›› 2010, Vol. 31 ›› Issue (5): 1657-1662.

• Numerical Analysis • Previous Articles     Next Articles

Mathematical model and nonlinear finite element equation for reservoir fluid-solid coupling

ZHANG Guang-ming1, LIU He 1, 2, ZHANG Jin3, WU Heng-an1, WANG Xiu-xi1   

  1. 1. Department of Modern Mechanics, Hefei 230026, China; 2.Research Institute of Petroleum Exploration Development, Petro China, Beijing 163453, China; 3. School of Petroleum and Gas Engineering, China University of Petroleum, Beijing 102200, China
  • Received:2008-11-28 Online:2010-05-10 Published:2010-05-24

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Abstract:

A mathematical model for fluid-solid coupling in reservoir was constructed based on the equilibrium equation of solid skeleton and continuity equation of wetting liquid in porous medium. Jaumann stress rate formula was adopted to describe the finite deformation behavior. The effects such as in situ stress, initial pore pressure, initial fluid density and initial porosity of the medium was also taken into account in the mathematical model. Finite element discretization was carried out on the mathematical model to get a fully coupled finite element equation with the parameters of element nodal displacement and element nodal pore pressure as unknown variables. Finally, the transient nonlinear finite element equation in incremental form for reservoir fluid-solid coupling is obtained by means of time discretization in implicit difference scheme. The resulted finite element formulation can simulate the reservoir behavior comprehensively and would have wide applications in petroleum engineering.

Key words: reservoir, fluid-solid coupling, mathematical model, nonlinear finite elements, porous medium

CLC Number: 

  • TB 115
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