Similarity solutions for flow of non-Newtonian fluids in porous media revisited under parameter uncertainty

Advances in Water Resources

Volumn 43, Issue , 2012, Pages 38-51

  Ciriello, Valentina ^a   Di Federico, Vittorio ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Non Newtonian; Polynomial Chaos Expansion; Porous medium; Self similar solution; Sobol' indices

Indexed keywords

NON-NEWTONIAN; POLYNOMIAL CHAOS EXPANSION; POROUS MEDIUM; SELF-SIMILAR SOLUTION; SOBOL' INDICES;

FLUID DYNAMICS; NON NEWTONIAN LIQUIDS; NONLINEAR EQUATIONS; POLYNOMIALS; POROUS MATERIALS;

NON NEWTONIAN FLOW;

FLOW MODELING; FLOW VELOCITY; FLUID FLOW; NON-NEWTONIAN FLUID; PERMEABILITY; POROUS MEDIUM; SENSITIVITY ANALYSIS; TRANSIENT FLOW; UNCERTAINTY ANALYSIS;

EID: 84860697865     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2012.03.028     Document Type: Article

References (70)

1. Suthersan S.S. Remediation engineering - design concepts 1997, CRC Press, Boca Raton, USA.
2. Theodoropoulou M., Karoutsosa V., Tsakiroglou C. Investigation of the contamination of fractured formations by non-Newtonian oil pollutants. Environ Forensics 2001, 2(4):321-334.
3. Birak P.S., Miller C.T. Dense non-aqueous phase liquids at former manufactured gas plants: challenges to modeling and remediation. J Contam Hydrol 2009, 105:81-98.
4. Vallero D.A. Engineering the risks of hazardous wastes 2003, Butterworth Heinemann.
5. Yan Y.-L., Deng Q., He F., Zhang X.-Q., Liu Y.-P. Remediation of DNAPL-contaminated aquifers using density modification method with colloidal liquid aphrons. Colloids Surf A Physicochem Eng Aspects 2011, 385(1-3):219-228.
6. Tosco T., Sethi R. Transport of non-Newtonian suspensions of highly concentrated micro- and nanoscale iron particles in porous media: a modeling approach. Environ Sci Technol 2010, 44:9062-9068.
7. Comba S., Sethi R. Stabilization of highly concentrated suspensions of iron nanoparticles using shear-thinning gels of xanthan gum. Water Res 2009, 43(15):3717-3726.
8. Martel K.E., Martel R., Lefebvre R., Gelinas P.J. Laboratory study of polymer solutions used for mobility control during in situ NAPL recovery. Ground Water Monit Remediation 1998, summer:103-113.
9. Hung Y-T., Butler E., Kuo C.Y., Yeh R.Y.L. Chemicals and allied products. Water Environ Res 2010, 82(10):1448-1467.
10. Wang S., Huang Y., Civan F. Experimental and theoretical investigation of the Zaoyuan field heavy oil flow through porous media. J Petrol Sci Eng 2006, 50:83-101.
11. Bazyleva A.B., Hasan M.D.A., Fulem M., Becerra M., Shaw J.M. Bitumen and heavy oil rheological properties: reconciliation with viscosity measurements. J Chem Eng Data 2010, 55(3):1389-1397.
12. Babadagli T. Development of mature oil fields - a review. J Petrol Sci Eng 2007, 57(3-4):221-246.
13. Wu Y.-S., Pruess K. Flow of non-Newtonian fluids in porous media. Adv Porous Med 1996, 3:87-184.
14. Nazar M.F., Shah S.S., Khosa M.A. Microemulsions in enhanced oil recovery: a review. Petrol Sci Technol 2011, 29(13):1353-1365.
15. Mikhailov D.N., Economides M.J., Nikolaevskiy V.N. Fluid leakoff determines hydraulic fracture dimensions: approximate solution for non-Newtonian fracturing fluid. Int J Eng Sci 2011, 49(9):809-822.
16. Hamed S.B., Belhadri M. Rheological properties of biopolymers drilling fluids. J Petrol Sci Eng 2009, 67(3-4):84-90.
17. Balhoff M.T., Thompson K.E. Modeling the steady flow of yield-stress fluids in packed beds. AIChE J 2004, 50(12):3034-3048.
18. Broniarz-Press L., Agacinski P., Rozanski J. Shear-thinning fluids flow in fixed and fluidised beds. Int J Multiphas Flow 2007, 33:675-689.
19. Fatimi A. Rheological behavior of biomaterials for osteoarticular and dental tissue engineering: synthetic extracellular matrix and calcium phosphate suspensions. IRBM 2009, 30(3):139-140.
20. Sochi T. Single-phase flow of non-Newtonian fluids in porous media. Technical report. London: Department of Physics and Astronomy, University College; 2009. arxiv:0907.2399v1.
21. Sochi T. Flow of non-Newtonian fluids in porous media. J Polym Sci B Polym Phys 2010, 48:2437-2767.
22. Vradis G.C., Protopapas A.L. Macroscopic conductivities for flow of Bingham plastics in porous media. J Hydraul Eng 1993, 119(1):95-108.
23. Momeni-Masuleh S.H., Phillips T.N. Viscoelastic flow in an undulating tube using spectral methods. Comput Fluids 2004, 33(8):1075-1095.
24. Pearson J.R.A., Tardy P.M.J. Models of non-Newtonian and complex fluids through porous media. J Non-Newton Fluid Mech 2002, 102(2):447-473.
25. Tsakiroglou C.D. A methodology for the derivation of non-Darcian models for the flow of generalized Newtonian fluids in porous media. J Non-Newton Fluid Mech 2002, 105:79-110.
26. Tsakiroglou C.D. Correlation of the two-phase flow coefficients of porous media with the rheology of shear-thinning fluids. J Non-Newton Fluid Mech 2004, 117(1):1-23.
27. Savins J.G. Non-Newtonian flow through porous media. Ind Eng Chem Fund 1969, 6(10):18-47.
28. Goldstein R.V., Entov V.M. Quantitative methods in continuum mechanics 1994, Wiley, New York, USA.
29. Shenoy A.V. Non-Newtonian fluid heat transfer in porous media. Adv Heat Transfer 1995, 24:102-190.
30. Chhabra R.P., Comiti J., Machač I. Flow of non-Newtonian fluids in fixed and fluidised beds. Chem Eng Sci 2001, 56:1-27.
31. Bird R.B., Stewart W.E., Lightfoot E.N. Transport phenomena 1960, Wiley, New York, USA.
32. Christopher R.H., Middleman S. Power-law flow through a packed tube. Ind Eng Chem Fund 1965, 4(4):422-426.
33. Kozicki W., Hsu C.J., Tiu C. Non-Newtonian flow through packed beds and porous media. Chem Eng Sci 1967, 22:487-502.
34. Teeuw D, Hesselink FT. Power-law flow and hydrodynamic behavior of biopolymer solutions in porous media. In: Paper SPE 8982 presented at the fifth international symposium on oilfield and geothermal chemistry in Stanford, California; 1980. p. 73-86.
35. Wu Y.-S., Pruess K. A numerical method for simulating non-Newtonian fluid flow and displacement in porous media. Adv Water Res 1998, 21:351-362.
36. Odeh A.S., Yang H.T. Flow of non-Newtonian power-law fluids through porous media. SPE J 1979, June:155-163.
37. Ikoku C.U., Ramey H.J. Transient flow of non-Newtonian power-law fluids in porous media. SPE J 1979, 164-174.
38. Vongvuthipornkai S, Raghavan R. Pressure falloff behavior in vertically fractured wells: non-Newtonian power-law fluids. In: SPEFE 1987, December 1987. p. 573-89.
39. Vongvuthipornkai S, Raghavan R. Well test analysis of data dominated by storage and skin: non-Newtonian power-law fluids. In: SPEFE 1987, December 1987. p. 618-28.
40. Pascal H., Pascal F. Flow of non-Newtonian fluid through porous media. Int J Eng Sci 1985, 23(5):571-585.
41. Pascal H. On the existence of self-similar solutions of the equations governing unsteady flow through a porous medium. Int J Heat Fluid Flow 1988, 9(4):381-389.
42. Pascal H. On non-linear effects in unsteady flows through porous media. Int J Nonlinear Mech 1991, 26(2):251-261.
43. Pascal H. On propagation of pressure disturbances in a non-Newtonian fluid flowing through a porous medium. Int J Nonlinear Mech 1991, 26(5):475-485.
44. Di Federico V., Ciriello V. Non-Newtonian flow through porous media due to an instantaneous mass injection. Transport Porous Med 2012, 10.1007/s11242-012-9944-9.
45. Barenblatt G.I. Scaling, self-similarity, and intermediate asymptotics 1996, Cambridge University Press, Cambridge, England.
46. Nakayama A., Koyama H. Buoyancy-induced flow of non-Newtonian fluids over a non-isothermal body of arbitrary shape in a fluid-saturated porous medium. Appl Sci Res 1991, 48:55-70.
47. Sobol' I.M. Sensitivity estimates for nonlinear mathematical models. Math Model Comput Exp 1993, 1:407-414.
48. Ghanem R.G., Spanos P.D. Stochastic finite elements - a spectral approach 1991, Springer, Berlin, Germany.
49. Park H.C., Hawley M.C., Blanks R.F. The flow of non-Newtonian solutions through packed beds. Polym Eng Sci 1975, 15(11):761-773.
50. Di Federico V., Pinelli M., Ugarelli R. Estimates of effective permeability for non-Newtonian fluid flow in randomly heterogeneous porous media. Stoch Environ Res Risk Assess 2010, 24:55-69.
51. Gogarty W.B. Rheological properties of pseudoplastic fluids in porous media. SPE J 1967, 7:149-159.
52. Van Poollen H.K., Jargon J.R. Steady-state and unsteady state flow of non-Newtonian fluids through porous media. Trans AIME 1969, 246:80-88.
53. Ghannam M.T., Shadi W., Hasan S.W., Abu-Jdayil B., Esmail N. Rheological properties of heavy and light crude oil mixtures for improving flowability. J Petrol Sci Eng 2012, 81:122-128.
54. Degan G., Akowanou K., Awanou N.C. Transient natural convection of non-Newtonian fluids about a vertical surface embedded in an anisotropic porous medium. Int J Heat Mass Transfer 2007, 50:4629-4639.
55. Fadili A., Tardy P.M.J., Pearson A. A 3D filtration law for power-law fluids in heterogeneous porous media. J Non-Newton Fluid Mech 2002, 106(2-3):121-146.
56. Orgéas L., Idrisa Z., Geindreaua C., Blochb J.F., Auriault J.L. Modelling the flow of power-law fluids through anisotropic porous media at low-pore Reynolds number. Chem Eng Sci 2006, 61:4490-4502.
57. Vajravelu K., Sreenadh S., Viswanatha Reddy G. Helical flow of a power-law fluid in a thin annulus with permeable walls. Int J Nonlinear Mech 2006, 41:761-765.
58. Kim M.C., Choi C.K. Linear analysis on the stability of miscible dispersion of shear-thinning fluids in porous media. J Non-Newton Fluid Mech 2011, 166:1211-1220.
59. Yilmaz N., Bakhtiyarov A.S., Ibragimov R.N. Experimental investigation of Newtonian and non-Newtonian fluid flows in porous media. Mech Res Commun 2009, 36(5):638-641.
60. Nield D.A., Bejan A. Convection in porous media 2006, Springer, New York, USA. 3rd ed.
61. Pascal J.P. Similarity solutions for axisymmetric plane radial power-law fluid flows through a porous medium. Comput Math Appl 1992, 23(12):25-41.
62. Gradshteyn I.S., Ryzhik I.M. Table of integrals, series and products 1994, Academic Press, New York, USA.
63. Saltelli A., Chan K., Scott E.M. Sensitivity analysis 2000, Wiley, New York, USA.
64. Archer G.E.B., Saltelli A., Sobol' I.M. Sensitivity measures, ANOVA like techniques and the use of bootstrap. J Stat Comput Simul 1997, 58:99-120.
65. Sobol' I.M. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 2001, 55:271-280.
66. Wiener N. The homogeneous chaos. Am J Math 1938, 60:897-936.
67. Xiu D., Karniadakis G.E. The Wiener-Askey polynomial chaos for stochastic differential equations. J Sci Comput 2002, 24(2):619-644.
68. Sudret B. Global sensitivity analysis using Polynomial Chaos Expansions. Reliab Eng Syst Safe 2008, 93:964-979.
69. Huang S., Sankaran M., Ramesh R. Collocation-based stochastic finite element analysis for random field problems. Probabilist Eng Mech 2007, 22:194-205.
70. Abramowitz M., Stegun I.A. Handbook of mathematical functions 1970, Dover Publications, New York, USA.