Abstract: Methods and apparatus for estimating values for formation parameters such as permeability, relative permeability, and skin factors for a plurality of locations in the formation are provided. Fluid is forced into a capped borehole at a measured rate, and a borehole logging tool is run in the borehole to measure indications of pressure and conductivity. Estimates of the parameters and the measured fluid flow rate(s) into the formation are used in conjunction with a jointly inverted pressure transient model and saturation-conductivity model in order to compute indications of expected pressure and indications of expected conductivity-related profiles as a function of depth and time. The expected pressures and expected conductivity related profile indications are then compared to the pressures and conductivity indications measured by the borehole logging tool, and an iterated comparison between the computed values and the measured values is used to provide determinations of the formation parameters.