A mathematical model for compaction in sedimentary basins

A 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.