Analytical solution of the borehole resistivity casing problem

摘要

There has been a strong interest in understanding how direct current flow is influenced by the presence of a metal casing in boreholes. In particular, when the current electrode is within the cylindrical borehole, the resulting potential in the external region is severely shielded. Nevertheless, it is possible to exploit the external potential, even though it is very weak. Basic investigations have been carried out by Kaufman (1990), and Kaufman and Wightman (1993) employing simplified analytical procedures and by Schenkel and Morrison (1990) using more complicated numerical schemes. In this note, we choose an idealized analytical model of a cylindrical borehole with a thin-walled metal casing that henceforth we refer to as the tube. The walls of the tube are characterized by a longitudinal conductance and the possibly polarized surfaces of the tube walls are described by interface impedances (Wait, 1959, 1982; Holladay and West, 1984; Williams and Wait, 1985).