MODELING OF DISCRETE FRACTURE NETWORK USING VORONOI GRID SYSTEM

1
MODELING OF DISCRETE FRACTURE NETWORK USING
VORONOI GRID SYSTEM
2
Dual Porosity Model

• Highly fractured
• Connected fractures
• No flow occurs between matrix blocks

• Limitations
• Not applicable to disconnected fractured media
• Not suitable to model a small number of fractures

3
Discrete Fracture Network (DFN)

• Isolated Fractures
• Disconnected Fractures

4
Discrete Fracture Network (DFN)

• Fractures are represented individually
• Complex fractured porous media

Matrix
Fracture
Difficult to be modeled with conventional
rectangular grid system
5
Geometrical Discretization -
SPE 79699
Using a Cartesian discretization
Number of Grids/Nodes gtgtgt
6
Fracture Network Delaunay Triangulation
SPE 79699
7
Where are we now ?
MODELING OF DISCRETE FRACTURE NETWORK USING
VORONOI GRID SYSTEM
8
MODELING OF DISCRETE FRACTURE NETWORK USING
VORONOI GRID SYSTEM
Three Modules

• Preprocessor
• - grid generation module (voronoi)
• - fracture network
• - connectivity
• Processor
• Black Oil (IMPES/IMPIS)
• Postprocessor
• - visualization

60
40
0
9
Preprocessor

• Grid Generation (VORONOI)
• Conventional rectangular grid system
• Hexagonal 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
Voronoi Grid Refinement
Delaunay edge
Voronoi edge
15
Conventional Rectangular Grid System
16
Hexagonal Grid Model
17
Conventional Grid Modelwith 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 2
Fracture Set 4
Fracture Set 1
Fracture Set 3
24
Modeling Fracture Network using voronoi
Geometrical domain
Computational domain
matrix
Flow connection
fracture
matrix
matrix
No Flow connection
Flow Connection
w
w fracture width
25
Voronoi with complex fracture network
645 - 2945 connection
26
Voronoi with complex fracture network
27
(No Transcript)
28
Processor Black Oil, 3P

• Flow Equation

• Cubic Law ? fracture
• Darcys Law ? matrix

• Data Structure (Template)

• Static Data not recoded for every time step
• Dynamic Data recorded for every time step

29
Static Data

• FRACTURE

• Cell/Grid

ID WIDTH PERM ROUGHNESS RELPERM_AND_Pc_ID PVT_ID
ID/NAME STATUS (ACTIVE/INACTIVE) GEOM
X,Y,Z CONNE FRACT/NOT_FRACT
TRANS_MULT AREA, H VOLUME

• AQUIFER (OPTIONAL)

ID MODEL VOLUME ROCK_PROP
ROCK_PROP kL kV POR
RELPERM_AND_Pc_ID PVT_ID PVMOD
30
Dynamic Data

• Wells

• Pressure

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)
Po (ID,time) Pw (ID,time) Pg (ID,time)

• Saturation

So (ID,time) Sw (ID,time) Sg (ID,time)

• Fluid Permeability

ko (ID,time) kw (ID,time) kg (ID,time)
31
Challenges

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