Introducing a novel, and fast matrix-independent method to determine least sampling points for mass balancing of flotation circuits

Mass balancing of mineral processing plants refers to material distributions to different streams of a circuit. Raw data required to produce mass balancing equations mainly includes elemental assays, moistures, mass rates, water, and material flowrates. Since running a complete sampling program to obtain all required information from all streams of a circuit is practically and economically impossible, a minimum number of streams should be determined to conduct a comprehensive mass balancing. In a conventional approach, this value is calculated using the number of feed streams and separating nodes obtained from a matrix presenting the relationship between these streams and nodes. Arrangement of such a connection matrix for complicated circuits is difficult; therefore, the present study aimed to introduce simple equations to calculate the minimum number of sampling points using the knowledge of the total number of streams and nodes included in the circuit. The suggested method eliminated the need for generating a connection matrix and relevant tables. Comparing the results of utilizing the conventional method and the presented new equation for different flotation circuits confirmed the superiority of the proposed method from both simplicity and rapidness points of view.