1. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 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, London10 th January 2003

2. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 IMPERIAL COLLEGE CONSORTIUM BHP UK Department of Trade and Industry & EPSRC Enterprise Oil Gaz de France Japan National Oil Corporation PDVSA-Intevep Schlumberger Shell Statoil Acknowledgements

3. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Contents  Introduction  Single-phase Background  Network Model  Results  Conclusions  Future Work

4. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Introduction Effects of non-Newtonian rheology on flow in porous media. EOR

5. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Introduction Effects of non-Newtonian rheology on flow in porous media. Pre Treatment: Flow restricted by radial geometry Post Treatment: Increased productivity through fractures EOR Fracturing in injection wells

6. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Introduction Effects of non-Newtonian rheology on flow in porous media. EOR Fracturing in injection wells Water blocking in producing wells

7. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Introduction Effects of non-Newtonian rheology on flow in porous media. 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. Production is dominated by water from high permeability channel Treatment fluid gels permanently to isolate watered out layer

8. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Single-phase Flow Background “Xanthan” Xanthomonas campestris (E415) M.P. Escudier et al. / J. Non-Newtonian Fluid Mech. 97 (2001) 99–124 Viscometric viscosity of xanthan gum solutions together with Carreau–Yasuda (—) Cross (– – – –) model fits & experimental points. Shear rate (s-1) Viscosity (Pa.s)

9. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Single-phase Flow Background Relating bulk and in situ properties Shear rate,  Viscosity,   = f (  ) ? Characteristic length:  = f (v) Velocity, v Viscosity, 

10. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Single-phase Flow Background Relating bulk and in situ properties Porous medium representation Capillary bundle approach “Average radius R” depending on medium properties (K, Φ, tortuousity…) Define “porous medium” shear rate

11. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Single-phase Flow Background Relating bulk and in situ properties Experiments Shear rate,  (s-1) Effective Viscosity,  (mPa.s) Rheology of Xanthan FLOCON 4800MX after Fletcher et al α: Correction Factor α Values in the literature: 1 < α < 15 Requires experimental determination !!

12. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 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 Network Model 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. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Network Model Cope with non-Newtonian rheology Truncated power-law

14. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Network Model Cope with non-Newtonian rheology Initial guess for viscosity Solve pressure field In each pore and throat Relate pressure drop to effective viscosity Update viscosity Base on single circular tube expression R ???

15. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Network Model Equivalent Radius Capillary bundle: based on medium properties (e.g. from Savins) Network approach: based on conductance (our approach)

16. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 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. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Results Sand pack comparisons Hejri et al studied the flow of Xanthan in sand packs Input rheology

18. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Results Sand pack comparisons

19. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Results Sand pack comparisons Permeability Difference: * Hejri et al experiment: 893mD * Our sand-pack: 101D re-scale all the network lengths by

20. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Results Sand pack comparisons

21. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 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. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Results Sand pack comparisons Vogel & Pusch studied the flow of biopolymer in sand packs

23. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Results Sandstone comparisons Greaves & Patel studied the flow of Xanthan in Elginshire sandstone

24. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Results Cannella et al studied the flow of Xanthan in Berea sandstone Sandstone comparisons

25. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Conclusions Capillary bundle model Simple…but does not have genuine predictive capabilities. Sand pack Sandstone Vogel & Pusch α = 1.34 Hejri et al α = 0.98 Greaves & Patel α = 7.6 Cannella et al α = 4.8 Same networks…similar rheologies ? ?

26. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 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. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 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. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 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, London10 th January 2003

29. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 2R Dimensionless pressure drop measurements for different contraction ratios, after Rothstein & McKinley [18].

30. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Water relative permeability reduction… Newtonian Case K rw,N (S) K ro, N (S) Non-Newtonian Case K rw, NN (S, ) Delta P = 1 Pa K rw, NN (S, ) Delta P = 10 Pa K rw, NN (S, ) Delta P = 100 Pa Multi-phase flow, NEWTONIAN and NON-NEWTONIAN

31. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Newtonian Case Non-Newtonian Case K rw, N (S) K rw, NN (S, ) Delta P = 1 Pa K rw, NN (S, ) Delta P = 10 Pa K rw, NN (S, ) Delta P = 100 Pa Water relative permeability reduction… Multi-phase flow, NEWTONIAN and NON-NEWTONIAN

32. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Network code results : …until sufficient pressure drop is achieved. Newtonian Case K rw,N (S) K ro, N (S) Non-Newtonian Case K rw, NN (S, ) Delta P = 100 Pa K rw, NN (S, ) Delta P = 300 Pa K rw, NN (S, ) Delta P = 10 5 Pa K rw, NN (S, ) Delta P = 10 4 Pa K rw, NN (S, ) Delta P = 10 3 Pa K rw, NN (S, ) Delta P = 600 Pa

33. Imperial College, PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10 th January 2003 Network code results : …until sufficient pressure drop is achieved. Newtonian Case Non-Newtonian Case K rw, NN (S, ) Delta P = 100 Pa K rw, NN (S, ) Delta P = 300 Pa K rw, NN (S, ) Delta P = 10 5 Pa K rw, NN (S, ) Delta P = 10 4 Pa K rw, NN (S, ) Delta P = 10 3 Pa K rw, NN (S, ) Delta P = 600 Pa K rw,N (S)