Bubble-column reactors are frequently employed in the biological, chemical and petrochemical industries. This paper presents a novel approach to model bubble-column flows using quadrature-based moment methods (QBMM). A fully two-way coupled flow solver is developed that solves the incompressible Navier-Stokes equation for the liquid phase and moment transport equations for the dispersed bubble phase. The moment transport equations for the dispersed bubble phase are solved using a kinetic theory approach. Contributions from the liquid-phase pressure gradient, vorticity, drag, virtual mass and gravity are accounted for in the bubble-phase force balance. The solution algorithm and coupling procedure are described in detail, and results are presented for a 2-D bubble column with two different gas flow rates (1.6 and 8.0 l/min). (C) 2011 Elsevier Ltd. All rights reserved.