Induction logging for vertical structures in the presence of a borehole fluid

Mapping hydraulic fractures with borehole instrumentation presents many problems. The resulting fracture eddy currents can be expected to be smaller than the corresponding borehole fluid currents. The transmitting and receiver coils are vertical and are in close proximity to each other. This orientation is necessary to couple strongly to vertical structures and is much more difficult to analyze than the case of horizontal coils. The coils must be physically but not electrically isolated from probable hostile temperature and pressure environment. Analytic expressions are presented which predict the effect of the cavity, misalignment of the coils in the cavity, and an upper bound on the effect of the borehole fluid.The analysis uses the mode matching method. The discrete cavity modes are matched to the continuous host rock modes through the boundary conditions. A nonstandard cavity expansion is developed which converges very rapidly in the usual situation where the cavity axial dimension between coils is much greater than the radial coil separation.A simple approximate expression for the received magnetic intensity components H (sub rho ) and H (sub phi ) is derived. The numerical results of the model predict that, in the limit when the borehole fluid is assumed to be perfectly conducting, the ratio of axial total electric field to axial primary field can be as large as 10 5 . The configuration is an efficient magnetic to electric field converter.An ideal vertical fracture model is also developed. For the case when the crack and the borehole are coincident, explicit modification formulas for the transmitter coil dipole angular patterns are given.