Implications of Cell Size on Modeling of Facies Proportions: A Modern Carbonate Platform Example*
By
Gregory Benson1 and Steve Bachtel2
Search and Discovery Article #50039 (2006)
Posted November 8, 2006
*Adapted from extended abstract prepared for presentation at AAPG Annual Convention, Houston, Texas, April 9-12, 2006
Click to view article in PDF format.
1Exxon Mobil Upstream Research Company ([email protected])
2ConocoPhillips
Abstract
In shallow carbonate platform interiors, a wide
variation in micro-environments and associated depofacies are found in close
proximity (example: patch reefs surrounded by skeletal grainstone rings within a
background of peloidal packstone). When these depofacies are larger than the
geologic model cell size, each cell can reasonably be assigned a discrete rock
type, as is done in object-based modeling. However, if the cells need to be made
so large that they encompass a mix of depofacies, the modeler has the choice to
either assign the cell only its most populous facies (ignoring minority rock
types that may contribute significantly to flow) or to characterize the cells as
a mixture of depofacies using
multiple facies proportions.
This pixel-based satellite image research using
LANDSAT 7 data investigates how the stochastic modeling parameters for facies
proportions need to change as a function of cell size. Generally, as cells get
larger the variance of facies proportions is progressively reduced because cells
become less likely to contain only a single facies. In other words, when cells
get larger they encompass more diversity, eventually becoming almost homogeneous
in their degree of diversity. This is the effect predicted from the Central
Limit Theorem.
Consider a simple example in which 50-meter wide patch
reefs are sparsely scattered across an area (Figure 1). The odds of a single model cell
containing more than one patch reef is a function of the spacing of these
relatively small patch reefs over the platform combined with the size of the
model cell. One of these 50-meter reefs would account for 100% of four
contiguous 25-meter model cells. But since the individual reefs are widely
separated, the surrounding model cells would contain 0% of patch reef depofacies.
In contrast, when using
100-meter model cells that same 50-meter patch reef can
account for no more than 25% of any cell. So, for 25 meter model cells the range
of expected patch reef proportions would vary from 0 to 100%, but for 100 meter
model cells the range of patch reef proportions would only range from 0 to 25%,
since no individual 50-meter reef could ever occupy more than ¼ of any 100m
model cell.
In addition to the facies proportion variance reduction observations mentioned above, experimental variogram ranges are observed to become longer as cell dimensions increase. Staying with the patch reef example (Figure 2), consider that the concentration and spacing of these small patch reefs changes across the platform. In some areas the patch reefs cluster more tightly, and in other areas they are relatively rare. At larger cell sizes the short wavelength data (detailed locations of individual patch reefs) are averaged out, but longer wavelength patterns of patch reef clustering begin to emerge. Thus cell size defines the frequency content, and this defines the minimum limit of the variogram range. The insights from this LANDSAT photo analysis are useful whether we are creating depofacies probability models for use as conditioning volumes for small, discrete cell assignments (OBM or SISIM) or as large, common-scale facies proportions for purposes of assigning flow characteristics for input to reservoir simulation (whole-cell effective property estimation).
Figure Captions
Figure 2. Semivariograms of the four cell
groupings. The dark blue line is the experimental variogram, and the green,
pink, and light blue curves are the Exponential, Spherical, and Gaussian
variogram regressions. The red curve is the 28.5 m variogram, repeated for each
cell grouping as a reference. The Exponential regression fits the experimental
data best for all cell grouping sizes for this depofacies. Note that the
variogram range (X axis |