APPARENT RESISTIVITY CURVES FOR AN INFINITE LINE SOURCE PARALLEL TO AN INCLINED CONTACT

Geophysics ◽  
1975 ◽  
Vol 40 (4) ◽  
pp. 689-693 ◽  
Author(s):  
Sri Niwas ◽  
S. K. Upadhyay
Keyword(s):  
Point Source ◽  
Line Source ◽  
Apparent Resistivity ◽  
Master Curves ◽  
Harmonic Method ◽  
Resistivity Data ◽  
Infinite Line

Investigations of apparent resistivity due to a point source over an inclined contact have been reported by Aldredge (1937), Unz (1953), Maeda (1955), and Chastenet de Gery and Kunetz (1956). In these investigations either the image or the harmonic method has been utilized. In this note, we propose to solve the same problem as follows: (1) Transform point‐source potential data into line‐source apparent resistivity data. (2) Interpret transformed apparent resistivities by the master curves provided.

Distortion in resistivity logging at shallow depth

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1058-1069 ◽  
Author(s):  
Tien‐Chang Lee ◽  
Brian N. Damiata
Keyword(s):  
Point Source ◽  
Line Source ◽  
Apparent Resistivity ◽  
Homogeneous Medium ◽  
Radial Distance ◽  
Ground Surface ◽  
Current Electrode ◽  
Potential Electrode ◽  
Resistivity Logging ◽  
Source Array

Owing to the proximity of an insulating ground surface, normal resistivity logging at shallow depths (less than 30 m) can yield an apparent resistivity that exceeds 200% of the formation resistivity for a homogeneous medium. The distortion is more acute for long‐normal than for short‐normal logging. Three examples from a landfill site in southern California are presented to show such distortion. The patterns of distortion are similar for logging devices consisting of either two point‐source electrodes or one point‐source and one finite length, line‐source electrode. The former electrode array is a generally accepted approximation of the latter. However, the simulated apparent resistivity for the line‐source array is greater than that for the point‐source array at any given depth. A resistivity contrast between the formation and the borehole fluid can shift the magnitude of the background apparent resistivity but does not significantly alter the pattern of distortion. The magnitude of the distortion can be reduced by placing the reference‐ground potential electrode at a radial distance that is about equal to the spacing between the downhole upper potential electrode and the upper current electrode. It can also be removed by including the radial distance in an array‐dependent geometric factor that accounts for the resistivity of the borehole fluid and the proximity of the logging device to the ground surface.

Determination of Dynamic Dispersion Coefficient for Solid Particles Flowing in a Fracture With Consideration of Gravity Effect

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Yanan Ding ◽  
Xiaoyan Meng ◽  
Daoyong Yang
Keyword(s):  
Particle Size ◽  
Point Source ◽  
Line Source ◽  
Dispersion Coefficient ◽  
Solid Particles ◽  
Gravity Effect ◽  
Dispersion Coefficients ◽  
Source Condition ◽  
Advection Diffusion Equation ◽  
Gravity Settling

Abstract A robust and pragmatic method has been developed and validated to analytically determine dynamic dispersion coefficients for particles flowing in a parallel-plate fracture, in which gravity settling has been considered due to its significant impact on particle flowing behavior. More specifically, a two-dimensional (2D) advection–diffusion equation together with the initial and boundary conditions has been formulated to describe the flow behavior of finite-sized particles on the basis of coupling the Poiseuille flow with vertical settling. Meanwhile, three types of instantaneous source conditions (i.e., point source, uniform line source, and volumetric line source) have been considered. Explicit expressions, which can directly and time-efficiently calculate dynamic dispersion coefficient, have been derived through the moment analysis and the Green’s function method. By performing the simulation based on the random walk particle tracking (RWPT) algorithm, the newly developed model has been verified to determine particle dispersion coefficients agreeing well with those obtained from the RWPT simulations. It is found that the point source is the most sensitive to gravity effect among different source conditions, while the volumetric line source is affected more than the uniform line source. For particle size larger than its critical value, an increased particle size leads to a decreased asymptotical dispersion coefficient for all the source conditions due to the significant gravity effect, while gravity positively affects the dispersion coefficient at early times for the point source condition. In addition, average flow velocity positively affects the dispersion coefficient for all the source conditions, while the associated gravity effect is influenced only at early times for the point source condition.

Optimized Model of Slotted Liners Completion Parameters in Horizontal Well

2012 ◽  
Vol 616-618 ◽  
pp. 804-811
Author(s):  
Quan Tang Fang ◽  
Wei Chen ◽  
Rong Wang
Keyword(s):  
Point Source ◽  
Line Source ◽  
Flow Resistance ◽  
Horizontal Well ◽  
Source Function ◽  
Geometric Model ◽  
Superposition Principle ◽  
Evaluation Index ◽  
Flow Convergence ◽  
Optimized Model

The transient flowing model of slotted liner completion was established by superposition principle based on the geometric model of slotted liners, with the point source function and the single slotting equal to line source, and then the optimized model of slotted liner completion parameter was established with the skin factor of slotted liners completion as evaluation index. After analyzing the parameter sensitivity with cases, the slot density is confirmed as the main reason leading to flow convergence and additional flow resistance. Furthermore, the optimization principles of slotted liners completion of horizontal well are determined. These results are significant in optimizing the slot distribution pattern and parameter allocation.

APPARENT RESISTIVITY FOR DIPPING BEDS—A DISCUSSION

Geophysics ◽  
1955 ◽  
Vol 20 (1) ◽  
pp. 140-144 ◽  
Author(s):  
Robert G. Van Nostrand ◽  
Kenneth L. Cook
Keyword(s):  
Exact Solution ◽  
English Translation ◽  
Apparent Resistivity ◽  
Resistivity Data ◽  
Successful Work ◽  
Foregoing Paper

Two groups of workers, here designated the “image school” and the “harmonic school” respectively, have attacked the problem of the interpretation of resistivity data over a dipping bed or dipping fault. The earlier attempts were made by the image school; but the more successful attempts have been made only recently by the harmonic school. The most successful work prior to that presented in the foregoing paper by Maeda has been done by the Russians, whose papers in their English translation are probably available to few American geophysicists. The purpose of this discussion is to appraise the relative merits of various prior solutions to the dipping bed problem in the light of the exact solution to the problem, which is given by Maeda. The terminology and symbols used herein are identical to those used by Maeda in his paper.

Transformation from 2-D to 3-D wave propagation for horizontally layered media

Geophysics ◽  
1994 ◽  
Vol 59 (12) ◽  
pp. 1920-1926 ◽  
Author(s):  
Lasse Amundsen ◽  
Arne Reitan
Keyword(s):  
Wave Propagation ◽  
Point Source ◽  
Line Source ◽  
Layered Media ◽  
Cylindrical Symmetry ◽  
Seismic Processing ◽  
Geometric Spreading ◽  
Processing Algorithms ◽  
The Relationship ◽  
D Wave

The relationship between 2-D and 3-D wave propagation in horizontally layered media was first investigated by Dampney (1971). In the last few years the usefulness and feasibility of transforming point‐source responses with 3-D geometric spreading to equivalent line‐source responses with 2-D geometric spreading have been thoroughly discussed (see Helgesen, 1990; Wapenaar et al., 1990, 1992; Herrmann, 1992; Helgesen and Kolb, 1993; Amundsen, 1993). In the case of cylindrical symmetry this transformation constitutes a required preprocessing step for several seismic processing algorithms based on 2-D wave propagation. The work of Dampney (1971) has apparently been missed by the authors discussing the 3-D to 2-D geometric spreading transform.

Repeatability study of helicopter-borne electromagnetic data

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. G285-G290 ◽  
Author(s):  
Haoping Huang ◽  
Allen Cogbill
Keyword(s):  
Apparent Resistivity ◽  
Correlation Coefficients ◽  
Flight Path ◽  
Control Line ◽  
Average Correlation ◽  
Plan View ◽  
Frequency Dependency ◽  
Electromagnetic Data ◽  
Resistivity Data ◽  
Phase Data

Helicopter-borne electromagnetic (EM) responses depend very much upon the altitude and plan-view flight path, especially when the resistivity of the terrain’s materials varies laterally and/or vertically. Spatially consistent flight paths are required for repeatability analysis of the EM data. Caution should be used in examining the repeatability of the EM data because poor repeatability could result from spatially inconsistent flight paths. However, the apparent resistivity converted from the EM responses is virtually independent of the sensor altitude and directly reflects variations in the resistivity. Therefore, more meaningful repeatability analyses are achieved if the apparent resistivity is used instead of the EM response itself. We have analyzed 32 flights over a control line by using the EM amplitude, the phase, and the apparent resistivity. Our results show that the crosscorrelation for all 496 paired combinations of flights is better for the apparent resistivity than for the EM amplitude or phase. The apparent-resistivity data have average correlation coefficients from 0.89 to 0.94 as the frequency increases, whereas the amplitude and the phase data have average correlation coefficients from 0.78 to 0.85 without obvious frequency dependency.

Sign in / Sign up

Export Citation Format

Share Document