Mechanical compaction models in ParaGeo

We have implemented Athy and Schneider mechanical compaction models in ParaGeo, so that now its straightforward for our users to adopt those mechanical compaction curves widely used in basin modelling applications (e.g. see Hantschel and Kauerauf, 2009) without requiring the input of a user-defined hardening law table (which involves calculation of a pre-consolidation pressure vs. plastic volumetric strain curve consistent with the remaining defined material properties).

Motivation

In forward geomechanical modelling over geological time scales we often adopt critical state constitutive models to simulate the sediment rheology of the clastic sediments. In such framework the compaction behaviour of sediments is directly related to the hardening law, which defines the evolution of sediment strength (pc) as a function of plastic volumetric strain (which is linked to porosity).

However, whereas the analytical cam clay hardening law may be sufficient to describe the compaction behaviour observed in lab experiments and may be calibrated to predict a given field measured porosity at a given depth,  it may not easily provide target porosities during the whole burial history of sediments. For example, in the figure below in grey colour we show several shale and argillaceous sediment compaction curves from different parts of the world published in Mondol et al. (2007) to provide a reference of field expected porosities. Let’s assume that our shale depositional porosity is 0.6 and we aim to calibrate the normal compaction trend (NCT) so that the porosity at 1 Km depth is 0.18 and at 5 km depth is 0.03. We would need to define a curve that fits the red circles in the image below.

Published compaction curves for shales and argilaceous sediments from different parts of the world (from Mondol et al. 2007)

We can calibrate a cam-clay compaction trend to predict the deep target porosity (yellow curve) or predict the shallow target porosity (brown curve) but if we want to predict both, we will need to decrease the depositional porosity to ~0.4 (blue curve). In other words, with cam-clay compaction curves we can fit two calibration points at the same time but not the three of them.

Different cam-clay NCTs attempting to fit the calibration points

The Schneider compaction model (a variation of the Athy model) provides the required flexibility to achieve a NCT calibration that successfully predicts all the target porosity-depth pairs as shown in the picture below.

Calibration of a Schneider compaction curve that fits all target calibration points

References

Hantschel, T., Kauerauf, A.I., 2009. Fundamentals of Basin and Petroleum Systems Modeling. Springer, Aachen, Germany.

Mondol, N.H., BjØrlykke, K., Jahren, J. and Høeg, K. (2007) Experimental mechanical compaction of clay

mineral aggregates—Changes in physical properties of mudstones during burial. Marine and Petroleoum Geology, 24, 289-311.