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A modified space - Time finite element method for simulation of immiscible incompressible two-phase flow in heterogeneous porous media

Ferdowsi, P. A ; Sharif University of Technology | 2007

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  1. Type of Document: Article
  2. DOI: 10.1002/fld.1162
  3. Publisher: 2007
  4. Abstract:
  5. In this paper, a modified space-time method is presented for the simulation of convection-diffusion equations. The new method differs from the original space-time method in the sense that the weight functions for space and time are different. The performance of the proposed algorithm is studied for numerical simulation of incompressible immiscible two-phase flow in porous media. The governing equations consist of one conservation of mass equation for each phase, the Darcy law and one capillary-saturation correlation for the flow. By defining a global pressure, the governing equations lead to a system of nonlinear equations in terms of this global pressure, the velocity components and the saturation of one phase. The flow equations are solved for the global pressure and velocity components using a stabilized mixed finite element method while the saturation equation is solved by the standard and modified space-time element methods. The performance of the proposed space-time method is compared with that of the original Petrov-Galerkin space-time method for both linear and nonlinear cases. The effect of the tuning parameters of the standard method, grid size and the capillary pressure are studied for a one-dimensional problem. A stability analysis is also carried out for the proposed space-time method. Finally, to demonstrate the capability of the proposed method in dealing with homogeneous and heterogeneous problems two-dimensional water-flooding five-spot test cases are studied. Copyright © 2005 John Wiley & Sons, Ltd
  6. Keywords:
  7. Incompressible flow ; Nonlinear equations ; Convection-diffusion equation ; Space-time element method ; Two phase flow ; Computer simulation ; Diffusion ; Finite element method ; Floods ; Galerkin methods ; Porous materials
  8. Source: International Journal for Numerical Methods in Fluids ; Volume 53, Issue 8 , 2007 , Pages 1221-1242 ; 02712091 (ISSN)
  9. URL: https://onlinelibrary.wiley.com/doi/10.1002/fld.1162