A transmission‐line model for electrical logging through casing

Abstract

Electrical logging in cased holes is a subject of strong current interest. In this paper we develop the conventional theory of physical responses of electrical logging through casing where the formation resistivity changes vertically and where the conductance of the casing varies. The theory is developed for a four‐electrode sonde with one current electrode, and three receiver electrodes that measure current leakage into the formation. All the theoretical developments in the paper are derived using approximate transmission‐line theory. An expression for the array coefficient is first derived and then used to obtain an expression for the apparent conductivity of the formation. Then a relation is established between the array coefficient, geometrical factor and conductance of the casing. This step led to a method of measuring casing conductance. Knowing casing conductance, the response of the array to vertical changes in formation conductivity is measurable. It was established, that when the array length is less than the thickness of the formation layer, the measured apparent conductivity is equivalent to the true conductivity of the formation, unlike the case of normal and induction logs. It was also established that measurement of apparent conductivity can be made accurately inside a casing of finite length when it essentially exceeds the length of the electrode array. The results contained in this paper show that electrical logging through casing is possible in wells with conventional casing strings that penetrate layered sedimentary formations.

Study on forward modeling of through-casing resistivity logging

“…Due to the limit of the methodology study and engineering accomplishment, there was no breakthrough progress in resistivity logging tool design in the past fifty years. Until 1988, Paramagnetic Well Logging Company (PML) in the USA first succeeded in testing the Through-Casing Resistivity Tool (TCRT) [3,4] . In 1990, Kaufman proposed the approximate theoretical model and measurement theory of cased hole resistivity logging based on transmission line equation [2][3][4] .…”

“…Until 1988, Paramagnetic Well Logging Company (PML) in the USA first succeeded in testing the Through-Casing Resistivity Tool (TCRT) [3,4] . In 1990, Kaufman proposed the approximate theoretical model and measurement theory of cased hole resistivity logging based on transmission line equation [2][3][4] . Then the research and development of through-casing resistivity logging is being supported by many oil companies and logging service companies.…”

“…After that, many researchers in the USA, France and Russia continued the study of measurement of through-casing resistivity. Vail in 1989 and [2][3][4][5][6][7][8][9][10][11] . Due to the limit of the methodology study and engineering accomplishment, there was no breakthrough progress in resistivity logging tool design in the past fifty years.…”

“…Y = 1/T, R c = ρ c /(2πaΔa) R c , S c = 1/R c , R c is unit length resistance of the metal casing and T is the transverse resistance of the formation corresponding to the unit length casing.Analytical solution of the conventional transmission line equation is usually used to study the response of the simple formation model with homogeneous bed in the radial direction[3,4] .The parameters of the transmission line equation are modified in this paper, so the so-called modified transmission line equation method (MTLEM) can be applied to complex formation model. Eqs.…”

New post-processing method for interpretation of through casing resistivity (TCR) measurements

“…In particular, vertical resolution of the measurement, effects caused by the cement sheath, casing inhomogeneities, and the finite length of the casing have been studied by Kaufman (1993), Schenkel and Morrison (1990), Schenkel and Morrison (1994), Singer (1995), Singer and Strack (1998), Tabarovsky (1994), and Zinger (1994).…”