1. M ODELING OF D ISCRETE F RACTURE N ETWORK U SING V ORONOI G RID S YSTEM

2. Dual Porosity Model Highly fractured Highly fractured Connected fractures Connected fractures No flow occurs between matrix blocks No flow occurs between matrix blocks Limitations: Not applicable to disconnected fractured media Not applicable to disconnected fractured media Not suitable to model a small number of fractures Not suitable to model a small number of fractures

3. Discrete Fracture Network (DFN) Isolated Fractures Isolated Fractures Disconnected Fractures Disconnected Fractures

4. Fracture Matrix Discrete Fracture Network (DFN) Fractures are represented individually Complex fractured porous media Difficult to be modeled with conventional rectangular grid system

5. Using a Cartesian discretization Geometrical Discretization - Number of Grids/Nodes >>> SPE 79699

6. Fracture Network & Delaunay Triangulation SPE 79699

7. Where are we now ? MODELING OF DISCRETE FRACTURE NETWORK USING VORONOI GRID SYSTEM

8. Preprocessor Preprocessor - grid generation module (voronoi) - grid generation module (voronoi) - fracture network - fracture network - connectivity - connectivity Processor Processor – Black Oil (IMPES/IMPIS) – Black Oil (IMPES/IMPIS) Postprocessor Postprocessor - visualization 60 % 40 % 0 % Three Modules

9. Preprocessor Grid Generation (VORONOI) Conventional rectangular grid system Conventional rectangular grid system Hexagonal grid system Hexagonal grid system Radial grid system Radial grid system Grid Refinement rectangular hexagonal radial random

10. Voronoi Grid Distribute points inside boundary Delaunay Triangulation Voronoi

11. What are Delaunay Triangulation & Voronoi Grid ?

12. Example : Delaunay Triangulation

13. Delaunay Triangulation & Voronoi Diagram

14. Delaunay edge Voronoi edge Voronoi – Grid Refinement

15. Conventional Rectangular Grid System

16. Hexagonal Grid Model

17. Conventional Grid Model with Grid refinement Near Wells

18. Flexible Grid Model Rectangular – Hexagonal and radial

19. Voronoi Diagram – Randomly distributed points 100 cells

20. Voronoi Diagram – Connection 90 cells - 462 connections

21. Voronoi with 500 Cells – 2766 connections

22. Modeling Fracture Network using voronoi Single Fracture Fracture Set #1

23. Modeling Fracture Network using voronoi Multiple Fracture Fracture Set #1 Fracture Set #2 Fracture Set #3 Fracture Set #4

24. Geometrical domain Computational domain Modeling Fracture Network using voronoi No Flow connection w w = fracture width matrix fracture Flow connection Flow Connection

25. Voronoi with complex fracture network 645 - 2945 connection

26. Voronoi with complex fracture network

28. Processor – Black Oil, 3P Flow Equation Flow Equation Cubic Law  fracture Darcy’s Law  matrix Data Structure (Template) Data Structure (Template) Static Data – not recoded for every time step Dynamic Data – recorded for every time step

29. Static Data Cell/Grid Cell/Grid ID/NAME STATUS ( ACTIVE/INACTIVE ) GEOM X,Y,Z CONNE FRACT/NOT_FRACT TRANS_MULT AREA, H VOLUME ROCK_PROP kL kV POR RELPERM_AND_Pc_ID PVT_ID PVMOD FRACTURE ID WIDTH PERM ROUGHNESS RELPERM_AND_Pc_ID PVT_ID AQUIFER (OPTIONAL) ID MODEL VOLUME ROCK_PROP

30. Dynamic Data Pressure Pressure Po (ID,time) Pw (ID,time) Pg (ID,time) Saturation Saturation So (ID,time) Sw (ID,time) Sg (ID,time) Wells Wells ID LOCATION ID Cells (COMPLETION) or X,Y,Z TYPE PROD/INJ CONSTRAINS INTERVAL t_start t_End PWF (min, max) DRD (min,max) O,G,W RATE (min,max) GOR,WOR (min,max) Fluid Permeability Fluid Permeability ko (ID,time) kw (ID,time) kg (ID,time)

31. Challenges Complex Fracture Network Complex Fracture Network Connectivity Connectivity Fully implicit finite difference or “Stabilized” IMPES formulation ?? Fully implicit finite difference or “Stabilized” IMPES formulation ?? Sparse matrix solver to solve linear equations ( no restriction ) - BiCGSTAB & ORTHOMIN Sparse matrix solver to solve linear equations ( no restriction ) - BiCGSTAB & ORTHOMIN (we will not have a banded matrix form) Computation time ??? Computation time ???