Preconditioning for Multiphase Sedimentary Basin Simulations

The simulation of sedimentary basins aims at reconstructing its historical evolution in order to provide quantitative predictions about phenomena leading to hydrocarbon accumulations. The code TEMIS3D developed by the Institut Francais du Petrole (IFP) and marketed by its subsidiary Beicip-Franlab represents such a tool. The kernel of this simulation is the numerical solution of a complex system of time dependent, three-dimensional partial differential equations (PDE) of mixed parabolic-hyperbolic type. A discretisation (Finite Volumes + Implicit Euler) and linearisation (Newton) of this system leads to very ill-conditioned, strongly non-symmetric and large systems of linear equations with three unknowns per mesh element, i.e. pressure, geostatic load, and hydrocarbon saturation.

The aim of the project is to find robust and efficient preconditioners for these systems and to implement them within TEMIS3D. The preconditioning strategy which we developed and implemented consists in three stages. First of all the equations for pressure and saturation are locally decoupled on each element. This decoupling aims not only at reducing the coupling, but also at concentrating in the ``pressure block'' the elliptic part of the system which is then in the second stage preconditioned by efficient methods like AMG or Line-SOR. The third step finally consists in ``recoupling'' the equations (e.g. Block Gauss-Seidel, combinative techniques,...).

In almost all our numerical tests on real test problems from case studies we observed a considerable reduction of the CPU-time for the linear solver, up to a factor 4.3 with respect to ILU(0) preconditioning (which is used at the moment in TEMIS3D). The performance of the preconditioner shows no degradation with respect to the number of elements, the size of the time step, high migration ratios, or strong heterogeneities and anisotropies in the porous media.

The details of this work can be found in:

In addition we have also parallelised the preconditioners and obtained very good speedups using the parallel AMG package BoomerAMG from the Hypre library (Lawrence Livermore National Lab, CA). The details are in

We have also carried out some preliminary results using two-level domain decomposition methods (Additive Schwarz with minimal overlap). Work is ongoing on this part.

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Last updated 26/06/2006