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The Usage of an Algebraic Multigrid Solver in Basin and Petroleum Systems Modeling

IP.com Disclosure Number: IPCOM000211603D
Publication Date: 2011-Oct-13
Document File: 2 page(s) / 115K

Publishing Venue

The IP.com Prior Art Database

Abstract

In basin and petroleum systems modeling pore pressure and temperature distributions within the sediments are commonly modeled by solving partial differential equations. The usage of algebraic multigrid solvers in combination with the finite element method for the discetization of the differential equations yields significant performance speed-ups compared to prior art.

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The Usage of an Algebraic Multigrid Solver in Basin and Petroleum Systems Modeling

Introduction / Summary of the Invention

In basin and petroleum systems modeling pore pressure and temperature distributions within the sediments are commonly modeled by solving partial differential equations. The usage of algebraic multigrid solvers in combination with the finite element method for the discretization of the differential equations yields significant performance speed-ups compared to prior art.

Prior Art

Differential equations for temperature and pore pressure in basin and petroleum systems modeling are often discretized and linearized with the finite element method to a set of linear algebraic equations and finally solved with iterative or with conjugate gradient solvers on a computer, see e.g. Zienkiewicz, O. C. (1984): Methode der finiten Elemente, 2nd edition, Carl Hanser Verlag, and  Press, W. H. et al. (2007): Numerical Recipes, Third Edition, Cambridge University Press (NR).

Algebraic multigrid techniques have already been applied in basin and petroleum systems modeling but have only been used for preconditioning of a set of linear equations which was derived with finite volume methods, see for example F. Willien et al (2009): AMG preconditioning for sedimentary basin simulations in Temis calculator, Marine and Petroleum Geology 26.

Detailed Description of Invention Including Examples

The evolution of pore pressure and temperature distributions in sedimentary basins over geological times can be described with partial differential equations, see for example T. Hantschel and A. I. Kauerauf (2009): Fundamentals of Basin and Petroleum Systems Modeling, Springer (FBPSM). The solution of these differential equations is a major step in basin modeling. The process of discretization, namely spatial gridding of a basin model, and the subsequent construction of a linear set of equations with the finite element method, which can be solved for temperature and pressure, is described in FBPSM. The resulting temperature and pressure fields are used for modeling of petroleum generation, migration, and accumulation for exploration and apprai...