We 6 Density/Porosity Versus Velocity of Overconsolidated Sands Derived from Experimental Compaction S. Narongsirikul* (University of Oslo), N.H. Mondol (University of Oslo and Norwegian Geotechnical Inst) & J. Jahren (University of Oslo) SUMMARY We present P- and S-wave velocities and density/porosity of seven natural sands experimentally mechanically compacted in various loading and unloading stages. The results show different velocitydensity/porosity relationships for overconsolidated stages compared to normally consolidated stages at the same stress level. We utilised different rock physics models to observe the data on velocity-density/ porosity and VP/Vs versus acoustic impedance crossplots. The velocity-porosity plot from overconsolidated sands plotted along the friable sand lines not only describe sorting deterioration but also differences in preconsolidation stresses. Well logs data from the Barents Sea show similar patterns to the measured data. The VP/VS versus acoustic impedance crossplot shows two additional trends (e.g. in the direction of reduced stress and increased precompaction stress). Fluid sensitivity is low in overconsolidated sands compared to normal consolidated sands as a function of increasing preconsolidation stress. These findings allow us better rock physics diagnostics of uplifted sediments and application of 4D seismic monitoring of uplifted basin like in the Basents Sea. 7 th EAGE Conference & Exhibition incorporating SPE EUROPEC 1 London, UK, -1 June 1
Introduction Rock physics models have long been used for diagnosing rock and fluid properties (Avseth et al., Fawad et al. 11). For high porosity sandstones, the most common theoretical model used to describe the velocity-porosity relation is the friable sand model introduced by Dvorkin and Nur (1996). The model is used as a bound to describe how velocity and porosity change due to sorting. Most rock physics models were established from either experimental and/or field data assuming normal burial compaction. However, in many sedimentary basins the sediments have experienced both burial and uplift, and even reburial. This complex stress history affects the velocitydensity/porosity relationships in different ways as the rock is previously stressed to higher levels. In this study, we utilised some of the available rock physics models to describe relations between seismic velocities and rock physical properties of seven natural sands of varying textural and mineralogy compositions compacted mechanically at various loading, unloading and reloading stages. We also study how the fluid sensitivity is affected as the rock undergoes uplift and reburial. The outcomes allow us to predict the velocity-density/porosity relationships of sands in the mechanical compaction domain and to better understand how rocks and fluids affected by uplift like in the Barents Sea might behave during 4D seismic reservoir monitoring. Experimental procedure The seven brine-saturated natural sand samples with varying mineralogical composition and texture (Figure 1) were compacted in a triaxial cell setup at the Norwegian Geotechnical Institute (NGI). Detail sample description can be found in Fawad et al. (11). We also included data from Zimmer et al. (7) for comparison. We allowed isotropically loading up to. MPa followed by uniaxial strain condition (K loading; the ratio between horizontal and vertical effective stresses) from. to MPa. At every,, and MPa effective stress, unloading and reloading cycles were applied to study the effects of preconsolidation in shallow overconsolidated but uncemented sandstones (Figure 1). Loading rates were kept constant at.7 MPa/hr during K consolidation. Creep were allowed and observed during the experiments. The deformations were continuously recorded during the loading and unloading cycles. The error in the vertical effective stress was ±. MPa (±.%). P- and S- wave velocities (V P and V S ) were measured using the pulse transmission technique. We recorded the V P and V S signals in steps of approximately every MPa. The velocities were calculated from absolute sample height changed at different target stress levels divided by the travelling times through the samples. The porosity and density were calculated using gravimetric analysis in which mass and volume of the sample were measured. Hence, the density can be calculated as a ratio between mass and volume changes. It is worth noting that since the sands were loose with well-connected pores, very little squirt affecting velocity dispersion was expected. Eff. Stress (MPa) Theoretical model Dvorkin and Nur (1996) introduced a friable sand model describing how the velocity-porosity changes as the sorting deteriorates for high porosity sands. The model is calculated using a combination of Hertz-Mindlin (HM) contact theory (Mindlin 1949) and modified Hashin- Shtrikman lower bound (196). Several studies show that HM theory overpredicts velocities Loading procedure when compared to measured data. In particular, Zimmer et al. (7) shows that HM theory vastly overpredicts shear moduli. For this reason, we utilised the shear and bulk moduli from the highest porosity dry sample (QA) used by Fawad et al. (11) to calculate the friable sand models. The models were used in velocity-porosity, velocity-density, and V P /V S - crossplots of the experimental mechanically compacted (normally loaded-unloaded-reloaded) sands. Results Ko-Consolidation Isotropic Loading path (Step number) Figure 1 (Top) Sample description. (Bottom) 7 th EAGE Conference & Exhibition incorporating SPE EUROPEC 1 London, UK, -1 June 1
Figures and show V P and V S, respectively, plotted as functions of total porosity and effective stress of all seven sands. The data were superimposed on friable sand models calculated for different effective stress levels. The initial porosity ranges between - 44% for all sand samples. As the effective stress increases, the loss of porosity and velocity increase were observed. Two significant velocity-porosity trends were observed in which unloading-reloading (blue) reveals steeper trends compared to normal compaction (red). The way the velocity-porosity ranges differ between the samples are attributed to mineralogical differences and textural variations. In particular, the samples with low quartz and high ductile minerals content show high compressibility (e.g. SA, AA, and FG). Sub Arkose 4 4 Arkosic Arenite 4 4 Quartz Arenite Sub Arkose 1 Quartz Arenite 1 4 4 Feldspartic Greywacke 4 4 Figure P-wave velocities versus total porosity of all seven sands (this study) and five sands from Zimmer et al. 7. See explanation in text. Figure S-wave velocities versus total porosity of all seven sands (this study) and five sands from Zimmer et al. 7. See explanation in text. The friable sand models calculated from the dry quartz-rich sand sample (Fawad et al. 11) at different stress levels fit reasonably well with the measured data for V P but overpredict the V S in some of the samples e.g. QA and Merrit. Sands overconsolidated to different stress levels plot on their Quartz Arenite 4 4 4 4 4 4 Gulf of Mexico* 4 4 Pomponio* Santa Cruz aggregate* Merritt* Galveston* 4 4 4 4 4 4 4 4 Eff. stress (MPa) * Data from Zimmer et al. 7 Sub Arkose Quartz Arenite 4 4 4 4 4 4 4 4 Arkosic Arenite Feldspartic Greywacke Sub Arkose 1 Quartz Arenite 1 4 4 4 4 4 4 4 4 Pomponio* Santa Cruz aggregate* Merritt* Galveston* 4 4 * Data from Zimmer et al. 7 4 4 Quartz Arenite 4 4 Gulf of Mexico* 4 4 Eff. stress (MPa) 7 th EAGE Conference & Exhibition incorporating SPE EUROPEC 1 London, UK, -1 June 1
current effective stress friable sand model line. For example, at MPa (yellow points) the data move along the friable sand model to the left as the increases. This pattern is found for both V P and V S. Figure 4 shows data from sample SA as seen in Figure at MPa effective stresses for better visualization. We also observed this pattern in well logs from the Barents Sea (Figure ). Figure shows how V P versus density plot for sandstones with Vsh. in four wells. The observed depth ranges for the data between 7 - m BSF (below sea floor). The calculated friable sand models from the QA sample overpredict the measured well logs. However, we still can see that the data trend of all wells both normally compacted and uplifted plot on the same model line. The well with little or no uplift shows the lowest V P and density compared to the uplifted wells. We also observed that the data points move along the model line to the left as the magnitude of uplift/erosion increases. Discussion The friable sand model was introduced as a bound to observe velocity-porosity changes as sorting varies. The data move along the model line as the sorting deteriorate. This is normally associated with increasing clay content or additional grains of different sizes within the pore space. We also see this effect in our data. Figure 6 shows the same data Barents Sea. See explanation in text. as Figures and plotted together. The P- and S-wave velocities are plotted versus bulk density with color-coded by effective stress. Difference in data point size is a measure of quartz content. We see that at any observed effective stress, the data fall on the friable sand model lines and move to the left as the quartz content decreases (smaller data points move to the left). This means that the velocitydensity relation of the samples with low quartz content was influenced by other minerals such as feldspar and clays which resulted in poorer sorting. On the same model line, different loading paths 1 Friab.=MPa. Friab.=MPa...1. Bulk density (g/cm)..1. Bulk density (g/cm) Our data Zimmer et al 7 1.9 Figure 6 P- and S-wave velocities versus density of all seven sands from this study and five sands from Our data Zimmer et al 7 1.9 1.9 introduce additional ambiguity. The data move to the left along the model line as the or degree of uplift increases. In addition, newly deposited sediments fall along the friable sand model (unconsolidated line) and will move away from this line with increasing diagenesis (Avseth et al. ). In the reloaded sediments associating to uplift, the data move away from the unconsolidated towards the cement line when stress increases during normal compaction but move back towards the unconsolidated line on a different path during stress release. Figure 7 shows V P /V S plotted versus acoustic impedance () of QA. The first Zimmer et al. 7. See explanation in text. plot highlights two significant trends separating normally compacted from overconsolidated sediments. The other four plots show the same data but are color-coded by porosity, effectives stress, reduced stress (maximum minus current stress), and maximum. The data are superimposed on the rock physics template (RPT) (Avseth et al. ) calculated from the dry QA sample (Fawad et al. 11) using Gassmann equation (Gassmann, 191) substituted with water at various effective stresses. The data fit reasonable well with the model at low effective stress 1.9 Eff. stress (MPa) 4 4 Figure 4 P-wave velocity versus porosity of SA at MPa effective stresses. 71/8- Increasing 71/8-1 degree of uplift/erosion 71/8-.. ing-reloading with at;,, and MPa Normal compaction...1 Bulk density (g/cm) Sub Arkose Increase maximum 71/8-1 71/8-71/8- no uplift. Figure Well logs data from the 7 th EAGE Conference & Exhibition incorporating SPE EUROPEC 1 London, UK, -1 June 1
but are rather conservative at higher stresses. The arrows show the trends corresponding to (1) increasing porosity, () decreasing effective stress, () increasing reduced stress (uplift), and (4) increasing maximum associated with maximum burial depth before uplift (Figure 7). The porosity and effective stress trends (1 and ) are similar to what are used for rock physics diagnostic. But we see that for overconsolidated sediments, two additional trends ( and 4) can be observed when plotting the data in RPT. Figure 7 versus of Quartz Arenite sample. See explanation in text. Figure 8 shows fluid sensitivity using Gassmann fluid replacement (Gassmann 191) from % water to % gas of the same sand observed at MPa effective stress. The data are superimposed on RPT. Varying the e.g.,, and MPa resulted in different fluid sensitivities as Effective stress MPa OC-max preload stress MPa porosity decreases due to the effect of 4 OC-max preload stress MPa OC-max preload stress MPa preconsolidation. The sand precompacted at the. Fully w ater saturation highest stress reveals lower fluid sensitivity at a.4 given stress compared to sand precompacted at. lower stresses..8 Quartz Arenite Normal compaction Overconsolidation. % gas saturation Model Porosity (fract.) 1 Conclusions Our experimental results show different velocitydensity/porosity relations for overconsolidated Figure 8 Fluid substitution. See text for explanation. sands compared to normally consolidated sands in different rock physics models and RPT. The data from overconsolidated sand samples plotting along the friable sand model lines not only describe deteriorating sorting but also differences in preconsolidation stresses. Well logs from the Barents Sea show similar patterns to the measured data acquired in this study. The V P /V S - relation shows additional trends e.g. in the direction of reduced stress and increased precompaction stress. As expected fluid sensitivity is low as preconsolidation stress increases. These findings allow better rock physics diagnostics for uplifted sediments like in the Basents Sea. Acknowledgements.8 Colored by porosity (%) Colored by effective stress (MPa) Colored by reduced stress (MPa) Colored by maximum stress (MPa) 4 4 ().8.8.8 () (1) We would like to thank the Norwegian Research Council (NFR) for the funding for BarRock (Barents Sea Rock Properties) project under the program PETROMAKS. We are also grateful to many NGI personnel for their dedicated help in sample preparation, experimental setup and testing program. References Avseth, P., Mukerji, T. and Mavko, G. [] Quantitative seismic interpretation: applying rock physics tools to reduce interpretation risk. Cambridge University Press. Dvorkin, J. and Nur, A. [1996] Elasticity of high-porosity sandstones: theory for two North Sea datasets. Geophysics, 61, 16 17. Fawad, M., Mondol, N. H., Jahren, J. and Bjørlykke, K. [11] Mechanical compaction and ultrasonic velocity of sands with different texture and mineralogical composition. Geophysical Prospecting, 9(4), 697-7. Gassmann, F. [191] Über die Elastizität poroser Medien, Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich, 96, 1. Hashin, Z. and Shtrikman, S. [196] A variational approach to the theory of the elastic behavior of multiphase materials. Journal of the Mechanics and Physics of Solids, 11(), 17 14. Mindlin, R.D. [1949]. Compliance of elastic bodies in contact. J. Appl. Mech. ASME 16, 9 68. Zimmer, M.A., Prasad, M., Mavko, G. and Nur, A. [7] Seismic velocities of unconsolidated sands: Part 1 Pressure trends from.1 to MPa. Geophysics, 7(1), 1 1 7 th EAGE Conference & Exhibition incorporating SPE EUROPEC 1 London, UK, -1 June 1 (4)