The electrical resistivity method in cased boreholes

Abstract

!&e Govermient reserves for itself and others acting on its behalf a royalty free, nonexclusive, irrevocable, world-wide license for governmental purposes t o publish, distribute, translate, duplicate, exhibit, and perform any such data aopyrighted by the amtractor.The United States Department of Energy has the right to use this thesis for any purpose whatsoever, including the right to reproduce all or any part thereof. THE ELECTRICAL RESISTIVITY METHOD IN CASED BOREHOLES by CLIFFORD J. SCHENKEL AbstractThe resistivity method in cased boreholes with downhole current sources is investigated using the integral equation (IE) technique. The casing and other bodies are characterized as conductivity inhomogeneities in a half-space. For sources located along the casing axis, an axially symmetric Green's function is used to formulate the surface potential and electric field (E-field) volume integral equations. The situations involving off-axis current sources and three-dimensional (3-D) bodies is formulated using the surface potential IE method. The solution of the 3-D Green's function is presented in cylindrical and Cartesian coordinate systems.The methods of moments is used to solve the Fredholm integral equation of the second kind for the response due to the casing and other bodies.The numerical analysis revealed that the current in the casing can be approximated by its vertical component except near the source and the axial symmetric approximation of the casing is valid even for the 3-D problem. The E-field volume IE method is an effective and efficient technique to simulate the response of the casing in a half-space, whereas the surface potential approach is computationally better when multiple bodies are involved.Analyzing several configurations of the current source indicated that the casing response is influenced by four characteristic factors: conduction length, current source depth, casing depth, and casing length. The conduction length, the most important factor, relates the casing conductance with the conductivity of the host medium and is an indicator of the ability of the pipe to carry the current along its length. When the source is located within the casing, the characteristic parameters can be reduced to three ratios: the conduction length to casing length I (conduction ratio), the source position to casing length, and the casing depth to casing length.For a conduction ratio that is approximately greater than two. the fields from the casing are similar to those produced by a line source. When the source is located beneath the casing, the distortion of the fields is also dependent on the casing-source separation distance. For a current source near the casing (e 100 casing diameters), the casing greatly distorts the fields when compared to those produced by a pole source. When the source is greater than 100 casing diameters from the pipe, only the region near the casing is affected. The numerical simulations indicate that cross-hole and downhole to surface time monitoring studies may be conducted with ve...

Electrical and electromagnetic responses over steel-cased wells

“…The factors that influence which regime is more representative are the physical properties of the casing and surrounding geology and the length of the casing. This can be summarized by the "conduction length" defined by Schenkel (1991), which is δ = √ σ c A c ρ, where σ c A c is the conductance of the casing (product of its conductivity and area), and ρ is the resistivity of the surrounding geology. If L c the length of the casing is much smaller than the conduction length (L c δ), then the well is in the "short" regime and the currents decay linearly.…”

Direct current resistivity with steel-cased wells

“…For more resistive wells, the charges follow an exponential decay, as shown in Figure 10. Schenkel (1991) described the decay of currents, and thus the distribution of charges along the length of a well, in terms of the conduction length,…”

“…For more resistive wells, the charges follow an exponential decay, as shown in Figure 10. Schenkel (1991) described the decay of currents, and thus the distribution of charges along the length of a well, in terms of the conduction length, The above examples considered an impairment that affects the entire circumference of the casing. This may be suitable in some scenarios where a particular geologic unit subjects the well to corrosive conditions, however, flaws may also be vertical cracks along the well (e.g.…”

“…The second paper extends the analysis for finite length wells. Schenkel & Morrison (1990); Schenkel (1991); Schenkel & Morrison (1994) pioneered numerical work analyzing the influence of steel-cased wells on geophysical data using an integral equation approach for solving the DC resistivity problem. They expand upon the logging-through-casing application and discuss limitations of the transmission line solution presented in Kaufman (1990) for this application.…”

Borehole cylindrical noise during hole–surface and hole–hole resistivity measurements

“…This work is based largely on the original patent by Alpin (1939), the more recent patents by Kaufman (1989), Gard et al (1989) and Vail (1991), and the study by Kaufman (1990). The effects of various casing conditions including heterogeneities within the casing, cement sheaths, finite length casings, and direct energizing of casings have been described by Wait (1982Wait ( , 1984Wait ( , 1995, Wait and Gruszka (1987), Schenkel andMorrison (1990, 1994), Schenkel (1991), Kaufman and Wightman (1993), and Singer and Strack (1998) among others. Fig.…”