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

B. Ataie-Ashtiani, D. Raeesi-Ardekani

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)373-389
Number of pages17
JournalGeotechnical and Geological Engineering
Publication statusPublished - 1 Jul 2010
Externally publishedYes


  • Newton-Raphson
  • Numerical model
  • Picard
  • Primary variables
  • Two-phase flow


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