Predrill pore-pressure prediction using 4-C seismic data COLIN M. SAYERS, Schlumberger, Houston, Texas, U.S. MARTA J. WOODWARD, WesternGeco, Houston, Texas, U.S. ROBERT C. BARTMAN, Devon Energy, Houston, Texas, U.S.

Knowledge of formation pore pressure is important for the

successful exploration and production of hydrocarbons. During exploration, knowledge of formation pore pressure allows the hydraulic connectivity and fluid migration pathways in a region to be assessed. Thus, an increase in pore pressure below a seismic horizon may indicate the presence of a seal, while different pore pressures either side of a fault may suggest that the fault forms a barrier to flow. In deepwater, wells are expensive, and the increased costs associated with deepwater drilling in overpressured environments demand a reliable predrill prediction of formation pore pressure. Too low a mud weight may allow formation fluids to enter the well which, in the worst case, could lead to loss of the well; on the other hand, too high a mud weight will give too low a rate of penetration and could lead to fracturing of the formation. The use of seismic data for pore-pressure prediction is well known (Pennebaker, 1970; Eaton, 1975; Bowers, 1995), but the seismic interval velocities used have often been derived from stacking velocities, which locally average the velocity over the seismic aperture used in the analysis. These velocities may not be suitable for pore-pressure prediction in the presence of lateral variations that can arise from the presence of dipping structures, lithology variations, salt layers of variable thickness, fault blocks, or variations in compaction and pore pressure. Reflection tomography gives improved spatial resolution and thus allows a more reliable predrill pore pressure estimate to be obtained (Lee et al., 1998; Sayers et al., 2000). However, seismic velocities can be influenced by changes in lithology and fluid content, as well as by changes in pore pressure. Both P- and S-wave velocities can be obtained in the marine environment using multicomponent receivers at the seafloor (Figure 1). The additional information provided by the S-wave velocity may help reduce the ambiguity between variations in pore pressure and variations in lithology and fluid content. The use of combined P- and S-wave tomography is demonstrated using an example from the Gulf of Mexico. Overpressure in shales. The porosity of shales decreases during burial, as clay platelets become aligned by the in-situ stress field (Sayers, 1999). This is accompanied by an increase in elastic wave velocity, as is illustrated by the loading curves in Figures 2 and 3. If the effective stress acting on the shale decreases due, for example, to a decreased total vertical stress resulting from uplift, or because of an increased pore pressure arising from temperature increase, shale dewatering, or hydrocarbon generation, the change in microstructure remains. The porosity and velocity upon unloading, therefore, lie on a curve that differs from the loading curve. Due to a combination of rapid burial and low permeability, undercompaction, resulting from pore fluid being unable to drain during burial, is believed the main cause of observed overpressure in young, rapidly deposited sediments. For mudrocks lying on the loading curve (i.e., for mudrocks that have never undergone unloading), the Swave velocity is expected to be linearly related to the P-wave 1056

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Figure 1. Acquisition of PP and PS seismic data in the marine environment.

Figure 2. Variation of porosity during loading and unloading as a function of effective stress.

Figure 3. Variation of seismic velocity during loading and unloading as a function of effective stress. SEPTEMBER 2001

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Figure 4. P- and S-wave velocities measured by Tosaya (1982) as a function of confining stress for a dry sample at atmospheric pressure and for fluid-saturated samples of Pierre Shale at a pore pressure of 10 and 400 bar.

Figure 5. Fit of equation 1 to the P- and S-wave velocities measured by Tosaya (left). Plot of VP/VS as a function of VP for the same data (right). velocity to a reasonable approximation. For example, Castagna et al. (1985) find the following empirical relation between P- and S-wave sonic logs (the “mudrock line”): Vs = aVp - b

(1)

where, a=0.862 and b=1.172 km/s for mudrocks. A decrease in the P-wave velocity due to overpressure is, therefore, expected to be accompanied by a decrease in the S-wave velocity if the overpressure is due to undercompaction, during which the sediment is expected to follow the loading curve in Figures 2 and 3. If the reduction in the P-wave velocity is instead due to the presence of gas, the S-wave velocity might be expected to be largely unaffected. As an example, consider the P- and S-wave velocities measured by Tosaya (1982) as a function of confining stress for a dry (gas-filled) sample at atmospheric pressure and for fluid-saturated samples of Pierre Shale at a pore pressure of 10 and 400 bar (Figure 4). Figure 5 shows a fit of equation 1 0000

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Figure 6. Tomographic velocity update scheme (after Woodward et al.). to the P- and S-wave velocities and a plot of VP/VS as a function of VP. While the behavior of the two fluid-saturated samples at different pore pressures is similar, the behavior of the gas-filled sample is dramatically different, with VP/VS increasing as VP increases, in contrast to the behavior of the fluidsaturated samples. Reflection tomography. Conventional seismic stacking velocity analysis assumes that velocity varies slowly both laterally and in depth. The resulting resolution is usually too low for accurate pore pressure prediction. Reflection tomography (Stork, 1992; Wang et al., 1995; Woodward et al., 1998) replaces the low resolution layered medium and hyperbolic moveout assumptions of the conventional method with a more accurate ray-trace modeling based approach. Where stacking velocity analysis evaluates moveout on time-domain CMP gathers, tomography evaluates moveout on prestack depth-migrated common image point (CIP) gathers. CIP tomography works on a simple principle: When the velocity model is correct, there is no moveout, and prestack depth migration will map a reflector to a common depth for all offsets at which it is illuminated. The method uses ray tracing to generate a system of residual migration equations that relate changes in moveout to changes in the velocity model, which can be of arbitrary spatial complexity. An initial reference model is chosen, CIP gathers are generated, depth deviations across offset are picked, and the tomographic equations are solved to yield cell-based model updates that minimize the residual moveout, given smoothness constraints. The process is iterated to convergence. The smoothness constraints are relaxed from iteration to iteration, with the most well determined, long-wavelength features solved for first and the least well determined, short-wavelength features solved for last (Figure 6). Gulf of Mexico example. Figure 7 shows PP and PS images for a 4-C line acquired in the Gulf of Mexico. Figure 8 shows the same images with the P-wave velocity superimposed on the PP image, and the S-wave velocity on the PS-image. Reflection tomography was used first to build the P-wave velocity model with the PP reflection data. Next the P-wave velocity was held fixed and reflection tomography was used to build the S-wave velocity model using the PS reflection data. The qualitative agreement between the P- and S-wave velocities is striking. Both the P- and S-wave velocity modSEPTEMBER 2001

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Figure 7. PP (top) and PS (bottom) images for a 4-C line acquired over an overpressured area in the Gulf of Mexico.

Figure 8. P-wave velocity (top) and S-wave velocity (bottom) obtained using reflection tomography for a 4-C line acquired over an overpressured area in the Gulf of Mexico. Slow velocities are red; high velocities are blue. 1058

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els show velocity inversions arising from the presence of a low-velocity zone in the center of the line. This suggests that the reversal in the P-wave velocity cannot be explained by the presence of a different pore fluid (e.g., gas) because the S-wave velocity is expected to be affected much less by a change in pore fluid than is the P-wave velocity. A sonic log and mud weights used during drilling were available for a vertical well to the left of the major fault in Figure 7, and for a deviated well approximately two thirds of the way along this line from the left of the figure. In addition, the deviated well also had traveltime/depth pairs available from a check-shot survey. Figure 9 compares the P-wave velocity obtained by tomography at the vertical well with the interval velocity obtained by upscaling the sonic log. A comparison of the Pwave velocity obtained by tomography at the deviated well with the interval velocity obtained by inverting the check shot, and by upscaling the sonic log available at this well is shown in Figure 10. Good agreement is observed with a noticeable velocity reversal about 2 km deep. Also shown is the S-wave velocity obtained by reflection tomography at the well, compared with the S-wave velocity predicted from the tomographic P-wave velocity using the mudrock line. Although not as pronounced as that predicted from the Pwave velocity using the mudrock line, the S-wave velocity shows a clear velocity reversal. In agreement with Figure 8, this suggests that the reversal in the P-wave velocity cannot be explained by the presence of a different pore fluid (e.g., gas) because the S-wave velocity is expected to be affected much less by a change in pore fluid than is the P-wave velocity. Wells drilled upthrown to the major fault (Figure 7) indicate a stratigraphic section that is predominately shale at the depth level indicated in Figure 8 by the slow P-wave and corresponding slow S-wave velocities. Figures 9 and 10 indicate that the S-wave velocities obtained by tomography are somewhat larger than those predicted using the mudrock line. One possible reason is that isotropy was assumed in the tomographic inversion. Seismic anisotropy, if present, acts to increase the ratio of the moveout velocities for S- and Pwaves (Sayers, 1999), and might explain why the S-wave velocities obtained using reflection tomography are greater than those predicted using the mudrock line. Future work will include anisotropy in the inversion in order to estimate the magnitude of this effect. A pore-pressure prediction was made using the P-wave velocities, obtained by tomography, using Eaton’s method (Eaton, 1975) with an exponent n=4 and a normal trend line given by V(z) = V0 + kz The velocity-to-pore pressure transform was calibrated using the mud weights at the vertical well. This gave parameters V0 = 1.507 km/s and k=0.793 s-1. Figure 11 shows the tomographic velocity, normal trend, pore pressure prediction and mud weights used in drilling the vertical well. Keeping the parameters fixed, the pore pressure was then predicted at the deviated well. The tomographic velocity, normal trend, pore pressure prediction, and mud weights used in drilling the deviated well are shown in Figure 12. Conclusion. A predrill estimate of formation pore pressure is a key requirement for the safe and economic drilling of deepwater wells. Although the use of seismic velocities for pore-pressure prediction is well known, the interval velocities need to be derived using a method capable of giving a spatial resolution sufficient for well design. Normal moveout velocities average the velocity over the seismic aperture. These velocities, therefore, may not be suitable for pore presSEPTEMBER 2001

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Figure 9. Comparison of the P-wave velocity obtained by tomography at the vertical well with the interval velocity obtained by upscaling the sonic log using Backus averaging (left). The tomographic S-wave velocity at the well compared to the prediction of the mudrock line using the tomographic P-wave velocities (right).

Figure 11. P-wave velocity at the vertical well using tomography compared with the normal trend. Porepressure prediction using Eaton’s method (right).

Figure 12. P-wave velocity at the deviated well using tomography compared to the normal trend (left). Porepressure prediction using Eaton’s method (right). Figure 10. Comparison of the P-wave velocity obtained by tomography at the deviated well with the interval velocity obtained by inverting the check shot and by upscaling the sonic log using Backus averaging (left). The tomographic S-wave velocity at the well compared to the prediction of the mudrock line using the tomographic P-wave velocities. sure prediction in the presence of significant lateral variations in the velocity. Reflection tomography gives improved spatial resolution of the seismic velocity field and thus allows a more reliable predrill pore pressure cube to be obtained. However, seismic velocities can be influenced by changes in lithology and fluid content, as well as by changes in pore pressure. Both P- and S-wave data can be acquired in the marine environment using multicomponent receivers at the seafloor. The additional information provided by the S-wave velocity may help to reduce the ambiguity between variations in pore pressure and variations in lithology and fluid content.

velocities in clastic silicate rocks” by Castagna et al. (GEOPHYSICS, 1985). “The equation for geopressure prediction from well logs” by Eaton (SPE 5544, 1975). “Illuminating the shadows: Tomography, attenuation, and pore pressure processing in the South Caspian Sea” by Lee et al. (TLE, 1998). “Seismic data indicate depth, magnitude of abnormal pressure” by Pennebacker (World Oil, 1970). “Stress-dependent seismic anisotropy of shales” by Sayers (GEOPHYSICS, 1999). “Predrill pore-pressure estimation from velocity data” by Sayers et al. (2000 IADC/SPE Drilling Conference). “Anisotropic velocity analysis using modeconverted S-waves” by Sayers (Journal of Seismic Exploration, 1999). “Reflection tomography in the postmigrated domain” by Stork (GEOPHYSICS, 1992). “Acoustical properties of clay-bearing rocks” by Tosaya (doctoral dissertation, Stanford University, 1982). “Macro velocity model estimation through model-based globally optimized residual-curvature analysis” by Wang et al. (SEG 1995 Expanded Abstracts). “Automated 3-D tomographic velocity analysis of residual moveout in prestack depth-migrated common image point gathers” by Woodward et al. (SEG 1998 E Expanded Abstracts). L Corresponding author: [email protected]

Suggested reading. “Pore pressure estimation from velocity data: Accounting for pore pressure mechanisms besides undercompaction” by Bowers (SPE Drilling and Completion, 1995). “Relationships between compressional-wave and shear-wave 0000

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