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.
A major challenge in well planning and in 3D reservoir modelling is to incorporate seismic information. In a North Sea setting, the wells constitute only a few pinpricks in the reservoir, while the seismic data are acquired in 3D over the whole field. Thus seismic data constitutes the only observations available in the interwell areas. In this paper we give an introduction to seismic inversion and present three North Sea case studies where inverted seismic data have been used. In the first study inverted seismic data was used to predict the thickness of a specific sand layer in the area around a planned well. In the second study seismic inversion has been used as a means for identifying fairly thick stringers of calcite cementation, In the third study inverted seismic data was used to guide 3D geological modelling. Seismic Inversion In Fig. 1 the principles of seismic modelling are shown. If the lithology is assumed to be known, acoustic impedance (density x velocity) values can be assigned to each facies Seismic signals are reflected at boundaries where the acoustic impedance changes from one layer to another and the strength of the reflections (reflection coefficients) can be calculated from the acoustic impedance model. The wavelet represents the character of the seismic signal present in the final processed seismic data and is used together with the reflection coefficients to calculate a synthetic trace. This trace is an estimate of how the real seismic response would appear under ideal noise free conditions. Seismic inversion is performed by reversing the modelling procedure; given a real seismic trace the underlying acoustic impedance model is estimated. The estimated acoustic impedance model can be checked at well positions by comparing it to the acoustic impedance log (based on the sonic and density logs). The estimated acoustic impedance model will help us to understand the lithology in the interwell areas since variations in acoustic impedance can be related to changes in lithology, porosity or pore fill. The main problem with seismic inversion is the nonuniqueness of the process; there exist several acoustic impedance models giving identical seismic response. The cause of this non-uniqueness is the limited frequency range present in the seismic signal. To overcome the non-uniqueness problem different seismic inversion techniques have been developed. The technique used in the three case studies presented in this paper is called recursive trace integration. This method assumes that the seismic data have been optimally processed to represent a band limited version of the Earth's reflection coefficient series. In addition to the seismic data a background model is established from available well logs and interpretation of main seismic horizons. In areas with seismic data of good quality the recursive trace integration technique has given comparable results with other more sophisticated inversion techniques. P. 65
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