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Development of a Reservoir Simulator with Unique Grid-Block System

Development of a Reservoir Simulator with Unique Grid-Block System. Emeline Chong. Master Division Student Paper Contest 2004 Harold Vance Department of Petroleum Engineering. Presentation Outline. Motivation Problem Definition Objectives Approach Results Conclusions. Motivation.

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Development of a Reservoir Simulator with Unique Grid-Block System

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  1. Development of a Reservoir Simulator with Unique Grid-Block System Emeline Chong Master Division Student Paper Contest 2004 Harold Vance Department of Petroleum Engineering

  2. Presentation Outline • Motivation • Problem Definition • Objectives • Approach • Results • Conclusions

  3. Motivation “Homogeneous Reservoir” Diagonal Parallel Not to scale

  4. Homogeneous Reservoir

  5. Motivation “Heterogeneous Reservoir” Diagonal Parallel Not to scale K1 >> K2 K1 K2

  6. Heterogeneous Reservoir

  7. Motivation Brand, Heinemann, and Aziz (1992) – “In general, Grid Orientation Effect cannot be overcome with grid refinement.” (SPE 21228)

  8. Motivation Sammon (1991) Chen & Durlofsky (1991) Mattax & Dalton (1990) Wolcott et.al. (1996) Shiralkar (1990) Brand et.al. (1991) Ostebo & Kazemi (1992) Yanosik & McCracken (1979) Shiralkar & Stephenson (1987) Pruess & Bodvarsson (1983) Todd et.al. (1972)

  9. Motivation Fractures with Multiple Joint Sets Courtesy of Imperial College Fractures create high permeability anisotropy in rock masses!

  10. Motivation General Darcy’s Law: Permeability Tensor: Simplified:

  11. Problem Definition Grid orientation and heterogeneity significantly affects the results of reservoir simulation

  12. Problem Definition

  13. Problem Definition We need a grid model that can incorporate permeability anisotropy in multiple directions – a full tensor representation must be considered!

  14. Objectives • Developing a 2-D, 3-Phase reservoir simulator using finite difference formulation • Reducing the grid orientation effects in a grid model • Creating a grid model that can be used to simulate multiple permeability directions

  15. Approach 2-D, 3-Phase IMPES finite difference simulator using VBA with unique grid model

  16. 2D,3-Phase HGB Model • Initial Condition • Rock/Fluid Properties Well Model Transmissibility Terms Well Constraints Grid Numbering IMPES Matrix Form Matrix Solver Pn+1, Son+1, Swn+1, Sgn+1 Program Validation

  17. I I I 1 2 3 4 5 J J J 1 N 2 NW NE W E 3 SE SW S 4 Hybrid Grid Block (HGB) System 1 2

  18. Example Grid: 5 x 4 Total Number of Grid Blocks = 61 I 1 2 3 4 5 J 1 2 3 4 Hybrid Grid Block (HGB) System

  19. IMPES MethodFinite Difference Equations • Oil • Water • Gas

  20. 1 of 3 17 11 12 18 4 5 6 13 7 8 14 1 2 3 15 9 10 16 Grid Numbering #1 & Matrix Form Example: 3x2

  21. 2 of 3 15 16 17 18 9 11 13 8 10 12 14 2 4 6 1 3 5 Grid Numbering #2 & Matrix Form Example: 3x2 7

  22. 3 of 3 Grid Numbering #3 & Matrix Form Example: 3x3 10 10 17 17 22 22 25 25 11 11 18 1 23 23 18 24 24 5 5 12 12 19 19 6 6 13 13 20 20 7 7 14 14 21 21 2 2 8 8 15 15 3 3 1 1 4 4 9 9 16 16

  23. Well Model Peaceman Well Model (1983): Δm For square gridblock, where, ro = effective wellbore radius

  24. Well Model for regular polygon (after Palagi,1992): j = neighbor of wellblock i bij = side of polygon dij = distance between gridpoints Θij = angle open to flow Well Model bij j Ɵij dij i

  25. Model Dimension: 640 ft x 640 ft x 10 ft Permeability: 100mD Porosity: 20% Well Constraints:- Const. Qinj Const. Qo Inj Prod Results: Case#1 Maximum Material Balance Error = 4.2602E-05%

  26. Results: Case#1 Contour Map 10 days 20 days 40 days

  27. Same dataset, except: 1 permeability direction Kmax = 500 mD Kmin = 100 mD Prod2 Inj Prod1 Results: Case #2 Maximum Material Balance Error = 2.587E-03%

  28. Results: Case #2 Contour Map 10 days 40 days 20 days

  29. Results: Case#2

  30. Prod2 Inj Prod1 Results: Case #3 • Same dataset, except: • 3 permeability directions • Kmax = 500 mD • Kmin = 100 mD Maximum Material Balance Error = 5.2654E-03%

  31. Results: Case #3 Contour Map 10 days 40 days 20 days

  32. Homogeneous reservoir 1 injector 4 producers Results: Case #4 Maximum Material Balance Error = 2.9696E-03%

  33. Results: Case #4 Pressure Distribution Chart

  34. Conclusions • Grid orientation and heterogeneityaffects significantly the results of reservoir simulation (ie. water breakthrough times & recovery) • A full tensor representation must be considered if reservoir flow performance is to be predicted accurately

  35. Conclusions • Proposed HGB model is able to • reduce the grid orientation effects • model different sets of permeability anisotropy

  36. Future Application Local Grid Refinement

  37. THANK YOU Acknowledgement • Dr. David Schechter • Dr. Erwin Putra • U.S Department of Energy

  38. Development of a Reservoir Simulator with Unique Grid-Block System Emeline Chong Master Division Student Paper Contest 2004 Harold Vance Department of Petroleum Engineering

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