dumux user meeting 12 june 2015, stuttgart€¦ · dumux user meeting 12 june 2015, stuttgart. ......

MODELING FLOW IN FRACTURED POROUS MEDIA

Modeling flow in fractured porous media

Alexandru Tatomir

DuMux User Meeting 12 June 2015, Stuttgart

MODELING FLOW IN FRACTURED POROUS MEDIA 2

𝒂𝒘𝒏

𝒑𝒄 𝑺𝒘

•Reservoir conditions (pH,T,..)

•Large scale heterogeneity

•Determination of flow parameters

•Requires constitutional relationships (pc-Sw-awn)

Ex.2

• Continuum scale properties

• Analogue fluids mimicking scCO2

• Test and verification for tracers

• Requires constitutional relationships (pc-Sw-awn)

Ex.1

Molecular model

Molecular target design

Pore-scale models

Determination of constitutive relationships from μCT scans

Laboratory-scale models

Core flooding experiments

Field-scale models

Designing optimized injection strategies

𝒒𝒏→𝒘𝑹 = 𝒌𝒏→𝒘

𝜿 𝒂𝒘𝒏

Current Research

Tatomir et al., 2015, IJGGC


Collaborations

• Rainer Helmig

• Bernd Flemisch

• Holger Class

• Adam Szymkiewicz – Univ. of Gdansk

• Sorin Pop – Univ. Eindhoven

• Nicolas Schwenck

• Alexander Kissinger

• Johannes Hommel

• Philipp Nuske


Fracture Model Concepts

• Determine a REV

• Simple

• Less computation power

• Determination of flow parameters

CFM

•Account explicitly for individual fractures

•Most accurate

•Expensive computation

•Extensive data requirements > Fracture generator

DFM

Very near field

Flow in a single very detailed defined fracture

Near field

Each fracture is described in detail

Far field

Flow occurs in overlapping continua

Very far field

Entire flow is described averaged


Fractured limestone, Bristol Fracture corridor in a clastic rock, Algeria

Heavily fractured exposed wall

Fractured asphalt Micrograph of an electrode in a ELAT-DS fuel cell

Fracture in a μCT scan of sandstone

FRACTURE = a separation of an object or material as a result of mechanical failure

Fractured systems


Interface conditions at media discontinuities(DFM)

Duijn et al. [1995] interface condition

The conditions that have to be valid at the interface:

• Continuity of the flux :

• Continuity of the capillary pressure:

• Cross-equilibrium concept (equality of potentials) :

(Reichenberger et al. [2003])

G1

G2

G3


Mathematical model (DFM)

Lower-dimensionalDFM - L

Equi-dimensionalDFM - E

ξ -coordinate along the fracture direction

(9)

𝑺𝒏𝑭, 𝒑𝒘

𝑭 , 𝑺𝒏𝑴, 𝒑𝒘

𝑴

matr

ixfr

actu

re7


INTRODUCTION

FRACTURE MODELS

UPSCALING

DISCRETIZATION

TOOLS

NUMERICAL SIMULATIONS

CONCLUSIONS

88

DFM Limitations

Odling et al .[1999]

High computational demands

• Fracture network generation

• Meshing

• Simulation


Continuum fracture models

SPSP DPSP DPDP

Schematic diagrams of connectivity

Fracture Grid

Rock Matrix GridTransfer functions /Shape factor

Multi-porosity models Dual-porosity models

9


MINC Concept

Coarse-block /

Fracture-Fracture

inter-connectivity

Fracture

Continuum

Matrix

Continua

M 1

1

M 1

2

M 1

3

M 5

1

M 5

2

M 5

3

M 1

4

Naturally fractured reservoir Idealized Reservoir

Model

2D crossection representing

the nested vol. elments

2D crossection representing

the nested vol. elments

Fracture-Matrix inter-

connectivity

Matrix-Matrix inter-

connectivity

• Large differences in the thermodynamic conditions -between matrix and fracture (i.e. pressures, saturations)

• The spatial variations within the fracture system or within certain regions in the matrix may be slow and dependent on the volume averaging

• Certain areas of the flow region can be lumped (e.g. the well connected fractures, portions of porous block) into several distinct continua which interact with each other

10


Extended MINC Method

Determination of the local subgrids of the coarse block (Matrix-Matrix)

NC0

NC1

NC2

NC3

NC4

NC5

NC6

(18)

(19)

Karimi-Fard et al .[2006]

Tatomir et al .[2011]

11


MINC mathematical model

Determination of the upscaled interblock transmissibility (Fracture –Fracture)

p = 0p = 1

Cell i Cell j

Interface

(20)

12


pdM = 1200 PapdF = 1000 Pa

DFM-LSim Time1.2e5 sec

eMINCSim Time2046 sec

DFM-L – „zig-zag“ curve

eMINC – continuous curves named SN_0 to SN_5

Quarter-five spot problem

13


Naturally fractured reservoir (Bristol)

14


Water –Air

System

Mass fluxes of wetting and non-wetting phase plotted over time at line (x = 1.8m)

pw =1.0e5 PaSn = 0.20

pw =2.0e5 PaSn = 0.80

Left Boundary

Right Boundary

pdM = 1200 PapdF = 1000 Pa

DFM-LSim Time3.3e5 sec

eMINCSim Time180 sec

DFM – eMINC Bristol Formation

15

dumux user meeting 12 june 2015, stuttgart€¦ · dumux user meeting 12 june 2015, stuttgart. ......

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