Feasibility and cost minimisation for a lithium extraction problem

Abstract

In this paper we address the problem of allocating extraction pumps to wells, when exploiting lithium rich brines, as part of the production of lithium salts. The problem of choosing the location of extraction wells is defined using a transportation network structure. Based on the transportation network, the lithium rich brines are pumped out from each well and then mixed into evaporation pools. The quality of the blend will be based on the chemical concentrations of the different brines, originating from different wells. The objective of the problem is then to determine a pumping plan such that the final products have predefined concentrations, and the process is operated in the cheapest possible way. The problem is modelled as a combinatorial optimisation problem and a potential solution to it is sought using a genetic algorithm. The evaluation function of the genetic algorithm needs a method to determine feasible minimum cost flows for the proposed pumping allocation, thus requiring the formulation of a blending model in a flow network for which a new iterative non-convex local optimisation algorithm is proposed. The model was implemented and tested to measure the algorithm's efficiency.