Borehole Resistivity

Basic Concept

The distribution of electrical potential around a current-carrying electrode depends on the distribution of the electrical resistivities of the materials surrounding the electrode. This principle is the basis for electrical resistivity borehole logging, which is essentially the downhole adaptation of the surface resistivity survey. By injecting electrical current into a mud or fluid-filled borehole and measuring the resulting potential difference (i.e., voltage), resistivity logging detects variations in the electrical resistivity of borehole-intersected formations

Electrical resistivity is a fundamental material property that describes its ability to resist the flow of electric current, and its inverse, conductivity, describes its ability to conduct current. Electrical properties can vary with variations in factors such as temperature, saturation, water content, porosity, clay minerals, and/or fluid conductivity. Thus, resistivity logs can aid the interpretation of resistivity-related material properties and are most commonly used to estimate salinity and delineate lithology for hydrogeological studies.

Theory

A single electrical resistivity measurement requires the use of four electrodes. A direct current (DC) is passed through a mud or fluid-filled borehole into the borehole-intersected materials using two current electrodes, which are denoted A and B. The voltage response is measured across the remaining two potential electrodes that are referred to as M and N. Ohm’s Law (i.e., V=IR) relates the measured voltage (V) to the applied current (I) and material resistance (R).

However, resistance is not itself a diagnostic material property because it depends upon both the type of material and the shape (i.e., volume) of the material. Thus, borehole resistivity logs are presented as continuous measurements of apparent resistivity (ρ_a) with depth over the length of the measured borehole. Apparent resistivity has units of ohmmeters (Ωm) and can be calculated by using a geometric factor, K, that is chosen based on electrode configuration.

In general, there exist two main types of resistivity logging methods. The more traditional logging technique is the normal-resistivity method, which measures the bulk-electrical resistivity of the materials surrounding the borehole using variably spaced electrodes. A commutated direct current is applied to and maintained across the current (i.e., A and B) electrodes. As such, the measured resistivity of the material between the potential (i.e., M and N) electrodes is proportional to the voltage drop measured across them.

Though not necessarily universal, the normal-resistivity method typically has the A electrode near the bottom of the sonde with the M electrode located above it. The B and N electrodes are remote and are situated far from the probe electrodes as well as each other. Generally, B is attached to the wireline and separated from the probe by an insulated cable, and N is typically situated on the ground surface.

Though 32- and 8-inch spacings are also used, the long- and short-normal resistivity sondes, which have 64 and 16 inches between the A and M electrodes, respectively, are most common. The radius of investigation (ROI) and vertical resolution are related to this spacing, and, as with most methods, there is a tradeoff between the two. The short-normal is sensitive to thin layers, but it may not sense the undisturbed formation past the disturbed zone due to its smaller ROI.

Conversely, long-normal tools can measure the undisturbed formation, but its large vertical resolution may render thin beds unnoticed. Furthermore, if the disturbed zone (i.e., mainly drilling mud) has a relatively low resistivity, current will flow parallel to the borehole instead of penetrating the formation. Although increasing inter-electrode distance may help, bed-thickness effects can make such logs unusable, especially when unit thicknesses are much less than the electrode spacing. Fortunately, these issues are resolved with the focused-resistivity tool.

Focused-resistivity sondes, which are also called guard-resistivity or laterologs, are able to image the thin beds and resistive formations that normal-resistivity methods are unable to characterize. Focused-resistivity sondes contain extra electrodes used to concentrate the current in a sideways, sheet-like pattern that is able to pass through the mud into the undisturbed formation. The focused-resistivity method yields apparent resistivity with increased vertical resolution while decreasing or eliminating the bed-thickness effects.

Typically, the focused-resistivity sonde is designed similarly to the normal-resistivity setup with the addition of two guard electrodes (i.e., A₁ and A₁'). The guard electrodes, which are positioned symmetrically on either side of the A current electrode, are kept at the same voltage potential as A. Current flows from high to low potential, and the guard electrodes oppose borehole-parallel current flow and drive the current from M into the surrounding formation.

Furthermore, the radius of investigation of a focused-resistivity tool is increased by increasing the lengths of the guard electrodes, and doing so has no negative effect on resolution. Electrical current is forced into the target formation and prevented from flowing into the disturbed zone or surrounding formations regardless of their resistivity. Thus, the focused-resistivity method is the preferred means by which thin and/or highly resistive formations are resolved.

Applications

Most mineral grains that comprise soils and rocks are essentially nonconductive (i.e., resistive), and subsurface resistivity depends primarily on the amount of water in pores/fractures and the dissolved solids within it. Though, to a lesser extent, resistivity can also decrease with the presence of certain ore minerals, fine grain materials (e.g., clays), and high temperatures. That said, resistivity logs are most commonly used and best suited to estimate salinity, delineate lithology, and differentiate formations with differing porosities.

The measured value of resistivity (i.e., formation resistivity (ρ_t)) is dependent on water saturation (S_w), pore water resistivity (ρ_w), and porosity (ϕ). As such, resistivity logs are often used along with ancillary methods and Archie’s equation to estimate these constituent formation properties (Archie, 1942). Resistivity logs can be enhanced by combining the results with other logging techniques such as natural gamma, spontaneous potential, neutron, and/or gamma-gamma (Mussett and Khan, 2000).

The normal-resistivity tool has a spherical volume of investigation with a radius approximately twice the space between the A and M electrodes, and each measurement represents the average value of this sample volume. As such, formation contacts may not appear as sharp as they actually are. Furthermore, the sample volume changes as a function of resistivity and formation thickness, and measured responses can be significantly affected by the ratio of electrode spacing to bed thickness.

The layer thicknesses depicted by the method are related to resistivity magnitude. Resistive layers appear thinner, and, conversely, conductive layers appear thicker than they are. Layer thickness is typically altered by an amount equal to the A-M spacing (i.e., one-half is added to or subtracted from the top and bottom of each layer). Though the effect that a conductive layer has on a measurement decreases as with decreasing thickness, conductive beds cannot be thin enough to go entirely unnoticed.

Resistive beds, however, are not favored in the same way. If the thickness of a resistive bed is greater than four-times the A-M spacing, true resistivity is measured. However, a resistive layer will appear as a conductive layer if its thickness is less than one-and-a-half times the A-M spacing. Thus, general stratigraphic knowledge prior to normal-resistivity logging is beneficial, and a focused-resistivity sonde is more appropriate for gathering information on thin formations.

The radius of investigation (ROI) and current beam thickness (i.e., vertical resolution) of focused-resistivity tools are related to guard-electrode length. The ROI is approximately three-times this length, whereas and vertical resolution equals this length. Additionally, as the length of the guard electrodes increases, so does the distance between the measuring electrode and the bottom of the borehole. Thus, there is a tradeoff between certain measurement parameters, which are chosen based on project requirements.

The geometric factor, K, used to convert focused-resistivity data to apparent resistivity is difficult to calculate. Thus, a calibration that directly translates voltage values measured in a test well into terms of resistivity is usually conducted by the manufacturer. Additionally, focused-resistivity data may require bed-thickness corrections if the beds are thinner than the length of the M electrode. Typically, however, measured resistivity values approach formation resistivity (ρ_t), and corrections are not necessary (Pirson, 1963).

Necessary electrical contact between the tool and borehole-intersected formations is achieved via conductive drilling mud, and, therefore, resistivity logs can only be collected in open, water- or mud-filled boreholes. If these conditions cannot be met, then induction logging, which has a greater vertical resolution and is unaffected by the borehole fluid, can be used instead. That said, the normal- and focused-resistivity methods have been applied in numerous borehole investigations and proven useful for the following:

Water-quality studies
Lithologic and stratigraphic interpretation
Fractured-rock aquifer studies
Geoengineering
Identification of areas of high permeability
Estimation of formation porosity
Estimation fluid saturation
Assessing mud invasion

Examples/Case Studies

Angula, B., Morales, T., Uriarte, J.A., and Antigüedad, I., 2011, Hydraulic conductivity characterization of a karst recharge area using water injection tests and electrical resistivity logging: Engineering Geology, v. 117, no. 1-2, p. 90-96, doi:10.1016/j.enggeo.2010.10.008.

Abstract: Water injection tests and electrical logging are particularly useful techniques in the characterization of geological media in engineering works. In this paper these techniques in conjunction with cracks measurements obtained from drilling cores, were used in the characterization of a singular location in a karst massif. The aim of our work is to determine the hydraulic characteristics of the investigated site, as well as to establish the relationship between the data obtained by the different techniques used. Thus, electrical resistivity records and fracture data were obtained from two boreholes of 100 and 120 m depth. Hydraulic conductivity was calculated from 25 low-pressure water injection tests (LPT) carried out at different depths in both boreholes. The relationship between hydraulic conductivity and fracture frequency was not very statististically significant (R2: 0.062–0.672; σest: 0.61–1.575). Conversely, electrical resistivity and hydraulic conductivity had a great relationship (R2: 0.725–0.935; σest: 0.159–0.738), so the electrical resistivity may be related to the functionality of the fractures. Finally, the LPT is shown as a very practical tool for determining the degree of the hydraulically interconnection with the surroundings, for establishing the hydraulic conductivity profile and for obtaining a measure of soil erosion-ability according to the significance of the fracture washing out processes recorded.

Jorgensen, D.G., 1991, Estimating geohydrologic properties from borehole-geophysical logs: Ground Water Monitoring and Remediation, v. 11, no. 3, p. 123-129, doi:10.1111/j.1745-6592.1991.tb00388.x.

Abstract: Borehole‐geophysical logs can be used to estimate geohydrologic properties based on in situ measurement of rock and water properties. Estimates of properties of both formation and water, such as coefficient of diffusion, formation factor, cementation exponent, hydraulic conductivity, irreducible water content and specific yield can be assessed from borehole‐geophysical data and selected algorithms and graphs. Water properties, such as resistivity, sodium chloride concentration, viscosity and density, can also be estimated using data from borehole‐geophysical logs. Water resistivity using the spontaneous‐potential method can be estimated if an empirical correction for fresh water is applied. Estimates of formation properties, such as porosity and permeability, can also be made using borehole‐geophysical data.

Kwader, T., 1985, Estimating aquifer permeability from formation resistivity factors: Groundwater, v. 23, no. 6, p. 762-766, doi:10.1111/j.1745-6584.1985.tb01955.x.

Abstract: A comparison of permeability results for individual producing zones obtained from pumping tests and flow‐meter logs showed a good correlation to calculated corresponding formation resistivity factors (F). Where F = a/Øm or F = R0/RW, and porosity (Ø) is obtained from the neutron log, m is the formation cementation factor, Ro is saturated formation resistivity from normal electric logs, and Rw is formation pore‐water resistivity. Unlike formations containing saline water where the electrical current is conducted through the pore fluid, in fresh‐water aquifers the electrical current appears to be conducted along the grain‐aqueous interface by surface conductance rather than through the grain or pore fluid. Surface conductance of the current serves to increase the current path length which is recorded as an increase in the measured saturated resistivity (Ro). The current path direction and length through the formation is directly related to the shape, diameter, and sorting of the grains, geometric packing arrangement, and degree of matrix cementation. Fortunately, all of these factors that serve to increase the current path [which in turn directly increase saturated formation resistivity (Ro) and F] also are factors that increase formation permeability. Relative changes in F values can be matched with known permeabilities from aquifer tests and flowmeter logs to quantify the relative productivity of the various zones analyzed. Once this relationship is established, F values can be used to assign relative permeabilities within a single borehole or from borehole to borehole for a given geographical area. This method has been successfully used to estimate permeability in both unconsolidated sands and Tertiary carbonate aquifers in the southeastern Coastal Plain of the United States.

Linder-Lunsford, J.B. and Bruce, B.W., 1995, Use of Electric Logs to Estimate Water Quality of Pre‐Tertiary Aquifers: Groundwater, v. 33, no. 4, p. 547-555, doi:10.1111/j.1745-6584.1995.tb00309.x.

Abstract: Electric logs provide a means of estimating ground‐water quality in areas where water analyses are not available. Most of the methods for interpreting these logs have been developed for the petroleum industry and are most reliable in saline aquifers (concentration of dissolved solids as sodium chloride greater than about 50,000 mg/l). The resistivity‐porosity and spontaneous‐potential methods were evaluated to determine if they could be applied to identify zones of fresh water (concentration of dissolved solids as sodium chloride less than 1,000 mg/l) in three potential aquifers in central Wyoming. The potential aquifers have different lithologies–sandstone, clayey sandstone, and carbonate. The two methods generally were reliable predictors of water quality in the sandstone and carbonate potential aquifers. In the clayey sandstone potential aquifer, predictions of the dissolved‐solids concentration using the two methods differed by more than an order of magnitude in several cases. When the resistivity values are corrected for the presence of clay and shale as identified on a natural gamma log, the agreement between the results of the two methods improved by an average of 58 percent.

Paillet, F.L., and Crowder, R.E., 1996, A generalized approach for the interpretation of geophysical well logs in ground-water studies—theory and application: Ground Water, v. 34, no. 5, p. 883-898, doi:10.1111/j.1745-6584.1996.tb02083.x.

Abstract: Quantitative analysis of geophysical logs in ground-water studies often involves at least as broad a range of applications and variation in lithology as is typically encountered in petroleum exploration, making such logs difficult to calibrate and complicating inversion problem formulation. At the same time, data inversion and analysis depend on inversion model formulation and refinement, so that log interpretation cannot be deferred to a geophysical log specialist unless active involvement with interpretation can be maintained by such an expert over the lifetime of the project. We propose a generalized log-interpretation procedure designed to guide hydrogeologists in the interpretation of geophysical logs, and in the integration of log data into ground-water models that may be systematically refined and improved in an iterative way. The procedure is designed to maximize the effective use of three primary contributions from geophysical logs: (1) The continuous depth scale of the measurements along the well bore; (2) The in situ measurement of lithologic properties and the correlation with hydraulic properties of the formations over a finite sample volume; and (3) Multiple independent measurements that can potentially be inverted for multiple physical or hydraulic properties of interest. The approach is formulated in the context of geophysical inversion theory, and is designed to be interfaced with surface geophysical soundings and conventional hydraulic testing. The step-by-step procedures given in our generalized interpretation and inversion technique are based on both qualitative analysis designed to assist formulation of the interpretation model, and quantitative analysis used to assign numerical values to model parameters. The approach bases a decision as to whether quantitative inversion is statistically warranted by formulating an over-determined inversion. If no such inversion is consistent with the inversion model, quantitative inversion is judged not possible with the given data set. Additional statistical criteria such as the statistical significance of regressions are used to guide the subsequent calibration of geophysical data in terms of hydraulic variables in those situations where quantitative data inversion is considered appropriate.

Saboorian-Jooybari, H., Dejam, M., Chen, Z., and Pourafshary, P., 2016, Comprehensive evaluation of fracture parameters by dual laterolog data: Journal of Applied Geophysics, v. 131, p. 214-221, doi:10.1016/j.jappgeo.2016.06.005.

Abstract: Reservoir quality and productivity of tight formations depend heavily on the degree of fracture development. In fact, hard and dense carbonate formations may not be considered as net pay without the presence of fractures that convey fluids towards the wellbore. The evaluation of fractures is key to effective reservoir characterization for purposes like well drilling and completion as well as development and simulation of fractured reservoirs. Although imaging technologies such as Formation Micro-Scanners and Imagers (FMS and FMI) provide useful information about fracture properties (i.e., dip angle, porosity, aperture, and permeability), they are very expensive and may not be available in all wells. In this work, fracture parameters are estimated using conventional dual laterolog (DLL) resistivity which includes shallow (LLS) and deep (LLD) responses. This technique is based on electrical resistivity anomalies resulting from the separation of shallow and deep laterolog curves. Fracture parameters that can be calculated by DLL include dip angle, aperture, porosity, permeability, and cementation factor. The accuracy of the parameters calculated using DLL data is validated by the results of FMI in a well in one of the Iranian fractured reservoirs. Contrary to the image logs, the conventional DLL is run routinely in all drilled wells. Therefore, if a reservoir has limited and insufficient data of image logs, as it is often the case, the DLLs can be used as a reliable replacement in the construction of fracture models. Furthermore, DLL has an advantage of deeper evaluation of fractures in comparison with the immediate borehole investigation of image logs.

Salazar, J.M., Wang, G.L., Torres-Verdín, C., and Lee, H.J., 2008, Combined simulation and inversion of SP and resistivity logs for the estimation of connate-water resistivity and Archie’s cementation exponent: Geophysics, v. 73, no. 3, p. 1MJ-Z46, doi:10.1190/1.2890408.

Abstract: Knowledge of initial water saturation is necessary to estimate original hydrocarbon in place. A reliable assessment of this petrophysical property is possible when rock-core measurements of Archie’s parameters, such as saturation exponent n and cementation exponent m, are available. In addition, chemical analysis of formation water is necessary to measure connate-water resistivity Rw. Such measurements are seldom available in most applications; if they are available, their reliability may be questionable. We describe a new inversion method to estimate Rw and Archie’s cementation exponent from the combined use of borehole spontaneous-potential (SP) and raw array-induction resistivity measurements acquired in water-bearing depth intervals. Combined inversion of resistivity and SP measurements is performed assuming a piston-like invasion profile. In so doing, the reservoiris divided into petrophysical layers to account for vertical heterogeneities. Inversion products are values of invaded and virgin formation resistivity, radius of invasion, and static spontaneous potential (SSP). Connate-water resistivity is calculated by assuming membrane and diffusion potentials as the main contributors to the SSP. Archie’s or dual-water equations enable the estimation of m. The new combined estimation method has been successfully applied to a data set acquired in a clastic formation. Data were acquired in a high permeability and moderately high-salt-concentration reservoir. Values of Rw and m yielded by the inversion are consistent with those obtained with a traditional interpretation method, thereby confirming the reliability of the estimation. The method is an efficient, rigorous alternative to conventional interpretation techniques for performing petrophysical analysis of exploratory and appraisal wells wherein rock-core measurements may not be available.

Shazly, T.F. and Tarabees, E., 2013, Using of Dual Laterolog to detect fracture parameters for Nubia Sandstone Formation in Rudeis-Sidri area, Gulf of Suez, Egypt: Egyptian Journal of Petroleum, v. 22, no. 2, p. 313-319, doi:10.1016/j.ejpe.2013.08.001.

Abstract: Fractures appear predominantly in brittle rocks; hence in consolidated formations they are usually sub-vertical and perpendicular to the plane of group of more or less parallel fractures. Vertical fractures refer to the high-angle events (parallel to the borehole) while the horizontal ones indicate the truly horizontal or sub-horizontal events. The unfractured parts of the block matrix in hard rocks are slightly affected by invasion. Added, fracture aperture was estimated using the Dual Laterolog (DLL), which includes the deep (LLD) and the shallow (LLS) resistivities. The area of study is Rudeis-Sidri area, Gulf of Suez, Egypt. Nine Wells were selected for applying the present technique to determine the reservoir performance of Nubia Sandstone Formation in the considered area. The technique depends on the separation between deep and shallow laterolog in case of vertical fracture and the sharp reduction of LLS log in case of horizontal fractures. In high-contrast formation the calculation of fracture aperture can be done if mud conductivity is also known. Also the dipping of the detected fracture is calculated to ensure the type of fracture. The obtained results show that the detected fractures are generally short vertical fractures with a few numbers in the Nubia Sandstone Formation which cannot be the main factor in production (if present) of this formation.

Taillet, E., Lataste, J.F., Rivard, P., and Denis, A., 2015, Characterization of discontinuities inside massive concrete structures with normal dc resistivity logging: Journal of Applied Geophysics, v. 120, p. 69-80, doi:10.1016/j.jappgeo.2015.06.005.

Abstract: Normal electrical resistivity logging was used to investigate the internal concrete structure. This study proposed an approach, presented by series of steps, to detect and characterize the conductive discontinuities. First is modeling, a database of electrical responses of discontinuities with an aperture range (0.005 m–0.030 m), resistivity contrast (5–40) and extension (0.05 m–20 m) was created. Second is the use of incremental analysis, employed on the created database, to obtain a first estimation of discontinuity parameters. However, the result is not yet sufficient in terms of dimension and activity. This led to the third step, the optimization method. In this last step simulated annealing was chosen to improve the results. This allowed reducing the possibilities of finding solutions to 2 or 3. In order to validate the proposed approach, application on numerical and experimental data was realized. Results show that normal electrical resistivity logging can detect and locate the conductive discontinuities. From the proposed approach, these conductive discontinuities can be characterized as ideal (i.e. without contact zone) and isolated. The ability to identify relevant parameters and provide discontinuity characteristics could eventually serve as basis for civil engineers in making efficient decisions regarding concerns on concrete structure.

References

Angula, B., Morales, T., Uriarte, J.A., and Antigüedad, I., 2011, Hydraulic conductivity characterization of a karst recharge area using water injection tests and electrical resistivity logging: Engineering Geology, v. 117, no. 1-2, p. 90-96, doi:10.1016/j.enggeo.2010.10.008.
Archie, G.E., 1942, The electrical resistivity log as and aid in determining some reservoir characteristics, Transactions of the AIME, v. 146, no. 1, p. 54-62.
Jorgensen, D.G., 1991, Estimating geohydrologic properties from borehole-geophysical logs: Ground Water Monitoring and Remediation, v. 11, no. 3, p. 123-129, doi:10.1111/j.1745-6592.1991.tb00388.x.
Kwader, T., 1985, Estimating aquifer permeability from formation resistivity factors: Groundwater, v. 23, no. 6, p. 762-766, doi:10.1111/j.1745-6584.1985.tb01955.x.
Linder-Lunsford, J.B. and Bruce, B.W., 1995, Use of Electric Logs to Estimate Water Quality of Pre‐Tertiary Aquifers: Groundwater, v. 33, no. 4, p. 547-555, doi:10.1111/j.1745-6584.1995.tb00309.x.
Mussett, A.E. and Khan, M.A., 2000, Well Logging and Other Subsurface Geophysics, in Looking into The Earth: An Introduction to Geological Geophysics: New York, Cambridge University Press, p 285-305.
Paillet, F.L., and Crowder, R.E., 1996, A generalized approach for the interpretation of geophysical well logs in ground-water studies—theory and application: Ground Water, v. 34, no. 5, p. 883-898, doi:10.1111/j.1745-6584.1996.tb02083.x.
Pirson, S.J., 1963, Handbook of Well Log Analysis: For Oil and Gas Formation: United States, Prentice-Hall, 326 p.
Saboorian-Jooybari, H., Dejam, M., Chen, Z., and Pourafshary, P., 2016, Comprehensive evaluation of fracture parameters by dual laterolog data: Journal of Applied Geophysics, v. 131, p. 214-221, doi:10.1016/j.jappgeo.2016.06.005.
Salazar, J.M., Wang, G.L., Torres-Verdín, C., and Lee, H.J., 2008, Combined simulation and inversion of SP and resistivity logs for the estimation of connate-water resistivity and Archie’s cementation exponent: Geophysics, v. 73, no. 3, p. 1MJ-Z46, doi:10.1190/1.2890408.
Shazly, T.F. and Tarabees, E., 2013, Using of Dual Laterolog to detect fracture parameters for Nubia Sandstone Formation in Rudeis-Sidri area, Gulf of Suez, Egypt: Egyptian Journal of Petroleum, v. 22, no. 2, p. 313-319, doi:10.1016/j.ejpe.2013.08.001.
Taillet, E., Lataste, J.F., Rivard, P., and Denis, A., 2015, Characterization of discontinuities inside massive concrete structures with normal dc resistivity logging: Journal of Applied Geophysics, v. 120, p. 69-80, doi:10.1016/j.jappgeo.2015.06.005.