1 / 60

Development of a 2-D Black Oil Reservoir Simulator with Unique Grid-Block System

Development of a 2-D Black Oil Reservoir Simulator with Unique Grid-Block System. Emeline Chong. July 7, 2004. Harold Vance Department of Petroleum Engineering. Presentation Outline. Motivation Problem Definition Objectives Approach Program Validation/Evaluation Conclusions.

buffy-blackburn
Download Presentation

Development of a 2-D Black Oil Reservoir Simulator with Unique Grid-Block System

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Development of a 2-D Black Oil Reservoir Simulator with Unique Grid-Block System Emeline Chong July 7, 2004 Harold Vance Department of Petroleum Engineering

  2. Presentation Outline • Motivation • Problem Definition • Objectives • Approach • Program Validation/Evaluation • Conclusions

  3. Motivation Diagonal Parallel Not to scale

  4. GRID ORIENTATED PARALLEL TO INJECTOR-PRODUCER PAIRS (PARALLEL RUNS) GRID ORIENTATED AT 45 TO INJECTOR-PRODUCER PAIRS (DIAGONAL RUNS)

  5. 20 acres Mobility Ratios : M = 0.5 M = 1.0 M = 10.0 10 acres

  6. Saturation Distribution at PVinj =1.0 for M=0.5

  7. Saturation Distribution at PVinj =1.0 for M=10.0

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

  9. 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)

  10. Problem Definition Grid orientation effect significantly affects the results of immiscible displacements in reservoir simulation

  11. Objectives • Developing a 2-D, 3-Phase reservoir simulator using finite difference formulation • Reducing the grid orientation effects in a grid model

  12. Approach 2-D, 3-Phase IMPES finite difference simulator with unique grid model  “Sim2D”

  13. 2D,3-Phase Cartesian Grid • Initial Condition • Rock/Fluid Properties Well Model Well Constraints HGB Grid IMPES Matrix Form Matrix Solver Pn+1, Son+1, Swn+1, Sgn+1 Cutback/Saturation Control Program Validation

  14. Sim2D Demo

  15. Sim2D VB Application

  16. Pressure Plots

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

  18. IMPES Steps… • Calculate coefficients of the pressure equation • Calculate solution of the pressure equation implicitly (matrix equation) for: pn+1 • Calculate solution of the saturation equations explicitly for: Son+1, Swn+1, and Sgn+1

  19. IMPES Method • 4 unknowns per block: pn+1, Son+1, Swn+1, and Sgn+1 • To find the unknowns, we need one more equation per block: Son+1 + Swn+1 + Sgn+1 = 1 • Assures fluid volumes fit the pore volume

  20. IMPES Method • Oil • Water • Gas

  21. IMPES Method Summing up all saturation equations:

  22. IMPES Method Approximate Vpn+1 on the right hand side using the identity: and a chord slope:

  23. IMPES Method Then, where, Likewise,

  24. IMPES Method Final equation can now be written as:

  25. Hybrid Grid Block (HGB) System

  26. I I J J N W E S Hybrid Grid Block (HGB) System NW NE SE SW

  27. Hybrid Grid Block (HGB) System

  28. Grid Numbering Numbering #1 Example: 18 Grid Blocks

  29. Grid Numbering Numbering #2 Example: 18 Grid Blocks

  30. Grid Numbering Numbering #3 Example: 25 Grid Blocks

  31. Well Model Peaceman Well Model (1983): Δm For square gridblock, where, α = mass species; oil/water ro = effective wellbore radius

  32. Well Model for regular polygon (Palagi, 1992): j = neighbor of wellblock i bij = side of polygon dij = distance between gridpoints N = number of equal sides Well Model i

  33. Cartesian Sim2D Cartesian Eclipse 100 HGB Sim2D Program Validation

  34. Example Case: Two-Dimensional Areal Model Showing Primary Depletion of an Undersaturated Reservoir (One Producer Well, One Injector Well, Isotropic, 2-Phase, Oil/Water)

  35. Validation with Eclipse

  36. Validation with Eclipse

  37. Application ofHGB grid system to Reduce Grid Orientation Error

More Related