Advances in resistivity processing improve well interpretation

Frank Hearn, Macmillan M. Wisler, Hal Meyer
Baker Hughes Inteq Houston

A new method for processing propagation resistivity log data allows for the simultaneous correction of anisotropy and dielectric constants, helping to improve horizontal and vertical well interpretation.

This method uses all measured data to identify, differentiate, and correct for environmental effects.

The method also corrects for bed-boundary effects using a distance to the nearest bed calculation. Without the removal of these effects, determining R_t (true resistivity) and analyzing the invasion profile remains complex and confusing.

Because logging-while-drilling (LWD) propagation resistivity tools operate at a higher frequency than induction and laterolog tools, the effects from the logging environment can become more severe for these tools.

When examining curve separation on resistivity logs, it is often assumed that the spread results from a single cause, such as invasion. In reality, however, it is likely that multiple effects influence the log.

Therefore, the key to proper log evaluation is in identifying and differentiating between the various environmental effects. Once all the effects become known, proper corrections can be applied for accurate log evaluation.

Benefits

Current LWD propagation resistivity technologies record more zones of radial measurements than earlier systems, providing geoscientists with more data for improved formation evaluation.

This results in new information about the borehole, near-borehole environment, and the formation. It provides additional benefits for high-angle and horizontal wells where it is more difficult to identify and differentiate between environmental effects.

These effects differ between horizontal and vertical wells. In vertical wells, environmental effects include shoulder beds, dielectric constant, and invasion. In horizontal wells, however, effects become more complex and include eccentricity, bed boundaries, dielectric anisotropy (e_v, e_h), resistivity anisotropy (R_v, R_h), and asymmetrical invasion.

Current software technology works in combination with the tool's multiple measurements to identify and correct for these effects. After the corrections are made, the software generates four resolution-matched resistivity curves with fixed radial depths of investigation of 10, 20, 35, and 60 in.

Eccentricity

Field comparisons with wire-line array resistivity measurements demonstrate the robustness of the method under a variety of formation-resistivity environments, clearly showing where interpretation methodology can be improved.

One environmental effect not addressed by these new processing methods is eccentricity. Fortunately, eccentricity is only a problem where large contrasts exist between the formation resistivity and mud resistivity and in enlarged boreholes.¹

Although the techniques and interpretation methodology outlined in this article were developed using Baker Hughes Inteq's Multiple Propagation Resistivity (MPR) tool, they should be applicable to any other resistivity tool with multiple investigation depths.

The MPR tool operates at two frequencies, 2 Mhz and 400 khz, and two spacings, 23 and 35 in. Phase difference and attenuation resistivities are measured at each frequency and spacing (Fig. 1 [110,103 bytes]), for a total of eight compensated and borehole-corrected resistivities.²

In addition, 32 raw phases and amplitudes are measured from each transmitter/receiver combination. A combination of both raw phases and compensated resistivities is used to generate the four fixed-depth curves, facilitating improved log interpretation in high angle and horizontal wells.

Vertical, low-angle holes

Work by Meyer has established and defined the processing methodology for low-angle and vertical wells. ³ This method selectively uses eight raw phases along with eight compensated resistivities to generate a resolution-matched, four-curve, fixed-depth of investigation similar in appearance to the modern multiarray, wire-line induction tools.

This low-angle method corrects the resistivities for shoulder-bed effect through a deconvolution routine and dielectric constant using a Complex Refractive Index Model.

Fixed depths of investigation are significant for propagation-resistivity logs because the investigation depth of phase difference and attenuation resistivities are heavily dependent on formation resistivity, making it difficult to accurately estimate invasion depth at any given resistivity without using radial response models.⁴

High-angle, horizontal wells

Because environmental influences change as relative dip angle increases, the processing methodology must change as well. Low-angle processing works only when relative angles are below 65°.

This is because of the limitations caused by the deconvolution routine. This routine therefore must be removed from the processing scheme.⁵ In addition, in horizontal wells, shoulder-bed effects are largely replaced by bed-boundary effects or the influence of beds under or overlying the formation that the tool is logging.

The effect is greatest on deeper reading measurements, especially where there are large resistivity contrasts between the bed that the tool is in and the adjacent bed.⁶ These effects can be difficult to account for since they are so heavily dependent on formation resistivities and resistivity contrasts at the bed boundary.

Another effect that requires correction in high-angle wells is resistivity anisotropy. The effects of anisotropy on propagation resistivity logs have been well documented in the literature.^7-9

Additional studies documented the complexities of correcting propagation-resistivity logs for anisotropy by demonstrating that solutions to anisotropic problems can be non-unique if only one spacing or frequency from the tool is used.¹⁰

To address this, the high-angle processing scheme first makes a correction for bed-boundary effects using a quantitative geosteering method that is an inversion of a two layer model.¹¹

In this case, the unknowns are the resistivity of the shoulder bed, the distance from the MWD tool to bed, and the horizontal and vertical resistivity of the bed.¹² This distance-to-bed inversion is done on a point-by-point basis rather than the large filtering operations typical of most deconvolutions.

After bed-boundary effects are removed, a second inversion simultaneously calculates a best-fit solution for dielectric constant at each frequency, anisotropy, and invasion parameter. These effects are best inverted together because any one of them will be miscalculated if inverted alone. Furthermore, the miscalculation of one of these parameters invariably leads to the miscalculation of the others.⁵

The last step in the processing routine transforms the corrected data into apparent resistivity values at fixed radial depths of investigation.

Pilot hole

Fig. 2 [410,408 bytes] shows the results of the high-angle processing method. This log was acquired by a 63/4-in. MPR tool in a 97/8 in. Gulf of Mexico pilot hole with a relative dip angle of 70° and a drilling fluid R _m (mud resistivity) of 0.6 ohm-m.

The eight compensated apparent resistivities are plotted in Track 2 and the high-angle, fixed-depth curves are contained in Track 3. For comparison, the low-angle fixed depth curves are included (Track 4).

The anisotropy ratio and invasion diameters are calculated from the high-angle method (Track 5). Three distinct zones characterize the log: a shale bed located above 5,030 ft, a gas sand from 5,030 to 5,100 ft, and a wet conductive zone below 5,100 ft.

Note the curve separation of the apparent compensated resistivities in the shale (Track 2). The two curves reading the highest are the shallow-reading short and long-spaced 2-Mhz phase difference resistivities. This curve order suggests either anisotropy or resistive invasion.

Of the two curves, the long-spaced, 2-Mhz phase difference reads higher than the short-spaced resistivity curve. This is not consistent with resistive invasion but is expected with anisotropy. Below 5,100 ft, the 2-Mhz resistivities are clearly affected by eccentricity.

Because the tool position relative to the borehole is not known, eccentricity effects on 2-Mhz resistivities cannot be corrected. However, this is where the value of the lower-frequency, 400-khz resistivities is realized.

The deeper resistivities-short and long-spaced attenuation-read consistently at 0.2 ohm-m, while the shallow reading curves read slightly higher, indicating very shallow resistive invasion. In these cases, the 400-khz resistivities can be used reliably for formation evaluation applications.

The low-angle, fixed-depth resistivities in Track 3 confirm the need for a high-angle processing method to correct for anisotropy or anomalous dielectric effects. The shale zone above 5,030 ft shows separation between the curves because anisotropy effects were not removed, resulting in a confusing pattern of apparent invasion where none exists.

The curve order in the gas sand from 5,030 to 5,100 ft is not consistent and is characterized by large separations. There is no correction for eccentricity effects in the conductive wet sand below 5,100 ft, resulting in an incorrect curve order.

The processing scheme suffers from two problems:

1. Poor deconvolution at high-contrast boundaries because of the high relative dip angle.
2. The presence of uncorrected anisotropy in the processed data.

The high-angle, fixed-depth data in Track 4 were processed with an intermediate algorithm that corrects for anisotropy but does not correct bed-boundary effects. This is because the 70° relative dip is not high enough to use the distance-to-bed inversion to correct for bed-boundary effects.

By comparing the low-angle, fixed-depth curves in Track 3, which have not been corrected for anisotropy, with the corrected high-angle curves in Track 4, it can be seen that all Track 4 curves above 5,030 ft are in agreement, reading a value of about 0.65 ohm-m.

Track 3 fixed-depth curves read consistently higher by about 1 ohm-m. This is consistent with an induction log from a nearby low-angle offset well that recorded resistivities of 0.67 ohm-m in the same shale.

The anisotropy correction also improved the gas-sand data between 5,030 and 5,100 ft. The correction pulls the three deepest curves closer together. The R10 curve shows the effects of shallow conductive invasion, consistent with the wet sand below, which also exhibits shallow invasion (see 400 khz resistivities in Track 2).

The curves, however, are still well separated near the high-resistivity contrast boundaries. Part of this problem is caused by the difficulty of deconvoluting high-contrast boundaries with high relative dip-angle data.

The presence of anisotropy adds complexity to the problem because the boundary effects between anisotropic layers are substantially different from those between isotropic layers.

In the conductive wet sand below 5,100 ft, the fixed-depth curves in Track 4 are essentially identical to those in Track 3. This is because both data sets suffer from eccentricity effects that are not corrected in either processing scheme.

A closer look at the plot of anisotropy ratio in Track 5 shows a higher ratio in the gas portion of the sand at 5,030 ft relative to the underlying wet zone 5,100 ft. This demonstrates the dependency of anisotropy on water saturation.

Horizontal well

The data used in the subsequent log examples were acquired while drilling a horizontal sidetrack off the pilot hole. After landing the well in the top of the gas zone at 90°, a 75/8-in. casing string was set and a 43/4-in. MPR tool was used with a directional assembly to drill a 63/4-in. borehole.

The objective was to stay 5 ft below the overlying shale while drilling 700 ft of drainhole. Before drilling the reservoir, the mud system was changed over to a more conductive fluid (0.05 ohm-m), creating a challenging borehole environment for propagation resistivity tools.

Log data as shown in Fig. 3 include eight compensated apparent resistivities (Track 2), eight compensated apparent resistivities with bed-boundary effects removed (Track 3), and calculated distance-to-bed and anisotropy ratio (Track 4).

The eight compensated resistivities illustrate the complexities of interpreting propagation resistivities in horizontal wells. It is a major challenge to determine R_t (true resistivity) or perhaps more appropriately, R_v (vertical resistivity) and R_h (horizontal resistivity), the distance to the overlying shale, and invasion depth.

The number of variables in the inversion process virtually guarantees the existence of more than one equally credible solution. However, there is no alternative to inverting all parameters. If one or more of the parameters are erroneously assumed, then this assumed knowledge will be transformed into errors for the other variables.

The curves in Track 3 illustrate the first step in the data-interpretation process. The distance to the shale has been calculated (see distance to bed curve in Track 4), and its effects have been removed from the data. There is still significant residual separation in the curves, indicating other factors such as anisotropy and invasion had some impact on the data.

At approximately 6,180 ft, there is an apparent high-resistivity zone with some curves exceeding 100 ohm-m. Although this could be explained by a decrease in water saturation or porosity, it seems unlikely because these high resistivities were not observed in the pilot hole or on the offset wire-line log.

A look at the distance-to-bed curve in Track 4 indicates the tool is in close proximity to the overlying shale, suggesting that the high resistivities are caused by a polarization horn.

Unfortunately, removing horns from field data is complex and generally very inaccurate, especially since horns seen in field data do not always resemble horns in modeled responses.

For example, the 400-khz, long-space phase difference in Track 3 shows an unrealistically high resistivity. The model used to remove the horn predicted a much smaller horn for this curve.

Even the curves reduced to more reasonable levels show some noise because of errors in the removal process. Even if the horns are the same between model and field data, the resistivity values change so rapidly that an error of just 1 in. in the distance-to-bed calculation, used to model the horn response, could result in large residuals in the data.

The next step inverts the data in Fig. 3 [357,182 bytes], Track 3, in a point-by-point manner. Variables determined in this process include anisotropy ratio, dielectric constants at each frequency, diameter of invasion, and invasion resistivity (R_xo).

Invasion parameters are inverted to improve the inversion of the other parameters. However, invasion effects are not removed from the data. Thus, invasion depth and type can be identified by evaluating the order of the fixed depth curves generated during the last step of the processing.

The 10, 20, 35, and 60-in. fixed depth curves are plotted in Fig. 4 [356,922 bytes], Track 2. Note the erratic nature of the fixed-depth data near 6,180 ft. The incomplete horn removal process as described above, causes this problem.

Regardless, a consistent pattern of conductive invasion is observed throughout the entire section. This pattern is consistent with invasion that occurred in this zone in the pilot hole. The 10-in. radius curve (R10), however, is much lower in the horizontal well than the pilot hole because the invading mud is much more conductive.

The 20-in. radius curve (R20) is also affected by invasion in some places suggesting that the invasion is deeper than in the pilot hole. It is important to note that the radial response of the fixed-depth curves is not very sharp at high formation resistivities.15 This suggests that the separation observed on the R20 curve is mostly because of invasion of less than 20-in. radius.

For purposes of comparison, fixed-depth curves processed without anisotropy or dielectric corrections are provided in Track 3. Resistivity values in Track 2 are consistently lower than in Track 3 although the difference between them varies because of the anisotropy correction.

In all cases, the horizontal resistivity value for each fixed-depth curve is plotted. Since the horizontal resistivities are used, anisotropy corrections produce lower values of all the apparent resistivities and, in some cases, much lower values.

Dielectric interpretation

The last inversion applied also determines the dielectric constant at each frequency, assuming the dielectric constant anisotropy ratio is identical to the resistivity anisotropy ratio. Although this assumption is less than rigorous, some assumptions must be made to ease the calculation burden. This method determines dielectric constant from the eight compensated apparent resistivities as opposed to using empirical relationships or models such as a Complex Refractive Index Model. ¹⁵

In this case, dielectric constants using the new method were calculated from the deepest curve in Track 2 of Fig. 4. The comparison between these two methods in relation to the dielectric constant calculation is significant because the dielectric constants in Track 3 were formerly used to correct MPR data.

In this case, the Complex Refractive Index Model calculated results are consistently higher than the results in Track 2. In other cases, particularly in shales and shaly sands, the CRIM calculations are too low.

An incorrect dielectric assumption correspondingly results in an incorrect resistivity value. Calculating the dielectric constant using the new method, for example from the phase difference and attenuation, should remove the source of the error.

Acknowledgments

The authors would like to thank the oil company operator for releasing the data used in this article. Additional thanks to Baker Hughes Inteq and especially Hal Meyer for their support. The author also thanks Ron Bitto, Stephen Scheffer, Mark Wilson, and Lori Stewart for preparation of the article and log examples.

References

1. Wu, J.Q., and Wisler, M.M., "Effect of Eccentering MWD Tools on Electromagnetic Resistivity Measurements," paper B, presented at the 31st SBWLA Annual Logging Symposium, June 24-27, 1990.
2. Meyer, W.H., Thompson, L.W., and Wisler, M.M., "A new slimhole multiple propagation resistivity tool," paper NN, presented at the SPWLA 35th Annual Logging Symposium, June 19-22, 1994.
3. Meyer, W.H., et al., 1997, "Multi-parameter propagation resistivity logging," paper GG, 38th SPWLA Annual Logging Symposium, June 15-18, 1997.
4. Barnett, W.C., and Meyer, and W.H., 1991, "Radial Response of a 2 Mhz MWD Propagation Resistivity Sensor," SPE paper 22706, 66th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Dallas, Oct. 6-9, 1991.
5. Meyer, W.H., "Interpretation of propagation resistivity logs in high-angle wells," paper D, 39th SPWLA Annual Logging Symposium, May 27-29, 1998.
6. Meyer, W.H., Thompson, L.W., and Wisler, M.M., "A new slimhole multiple propagation resistivity tool," paper NN, presented at the SPWLA 35th Annual Logging Symposium, June 19-22, 1994.
7. Anderson, B., Bonner, S., Luling, M., and Rosthal, R., "Response of 2 Mhz LWD resistivity and wire line induction tools in dipping beds and laminated formations," paper A, presented at the 31st SPWLA Annual Logging Symposium, 1990.
8. Hagiwara, T., "A new method to determine horizontal resistivity in anisotropic formations without prior knowledge of relative dip," paper Q, presented at the 37th SPWLA Annual Logging Symposium, June 16-19, 1996.
9. Bittar, M., and Rodney, P., 1996, "The effects of rock anisotropy on MWD electromagnetic wave resistivity sensors," The Log Analyst, January-February 1996.
10. Wu, J.Q., Wisler, M.M., and Meyer, H., "Measurement of dip angle and horizontal and vertical resistivity using multiple frequency propagation resistivity tools," paper C, presented at the 38th SPWLA Annual Logging Symposium, June 15-18, 1997.
11. Meyer, W.H., "New two frequency propagation resistivity tools," paper XX, presented at the SPWLA 36th Annual Logging Symposium, June 26-29, 1995.
12. Meyer, W.H., "Interpretation of propagation resistivity logs in high-angle wells," paper D, 39th SPWLA Annual Logging Symposium, May 27-29, 1998.
13. Meyer, W.H., "Interpretation of propagation resistivity logs in high-angle wells," paper D, 39th SPWLA Annual Logging Symposium, May 27-29, 1998.
14. Meyer, W.H., et al., "Multi-parameter propagation resistivity logging," paper GG, 38th SPWLA Annual Logging Symposium, June 15-18, 1997.
15. Wisler, M.M., "Method for evaluating a borehole formation based on a formation resistivity log generated by a wave propagation formation evaluation tool," U.S. Patent 5,144,245, 1992.

The Authors