Next Generation Geological Modeling for Hydrocarbon Reservoir Characterization - Advances in Data, Methods, Models and Their Applications in Geoscience - page 225

property remains “substantially the same”, e.g. within 10%. This allows flexibility in
specifying local directions of maximum continuity and interpolation of properties in 3D
geological models, aligned with underlying geological structure. The PV property
interpolation workflow follows the methodology of Maučec et al. 2010:
1. Define structural model and 3D grids where MCF is stored and the property values are
interpolated.
2. Define the MCF, using some predefined azimuth map (see Fig. 9b) and the local dip (an
angle from the horizontal/azimuth plane) of the horizons.
3. Pre-process of all the fault displacements in the 3D grid (see Fig. 9c).
4. Add known data points ( i.e. spatially located known reservoir property) to the model,
create the covariance neighborhood and the variogram. The covariance calculations
take local continuity into account by aligning the axes of the variogram with the local
continuity direction.
5. Run ordinary kriging estimator (see Eq. 2), using the created covariance neighborhood.
For each point to estimate, the kriging finds the nearest set of known data along
shortest geometrical (or Euclidean) distances.
The 2D implementation of property interpolation is schematically depicted in Fig. 8.
The center of the search ellipse (or ellipsoid in 3D) is associated with the location of MCV
denoted by V1 and V2. The data points, detected inside the search ellipse (“blue” triangles)
are considered in the interpolation along the MCV while the data outside the ellipse (“red”
squares) are not included. The relative dimensions of the search ellipsoid, i.e. the ratios
between major (M), intermediate (I) and minor (m) axis length correspond to “local”
anisotropy factor. In a faulted reservoir the property associated with MCV V2 is interpolated
across the fault line, following the fault throw vector FT. To validate the PV method, the
sealed structural framework, containing top and bottom horizons with a single internal
fault, was built from a fluvial reservoir of the Brugge synthetic model (Peters e t al. , 2009).
Additional details on the validation of PV method are available in Maučec et al. 2010.
In Fig. 9a an example of a facies realization for the Brugge fluvial reservoir zone is given.
The blue area represents the sand body (pay zone) distributed on shale (non-pay zone in
red). Using the facies distribution as a basis or constraint for the generation of a vector field
emulates a certain “pre-knowledge” on the geological structure but is in no way a required
step. Fig. 9b represents MCF defined on virtually regular mesh of points. No particular
continuity information was assumed for the shale zone, only for the discrete sand bodies.
The azimuth alone is used from the MCF; the dip angle is calculated as the normal direction
relative to the local curvature of the horizon. Fig. 9c visualizes fault displacement vector
field with a constant throw of ~50 m.
An example permeability distribution, generated with the MCF-based method of reservoir
property interpolation is shown in Fig. 9d, depicting the flattened 2D map view of the
major-minor plane and the fault location. The PV method allows the user to define variable
sizes of search ellipsoids throughout the model volume of interest (VOI). By this notion, a
single-size search sphere was defined for the shale facies, where no particular continuity
information was assumed (see Fig. 9b). A variable sized search ellipsoid and different
anisotropy factors ( i.e. ratios between the length (in ft) of the major direction and minor
direction of the search ellipsoid in M-m plane) were considered for the sand zone to validate
the impact on the interpolation. Qualitatively, the anisotropy ratio of 10:1 (major/minor =
10000/1000) can be interpreted for example as the case with less uncertain (and more
trusted) MCF data, used to obtain permeability distribution as depicted in Fig. 9d. The