A time-dependent multiphysics, multiphase model is proposed and fully developed here to describe carbon nanotubes (CNTs) fabrication using chemical vapor deposition (CVD). The fully integrated model accounts for chemical reaction as well as fluid, heat, and mass transport phenomena. The feed components for the CVD process are methane (CH4), as the primary carbon source, and hydrogen (H-2). Numerous simulations are performed for a wide range of fabrication temperatures (973.15-1273.15 K) as well as different CH4 (500-1000 sccm) and H-2 (250-750 sccm) flow rates. The effect of temperature, total flow rate, and feed mixture ratio on CNTs growth rate as well as the effect of amorphous carbon formation on the final product are calculated and compared with experimental results. The outcomes from this study provide a fundamental understanding and basis for the design of an efficient CNT fabrication process that is capable of producing a high yield of CNTs, with a minimum amount of amorphous carbon. (C) 2009 American Institute of Chemical Engineers AIChE J, 55: 3152-3167, 2009