A dynamic model for state profiles of a plug flow reactor is developed, including multiple fluid and solid phases. The model is based on conservation of reactor state profile moments along the spatial dimension of the reactor. These moments are transformed analytically into a polynomial approximation at each time step. The method is flexible, and low as well as high order numerical schemes are resulted in by appropriate choice of parameters. A significant advantage of the present method is that boundary conditions of the partial differential equation reactor model are implicitly satisfied via the moment transformation, whereas the polynomial profile in the numerical solution does not have to be forced to satisfy the boundary conditions. The method is tested numerically against analytical solutions in three numerically challenging benchmark cases: prediction of breakthrough curve in packed bed adsorbers; simulation of chromatographic separation; and feeding a step impulse in a plug flow dimerization reactor. It is shown that the high resolution methods result in considerably smaller numerical errors than a simple low-order assumption of piecewise continuous solution. (C) 2007 Elsevier Ltd. All rights reserved.