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The effect of a rigid layer below a compacting reservoir

PhD student Pamela Tempone has extended the analytical geomechanical model derived by Geertsma to include a rigid basement below a compacting reservoir layer (shown in blue on Figure 1). She finds that the vertical displacements and the 4D vertical timeshifts increase when the rigid basement is included in the geomechanical modeling, as shown in Figure 1. Based on these observations, it is expected that a soft overburden layer will have similar effects on the overburden time shifts, but this has not been studied so far. Pamela’s future plans include a case study for the Kristin Field offshore Norway, which is a deep, high pressure field, where compaction of the sand stone reservoir is expected.

Figure 1: A simplified model (top left) for a compacting reservoir (blue rectangle at 800 m depth), and the corresponding modeled vertical displacement field (top right) and estimated 4D time-shifts (bottom). Figure taken from Pamela Tempone’s 2009 SEG extended abstract.

Clay and shale physics

Clays and shales are the predominant overburden sediments and sedimentary rocks. It is important to recognize and be able to characterize such formations from seismic data, for instance in order to drill safe and stable wells, to detect seal capacity, and possibly identify source rocks. 4D seismic data have shown that stress changes in the overburden (and underburden, as discussed above) lead to observable time-shifts that help identify depleting reservoir zones. Within the ROSE program, we focus on experimental and theoretical analysis of stress sensitivity of clays and shales, and in particular on the role of bound vs. free water in nanometer scale inter- and intra-granular pore space. Experiments within the ROSE program are performed in collaboration with SINTEF Petroleum Research, and include measurements of multi-directional P- and S-wave velocities along different stress paths, corresponding to different depletion / inflation scenarios in reservoir / surrounding formations. As an example, Figure 2 shows how axial P-wave velocity is reduced in a sample of compacted clay when axial stress is reduced along a stress path that mimics the stress alteration in the overburden above a depleting reservoir. This kind of experiment permits quantification of the expected 4D seismic time shift.

Figure 2: Relative axial P-wave velocity in a test with compacted clay (Kaolinite) and brine, precompacted to 16 MPa axial stress, 13 MPa confining stress, and 10 MPa pore pressure. The test is performed by reducing axial stress and increasing confining stress in undrained conditions such that the total mean stress is constant.

As part of the same experiment, measured strain in hydrostatic constant net stress conditions permit an estimate of the bulk modulus of the solid grain material; or rather, the immobile constituents of the sample. The estimated solid bulk modulus is for this particular case 6 GPa, which is much lower than the value expected for a normal solid. A plausible explanation is that water adsorbed / bound to the clay particle surfaces contributes to reduce the stiffness of the pure solid. As a parallel activity to the experiments, Morten Kolstø is in his PhD working with a discrete particle model that enables computation of mechanical properties of bound water in clays based on interatomic forces. His preliminary results were presented at the recent (2009) ROSE meeting, and support the experimental observations.

Estimating porosity and permeability from production and 4D seismic data

PhD student Mohsen Dadashpour has developed an inversion scheme where the inner kernel is a standard fluid flow simulator, and the input to the inversion is production data and 4D seismic data. Through cooperation with researchers at Stanford he has been able to significantly speed up this inversion scheme. So far, his scheme has been tested for 2D data sets only, and the computing time is a key challenge when the procedure should be adapted to a full 3D case. Figure 3 shows a typical result of the inversion. As expected, the inversion is not capable of detecting thin high permeable layers, they tend to be represented as thicker layers with lower permeability.

Figure 3: Comparison of true and estimated porosity (left) and permeability fields for a synthetic data set, using both 4D seismic and production data as input to the inversion procedure. This figure is a part of paper submitted for publication in the Journal of Evaluation and Engineering, by Dadashpour et al..

4D diffraction analysis

Martin Landrø and Bård Osdal have investigated the possibility of using seabed diffractions for improved determination of water layer velocity changes between time lapse surveys. They find that accurate analysis of such diffraction hyperbolas is possible, and estimate a velocity change of 2.4 m/s with an uncertainty of 1 m/s. An example of the seabed topography map, showing two seismic profiles overlaid, is presented in Figure 4.

Figure 4: Seabed topography and associated seabed diffractions as observed on two in-lines. Selected diffraction hyperbolas are used for the time lapse seismic analysis. Figure presented by Landrø and Osdal at the EAGE meeting in Amsterdam 2009; printed with permission from StatoilHydro.

Current 4D streamer acquisition is very accurate, we found typical errors in the the CMP-positions of about 1-2 meters only, for two succeeding time lapse surveys. However, 4D diffraction analysis is extremely sensitive to such positioning errors, and we therefore developed a technique were the left hand and right hand side of the hyperbola were added together prior to the analysis, and then such positional errors can be reduced significantly. The standard way of estimating water velocity changes between two surveys is to first correct for the tidal changes and then use a simple cross-correlation technique to estimate a residual time shift caused by the water velocity change. We find that this standard technique works well for the field example studied. However, we believe that time lapse diffraction analysis can be used as a complementary QC tool in areas with a complex sea bed topography.

Seismic imaging of converted waves

Ørjan Pedersen is finishing his PhD project on seismic imaging in anisotropic media. The earth is anisotropic in nature and in particular sedimentary rocks exhibit anisotropy. These sedimentary rocks may often be described as being transverse isotropic with a symmetry axis perpendicular to the bedding plane. A homogeneous medium which is fractured may also be described as transverse isotropic, with a symmetry axis  perpendicular to the fractures. By deploying both hydrophones and geophones at the seafloor (OBS) it is possible to record both pressure and shear waves from the subsurface. Converted shear-wave data can possibly be used to image subsurface reflectors which are weak using pressure data alone, especially in gas-charged formations, hence reducing the risk in hydrocarbon exploration and production. Shear wave information may also help improve reservoir characterization by providing further constraints on rock properties, lithology, and fracture density and orientation.

The characteristics of wave-propagation in a VTI (media with a vertical symmetry axis) medium can be described by the dispersion relation, relating the vertical and horizontal phase-slowness. Taking into account a vertically transverse isotropic earth, we derive approximate phase-slowness expressions for quasi-P and quasi-SV waves which are used in an implicit one-way wave-equation pre-stack depth migration scheme. Numerical examples demonstrate that the slowness approximations are valid for wide-angle propagation. The migration algorithms were applied to a field OBS dataset which was acquired in 2002 in the central North Sea over the Volve field. A 2D subset of the entire 3D survey was extracted for input to a common-shot migration scheme. Figure 4 shows a comparison between the PP image and the PS image. The imaged reflectors in the two sections correlate well in depth. Some differences are found between the strength and distinction of some of the reflectors. These differences are most probably due to differences in PP and PS reflectivity related to lithology and, possibly, fluid content.

Figure 5: Migrated sections of the real data example from offshore Norway. Comparison of the PP (left) and PS (right) depth migrated sections. (data from StatoilHydro).