A mathematical model for compaction in sedimentary basins

A mathematical model for the non‐equilibrium compaction of clay rocks in sedimentary basins is formulated. The model generalizes those of earlier authors. The simplest assumptions are made concerning the rheology, and diagenesis is neglected. In this case, we show that the model reduces to a generalized consolidation equation, which for the classical Darcy flow is a non‐linear diffusion equation for the porosity, with a free boundary. The model is non‐dimensionalized, and it is shown that solutions depend on one significant dimensionless parameter Λ, which is the ratio of the Darcy flow rate and the sedimentation rate. The model is solved numerically, and asymptotic descriptions of the solutions are given for the cases of large and small Λ.