Shale compaction and statistical physics

Abstract

investigations t o date have furnished strong evidence that the behavior under pressure of the purer types of argillaceous sediments, clays and shales sensu stricto, is different from that of other sediments and while variable in detail is also in a general way uniform. The importance and universality of the phenomenon o f compaction in these rocks are believed t o justify considerable effort to obtain as accurate an idea of the general quantitative relations between pressure and volume as the nature of the problem will permit. H. D. Hedberg ( 1 936)Summary. After a short historical outline of the development of the ideas on the compaction of clays and shales it is shown that the exponential porositydepth dependence of compacted shales expressed by Athy's law can be derived using standard methods o f statistical physics. The main result of the paper states that the exponential compaction law expresses the maximumentropy equilibrium state of the pores in the rock, that is compaction is an irreversible process where clay particles tend towards a statistically defined final equilibrium. Connections with the classical theory of consolidation are pointed out. Historical and problem discussionAthy's law, expressing the density (or porosity) decrease as a function of depth of thick pure shale columns is one of the most unanimously accepted and widely used empirical expressions in applied geophysics. With Athy's (1 930a) original notations, the compaction law states that:where D is the density t o be calculated, B is the density of surface clay, A is the maximum density increase possible, b is a constant, x is depth of burial. In recent usage, the compaction law is generally quoted as: P(Z> = P O + (P--P O ) [1 -exp (-kz)l

Factors controlling the evolution of the Perdido Fold Belt, northwestern Gulf of Mexico, determined from numerical models

“…For compacting material, a new density is calculated each time step for each element depending on its burial depth z [Korvin, 1984].…”

Patterns of Sediment Compaction at Ocean Drilling Program Sites 645, 646, and 647, Baffin Bay and Labrador Sea

“…Equation 1 (Athy's Law) was proposed by Athy (1930) to represent the porosity-depth relationship in shales and is a widely used expression in applied geophysics. It is an empirically established expression, although a mathematical-physical derivation verifying the relationship was provided by Korvin (1984). In strict usage, Athy's Law describes the final equilibrium state of fine-grained sediments after water has migrated vertically upward.…”

A 3-D Backstripping Method and Its Application to the Eromanga Basin In Central and Eastern Australia

“…The porosity-depth relationship for common sediments (sandstone, siltstone and shale) can be modelled in the form 442) = &I exp (-cz> (11) where @ ( z ) is the porosity at depth z , is the porosity at the surface ( z = 0) and c is the compaction constant. Korvin (1984) has shown that if equilibrium compaction occurs by vertical migration of pore fluid then the porosity should be an exponential function of depth such as equation (11), which is in fact observed in many studies of porosities in sediments (see Korvin 1984 for references and Gallagher & Lambeck 1989). …”