4. Data Adjustment Procedures for Mass Balances

Steady-state material balances calculated from data measured at various locations around process units are useful for many purposes, such as metallurgical accounting, on-line control, and the development of mathematical models. Often it is possible to calculate material balances by several independent procedures when excess measurement information, i.e., redundant data, is available. Clearly, if the data were collected without measurement errors, a theoretical condition never found in practice, all material balances calculated from redundant data would be in agreement. The real situation is that error exists in practical measurements, so that the results of material balances determined from available optional procedures differ. Consequently, best fit computational procedures to improve the material balances by taking measurement errors into account have been formulated. Such procedures can be used also to judge whether measurements are grossly in error due to either faulty observations or defective data sensing devices. A variety of mathematical techniques are available which serve to adjust raw data. The adjusted data permit mass balancing that does not depend on the computational method. To illustrate the need for an adjustment procedure, Table 1 shows a raw data set acquired around the Brenda Mines Ltd. No. 4 grinding circuit shown schematically in Fig. 1. At least seven optional ways to calculate a circulating load ratio may be employed. These are shown in Table 2 where, depending upon the calculation [ ]