A mathematical formulation for the electric potential from point current‐sources coaxial with a metal casing has been obtained. The excitation caused by the axial point‐sources will produce currents in the pipe. By assuming that the pipe can be divided into many cylindrical ring segments with constant axially‐directed current, the solution of the fields inside and outside the pipe can be formulated in an integral form. The integral equation applied to the segmented pipe yields a set of simultaneous linear equations which are solved for the currents in the pipe; these are then used to calculate the potentials anywhere outside the pipe in the medium. This solution has been used to study the distribution of the potentials in a half‐space for a single current‐source at and beyond the bottom of a finite length of casing. For a casing 0.1 m in radius and 0.006 m in wall thickness with a conductivity of 106 S/m, in a half‐space of 10‐2 S/m, it was found that only in a region very near the pipe does the pipe exert substantial influence on the fields of a point‐source 100 casing diameters beyond the end of the pipe. It appears that cross‐hole resistivity surveys can be implemented without corrections for the casing if the source is located at least 50–100 casing diameters beyond the end of the casing. Hole‐to‐surface surveys are much more affected by the pipe. For a pipe‐source separation of 100 casing diameters, the surface measurements must not be closer than a half pipe length for a 5% or less field distortion.

Methods using dc electrical arrays to measure formation resistivity through casing have relied on approximate forms for the current and potential distributions to derive a simple relationship between the formation resistivity and the transverse resistance calculated from measurements of the potential and its second derivative inside the casing. We have derived a numerical solution for the potentials and their derivatives to examine the accuracy of the approximate forms for casing of finite‐length, annular zones of varying radius, and for vertical discontinuities such as layers or abrupt changes in annular zone radius. For typical conductivity contrasts between the casing and formation, the approximate relationships may be off by as much as 60 percent for long casing and may show variations of 20 to 30 percent as the electrode array moves along the casing. In principle an iterative scheme could be devised to correct the readings if high accuracy was required. The numerical results show that to first order the current flow from the casing is radial, and that all the analytic expressions based on this assumption for evaluating layer resolution and the effects of annular layers are valid. An interesting byproduct of this study has been the discovery that the distortion of the potentials in a nearby well by an annular disk (e.g., an injected steam zone) surrounding the current injection well is greater if the injection well is cased. Crosswell resistivity surveys appear feasible if one of the wells is cased.

!&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...

A steamflood recently initiated by Mobil Development and Production U.S. at the Lost Hills #3 oil field in California is notable for its shallow depth and the application of electromagnetic (EM) geophysical techniques to monitor the subsurface steam flow. Steam was injected into three stacked eastward-dipping unconsolidated oil sands at depths from 60 to 220 m; the plume is expected to develop as an ellipsoid aligned with the regional northwest-southeast strike. Because of the shallow depth of the sands and the high viscosity of the heavy oil, it is important to track the steam in the unconsolidated sediments for both economic and safety reasons. Crosshole and surface-to-borehole electromagnetic imaging were applied for reservoir characterization and steamflood monitoring. The crosshole EM data were collected to map the i n t m e l l distribution of the high-resistivity oil sands and to track the injected steam and hot water. Measurements were made in two fiberglass-cased observation wells straddling the steam injector on a northeast-southwest profile. Field data were collected before the steam drive, to map the distribution of the oil sands, and then 6 and 10 months after steam was injected, to monitor the expansion of the steam chest. Resistivity images derived from the collected data clearly delineated the distribution and dipping structure of the target oil sands. Difierence images from data collected before and during steamflooding indicate that the steam chest has developed only in the middle and lower oil sands, and it has preferentially migrated westward in the middle oil sand and eastward in the deeper sand. Surface-to-borehole field data sets at Lost Hills were responsive to the large-scale subsurface structure but insuficiently sensitive to model steam chest development in the middle and lower oil sands. As the steam chest develops further, these data will be of more use for process monitoring. This project was initiated from discussions between Ranga Ranganayki at Mobil Research and Michael Wilt at Lawrence Livemore National Laboratory (LLNL) in 1990. The field operators at Mobil Lost Hills became involved with the onset of field adivities in 1991. Much of the technical work was accomplished through the crosshole EM