1. Pore-Scale Model for Rate Dependence of Two-Phase Flow in Porous Media Mohammed Al-Gharbi Supervisor: Prof. Martin Blunt

2. Presentation outline Why rate-dependent effects are important Methodology for rate-dependent modelling Project structure Future development of the model

3. Why rate-dependent effects are important The significance of rate effects is determined by the capillary number: N cap =  q/ 

4. Why rate-dependent effects are important 2.Rate effects are significant for:  Low interfacial tensions – gas condensates, near-miscible gas injection, surfactant floods.  High flow rates – near well-bore flows.  High viscosities – polymer injection.  Cases where flow in wetting or spreading layers is significant.

5. Why rate-dependent effects are important 1.Lab exp.: Richardson (1952)  Aim: Effect of displacement rate on residual saturation.  Result: Less trapping as flow rate increases.  Deduction: Rel.perm. & residual S o = f(Q inj ).

6. Pore-scale displacement processes Competition between different displacement processes. Which process dominates depends on capillary number:  Piston like: high flow rates and little trapping.  Snap-off : low flow rates and large amounts of trapping.

7. Micromodel experiments Lenormand and Zarcone (a) N cap = 3x10 -4, (b) N cap = 1.4x10 -5, (c) N cap =6x10 -7

8. Dynamic vs. static pore-scale modelling Static – overall capillary pressure controls the fluid configuration. At any time all interfaces are static. Displacement sequence controlled by invasion capillary pressures. Dynamic – fluid volume in each pore controls the configuration and local capillary pressure. All interfaces may move. Mass balance used to move fluid between pores.

9. Dynamic model features Irregular pore shapes. Random distribution with variable pore radii. More than one meniscus in a circular throat. Variable radii of curvature of the wetting layer. So far – assume one contact angle everywhere.

10. Project structure (principles) The amount of the wetting phase and  used to define the fluid configuration and local capillary pressure. Compute wetting phase pressure using mass balance. Non-wetting phase pressure = wetting pressure + capillary pressure.

11. Project structure (Mathematical model) 1.Irregular element geometry with constrictions (Man and Jing).

12. Project structure (Mathematical model) 2.Fluids configuration

13. Project structure (Mathematical model) 2.Fluids configuration a)General case: x

14. Project structure (Mathematical model) 2.Fluids configuration b)special case: Water x2x2 x1x1 LtLt RLRL R

15. Example of the special case (Wat.Volume Vs. pc) Volume in the wetting layers

16. Example of the special case (Interfaces distance Vs. pc)

17. Project structure 3.Fluids conductance. Film conductance. Bulk conductance.

18. Project structure (Mathematical model) 4.Computing the volumetric rates and pressures.

19. Project structure (Mathematical model) 5.Updating fluid volumes & selection of time step.

20. Future development of the model (Mixed-wettability system) Water Layers Oil Layers Water

21. Future development of the model (Mixed-wettability system)

22. Recap Presented methodology for a general rate-dependent pore-scale model. Shown how to compute configuration (interface location) and capillary pressure from known wetting phase volume. Next steps: compute conductance and from this use mass balance to move fluid between pores.