We present a new steady state algorithm for modeling the hydrodynamics and mass transfer behavior of liquid extraction columns based on the SQMOM in a one dimensional domain. The SQMOM is extended to solve the spatially distributed bivariate population balance equation (w.r.t. droplet diameter and the solute concentration) at steady state. The integral spatial numerical flux is closed using the Multi Primary one Secondary Particle Method, while the hydrodynamics integral source terms are closed using the analytical Two-Equal Weight Quadrature formula. To facilitate the source terms implementation, an analytical solution based on the algebraic velocity model is derived to calculate the required dispersed phase mean droplet velocity. In addition to this, the hydrodynamics moment transport equations are coupled with the One Primary One Secondary Particle Method to close the mass transport equations. The resulting system of ordinary differential equations is solved using a fifth order numerical scheme in space. As a case study, the model prediction is validated using published experimental data for DN80 Kuhni extraction column. By using SQMOM, fifteen sections (w.r.t. the droplet diameter as an internal coordinate) are found enough to predict the droplet volume distribution and the column hydrodynamics as compared to the experimental data. On the other hand, one section (w.r.t. the droplet solute concentration) along droplet size distribution is found enough to predict the mass transfer profiles along the column height. (C) 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.