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Comparison of numerical formulations for Two-phase flow in porous media

Ataie Ashtiani, B ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. DOI: 10.1007/s10706-009-9298-4
  3. Publisher: 2010
  4. Abstract:
  5. Numerical approximation based on different forms of the governing partial differential equation can lead to significantly different results for two-phase flow in porous media. Selecting the proper primary variables is a critical step in efficiently modeling the highly nonlinear problem of multiphase subsurface flow. A comparison of various forms of numerical approximations for two-phase flow equations is performed in this work. Three forms of equations including the pressure-based, mixed pressure-saturation and modified pressure-saturation are examined. Each of these three highly nonlinear formulations is approximated using finite difference method and is linearized using both Picard and Newton-Raphson linearization approaches. Model simulations for several test cases demonstrate that pressure based form provides better results compared to the pressure-saturation approach in terms of CPU_time and the number of iterations. The modification of pressure-saturation approach improves accuracy of the results. Also it is shown that the Newton-Raphson linearization approach performed better in comparison to the Picard iteration linearization approach with the exception for in the pressure-saturation form
  6. Keywords:
  7. Picard ; Primary variables ; CPU time ; Critical steps ; Highly nonlinear ; Model simulation ; Newton-Raphson ; Newton-Raphson linearization ; Number of iterations ; Numerical approximations ; Numerical formulation ; Numerical models ; Picard iteration ; Pressure-based ; Subsurface Flow ; Test case ; Computer simulation ; Differential equations ; Differentiation (calculus) ; Linearization ; Numerical methods ; Porous materials ; Finite difference method ; Nonlinearity ; Numerical model ; Porous medium ; Subsurface flow ; Two phase flow
  8. Source: Geotechnical and Geological Engineering ; Volume 28, Issue 4 , 2010 , Pages 373-389 ; 09603182 (ISSN)
  9. URL: http://link.springer.com/article/10.1007%2Fs10706-009-9298-4