S U M M A R YA mathematical model for the non-equilibrium compaction of clay rocks in sedimentary basins is formulated. T h e model generalizes those of earlier authors. T h e simplest assumptions a r e made concerning the rheology, and diagenesis is neglected. In this case, we show that the model reduces t o a generalized consolidation equation, which for t h e classical Darcy flow is a non-linear diffusion equation for the porosity, with a free boundary. The model is non-dimensionalized, a n d it is shown that solutions depend on o n e significant dimensionless parameter A, which is the ratio of the Darcy flow rate a n d the sedimentation rate. The model is solved numerically, and asymptotic descriptions of the solutions are given for the cases of large and small A.
A continuum mechanics model for the gravitational compaction of sediments is derived by assuming that the sediments are normally pressured and in a one‐dimensional state of stress. Sediment strength is characterized in terms of effective stress laws adopted from soil mechanics. The model is a relatively simple mathematical formula that gives the porosity as a function of burial depth. The shape of the porosity profile is controlled by two mechanical parameters, the compression index and the void ratio at an effective stress of 100 kPa. The model was verified by analysing the porosity—depth data of oozes and chalk from the Ontong Java Plateau, gathered during Leg 130 of the Ocean Drilling Program. The mechanical parameters of the sediments were estimated using a least‐squares method to fit the theoretical profile to the porosity data. The theoretical profile described accurately the ooze porosity data over depth ranges of 100 m or more. However, over smaller length‐scales of 10–50 m there were systematic deviations between the theoretical porosity values and the ooze porosity data. The porosity deviations correlated with variations in the mean grain size of the sediments, due in part to changes in the foraminifera abundance. In the case of the oozes, the estimated mechanical parameters were consistent with published values obtained from one‐dimensional compression tests. In contrast, the estimated mechanical properties for the chalks differed from published values. The chalk porosities were lower than could be explained by mechanical compaction. This explanation is supported by the compressional (P‐wave) velocity data. In the chalk sections, the P‐wave velocity increases more rapidly with burial depth than it does in the ooze sections, suggesting that sediment elastic properties are increasing due to interparticle binding.
The gravitational compaction of sediments is an important process in forward basin modelling. This paper presents a mathematical model for the onedimensional compaction of an accreting layer of argillaceous sediments. Realistic constitutive laws for the clay cornpressibility and the clay permeability, based on soil mechanics tests, were incorporated into the model. The governing equations were put in dimensionless form and the extent of abnormal pore fluid pressure development was found to depend on the sedimentation parameter, a dimensionless group representing the ratio of the sediment hydraulic conductivity to the sediment accumulation rate. The effects of clay compressibility were studied and highly colloidal clays such as montmorillonite developed higher overpressures than less compressible materials. The results also showed that overpressuring developed in shales for cases in which the clay permeability did not go to zero in the limit of zero porosity. Linear models based on simplifying assumptions inappropriate for sedimentary basins were found to give significantly different estimates for the conditions leading to overpressuring. Using reasonable ,parameters, the model adequately reproduced porosity and pore pressure profiles measured in t'he s a n d s h a l e sequences of the South Caspian Sea. KEITH, L. A. & RIX~STIDT, J. D. (1985) A numcrical compaction model ofoverpressuring in shaln. Math. Gol. 17,1l5-l35. MAGARA, K. (1 975a) Reevaluation of montmorillonitc dehydration as cause of abnonn;il pressure and hydrocarbon migration. B d . 1960) Hjdnulic flow through saturated clays. CfaysCfayMinrr. 11,131-161. PALCIAUSKAS. V. V. (1988) Comment on "A numerical model of compaction4riven groundwater flow and heat transfer and its application to the paleoliydrology of intncratonic sedimentary basins" by Craig M. Bcthke.J.geophys. Res. 93,3497-3505. POWERS, M. C (1967) Fluid-relew mechanisms in compacting marine mudrocks and their importance in oil exploration. BUN.
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