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PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP

PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP. Pore Scale Modeling of Single-Phase Non-Newtonian Flow. Xavier Lopez Martin Blunt. Imperial College of Science, Technology and Medicine, London. 10 th January 2003. BHP UK Department of Trade and Industry & EPSRC Enterprise Oil

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PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP

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  1. PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP Pore Scale Modeling of Single-Phase Non-Newtonian Flow Xavier Lopez Martin Blunt Imperial College of Science, Technology and Medicine, London 10th January 2003

  2. BHP UK Department of Trade and Industry & EPSRC Enterprise Oil Gaz de France Japan National Oil Corporation PDVSA-Intevep Schlumberger Shell Statoil Acknowledgements IMPERIAL COLLEGE CONSORTIUM

  3. Contents • Introduction • Single-phase Background • Network Model • Results • Conclusions • Future Work

  4. Introduction Effects of non-Newtonian rheology on flow in porous media. • EOR

  5. Introduction Post Treatment: Increased productivity through fractures Pre Treatment: Flow restricted by radial geometry Effects of non-Newtonian rheology on flow in porous media. • EOR • Fracturing in injection wells

  6. Introduction Effects of non-Newtonian rheology on flow in porous media. • EOR • Fracturing in injection wells • Water blocking in producing wells

  7. Introduction Production is dominated by water from high permeability channel Treatment fluid gels permanently to isolate watered out layer Treatment fluid is pumped from surface without mechanical isolation. Fluid invades all zones Treatment fluid provide weak gel through physical interactions. Back flow of oil disrupts and disperses treatment fluid, while flow of water is inhibited. Effects of non-Newtonian rheology on flow in porous media.

  8. Single-phase Flow Background Xanthomonas campestris (E415) M.P. Escudier et al. / J. Non-Newtonian Fluid Mech. 97 (2001) 99–124 “Xanthan” Viscosity (Pa.s) Shear rate (s-1) Viscometric viscosity of xanthan gum solutions together with Carreau–Yasuda (—) Cross (– – – –) model fits & experimental points.

  9. Single-phase Flow Background ? Characteristic length: Viscosity,  Viscosity,  = f (v) = f () Shear rate, Velocity,v Relating bulk and in situ properties

  10. Single-phase Flow Background Capillary bundle approach Relating bulk and in situ properties • Porous medium representation • “Average radius R” depending on medium properties (K, Φ, tortuousity…) • Define “porous medium” shear rate

  11. Single-phase Flow Background α Effective Viscosity,  (mPa.s) Shear rate, (s-1) Rheology of Xanthan FLOCON 4800MX after Fletcher et al Relating bulk and in situ properties α: Correction Factor • Experiments Values in the literature: 1 < α < 15 Requires experimental determination !!

  12. Network Model Berea Permeability: 3D Porosity : 24.02 % Average connection number: 4.19 12349 Pores, 26146 Throats Triangular Shape 92.27 % Throat size: 1.8 – 113 μm Pore size: 7.24 –147 μm Sand pack Permeability: 101D Porosity : 34.6 % Average connection number: 5.46 3567 Pores, 9923 Throats Triangular Shape 94.7 % Grain size: 100- 425 μm

  13. Network Model Cope with non-Newtonian rheology Truncated power-law

  14. Network Model Update viscosity R ??? Relate pressure drop to effective viscosity Cope with non-Newtonian rheology Base on single circular tube expression Initial guess for viscosity Solve pressure field In each pore and throat

  15. Network Model Equivalent Radius Capillary bundle: based on medium properties (e.g. from Savins) Network approach: based on conductance (our approach)

  16. Network Model Underlying assumptions • Power law behavior across the entire cross section of each element (then cut-offs) • No visco-elastic effects • No adsorption • No polymer exclusion (excluded volume) • Newtonian viscosity plateaux

  17. Results Sand pack comparisons Hejri et al studied the flow of Xanthan in sand packs Input rheology

  18. Results Sand pack comparisons

  19. Results Sand pack comparisons Permeability Difference: * Hejri et al experiment: 893mD * Our sand-pack: 101D re-scale all the network lengths by

  20. Results Sand pack comparisons

  21. Results Sand pack comparisons Permeability Difference: * Hejri et al experiment: 893mD * Our sand-pack: 101D re-scale all the network lengths by For simplicity we re-scale the velocity

  22. Results Sand pack comparisons Vogel & Pusch studied the flow of biopolymer in sand packs

  23. Results Sandstone comparisons Greaves & Patel studied the flow of Xanthan in Elginshire sandstone

  24. Results Sandstone comparisons Cannella et al studied the flow of Xanthan in Berea sandstone

  25. Conclusions Capillary bundle model Simple…but does not have genuine predictive capabilities. Vogel & Pusch α = 1.34 Hejri et al α = 0.98 Sand pack ? Same networks…similar rheologies Cannella et al α = 4.8 Greaves & Patel α = 7.6 Sandstone ?

  26. Conclusions Our model • Our approach allows predictions to be made for 2 types of network with no empirical correction needed. • Experimental evidence of pore blocking ? • Lower Newtonian plateau apparent

  27. Future Work Single-phase flow • Variations of alpha • Elasticity • Depleted layers effects • More complex rheology Multi-phase flow • Relative permeability • Constant Q • Wettability effects

  28. PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP Pore Scale Modeling of Single-Phase Non-Newtonian Flow Xavier Lopez Martin Blunt Imperial College of Science, Technology and Medicine, London 10th January 2003

  29. 2R <v> Dimensionless pressure drop measurements for different contraction ratios, after Rothstein & McKinley [18].

  30. Krw,N(S) Kro, N(S) Krw, NN(S, ) Delta P = 1 Pa Krw, NN(S, ) Delta P = 10 Pa Krw, NN(S, ) Delta P = 100 Pa Multi-phase flow, NEWTONIAN and NON-NEWTONIAN Newtonian Case Non-Newtonian Case • Water relative permeability reduction…

  31. Krw, N(S) Krw, NN(S, ) Delta P = 1 Pa Krw, NN(S, ) Delta P = 10 Pa Krw, NN(S, ) Delta P = 100 Pa Multi-phase flow, NEWTONIAN and NON-NEWTONIAN Newtonian Case Non-Newtonian Case • Water relative permeability reduction…

  32. Krw,N(S) Kro, N(S) Krw, NN(S, ) Delta P = 100 Pa Krw, NN(S, ) Delta P = 300 Pa Krw, NN(S, ) Delta P = 600 Pa Krw, NN(S, ) Delta P = 103 Pa Krw, NN(S, ) Delta P = 104 Pa Krw, NN(S, ) Delta P = 105 Pa Network code results: Newtonian Case • …until sufficient pressure drop is achieved. Non-Newtonian Case

  33. Krw,N(S) Krw, NN(S, ) Delta P = 100 Pa Krw, NN(S, ) Delta P = 300 Pa Krw, NN(S, ) Delta P = 600 Pa Krw, NN(S, ) Delta P = 103 Pa Krw, NN(S, ) Delta P = 104 Pa Krw, NN(S, ) Delta P = 105 Pa Network code results: Newtonian Case • …until sufficient pressure drop is achieved. Non-Newtonian Case

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