Suboptimal flowrate estimators and their application to the design of measurement strategies

In mineral or metallurgical processing plants, it is a common practice to analyze physical properties or chemical content of the flowing material. However, only a few strategic flowrates, such as global plant or specific process unit feed flowrates, are usually measured. Other flowrates must then be estimated using data reconciliation or suboptimal direct estimation methods. Despite the optimality of data reconciliation, direct methods are still widely used in the industry because of their simplicity. Typical applications of suboptimal methods are to provide reliable estimates for data reconciliation algorithm initialization, support the selection of components to be analyzed, and to detect faults prior mass balancing calculations. Falling into the category of suboptimal methods are the minimal estimability (generalization of the classical n-product formula), ordinary regression, and node imbalance methods. The objectives of the paper are to review these methods under a unified approach, to compare their performance in terms of estimated flowrate variance, and to propose a systematic method to design measurement strategies maximizing the performance of flowrates estimation. The concepts are illustrated using both simulated and real plant data from the mineral processing industry.