Fracture Characterization

7/25/2019 Fracture Characterization

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Tayfun Babadagli, PhD, PEng Short Course Reservoir Characterization File-16 1

NATURALLYFRACTUREDRESERVOIRSNFR

Dataacquisition?????Reservoirsimulation

Dilemma: Howtoincorporatedifferent(andlimited)datasetsandmapthe

fracturenetwork.

NFRcharacterizationismainlybasedonthefracturesetsseeninthelogsand

cores.

FRACTURE CHARACTERIZATION


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Tayfun Babadagli, PhD, PEng Short Course Reservoir Characterization File-17

Evaluation

of

Outcrop

Fracture

Patterns

Babadagli, T.: Fractal Analysis of 2-D Fracture Networks of Geothermal Reservoirs in South-Western Turkey,J. of Volcanology and Geothermal Res., vol. 112/1-4, Dec. 2001, 83-103.

Babadagli, T.: Evaluation of Outcrop Fracture Patterns of Geothermal Reservoirs in Southwestern Turkey,

2000 World Geothermal Congress, Kyushu-Tohoku, Japan, May 28-June 10, 2000.


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STATEMENT

OF

THE

PROBLEM

Quantification of fracture network properties

(density, spatial distribution, orientation,

connectedness, length etc.) for modeling studies:

FRACTAL ANALYSIS

OBJECTIVE

Fractalanalysisoffracturenetworks

Usingdifferentmethods.

Outcropfracturepatterns

DifferentproducingformationsofgeothermalreservoirsinSouthwestern

Turkey


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r1

r2SAND BOX

TECHNIQUE

r1 r2r3

BOX COUNTING TECHNIQUE

N(r)~rD

i=1,2,3,...


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MID (or INTERSECTION) POINT DISTRIBUTION

MASS DIMENSION (SAND-BOX METHOD)

L1L2L3L4

N(L) ~ LDMID

(OR INTERSECTION)

POINTS OF FRACTURESN : Number of points


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NUMBER OF FRACTURES PER UNIT AREA

MASS DIMENSION (SAND-BOX METHOD)

L1L2

L3L4

N(L) ~ LDFRACTURES

BOX

SIZES

}

N : Number of points


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METHODS APPLIED

BOX COUNTING(BOX DIMENSION)

MID-POINT DISTRIBUTION

(MASS DIMENSION - SAND-BOX METHOD)

INTERSECTION POINT DISTRIBUTION(MASS DIMENSION - SAND-BOX METHOD)

NUMBER OF FRACTURES PER UNIT AREA(MASS DIMENSION - SAND-BOX METHOD)


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N

a b


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Fracture mid-points and intersection points


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FRACTAL DIMENSIONS FOR DIFFERENT

SCALES USING DIFFERENT METHODSGIGA (km) MEGA (m) MACRO (cm) MICRO (m)METHOD

BC : BOX COUNTING

MPD : MID-POINT DIST.

IPD : INTERSECTION-POINT DIST.

NFA : NUMBER OF FRACTURE PER UNIT AREA

BC

MPD

IPD

NFA

1.57 - 1.581.14 - 1.52

1.71 - 2.00

1.10 - 1.81

1.07 - 1.89

1.16 - 1.25 1.01 - 1.04


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PATTERN NO FRACTAL DIM.

Fig. 3-a 1.15

Fig. 3-b 1.39

Fig. 3-c 1.41

Fig. 3-d 1.25

Fig. 3-e 1.29

Fig. 3-f 1.39Fig. 3-g 1.15

Fig. 3-h 1.50

Fig. 3-i 1.46

Fig. 3-j 1.40Fig. 3-k 1.35

Fig. 3-l 1.27

Fig. 3-m 1.39

FRACTAL DIMENSION - BOX COUNTING


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KIZILDERE FIELD GERMENCIK FIELD

Region Fractal

Dim.

Region Fractal

Dim.

Upper Prod. Form. 1.393 Germencik 1.396





Lower Prod. Form. 1.250 Germencik 1.392Germencik 1.462



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ROCK PIECES THIN SECTIONS1.175 1.015

1.255 1.035

1.252 1.015

1.164 1.013

1.189 1.020



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FRACTAL DIMENSION - BOX COUNT. and SAND BOX

PATTERN

NO

MID POINT

DISTRIBUTION

INTERSECTION

POINTDISTRIBUTION

NUMBER OF

FRACTURESPER UNIT AREA

(FNUA)

FRACTURE

LENGTHPER UNIT AREA

(FLUA)

Fig. 2-a 1.74 1.71 1.05 1.85

Fig. 2-b 1.99 1.74 2.04 1.80

Fig. 2-c 1.17 1.31 1.55 1.99

Fig. 2-d 1.59 1.39 1.48 1.76Fig. 2-e 1.91 1.82 1.44 2.10

Fig. 2-f 1.54 1.70 1.48 1.85

Fig. 2-g 1.17 1.09 1.47 1.51

Fig. 2-h 1.62 1.80 2.01 1.39

Fig. 2-i 1.21 1.23 1.60 0.90

Fig. 2-j 1.22 1.50 1.50 0.74

Fig. 2-k 2.01 1.81 2.03 0.95

Fig. 2-l 1.63 1.58 1.94 1.35

Fig. 2-m 1.92 1.74 1.60 1.87


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PATTERN

NUMBER

SCANLINE

DIRECTION

FRACTAL

DIMENSION

Fig. 2-a W - E 1.620

Fig. 2-a N - S 1.383

Fig. 2-a NW -SE 2.368

Fig. 2-a NE -SW 1.382

Fig. 2-b W - E 1.973

Fig. 2-b N - S 1.919

Fig. 2-b NW -SE 2.004

Fig. 2-b NE -SW 1.824

Fig. 2-c W - E 1.398

Fig. 2-c N - S 1.414

Fig. 2-c NW -SE 1.321

Fig. 2-c NE -SW 1.269

Fig. 2-d W - E 1.726

Fig. 2-d N - S 1.547

Fig. 2-d NW -SE 1.623

Fig. 2-d NE -SW 1.472

Fig. 2-e W - E 1.588

Fig. 2-e N - S 1.442

Fig. 2-e NW -SE 1.710

Fig. 2-e NE -SW 1.314

Fig. 2-f W - E 1.699

Fig. 2-f N - S 1.724

Fig. 2-f NW -SE 1.686

Fig. 2-f NE -SW 1.599

PATTERN

NUMBER

SCANLINE

DIRECTION

FRACTAL

DIMENSION

Fig. 2-g W - E 1.372

Fig. 2-g N - S 1.551

Fig. 2-g NW -SE 1.369

Fig. 2-g NE -SW 1.402

Fig. 2-h W - E 1.662

Fig. 2-h N - S 1.561

Fig. 2-h NW -SE 1.549

Fig. 2-h NE -SW 1.554

Fig. 2-i W - E 1.580

Fig. 2-i N - S 1.815

Fig. 2-i NW -SE 1.230

Fig. 2-i NE -SW 1.219

Fig. 2-j W - E 1.256

Fig. 2-j N - S 1.018

Fig. 2-j NW -SE 1.119

Fig. 2-j NE -SW 1.226

Fig. 2-k W - E 1.748

Fig. 2-k N - S 1.689

Fig. 2-k NW -SE 1.655

Fig. 2-k NE -SW 1.644

Fig. 2-l W - E 1.652

Fig. 2-l N - S 1.741

Fig. 2-l NW -SE 1.714

Fig. 2-l NE -SW 1.676

Fig. 2-m W - E 1.611

Fig. 2-m N - S 1.391

Fig. 2-m NW -SE 1.532

Fig. 2-m NE -SW 1.546


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FractureNetworks

KIZILDERE

FIELD

GERMENCIK

FIELD

Fracture network mapping: WELL DATA and OUTCROP

How much fractal properties help? Which fractal properties are critical?

Network Permeability or Single Fracture Permeability

cmmmmmm

km

1.10

1.30

1.50

1.00

1.20

1.40

1.60

FRACTAL

DIM

EN

SION,D

Giga(km)

Mega(m)

Makro(cm)

Mikro( m)

SCALE


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5.00 5.20 5.40 5.60

log(r)

2.20

2.60

3.00

2.00

2.40

2.80

log

N(r)

Germencik Field(Slope = D = 1.56)

Kizildere Field(Slope = D = 1.58)

Babadagli, J. Vol. and Geot. Res., 112, 2001

KIZILDERE

FIELD

GERMENCIK

FIELD


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DIFFUSION OVER FRACTAL OBJECTS

dD

o

o

r

rkrk )( similarly

dD

o

o

r

rr

)(

01

2

2

t

Pr

r

P

r

D

r

P

1lim 10

r

PrD

r

1

)1(2

)2)((

)2()( t

DtPw

2

D0and=0.5(linearflow),1(radialflow),1.5(sphericalflow)

conductivityindex,>0forfracturenetworksnotperfectlyconnecteddiffusiondelayedornotnormal


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Acuna and Yortsos, 1995, Water Res. Res.

After Warren and Root, SPEJ Sept. 1963


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Acuna, Ershaghi, Yortsos, 1991


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FRACTAL WELLS TESTS SPE Form. Eval. Sept, 1995


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FRACTAL WELLS TESTS SPE Form. Eval. Sept, 1995


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FRACTAL WELLS TESTS SPE Res. Eval. And Eng., Feb. 2003Short and long time approximations with matrix participation

sttP DDwD

)1)(1(

)2()(

12

)2(

)2()2()1/(

223211

stD

221

dmfd


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FRACTAL WELLS TESTS SPE Res. Eval. And Eng., Feb. 2003

Determination of fractal parameters

2

1

v

Introduced solutions for v>0

and v


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SPE 63286, Baker and Kuppe


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2

CORES:

Usedto

determine:

Origin,geometryandoccurrenceoffractures

Geomechanicalmodification

Fractureorientation

Fracturediprelativetocoreaxisandtobedding,as

wellasrelativeorientationoffracturesshouldbe

measured.

Fractureapertureandheight: Neededforfracture

density,porosity,etc.

After Narr, Schechter, Thompson

Naturally Fractured Reservoir Characterization SPE, 2006

IMAGE LOGS


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3

IMAGELOGS

Directsourceofinformation.

Twotypes; resistivitybasedandacoustic.

(a)Openfracturesinresistivityimage(darksinusoids),(b)Coreformthe

samewell,(c)imageofwholecore

(CourtesyFrankLim,NFRSPE)

After Narr, Schechter, Thompson

Naturally Fractured Reservoir Characterization SPE, 2006


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Apparentfractureheightcanbemeasured

fromimagelogs.

Openfractures:

filled

with

conductive

mud

filtrate

Closedfractures: filledwithresistive

mineralization

Imagelogsaregoodfororientations.

Aperturecouldalsobecomputed.

After Narr, Schechter,Thompson

Naturally Fractured Reservoir

Characterization SPE, 2006


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Othertools:

StoneleyWavelog

Photoelectriclog(usedtocorrectdensitylogs)

Sonicordensitylogs.

Productionlog(PLT): whichfracturesorzonescontributetoflow.

Lostcirculation

Gasshowsinmudlog

Mechnicalindications(caliperlogs)


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FRACTUREDENSITY

Fracturesurfaces

area/unit

volume

Fracturesurfacearea: computedformcoresorimagelogs.

rr hDV

2

2

r

n

i

fi

r

n

i

fi

fDh

h

V

Ad

ff

11

L2/L3 isreducedto1/L. Forasetofparallelfractures,Lisequaltotheiraverage

spacing(perpendiculardistancebetweenfractures).

Fracturedensityprovidesfracturespacing

r

n

i

fifi

r

n

i

fifi

f

Dh

ha

V

Aaff

11

afisfractureaperture.


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7

FracturePermeability

12

2

of

Wk MuskatEq.

swk of12

3

LambsEquation

IFs

wk of

*12

3

Ifwisininches(IF=#fractures/ft) IFwkf **10*54.436

Ifwisincm(IF=#fractures/ft) IFwkf **10*77.235

DIRECTPROPORTIONALITY!!!!


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8Nelson, R.A. Geological Analysis of Naturally Fractured Reservoirs, Gulf Publ. 2001

FRACTURE SPACING

Calculated in core and outcrops by counting the number of fracturesencountered along a line of some given length perpendicular to the

fracture set an dividing the length of measurement line.

In more complex environments, the same is done along lines in specific dimensions.


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FRACTURE (NETWORK) SYSTEM

Fracture orientation

Fracture typology (open/closedFracture density (spacing, heights)

Fracture apertures

Fracture connectivity

Fracture continuitySize distribution (Power law)

Are fracture affecting the reservoir performance?

If so, can we optimize production or ultimate recovery based onfracture properties.

9


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QUANTIFICATION OF FRACTURE NETWORK PROPERTIES

Impedance Factor = # of fractures stopped/Total # of fractures (SPE 59045)

Fracture Spacing, S = Diameter of core / Fracture occurrence (SPE 25852)

Diameter of core / Fraction of cores that contained fractur

Fracture Permeability, kf= 5.4x109

w2

keff= kf w2 / Ls

w = aperture (m) , k = Darcy. Ls = Fracture spacing

Fracture spacing ratio, (SPE 25612)

T = bed boundary thickness, l = Transmissibility between matrix and fracture

8RK

TKFSR

2

ww

2

f

10


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Fracture density and permeability (multiplier)

Obtained by history matching and non-linear

(SPE 58995)

nf = number of fractures

1)1nflog(

)1nflog(9m

max

11


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The Weyburn Field(SPE 63286)

Medium quality oil from fractured, low perm, carbonate (Midale beds).

Discovered in 1956.

Porosity = 26 % (average, ranging between 16 and 38 %)Permeability 1 to 100 md.

Waterflood began in the early 1960s.

Ultimate secondary recovery was 25-35 %.

For waterflood optimization, horizontal wells and assessment of miscibleDisplacement, extensive characterization needed

12


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Reservoir performance (production and pressure)

Geological data

CoresPetrophysical data

Injection profile logging

Pressure transient tests

Vertical pulse testing

Vertical and horizontal coresWireline logs

RFT

FMS Neighboring Midale field experience

13


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Significant differences in intensity for limestone and dolomite

Three ages of fractures, some filled with anhydrite

Vertical, subvertical and oriented N45oE.

Fracture intensity decreased as porosity increased.

Relationship between lithology and intensity was used for mapping

Fracture permeability was obtained from fracture spacing (and aperture) data.

14


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The Spraberry Field(SPE 63286)

First developed in the early 1950s

Many wells with 500 bopd initial production. But diminished rapidly.

10 billiion bbls OOIP, less than 10% recovered

60,000 bbls/day from 7,500 wells

700,000,000 bbls produced

First waterflood began in 1956,

Generally unsuccessful due to bypassing matrix oil

Similar fracture spacing as Weyburn but waterflood recovery is 2-5%

(Weyburn has 16-25% incremental waterflood recovery15


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QUANTIFICATION OF FRACTURE NETWORK PROPERTIESThe Spraberry Field

(SPE 63286)

Low matrix perm was problem (< 1 md) and reservoir was no water-wet resultingin slow imbibition rates.

Tests conducted include horizontal cores (orientation), pulse/interference,

tracer tests (orientation),,

build up and fall off (fracture permeability and connectivity),FMI (specific fracture trends) , outcrop etc.

Important to quantify fracture spacing for waterflooding and CO2 injection

Fracture orientation is NE to SW

Average fracture spacing in three different sets are 3.2, 1.6, and 3,8 ft.

16


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FRACTURE RESERVOIR CHARACTERIZATIONYATES FIELD

(Dershowitz et al., SPE Res. Eng. and Eval., April 2000)

Field discovered in 1926 and 1.3 billion bbls of oil produced until 1993.

1100 producers and 57 injectors.

To maximize withdrawals from high-rate, high efficiency wells,400 wells were shut in while keeping the stable daily production rate

between 1992 and 1994.

In the same period, more than 30 new short radius wells were drilled.

A discrete fracture network modeling was used to study the spatial

distribution of fractures of to optimize location and orientation of new

horizontal wells.

17


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FRACTURE RESERVOIR CHARACTERIZATION

YATES FIELD

(Dershowitz et al., SPE Res. Eng. and Eval., April 2000)

DISCRETE FRACTURES Faults deterministically , fractures fromborehole data

ORIENTATION Seismic For faults, fractures using Fisher distribution

SIZE DISTRIBUTION Power law distribution D=1.81, min. radius = 0.30 m.

(Stochastic)INTENSITY 0.105 to 0.21 sq m/cu m depending on shale porosity/content

(Stochastic)

TRANSMISSIVITY Log normal distribution,

faults: log mean=-4, log std. dev. = 1

fractures: log mean=-4.5, log std. dev. = 1

APERTURE Correlated to transmissivity by cubic law, a = 0.00117 T0.32

MODEL DIMENSIONS 2130 x 2130 x 350 m.

18


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Single FracturePERMEABILITY

-Is it only the roughness or mean aperture?

-Whichever it was, can we detect it for whole

reservoir and its distribution at all?

kf= 5.4x109 w2 keff= kf w

2 / Ls

w = aperture (m)

Ls = Fracture spacing (# of fractures/area)

cF= Fraction of pore volume occupied by fissures (fraction) = total porosity (fraction)

RELATIVE PERMEABILITY

-Straight line function? No answer yet. There

exist deviations due to roughness?-Recent studies showed natural porous media

type kr for steam-water.

2

fF wc33k

19

Displacement patterns in a single fracture: Effect of roughness


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INVASION

PERCOLATION

CLUSTERS

FBMLATT

ICESWITH

DIFFERENTHVALUES

H=0.5, D=2.5 H=0.7, D=2.3 H=0.9, D=2.1H=0.1, D=2.9

Displacement patterns in a single fracture: Effect of roughness

20

Fracture Networks


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KIZILDERE

FIELD

GERMENCIKFIELD

Fracture network mapping: WELL DATA and OUTCROP

How much fractal properties help? Which fractal properties are critical?

Network Permeability or Single Fracture Permeability

cm-mmm-mm

km

1.10

1.30

1.50

1.00

1.20

1.40

1.60

FRACTALD

IM

ENSION,D

Giga(km)

Mega(m)

Makro(cm)

Mikro( m)

SCALE

21

FRACTURE NETWORK MAPPING: Does Fractal help?


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Acuna and Yortsos, 1995, Water Res. Res.Warren and Root, SPEJ Sept. 1963

D=2.78 D=2.65 D=2.48

D=2.85, Isotropic fracture,

D=1.85 (plane dimension)D=0.85 (Any random hole)

Sammis and Steacy, in Fractals in the Earth Sciences,

Barton and LaPointe, 1995

p

Fracture orientation

Fracture typology (open/closed0

Fracture density-intensity (spacing,

heights)

Fracture aperturesFracture connectivity

Fracture continuity

Size distribution (Power law)

NETWORK CHARACTERISTICS

22

FRACTURE NETWORK MAPPING: Does Fractal help?


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WELL #1 WELL #2

Mega-Giga Scale Outcrops

23

Characterization of Fracture Network System of the Midale Field


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MidaleField History

CharacterizationofFractureNetworkSystemoftheMidaleField

(CIPC2007,BogatkovandBabadagli)

Discovery 1953

Waterflood 1962

Infilldrilling mid1980s

Horizontaldrilling late1980s

CO2floodpilot 1984

MidaleCO2

Flood

DemonstrationProject(10%ofUnit) 1992

Multileggedperpendicular

Horizontalwellsdrilled mid1990s

AcquisitionofthefieldbyApache 2000

Infilldrilling(hor.wells),injection&throughputx3,CO2feasibility

study

Midale


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MidaleField FractureSystem Suggestedfracturelengths:

100m,


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Data

Mining Datacollectedtodate beinganalyzed

CO2FloodPilotArea:

Logs,cores

(pictures)

for

all

wells

Coreanalysis(petrophysical)reports

Thinsectionstudies

Wellfiles

Simulationstudies

Projects,etc.

Restof

field

Logs,cores,maps

Simulationstudies,petrophysicalstudiesetc.


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Data

Analysis

Analysistodate(asdictatedbyFRACA):

Stratigraphicparameters

Layers,thicknesses,depths

Formationproperties

Porosity,permeability,

compressibility,

saturations

Result:simplestructuralmodelinFRACA

Layercake:9parallellayerswithdistinctparameters

Area=200x200m 200x200x9blocks


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DataAnalysis

Facies

Layer

Depth

(m below

datum)2

Thickness1

(m)

Porosity1

(fraction)

kh(mD)1

kv/kh4,5 Swi

1,3 kro6,7

Sigma

for

Thickness8

Formation

compressibility

(bar-1)9

M1 1393.50 1.50 0.225 4.2 0.366 0.600 0.02 0.282 1.10E-07

M2 1395.00 1.40 0.113 0.4 0.335 0.918 0.00 0.302 2.20E-07

M3 1396.40 1.67 0.311 23.7 0.548 0.516 0.20 0.127 7.99E-08

M4 1398.07 0.88 0.132 0.6 0.428 0.707 0.00 0.411 1.88E-07

V1 1398.95 2.39 0.104 6.4 0.286 0.882 0.00 0.579 2.39E-07

V2 1401.34 2.01 0.065 0.6 0.196 0.793 0.00 0.500 3.82E-07

V3 1403.35 2.33 0.103 12.2 0.244 0.634 0.10 0.707 2.41E-07

V4 1405.68 1.05 0.063 0.5 0.190 0.932 0.00 0.574 3.95E-07

V5 1406.73 2.09 0.139 4.9 0.310 0.692 0.04 0.588 1.79E-07

F t M d l i FRACA


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FractureModelinFRACA

Fracture Model in FRACA


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7

FractureModelinFRACA

DFNmodel


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Tayfun Babadagli, PhD, PEng Short Course Reservoir Characterization File-18811/23/2011 8

DFNmodelcalibration


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Perform

welltestsimulation

Populate

withfractures

Prepare

apetrophysicalmodel

Check

againstreal

data

Sensitivitystudyresults


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Most influential parameters (for history match)

S1 I2 I3 I4

Parameter #1 Matrix Matrix Matrix MatrixRelative effect, % 96.368 98.940 93.144 93.525

Parameter #2 Fr. cond. Matrix*Fr. length Matrix*Fr. length Fr. cond.

Relative effect, % 3.632 0.291 2.743 1.942

Parameter #3 N/A Matrix*Fisher strike Matrix*Fr. cond. Fr. length

Relative effect, % N/A 0.197 2.571 0.882

1. Strongmatrixeffect:

Matriximportantsource,probablymatrixflowispresent,

Fracturesenhancepermeability,facilitateinterwellconnectivity;

2. Matrix/fractureinteraction

is

important:

probably

the

controlling

parameter;

3. Individualfracturescanbeveryimportant,howeverdifficulttopredict.

Sensitivitystudyresults


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Design-Expert SoftwareOriginal ScaleI2-MRE

5

3.3

X1 = A: Frac spacing, MX2 = B: Frac spacing, V

Actual FactorsC: Fracture length = 100

D: Fisher strike = 1E+020E: Frac cond = 10.0F: Matrix = Mediocre

0.3

0.5

0.8

1.0

1.2

0.3

0.50.7

0.9

1.1

3.3

3.8

4.2

4.6

5.1

I2-MRE

A: Frac spacing, M

B: Frac spacing, V

ResponsesurfaceforWellI2:MRE(A,B)

020

4060

80100

S1

I2

I3

I4

96.37

98.94

93.14

93.52

3.63

1.10E-07

0.27

1.94

Relative effect, %

Wellna

me

Matrix quality and fracture conductivityfactors in fitted MRE models

Fracture conductivity

Matrix

Transienttestsimulation


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0

20

40

60

80

100

120

140

160

0 2 4 6 8

Wellbottomholepressure(bar)

Time(day)

WellS1producer

0

20

40

60

80

100

120

140

160

0 2 4 6 8

Wellbottomholepressure(bar)

Time(day)

WellI2diagonalobserver

0

20

40

60

80

100

120

140

160

0 2 4 6 8

Wellbottomhole

pressure(bar)

Time(day)

WellI3diagonalobserver

0

20

40

60

80

100

120

140

160

0 2 4 6 8

Wellbottomhole

pressure(bar)

Time(day)

WellI4diagonalobserverRealtest

Discrete

simulation

Single

continuum

simulation

Dual

continuum

simulation

D:13.45% SP:6.73% DK:13.13% D:6.21% SP:2.38% DK:1.79%

D:0.92% SP:5.37% DK:5.25% D:1.47% SP:2.36% DK:3.30%

Tracertestsimulation


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Injection

well ID Salt

Concentration

(mole fraction) Vslug, m3

I1 KI 0.0203 4.1

I2 NH4SC 0.1022 2.2

I3 N3H4NO 0.1041 6.7

I4 KBr 0.0275 4.1

Totaltest

time:

240

days

Tracerslugfollowedby

continuouswaterinjection.



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0.00

0.50

1.00

1.50

2.00

2.50

3.00

FS1 S1 S2 S3

0.500

1.400 1.400

3.000

0.0800.210

Breakthroughtime(da

y)

Producer well

Iodide

0.00

0.10

0.20

0.30

0.40

0.50

FS1 S1 S2 S3

0.100

0.500

0.0400.080

0.1700.130

Breakthroughtime(day)

Producer well

Thiocyanate

0

3

6

9

12

15

FS1 S1 S2 S3

13.400

9.400

0.1000.080 0.080Breakthrough

time(day)

Producer well

Nitrate

0.000

2.000

4.000

6.000

8.000

10.000

FS1 S1 S2 S3

8.500 8.500

0.4000.210 0.130

Breakthroughtime(day)

Producer well

BromideReal testSimulated

No

BT

No

BT

No

BT

No

BT

No BTNo BTNo

BT

No

BT



68/142


0

100

200

0 100 200

(axes in m)

Wellconnectivity

N

main trend

S2

S1

S3

I4

I3

FS1

I2

I1

basedonsimulatedtracerbreakthrough time(day)

Thiocyanate

Iodide

Bromide

Nitrate

0.08

0.08

0

100

200

0 100 200

(axes in m)

Wellconnectivity

N

main trend

S2

S1

S3

I4

I3

FS1

I2

I1

basedontracerbreakthrough time(day)

Thiocyanate

Iodide

Bromide

Nitrate

0.1

1.4

9

38

Sensitivitystudy


69/142


Aim:

Tostudy

the

effects

of

various

matrix

and

fracturepropertiesonthetracertransport.

Parameters:

1.Fracturedensity,

2.Fracturepermeability,

3.Dispersioncoefficients,

4.Matrixpermeability,

5.Matrixfracturetransmissibility,

6.Relativepermeability.

Tools:

Tracertestsimulation.

Sensitivitystudy


70/142


0

100

200

0 100 200

(axes in m)

Wellconnectivity

N

main trend

S2

S1

S3

I4

I3

FS1

I2

I1


Thiocyanate

Iodide

Bromide

Nitrate

0.08

0.08

0

100

200

0 100 200

(axes in m)

Wellconnectivity

N

main trend

S2

S1

S3

I4

I3

FS1

I2

I1


Thiocyanate

Iodide

Bromide

Nitrate

23

Sensitivitystudy


71/142


0

100

200

0 100 200

(axes in m)

Wellconnectivity

N

main trend

S2

S1

S3

I4

I3

FS1

I2

I1


Thiocyanate

Iodide

Bromide

Nitrate

0.08

0.08

0

100

200

0 100 200

(axes in m)

Well

connectivity

N

main trend

S2

S1

S3

I4

I3

FS1

I2

I1


Thiocyanate

Iodide

Bromide

Nitrate

0.17

Fracturenetworkrepresentation


72/142


Idealised fracture network Realistic fracture network

Dualporositymodels:1. Fracturenetworkasaregularmesh;

2. Fracturedip,strike,heightarenotvariable;

Discretemodels:1. MorerealisticrepresentationofNFN

2. Anydesireddegreeofvariabilityavailable;


73/142


Non

classical

techniques Manydifferentapproaches

Stochastic

Involverandomness

20


74/142


What

is

Random

Walk? Fluidflowrepresentedbymovementof

walkers

Eachwalker

represents

certain

volume

or

mass

Walkersmoverandomly;randomnessdefinedbyphysicsofthesystem:Probability ofparticle

tomove

in

certain

direction

is

defined

by

physicsoftheprocess(pressures,saturation,permeabilities,viscosities)

If

we

are

modeling

two

phase

flow,

we

will

considertwotypeofparticlesmoving.

21


75/142


What

is

Random

Walk?

22

Movement=convective

+random

Convectivecomponent

followsDarcysLaw

Random

component

satisfiesADE

(Delayetal.2005)

v solutionofDarcyseqn

z~N(0,1)

D dispersioncoefficient


76/142


FieldCase:

Sensitivity

23

Highesteffect:Ontrendfracturewidths

Ch=(offtrendsp)/(ontrendsp)

FieldCase:HistoryMatching


77/142



78/142


FieldCase:

History

Matching

25

Shortcomputationaltime=>automatedHM

Small

#

of

parameters

or

flexibility?Result:qualitativeHM

observed RWPT DP

from:Bogatkov,M.Sc.thesis.

ASensitivityAnalysisforEffective


79/142


Parameterson

Fracture

Network

Permeability

Jafari, A.R. and Babadagli, T.: A Sensitivity Analysis for Effective Parameters on 2-D Fracture Network Permeability,

SPE Res. Eval. and Eng., vol. 12, no. 3, June 2009, 455-469.

Jafari, A. and Babadagli, T.: Effective Fracture Network Permeability of Geothermal Reservoirs, Geothermics, vol. 40,

25-38, 2011.

Jafari, A.R. and Babadagli, T.: Generating 3-D Permeability Map of Fracture Networks Using Well, Outcrop, and Pressure

Transient Data, SPE Res. Eval. and Eng, vol. 14, no. 2, April 2011, 215-224.

Jafari, A. and Babadagli, T.: Equivalent Fracture Network Permeability of Multi-Layer-Complex Naturally Fractured Reservoirs,

Tran. in Porous Media, 2011 (in print).

Jafari, A.: Permeability Estimation of Fracture Networks, Ph.D. Thesis, Univ. of Alberta, Oct. 2010

SyntheticPatterns:DifferentScenarios


80/142


Length (m)

20

40

60

80

Density (#/domain)

100

50

150

200

250

Orientation

NS&WE

NWSE&NESW

Random

Topology:RandomOrientation


81/142


3

Topology:NWSE&NESWOrientation


82/142


4

Dataset#1:NWSE&NESW


83/142


5

L(m)

Density(#/square)

FD

using Box

Counting

FD

using Sand

boxFD using

ScanningLine in X

direction

FD using

ScanningLine in Y

direction

ConnectivityIndex

Maximum

Touch with XScanning Line

Maximum

Touch with YScanning Line

FD

using Box

Counting Permeability(md)

I. P. M. P. I. P. M. P. Lines

20 50 1.080 1.408 1.328 1.555 1.605 1.437 0.616 7072.2 7070.8 1.293 6.575

20 100 1.555 1.638 1.604 1.707 1.318 1.324 1.199 14142.2 14145.9 1.465 10.553

20 150 1.740 1.733 1.551 1.503 1.338 1.317 1.812 21212.8 21216.3 1.552 36.958

20 200 1.835 1.817 1.681 1.491 1.347 1.370 2.477 28282.4 28283.2 1.620 62.765

20 250 1.878 1.857 1.856 1.541 1.363 1.365 2.976 35350 35354.3 1.648 84.162

40 50 1.564 1.401 1.650 1.366 1.131 1.145 2.902 14140.2 14142.5 1.429 28.059

40 100 1.803 1.647 1.565 1.404 1.112 1.113 5.911 28283.3 28285 1.583 82.722

40 150 1.867 1.745 1.671 1.428 1.118 1.115 8.776 42427 42426.6 1.651 144.026

40 200 1.911 1.817 1.886 1.352 1.132 1.134 11.499 56569.2 56571.8 1.700 201.535

40 250 1.915 1.854 1.935 1.403 1.126 1.122 14.575 70714.1 70710.6 1.737 261.725

60 50 1.703 1.398 1.590 1.265 0.930 0.932 7.444 21213.1 21213.2 1.457 66.995

60 100 1.812 1.641 1.531 1.198 0.940 0.934 14.875 42426.5 42424.9 1.596 112.958

60 150 1.841 1.754 1.700 1.241 0.929 0.932 22.666 63638.5 63639.4 1.682 184.213

60 200 1.849 1.823 1.620 1.342 0.934 0.936 30.224 84852.2 84850.3 1.722 264.453

60 250 1.855 1.859 1.632 1.286 0.928 0.929 37.907 106066.6 106062.6 1.760 342.236

80 50 1.727 1.401 1.903 1.501 0.860 0.859 12.064 28282.7 28284.9 1.456 76.150

80 100 1.780 1.638 1.773 1.903 0.859 0.859 24.008 56568.4 56567.6 1.586 139.468

80 150 1.800 1.754 1.771 2.122 0.859 0.859 36.095 84852.8 84855 1.665 210.461

80 200 1.801 1.817 1.671 1.788 0.859 0.859 47.925 113136.7 113137.6 1.705 296.081

80 250 1.804 1.860 1.740 1.808 0.859 0.859 59.979 141420.9 141422.2 1.730 352.534

Exponential:

Ln(Y)=a*exp(b*x1)+c*ln(x2)+d*ln(x3)+e*ln(x4)+f*ln(x5)+g*ln(x6)+h

EFRP Correlations


84/142


EXLnDXLnCXBAKLn )(.)(.).exp(.)( 321

FXLnEXLnDXLnCXBAKLn )(.)(.)(.).exp(.)( 4321

GXLnFXLnEXLnDXLnCXBAKLn )(.)(.)(.)(.).exp(.)( 54321

HXLnGXLnFXLnEXLnDXLnCXBAKLn )(.)(.)(.)(.)(.).exp(.)( 6543210.4276

0.5695

0.4034

0.0653

R-squaredDerived EquationIndependent

Variables

( ) p( ) ( ) ( ) ( ) ( ) g ( )

Powerlaw:

Log(Y)=a*x1^b+c*log(x2)+d*log(x3)+e*log(x4)+f*log(x5)+g*log(x6)+h

Thefirst

type

was

found

superior

to

the

second

one

and

further

parametricanalysiswasperformedusingthistypeofcorrelation.

ExperimentalDesign:Analysis2


85/142


7

variable Optimistic(1) Pesimistic(-1)

Length 80 20

Density 250 50

Orientation N-S&E-W NW-SE&NE-SW

Conductivity 2000 500

Orientation

Length/Orientation

Length/Density/Conductivity

Length/Conductivity

Density/Conductivity

Length/DensityConductivity

LengthDensity

Orientation/Conductivity

Density/Orientation/Conductivity

Length/Oriention/ConductivityLength/Density/Orientation/Conductivity

Density/Orientation

Length/Density/Orientation

0 100 200 300 400 500 600

Absolute Effect



86/142


8


Length 80 20

Density 250 50




Length/Conductivity

Conductivity

Length/Density

Density

Length

0 200 400 600 800 1000 1200 1400 1600

Absolute Effect



87/142


9


Length 60 40

Density 150 50



Length/Density

Length/Conductivity

Length


Density

Conductivity

0 50 100 150 200 250

Absolute Effect

300


88/142


0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80 90 100

Leng th o f dom ain s ides (X and Y), m

Permeability,mD

Permeability in X-direction, Kx

Permeability in Y-direction, Ky

VERIFICATION PATTERNS


89/142


Independent

Variables Derived Equation


90/142


12

4 Ln(K) = a*exp(b*x1)+c*ln(x2)+d*ln(x3)+ln(x4)+f

5 Ln(K) = a*exp(b*x1)+c*ln(x2)+d*ln(x3)+e*ln(x4)+f*ln(x5)+g

6 Ln(K) = a*exp(b*x1)+c*ln(x2)+d*ln(x3)+e*ln(x4)+f*ln(x5)+g*ln(x6)+h

0

1

2

3

4

5

6

0 1 2 3 4 5 6

LnK(actual), mD

LnK(estimat

ed),mD

ActualEFNPsvs.estimatedonesusingtheJafari

andBabadagli(2008)equationwith4

independentvariablesfornaturalpatterns.

ActualEFNPsvs.estimatedonesusingtheequation

with4independentvariablesfornaturalpatterns.

0

1

2

3

4

5

6

0 1 2 3 4 5 6

LnK(actual), mD

LnK(estimated),mD

80

100

120

y,m

D

Welltest K

Fraca Kx

ADDITION OF WELL TEST DATA


91/142


13

0

20

40

60

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19Pattern

Permebaility

ComparisonofactualEFNP(FRACAKx)intheXdirectionandaverage

permeabilityobtainedfromdrawdownwelltest.

0

20

40

60

80

100

120

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Pattern

Permeability,mD

Welltest K

Fraca Ky

ComparisonofactualEFNP(FRACAKy)intheYdirectionandaveragepermeability

obtainedfromdrawdownwelltest.

Image log Outcrop


92/142


Image log

(1D data)

Outcrop

(2D data)

DFN (3D permeability

map)

Courtesyof

Steve

Hansen,

Schlumberger

Bourbiauxetal.1998

Bourbiauxet

al.

1998

Integrating 1D, 2D and 3D DataWelltest Analysis

Integrating1D,2D,and3DDataCont.

FD (Box- Max Max FD (Box-


93/142


Pattern

(

Counting) Connectivity

Index

Touch

with X

Scanning

Line

Touch

with Y

Scanning

Line

(

Counting) Welltest

Permeability,

mD

Fracture

spacing

Fracture-

wellbore

Intersection

Kx,

mDIntersection

PointLines

1 1.867 1.064 15608 21143 1.557 29.769 1.970 4 29.545

2 1.820 1.704 15396 17481 1.521 45.348 2.737 3 118.545

3 1.892 1.516 19585 24571 1.598 56.999 1.122 7 120.077

4 1.750 1.407 13331 15887 1.443 51.362 2.444 4 78.485

5 1.774 1.465 15486 16721 1.487 53.660 3.731 2 112.141

6 1.870 1.422 18933 24001 1.576 53.659 7.071 1 112.141

7 1.872 1.275 15916 31323 1.630 50.514 1.729 5 115.117

8 1.800 1.271 13364 16592 1.528 43.774 4.092 2 56.001

9 1.769 1.745 16978 17563 1.567 51.395 2.459 3 71.010

10 1.770 1.496 14366 18920 1.562 49.397 3.235 3 81.104

11 0.797 1.091 114 266 1.264 19.264 4.981 2 38.542

12 1.672 1.218 4720 5612 1.484 16.949 3.049 3 36.981

13 1.660 1.149 4071 3094 1.493 19.649 3.550 2 9.825

14 1.378 1.020 860 1210 1.481 28.733 7.071 1 88.872

15 1.577 1.041 4697 2680 1.513 26.524 2.538 3 15.212

16 1.893 2.611 4767 5473 1.682 60.970 2.088 4 169.827

17 1.647 1.369 1687 1758 1.583 33.349 2.739 3 23.733

18 1.653 1.558 996 1281 1.515 28.947 4.311 2 53.588

Integrating 1 D 2 D and 3 D Data Cont


94/142


Only1D

and

3D

data:

435.297)(734.19

)(884.28)(412.88)(

3

21

XLn

XLnXLnKxLn

Integrating 1-D, 2-D, and 3-D Data Cont.

Kx:Equivalentfracturenetworkpermeability

X1:WelltestPermeability

X2:Fracturespacing

X3:Numberoffracturesintersectingwellbore

Integrating 1 D 2 D and 3 D Data Cont


95/142



X1:FD ofintersectionpointsusing boxcountingdimension

X2:Connectivityindex

X3,X4:MaximumtouchwithscanninglinesintheXandYdirection

X5:

FD of

fracture

lines

using

box

counting


64.17)6(132.1)(362.1)(112.1

)(111.1)(894.0)011.0exp(37.17)(

54

321

XLnXLnXLn

XLnXLnXKxLn

Only 2-D and 3-D data:


Integrating 1-D 2-D and 3-D Data Cont


96/142


677.14)8(763.0)7(555.0)6(979.0)(277.1

)(280.1)(218.1)(182.1)004.0exp(858.15)(

5

4321

XLnXLnXLnXLn

XLnXLnXLnXKxLn

All 1-D, 2-D and 3-D data:


X1:FD ofintersectionpointsusing boxcountingdimension

X2: Connectivityindex

X3,X4:MaximumtouchwithscanninglinesintheXandYdirection

X5:

FD of

fracture

lines

using

box

counting


X7:Fracturespacing

X8:Numberoffracturesintersectingwellbore


100

120

140

160

180

200

ability,mD

Welltest K

Fraca Kx

Predicted Kx using 6 independents



97/142


0

20

40

60

80

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Pattern

Permea

0

20

40

60

80

100

120

140

160

180

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Pattern

Permeability,mD

Welltest KFraca KxPredicted Kx using 8 independentsPredicted Kx using 6 independents


Multi-Layer Naturally Fractured Reservoirs


98/142


20

Multi-Layer Naturally Fractured Reservoirs Cont.


99/142


FracturedReservoir

Configurations

21

Multi-Layer Naturally Fractured ReservoirsCont


100/142


Only1DData:

22

076.8)(367.1)(063.1)( 21 XLnXLnKLn ave

Multi Layer Naturally Fractured ReservoirsCont.


X1: Numberoffracturesintersectingwellbore

X2:Fracturespacing



101/142


026.2)(278.0)(168.0

)(301.0)(098.0)(142.0)(

54

321

XLnXLn

XLnXLnXLnKLn ave

Only 3-D Data:


X1:WelltestpermeabilityfromWell#1

X2: WelltestpermeabilityfromWell#2


X4:

Welltest

permeability

from

Well#4





102/142


12.8)(02.1)(69.1)(59.0

)(26.0)(5.0)(143.0)(41.0)(

765

4321

XLnXLnXLn

XLnXLnXLnXLnKLnave

1-D and 3-D Data:





X4:

Welltestpermeability

from

Well#4


X6: Numberoffracturesintersectingwellbore

X7:Fracturespacing




103/142


12.2)(0856.0)(187.0

)(14.0)(113.0)(09.0)(012.0)(

65

4321

XLnXLn

XLnXLnXLnXLnKLnave

2-D and 3-D Data:





X4:Welltest

permeability

from

Well#4



y yCont.

Multi-Layer Naturally Fractured Reservoirs

Cont.


104/142


26

07.1)(1.0)(1.0)(4.0

)(02.0)(09.0)(02.0)(06.0)(14.0)(

876

54321

XLnXLnXLn

XLnXLnXLnXLnXLnKLnave

1-D, 2-D and 3-D Data:


X1:

Welltestpermeability

from

Well#1





X6:Numberof

fractures

intersecting

wellbore

X7:Fracturespacing


Independent

VariablesDerived Equation R1 R2 R3

3 Ln(K) =A.exp(B.X1)+C.Ln(X2)+D.Ln(X3)+E 0.73 0.87 0.865 Ln(K) = A.exp(B.X1)+C.Ln(X2)+D.Ln(X3)+E.Ln(X4)+F.Ln(X5)+G 0.93 0.93 0.90

Jafari and Babadagli, Geothermics, 2010


105/142


27

6 Ln(K) =A.exp(B.X1)+C.Ln(X2)+D.Ln(X3)+E.Ln(X4)+F.Ln(X5)+G.Ln(X6)+H 0.93 0.94 1.0


106/142


SCALING EQUATIONS FOR FRACTURED SYSTEMS

0.5

0.4e)


107/142


50 150 250 3500 100 200 300 400

0.1

0.3

0.0

0.2

0.4

Water Injected (Pore Volume)

Oi

lProduced(Po

reVolume

q=0.60 cc/min

q=0.50 cc/min

q=0.35 cc/min

q=0.20 cc/min

q=0.05 cc/min

q=0.02 cc/min

Colton Sandstone


108/142


0.5

0.4e)


109/142


100 300 500 7000 200 400 600 800

0.1

0.3

0.0

0.2

0.4

Time, minutes

OilProduced(Po

reVolume

q=0.60 cc/min

q=0.50 cc/min

q=0.35 cc/min

q=0.20 cc/min

q=0.05 cc/min

q=0.02 cc/min

Colton Sandstone

Babadagli, Tran. in Porous Media, Oct. 2000

Capillary

Imbibition

Transfer

During

Continuous

Flow

of

WaterinFracture

DYNAMIC CONDITIONS


110/142


Water

EFFICIENCY


111/142


Needtoknowtotalamounttobeinjected

DynamicexperimentsareneededBUT

ThermalismoreefficienteventhoughhigherCAPEXisrequiredanditisalwaysEFFECTIVEwithalsootheradditional

mechanisms.

0.5

0.6

20 min.

Berea Sandstone


112/142


0.2 0.6 1.00.0 0.4 0.8 1.2

Injection Rate, cc/min

0.1

0.3

0.0

0.2

0.4

OilProduced(PoreVolume)

2 min.

5 min.

7 min.

10 min.


0.5

0.6

175 min.

Aust in Chalk


113/142


0.05 0.15 0.25 0.350.00 0.10 0.20 0.30 0.40


0.1

0.3

0.0

0.2

0.4


15 min.

45 min.

60 min.

100 min.


0.5

0.4

0.5

Colton Sandstone


114/142


0.10 0.30 0.50 0.700.00 0.20 0.40 0.60


0.1

0.2

0.3

0.4

0.0

0.1

0.2

0.3


25 min.

60 min.

120 min.

225 min.

300 min.


1.0

0.8

x(OPF

M)

IW)

Berea Sandstone Experiments

Austin Chalk Experiments

Colton Sandstone Experiments


115/142


1 3 50 2 4 6

0.2

0.6

0.0

0.4


OilP

roducedFromMatrix

T

otalInjectedWater(T

Numerical Results

Critical rates for each sample.


3

4

in

Berea

Sandstone


116/142


10 30 50 700 20 40 60

1

0

2

CriticalRa

te,

cc/m

P k , (psi-md)c,max m

ColtonSandstone

Aust in

Chalk


1.0

1.2

Berea Sandstone

Austin Chalk

Colton Sandstone(O

PFM

)

IW)


117/142


0.01 0.10 1.00 10.00 100.00

0.2

0.6

0.0

0.4

0.8

O

ilProducedFromMatrix(

TotalInjected

Water(TI

Fracture Capillary Number, Nca,f

mc

fw

cafkP

kv

Nmax,

,


)(

Cos

vN wca CAPILLARY NUMBER :


118/142


From Abrams, SPEJ Oct. 1975

m

i

c k

SJ

P

)(cos max.

m

fw

VCfA

Av

capillary

viscousN

cos,


119/142


mwiSJ )(

)()()()(

)()/()527.1(

2max,

,

cmAmdkSJpsiP

cphrccqEN

m

m

m

wi

c

winj

VCf

m

m

m

wi

c

winj

VCf

AkSJ

P

qN

)(

max,

,

)()(

)(

)(

)()/()505.9(

2max,

,

ftAmdk

SJ

psiP

cpdaySTBqEN

m

m

m

wi

c

winj

VCf

FromPutraetal.,2001,SPE


120/142


Modelusedinthenumericalsimulationof

singlematrixoilrecovery

= 300 cp


121/142


(0.115cc/min)

o

300cp

L AYER 1

L AYER 2

LAYER 3 (Fracture)Injection

Production

2.5 ft

0.75 ft.(0.55 ft)(0.95 ft)(1.25 ft)

(1.50 ft)

0.75 ft.

(0.05 ft.)

1.00

0.80t=10 min.

ure(T

n)


122/142


0 4 8 12 16 201/FHTI (uL / ), dimensionless

0.20

0.60

0.00

0.40

t=30 min.

t=50 min.

m m

Critical FHTINormalizedTemp

eratu

EFFECTIVENESS

~

EFFICIENCY INJECTIONRATEstb/day

OPTIMUM

?


123/142


EFFECTIVENESS

:

Oil

recovery

/

time

EFFICIENCY:Oilrecovery/Steaminjected

?

DISCOUNTEDCUMULATIVENETGAIN

(DCNG)


124/142


1 MMBtu = 2.4 US $Discount Rate = 10 %

DCNG = Amount gained by OIL RECOVERY - Cost of STEAM

(only the cost of steam, no operational cost)

40000

50000

ain,

US

$ q=25 STB/day

q=60 STB/day

q = 100 STB/day


125/142


1 10 100 1000Time,days

0

10000

20000

30000

Discoun

tedcumulativenetga q 100STB/day

q=150STB/day

Continuousfracturecase

50000

40000

ain,

US

$

q=150STB/day

q=100

STB/day

q=60 STB/day


126/142


1 10 100 1000Time,days

10000

30000

0

20000

Discountedcumulative

netga

Continuousfracturecase

q=25 STB/day

B b d li T O ti St I j ti St t i f N t ll F t d


127/142


Babadagli,T.:OptimumSteamInjectionStrategiesforNaturallyFractured

Reservoirs,PetroleumScienceandTechnology,vol.18,no.34,375405,2000.

Babadagli,T.:EfficiencyofSteamfloodinginNaturallyFracturedReservoirsSPE

38329,67thSPEWesternRegionalMeeting,LongBeach,CA2527June,1997,665

675.

Babadagli,T.:

Effect

of

Fracture

Properties

on

Steam

Efficiency

in

Naturally

Fractured

Reservoirs,No:1998.020,7thUNITARInt.Conf.onHeavyCrudeandTarSands,2730

Oct.,1998,Beijing,China,pp:179188.


128/142


FracturedvsHomogeneous


129/142


fw kv

ImprovedModelingofOilWaterFlowinNFRs

mc, kP max fw

kv

3

1


130/142


mc, kP max fw kv mc, kP max310*127.1

orwi

wiw

SS

SSS

1

)1( nro Sk

m

rw Sk 22 ))/1)(log(1113.0()log( n 1863.0))/1)(log(3421.0(

2))/1)(log(0604.0()log( m 2554.0))/1)(log(2999.0(


131/142



132/142


ktt

A Practical Approach for Field Scale Performance Estimation of

Water Injection in Fractured Oil Reservoirs

2

mawL


133/142


2

Ltt

w

D

mawDk

2

max,

m

r

fw

mc

L

L

kv

kP

2

max,310*127.1

1

r

m

mc

fw

L

L

kP

kv

2

max,

2.01

rm

mc L

L

kP

q

Teflon heat-shrinkable tub

Matrix

Silicon

Plaxy glass core-holder

MISCIBLE


134/142


Matrix

MatrixFracture

Silicon

ISCO

Pump

Refractometer

Production Line

Heptane

Source

Core

Holder

TrivediandBabadagli,SPE100411

0.2

0.4

0.6

0.8

1

TotalOilP

roduced

(PV)

6 ml/hr

3 ml/hr

1 ml/hr

0.2

0.4

0.6

0.8

1

TotalOilP

roduced(PV) 6 ml/hr6 ml/hr

3 ml/hr

1 ml/hr


135/142


Gravity Effect

Gravity Effect -

Ultimate RecoverySlower rate - Minimal

Higher rate- Profound

Time Recovery

High rate : Faster/Lower

Slow rate : Slower /High

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5Tota

lSoluteRecovere

d(PV)

Total Solvent Injected (Pore Volume)

BSH-3 BSH-6 BV-3 BV-6

0

0 1 2 3 4

Total Solvent Injected (PV)BSV-1 BSV-3 BSV-6

0

0 50 100 150 200

Time (hr)BSV - 1 BSV - 3 BSV - 6

FDI=

High solvent injection rate : Most of the recovery is from the fracture

max,

,*

**

cm

wf

CafPk

vkN

om

sf

Dk

fvk

**

*)(**


136/142


Highsolventinjectionrate:Mostoftherecoveryisfromthefracturethroughviscousflowandrecoveryfrommatrixislowduetopoor

diffusioninto

matrix

higher

FDI.

Lowerinjectionrates:ThediffusiondominatestherecoveryLowerFDI.

HigherFDI:indicatesafasterrecoverywithmoresolventinjectionandpresumably

less

ultimate

recovery

from

the

matrix.

LowerFDI:Indicatesslowbutmoreefficientrecovery.Thismightyieldhigherultimaterecoveriesfromthematrix,theprocessbeingslowduetolowinjectionrate.

31


137/142



Horizontal Berea Sandstone

1


138/142


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

2 3 4 5 6 7 8 9 10

Flow rate (ml/hr)

To

talOilProducted(PV)

20 hrs 30 hrs 40 hrs 80 hrs


Horizontal Indiana Limestone

0.5


139/142


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

2 3 4 5 6 7 8 9 10

Flow Rate (ml/hr)

T

otalOilProduced(PV

)

10 hrs 20 hrs 25 hrs 50 hrs 70 hrs


Horizontal Aged Berea Sandstone

0.7

0.8

)


140/142


0

0.1

0.2

0.3

0.4

0.5

0.6

2 3 4 5 6 7 8

Flow Rate (ml/hr)

TotalOilProduced(PV)

10 hr 20 hr 35 hr 50 hr


0.5

0.6

0.7

tInjected(PV)


141/142


0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5 6 7 8

FDI

TotalOilProduced(PV)/Total

Solvent

om

sf

Dkfvk

***)(**


(NMFD)v/s(TOP/TSI)

37

Ng

ArPe

r

L

gDk

buN M

mmF

TFDM

*20

0.45

0.5

cted


142/142


R2= 0.8247

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.E+00 2.E+07 4.E+07 6.E+07 8.E+07 1.E+08 1.E+08 1.E+08 2.E+08

Matrix-Fracture Diffus ion Group (NM-FD)

To

talOilP

roduced(

PV)/TotalSolven

tInjec

(PV)

Documents

Fracture Characterization