A new simulation logic and thermodynamic equilibrium analysis algorithm combined with a new model simplification technique was developed to simulate the solvent extraction process for purifying rare earth metals from chloride solution with 2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester (PC88A) as a solvent. The proposed model simplification method significantly reduces the number of the nonlinear equilibrium equations to be simultaneously solved to overcome the initial guess problem and obtain numerically stable convergence pattern in solving the equilibrium analysis problem and performing the rigorous simulation of the extraction process. A new equilibrium analysis algorithm on the basis of the simplified nonlinear equilibrium equations is also proposed to estimate the equilibrium concentrations by solving the rigorous first principle extraction model. Finally, a solvent extraction simulator is developed to estimate all the concentrations of all the stages of the solvent extraction process by solving the equilibrium analysis problem at each stage in a sequential way. The proposed simulator doe not suffer from the initial guess problem and shows very robust convergence pattern without any numerical problems.