A numerical method for the treatment of moving discontinuities in model equations of chemical engineering systems is presented. The derived model describing the effect of condensation and evaporation in a regenerative air-to-air heat exchanger yields an illustrative example for the so called moving boundary problems. The presented adaptive moving grid method is based on the algorithm PDEX for parabolic partial differential equations. It is shown that the method is well suited for problems where the discontinuities cause low rates of convergence if the equations are solved with a static grid.