Pore-scale modelling of WAG: impact of wettability

1. Pore-scale modelling of WAG:impact of wettability Rink van Dijke and Ken Sorbie Institute of Petroleum Engineering Heriot-Watt University WAG Workshop FORCE, Stavanger, 18 March 2009 1

2. Introduction • 3-phase (immiscible) flow processes, e.g. • water-alternating-gas injection (WAG): improved oil recovery • NAPL in unsaturated zone: ground water remediation • modelled with Darcy’s law: • capillary pressure and relative permeability functions • difficult to measure • pore-scale modelling

3. water, oil, gas Introduction • Pore-scale modelling: • pore space structure: • connectivity (topology) • geometry (pore sizes and shapes) • flow mechanisms: • capillary forces • conductance (viscous forces) • wettability (contact angles) • incorporated in • idealized network models (quasi-static “invasion percolation” or dynamic) • capillary bundle models 3

4. Introduction • Capillary forces: • invasion of a single tube (cylinder): • ‘rule’ for displacement of water by oil:with capillary ‘entry’ pressure according to Young-Laplace: 4

5. Introduction • Wettability: • wettability of pore surface defined in terms of oil-water contact angle (measured through water) • water-wet if • oil-wet if oil water SOLID SURFACE 5

6. Introduction • Wettability: • in 3-phase flow contact angles: • related by Bartell-Osterhof equation: • constitute capillary entry pressures for gas-water and gas-oil displacements, e.g. • determine presence of wetting films and spreading layers 6

7. 50 m 250 m pore cross-section: wide and shallow Introduction • Micromodel experiments: • understand flow mechanisms • validate pore-scale network models • Sohrabi et al. (HWU) 7

8. Outline: effects of wettability • Saturation-dependencies of three-phase capillary pressures and relative permeabilities • Intra-pore physics: • fluid configurations • capillary entry pressures and layer criteria • non-uniform wettability • Network displacement mechanisms: • phase continuity and displacement chains • WAG simulations • comparison simulations and WAG micromodel experiments • Concluding remarks 8

9. Saturation-dependencies • Traditional example (Corey et al., 1956) • Curved oil isoperms • Straight water and gas isoperms

10. Saturation-dependencies Traditional assumptions for saturation-dependencies Water-wet system: water wetting to oil wetting to gas  water in small pores, gas in big pores pore occupancy (number fraction) water oil gas pore size r

11. Saturation-dependencies Wettability distributions in porous medium often correlated to pore size: mixed-wet with larger pores oil-wet (MWL): may occur after primary drainage and aging (similarly MWS) 1 water-wet rwet 0 r oil-wet -1 11

12. gas water flood gas flood oil water Saturation-dependencies • Paths in saturation space: gas flood into oil, followed by water flood into gas and oil • capillary bundle model water-wet oil-wet I II III

13. Saturation-dependencies • Regions in saturation space: iso-capillary pressure curves II II II gas is “intermediate-wetting”

14. Saturation-dependencies • Regions in saturation space: iso-relative permeability curves II II II gas is “intermediate-wetting”

15. numerical example FW capillary bundle Saturation-dependencies

16. Intra-pore physics • Films and layers: • water-wet micromodel: WAG flood • water wetting films around both oil and gas • possible oil layers separating water and gas 16

17. Intra-pore physics • Fluid configurations in angular pores: • water-wet pores, e.g. strongly water-wet: all close to 0 • water wetting films around both oil and gas • possible oil layers separating water and gas: affected by oil spreading coefficient • oil-wet pores, e.g. weakly oil-wet: close to 90 degrees, close to 0 • no oil wetting films around water • only oil wetting films around gas • ensures phase continuity along pores 17

18. Intra-pore physics • true 3-phase capillary entry pressures (improved Y-L) • gas-oil entry pressure depends on water wetting film pressure • determined by free energy calculation (MS-P) • also criterion for (oil) layers bulk displacement layer displacement 18

19. Intra-pore physics • consistent relation 3-phase pressure differences and occupancies oil-water bulk displacement gas-oil bulk displacement (true varying) gas-oil bulk displacement, with layer (constant) layer displacement

20. Intra-pore physics • mixed-wet bundle of triangular pores: • small pores strongly water-wet • large pores weakly oil-wet: 20

21. Intra-pore physics • water injection • no difference true (3-phase) and constant (2-phase) during invasion of water-wet pores • huge differences during invasion of oil-wet pores • true: simultaneous w->o and w->g • volume effectoil films 21

22. Intra-pore physics • nonuniform wettability: • after primary - after imbibition drainage • strongly affects water flood Sor (Ryazanov et al., 2009) surface rendered oil-wet: aging(Kovscek) oil layers (2-phase) oil water 22

23. Intra-pore physics • non-uniform wettability • layers in 3-phase configuration • consistent entry pressures and layer criteria 23

24. gas injection Intra-pore physics high Pow drainage 24

25. Network displacement mechanisms phase continuity: connectivity films and layers (wettability) water-wet micromodel: WAG flood 25

26. Network displacement mechanisms • connected, trapped and disconnected phases • phase cluster map disconnected oil cluster water cluster connected to outlet invading gas cluster outlet inlet trapped oil cluster oil cluster connected to outlet disconnected water cluster disconnectedgas cluster 26

27. multiple displacement chains displace disconnected clusters based on “target” pressure difference determining lowest target requires shortest path algorithm Network displacement mechanisms disconnected oil cluster water cluster connected to outlet invading gas cluster outlet inlet trapped oil cluster oil cluster connected to outlet disconnectedgas cluster disconnected water cluster e.g. gas->oil->gas->water

28. Network simulations • 3-phase flow simulator 3PhWetNet: regular lattice, arbitrary wettability, capillary-dominated flow • few free parameters describing essence of pore-scale displacements (needs “anchoring”) • coordination number z • pore size distribution • volume and conductanceexponents • wettability (contact angledistribution) • film and layers (notional)

29. Network simulations Network model: parameters “anchored” to easy-to-obtain data: network structure and wettability example mixed-wet North Sea reservoir data mixed-wet (MWL) water-wet water flood gas flood 29

30. Network simulations Network model: predict difficult-to-obtain data, e.g. 3-phase kr and Pc three-phase gas relperms three-phase gas injection displacement paths 30

31. WAG network simulations • mixed-wet • no films or layers • varying coordinationnumber z • high residual, but additional recovery during WAG for z=3

32. WAG network simulations • displacement statistics (chain lengths), z=5 • few multiple, many double displacements • continuing phase “movement” but no additional recovery

33. WAG network simulations • displacement statistics (types), z=5 • mainly 3 displacement types, corresponding to doubles, e.g. g->o and o->w during gas flood

34. WAG network simulations • WAG occupancy statistics (z=5): end gas flood 2 • oil and gas in both water-wet and oil-wet pores

35. WAG network simulations • Chain lengths (z=3) significant number of multiple chains z=5

36. WAG network simulations • Displacementtypes (z=3) z=5 additional types of displacements g->o for water and o->g for gas floods

37. WAG simulation micromodel experiment • weakly wetted: little evidence of (continuous) water and oil wetting films (around water) • spreading oil: assume oil layers and oil wetting films around gas water-wet oil-wet mN/m 41

38. WAG simulation micromodel experiment • Fractionally-wet • 50% water-wet & oil-wet pores • angles distributed between 60-120 degrees • oil layers and oil wetting films around gas • Comparison simulated and experimental recoveries • recoveryceases afterWAG 2 42

39. WAG simulation micromodel experiment • Displacement chain lengths • many multiples (few films: low phase continuity) • multiples dying out after WAG 3 43

40. WAG simulation micromodel experiment • Type of displacements • all types of displacements occur • many displacements involving oil movement • after WAG 3 mainly w->g, g->w 44

41. WAG simulation micromodel experiment • fluid distributions aftergas flood 1 • narrow gas finger in both simulation and experiment • significant amount of oil displaced • multiple displacements: e.g. gas->oil->gas->water 45

42. WAG simulation micromodel experiment • fluid distributions after water flood 1 • water disperses gas • slightly more extensive in experiment 46

43. WAG simulation micromodel experiment • fluid distributions after gas flood 2 • different gas finger appears • additional oil production 47

44. WAG simulation micromodel experiment • fluid distributions after gas flood 3 • new gas finger in simulation • some additional oil displaced (“jump” in recovery) • after this flood mainly water displacing gas and vice versa 48

45. Conclusions Mixed wettability leads to three types of pore occupancy and corresponding saturation-dependencies of three-phase capillary pressures and relative permeabilities: difficult to capture in empirical model True three-phase capillary entry pressures and layer criteria essential for consistent and accurate modelling Phase continuity driver for WAG at pore-scale strongly affected by network connectivity and presence films and layers: precise wettability multiple displacement chains new fluid patterns during each cycle (micromodels) recovery ceases after few WAG floods, oil movement may continue 49

46. Near-miscible WAG: micromodel After 2 hours After 1 hour Continued gas injection in strongly water-wet experiment: • Much oil displaced through film flow + mass transfer (?) 50