Effects of transport and phase equilibrium on fast, nearly irreversible reactive extraction

Integration of reaction and separation can be exploited to drive reversible reactions in the direction of the desired product using multiphase flow contacting. In the case of nearly irreversible, fast reactions, however, the dynamics of the product have little influence on the reactor efficiency in say liquid–liquid reactive extraction. A similar intensification in reaction efficiency to reactive separation can be achieved by exploiting phase equilibrium or asymmetry in mass transfer rates of the reactants. Here, a model for two-layer biphasic flow and homogeneous reaction is proposed for co-current reactive extraction, demonstrating that localization and intensification of reaction occurs in the region between the entrance and crossover. Crossover occurs if the reactant in stoichiometric deficit preferentially populates the reacting phase due to sufficient imbalance in either mass transfer coefficients or phase equilibrium. We develop an infinite Peclet number (convection dominates over bulk diffusion) model that indicates that crossover occurs whenwhen1>u0v0>1κu2+1κu1hU1κv2+1κv1hVfor fast, irreversible reactions. u0u0 and v0v0 are initial charges to the tubular reactor, the κκ's are mass transfer coefficients for each side of the fluid interface and the hh's are Henry's Law coefficients for reactants UU and VV. The interpretation of this formula is that if v0>u0v0>u0, then crossover will occur if the overall mass transfer rate of UU is faster than the overall mass transfer rate for VV. Downstream of the crossover point, the reactant in stoichiometric excess also dominates the reacting phase due to relative exhaustion of the more-mobile component. A finite Peclet number theory for fast, irreversible reaction shows that the above formula is a conservative limit for crossover—if it holds, crossover will occur regardless of the Peclet number. A formula for the larger parametric region for crossover with finite Peclet number is derived. Verification that crossover is achieved is found by finite-element numerical analysis of the full governing equations. Both theory and numerical analysis predict localization and intensification of the reaction due to crossover. Crossover sets the length scale as approximately two and a half crossover lengths for completed reaction for sufficiently high Peclet number with strong kinetic asymmetry. The theory predicts that taking the ratio of inlet concentrations S=u0/v0S=u0/v0 to be the critical value at fixed physical parameters for mass transfer and phase equilibrium maximizes localization and reactor efficiency. Similarly, the kinetic asymmetry should be as large as possible to exploit the benefits of crossover.