**Subseismic fault modeling in reservoirs**

Within any faulted reservoir there are large numbers of faults that are below the resolution of seismic surveys. Some of these faults are encountered in wells, but vast majority of them remain undetected. Such subseismic faults can significantly influence the flow of hydrocarbons during production. The size distribution of subseismic faults can be predicted by extrapolating the size distribution measured at the seismic scale down to the subseismic scale. However, the positions and orientations of the subseismic faults are more difficult to determine.

We have developed a method based on mechanical modeling to constrain the positions and orientations of subseismic faults. The large seismically-resolvable faults are brought into a 3D numerical mechanical model in order to determine the stress conditions near these faults at the time of faulting. The stress field is then combined with a failure criterion in order to predict the orientations and densities of the smaller faults. This information is represented on a pair of grids (i.e. a density and strike grid). The grids are then used to condition 2D or 3D stochastic models of faulting, which use a power-law distribution and/or stochastic growth processes to simulate subseismic faults.

*Chart showing where Poly3D stands in the general workflow for characterizing fractured reservoirs in the oil and gas industry.*

**Seismic Data Analysis
**

The Oseberg Sør field, Northern North Sea is used as an example of the application of these methods. The 3D seismic reflection survey is interpreted and depth converted. The interpreted fault segments and seismic horizons are imported into software tools in order to produce a 3D model of the seismic fault surfaces. Variation in the dip-slip component of displacement over each fault surface, determined from seismic horizon cut-offs, also are analyzed and associated with the fault surfaces.

*Location of the Oseberg S**ø**r field, Northern North Sea.*

**Poly3D mechanical modeling
**

We approximate the rock mass of the upper crust as a homogeneous isotropic linear elastic material cut by discontinuities that accurately represent the geometry of the seismically mapped faults. In order to model subseismic faults, all the known seismic faults were included in the model. The six major normal faults of the area, interpreted as lower to upper Jurassic faults, as well as the 54 other seismic scale faults interpreted as upper Jurassic normal faults, were triangulated and imported into the mechanical models. Variation in the dip-slip component of displacement over each fault surface, determined from the seismic interpretation and fault analysis, were imported and used as displacement boundary conditions. Across each element, the displacement discontinuity was constrained to be pure dip-slip with no oblique component and no opening component. A three-dimensional strain, used as remote boundary conditions, was obtained from palinspastic restoration of five seismic horizons over the entire field. The restoration suggests a direction of greatest extension of N80.

*Poly3D model configuration.*

Based on the boundary conditions and mechanical parameters, one can compute the perturbed elastic stress fields at observation points placed anywhere in the surrounding rock volume. The stress tensor is then combined with a failure criterion to create a grid of both the predicted fault strike and the predicted fault density. The modeled fault strike is estimated using the Coulomb failure criterion. Two conjugate failure planes intersect along s_{2} and the fault orientation is influenced only by m and the orientation of the principal stresses. We used the maximum Coulomb shear stress (Sc) as an index for fault density. Sc is the maximum shear stress that would occur on optimally oriented conjugate shear fractures.

*Coulomb conjugate shear failure representation.*

**3D visualization of the failure planes. The color scale represents the value of Sc.**

The computed strike and density maps used to constrain the following stochastic models are shown below.

*Computed strike and density grids use to constain stichastic simulations.*

**Stochastic modeling
**

Two contrasting stochastic methods are used to model the subseismic faults: i) a method (Havana^{TM}) in which the subseismic faults are placed in the volume as fully-grown structures and ii) a method (Fraca^{TM}) in which the faults are allowed to grow and interact.

The statistical results from a stochastic single simulation using the marked point process (Havana^{TM}) show that the resultant map gives results that look geologically plausible. A feature of the simulation is that there is a lack of subseismic faults close to the smaller seismic faults. This is because in the mechanical modeling, the faults are associated with stress shadows, which are zones of low predicted fault density.

The results of a stochastic single simulation using the growth algorithm (Fraca^{TM}) show that, as for the marked point process, the resultant map gives results that look geologically plausible. A feature of the simulation is that the fault strike is well simulated. However, as opposed to the marked point process, fault density is not so well represented. This is because the “pseudo-energy” consumed by a growing fault, has not been chosen high enough. In this case some faults have enough energy to grow, and so few of them are generated in the areas with low energies (e.g. density).

*Two stochastic simulations using (a) Havana ^{TM} and (b) Fraca^{TM}..*

Copyright © The Stanford Rock Fracture Project 2002