Compositional modeling of three-phase flow with gravity using higher-order finite element methods

Water Resources Research

Volumn 47, Issue 5, 2011, Pages

  Moortgat, Joachim ^a   Sun, Shuyu ^b   Firoozabadi, Abbas ^a,c  

^a RESERVOIR ENGINEERING RESEARCH INSTITUTE   (United States)

^b KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Saudi Arabia)

^c Yale University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACCURATE PREDICTION; CARBON SEQUESTRATION; COMPLEX GEOMETRIES; COMPOSITIONAL FLOW; COMPOSITIONAL MODELING; COUNTER-CURRENT FLOW; ENHANCED OIL RECOVERY; GASPHASE; GRAVITATIONAL INSTABILITY; HIGHER-ORDER FINITE ELEMENT METHODS; HIGHER-ORDER METHODS; MULTIPHASE PROCESS; NONAQUEOUS PHASE LIQUIDS; NUMERICAL EXAMPLE; NUMERICAL SIMULATION; SHARP SOLUTIONS; SUBSURFACE FLOW; THREE-PHASE FLOW; UPWINDING;

ALGORITHMS; CARBON DIOXIDE; ENHANCED RECOVERY; FINITE ELEMENT METHOD; NUMERICAL METHODS; POROUS MATERIALS;

FLOW SIMULATION;

ACCURACY ASSESSMENT; ALGORITHM; CARBON DIOXIDE; CARBON SEQUESTRATION; COMPUTER SIMULATION; FINITE ELEMENT METHOD; GAS PHASE REACTION; GEOMETRY; MATHEMATICAL ANALYSIS; NUMERICAL MODEL; THREE PHASE FLOW; VAPORIZATION; VISCOSITY;

EID: 79957486358     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2010WR009801     Document Type: Article

References (58)

1. Acs, G., S. Doleschall, and E. Farkas (1985), General purpose compositional model, SPE J., 25(4), 543-553.
2. Adenekan, A. E., T. W. Patzek, and K. Pruess (1993), Modeling of multiphase transport of multicomponent organic contaminants and heat in the subsurface: Numerical model formulation, Water Resour. Res., 29(11), 3727-3740.
3. Arnold, D. (1982), An interior penalty finite element method with discontinuous elements, SIAM J. Numer. Anal., 19, 742-760.
4. Ashcroft, S., and M. Ben Isa (1997), Effect of dissolved gases on the densities of hydrocarbons, J. Chem. Eng. Data, 42(6), 1244-1248. (Pubitemid 127649457)
5. Babuška, I. (1973), The finite element method with penalty, Math. Comput., 27(112), 221-228.
6. Babuška, I., and M. Zlamal (1973), Nonconforming elements in the finite element method with penalty, SIAM J. Numer. Anal., 10, 863-875.
7. Brezzi, F., and M. Fortin (1991), Mixed and Hybrid Finite Element Methods, Springer, New York.
8. 2 solubility in water, SPE Reservoir Eval. Eng., 1(2), 155-160.
9. Cockburn, B., G. E. Karniadakis, and C. E. Shu (2000), Discontinuous Galerkin Methods, Theory, Computation, and Applications, Springer, Berlin.
10. Courant, R., K. Friedrichs, and H. Lewy (1928), Partial differential equations of mathematical physics, Math. Ann., 100, 32-74.
11. Dawson, C., S. Sun, and M. F. Wheeler (2004), Compatible algorithms for coupled flow and transport, Comput.Meth. Appl.Mech. Eng., 193, 2565-1029.
12. Delshad, M., and G. A. Pope (1989), Comparison of the three-phase oil relative permeability models, Transp. Porous Media, 4, 59-83.
13. 2 sequestration using a non-isothermal compositional model, paper presented at International Mechanical Engineering Congress and Exposition, Am. Soc. of Mech. Eng., Boston, Mass.
14. 2 sequestration using a sequentially coupled Iterative-IMPEC-Time- Split-Thermal' compositional simulator, paper presented at 11th European Conference on the Mathematics of Oil Recovery, ECMOR XI, Eur. Assoc. of Geosci. and Eng., Bergen, Norway.
15. Delshad, M., S. G. Thomas, and M. F. Wheeler (2009), Parallel numerical simulations of non-isothermal compositional flow and chemistry, Rep. SPE 118847, Soc. of Petrol. Eng., Richardson, Tex.
16. Ewing, R. E., R. D. Lazarov, and J. Wang (1991), Superconvergence of the velocity along the gauss lines in mixed finite element methods, SIAM J. Numer. Anal., 28, 1015-1029. (Pubitemid 21682134)
17. Falta, R. W., K. Pruess, I. Javandel, and P. A. Witherspoon (1992), Numerical modeling of steam injection for the removal of nonaqueous phase liquids from the subsurface: 1. Numerical formulation, Water Resour. Res., 28(2), 433-449.
18. 2 injection projects, Int. J. Heat Mass Transfer, 50, 5054-5064. (Pubitemid 350180875)
19. Firoozabadi, A. (1999), Thermodynamics of Hydrocarbon Reservoirs, 355 pp., McGraw-Hill, New York.
20. 2 sequestration, AIChE J., 56(6), 1398-1405.
21. Firoozabadi, A., D. Katz, H. Soroosh, and V. A. Sajjadian (1988a), Surface tension of reservoir crude-oil/gas systems recognizing the asphalt in the heavy fraction, SPE J., 13826, 265-272.
22. 2, SPE Reservoir Eng., 3, 673-648.
23. Geiger, S., S. Matthäi, J. Niessner, and R. Helmig (2009), Black-oil simulations for three-components, three-phase flow in fractured porous media, Rep. SPE 107485, Soc. of Petrol. Eng., Richardson, Tex.
24. Girault, V., S. Sun, M. F. Wheeler, and I. Yotov (2008), Coupling discontinuous Galerkin and mixed finite element discretizations using mortar finite elements, SIAM J. Numer. Anal., 46(2), 949-979.
25. 2/NGL EOR, paper presented at Annual Technical Conference and Exhibition, Soc. of Petrol. Eng., New Orleans, La.
26. Hoteit, H., and A. Firoozabadi (2005), Multicomponent fluid flow by discontinuous Galerkin and mixed methods in unfractured and fractured media, Water Resour. Res., 41, W11412, doi:10.1029/2005WR004339. (Pubitemid 43041787)
27. Hoteit, H., and A. Firoozabadi (2006a), Compositional modeling by the combined discontinuous Galerkin and mixed methods, SPE J., 11(1), 19-34.
28. Hoteit, H., and A. Firoozabadi (2006b), Compositional modeling of discretefractured media without transfer functions by the discontinuous Galerkin and mixed methods, SPE J., 11(3), 341-352. (Pubitemid 44541496)
29. Hoteit, H., and A. Firoozabadi (2008), Numerical modeling of two-phase flow in heterogeneous permeable media with different capillarity pressures, Adv. Water Res., 31(1), 56-73. (Pubitemid 350082673)
30. Hoteit, H., and A. Firoozabadi (2009), Numerical modeling of diffusion in fractured media for gas-injection and -recycling schemes, SPE J., 14(2), 323-337.
31. 2 storage, Adv. Water Res., 33(8), 867-879.
32. 2 displacements of reservoir oils from long berea cores: laboratory and simulation results, SPE J., 14306, 496-504. (Pubitemid 18624851)
33. 2-oil displacement mechanisms, SPE J., 8368, 89-97.
34. Lemmon, E., M. McLinden, and D. Friend (2010), Thermophysical properties of fluid systems, in NIST Chemistry WebBook, Stand. Ref. Database, vol. 69, edited by P. J. Linstrom and W. G. Mallard, Natl. Inst. of Stand. and Technol., Gaithersburg, Md. (Available at http://webbook.nist.gov.)
35. Li, Z., and A. Firoozabadi (2009), Cubic-plus-association equation of state for water-containing mixtures: Is "cross association" necessary?, AIChE J., 55(7), 1803-1813.
36. Lohrenz, J., B. G. Bray, and C. R. Clark (1964), Calculating viscosities of reservoir fluids from their compositions, J. Petrol. Technol., 16(10), 1171-1176.
37. Mikysta, J., and A. Firoozabadi (2010), Implementation of higher-order methods for robust and efficient compositional simulation, J. Comput. Phys., 229, 2898-2913.
38. Moortgat, J., and A. Firoozabadi (2010), Higher-order compositional modeling with Fickian diffusion in unstructured and anisotropic media, Adv. Water Resour., 33(9), 951-968.
39. 2 injection schemes, Rep. SPE 124803, Soc. of Petrol. Eng., Richardson, Tex.
40. Niessner, J., and R. Helmig (2007), Multi-scale modeling of three-phasethree- component processes in heterogeneous porous media, Adv. Water Resour., 30(11), 2309-2325. (Pubitemid 47336891)
41. Niessner, J., and R. Helmig (2009), Multi-physics modeling of flow and transport in porous media using a downscaling approach, Adv. Water Resour., 32(6), 845-850.
42. Nitsche, J. (1971), Über ein Variationsprinzip zur Lösung von Dirichlet- Problemen bei verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind, Abh. Math. Sem. Univ. Hamburg, 36, 9-15.
43. 2 storage in saline aquifers, Adv. Water Resour., 33(4), 443-455.
44. Peng, D.-Y., and D. B. Robinson (1976), A new two-constant equation of state, Ind. Eng. Chem. Fundam., 15(1), 59-64, doi:10.1021/i160057a011.
45. Raviart, P. A., and J. M. Thomas (1977), Primal hybrid finite-element methods for second-order elliptic equations, Math. Comput., 31(138), 391-413.
46. Reed, W., and T. Hill (1973), Triangular mesh methods for the neutron transport equation, technical report, Los Alamos Natl. Lab. Res. Libr., Los Alamos, N. M.
47. 2-liquid systems, submitted.
48. 2-reservoir oil systems, SPE J., 18(1), 20-26. (Pubitemid 8583169)
49. Stone, H. (1970), Probability model for estimating three-phase relative permeability, J. Petrol. Technol., 214, 214-218.
50. Stone, H. (1973), Estimation of three-phase relative permeability and residual oil data, J. Can. Petrol. Technol., 12, 53-61.
51. Sun, S., and M. F. Wheeler (2005a), Discontinuous Galerkin methods for coupled flow and reactive transport problems, Appl. Numer. Math., 52(2-3), 273-298.
52. Sun, S., and M. F. Wheeler (2005b), Symmetric and nonsymmetric discontinuous Galerkin methods for reactive transport in porous media, SIAM J. Numer. Anal., 43(1), 195-219.
53. Sun, S., and M. F. Wheeler (2006), Analysis of discontinuous Galerkin methods for multicomponent reactive transport problems, Comput. Math. Appl., 52(5), 637-650. (Pubitemid 46227808)
54. Sun, S., B. Riviere, and M. F. Wheeler (2002), A combined mixed finite element and discontinuous Galerkin method for miscible displacement problems in porous media, paper presented at International Symposium on Computational and Applied PDEs, Zhangjiajie Natl. Park, Zhangjiajie, China.
55. Wang, Y., C.-Y. Lin, C. Bidinger, V. Muralidharan, and S.-T. Lee (2003), Compositional modeling of gas injection with three hydrocarbon phases for schrader bluff eor, paper presented at Annual Technical Conference and Exhibition, Soc. of Petrol. Eng., Denver, Colo.
56. Watts, J. W. (1986), A compositional formulation of the pressure and saturation equations, SPE Reservoir Eng., 1(3), 243-252.
57. Wheeler, M. F. (1978), An elliptic collocation finite element method with interior penalties, SIAM J. Numer. Anal., 15, 152-161.
58. Xu, X., S. Chen, and D. Zhang (2006), Convective stability analysis of the long-term storage of carbon dioxide in deep saline aquifers, Adv. Water Resour., 29(3), 397-407. (Pubitemid 43009159)