A new look at multiphase invasion with applications to borehole resistivity interpretation

In well log interpretation, it is frequently necessary to correct logs for invasion. Invasion occurs in permeable formations when there is a radial differential pressure (RDP) between the borehole and formation. Other factors on which invasion depend include saturation, mobility, pressure (RDP) and capillary pressure, permeability and viscosity of fluids, and temperature transient effects associated with the mud filtrate injected into the formation. Thus, simulation of realistic invasion is not an easy task. This work reviews the famous Buckley–Leverett mathematical model in cylindrical coordinates appropriate for borehole geometries. The model predicts multiphase invasion in porous media when gravity, capillary pressure, and mud cake can be neglected. One application is to correct logging while drilling (LWD) and wireline resistivity logs for time-dependent invasion and formation temperature effects. This is important, for example, when there are possible large differences in formation and mud temperature. Modeling studies show these effects can be large enough to noticeably influence resistivity logs. However, after correction, difference in LWD and wireline logs arising from the time-dependent heat process are explained. Thus, the method, when coupled to a time-dependent heat flow model, and a response function formulation of resistivity, yields new insight into the influence of thermal and electrical transients in log interpretation.