Contact Cement
Learning objectives
- Explain the Dvorkin-Nur picture: cement precipitated at the grain contacts stiffens the pack far faster than compaction does
- Read the near-vertical rise from the critical porosity: for quartz cement, K climbs from about 7.12 GPa at half a percent to 12.76 at six percent
- Contrast cement against compaction: two percent of cement gives K about 9.89 GPa where the friable frame at the same porosity is only 2.35
- See that a softer cement raises the frame more gently, and set up the three-way diagnostic of the closer
Cement Where It Counts
The soft and stiff lines both lost porosity by rearranging grains. Cement does something different: it precipitates from pore fluids and lands, in the model that matters most, right at the grain contacts, the very places that carry the load. Dvorkin and Nur (1996) worked out the elasticity of that arrangement, and its signature is a rise so steep it is almost vertical. A contact is a small, highly stressed patch, and welding it with even a thin rind of stiff mineral enlarges the load-bearing bridge dramatically. Because the effect is concentrated exactly where the frame is weakest, a very little cement buys a great deal of stiffness. The model starts at the critical porosity and, as cement fills the pore space and porosity drops, climbs sharply away from the loose-pack point.
How Steep the Climb Is
Put quartz cement on a quartz pack, coordination number 9, starting at . At half a percent of cement, porosity 0.355, the dry-frame bulk modulus is already GPa. At one percent it is 8.40, at two percent 9.89, at four percent 11.62, and at six percent 12.76. The first crumbs of cement do the most work: half a percent alone lifts the frame from the 2.05 GPa of the bare pack to over 7. Now set that against compaction. On the friable line, a sand squeezed all the way down to a porosity of 0.20 reaches only 5.74 GPa. The two-percent-cemented sand, still sitting at a porosity of 0.34, beats it at 9.89. A whisper of cement at the contacts outstiffens a great deal of mechanical compaction, and it does so while the rock keeps most of its porosity.
Not All Cement Is Quartz
The steepness depends on what the cement is made of. Quartz cement is stiff, so it gives the sharpest rise. A softer cement, clay for instance, welds the contacts less firmly and lifts the frame more gently: at two percent, clay cement gives a dry-frame bulk modulus near 8.46 GPa against the 9.89 of quartz cement, and the gap widens as more is added. The rise is still far steeper than the friable line, because even a soft cement is bridging the contacts, but the cement mineral is a real lever on the answer. This near-vertical cement trend, rising steeply from , is the third of the three shapes a granular sand can take. The closer of this part lays all three on one plot, the friable line, the stiff-sand line, and this cement line, and asks the question that a measured sand can now answer: was its stiffness bought by sorting, or by cement?
References
- Dvorkin, J., & Nur, A. (1996). Elasticity of high-porosity sandstones: Theory for two North Sea data sets. Geophysics, 61(5), 1363-1370.
- Mavko, G., Mukerji, T., & Dvorkin, J. (2009). The Rock Physics Handbook (2nd ed.). Cambridge University Press.