GEOPHYSICS, VOL. 73, NO. 2 共MARCH-APRIL 2008兲; P. E59–E65, 10 FIGS., 1 TABLE. 10.1190/1.2821861
Investigation of core data reliability to support time-lapse interpretation in Campos Basin, Brazil
Marcos Hexsel Grochau1 and Boris Gurevich2
might result in misinterpretation of time-lapse effects. Several studies have investigated core damage as a result of the stress release during the drillout. Holt et al. 共2000兲, using synthetic rocks manufactured under stress, measure material properties in virgin conditions and compare these to properties of cores that have been unloaded to simulate coring and subsequently reloaded to in situ conditions. Nes et al. 共2002兲 use synthetic sandstones formed under stress to systematically study stress release, which in turn induces core-damage effects. The validity of acoustic core measurements can be assessed by comparing them to in situ measurements. Perhaps the most reliable in situ measurements of elastic properties of rocks are provided by the sonic log. This paper assesses the adequacy of ultrasonic measurements on core samples by comparing measured ultrasonic velocities at reservoir pressures with sonic-log data from a well in an oil field in Campos Basin, offshore Brazil. The well was chosen because of an unusually large number of core sample measurements; 43 samples of sandstone were available from 45 m of the turbidite reservoir, providing a relatively good representation of reservoir properties. Measurements of ultrasonic P- and S-wave velocities, as functions of confining pressure, were performed on these samples under room-dry conditions. The Gassmann equation was then applied to compute the properties of the saturated samples 共Mavko et al., 1998兲, which is expected to give the static limit of the elastic properties. By using dry measurements, we avoid the effects associated with the dispersion between sonic and ultrasonic frequencies, which can be large for fluid-saturated samples 共Mavko and Jizba, 1991; Batzle et al., 2006兲. Still, the difference may occur because of dispersion between low-frequency 共Gassmann兲 velocities and sonic-log velocities measured at the kilohertz frequency range. By mitigating the effect of dispersion, we can focus on the effect of core damage. To assess the magnitude of this effect, we compare the saturated low-frequency elastic-wave velocities at reservoir con-
ABSTRACT Quantitative interpretation of time-lapse seismic data requires knowledge of saturation and pressure effects on seismic velocities. Although the former can usually be modeled adequately using the Gassmann equation, the latter is obtained mainly by laboratory measurements, which can be affected by core damage. We investigate the magnitude of this effect on compressional-wave velocities by comparing laboratory experiments and log measurements. We use Gassmann fluid substitution to obtain low-frequency saturated velocities from dry core measurements 共thus mitigating the dispersion effects兲 taken at reservoir pressure. The analysis is performed for an unusual densely cored well from which 43 cores were extracted over a 45-m-thick turbidite reservoir. These computed velocities show very good agreement with the sonic-log measurements. This confirms that, for this particular region, the effect of core damage on ultrasonic measurements is less than the measurement error. Consequently, stress sensitivity of elastic properties as obtained from ultrasonic measurements is adequate for quantitative interpretation of time-lapse seismic data.
INTRODUCTION Analysis of pressure changes from time-lapse seismic data requires knowledge of the effect of pressure on elastic properties of rocks. This effect is usually inferred from ultrasonic measurements on core samples at different pressures. However, cores may be irreversibly damaged during the drilling and extraction processes, creating cracks and consequently increasing stress sensitivity. Therefore, laboratory measurements — mainly pressure effect on seismic velocities — may not be representative of the in situ formation and
Manuscript received by the Editor 27 July 2007; revised manuscript received 30 September 2007; published online 10 January 2008. 1 Curtin University of Technology, Department of Exploration Geophysics, Perth, Australia and PETROBRAS-Petroleo Brasileiro S.A, Rio de Janeiro, Brazil. E-mail:
[email protected]. 2 Curtin University of Technology, Department of Exploration Geophysics, Perth, Australia and CSIRO Division of Petroleum Resources, ARRC, Perth, Australia. E-mail:
[email protected]. © 2008 Society of Exploration Geophysicists. All rights reserved.
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ditions 共computed from the laboratory measurements兲 with soniclog data recorded in the well.
DESCRIPTION OF FIELD DATA The well logs and cores analyzed were obtained from a well in the southern portion of Campos Basin, roughly 100 km off the coast of Rio de Janeiro 共southeastern Brazil兲 in a water depth of approximately 700 m. In this basin, there are more than 40 oil fields from different ages 共Figure 1兲, representing a mosaic of reservoir properties. Each field and each reservoir has its own characteristics in terms of lithology, grain size, and cementation. In deep and ultradeep water projects, it is important to avoid costly workovers; therefore, programs of pressure maintenance are frequently used 共Bruhn et al., 2003兲. Close to the water injection wells, pore pressure can increase significantly; in other wells, it could decrease because of depletion, resulting in higher effective pressure. Considering the vast range of reservoir properties and the lateral variation of effective pressure within the reservoir, local and specific petrophysical studies should be done to guide 4D interpretations. The reservoir is made up of gravel-to-sand-rich lobes from confined turbidites related to a Cretaceous 共Santonian/Campanian兲 marine transgressive megasequence. This 45-m reservoir is composed of an amalgamation of six turbidite events measuring 2.5–14.5 m each in thickness with grain size ranging from sand conglomerate at
the base to medium/coarse sandstone at the top 共Figure 2兲. Figure 3 shows a representative thin section with its mineral composition; the reservoir rock can be classified as arkosic sandstone. After the discovery in 1984, oil production started in 1985, and the reservoir has been depleted by natural water aquifer and water injection. Twenty-five wells produce 29°API oil; permeability is 1500 mD, and temperature is 89 °C. The current and forecast recovery factors are 38% and 55%, respectively, and reservoir monitoring is important to locate unswept areas. The reservoir pressure 共pore pressure兲 initially was close to 25.51 MPa 共3700 psi兲, and the average oil saturation in the interval under investigation is 90%.
METHODOLOGY The main objective of this study is to test the adequacy of using ultrasonic measurements on core samples for quantitative interpretation of time-lapse seismic data. This strategy can be compromised by the following factors.
Compromising factors Underrepresentation Core samples are small, and core extraction is usually extremely sparse compared to the volume of rock sampled by seismic waves. Furthermore, cores are more easily taken from well-consolidated intervals, although more friable samples fall apart. Thus, core samples may not be representative of the entire formation interval. Dispersion Core measurements usually are performed at ultrasonic frequencies 共0.25–1 MHz兲 and may not be representative of the properties at seismic frequencies 共10–100 Hz兲 because of dispersion 共variation of elastic-wave velocity with frequency兲. Core damage Cores may be irreversibly damaged during the drilling and extraction processes. Specifically, these processes can create cracks that increase the stress sensitivity of the cores as compared to the intact formation 共Holt et al., 2000, 2005兲. The proposed methodology to assess the adequacy of ultrasonic measurements to the properties of the intact rock and to test the significance of these factors, consists of seven steps. 1兲 2兲
3兲
4兲 5兲 Figure 1. Map of the Campos Basin oil fields, showing the location and age of the main reservoirs 共Bruhn et al., 2003兲.
Extract as many cores as possible along the reservoir interval. Perform dry ultrasonic measurements on these cores, obtaining the relationship between stress and velocities. Estimate effective pressure at the reservoir level, taking into account pore pressure and overburden pressure. Estimate rock and fluid properties existing in the reservoir interval. Apply Gassmann’s equation to compute saturated velocities from the dry ultrasonic measurements at the reservoir effective pressure.
Ultrasonic versus log velocities for time-lapse 6兲
7兲
Perform quality control to discard some samples where the vertical variations in rock properties could not be sampled adequately by both logs and cores 共resolution problems兲. Compare the calculated saturated velocities with sonic-log measurements. Key elements of our approach are discussed below.
Log and core measurements Gamma-ray, saturation, sonic 共velocity兲, porosity, and density logs were available in the reservoir zone 共Figure 4兲. Cores were extracted continuously from 49.5 m of rocks in and close to the reservoir zone. Core measurements were performed by positioning dry cylindrical samples 共3.8 cm in diameter兲 between two pairs of piezoelectric transducers 共for P- and S-waves兲. Cores were oriented vertically within the core holder, and all were immersed together in a pressure chamber with hydraulic oil 共Figure 5兲.
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The confining pressure was increased up to 41.37 MPa 共6000 psi兲 with 3.45-MPa steps 共500 psi兲 from 3.45 up to 20.68 MPa 共3000 psi兲, then with 6.89-MPa steps 共1000 psi兲. A period of a sinusoidal pulse with 500 KHz central frequency was propagated through the sample. For each step of pressure, increment velocities were determined from the traveltime and length of each sample 共J. E. Lira, A. Sobrinho, and J. Pinheiro, personal communication, 2007兲. We focus on P-wave velocities, but S-wave velocities were also used to compute dry bulk modulus. The measurement data are given in Table 1.
Figure 3. Representative thin section from the analyzed reservoir with mineralogic composition 共quartz, 39.5%; feldspar, 25.5%; rock fragments, 10.5%; other minerals 共biotite/granade兲, 1.5%; cement, 0.5%; and porosity, 22.5%兲. GR (API) Depth (Gamma ray) (m) 0.0 ------- 150.0
Sw (fraction) (Water saturation)
Phi (fraction)
VP (m/s)
0.0 ---- (Porosity) --- 0.35
(P-wave velocity)
0.0 ---------- 0.5 2500.0 -------------------------------------------- 5000.0
Rho (g/cm3)
2.0 ----- (Density) ------ 3.0
3040 Top reservoir
3050
3060 3070 3080 3090 Bottom reservoir
3100
Figure 4. Gamma-ray, water-saturation, P-wave velocity, porosity, and density data from the studied well.
1 cm
Sample assembly
Hydraulic Vessel
Electric signal input/output Pore pressure tube
Rock sample
Transducers
Heating coil Hydraulic fluid
To pump system
Figure 2. Coarse sandstone representative of confined turbidites present in this field in Campos Basin.
Figure 5. Measurement system device.
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Table 1. Laboratory measurements at reservoir effective pressure „5000 psi… of 43 samples extracted over the reservoir interval.
Sample
Depth 共m兲
Vp 共m/s兲
Vs 共m/s兲
Density mineral 共kg/m3兲
Porosity 共%兲
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
3053.65 3054.70 3055.70 3056.70 3058.70 3059.70 3062.25 3063.30 3064.30 3065.25 3066.15 3067.10 3068.20 3069.25 3070.45 3071.20 3072.25 3073.60 3074.25 3075.05 3075.90 3076.80 3077.70 3078.80 3079.45 3080.35 3081.25 3082.10 3083.00 3083.85 3084.65 3085.90 3086.80 3087.80 3088.75 3089.65 3090.55 3091.50 3093.45 3094.70 3095.80 3097.00 3098.30
3060 3084 3089 3182 3297 3381 5974 3854 3095 3136 3250 3277 3196 3331 3603 3377 3306 3444 3477 3437 3492 3355 3469 4159 5268 3905 3742 3364 3482 3499 3409 3441 2783 3534 3555 3439 3531 3668 3803 3640 3666 4070 4040
1818 1861 1923 1924 1936 2050 3334 2075 1892 1886 1964 1991 1966 1982 2085 2057 2057 2113 2175 2110 2114 2047 1949 2176 3276 2131 2164 2085 2134 2139 2072 2108 1551 2162 2136 2098 2139 2230 2195 2106 2065 2248 2339
2680 2670 2080 2680 2690 2690 2710 2700 2700 2700 2690 2700 2700 2690 2690 2700 2690 2690 2690 2700 2700 2700 2630 2650 2720 2780 2680 2690 2710 2690 2700 2690 2690 2700 2690 2690 2690 2700 2700 2690 2690 2680 2670
0.261 0.249 0.249 0.238 0.221 0.210 0.031 0.191 0.265 0.227 0.228 0.231 0.232 0.201 0.197 0.204 0.218 0.204 0.203 0.219 0.200 0.224 0.198 0.195 0.010 0.199 0.194 0.215 0.220 0.212 0.216 0.208 0.200 0.203 0.204 0.205 0.194 0.196 0.192 0.206 0.190 0.183 0.136
Estimating the reservoir’s effective pressure To estimate the effective pressure Peffec affecting elastic-wave velocities in the reservoir, we used the following equation:
Peffec ⳱ Pover ⳮ Ppor ,
共1兲
where Ppor is the pore pressure, is the effective stress coefficient, and Pover is the overburden pressure, calculated as
Pover ⳱ Ahw Ⳮ B共hr ⳮ hw兲,
共2兲
where A and B are ocean water and lithostatic pressure gradients and where hw and hr are water and reservoir depths, respectively. Pore pressure was obtained from repeat formation tester 共RFT兲 well measurements, made when the logs were acquired, provided constant values over the reservoir interval. The effective stress coefficient for velocities was assumed to be one. Because the sensitivity of elastic properties to pressure in this stress range is relatively weak, this assumption is unlikely to influence our results. The resulting value of effective pressure was 34.47 MPa 共5000 psi兲 for the interval under investigation.
Calculation of elastic modulus Once the laboratory measurements were made on dry cores, the saturated bulk modulus Ksat was computed using Gassmann’s equation:
冉
冊
Kdry 2 Kmin Ksat ⳱ Kdry Ⳮ , 1ⳮ Kdry Ⳮ ⳮ Kfluid Kmin 共Kmin兲2
共3兲
2 2 Kdry ⳱ dry共VPdry ⳮ 4VSdry /3兲
共4兲
1ⳮ
where
is the bulk modulus of the dry rock, Kmin is the effective modulus of the solid grains, Kfluid is the effective modulus of the saturating fluid, VPdry and VSdry are the compressional- and shear-wave velocities measured in the dry sample, is the porosity, and dry is the density of the dry sample. The petrologic description of the reservoir sands suggests some heterogeneity of the mineral composition of the reservoir. This may lead to a depth-dependent composite mineral modulus. Considering that we did not have the mineral composition for different depths, we used a representative bulk mineral modulus 共Km兲. We also performed a sensitivity analysis to evaluate the impact of variations of Km 共and K f 兲 on fluid substitution 共Figure 6兲. This analysis shows that 10% variations in mineral and fluid modulus have small effect on velocities 共Ⳮ8 to ⳮ11 m/s and 14 to ⳮ13 m/s, respectively兲, which are insignificant for our study. A saturation log was available, so it was taken into account to calculate the fluid bulk modulus using Wood’s equation 共Reuss average of fluid moduli兲:
1 Kfluid
⳱
1 ⳮ Sw Sw Ⳮ , Kw Ko
共5兲
Ultrasonic versus log velocities for time-lapse
–25
0
25
50
75
100
1
–100 1
3
3
5
5
7
7
9
9
11
11
13
13
15
15
17
17
Core sample
19 21 23 25
–50
–25
0
25
50
75
100
19 21 23 25
27
27
29
29
31
31
33
33
35
35
37
37
39
39
41
41
43
–75
43
Kf (orig) – Kfluid + 10% Kf (orig) – Kfluid – 10%
Km (orig) – Km + 10% Km (orig) – Km – 10%
Vpsat (m/s)
b)
Quality control and selection of subset
Kfluid (+10%)
3575 3570 3565 3560 3555 3550 3545 3540 3535 3530 Kfluid orig
where G ⳱ V is the shear modulus of the rock, fluid ⳱ Sw w Ⳮ 共1 ⳮ Sw兲 o is the composite fluid density, and sat ⳱ fluid Ⳮ dry is the density of the saturated rock. Dry rocks are usually assumed to have little or no velocity dispersion, at least relative to the large dispersion that occurs when pore liquids are introduced 共Winkler, 1986; Mavko and Jizba, 1995兲. Therefore, the velocities computed from dry measurements using Gassmann’s equation can be considered as measured in the low-frequency 共quasi-static兲 limit. As a result of this calculation, elastic moduli and saturated velocities were obtained for 43 samples for each effective pressure step 共3.45– 41.37 MPa兲. As an example, Figure 7 shows the dependency of velocities on effective pressure for six samples. To compare with log measurements, we selected velocities corresponding to the estimated effective pressure present in situ 共34.47 MPa兲. 2 S dry
–50
Kfluid (-10%)
共6兲
–75
Km ( + 1 0 % )
,
Variation in VPsat (m/s)
Variation in VPsat (m/s) –100
Km orig (41.2GPa)
冣
1/2
Core sample
冢
4 Ksat Ⳮ G 3 VPsat ⳱ sat
a)
Km (-10%)
where Sw is water saturation and Ko and Kw are the bulk moduli of the oil and water phases, using equations from Batzle and Wang 共1992兲. Finally, the saturated compressional velocity VPsat was obtained using the standard equation
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Vp core saturated (m/s)
Considering the large number of cores available, it was possible to discard some samples deemed to be nonrepresentative of the reservoir Figure 6. The effect of 10% variation in bulk mineral Km and fluid moduli Kfluid on saturated P-wave velocities VPsat: 共a兲 sample-by-sample and 共b兲 averaged over the reservoir inproperties. As can be seen in Figure 8, the reserterval. A variation in bulk mineral modulus of Ⳳ10% will result in VPsat changes of 8 and voir interval contains a few low-porosity zones ⳮ11 m/s. The same percentage of change in fluid modulus will cause 14 and ⳮ13 m/s related to the presence of concretions containing changes, respectively. large quantities of calcite cement either as small balls or lenses. These concretions usually form very thin layers that are undersampled 共smoothed over兲 by both porosity and sonic logs. At the same time, core samples can come either from concretions or from surrounding reservoir rock. In both cases, 3700 this may result in a large discrepancy between log and core porosities. 3500 Therefore, the porosity criterion was used primarily to discard the 3300 samples where the difference between the core and log porosities was greater than 3%. Figure 8 shows both measurements of porosity, 3100 as well as the discarded samples 共in gray兲. From the original data set 2900 3053.65 of 43, we retain 27 samples, which were considered representative of 3059.70 the reservoir sandstone and potentially comparable with log mea2700 3066.15 3074.25 surements. 2500
RESULTS
3083.00 3091.50
2300 3
7
10
14
17
21
28
34
41
Effective pressure (MPa)
Figures 9 and 10 compare the saturated velocities computed for the selected subset from cores 共blue dots兲 against corresponding sonic-log data. We see very good agreement between the two sets of
Figure 7. Velocity versus effective pressure for a selection of core samples at different depths.
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Grochau and Gurevich
Porosity (ffracttion) 0.00 3050
0.10
0.20
Vp log - Vp core saturation (m/s)
0.30
0.40
–350
–150
–50
50
150
250
350
–62
Phi log
3055
–250
–150 –171
Phi core
–51 –28
3060 –180
159 93 –99 –74
3070
2 11
Samples
De epth (m)
3065
3075 3080
83 –52 –7 30 –14 110
3085
46 –206
3090
–4 224 –133
3095
–84 –186
3100
–85 –25
Figure 8. Porosity from log versus porosity from cores showing the discarded samples 共in gray兲, based on the porosity criteria.
Vp (m/s) 2700 3050
2900
3100
3300
3500
3700
3900
Vp log 3055
Vp core sat
3060
3065
Depth (m)
3070
3075
3080
3085
3090
3095
3100
Figure 9. Comparison of saturated P-wave velocities computed using Gassmann’s equation from dry core measurements 共dots兲 against a sonic log 共line兲.
Figure 10. Differences between saturated P-wave velocities computed using Gassmann’s equation from dry core measurements and the sonic log. We can see that differences are usually smaller than 200 m/s. Percentage of change in fluid modulus will cause 14 and ⳮ13 m/s changes, respectively. data. The average difference 共systematic error兲 between the two sets is ⳮ32 m/s 共0.93%兲, which is within the core measurement error range 共up to 3%兲. The rms of the differences between the sonic log and the computed core velocities is 110 m/s. The fact that random errors are larger than systematic ones suggests that the effect of core damage is insignificant because this effect is expected to result in a systematic weakening of the samples. A similar result was observed in Schiehallion field by Meadows et al. 共2005兲.
CONCLUSIONS We have described a methodology to assess the adequacy of ultrasonic velocities measured in the laboratory for use in sonic and seismic modeling 共with potential use in time-lapse interpretation兲, focusing on the effect of core damage. Dispersion effects have been minimized by using dry cores and then computing saturated velocities 共Gassmann兲; underrepresenting cores are reduced by extracting many cores over the reservoir interval. The main conclusion is that the saturated velocities computed from core measurements on dry samples match the sonic-log velocities quite well. This means the effect of core damage on the elastic properties of the core samples is small, i.e., below the measurement errors. Consequently, stress sensitivity of elastic parameters, as obtained from ultrasonic measurements, is adequate for quantitative interpretation of time-lapse seismic data. The results also suggest the usefulness of laboratory measurements on cores, including core preservation during extraction.
Ultrasonic versus log velocities for time-lapse The results of the study relate to a particular reservoir in the Campos Basin, offshore Brazil. Other studies in the same basin and other parts of the world are needed to verify how general this conclusion is.
ACKNOWLEDGMENTS The authors would like to thank Petrobras for providing log and core data, granting permission to publish this paper, and funding the Ph.D. scholarship of Marcos Grochau. The financial support of the sponsors of the Curtin Reservoir Geophysics Consortium is gratefully acknowledged. We are also grateful to David Lumley, David Dewhurst, Guilherme Vasquez, and Silvia Malagutti for their ideas, opinions, and comments.
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Batzle, M., and Z. Wang, 1992, Seismic properties of pore fluids: Geophysics, 57, 1396–1408. Bruhn, C. H. L., C. Del Lucchese, J. A. T. Gomes, and P. R. S. Johann, 2003, Campos basin: Reservoir characterization and management — Historical overview and future challenges: Offshore Technology Conference, OTC 15220, Expanded Abstracts, 1–14. Holt, R. M., M. Brignoli, and C. J. Kenter, 2000, Core quality: Quantification of coring-induced rock alteration: International Journal of Rock Mechanics and Mining Sciences, 37, 889–907. Holt, R. M., O. M. Nes, and E. Fjaer, 2005, In-situ stress dependence of wave velocities in reservoir and overburden rocks: The Leading Edge, 24, 1268–1274. Mavko, G., and D. Jizba, 1991, Estimating grain-scale fluid effects on velocity dispersion in rocks: Geophysics, 56, 1940–1949. Mavko, G., T. Mukerji, and J. Dvorkin, 1998, The rock physics handbook: Tools for seismic analysis of porous media: Cambridge University Press. Meadows, M., D. Adams, R. Wright, A. Tura, S. Cole, and D. Lumley, 2005, Rock physics analysis for time-lapse seismic at Schiehallion field, North Sea: Geophysical Prospecting, 53, 205–213. Nes, O. M., R. M. Holt, and E. Fjaer, 2002, The reliability of core data as input to seismic reservoir monitoring studies: Annual Technical Conference and Exhibition, Society of Petroleum Engineers, Expanded Abstracts, 79– 86. Winkler, K. W., 1986, Estimates of velocity dispersion between seismic and ultrasonic frequencies: Geophysics, 51, 183–189.
