Calculation of Extraction Equilibrium in Multi-Component System by Newton-Raphson Algorithm

摘要

Based on the extraction equilibrium and mass balances in countercurrent extraction systems, a novel method was studied for dealing with the extraction equilibrium and the mass distribution in a multi-component (λ-component) system. The relationships of mass distribution (x_i, y_i i=1,...,λ) between two phases were expressed by 2λ dimensional simultaneous equations. These simultaneous equations can be converted to a one-dimension nonlinear equation, then it was solved by Netwon-Raphson algorithm within a few number of iteration. Compared with the regular calculation method for the 2λ dimension simultaneous equations, Newton-Raphson algorithm can decrease the number of iteration, increase the convergence of the equations and accelerate the spaced of simulation. It was verified in many multi-component systems with satisfactory results. As an example, a five-component system is demonstrated in this paper.