A computational fluid dynamics study was conducted to model the plume resulting from the laser ablation of a carbon target in a laser ablation oven for the production of carbon single-walled nanotubes (SWNTs). The goal is to gain understanding into the fluid dynamics and thermodynamics of the plume to ultimately improve SWNT production techniques. The simulations were carried out with a 12-species, 14-reaction chemistry model that included carbon species from C to C6. Metal catalysts in the carbon target were ignored for these simulations. Simulation times ranged from immediate ablation onset to 8 ms past the initial onset of ablation. A secondary goal of the study was to compare computational results with experimental results for three different background gases in the laser ablation oven-argon, helium, and nitrogen. Computational results indicated that lighter carbon species were more quickly diffused into the background gas for helium and nitrogen, resulting in lower localized mass fractions of carbon nanotube "feedstock." The expectation is that this effect will reduce the production of carbon nanotubes, which has been confirmed by experimental evidence. From this investigation, a possible "indicator species" for the production of SWNT appears to be C5.