New Method for Simulation Of Fractures

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This is a fully developed simulator capable of numerical simulation of discrete fractures. To our knowledge, this technique has not been previously presented. I would like find partners to develop this for commercial purposes.

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New Method for Simulation Of Fractures

  1. 1. SIMULATION OF DISCRETE FRACTURE NETWORKS USING FLEXIBLE VORONOI GRIDDING Zuher Syihab David S. Schechter
  2. 2. Outline <ul><li>Problem Statement </li></ul><ul><li>Objectives </li></ul><ul><li>Introduction to Gridding Techniques </li></ul><ul><li>Modeling Of Discrete Fracture Network (DFN) Using Voronoi Gridding </li></ul><ul><li>Conclusion </li></ul>
  3. 3. PROBLEM STATEMENT <ul><li>Complex reservoir geometry (faults, fractures, etc) </li></ul><ul><li>Limitation of the existing approach </li></ul><ul><li>Fracture aperture measurements using X-Ray CT Scan. </li></ul><ul><li>Capabilities of existing reservoir simulators </li></ul>
  4. 4. DUAL POROSITY MODEL <ul><li>Highly fractured media </li></ul><ul><li>Connected fractures </li></ul><ul><li>No flow occurs between matrix blocks </li></ul>Idealization of fractured reservoirs (Warren and Root, 1963)
  5. 5. DUAL POROSITY MODEL - LIMITATIONS <ul><li>Not applicable for disconnected fractured media </li></ul><ul><li>Not suitable to model a small number of large-scale fractures </li></ul>Discrete Fracture Network (DFN) Model After SPE 79699 Karimi-Fahd, M., Durlofsky, L. J., and Aziz, K
  6. 6. Fracture Matrix <ul><li>Fractures are represented explicitly. </li></ul><ul><li>Disconnected and isolated fractures </li></ul><ul><li>Complex fractured porous media </li></ul><ul><li>Difficult to be modeled with conventional rectangular grid system </li></ul><ul><li>Current DFN model assumes the fracture apertures are uniform </li></ul>DISCRETE FRACTURE NETWORK (DFN)
  7. 7. OBJECTIVES <ul><li>Develop a general flexible mesh generation technique based on Voronoi diagram algorithm. </li></ul><ul><li>Developing a black-oil reservoir simulator to model fractured and unfractured systems. </li></ul><ul><li>Honoring experimental work by incorporating fracture aperture distribution into simulation model. </li></ul><ul><li>Performing simulation of a system with complex intersecting fractures and fracture networks generated using fractal approach </li></ul>
  8. 8. Gridding Techniques <ul><li>Globally Orthogonal Grid </li></ul><ul><li>Corner Point Grid </li></ul><ul><li>Locally Orthogonal </li></ul><ul><li>Grid (PEBI/VORONOI) </li></ul>
  9. 9. History & Application of Voronoi Grid <ul><li>It was first applied by Heinrich into the reservoir simulation (1987). </li></ul><ul><li>Heinmann named this grid as a PEBI grid (1989) </li></ul><ul><li>Economides et. al applied PEBI grid to model horizontal wells (1991) </li></ul><ul><li>Palagi studied the PEBI grid generation method (1994). </li></ul><ul><li>Chong et. al had also shown that the kind of grid is able to reduce grid orientation effect (2004) </li></ul>
  10. 10. VORONOI AND DELAUNAY TRIANGULATION For a set S of points in the Euclidean plane, the unique triangulation DT(S) of S such that no point in S is inside the circumcircle of any triangle in DT(S). The Voronoi grid is formed by the perpendicular-bisectors of the edges of the Delaunay triangles. Circumcircle: a unique circle that passes through each of the triangles three vertices Delaunay Edges Voronoi Edges
  11. 11. MODELING DFN Workflow <ul><li>- Neural network </li></ul><ul><li>Outcrop </li></ul><ul><li>Kim’s network (fractal) </li></ul>
  12. 12. MODELING DFN (Fracture Gridding) Geometrical domain Computational domain matrix No Flow connection w matrix matrix Flow connection (Line = fracture) Voronoi edge w = fracture width Flow Connection Additional Nodes for Fracture
  13. 13. APERTURE DISTRIBUTION AND VOLUME CORRECTION The bulk volume of fracture segments can be computed based on given fracture apertures. The bulk volume of the matrix block adjoining with the fracture should be corrected due to the volume taken by the fractures Aperture distribution A B C A’ B’ C’ D E F D’ E’ F’ Geometrical domain Computational domain
  14. 14. Fracture Network & Voronoi Algorithm Multiple-Fracture Single-Fracture Voronoi Edges Voronoi nodes
  15. 15. FRACTURES AND VORONOI DIAGRAM/PEBI (Example)
  16. 16. Kim’s Fracture Network (Fractal Geometry)
  17. 17. <ul><li>Implemented using Visual basic (GUI for pre & post processor) and C++ (processor) </li></ul><ul><li>Fully implicit numerical method. </li></ul><ul><li>3D, 3-Phase black oil simulator. </li></ul><ul><li>Structured and unstructured grid systems. </li></ul><ul><li>Grid refinement features. </li></ul><ul><li>- Radial-like grids </li></ul><ul><li>- Hexagonal grids </li></ul><ul><li>- Rectangular grids </li></ul><ul><li>- Radom </li></ul><ul><li>Validated with analytical solution (Pressure Transient Analysis) </li></ul><ul><li>Compared with IMEX (CMG) for homogeneous & heterogeneous cases. (25 and up to 150,000 grid blocks in desktop PC). </li></ul>DFN Simulator
  18. 18. MATERIAL BALANCE EQUATIONS Rate of accumulation = Net flow rate = , e = Evaluated cell NCon = Number of connection of cell# e. Con. List(i) = the ith element in the connection list of cell# e e Con. List(i)
  19. 19. RESIDUAL FUNCTIONS
  20. 20. Wellbore Modeling Cartesian Grid Block Peaceman’s Well model
  21. 21. Wellbore Modeling Arbitrary Polygon Palagi’s Well model Regular Polygon
  22. 22. THE SIMULATOR (Implementation Technique) Create Control Volume Objects Connection List PVT ID Rock ID etc Connection type Vectorization Solve the matrix using Sparse Matrix Solver (SparseLib++) (BICG-STAB/GMRES/RI/BICG/CG) Residual Error Checking Calculate flow coef.
  23. 23. SIMULATION WORKFLOW
  24. 24. VALIDATION AND COMPARISON STUDY <ul><li>DFN simulation and analytical model (Pressure Transient Solution) </li></ul><ul><li>DFN simulation and IMEX on modified SPE-1 comparative study </li></ul><ul><li>DFN simulation and IMEX on heterogeneous case </li></ul><ul><li>DFN simulation and IMEX on unstructured grid case </li></ul><ul><li>DFN simulation and dual-porosity shape factor </li></ul>
  25. 25. DFN SIMULATOR & ANALYTICAL MODEL (Constant Pressure Boundary) k = 215.0 md h = 100.0 ft p i = 4790 psia p = 4790 psia p = 4790 psia p = 4790 psia p = 4790 psia
  26. 26. DRAWDOWN & BUILDUP DERIVATIVE PLOTS (Constant Pressure Boundary) Radial Flow Regime Boundary Effect
  27. 27. DFN & IMEX ON MODIFIED SPE-1 COMPARATIVE STUDY
  28. 28. DFN & IMEX ON HETEROGENEOUS CASE
  29. 29. DFN & IMEX ON UNSTRUCTURED GRID CASE
  30. 30. DFNSIM AND DUAL-POROSITY SHAPE FACTOR “ shape factor” is the value to quantify the matrix-fracture drainage in the dual-porosity model. Matrix-fracture drainage in the dual-porosity:
  31. 31. DFNSIM AND DUAL-POROSITY SHAPE FACTOR
  32. 32. DFNSIM AND FRACTURE APERTURE DISTRIBUTION Descriptions CASE 5.A1 CASE 5.A2 Grid dimension 33x33x1 33x33x1 Fracture spacing 1,220 ft 1,220 ft Model width/ Length 5,380.4 ft 5,380.4 ft Model thickness 100 ft 100 ft Matrix permeability 50 md 50 md Fracture permeability Constant 9,055 md Log-normally distributed 24 md – 300 D (mean = 9,055 md) Matrix porosity 0.25 0.25 Fracture porosity 0.5 0.5 Fluid properties SPE-1 SPE-1 Initial conditions SPE-1 SPE-1 Other rock properties SPE-1 SPE-1 Producing rate Oil, 15,000 STB/D Oil, 15,000 STB/D Minumum produce BHP 1,000 psia 1,000 psia Injection rate Gas, 50 MMSCF/D Gas, 50 MMSCF/D
  33. 33. DFNSIM AND FRACTURE APERTURE DISTRIBUTION
  34. 34. DFNSIM AND ISOLATED FRACTURE NETWORK
  35. 35. DFNSIM AND ISOLATED FRACTURE NETWORK
  36. 36. SIMULATION ON FRACTAL DISCRETE FRACTURE NETWORK
  37. 37. SIMULATION ON FRACTAL DISCRETE FRACTURE NETWORK
  38. 38. SIMULATION ON FRACTAL DISCRETE FRACTURE NETWORK
  39. 39. Numerical Parameters No fracture, isolated and Connected Fractures Numerical Controls No Fracture Isolated Fractures Complex Fractures Maximum residual error 1.0E-4 1.0E-4 1.0E-4 Max. Newton iteration 25 25 25 Max. linear solver iteration 40 40 140 Linear solver tolerance 1.0E-5 1.0E-5 1E-5 Time step 152 324 2,045 Newton iteration 976 6,576 34,285 Solver iteration 28,315 216,445 1,420,171 Solver failure 0 5 103 Time step cut 7 183 228 Simulation time 458 sec. 8,009 sec. 56,125 sec.
  40. 40. CONCLUSION <ul><li>Dual Porosity models are not applicable for small scale and disconnected fractured media. </li></ul><ul><li>The DFN simulator provides results in good agreement with commercial finite-difference simulators in the cases in which direct comparisons are possible. </li></ul><ul><li>Fracture aperture distribution can be descritized using DFN model. </li></ul><ul><li>DFN model using Voronoi grid system can be used for fractured and unfractured system. </li></ul>
  41. 41. <ul><li>The aperture distribution plays very important role reservoir performance. </li></ul><ul><li>Numerically, simulation on fractured systems, whether disconnected or connected, are very challenging. It requires an extensive amount of time to build the grid model and run the simulation. </li></ul><ul><li>DFN simulator capability for multiple reservoir has been tested and it can be a potential tool for sensitivity studies. </li></ul>CONCLUSION

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