We present hydrodynamical simulations of the interaction of Coronal Mass Ejections (CME) in the Interplanetary Medium (IPM). In these events, two consecutive CMEs are launched from the Sun in similar directions within an interval of time of a few hours. In our numerical model, we assume that the ambient solar wind is characterized by its velocity and mass-loss rate. Then, the CMEs are generated when the flow velocity and mass-loss rate suddenly change, with respect to the ambient solar wind conditions during two intervals of time, which correspond to the duration of each CME. After their interaction, a merged region is formed and evolve as a single structure into the IPM. In this work, we are interested in the general morphology of this merged region, which depends on the initial parameters of the ambient solar wind and the CMEs involved. In order to understand this morphology, we have performed a parametric study in which we characterize the effects of the initial parameters variations on the density and velocity profiles at 1 AU, using as reference the well-documented event of July 25th, 2004. Based on this parametrization we were able to reproduce the main features of the observed profiles ensuring the travel time and the speed and density magnitudes. Then, we apply the parametrization results to the interaction events of May 23, 2010; August 1, 2010; and November 9, 2012. With this approach and varying the values of the input parameters within the CME observational errors, our simulated profiles reproduce the main features observed at 1 AU. Even though we do not take into account the magnetic field, our models give a physical insight into the propagation and interaction of ICMEs.