In order to characterize conductivity profiles due to drilling fluid invasion into a hydrocarbon formation, a model for radial fluid transport is presented. The model assumes a water-based mud and accounts for the convective movement of oil, water, and salt. A mathematical analysis of the model using the method of characteristics is given. An equivalent graphical construction is also provided. Computations of radial conductivity profiles for specified formation characteristics and total filtrate loss are given. For typical fractional flow curves, it is shown that three qualitatively different profiles may occur depending on the initial water saturation. These results are compared with numerical simulations that include capillary pressure and gravity segregation. Next, the important issue of the inverse problem is analyzed. It is shown that from a single snapshot of the conductivity profile, an exact calculation of filtrate loss and formation fractional flow curve is possible. The calculation is valid provided there is a resistivity contrast between the drilling fluid filtrate and the formation water. For practical application, we show the limits of applicability of this result with complete numerical calculations. Thus, if wireline logs of resistivity variation away from the wellbore are available, formation oil producibility and water cut at native conditions may be estimated. ©1997 American Institute of Physics.