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The elastic constitutive laws employed in the restorations are simple approximations of the naturally complex deformation processes that govern the growth of geologic structures. Thus, in the first year of our study, we rigorously benchmarked these new methods by restoring a series of mechanical forward models developed with the discrete element method (DEM). These DEM models generate complex structures similar in many respects to natural systems, yet we know the full displacement, strain, and stress fields for these mechanical models. Applying the restoration methods to these forward models gave us an ability to assess quantitatively how well the restoration technique performs in describing complex deformations.

This past year's efforts focused on applying these restoration techniques to natural petroleum traps, and comparing strain patterns derived from the restoration with geophysical attributes and geologic observations that help to constrain reservoir properties such as fracture density. In these efforts, we have collaborated with the Nancy School of Geology and a number of industry sponsors, including Saudi Aramco, Chevron, and ExxonMobil. Our current project areas include fields in California, China, the Caspian Sea, and the Arabian Peninsula.

The first step in applying these methods to natural structures is to build a 3D model and computational mesh that adequately describe the geometry and structure of the trap. This process generally involves mapping structures in 3D seismic data, and using these interpretations to build a structural model in a computer-aided design (CAD) tool. These models represent the major stratigraphic units in the field, including the reservoir section(s), as well as the faults and folds that control the evolution of the trap. After generating a tetrahedral mesh of the model, we then define physical properties of the strata (specifically elastic properties such as the bulk and shear moduli, and Poisson's ratio), using petrophysical data from well logs and/or geophysical attributes from 3D seismic reflection data. Once composed, the models are sequentially restored using appropriate boundary conditions.

Figure 1. Perspective view of a 3D structural model and mesh of a petroleum trap constructed from interpretation of 3D seismic data. Mechanical rock properties applied to the model are  derived from well logs and petrophysical data. These models serve as the starting point for 3D structural restorations.

We have been successful in restoring a number of different types of geologic structures, including detachment, fault-bend, and fault-propagation folds in contractional settings, as well as structures in rift and wrench tectonic environments. These restorations yield fully 3D displacement field that describe the kinematic evolution of these structures through geologic time. In addition, the method calculates the full strain tensor for each element in the model. A primary goal of our research effort is to establish how well these calculated strain fields represent the natural strains that occur in the strata represented in the models. We generally focus our efforts on comparing components of the calculated strain fields in the reservoir sequences with well and seismic data that independently constrain deformation fabrics, such as natural fractures. In a number of cases, we find that values of dilatation and elongation derived from the restorations generally correlate most strongly with natural fracture densities and orientations observed in well data. In addition, we find that cross correlation of restorations strains with geophysical attributes such as seismic coherency yield significant predictive power in defining areas of the reservoirs with numerous, dilatent natural fractures. These correlations are further examined by comparing strain and seismic attributes with dynamic production data, helping to quantify the role of natural fractures in determining effective reservoir permeabilities.

Our goals for the remainder of the project include completing the benchmarking studies of the restoration tools that we began in the first year of the project, and continuing to work with industry sponsors to evaluate and improve the ability of the restoration tools to help define reservoir properties. We plan to publish results of this work in several articles within peer-reviewed journals in partnership with our industry collaborators.

Figure 2. Perspective view of the calculated restoration strain field for the model shown in Figure 1. Dilation (volume change) values are shown on the tops of each of the stratigraphic tops represented in the model, and generally vary from ±15% (-0.015 to 0.015 in the scale). We compare the dilatation and other strain values at the reservoir level with data from production wells and seismic attributes that define fracture distributions. In this example, we established a robust correlation between high value of negative dilatation (volume expansion in a forward geologic sense) and fracture enhanced permeability in wells.