Evaluating influence of eccentricity on response of electromagnetic wave resistivity logging while drilling by vector eigenfunction expansion formulae for dyadic Green 's functions

Key words:  electromagnetic wave resistivity  logging while drilling  eccentricity  dyadic Green 's functions  vector eigenfunction

Abstract:

The vector eigenfunction expansion formulae of the magnetic current source dyadic Green 's functions for radial layered medium in cylindrical coordinate system were derived to compute the response of electromagnetic wave resistivity logging while drilling and to investigate the influence of instrument 's eccentricity on the response within the borehole. The radially layered cylindrical formation model is adopted, and it is assumed that the formation within each layer is homogeneous and isotropic. The electromagnetic wave within each layer is the superposition of cylindrically symmetric wave and different orders of asymmetric waves. It has shown from computation that the influence of the instrument 's eccentricity increases with the frequency rising. For resistive mud, the influence of the instrument 's eccentricity should be corrected when the resistivity of the formation is low. For conductive mud, the influence of the instrument 's eccentricity should be corrected when the resistivity of the formation is high.