M ODELING OF D ISCRETE F RACTURE N ETWORK U SING V ORONOI G RID S YSTEM.
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M M ODELING OF ODELING OF D D ISCRETE ISCRETE F F RACTURE RACTURE N N ETWORK ETWORK U U SING SING V V ORONOI ORONOI G G RID RID S S YSTEM YSTEM
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Transcript of M ODELING OF D ISCRETE F RACTURE N ETWORK U SING V ORONOI G RID S YSTEM.
MMODELING OF ODELING OF DDISCRETE ISCRETE
FFRACTURE RACTURE NNETWORK ETWORK UUSING SING
VVORONOI ORONOI GGRID RID SSYSTEMYSTEM
MMODELING OF ODELING OF DDISCRETE ISCRETE
FFRACTURE RACTURE NNETWORK ETWORK UUSING SING
VVORONOI ORONOI GGRID RID SSYSTEMYSTEM
Dual Porosity ModelDual Porosity Model Highly fracturedHighly fractured Connected fracturesConnected fractures No flow occurs No flow occurs
between matrix blocksbetween matrix blocks
Limitations:Limitations: Not applicable to disconnected fractured mediaNot applicable to disconnected fractured media Not suitable to model a small number of fractures Not suitable to model a small number of fractures
Discrete Fracture Network (DFN)Discrete Fracture Network (DFN)
Isolated FracturesIsolated Fractures Disconnected FracturesDisconnected Fractures
Fracture
Matrix
Discrete Fracture Network (DFN)Discrete Fracture Network (DFN)
• Fractures are represented individually
• Complex fractured porous media
Difficult to be modeled with conventional rectangular grid system
Using a Cartesian discretization
Geometrical DiscretizationGeometrical Discretization - -
Number of Grids/Nodes >>>
SPE 79699
Fracture Network & Delaunay Triangulation SPE 79699
Where are we Where are we now ?now ?
MODELING OF DISCRETE FRACTURE MODELING OF DISCRETE FRACTURE NETWORK USING VORONOI GRID SYSTEMNETWORK USING VORONOI GRID SYSTEM
MODELING OF DISCRETE FRACTURE MODELING OF DISCRETE FRACTURE NETWORK USING VORONOI GRID NETWORK USING VORONOI GRID
SYSTEMSYSTEM
Preprocessor Preprocessor - grid generation module (voronoi)- grid generation module (voronoi) - fracture network - fracture network - connectivity- connectivity ProcessorProcessor – – Black Oil (IMPES/IMPIS)Black Oil (IMPES/IMPIS) Postprocessor Postprocessor
- visualization- visualization
60 %
40 %
0 %
Three Modules
PreprocessorPreprocessorGrid Generation (VORONOI)Grid Generation (VORONOI) Conventional rectangular grid systemConventional rectangular grid system Hexagonal grid systemHexagonal grid system Radial grid systemRadial grid system
Grid RefinementGrid Refinement rectangular rectangular hexagonal hexagonal radial radial random random
Voronoi GridVoronoi Grid
Distribute points inside boundary
Delaunay Triangulation
Voronoi
What are Delaunay Triangulation & Voronoi Grid ?
Example : Delaunay Triangulation
Delaunay Triangulation & Voronoi Diagram
Delaunay edge
Voronoi edge
Voronoi – Grid Refinement
Conventional Rectangular Grid SystemConventional Rectangular Grid System
Hexagonal Grid Model
Conventional Grid ModelConventional Grid Modelwith Grid refinement Near Wellswith Grid refinement Near Wells
Flexible Grid Model Flexible Grid Model Rectangular – Hexagonal and radialRectangular – Hexagonal and radial
Voronoi Diagram – Randomly distributed points
100 cells
Voronoi Diagram – Connection
90 cells - 462 connections
Voronoi with 500 Cells – 2766 connections
Modeling Fracture Network using voronoi
Single Fracture
Fracture Set #1
Modeling Fracture Network using voronoi
Multiple Fracture
Fracture Set #1
Fracture Set #2
Fracture Set #3
Fracture Set #4
Geometrical domain Computational domain
Modeling Fracture Network using voronoi
No Flow connection
w w = fracture width
matrix
matrix
matrix
fractureFlow connection
Flow Connection
Voronoi with complex fracture network
645 - 2945 connection
Voronoi with complex fracture network
Processor – Black Oil, 3PProcessor – Black Oil, 3P
Flow EquationFlow 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
Static Data Static Data Cell/GridCell/Grid
ID/NAMESTATUS (ACTIVE/INACTIVE)GEOM
X,Y,ZCONNE FRACT/NOT_FRACT TRANS_MULTAREA, HVOLUME ROCK_PROP
kL kV POR RELPERM_AND_Pc_IDPVT_IDPVMOD
• FRACTUREIDWIDTHPERMROUGHNESSRELPERM_AND_Pc_IDPVT_ID
• AQUIFER (OPTIONAL)IDMODELVOLUMEROCK_PROP
Dynamic DataDynamic Data PressurePressure
Po (ID,time) Pw (ID,time) Pg (ID,time)
SaturationSaturation So (ID,time) Sw (ID,time) Sg (ID,time)
WellsWellsID
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 PermeabilityFluid Permeability
ko (ID,time) kw (ID,time) kg (ID,time)
ChallengesChallenges Complex Fracture NetworkComplex Fracture Network
ConnectivityConnectivity
Fully implicit finite difference or “Fully implicit finite difference or “StabilizedStabilized” ” IMPES formulation IMPES formulation ????
Sparse matrix solver to solve linear equations (Sparse matrix solver to solve linear equations (no no restrictionrestriction) ) - - BiCGSTAB & ORTHOMINBiCGSTAB & ORTHOMIN(we will not have a banded matrix form) (we will not have a banded matrix form)
Computation time ???Computation time ???
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