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Stress-velocity sensitivity in Gullfaks Brent reservoir sands Anders Dræge*, Anne-Kari Furre, Youness El Ouair, Statoil ASA Summary There is a general perception of core plugs having larger stress sensitivity than in-situ stress sensitivity. Measurements and estimations of the in-situ stress are commonly considered complicated, and few studies have proposed efficient strategies for the purpose. This paper uses a well-measurement based method that estimates the in-situ stress dependency of Brent reservoir sands in the Gullfaks field. The results show porosity dependent velocity increase for increasing net stress. The increase is compared with stress dependency in core plugs taken from the same sands. Introduction The Gullfaks oil field is located in the Norwegian sector of the northern North Sea. It is a structurally complex field with sandstone reservoir units of Cretaceous to Triassic age. The reservoir quality is generally very good, with porosities in the range of 30-35% and permeability up to several Darcys in the most important Brent Group reservoir. Brent consists of five main formations; Broom, Rannoch, Etive, Ness and Tarbert, of which the four last named constitute reservoir sands at Gullfaks. The drainage strategy is to maintain pressure with the use of both water and gas injection. The last decade, increased oil recovery (IOR) methods like time-lapse seismic have received a strong focus. The baseline streamer survey was acquired in 1985, one year before production start. This survey was repeated in 1996, 1999, 2003 and 2005. Three OBS surveys were acquired in 2001, 2003 and 2005 in order to cover the shadow areas of poor data coverage in the streamer data around the existing installations. The repeated (time-lapse) surveys are used for monitoring fluid movement, identify bypassed reserves, provide possible sites for infill drilling and to monitor pore pressure changes. Since hydrocarbon production and injection alter pore pressures, it is important to be able to separate saturation and stress effects both in forward and inverse seismic modelling (El Ouair and Strønen, 2006). Stress sensitivity studies on core-plugs from the reservoir sands have been performed, and shown significant velocity increase with increasing effective stress (decreasing pore pressure). But core studies rely on the assumptions that the core is representative for the rock in situ, and that the laboratory conditions are representative for the conditions in situ. Limitations of core plug studies are well known (e.g. MacBeth, 2004; Eiken and Tøndel, 2005; Furre et al. 2007). This paper applies a strategy that enables stress sensitivity analyses from in situ measurements in well logs.

Only P-wave velocities (Vp) are considered, due to lack of shear-wave velocity (Vs) data. The velocity increase for each Brent formation with increasing net stress is presented, and the results are compared with core measurements. Net stress is defined as the difference between mean surrounding stress and pore pressure, and it is normalized to the relevant in-situ stress state (5 MPa). The mean of vertical stress and minimum horizontal stress is defined as the mean surrounding stress. There are no estimations of maximum horizontal stress, but the small discrepancy between vertical and minimum horizontal stresses supports the procedure. Method The method applied is described in detail by Furre et al. (2007), and is based on well log data (porosity, saturation, clay content, density, sonic (DT) logs and formation pressure readings). In addition temperature and confining stress were obtained from depth dependent relationships. Modified Gassmann theory (Mavko et al., 2003) was used to invert for dry compressional modulus. The FLAG program based on Batzle and Wang (1992) equations was used to account for pressure dependent fluid effects in the inversion. The method utilizes the fact that even though all logs are obtained prior to production in the specific well, the majority of the Gullfaks production wells are drilled in pressure depleted areas relative to initial (pre-production) pore pressure, due to production from other wells. Since the level of pressure depletion varies from well to well, velocities in similar formations can be compared for different pressure states, to find velocity sensitivity with increasing net stress/decreasing pore pressure. Figure 1 illustrates the depletion states in the data used in this study. Only sands with less than 15 % clay content are used, to prevent that clay content becomes a significant parameter. To minimize porosity effects, the sands are divided into two porosity classes with approximately the same amount of data in them; class 1: 30 – 34 % porosity, class 2: 34 – 40 % porosity. Formation pressure logs are not continuously sampled, so interpolation of existing measurements in each well was necessary to enhance the database of this study, see Figure 2. Filtering of extreme velocity data was necessary. Anomalous velocities can be due to erroneous log data or deviating mineralogy like calcite cement or coal, which is not registered in the well logs used. The filter was defined to remove all points that deviated more than the standard deviation from the median velocity for a given net stress. This process removed some of the upper and lower velocities. When analyzing the results, the increase in net stress was defined in steps of 0.25

2857SEG/San Antonio 2007 Annual Meeting

Stress sensitivity in Gullfaks reservoir sands

Figure 1. Left: Net stress for undepleted formation (blue) and from log recordings (black). Right: Pressure depletion in various wells. The highest depletion seen in the wells is around 6.5 MPa.

Figure 2. Interpolation between formation pressure readings (black stars) are performed to create continuous pressure logs (grey line). Unless formation pressure readings indicate it, interpolation over faults (red zigzag) and potential lithological pressure barriers (black stippled) is omitted. Estimated undepleted pore pressure is shown as a blue stippled line while internal sands are marked with vertical white stippled lines. MPa, and all stresses are regressed to this sampling. Each pressure depletion value is weighted equally, to avoid that the large amount of data with low changes in net stress dominates the whole trend. Results The sensitivity of dry P-wave velocity due to increasing net stress is shown in Figure 3 for both porosity classes. A net stress increase of 1 MPa entails a Vp increase of around 1.3 % and 0.25 %, respectively. When looking at each individual Brent formation, the two porosity classes are merged to increase the amount of data and reduce dominating anomalies, see Figure 4. Two different gradients are used to analyze the velocity-stress trends; the least square (Lsq) gradient puts highest weight

Figure 3. Stress sensitivity of dry P-wave velocities in Gullfaks Brent sands. Above: Normalized dry velocity increase with increasing net stress for porosities ranging from 30 – 34 %. Below: Normalized dry velocity increase for porosity values higher than 34 %.. on the data deviating most from the trend (L2 norm), while the robust fit (L1 norm) in a higher degree ignores the outlier velocities. The latter seems to best describe the velocity dependence in this study, since anomalous high velocities occur at low net stresses in some sands (Figure 4). This leads to a seemingly too low, and in one case even negative, velocity gradient (Rannoch). The core plug measurements are normalized to the in situ net stress (5 MPa) in order to compare with the in situ velocities, see Figure 5. The core sample data were fitted to an exponential equation given by Furre (2002). The figure indicates that the average velocity versus net stress trend in the Brent reservoir sands are lower for both class 1 and class 2 sands than in the core plugs. The core plugs display large scatter for most sands, but all the average core plug trends in the lower plot lie close to each other.



Figure 4. Normalized stress sensitivity of individual Brent sands.

Figure 5. Comparison of core plug velocities and velocities from individual sands (colored lines with superposed diamonds) and average Brent sand trends for porosity class 1 (circles on red line) and class 2 (stars on red line). The symbols elongate the velocity trends from this study to higher stress-changes. Discussion In order to compare stress fits from logs and laboratory measurements, the data were normalized to 5 MPa, which is approximately the expected net stress in the undepleted reservoir sands. The choice of normalization stress influences the final stress trends of the core plugs, but enables a more realistic comparison with the reservoir velocities than without normalizing. Net stress increase in this study ranges from 0 - 3.5 MPa (Rannoch and Etive) to 0 - 6.5 MPa (Tarbert and Ness), which is far lower than the net stresses exerted on the core plugs. Ideally the stress range should have been larger to increase the effects of stress changes relative to uncertainties in the study.

Class 1

Class 2



The high stress dependence found in Etive sands might be due to mineralogical effects like calcite cementing in some of the samples with highest depletion, coal that lowers the velocities in the samples with low depletion or a combination of both. Etive is however the sand with fewest log data, which might allow anomalous data to dominate the seemingly very high stress dependency. For the Etive and Rannoch sands, the maximum change in net stress is 3.5 MPa, which is probably close to a limit of detection. When the average stress trends for all Brent sands are studied, significant differences are observed between the two porosity classes. Class 1 seems to follow the Rannoch trend, while class 2 follows the Ness trend, although Rannoch and Ness are approximately equally presented in both classes. The well log data can not explain why the velocities in the high porosity sands seemingly have lowest net stress dependence, but it might be due to mineralogical differences. Both class 1 and 2 trends give a lower stress dependency than the core plugs, although the trend for class 1 is close to the core plug trends. The proximity might partly be explained by a natural high stress dependency of the very loose and unconsolidated high porosity reservoir sand found in Gullfaks Brent sands. It can, however, be difficult to perform high-stress measurements in dry cores taken from such unconsolidated reservoirs. Therefore the cores are taken from the low porosity and more consolidated end members of the sands, averaging to a porosity of 24.5 %. The low porosity can be due to calcite cement, which stabilizes the rock and lowers stress sensitivity. This hypothesis is supported by CT-scans performed on the cores, which show heterogeneities and scattered areas with densities sometimes approaching the density of the solid phase (approximately 2.65 g/ccm). Direct mineralogical analyses of the core plugs have however not been performed. The robust curve fitting commonly gives steeper velocity-stress trends for the individual sands, but when the dataset gets sufficiently large (e.g. for the whole Brent Group) the trends are almost identical, see Figure 3. Some factors might introduce uncertainties in the well log data used in this study. To minimize invasion effects, only wells with the same mud type are used, but no further corrections for invasion effects were conducted. Intrinsic anisotropy was neglected, since only relative clay-free sandstones were used in the study. Therefore wells with varying wellbore deviations (from vertical to horizontal) were used. This might introduce varying stress conditions along the wellbore (the measuring direction varies). There is no information about these stress conditions, so mean stress is used for all data as previously explained. Figure 3 shows that even after filtering the data and removal of shoulder points (samples that lie within one meter of a shale), the scatter is significant. The well log porosities range from 30 % to around 40 %. This interval embraces ca 85 % of all log data in clean sands. The large

difference between class 1 and class 2 trends indicates that porosity-induced stress dependency might cause some of the scatter. It is also important to stress the importance of having a large database with data distributed along the whole stress interval when estimating trends, since a large variation of trends can arise when the dataset get small. The velocity-stress trends are often considered to be exponential, but for the small stress intervals and large scatter in this study a linear trend is clearly the best alternative. Conclusions Although some scatter in the data, the method used in this paper can be a good and realistic alternative to core plug measurements in established fields with good well coverage worldwide. The robust curve fitting gave linear increasing velocities with stress for all Brent sands. For the whole Brent Group in Gullfaks, the highest stress dependency was found for velocities in sands with porosities ranging from 30 to 34 %. Sands with higher porosities showed smaller velocity increase with increasing net stress. Both trends were lower than the velocity–stress trends found in core plugs. These results can be applied to provide a better basis for prediction and interpretation of time-lapse seismic effects at the Gullfaks field, e.g. in seismic modeling or inversion. Acknowledgement The authors would like to thank Statoil and the Gullfaks partners Hydro and Petoro for accepting publication of the results. Statoil colleague Inge Kaas is acknowledged for helpful discussions and comments.


EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2007 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES Batzle, M., and Z. Wang, 1992, Seismic properties of pore fluids: Geophysics, 57, 1396–1408. Eiken, O., and R. Tøndel, 2005, Sensitivity of time-lapse seismic data to pore pressure changes: Is quantification possible?: The

Leading Edge, 24, 1250–1254. El Ouair, Y., and L. K. Strønen, 2006, Value creation from 4D seismic at the Gullfaks Field: Achievements and new challenges:

76th Annual International Meeting, SEG, Expanded Abstracts, 3250–3254. Furre, A. K., 2002, The effective stress coefficient for wave velocities in saturated grain packs: 64th Annual Conference and

Exhibition, EAGE, Extended Abstracts, P093. Furre, A. K., M. Andersen, A. S. Moen, and R. K. Tønnessen, 2007, Sonic log derived pressure depletion predictions and

application to time-lapse seismic interpretation: 69th Annual Conference and Exhibition, EAGE, Extended Abstracts, P077.

MacBeth, C., 2004, A classification for the pressure-sensitivity properties of a sandstone rock frame: Geophysics, 69, 497–510. Mavko, G., T. Mukerji, and J. Dvorkin, 2003, The rock physics handbook: Cambridge University Press.


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