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. SIMULATION OF DISCRETE FRACTURE NETWORKS USING FLEXIBLE VORONOI GRIDDING Zuher Syihab David S. Schechter
- 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 circleย that passes through each of the triangles three vertices Delaunay Edges Voronoi Edges
- 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. 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 Aโ Bโ Cโ D E F Dโ Eโ Fโ Geometrical domain Computational domain
- 14. Fracture Network & Voronoi Algorithm Multiple-Fracture Single-Fracture Voronoi Edges Voronoi nodes
- 15. FRACTURES AND VORONOI DIAGRAM/PEBI (Example)
- 16. Kimโs Fracture Network (Fractal Geometry)
- 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)
- 20. Wellbore Modeling Cartesian Grid Block Peacemanโs Well model
- 21. Wellbore Modeling Arbitrary Polygon Palagiโs Well model Regular Polygon
- 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.
- 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. DRAWDOWN & BUILDUP DERIVATIVE PLOTS (Constant Pressure Boundary) Radial Flow Regime Boundary Effect
- 27. DFN & IMEX ON MODIFIED SPE-1 COMPARATIVE STUDY
- 28. DFN & IMEX ON HETEROGENEOUS CASE
- 29. DFN & IMEX ON UNSTRUCTURED GRID CASE
- 30. DFNSIM AND DUAL-POROSITY SHAPE FACTOR โ shape factorโ is the value to quantify the matrix-fracture drainage in the dual-porosity model. Matrix-fracture drainage in the dual-porosity:
- 31. DFNSIM AND DUAL-POROSITY SHAPE FACTOR
- 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 โ 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. DFNSIM AND FRACTURE APERTURE DISTRIBUTION
- 34. DFNSIM AND ISOLATED FRACTURE NETWORK
- 35. DFNSIM AND ISOLATED FRACTURE NETWORK
- 36. SIMULATION ON FRACTAL DISCRETE FRACTURE NETWORK
- 37. SIMULATION ON FRACTAL DISCRETE FRACTURE NETWORK
- 38. SIMULATION ON FRACTAL DISCRETE FRACTURE NETWORK
- 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.