Wave reflections in counter-current separation processes with unequal mass transfer coefficients

Abstract

In this paper, the influence of finite mass transfer resistance on the steady state and dynamic behavior of spatially distributed counter-current separation processes is analyzed. Special attention is given to the pinch states, at which thermodynamic equilibrium between the phases prevails. In a classical paper, Sundaresan et al. (1987) have shown that these pinch states may depend on the mass transfer coefficients. It is shown that this apparent contradiction can be explained by means of wave reflections at the system boundaries, which are reported here to the best of our knowledge for the first time. As an application example, a counter-current adsorption process as introduced in the above reference is considered, and it is shown how these wave solutions can be constructed in the concentration phase space by using the characteristic curves of equilibrium theory in combination with the wave trajectories generated with a non-equilibrium model.