method is extended to cases with bilinear constraints, involving unknown parameters such as split fractions.Chi-square and normal statistics are used to test for overall gross measurement errors, for gross error in each node imbalance which is fully measured, and for each measurement adjustment.AIChE Journal 11/1983; 29(6):881 - 888. DOI:10.1002/aic.690290602 · 2.75 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**On-line optimization provides a means for maintaining a process near its optimum operating conditions by providing set points to the process’s distributed control system (DCS). To achieve a plant-model matching for optimization, process measurements are necessary. However, a preprocessing of these measurements is required since they usually contain random and—less frequently—gross errors. These errors should be eliminated and the measurements should satisfy process constraints before any evaluation on the process. In this paper, the importance and effectiveness of simultaneous procedures for data reconciliation and gross error detection is established. These procedures depending on the results from robust statistics reduce the effect of the gross errors. They provide comparable results to those from methods such as modified iterative measurement test method (MIMT) without requiring an iterative procedure. In addition to deriving new robust methods, novel gross error detection criteria are described and their performance is tested. The comparative results of the introduced methods are given for five literature and more importantly, two industrial cases. Methods based on the Cauchy distribution and Hampel’s redescending M-estimator give promising results for data reconciliation and gross error detection with less computation.Computers & Chemical Engineering 03/2004; 28(3-28):381-402. DOI:10.1016/j.compchemeng.2003.07.001 · 2.78 Impact Factor

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