Numerical Algorithms for Network Modeling of Yield Stress and other Non-Newtonian Fluids in Porous Media

Transport in Porous Media

Volumn 93, Issue 3, 2012, Pages 363-379

  Balhoff, Matthew ^a   Sanchez Rivera, Daniel ^a   Kwok, Alan ^a   Mehmani, Yashar ^a   Prodanović, Maša ^a  

^a The University of Texas at Austin   (United States)

Author keywords

Invasion percolation with memory; Non Newtonian flow; Pore scale modeling; Threshold path; Yield stress

Indexed keywords

ENHANCED OIL RECOVERY; FIXED-POINT ITERATIONS; FLOW BEHAVIORS; FLOW EQUATIONS; INVASION PERCOLATION; ITERATIVE IMPROVEMENTS; JACOBIAN METHOD; MASS CONSERVATION; NETWORK MODELING; NEWTON ALGORITHM; NEWTON'S METHODS; NEWTON-RAPHSON; NON-NEWTONIAN FLUIDS; NONLINEAR PROBLEMS; NUMERICAL ALGORITHMS; NUMERICAL APPROACHES; NUMERICAL SOLUTION; ORDERS OF MAGNITUDE; POLYMER FLOODING; PORE-SCALE MODELING; POWER LAW FLUID; PROPPANT SUSPENSION; RELAXATION FACTORS; SEARCH ALGORITHMS; SHEAR THINNING FLUIDS; STRONG NONLINEARITY; SUBSURFACE MEDIA; SYSTEMS OF EQUATIONS; THRESHOLD PATH; THRESHOLD PRESSURE GRADIENT; TIME DEPENDENT SIMULATION;

COMPUTER SIMULATION; ENHANCED RECOVERY; FLOW MEASUREMENT; HYDRAULIC FRACTURING; LEARNING ALGORITHMS; NEWTON-RAPHSON METHOD; NON NEWTONIAN FLOW; NON NEWTONIAN LIQUIDS; NUMERICAL METHODS; OPTIMIZATION; PERCOLATION (FLUIDS); PERCOLATION (SOLID STATE); POROUS MATERIALS; RHEOLOGY; SHEAR THINNING; VISCOUS FLOW;

YIELD STRESS;

ALGORITHM; COMPUTER SIMULATION; ENHANCED OIL RECOVERY; HEAVY OIL; HYDRAULIC FRACTURE; NON-NEWTONIAN FLUID; NUMERICAL MODEL; POROUS MEDIUM; POWER LAW; RESERVOIR FLOODING; STRESS;

EID: 84862129398     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-012-9956-5     Document Type: Article

References (36)

1. Ahuja R. K., Magnanti T. L., Orlin J. B.: Network Flows: Theory, Algorithms, and Applications. Prentice Hall, Englewood Cliffs (1993).
2. Al-Raoush R., Thompson K. E., Willson C. S.: Comparison of network generation techniques for unconsolodated porous media. Soil Sci. Soc. Am. J. 67(6), 1687-1700 (2003).
3. Bakke S., Øren P. E.: 3-D pore-scale modelling of sandstones and flow simulations in the pore networks. SPE J. 2(2), 136-149 (1997).
4. Balan H., Balhoff M., Nguyen Q., Rossen W.: Network Modeling of Gas Trapping and Mobility in Foam EOR. Energy and Fuels 25(9), 3974-3987 (2011).
5. Balhoff M. T.: Modeling the flow of crosslinked guar gum in porous media. Polym. Prepr. 45(2), 128-129 (2004).
6. Balhoff M., Thompson K.: A macroscopic model for shear-thinning flow in packed beds based on network modeling. Chem. Eng. Sci. 61(2), 698-719 (2006).
7. Balhoff M., Thompson K.: Modeling the steady flow of yield-stress fluids in packed beds. AIChE J. 50(12), 3034-3048 (2004).
8. Balhoff M. T., Miller M. J.: An analytical model for cleanup of yield-stress fluids in hydraulic fractures. SPE J. 10(1), 3-11 (2005).
9. Balhoff M. T., Wheeler M. F.: A predictive pore scale model of non-darcy flow in porous media. SPE J. v14(4), 579-587 (2009).
10. Blunt M., Jackson M., Piri M., Valvatne P.: Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Adv. Wat. Res. 25(8-12), 1069-1089 (2002).
11. Bruschke M. V., Advani S. G.: A finite element/control volume approach to mold filling in anisotropic porous media. Polym. Compos. 11, 398-405 (1990).
12. Bryant S., Pallatt N.: Predicting formation factor and resistivity index in simple sandstones. J. Petroleum Sci. Eng. 15(2-4), 169-179 (1996).
13. Chabbra R. P.: Bubbles, drops, and particles in non-newtonian fluids. CRC press, Boca Raton (2000).
14. Chapra S., Canale R.: Numerical methods for engineers, 6th edn. McGraw-Hill, Boston (2010).
15. Chen M., Rossen W., Yortsos Y.: The flow and displacement in porous media of fluids with yield stress. Chem. Eng. Sci. 60(15), 4183-4202 (2005).
16. Fatt I.: The network model of porous media I. Capillary characreristics. Pet. Trans. AIME 207, 144-159 (1956a).
17. Fatt I.: The network model of porous media II. Dynamic properties of a single size tube network. Pet. Trans. AIME 207, 160-163 (1956b).
18. Fatt I.: The network model of porous media III. Dynamic properties of networks with tube radius distribution. Pet. Trans. AIME 207, 164-181 (1956c).
19. Gani, M. R., Bhattacharya, J. P.: Bed-scale facies architecture of an ancient delta lobe deposit of the wall creek member, Central Wyoming, U. S. A., In: Proceedings of the AAPG Annual Convention & Exhibition, Salt Lake City, UT, 11-14 May (2003).
20. Jodrey W., Tory E.: Computer simulation of close random packing of equal spheres. Phys. Rev. A. 32(4), 2347-2351 (1985).
21. Joekar-Niasar V., Prodanović M., Wildenschild D., Hassanizadeh S. M.: Network model investigation of interfacial area, capillary pressure and saturation relationships in granular porous media. Wat. Resour. Res. 46(6), W06526 (2010).
22. Kharabaf H., Yortsos Y.: Invasion percolation with memory. Phys. Rev. E. 55(6), 7177-7191 (1997).
23. Lopez X., Valvatne P. H., Blunt M. J.: Predictive network modeling of single-phase non-newtonian flow in porous media. J. ColloidInterf. Sci. 264(1), 256-265 (2003).
24. May, E., Britt, K., Nolte, K: The effect of yield stress on fracture fluid cleanup. In: Paper SPE 38619 presented at the 1997 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 5-8 Oct 1997.
25. Prodanovic M., Lindquist W., Seright R.: Porous structure and fluid partitioning in polyethylene cores from 3D X-ray microtomographic imaging. J. Colloid Interf. Sci. 298(1), 282-297 (2006).
26. Sahimi M.: Flow phenomena in rocks: from continuum models to fractals, percolation, cellular automata, and simulated annealing. Rev. Mod. Phys. 65, 1393-1534 (1993).
27. Shah C., Yortsos Y.: Aspects of flow of power-law fluids in porous media. AIChE J. 41, 1099-1112 (1995).
28. Shah, C., Kharabaf, H., Yortsos, Y. C.: Immiscible Displacements Involving Power-Law Fluids in Porous Media. In: Proceedings of the 7th UNITAR International Conference on Heavy Oils and Tar Sands, Beijing, China, 27-30 Oct (1998).
29. Shah, C., Kharabaf, H., Yortsos, Y.: In Flow and Displacement of Bingham Plastics in Porous Media. In: Proceedings of the 6th UNITAR Conference On Heavy Oils and Tar Sands, Houston, TX, 16 Feb (1995).
30. Sheppard, A., Sok, R., Averdunk, H.: improved pore-network generation methods. In: 19th International Symposium of the Society of Core Analysts. Society of Core Analysts, Austin, TX (2005).
31. Sochi T., Blunt M.: Pore-scale network modeling of Ellis and Herschel-Bulkley fluids. J. Petroleum Sci. Eng. 60(2), 105-124 (2008).
32. Sochi T.: Modelling the flow of yield-stress fluids in porous media. Trans. Porous Med. 85, 489-503 (2010).
33. Sorbie K., Clifford P., Jones E.: The rheology of pseudoplastic fluids in porous media using network modeling. J. Colloid Interf. Sci. 130, 508-534 (1989).
34. Thompson K., Willson C., White C., Nyman S., Bhattacharya J., Reed A.: Application of a new grain-based reconstruction algorithm to microtomography images for quantitative characterization and flow modeling. SPE J. 13(2), 164-176 (2008).
35. Valvatne P. H., Blunt M. J.: Pore-scale modeling of longitudinal dispersion. Wat. Resour. Res. 40, W07406 (2004).
36. Wang, D., Cheng, J., Yang Q., Gong W., Li Q., Chen, F.: Viscous-elastic polymer can increase microscale displacement efficiency in cores. In: SPE 63227, presented at the 2000 SPE Annual Technical Conference and Exhibition held in Dallas, Texas, 1-4 Oct (2000).