Mass balance can be considered as a process of correcting measured data from the gold mill to determine the gold recovery under the assumption that the samples were taken when the circuit was at steady state. It is important to mention that when the methods of mass balance were first introduced to gold processing plants, there was a lot of resistance due to many people considered that the data was adjusted negatively. The ides has since changed somewhat, but it always important to explain some items about the mass balance process.
Basically, a first idea to determine a mass balance is that the information processes is to be compared to simulators producing data that was balance and these values were taken from steady state circuits. Also, for accounting, both metallurgical and financing, it is essential to balance the input and output of gold processing plants. Other important argument is related to the fact that balanced data are on average closer to true data than are raw data. This can be explained when a metallurgist tries to study a hydrocyclone. In this case the hydrocyclone efficiency curve with adjusted information is smoother than with raw data. Theoretical proofs of the superiority of adjusted data can be easily obtained, but may not be as convincing to the operator. Some metallurgists consider that benefits obtained using Monte-Carlo simulations are the best indicator or reference point to adjust data from gold processing plants.
It may be considered that mass balance is in fact something most of people in mineral processing use without recognizing it as such. If we consider a single stream sampled simultaneously n times following the survey plan. Each sample must be assayed and a grade Ai, i = 1, 2,…, n. Naturally the best estimated of the true grade is A = (A1 + A2 + A3 + … An)/n, which is the average assay. Note that most likely, none of the n measurements is necessarily equal to A. what has been done in fact is to adjust all measurements to A. Nevertheless, n conflicting measurements were made, and as only one estimate of A must be given, all measurements must be adjusted to this one value. This is the basic idea of redundant data, more data than required to estimate the estate of the system.
It is important to mention that all measurements must be implicated assumed to have the same accuracy, and must be weighed equally to estimate A. The average measurement is usually selected as the best estimate because it minimizes the sum of squared adjustments. If some measurement had been known to be more accurate than others, they would have been weighted more heavily; this consideration can be extended to other systems with different level of complexity. The common problem is to satisfy all known mass balance constraints while minimizing the sum of the weighted squared adjustments. The variance is introduced as a weighting factor to take into account the quality of each gold assay. In this way, for a poor assay, of large variance, a larger correction will be tolerated.