Generalized differential equations time, and exposure time during reactive transport are specified for simple cases involving linear reversible reactions between two states. Solutions are obtained for demonstration problems involving batch and column conditions. The exposure-time coordinate serves as a measure of residence time of materials that are convected (aged) along this dimension depending on the phase in which the material resides, and this exposure-time convection is used to determine the way in which material residence-time (to a particular phase) distributions evolve during reactive transport. The model is simplified to the form of a generalized batch reactor, and the solution is developed by recognizing that this model is identical to the one-dimensional purely convective reactive transport model involving the same boundary conditions and reactions. This places the derived differential equation as the governing equation for the classical Giddings and Eyring <1955> solution for residence time distributions in the two-state Markov chain representation of the batch. In the more general case where reaction rate varies with memory of phase association, the present formulation may be viewed as an extension of composite Markov process modeling to generally non-Markovian reactions. The model is specified for reactive transport in a porous medium in a one-dimensional column and applied to bacterial transport data from a published study where residence time to surfaces controlled the reaction. The formulation and numerical solution are described, and the simulations illustrate the evolution of material density over space, time, and exposure time representing residence time sorbed. ¿ 2000 American Geophysical Union