Carbonate Pore Types

The Carbonate Scatter

Plot velocity against porosity for a set of carbonates and the points do not fall on a line; they scatter across a wide band, one rock fast and another slow at the very same porosity. For decades this looked like noise. The inclusion models of this part say it is not noise at all, it is pore type made visible. Xu and Payne adapted the Xu-White idea to carbonates by recognizing three characteristic pore families, each with its own aspect ratio: interparticle porosity, the reference space between grains, at a moderate aspect ratio of 0.15; moldic and vuggy porosity, round holes left where grains or fossils dissolved away, stiff at an aspect ratio of 0.8; and microcracks, thin and devastating, at 0.02. A carbonate's velocity depends on which of these it has.

Same Porosity, Three Velocities

Fix the porosity at 15 percent, saturate with brine, and build each pore type into calcite with DEM followed by Gassmann. The interparticle rock, the reference trend, gives a dry frame bulk modulus of 28.19 GPa and a saturated Vp of 4.92 km/s. The moldic rock, its porosity in stiff round vugs, holds a dry modulus of 49.43 GPa and races to Vp 5.81 km/s. The cracked rock, the same 15 percent of porosity but in thin cracks, has a dry modulus of just 0.81 GPa and crawls at Vp 2.72 km/s. One porosity, one mineral, one fluid, and Vp spread over more than 3 km/s purely by the shape of the pores. The moldic rock is fast because round vugs barely soften the stiff calcite frame; the cracked rock is slow because a little crack porosity guts it.

Why Porosity Alone Cannot Predict Velocity

The consequence is sharp. Because pore type moves velocity so far, porosity by itself is not enough to predict how fast a carbonate is. A moldic carbonate at 15 percent porosity, at Vp 5.81 km/s, is actually faster than an interparticle carbonate at only 8 percent porosity, which reaches about 5.65 km/s. The rock with more pore space is the quicker one, because its pores are the stiff kind. Any interpretation that reads carbonate porosity straight off velocity, or velocity straight off porosity, will be wrong wherever pore type varies, and in carbonates it varies constantly. The Xu-Payne model is how the industry brings that scatter under control, by asking not just how much porosity a carbonate has but what shape it is in.

Closing Part 6, and the Turn to Data

Step back over the last two parts. Part 5 built a rock's dry frame from the geometry of grain contacts, a pack pressed together and stiffened by cement. Part 6 built it from the geometry of pore shapes, an oblate spheroid's aspect ratio driving a family of inclusion models from Kuster-Toksoz through DEM and the self-consistent medium to Xu-White and Xu-Payne. Both approaches share a quiet dependence: every one of these models needed parameters that someone had to choose, a coordination number, a cement fraction, an aspect ratio, a clay split. Geometry can tell you how a rock behaves given those numbers, but it cannot tell you the numbers. Part 7 turns to the other source of truth, data. It takes up the empirical backbones that real rocks obey, the Han relations, Castagna's mudrock line, and Gardner's density law, and it calibrates a physical model to the Ogbon-1 well before assembling the rock physics template that ties the whole subject together.

References

• Xu, S., & Payne, M. A. (2009). Modeling elastic properties in carbonate rocks. The Leading Edge, 28(1), 66-74.
• Mavko, G., Mukerji, T., & Dvorkin, J. (2009). The Rock Physics Handbook (2nd ed.). Cambridge University Press.