The matrix reduction algorithm for solving separation circuits

• The effectiveness of the traditional linear circuit analysis method is examined.
• A new algorithm for rapidly producing complex circuit solutions is described.
• A procedure for spreadsheet implementation of the algorithm is introduced.
• A review of 31 basic circuit configurations indicates gaps in prior design rules.

Mineral processing circuits typically employ multi-unit staged separation in order to produce a product with sufficient recovery and quality. The design of these separation circuits is largely driven by trial-and-error, incorporating several stages of experimental testing and computer simulation. Linear circuit analysis is a 30 year old fundamental technique that may supplement the more rigorous simulation methods to streamline the formulation of an optimal solution. Unfortunately, linear circuit analysis remains underutilized due to the manual and cumbersome algebra involved. This paper presents a new matrix-based algorithm that allows efficient and automated generation of analytical circuit solutions required for linear circuit analysis. A major advantage of this technique is that it may also be applied numerically to allow simple spreadsheet-based simulation without circular references and iteration. In this communication, the algorithm is thoroughly demonstrated in a trial case, and the analysis is expanded to include 31 simple two and three-unit circuit configurations as well as two especially complex circuits (>15 units). Such large-scale circuit analysis was prohibitively complicated using prior methods. The overall results indicate that while the linear circuit analysis approach is valid, exceptions do exist for many of the original derived design rules.