A numerical investigation of methanol droplet combustion in a zero-gravity and low-pressure convective environment is presented. Simulations have been carried out using a predictive, transient and axisymmetric model, which includes droplet heating, liquid-phase circulation and water absorption. First, a suspended droplet (constant relative velocity) burning in an ambient of air at 300K is considered. A nearly quiescent environment (initial Reynolds number Re0=0.01) is used to impose a weak gas-phase convective flow, introducing a deviation from spherical symmetry. The resulting weak liquid-phase circulation is greatly enhanced due to surface tension effects, which create a complex, time-varying, multi-cellular flow pattern within the liquid droplet. The complex flow pattern, which, in the presence of surface tension, results in nearly perfect mixing, causes increased water absorption within the droplet, leading to larger extinction diameters. Surface tension effects are shown to be dominant in causing water absorption, even at initial Reynolds numbers as high as 5. Results for combustion in a nearly quiescent environment (Re 0=0.01) with varying initial droplet diameters, (do = 0.16 to 1.72 mm), show that predictions of droplet extinction diameters, although they are still below the experimental data, do improve substantially when surface tension effects are included. Next, results for suspended droplets and for moving droplets burning in an ambient of air at 1200K, for a range of initial Reynolds numbers that are of interest in spray combustion (Re0=1-100) are presented. It is shown that, for moving droplets, due to the presence of an envelope flame at some stage during the droplet lifetime, surface tension is important over the entire range of Re0 considered; the extinction diameter decreases with increasing Re0. Extinction is not observed for a moving droplet when surface tension effects are neglected. For suspended droplets, when transition or envelope flame is present, which corresponds to Re0 less than approximately 15, surface tension is important; when an envelope flame is present (Re0 less than approximately 10), the extinction diameter increases with Re0. The variation of droplet lifetime with Re0 is much stronger for suspended droplets than for moving droplets. Depending on the Reynolds number, results on methanol droplet lifetimes and extinction diameters measured through suspended droplet experiments may not be applicable to moving droplets.