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 ???