For transient scalar transport in a tube packed with two-zone heterogeneous porous media, presented in this paper is an extension of the existing study to determine the steady dispersivity for the long term process of Taylor dispersion (Chen and Wu, 2012). For the initial phase of Taylor dispersion with essential implications to various applications, this work aims to illustrate the asymptotic time variation of the dispersivity, by means of Aris's method of concentration moments originally devised for the analysis of dispersion in a flow through an empty tube. The analytical solution of the dispersivity covering both the initial and long term phases is rigorously derived to reflect the asymptotic structure of the dispersivity as characterized by relevant dimensionless parameters which represent the relative magnitude of properties and the combined influences of two zones. (C) 2014 Elsevier Ltd. All rights reserved.