A well logging system and method are disclosed for detecting the presence and estimating the quantity of gaseous and liquid hydrocarbons in the near wellbore zone. The system uses a gradient-based, multiple-frequency NMR logging tool to extract signal components characteristic for each type of hydrocarbons. To this end, new data acquisition methods are proposed in which measurements at different frequencies are interleaved to obtain, in a single logging pass, multiple data streams corresponding to different recovery times and/or diffusivity for the same spot in the formation. The resultant data streams are processed to determine mineralogy-independent water and hydrocarbon saturations and porosity estimates. Gas and oil saturations are used to obtain accurate estimates of the water content, permeability and other parameters of interest. In another aspect, a novel diffusion-enhanced data acquisition sequence is disclosed for use with low field gradient tools.