Fractionation of Li-ion battery waste leachates into high-purity Li, Ni, and Co streams in a liquid-liquid extraction circuit was studied using numerical simulations. A new mechanistic mathematical model explaining the phase equilibrium in the loading, scrubbing, and stripping stages using bis(2,4,4-trimethylpentyl)phosphinic acid (Cyanex 272) as extractant was developed. Including the distribution equilibrium of ammonia in the model enabled simulation of metal extraction with partially neutralized extractant. The model facilitates the design and optimization of liquid liquid extraction circuit for fractionation of Li-ion battery leachates. Four leachates from recent research articles were selected to the study in order to cover a wide composition variation. In the separation process scheme studied, Co and Ni are first selectively extracted, yielding a pure Li raffinate, and then separated as pure products in the stripping steps. The simulation results confirm the viability of the scheme. The influence of the leachate composition on the feasible range of O/A ratios in loading and scrubbing as well as acid concentration in Ni stripping was quantified. With proper operating parameters, high recoveries of Li and Co (> 99.9%) are achieved for all leachate compositions. The leachates containing 10-25 g/L Co, > 10 g/L Ni, and > 2.5 g/L Li are particularly suitable for fractionation of the metals into high-purity (> 99%) Li, Ni, and Co streams.