A method of sequentially transporting a first and a second fluid at a volumetric flow rate through a conduit having a cross-section, wherein the first and second fluids have different densities, which method comprises the steps of estimating a critical stratification condition for a fluid density profile along the conduit, which condition takes into account the densities of the first and second fluids, the cross-section of the conduit and the volumetric flow rate, and wherein violating the critical stratification condition likely results in stratification of fluids to occur; and feeding sequentially only first fluid, a buffer fluid and only second fluid into the conduit, wherein the buffer fluid has a density between the densities of the first and second fluids, such that a density profile of fluid along the conduit is provided, which does not violate the critical stratification condition.