✍ Scribed by Jan Søreng
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A mathematical model treating the compaction of sediments in geological basins is derived. The model is based on the principle of conservation of mass and energy, and gives a consistent and complete set of equations for compaction, pressure and temperature history of sedimentary basins.
Further, the paper describes a numerical model based on the mathematical equations, derived by using the finite element method. This derivation starts with the time-diycretized versions of the conservation laws of mass and energy. The result is the timediscretized equations for pressure and temperature. The numerical derivation is parallel with the mathematical deductions. By integrating these timediscretized equations spatially the element equations are obtained. Hence, the element equations are derived directly from the underlying physical laws. This approach to developing element equations in a compacting medium is believed to be new. The model has been tested successfully on some geological basins, and the results of a simulation are included at the end of the paper.
📜 SIMILAR VOLUMES
We show that for the P N -P N-2 spectral element method (SEM), in which the velocity and pressure are approximated by polynomials of order N and N -2, respectively, numerical instabilities may occur in Navier-Stokes simulations. These instabilities depend on the formulation of the convection operato