f Comparison of Loop and Magnetic Dipole Antenna Models for MWD Resistivity Tool Responses

The magnetic dipole approximation is commonly used for induction and MWD (measurement while drilling) resistivity models. This approximation is valid when the magnetic flux is does not vary appreciably over the cross-sectional area of the measurement sonde transmitter and receiver loops. There are several logging situations where this condition may not be satisfied. Short spacing coil pairs or highly conductive borehole fluid environments are perhaps the most common situations where the dipole approximation is not adequate. MWD measurements are commonly made with an operating frequency of I or 2 MHz. The higher operating frequency causes the electromagnetic fields to have a more rapid variation than in induction logging tools.that typically operate at 10 or 20 kHz. In addition, wireline resistivity tools are usually run with centralizers, keeping the tool near the center of the borehole. In this case the borehole signal usually behaves in a predictable manner and is not difficult to compensate. MWD resistivity measurement tools are increasingly run in highly deviated or horizontal well completions. Drill pipe rotation can produce continuous lateral as well as axial motion of the resistivity tool. The measured apparent resistivity is a function of the tool standoff distance x, from the borehole wall. When x, is small, the tool surface is near the borehole wall. In this case, and when the ratio of formation to borehole conductivity departs significantly from unity, the effect can be large. In this regime, the magnetic dipole mathematical model, particularly for short array spacings, is not adequate. This paper formulates and computes the finite-size loop electromagnetic response near an idealized interface. Graphical results compare the proximity effect predicted by loop and dipole theories.