A 3D global circulation model is adapted to the atmosphere of Venus to explore the nature of the planet's atmospheric superrotation. The model employs the full meteorological primitive equations and simplified forms for diabatic and other nonconservative forcings. It is therefore economical for performing very long simulations. To assess circulation equilibration and the occurrence of atmospheric superrotation, the climate model is run for 10,000--20,000 day integrations at 40 W 50 latitude-longitude horizontal resolution, and 56 vertical levels (denoted L56). The sensitivity of these simulations to imposed Venus-like diabatic heating rates, momentum dissipation rates, and various other key parameters (e.g., near-surface momentum drag), in addition to model configuration (e.g., low versus high vertical domain and number of atmospheric levels), is examined. We find equatorial superrotation in several of our numerical experiments, but the magnitude of superrotation is often less than observed. Further, the meridional structure of the mean zonal overturning (i.e., Hadley circulation) can consist of numerous cells which are symmetric about the equator and whose depth scale appears sensitive to the number of vertical layers imposed in the model atmosphere. We find that when realistic diabatic heating is imposed in the lowest several scales heights, only extremely weak atmospheric superrotation results.