This paper presents an extension of a ballistic compact model to the case of nonballistic transport for the conventional carbon nanotube FET featuring a MOSFET-like operation. A large part of the novelty lies on the analytical implementation of acoustic phonon (AP) and optical phonon (OP) scattering mechanism. To carry out this implementation, some simplifications of the theoretical description are proposed while staying as close as possible to physics and keeping the high-speed simulation and good convergence capability of the compact model. The compact model simulation results are systematically compared and validated with respect to nonequilibrium Green function simulation results. Then, we have investigated the impact of AP and OP scattering on transistor figures of merit. Taking into account the scattering processes is of utmost importance for both analog and digital circuit designs, since neglecting the scattering leads to an overestimation of more than 70% of the main figures of merit and will mislead designers when optimizing the operating point for analog applications.