Potential-based reduced Newton algorithm for nonlinear multiphase flow in porous media

Journal of Computational Physics

Volumn 227, Issue 1, 2007, Pages 706-727

  Kwok, Felix ^a   Tchelepi, Hamdi ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Black oil model; Nonlinear multiphase flow; Nonlinear solvers; Porous media; Potential ordering; Reduced Newton

Indexed keywords

ALGEBRA; MULTIPHASE FLOW; NEWTON-RAPHSON METHOD; NUMERICAL METHODS;

BLACK-OIL MODELS; MULTIPHASE FLOW IN POROUS MEDIAS; NEWTON ALGORITHM; NEWTON'S METHODS; NON-LINEAR SOLVER; NONLINEAR MULTIPHASE FLOW; PHASE BASED; POROUS MEDIUM; POTENTIAL ORDERING; REDUCED NEWTON;

POROUS MATERIALS;

EID: 35348866150     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.08.012     Document Type: Article

References (13)

1. John R. Appleyard, Ian M. Cheshire, The cascade method for accelerated convergence in implicit simulators, in: European Petroleum Conference, 1982, pp. 113-122.
2. Aziz K., and Settari A. Petroleum Reservoir Simulation (1979), Applied Science Publishers, New York
3. Brent R.P. Algorithms for Minimization without Derivatives (1973), Prentice-Hall, Englewood Cliffs, NJ (Chapter 3-4)
4. Hui Cao. Development of Techniques for General Purpose Simulators, PhD thesis, Stanford University, Stanford, CA, June 2002.
5. Christie M.A., and Blunt M.J. Tenth SPE comparative solution project: a comparison of upscaling techniques. SPE Reservoir Eval. Eng. 4 4 (2001) 308-317
6. Coats K.H. A note on IMPES and some IMPES-based simulation models. SPEJ 5 3 (2000) 245-251
7. D'Azevedo E.F., Forsyth P.A., and Tang W.-P. Ordering methods for preconditioned conjugate gradient methods applied to unstructured grid problems. SIAM J. Matrix Anal. Appl. 13 3 (1992) 944-961
8. Fayers F.J., and Matthews J.D. Evaluation of normalized Stone's methods for estimating three-phase relative permeabilities. SPE J. 24 (1984) 224-232
9. Felix Kwok. Scalable Linear and Nonlinear Algorithms for Multiphase Flow in Porous Media, PhD thesis, Stanford University, Stanford, CA, December 2007.
10. Odeh A.S. Comparison of solutions to a three-dimensional black-oil reservoir simulation problem. JPT (1981) 13-25
11. Rudin W. Principles of Mathematical Analysis. third ed. (1976), McGraw-Hill
12. Saad Y., and Schultz M.H. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7 3 (1986) 856-869
13. J.R. Wallis, R.P. Kendall, T.E. Little, Constrained residual acceleration of conjugate residual methods, in: Eighth SPE Symposium on Reservoir Simulation, 1985, pp. 415-428,.