Rock physics models for fluid and stress dependency in reservoir rocks are essential for quantification and interpretation of 4D seismic signatures during reservoir depletion and injection. However, our ability to predict the sensitivity to pressure from first principles is poor. The current state-of-the-art requires that we calibrate the pressure dependence of velocity with core measurements. A major challenge is the fact that consolidated rocks often break up during coring, and hence the stress sensitivity is likely to be overpredicted in the laboratory relative to the in-situ conditions (Furre et al., 2009). For unconsolidated sands, acquisition of core samples is not very feasible due to the friable nature of the sediments. One physical model that has been applied to predict pressure sensitivity in unconsolidated granular media is the Hertz-Mindlin contact theory. Several authors (Vernik and Hamman, 2009, among others) have suggested empirical models with fitting parameters that correlate with microcrack intensity, soft porosity, and aspect ratio of the rock, and feasibility studies can be undertaken based on assumptions about these parameters. These models may not be easy to use for poorly to moderately consolidated sandstones with contact cement, where crack parameters and aspect ratios are difficult to quantify.

The patchy cement model predicts stress sensitivity in poorly to moderately consolidated sandstones using a multiply nested Hashin-Shtrikman approach combined with contact theory. This model can be used to quantify stress sensitivity in reservoir sandstones where core samples are lacking or unreliable. We demonstrate a strategy based on this model that can be used to quantify 4D seismic time shifts and time-shift derivatives associated with stress changes. The time shifts will be a function of the rock stiffness (i.e., volume of patchy cement); therefore, it is important to determine the local changes in rock properties before we can predict stress and fluid changes from time-shift attributes. We apply this approach to four exploration wells in the Visund Field area where we have good control on the rock properties. We first compare modeled time shifts with observed 4D time shifts in the Visund S1 segment where pressure data are available, and we obtain a very good match at two selected well locations. Next, we use the observed seismic time shifts as constraints to estimate the pore-pressure changes in the Pan and Pandora segments just south of the depleting S1 segment. Pressure changes are significantly lower than in the S1 segment but still indicate potential pressure communication between these segments and the main Visund, in spite of fault barriers and deeper fluid contacts.

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A B S T R A C TRock physics models for fluid and stress dependency in reservoir rocks are essential for quantification and interpretation of 4D seismic signatures during reservoir depletion and injection. For siliciclastic sandstone reservoirs, the Gassmann theory successfully predicts changes in seismic properties associated with fluid changes. However, our ability to predict the sensitivity to pressure from first principles is poor, especially for cemented sandstones. In this study, we demonstrate how we can use a patchy cement rock physics model to quantify the combined effect of stress and fluid changes in terms of seismic time-shifts and time-shift derivatives during depletion or injection. The time-shifts are estimated directly from well log data without core calibration of stress sensitivity. By assuming non-uniform grain contacts where some grain contacts are cemented and others are loose, we can combine the contact theory for cemented sandstones with the contact theory for loose sands in order to predict stress sensitivity in a patchy cemented sandstone reservoir. Time-shift derivatives are also useful estimates, as this parameter reveals which part of the reservoir is most stress sensitive and contributes most to the cumulative time-shift.We test out our new approach on well log data from Troll East, North Sea and compare the predicted time-shifts with observed 4D seismic time-shifts. We find that there are good agreements between predicted time-shifts and observed time-shifts. Furthermore, we confirm that there are local geological trends controlling the fluid and stress sensitivity of the reservoir sands on Troll East. In particular, we observe a lateral stiffening of the reservoir from west to east, probably associated with the tectonic and burial history of the area. The combined effect of a thinning gas cap and stiffening reservoir sands amplifies the eastward decrease in time-shifts associated with reservoir depletion. We manage to disentangle these two effects using rock physics analysis. It is essential to identify and map the static rock stiffness spatial trends before interpreting time-shifts and time-shift derivatives in terms of dynamic (i.e., 4D) pressure and fluid changes.

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