Capstone 3: Fluvial channel reservoir (multipoint statistics)

Fluvial channel reservoirs (point bars, channel belts, levee deposits) are the reservoir family where MULTIPOINT STATISTICS becomes essential. Two-point variograms cannot represent channel CONNECTIVITY — they capture average distances but not the geometric continuity that drives drainage volumes and well performance.

The training-image approach

Step 1: build (or acquire) a TRAINING IMAGE — a 2D or 3D analog model showing channel-deposit geometry. Sources: outcrop maps, satellite imagery of modern rivers, prior geological models, geomorphic simulators. The TI captures the multipoint patterns the analyst wants the realizations to honor.

Step 2: SCAN the TI with a template (e.g., 4 nearest neighbours = 4-bit pattern), counting occurrences of each (pattern → centre-value) pair. Build a CONDITIONAL DISTRIBUTION p(centre | pattern) for each of the 2^4 = 16 patterns.

SNESIM-style realization generation

Step 3: visit grid cells in random order. At each cell, look up its current template pattern in the catalog, sample the centre value from the conditional distribution. This makes the realization HONOR the multipoint statistics of the TI.

The widget below shows: training image (top-left), then two realizations. Note the channels in the realizations preserve the sinuous geometry of the TI, even though pure SISIM would produce only "blobby" patches.

Connectivity as a development metric

For each realization, compute the largest connected sand body (flood-fill). Histogram across realizations — this is the CONNECTIVITY UNCERTAINTY. For development-well placement, you want realizations that consistently show LARGE connected bodies → high-confidence drainage volumes. Realizations with small connected bodies signal compartmentalization risk.

Try it

• Defaults (3 channels, sinuosity 6, width 4). The TI shows three sinuous channels; realizations preserve the sinuosity. Largest-body P90 typically ~200-300 cells (substantial connected volume).
• Drop nChannels to 1, raise sinuosity to 10. Single highly-meandering channel. Realizations have very long, narrow connected bodies. P10/P50 gap can be large because the channel is the ONLY sand body — connectivity uncertainty matters.
• Raise nChannels to 6 with width 2. Many thin channels. Cumulative sand fraction is similar but per-body size shrinks dramatically. Compare P50 body size to defaults.
• Compare against a pure two-point SISIM with same overall sand fraction — same average φ but with much smaller maximum connected bodies (no channel geometry). MPS REALIZATIONS have larger connected components for the SAME mean-fraction.
• Examine connectivity uncertainty across realizations. P90/P10 ratio for largest-body size is a development-decision-relevant uncertainty metric — comparable to OOIP P90/P10 for clastic.

A field-development team is considering 5 producer wells in a fluvial reservoir. The MPS realizations show largest-body P10 = 80 cells (~ 12 acres) but P90 = 380 cells (~ 60 acres). What does this connectivity uncertainty imply for the well-spacing decision, and what additional data would most reduce the uncertainty?

What you now know

You can run MPS realizations of channel reservoirs. The same machinery scales to 3D, multi-facies (channel + crevasse + overbank), and to richer templates (8 neighbours, 24 neighbours). Modern industry workflows (DeeSse, Petrel MPS, FLUMY) implement variants of this approach. For development decisions, connectivity statistics from MPS realizations are the most directly decision-relevant outputs.

Mark capstone complete →

References

• Strebelle, S. (2002). "Conditional simulation of complex geological structures using multiple-point statistics." Math. Geol. 34(1), 1–21. (Foundational SNESIM paper.)
• Mariethoz, G., Caers, J. (2014). Multiple-point Geostatistics. Wiley-Blackwell.
• Pyrcz, M.J., Deutsch, C.V. (2014). Geostatistical Reservoir Modeling, 2nd ed. Oxford. (Channel modeling chapter.)
• Boucher, A., Dimitrakopoulos, R. (2009). "Block simulation of multiple correlated variables." Math. Geosci. 41, 215–237.
• Mariethoz, G., Renard, P., Straubhaar, J. (2010). "The direct sampling method to perform multiple-point geostatistical simulations." Water Resources Research 46(11).