Moly-Cop Tools / BallBal_Reverse__C-2.xlsx Page 1 04/14/2024 / 03:15:26 Moly-Cop Tools, Version 3.0 About the BallBal_Reverse Spreadsheet ... Scope : The BallBal_Reverse spreadsheet was designed to compute the Size-by-Size Mass Balance around the Hydrocyclone Classifiers of any given Conventional Ball Mill circuit, operating under the Reverse configuration (see Flowsheet), on the basis of actual plant measurements. Theoretical Framework : Whenever actual grinding data are collected in a plant environment, they will invariably be affected by natural experimental and measurement errors, in such a way that the basic mass balance equation around the circuit, for particles of size d i : f i F F + f i MD MD = f i U U + f i O O ??? , for i = 1,n will never be satisfied. In the above expression F, MD, U and O represent the mass flowrate of solids in the circuit fresh feed, mill discharge, underflow and overflow streams, respectively. Similarly, f i F , f i MD , f i U and f i O represent the fraction of those total respective streams corresponding to particles of size d i . The Ballbal_Reverse routine allows for the calculation of a whole new set of corresponding adjusted or fitted values f i F , f i MD , f i U and f i O , such that the objective functions : f i = [ w F (f i F - f i F ) 2 + w MD (f i MD - f i MD ) 2 + w U (f i U - f i U ) 2 + w O (f i O - f i O ) 2 ] ,for every particle size d i are minimized and the adjusted values so generated strictly satisfy the mass balance restrictions : f i F F + f i MD MD = f i U U + f i O O , for i = 1,n where w F , w MD , w U and w O are user defined weighting factors included to represent the relative quality and reliability of the samples from each of the 4 streams and the mass flowrates F, MD, U and O are calculated as : F = F MD = F (CL) U = F (CL) O = F and the Circulating Load (CL) is estimated from : CL = { u sd S [(f i O - f i F ) / (f i MD - f i U )] + u fs (1/f S O - 1/f S F ) / (1/f S MD -1/f S U ) } / (u sd + u fs ) all i where f s F , f s MD , f s U and f s O are the weight fractions of total solids in the fresh feed, mill discharge, underflow and overflow streams, respectively, and also u sd and u fs are user defined weighting factors included to represent the relative quality and reliability of the size distribution measurements vs. the percent solids measurements in all 4 streams. In general, a high relative value of a weighting factor is indicative of a more reliable measurement with respect to the other measurements participating in the same equations.