The ability of carbon nanotubes to enter the cell membrane acting as drug-delivery vehicles has yielded a plethora of experimental investigations, mostly with inconclusive results because of the wide spectra of carbon nanotube structures. Because of the virtual impossibility of synthesizing CNTs with distinct chirality, we report a parametric study on the use of molecular dynamics to provide better insight into the effect of the carbon nanotube chirality and the aspect ratio on the interaction with a lipid bilayer membrane. The simulation results indicated that a single-walled carbon nanotube utilizes different time-evolving mechanisms to facilitate their internalization within the membrane. These mechanisms comprise both penetration and endocytosis. It was observed that carbon nanotubes with higher aspect ratios penetrate the membrane faster whereas shorter nanotubes undergo significant rotation during the final stages of endocytosis. Furthermore, nanotubes with lower chiral indices developed significant adhesion with the membrane. This adhesion is hypothesized to consume some of the carbon nanotube energy, thus resulting in longer times for the nanotube to translocate through the membrane.