Modeling HFM contactors for systems with interfacial reactions using Voronoi Tessellations: Fundamental rigorous models and simpler film theory methods using facilitation factors

Most studies to date in the modeling of hollow fiber membrane for liquid/liquid extraction processes have used the simplified film theory approach. Others have used a more rigorous approach to modeling hollow fiber membranes using a single fiber approach and the fundamental equations of transport coupled with reaction kinetics to study the membrane transfer mechanisms but do not study the module as a process as a whole. In this study the hollow fiber membrane contactor for liquid/liquid extraction of metals is investigated from a rigorous fundamental approach using transport theory, kinetic mechanisms, facilitation factors, effects of interfacial phenomenon (Marangoni effects), and the maldistribution of fluid flow in the annulus due to random geometrical placement of the membrane fibers. This maldistribution of flow is modeled using Voronoi Tessellations.; A less rigorous semi-analytical model and computer simulation to evaluate and predict performance of Hollow Fiber Membrane Contactor Modules is presented for the extraction of compounds with interfacial chemical reactions. The model is based on the classical film theory approach previously defined in the literature for this process without chemical reactions. Mass transfer coefficients are calculated using published correlations and chemical reaction effects are accounted for by calculated facilitation factors. The shell side flow maldistribution due to random packing of fibers in the module bundle is estimated using Voronoi Tessellations and the Rheme f {dollar}cdot{dollar} Re factor. The computer simulation of random packing is accomplished using Random Sequential addition. The model is correlated with experimental data on the extraction of Uranyl nitrate from an acidic aqueous medium into TBP/DIPB extractant. The model correlates experimental data very well for this system. By accounting for the non-linearity of the interfacial effects in this way the very rigorous solution of a system of coupled non-linear PDEs may be avoided, but still provide accurate predictive design and analysis information on the system. This model has the limitation of first order kinetic mechanism as the extraction with tri-butyl phosphate (TBP).