QUANTITATIVE STUDIES OF RELATIVE DIP ANGLE AND BED - THICKNESS EFFECTS ON LWD DENSITY IMAGES ACQUIRED IN HIGH-ANGLE AND HORIZONTAL WELLS

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1 QUANTITATIVE STUDIES OF RELATIVE DIP ANGLE AND BED - THICKNE EFFECTS ON LWD DENSITY IMAGES ACQUIRED IN HIGH-ANGLE AND HORIZONTAL WEL E.A. Uzoh, A. Mendoza, and C. Torres-Verdín, The University of Texas at Austin; W.E. Preeg, Consultant, E. Stockhausen; Chevron Energy Technology Company Copyright 2007, held jointly by the Society of Petrophysicists and Well Log Analysts (SPWLA) and the submitting authors. This paper was prepared for presentation at the SPWLA 48 th Annual Logging Symposium held in Austin, Texas, June 3-6, short-spaced and long-spaced sensors included in the tool. ABSTRACT Logging While Drilling (LWD) density images acquired in high-angle and horizontal (HA/HZ) wells can reveal much about the sedimentary structure of rock formations penetrated by the well. However, the effect of sedimentary structure on the measured density has only now begun to be explored. This paper describes numerical simulations undertaken to quantify the influence of relative dip angle and bed thickness on LWD density images acquired in HA/HZ wells penetrating thinly-bedded formations comprised of alternating sands and shales. Typically, the azimuthal binning scheme used to construct LWD density images divides the tool into 16 azimuthal sectors, each sector subtending an angle of 22.5 o from the center of the tool. Count rate data are binned to angular sectors facing density detectors. Our objective is to assess the effects of adjacent beds on sector density measurements due to finite bed thickness and variable relative dip. The Monte Carlo N-Particle (MCNP) transport code is used to simulate LWD density measurements from several combinations of relative dip angle and bed thickness. Commercial count-rate processing techniques are applied to the short-spaced and longspaced detector measurements in each sector. The assumed source-sensor configuration corresponds to the commercial adnvision675 LWD nuclear tool designed to operate with an 8.25-in stabilizer in an 8.5- in borehole. Our study provides a way to estimate the corresponding depth shifts in true stratigraphic thickness (TST) observed in HA/HZ wells, which are caused by the difference in the radial lengths of investigation of the Mark of Schlumberger 1 INTRODUCTION The interpretation of LWD measurements acquired in HA/HZ wells is often questioned because of the effects of well geometry together with the geometrical and environmental properties of the rock formations penetrated by the wells. Well geometry includes relative dip angle, while rock formation properties include bed thickness and formation density. Therefore, reliable interpretation of log measurements and quantitative evaluation of potential hydrocarbon deposits requires understanding how geometrical and borehole environmental effects as well as properties of rock formations influence LWD measurements. There is a limited volume of technical literature available on the effects of borehole geometry and rock formation properties on nuclear measurements. Passey et al. (2005) summarized the technical challenges associated with quantifying rock properties from HA/HZ wells. Ellis and Chiaramonte (2000) simulated neutron measurements acquired in HA/HZ wells and used the results to explain how modeling improves the understanding of complicated measurements acquired in HA/HZ wells. Furthermore, Yin et al. (2006) assumed theoretical LWD density and neutron tools to examine the effects of borehole shape, azimuthal angle, bed thickness, and relative dip on nuclear measurements acquired in HA/HZ wells. They found that the response of short- and long-spaced detectors in HA/HZ wells depends on the tool s azimuthal position as well as on the relative dip angle. Their analyses were based on the raw response of the detectors and they emphasized the need to perform more studies using specific source-sensor configuration of commercial nuclear tools. Badruzzaman et al. (2007) assumed a generic wireline tool to study sensitivity of density measurements to bed thickness, azimuth, and borehole angle. They analyzed the influence of processing techniques on density measurements acquired across thin beds. Radtke et al. (2006) evaluated the response M

2 of a commercial LWD density tool to sandwiched rock formations of varying bed thicknesses using numerical modeling. Their study excluded the effects of relative dip since they primarily focused on the simulation of rock formations penetrated by horizontal and vertical wells. Radtke et al. (2006) found that for the case of thinly-bedded reservoirs, density measurements acquired in horizontal wells resolved thinner beds than in vertical wells. They also emphasized the technical challenges of estimating accurate bed boundaries and formation density in reservoirs with thin beds. According to Radtke et al (2006), it is possible to improve the reliance on density measurements by estimating the bed thickness from density images. Clearly, more information is needed to interpret measurements acquired in HA/HZ wells, particularly for decreasing values of bed thickness. Density images embody a wealth of information about borehole geometry and formation environment. They facilitate the selection of bed boundaries and the estimation of relative dip angles and are commonly used in geosteering and completion decisions. However, quantitative use of density images is yet to be explored in formation evaluation. In this paper, we use density images to quantify the effects of high relative dip angle, bed thickness, and tool standoff on LWD density measurements acquired in HA/HZ wells. To that end, we simulate the response of a commercial LWD density tool in measured depth to variations of bed thickness and relative dip using the MCNP code developed by Los Alamos National Laboratory. In so doing, we maintain a fixed quarterinch difference between the tool and the top of the hole and a zero standoff at the bottom of the hole as is typically the case in HA/HZ wells. Two dimensional (2D) measurements are simulated from the sequential translational and rotational motions of the density tool, similar to the actual measurement acquisition environment during drilling. These simulated 2D measurements are subsequently used to construct the borehole image. In the remainder of the paper, we examine the individual detector response for each sector together with the processed density data along the well trajectory. Visualizing the detector response for each azimuth facilitates the quantitative analysis of effects due to HA/HZ well geometry on density measurements. Important observations made from the simulation results include that short- and long-spaced detector response are out of phase; therefore their modulation amplitudes do not coincide as in the case of vertical wells. This phase difference is due to the discrepancy in the radial length of investigation (LOI) of the two detectors. In addition, we attempt the estimation of the relative dip angles using similar techniques commonly applied to azimuthal borehole resistivity logs. Through a back calculation, we estimate values for the correction term usually included in the assessment of electrical penetration. Finally, we compare the effects of drilling up-section versus down-section on LWD density measurements acquired in HA/HZ wells. METHODOLOGY Azimuthal Binning Scheme of the LWD Density Tool Figure 1 describes the azimuthal binning scheme applied on LWD density tool measurements in this study. As described by Radtke et al. (2003), the tool is divided into 16 sectors, each subtending an angle of 22.5 o from the center of the tool. To conform to conventions used in the LWD industry, tool rotation commences and stops in the top quadrant. In our modeling, we assume that the tool is eccentered in the borehole and exhibits a maximum tool standoff when the tool faces the top quadrant. The start and end positions of the tool are designated by sectors 0 and 15, as shown in the diagrams of Fig. 1a and Fig. 1b, respectively. As shown in Fig. 1, to simulate the density measurement, the LWD tool is placed at the center of each sector (at an angle of o ). In so doing, we assume that a measurement obtained in a sector of the tool represents the average LWD density measurement for that sector. To justify this assumption, we analyzed the azimuthal sensitivity of a commercial LWD density tool. Figures 2a, 2b, and 2c describe the sensitivities of the source, short- and long-spaced detectors of the assumed LWD tool around the perimeter of the borehole. Based on this figure, we can conclude that as much as 80% of the azimuthal density response originates from an azimuthal angle of about 25 o of the borehole, thus validating our assumption. Mendoza et al. (2007) provide a comprehensive description of the procedures involved in obtaining the azimuthal measured sensitivities shown in Fig. 2. Description of the Formation The formation models adopted in this paper are similar to those described by Radtke et al. (2006). Beds alternate between high and low densities but have a constant thickness. While the density of the low-density bed is 2.0 g/cm 3, the highdensity bed has a density of 2.6 g/cm 3. Such a density range is representative of the typical values found in practice. The same density range also allows us to study density measurements acquired across large density contrasts between formation layers. Table 1 provides a summary of fluid and rock-formation properties used in the modeling of alternating sand-shale sequences. In our simulations, we assumed an 8.5-in borehole drilled with freshwater mud. Likewise, we assume that tool 2

3 standoff varies from 0 in at the bottom quadrant to 0.25 in at the top. SIMULATION OF DENSITY MEASUREMENTS Simulations of density measurements were performed using the MCNP code. Because the tool is symmetric, we simulated only the tool s response to one-half of the perimeter of the borehole. Therefore, we rotated the tool in the clockwise direction from an azimuth of o (top quadrant) to 168 o (bottom quadrant). An azimuthal sampling rate of 22.5 o was used to ensure that the tool remained in the mid-point of each sector. Thus, for each depth sampling point, there were eight density simulations around the borehole perimeter. The general principle of operation of the density tool is such that gamma rays emitted from the source are scattered to the scintillating detectors. The received gamma ray flux is inversely proportional to the electron density of the formation, which is related to the bulk density by the expression ρe = 2 ( Z / A) ρ, (1) b where ρ e is electron density, ρ b is formation density and (Z/A) is the ratio of the atomic number to the atomic weight of the formation. Using MCNP, we tracked the transport of photons from the gamma ray source to the detectors. Three bed thicknesses (2in, 4in, and 6in) were considered in the laminated formation models used in this study. Each of these formations was penetrated by wells inclined at three different angles from the vertical. Well inclinations span across HA/HZ wells as described in the technical literature. According to Passey et al. (2005), HA wells are inclined at 60 o 80 o from the vertical axis while HZ wells include those with inclination greater than 80 o from the vertical axis. Therefore, in the simulations we considered wells with relative dip angles of 95 o, 100 o, and 105 o relative to the top of the hole. We note that the 90 o case has been previously studied by Radtke et al. (2006) Figure 3 describes the measurement acquisition in a HA/HZ well penetrating a laminated formation. The true vertical depth (TVD) is measured from the bottom of the borehole as described by Radtke et al. (2006). Furthermore, the zero-depth position is the interface between the high-density and low-density bed with the low density bed located above this interface. To secure acceptable resolution and save CPU time, we assumed a sampling rate in TVD of 1.2 in for 6-in beds, 1 in for 4- in beds, and 0.5 in for 2-in beds. In measured depth, these sampling rates vary with relative dip angle. However, field measurements are sampled at a higher density of 1.2 in in measured depth. 3 Approximately 300 minutes of CPU time were required to simulate density measurements for each detector at each measurement location in the HA/HZ wells. To ensure a statistical error below 0.7%, 120 million particle histories were used to compute the short- and long-spaced density measurements. Processing techniques and algorithms applied to the count rates from each detector are those used with commercial software developed for the tool. Specifically, rib corrections were applied to compensate for standoff between the tool and formation based on the difference between short- and long-spaced densities. Density Measurement in a 95 o Well Figure 4 displays the azimuthal density response of each detector and their density correction curves when measurements are acquired in a 95 o well penetrating 6-in laminated beds. We note that the short- and long-spaced detector density curves are out of phase. This exercise represents the LWD tool drilling up-section. Figure 5 shows the density images for a 95 o well penetrating 6-in laminated beds. Figure 6 shows the density response when the 95 o well penetrates 4-in laminated beds. The observed effect of bed thickness is the decrease in the amplitude of the long-spaced density modulation below that simulated for the 6-in formation. Figure 7 shows the density images simulated for this case. Figure 8 shows the simulated density response with the 95 o well penetrating 2-in laminated beds. The simulated short- and long-spaced density curves average bed densities in a similar manner to what was observed by Radtke et al. (2006). Figure 9 shows the density images associated with this well. Density Measurements in a 100 o Well We now consider the case of a 100 o well penetrating alternating beds. Figure 10 displays simulated short- and longspaced density measurements in 6-in laminated beds. Figure 11 displays the images acquired in this case. Figure 12 summarizes the simulated density for the various detectors when measurements are in a 100 o well penetrating 4-in laminated beds. The amplitude of the oscillations of the short- and long-spaced density curves are slightly lower than those simulated for the 4-in formation penetrated by a 95 o well. Figure 13 shows the density images acquired when the 100 o well penetrates 4-in beds. Figure 14 shows the various detector measurements as well as the density correction curves when the 100 o well penetrates 2-in bed laminations. As expected, peaks of the density fluctuations simulated for this well M

4 are lower than those simulated when a 95 o well penetrates 2-in bed laminations. Density images simulated from the 100 o well penetrating the 2-in bed laminations are shown in Fig. 15. Density Measurements in a 105 o Well Finally, we consider the case of a 105 o well penetrating 6-in, 4-in, and 2-in bed laminations. Figure 16 shows the simulated azimuthal density measurements for various detectors, acquired for the 105 o well penetrating 6-in laminated beds. Peaks of the short- and long-spaced density modulation remain similar to those obtained when a 95 o or 100 o well penetrates 6-in bed laminations. Furthermore, as in the case of 95 o and 100 o wells, the corresponding density images, shown in Fig. 17, accurately resolve the bed thickness. Figure 18 shows the short- and long- spaced density curves for the case of 4-in bed laminations. Figure 19 shows the density images simulated for this case. Figure 20 shows the simulated short- and long-spaced density logs when the 105 o well penetrates 2-in bed laminations. At the top quadrant, the long-spaced density curve has slight deflections. Figure 21 shows the density images simulated for this case. These density images do not resolve the bed thickness as for the case of 4-in or 6-in beds. SUMMARY AND CONCLUSIONS Simulated azimuthal density measurements acquired with the short- and long-spaced detectors have been applied in this study to assess the effects of relative dip angle, tool standoff, and bed thickness in HA/HZ wells. While the maximum standoff was assumed to be in throughout the study, relative dip angles and bed thicknesses were varied to include a practical range of environmental and geometrical conditions. Our simulation work indicates a general depth difference between short- and long-spaced detector measurements as the tool rotates around the perimeter of an inclined borehole. Relative to the short-spaced density curve, the long-spaced density curve assumes the following positions: first, it is above the short spaced response when the tool faces the top quadrant (sector 0); second, it is in phase with the short-spaced response when the tool faces the left/right quadrant; third, it shifts above the short-spaced density curve when the tool faces the bottom quadrant. These depth shifts are associated with HA/HZ wells and are due to the difference in the radial lengths of investigation of the long-spaced and short-spaced density detectors. We estimated the relative dip angle, α, from simulated short- and long-spaced, and compensated density images. To that end, we applied the same technique used in electrical images (Yin et al., 2006). Accordingly, as shown in Figs. 22 through 24, we fit a sinusoid to the bed boundary. The vertical axis of these images is in measured depth: A, is the crest of the sinusoid and B is the trough. Relative dip angle is calculated with the equation 1 A B α = tan, (2) D+ 2ΔR where D is the bit size and ΔR is referred to as the electrical penetration. Table 2 describes estimates of ΔR required to yield accurate relative dip angles from short- and long-spaced, and compensated density images. From back calculations, we note that ΔR must be 1.5in and 1in to estimate accurate relative dip angles from the compensated and long-spaced density images, respectively. Relative dip angles estimated from the short-spaced density images require no correction for measurement penetration. Finally, we compared the effect of the drilling direction on LWD measurements acquired in HA/HZ wells. Figures 23 and 24 display the simulated density measurements while the tool is assumed to travel downsection. We note that measurements simulated in this case are similar to those acquired while drilling upsection. The estimated relative dip angles with respect to the top of the borehole are also listed in Table 2 for this case. Therefore, we conclude that there are no significant differences between LWD measurements acquired drilling up-section or down-section in HA/HZ wells. ACKNOWLEDGEMENTS We thank Schlumberger for providing the tool configuration used in this paper and M. Evans, R.J. Radtke, and J. Rasmus of Schlumberger for their expert guidance throughout the project. The work reported in this paper was funded by The University of Texas at Austin s Research Consortium on Formation Evaluation, jointly sponsored by Anadarko, Aramco, Baker Atlas, BP, British Gas, ConocoPhilips, Chevron, ENI E&P, ExxonMobil, Halliburton Energy Services, Hydro, Marathon Oil Corporation, Mexican Institute for Petroleum, Occidental Petroleum Corporation, Petrobras, Schlumberger, Shell International E&P, Statoil, TOTAL, and Weatherford. REFERENCES Badruzzaman, A., Mendoza, A., Stockhausen, E.J., and Reik, B. A., 2007, Density measurement sensitivity 4

5 to varying angle and tool azimuth in medium to thin beds, 2007 SPWLA Annual logging Symposium, Austin, Texas, June 3-6. Ellis, D.V., and Chiaramonte, J.M., 2000, Interpreting neutron logs in horizontal wells: a forward modeling tutorial, Petrophysics, vol. 41, no. 1, pp Mendoza A., Torres-Verdín, C., and Preeg, W.E., 2007, Rapid simulation of borehole nuclear measurements based on approximate spatial flux-scattering functions, 2007 SPWLA Annual logging Symposium, Austin, Texas, June 4-7. Passey, Q.R., Yin, H., Rendeiro, C.M., and Fitz, D.E., 2005, Overview of high angle and horizontal well formation evaluation: issues, learning, and future directions, 2005 SPWLA Annual Logging Symposium, Paper A, New Orleans, Louisiana, June Radtke, R.J., Evans, M., Rasmus, J.C., Ellis, D., Chiaramonte, J.M., Case, R.C., and Stockhausen, E., 2006, LWD density response to bed laminations in horizontal and vertical wells, 2006 SPWLA Annual Logging Symposium, Paper ZZ, Veracruz, Mexico, June 4-7. Radtke, R.J., Adolph, R. A., Climent, H., and Ortenzi, L., 2003, Improved formation evaluation through image-derived density SPWLA Annual Logging Symposium, Paper P, Galveston, Texas, June Yin, H., Han, X., Xu, L., Guo, W., Shehata, A., and Gardener, R.P., 2006, Field and benchmark studies of LWD nuclear tool response in high-angle and horizontal wells, 2006 SPWLA Annual Logging Symposium, Paper AAA, Veracruz, Mexico, June 4-7. ABOUT THE AUTHORS Echezona Uzoh is a Graduate Research Assistant and a M.Sc. candidate in the Department of Petroleum and Geosystems Engineering of The University of Texas at Austin. He obtained a B.Sc. degree in Mechanical Engineering from the University of Lagos, Nigeria in He is a recipient of the 2005 Moni Pulo/Baker Hughes Endowed Scholarship. He has worked as a nuclear scientist intern with Baker Hughes/INTEQ. His research focuses on petrophysics and well-log interpretation. Alberto Mendoza is a Graduate Research Assistant and a Ph.D. student in the Department of Petroleum and Geosystems Engineering of The University of Texas at Austin. He received both B.Sc. and M.Sc. degrees in Petroleum Engineering from The University of Texas at Austin in 2002 and 2005, respectively. From 2002 to 2003 he worked for Schlumberger as a field engineer in the area of well testing. He has been an intern with Schlumberger-Doll Research and Chevron. He was granted a scholarship by the SPWLA. His research interests include petrophysics, log analysis, inverse problems, and well testing. Carlos Torres-Verdín received a Ph.D. degree in Engineering Geoscience from the University of California, Berkeley, in During he held the position of Research Scientist with Schlumberger-Doll Research. From , he was Reservoir Specialist and Technology Champion with YPF (Buenos Aires, Argentina). Since 1999, he has been with the Department of Petroleum and Geosystems Engineering of The University of Texas at Austin, where he currently holds the position of Associate Professor. He conducts research on borehole geophysics, well logging, formation evaluation, and integrated reservoir characterization. Torres-Verdín has served as Guest Editor for Radio Science, and is currently a member of the Editorial Board of the Journal of Electromagnetic Waves and Applications, and an associate editor for Petrophysics (SPWLA) and the SPE Journal. He is co-recipient of the 2003 and 2004 Best Paper Award by Petrophysics, and is recipient of SPWLA s 2006 Distinguished Technical Achievement Award. William E. Preeg received a Ph.D. degree in Nuclear Science Engineering from Colombia University in From 1980 to 2002, he held various positions with Schlumberger, including Director of Research at Schlumberger-Doll Research, Vice President of Engineering Houston as well as Manager of the Nuclear Department at Schlumberger-Doll Research. Prior to 1980, he worked for Los Alamos Scientific Laboratory, Aerojet Nuclear Systems Company, and the Atomic Energy Commission, largely in the area of nuclear radiation and transport. He has also served on advisory committees at The University of Texas at Austin, Texas A&M University, Colorado School of Mines, and Georgia Tech. Ed Stockhausen is a staff research scientist with Chevron Energy Technology Company and is based in Houston, Texas. Ed graduated from the University of Florida with an M.Sc. degree in geology in Over the next 16 years, he held various exploration and production geology positions for Chevron in New Orleans, focusing on Gulf-of-Mexico field development. For the past eight years, Ed has been responsible for leading the development and deployment of geosteering technology for Chevron worldwide. M 5

6 Table 1: Rock and fluid properties assumed in the simulation of borehole density measurements Variable Units Value High density bed g/cm Low density bed g/cm Borehole fluid density g/cm Borehole diameter in 8.5 Maximum tool standoff in 0.25 % Quartz in high density bed 60 % Calcite in high density bed 0 % Illite in high density bed 0 %Water in high density bed 40 % Quartz in low density bed 62 % Calcite in low density bed 30 % Illite in low density bed 4 %Water in low density bed 4 Table 2: Estimates of relative dip angle from short- spaced, long-spaced, and compensated density images. density density Compensated density Bed (in) L True Dip ( o ) Est. Dip ( o ) Est. ΔR (in) Est. Dip ( o ) Est. ΔR (in) Est. Dip ( o ) Est. ΔR (in) U mud l B 0 R 15 U mud col Fig. 1: Cross section of an LWD density tool showing the relative location of the borehole and the azimuthal binning scheme. The brown region is the gamma ray sensors; dark blue is tungsten shield; light gray is the collar and stabilizer; light blue is drilling mud. The arrow shows the direction of tool rotation. Sector 0 is the tool s start position (top of hole). The bottom (B), right (R), up (U) and, left (L) quadrants are used in reference. Sector 15 is the tool s end position. L B R (c) Fig. 2: Spatial Sensitivity of the gamma- ray source (Cs -137) of the commercial density tool. The upper panel displays the spatial sensitivity in the radial and azimuthal directions while lower panel contains spatial sensitivity in the azimuthal direction only. Similar to but for the short-spaced detector of the density tool. (c) Similar to but for the long-spaced detector of the density tool. 0 α Fig. 3: Section views of a density tool in a well with relative dip angle, α, and 8.5-in borehole. Bed thickness is 2in; dark gray is the drill collar; dark blue is tungsten shielding and the sensors are orange. Brown layers have a low density and light gray layers have a high density. The arrow shows the direction of drilling (up-section). Standoff between the tool and the borehole wall is largest at the top quadrant. True vertical depth is measured from the interface tangent to the bottom of the borehole as indicated by the number 0 in the figure in the right panel. This convention implies that the logs in the figures reference the source as the measurement point, unlike commercial processing. 6

7 M Fig. 4: Filtered short- and long-spaced detector response in a 95 o well penetrating 6-in bed laminations. Light brown blocks identify low-density beds and white blocks identify high-density beds. The tool position in each sector is indicated at the top of each panel. Density correction (Δρ) curves. (c) (d) (e) Fig. 5: Filtered short-spaced detector density image from a 95 o well penetrating 6-in bed laminations. Light brown blocks identify low-density beds and dark brown blocks identify high-density beds. Long-Spaced detector density image. (c) Density correction (Δρ) image. (d) Compensated density image. (e) Alpha-processed density image. 7

8 Fig.6: Filtered short- and long-spaced detector response in a 95 o well penetrating 4-in bed laminations. Light brown blocks identify low-density beds and white blocks identify high-density beds. The tool position in each sector is indicated at the top of each panel. Density correction (Δρ) curves. (c) (d) (e) Fig. 7: Filtered short-spaced detector density image from a 95 o well penetrating 4-in bed laminations. Light brown blocks identify low-density beds and dark brown blocks identify high-density beds. Long-Spaced detector density image. (c) Density correction (Δρ) image. (d) Compensated density image. (e) Alpha-processed density image. 8

9 M Fig. 8: Filtered short- and long-spaced detector response in a 95 o well penetrating 2-in bed laminations. Light brown blocks identify low-density beds and white blocks identify high-density beds. The tool position in each sector is indicated at the top of each panel. Density correction (Δρ) curves. (c) (d) (e) Fig. 9: Filtered short-spaced detector density image from a 95 o well penetrating 2-in bed laminations. Light brown blocks identify low-density beds and dark brown blocks identify high-density beds. Long-Spaced detector density image. (c) Density correction (Δρ) image. (d) Compensated density image. (e) Alpha-processed density image. 9

10 Fig. 10: Filtered short- and long-spaced detector response in a 100 o well penetrating 6-in bed laminations. Light brown blocks identify low-density beds and white blocks identify high-density beds. The tool position in each sector is indicated at the top of each panel. Density correction (Δρ) curves. (c) (d) (e) Fig. 11: Filtered short-spaced detector density image from a 100 o well penetrating 6-in bed laminations. Light brown blocks identify low-density beds and dark brown blocks identify high-density beds. Long-Spaced detector density image. (c) Density correction (Δρ) image. (d) Compensated density image. (e) Alpha-processed density image. 10

11 M Fig. 12: Filtered short- and long-spaced detector response in a 100 o well penetrating 4-in bed laminations. Light brown blocks identify low-density beds and white blocks identify high-density beds. The tool position in each sector is indicated at the top of each panel. Density correction (Δρ) curves. (c) (d) (e) Fig. 13: Filtered short-spaced detector density image from a 100 o well penetrating 4-in bed laminations. Light brown blocks identify low-density beds and dark brown blocks identify high-density beds. Long-Spaced detector density image. (c) Density correction (Δρ) image. (d) Compensated density image. (e) Alpha-processed density image. 11

12 Fig. 14: Filtered short- and long-spaced detector response in a 100 o well penetrating 2-in bed laminations. Light brown blocks identify low-density beds and white blocks identify high-density beds. The tool position in each sector is indicated at the top of each panel. Density correction (Δρ) curves. (c) (d) (e) Fig. 15: Filtered short-spaced detector density image from a 100 o well penetrating 2-in bed laminations. Light brown blocks identify low-density beds and dark brown blocks identify high-density beds. Long-Spaced detector density image. (c) Density correction (Δρ) image. (d) Compensated density image. (e) Alpha-processed density image. 12

13 M Fig. 16: Filtered short- and long-spaced detector response in a 105 o well penetrating 6-in bed laminations. Light brown blocks identify low-density beds and white blocks identify high-density beds. The tool position in each sector is indicated at the top of each panel. Density correction (Δρ) curves. (c) (d) (e) Fig. 17: Filtered short-spaced detector density image from a 105 o well penetrating 6-in bed laminations. Light brown blocks identify low-density beds and dark brown blocks identify high-density beds. Long-Spaced detector density image. (c) Density correction (Δρ) image. (d) Compensated density image. (e) Alpha-processed density image. 13

14 Fig. 18: Filtered short- and long-spaced detector response in a 105 o well penetrating 4-in bed laminations. Light brown blocks identify low-density beds and white blocks identify high-density beds. The tool position in each sector is indicated at the top of each panel. Density correction (Δρ) curves. (c) (d) (e) Fig. 19: Filtered short-spaced detector density image from a 105 o well penetrating 4-in bed laminations. Light brown blocks identify low-density beds and dark brown blocks identify high-density beds. Long-Spaced detector density image. (c) Density correction (Δρ) image. (d) Compensated density image. (e) Alpha-processed density image. 14

15 M Fig. 20: Filtered short- and long-spaced detector response in a 105 o well penetrating 2-in bed laminations. Light brown blocks identify low-density beds and white blocks identify high-density beds. The tool position in each sector is indicated at the top of each panel. Density correction (Δρ) curves. (c) (d) (e) Fig. 21: Filtered short-spaced detector density image from a 105 o well penetrating 2-in bed laminations. Light brown blocks identify low-density beds and dark brown blocks identify high-density beds. Long-Spaced detector density image. (c) Density correction (Δρ) image. (d) Compensated density image. (e) Alpha-processed density image. 15

16 (c) Fig. 22: Estimation of relative dip angle from a short-spaced density image acquired from a 95 o well penetrating 6-in bed laminations. The black line identifies the modeled bed boundary. The letter A identifies the trough and the letter B identifies the crest Similar presentation as in but for a long-spaced density image (c) Similar presentation as in but for a compensated density image. Fig. 23: Filtered short- and long-spaced detector response in an 85 o well penetrating 6-in bed laminations with drilling down-section. Light brown blocks identify low-density beds and white blocks identify high-density beds. The tool position in each sector is indicated at the top of each panel. (c) (d) (e) Fig. 24: Filtered short-spaced detector density image from an 85 o well penetrating 6-in bed laminations with drilling down-section. Light brown blocks identify low-density beds and dark brown blocks identify high-density beds. Long-Spaced detector density image. (c) Density correction (Δρ) image. (d) Compensated density image. (e) Alpha-processed density image. 16