Implementation of higher-order methods for robust and efficient compositional simulation

Journal of Computational Physics

Volumn 229, Issue 8, 2010, Pages 2898-2913

  Mikyška, Jiř ^a,b   Firoozabadi, Abbas ^a  

^a RESERVOIR ENGINEERING RESEARCH INSTITUTE   (United States)

^b CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

Author keywords

Compositional flow; Discontinuous Galerkin method; Gas injection; Laws slope limiter; Mixed finite elements; Monotone upwind scheme for conservation; Two phase flow

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; CONSERVATION; EFFICIENCY; FINITE ELEMENT METHOD; GALERKIN METHODS; NUMERICAL METHODS;

COMPOSITIONAL FLOW; DISCONTINOUS GALERKIN METHODS; GAS INJECTION; HIGH-ORDER METHODS; LAW SLOPE LIMITER; MIXED FINITE ELEMENTS; MONOTONE UPWIND SCHEME FOR CONSERVATION; SLOPE LIMITER; TWO PHASES FLOW; UP-WIND SCHEME;

TWO PHASE FLOW;

EID: 77957021576     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.12.022     Document Type: Article

References (20)

1. R.J. Leveque, Finite volume methods for hyperbolic problems, Cambridge Texts in Applied Mathematics, Cambridge University Press, 2002.
2. J.E.P. Monteagudo, A. Firoozabadi, Control-volume model for simulation of water injection in fractured media: incorporating matrix heterogeneity and reservoir wettability effects, SPEJ (2007).
3. H. Hoteit, A. Firoozabadi, Multicomponent fluid flow by discontinuous Galerkin and mixed methods in unfractured and fractured media, Water Resour. Res. 41 (2005) W11412, doi:10.1029/2005WR004339.
4. H. Hoteit, A. Firoozabadi, Compositional modeling by the combined discontinuous Galerkin and mixed methods, SPEJ (2006).
5. Z. Chen, B. Cockburn, J.W. Jerome, C.-W. Shu, Mixed-RKDG finite element methods for the 2D hydrodynamic model for semiconductor device simulation, VLSI Des. 3 (2) (1995) 145-158.
6. G. Ács, S. Doleschall, É. Farkas, General purpose compositional model, SPEJ 25 (4) (1985) 543-553 (SPE-10515-PA).
7. J. Lohrentz, B. Bary, R. Clark, Calculating viscosities of reservoir fluids from their compositions, J. Pet. Technol. 16 (1964) 1171-1176.
8. A. Firoozabadi, Thermodynamics of Hydrocarbon Reservoirs, McGraw-Hill, New York, 1999.
9. D.-Y. Peng, D.B. Robinson, A new two-constant equation of state, Ind. Eng. Chem. Fundam. 15 (1) (1976) 59-64.
10. B. van Leer, Towards the ultimate conservative difference scheme. I. The quest of monotonicity, Springer Lect. Note Phys. 18 (1973) 163-168.
11. B. van Leer, Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second order scheme, J. Comput. Phys. 14 (1974) 361-370.
12. B. van Leer, Towards the ultimate conservative difference scheme. III. Upstream-centered finite-difference schemes for ideal compressible flow, J. Comput. Phys. 23 (1977) 263-275.
13. B. van Leer, Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection, J. Comput. Phys. 23 (1977) 276-299.
14. B. van Leer, Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov's method, J. Comput. Phys. 32 (1979) 101-136.
15. P.H. Sammon, An analysis of upstream differencing, SPE Reserv. Eng. (1988) 1053-1056.
16. F. Brezzi, M. Fortin, Mixed and Hybrid Finite Element Methods, Springer, New York, 1991.
17. P. Raviart, J. Thomas, A mixed hybrid finite element method for the second order elliptic problem, Lect. Note Math. Ser., vol. 606, Springer, New York, 1977.
18. A. Younes, P. Ackerer, F. Lehmann, A new mass lumping scheme for the mixed hybrid finite element method, Int. J. Numer. Method Eng. 67 (2006) 89- 107.
19. G. Chavent, J.E. Roberts, A unified physical presentation of mixed, mixed-hybrid finite elements and standard finite difference approximations for the determination of velocities in waterflow problems, Adv. Water Resour. 14 (6) (1991) 329-348.
20. M. Feistauer, J. Felcman, Straškraba, Mathematical and Computational Methods for Compressible Flow, Clarendon Press, Oxford, 2003.