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Formation resistivity determination

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Resistivity is the one of the most difficult formation parameters to measure accurately because of the complex changes that occur during and after drilling a well and that may still be occurring during logging. The various components of the downhole environment may have strongly contrasting resistivities, some of which cannot be measured directly, and their physical dimensions may not be readily available.

Challenges in measuring resistivity

Fig. 1 shows an idealized relationship of the main environmental components. The resistivities and dimensions of all these "layers" (mud, mudcake, flushed zone, and zone of transition) influence all deep-reading resistivity measurements. There is no direct measurement of Rt. It must be inferred from the multiple-depth resistivity measurements.

In a permeable formation, mud resistivity is commonly 1 to 3 orders of magnitude lower than the formation resistivity, or, in the case of oil-based mud (OBM), it can be much higher. The downhole mud resistivity can be estimated approximately by measuring the resistivity of a surface sample taken just before mud circulation was stopped before logging and adjusting it for the difference in temperature using an appropriate chart or equation. The shape and size of the borehole and the position of the logging tool in the hole have an influence on resistivity measurements that will not be apparent from a single hole-size measurement.

Attempts to measure the resistivity of an artificially formed sample of mudcake is unlikely to represent in-situ mudcake resistivity accurately. Mudcake thickness cannot be directly measured with current logging tools; it can only be estimated with some uncertainty.

The resistivity of the flushed zone can be measured with reasonable precision if the depth of invasion is greater than the depth of investigation of the Rxo logging tool, but the depth of invasion and the resistivity profile and geometry of the zone of transition are difficult to estimate.

Traditional methods

Evaluation of the uninvaded formation resistivity Rt is sometimes referred to as invasion correction. It is usually performed assuming a simple three-parameter, step-profile invasion model consisting of a flushed zone of uniform resistivity Rxo with a sharp boundary at the diameter of invasion di to resistivity Rt. This is clearly not realistic, but it allows a complex problem to be solved relatively simply, usually with acceptable accuracy, by using a minimum of three resistivity measurements with different depths of investigation.[1]

A shallow microresistivity measurement, such as the MicroSFL log, is corrected for the influence of the mudcake by using the best available estimates of mudcake thickness and resistivity. It is assumed that di is greater than the depth of investigation of the MicroSFL, so that the MicroSFL log reads only the flushed zone and the mudcake-corrected MicroSFL reading is Rxo.

Next, the deep- and medium-resistivity measurements are corrected for environmental effects using the charts for the tool used. These effects are always corrected in the following order:

  • Borehole effect
  • Bed thickness
  • Shoulder effect

Then the invasion parameters (Rxo, Rt, di) can be found for induction tools using tornado charts. For laterolog tools, butterfly charts are used. Some service companies offer charts for Rt and di when Rxo is known from a microresistivity device.

Inversion for invasion parameters

The latest array-induction and array-electrode tools all use some form of inversion (rather than charts) to estimate the invasion parameters—invasion radius or diameter, di, Rxo, and Rt. There are two types of inversion used: 1D and 2D. The formation geometry of each is shown in Fig. 2.

Inversion means first building a parametric model of the formation, then estimating from the log values a "first guess" of the parameter values. Then, a modeling code is used to compute the log response to the model. This is compared with the actual logs. The difference between modeled and measured is used to pick a new set of model parameters, and the log response computed. Again, the modeled logs are compared to the actual logs. This continues until the difference reaches some preset minimum, and then the model parameters are output as the invasion parameters.

Induction response is mostly a function only of coil spacings, with a weak response to the large-scale average formation conductivity. If we can assume that each formation layer is more or less uniformly invaded, then an inversion through a 1D radial forward model[2] will give a close estimate of invasion parameters Rxo and Rt. This is most often true when Rxo > Rt.

Laterolog tools are much more affected at the same time by both bed thickness and invasion parameters in that bed. For this reason, when the formation of interest consists of thin (< 30 ft [10 m]) beds, 2D inversion is necessary for accurate estimation of Rxo, Rt, and di. 1D inversion tends to be used in real-time processing, and 2D inversion is used at the computing center. Some commercial 2D-inversion applications allow very sophisticated choices of parametric models, including transition zones and annulus models.

Inversion methods also return "goodness-of-fit" criteria. At the same time, the modeled logs can be compared with the actual logs as a quality control. Inversion methods also allow the parametric model to be selected to better fit the situation at hand. A four-parameter inversion model, with a zone of transition defined from di to the diameter of the limit of invasion at dj, gives reliable answers in a much wider range of conditions than the traditional three-parameter model. It also generates "quality-of-fit" parameters that indicate when the log readings are not consistent with the model.

Annulus formation is a common phenomenon, caused by the sweeping of conductive ions from the formation by the invading borehole fluid. Fluid-flow models predict annulus formation in a wide range of formation/borehole fluid conditions. Annulus formation has been observed with both water-based mud (WBM) and oil-based mud (OBM). Even with five or six depths of investigation, the information content is not sufficient to solve for the five annulus parameters (Rxo, Rann, Rt, r1, and r2) independently. However, by invoking the constraint of material balance[3] and supplying an estimate of Rw, the annulus problem can be reduced to three parameters: Rxo, r1, and Rt. r2 is tied to r1 through the material-balance constraint, and Rann can be estimated from Rmf, Rxo, and Rw.

Invasion also changes with time, sometimes rapidly. For this reason, the combination of data taken at different times (e.g., wireline and logging while drilling (LWD), or LWD time-lapse), must be done with care. One method that has shown promise is to use a consistent parametric model (step or annulus) and assume Rxo and Rt are constant, allowing only for the invasion radius to change.

Before performing an inversion for invasion parameters, be sure the cause of curve separation is actually invasion. Causes of curve separation include:

  • Tool-response effects such as shoulder effect
  • Not matching the resolution of the curves
  • Improper borehole correction

Other formation effects that can cause curve separation include:

  • Dipping beds
  • Drilling-induced fractures

The introduction of array-resistivity tools has clearly delineated invasion profiles that were not as expected, even after years of logging in a region. In some regions, it was assumed that the formation was uninvaded because the ILd, ILm, and SFL logs all were very close in pay zones. Logs made by an array-induction tool showed an Rxo < Rt profile. The discrepancy exists because the SFL, being a laterolog, can have a depth of investigation as deep as ILd under Rxo < Rt conditions. The ILm was long considered an inferior measurement to ILd because it would lie lower in resistivity than either SFL or ILd. Modeling shows that either an annulus or Rxo < Rt will produce this curve order.

A powerful method for handling the fundamentally underdetermined problem of invasion correction of resistivity logs is iterative forward modeling.[1] Complex formation geometries and invasion profiles can be worked out by:

  • Building a model of the best estimate of formation parameters from:
    • Logs
    • Field knowledge
    • Petrophysical constraints
  • Modeling the resistivity logs
  • Varying the parameters until a fit is obtained

Finally, keep in mind that Rt cannot be measured directly, but must be inferred from multiple-depth resistivity measurements.

Resistivity imaging

Many modern resistivity- and microresistivity-logging tools have arrays of sensors that make multiple measurements, enabling the creation of 2D images of formation resistivity. The images represent resistivity variations with the azimuth around the borehole or with distance away from the borehole.

Inspired by the images produced by early acoustic borehole televiewer tools, borehole resistivity imaging was developed to see actual formation variations, rather than the surface effects that the acoustic images depicted. The first practical resistivity images were produced by an array of closely spaced, shallow-reading button electrodes applied to the borehole wall.

The borehole coverage of this high-resolution microresistivity image was increased on later tools, and deeper reading tools with imaging capabilities have been subsequently developed.

Microresistivity images

The first microelectrical imaging tool had an array of button electrodes mounted on an enlarged section of the tool mandrel. Electrodes were then placed on two of the four pads of the Dual Dipmeter tool. The Fullbore Formation MicroImager (FMI) tool[3] has button electrodes on all four pads, with extension flaps on each pad to increase the borehole coverage.

FMI image data have sufficient resolution and character to allow using selected electrode signals for conventional dipmeter computations, and the tool’s borehole coverage provides a detailed visual appreciation of geologic features, Fig. 3. Formation dips and fracture orientations can also be derived directly from the images.

Seeing the shape of formation-resistivity variations often provides understanding of the lack of coherent dip found by a dipmeter computation program.

Halliburton’s Electromagnetic MicroImager (EMI) tool is a six-arm resistivity borehole imager tool. Its principle of operation is similar to the FMI tool. Baker Atlas’ Simultaneous Acoustic and Resistivity (STAR) Imager tool integrates resistivity and acoustic borehole imaging sensors into one instrument. The resistivity imager is a six-arm device with powered centralization to keep the acoustic transducer centered. The acoustic sensor also works in OBM where the resistivity imager performance is poor.

ARI images

The formation resistivity around the borehole is displayed in ARI images as a 2D azimuthal image, with the same dimensions of well depth and azimuthal angle around the well as FMI images. This image has much lower spatial resolution than acoustic or microelectrical images from the UBI and FMI tools, but it complements them well because of its sensitivity to features beyond the borehole wall and its lower sensitivity to shallow features.

AIT images

The AIT provides images of variations in formation resistivity or conductivity with distance away from the borehole. This capability brings a new dimension to formation image data, because the image contains invasion information useful for understanding how deeply the formation can be invaded.

Radial response functions are used to invert the set of matched vertical resolution logs in the four-parameter invasion model, producing a detailed description of the radial resistivity. Introducing other petrophysical parameters, such as F, Rw, and Rt, and a suitable saturation equation (see Saturation Determination section) allows imaging-computed virgin and invaded-zone saturations.

LWD resistivity images

The GVR tool incorporates three 1-in.-diameter azimuthal button electrodes that produce borehole resistivity images during rotary drilling by recording 56 resistivity measurements per rotation with each electrode. The data are processed and recorded downhole for later retrieval.

Because the GVR button electrodes are larger than FMI electrodes and are not in contact with the formation, GVR images are less sharp than FMI images, as seen in Fig. 4. However, often the timeliness of the images more than makes up for the resolution. A compression algorithm allows the images to be sent up in real time for geosteering.

Formation dip from LWD images

Dip computation by conventional dipmeter data processing is most effective when the apparent dips (i.e., dips relative to tool inclination) are less than approximately 70°, which is suitable for most vertical and normally deviated wells. LWD has major applications (e.g., geosteering) in highly deviated and horizontal wells, where apparent dips are commonly greater than 70°. A dip-computation process that returns dip from the GVR in real time was developed for high-angle wells.[4] The dip-azimuth and magnitude computations are performed by a robust algorithm in the downhole tool, allowing real-time transmission of the dip data. Although the well deviation is accurately measured by instruments in the drill collar, the relative dip with respect to the bedding is important for geosteering wells along the bedding planes. This method allows improved well placement.

The confidence in computed GVR dips is increased by using data from all three electrodes. Because the electrodes are at fixed distances from each other, irregular tool movement in the hole is unimportant.


R = resistivity (ohm•m)
Rann = resistivity of the annulus
Rh = resistivity in the horizontal direction (ohm•m)
Rm = resistivity of the mud column (ohm•m)
Rmc = resistivity of the mudcake
Rmf = resistivity of the mud filtrate
Rxo = resistivity of the invaded zone
Rt = resistivity of the uninvaded formation
Rv = resistivity in the vertical direction (ohm•m)
Rw = resistivity of the formation connate water (ohm•m)
Rwa = apparent water resistivity from deep resistivity and porosity
Sxo = water saturation of the invaded zone


  1. 1.0 1.1 Anderson, B.I. 2001. Modeling and Inversion Methods for the Interpretation of Resistivity Logging Tool Response. Delft, The Netherlands: Delft U. Press.
  2. Howard, A.Q. 1992. A New Invasion Model for Resistivity Log Interpretation. The Log Analyst 33 (2): 96.
  3. 3.0 3.1 Gondouin, M., Hill, H.J., and Waxman, M.H. 1962. A Tri-Chemical Component of the SP Curve. J Pet Technol 14 (3): 301.
  4. Rosthal, R.A., Bornemann, E.T., Ezell, J.R. et al. 1997. Real-Time Formation Dip From a Logging-While-Drilling Tool. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 5-8 October. SPE-38647-MS.

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See also

Resistivity and spontaneous (SP) logging

Well log interpretation

Log analysis in shaly formations