Coaxial and Coplanar Arrays in the Triaxial Induction Tools: Dipole and Loop Models

The more recent induction tools often include the unconventional coplanar coil arrays, in order to investigate thinly laminated reservoirs and to locate axially asymetrical anomalies like vugs and fractures. To simplify numerical modeling of conventional borehole induction responses, point dipole sources and receivers are used instead of the more accurate loop field models. However, this approximation may not be very accurate for a coplanar array, in which the source and sensor axes are perpendicular to both tool and borehole axes. The main interest here is to quantify the relative difference between magnetic point dipole and finite-size loop source and receiver models in both coil arrays. We examined a range of conductivities, multiple frequencies and source-receiver distances. We show that the relative differences between these responses vary inversely with the source-receiver spacing and directly with the conductivity and frequency range, applied in standard wireline induction logging as well as in Measurement While Drilling (MWD) conditions. For both coil arrays, coaxial and coplanar, the magnetic dipole mathematical model, particularly for shorter spacings and higher frequencies and conductivities, may not be adequate. In some very common cases the discrepancy in the voltage induced in the sensors may be almost 1% for the real component and 2% for the imaginary.