Numerical simulation of cation exchange in fine coarse seawater slurry pipeline flow

Abstract

Slurry pipelines transporting a coarse—the comminution product—and a fine fraction, both in the presence of seawater, can cause an alteration of the liquid phase chemical composition. In the present paper, we present the result of two-dimensional numerical simulations using a mixture model using the OpenFOAM library solving the momentum equations for both the coarse and fine species, the liquid phase, mass transport equations for three ionic species (Ca2+, Na+ and Mg2+) and the mean flow continuity. The flow is assumed turbulent, and to this purpose, the k-ε model is used. The mass transport has been modeled using a two-species first order kinetic model derived from the Gaines-Thomas exchange equation, assuming the relation between the rate of Ca+2–Na+ and that between Na+2–Mg+2. The presence of an inhomogeneous concentration distribution in the vertical and the fine fraction vertical mobility via settling, reveals a strongly inhomogeneous mass transfer characteristic within the pipe section. In particular, the higher particle concentration near the bottom along with lower local velocities of the continuous phase compared to the mid-section imply larger residence times, as confirmed by the numerical results. Both aspects in combination, promote higher Ca2+–Na+ and Mg2+–Na+ exchange rates near the bottom than in the axis of the pipe. This observation suggests that particle flow heterogeneity may promote or hinder adsorption-desorption processes when compared to homogeneous slurry flows. Results also reveal the potential for the control of the electrolyte structure given the cation exchange capacity (CEC), type and concentration of clays and coarse phase concentration, the latter conditioning the flow structure.