Flowsheet Analysis For Mass Balance Calculations In Overdefined Metallurgical Systems With Recycle

Calculation of consistent steady-state mass balances in operating metallurgical plants and pilot plants is of interest for many reasons. In general, enough data can - and should - be collected to overdefine the system, i.e., permit calculation of nonmeasured quantities via more than one path. In such cases, resulting steady-state metallurgical mass balances rarely close due to sampling, analysis and/ or instrument error. Indeed, determination of a valid calculational sequence for complicated process flowsheets with multiple recycle streams can prove quite difficult. Here we present and discuss a method that has proven useful in analysis of numerous grinding circuit flowsheets of varying-degrees of complexity our technique requires only a consistent process flowsheet with appropriate associated data and arbitrary numbering of streams and equipments. Process topology and user data are decoded to yield a set of "search" or base variables and a set of "calculated" variables in solids, water, particle size and splitter parameter space. This procedure greatly speeds subsequent actual mass balance adjustment calculations since perturing certain variables (e.g., a solids value) does not require recalculation of other variables (e.g., the water balance). Finally, internal search and calculated variables are back converted to User units and used in a Sum-of-Squares criterion. Global minimization of this performance functional then yields a consistent mass balance in a least, squares sense. Weighting factors of choice can be used. Examples illustrate application of these methods.