[Holditch] SPE 025898 (Ning) Measurement of Matrix and Fracture Prop Naturally Frac Cores
Transcript of [Holditch] SPE 025898 (Ning) Measurement of Matrix and Fracture Prop Naturally Frac Cores
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7/25/2019 [Holditch] SPE 025898 (Ning) Measurement of Matrix and Fracture Prop Naturally Frac Cores
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Sochtvof
Pobolsum Eftninssr9
The Measurement of Matrix and Fracture Properties in Naturally
Fractured Cores
Xiuxu Ning,* Jin Fan, S.A, Holditch,* and W.J. Lee,* Texas A&MU.
SPE Members
owwfffhlf333, Scci.fy of pafrol~um Enolnaara,Inc.
This p par wao prepared for praaantatkmt tfte SPERockyMnlmtain Ragiond/Low PermeabilityReaarvolrsSymposiumheld in Denver,cO, U.S.A., April 12-14, 1993,
Thlapapar waaMacfad for presantaliomby n SPEProgram .smmittea Io fowingreview of informalkmcmfained m an abalracl submlnad by the author(s).Contentsof the p?.par,
aaorawntod, havanot MO roviawodby ha Soclefyof PolrolaumEnginaeraandare subjacl to e=arrootlony the author(s).Tfw -. vial, es preeanwd, dooanot necessarilyreflect
~Y P@t~n of tha 60Cti of petrtium EMraara, Itsoffkara, ormembers.PaParspreaantodat SPEmeetlngaaresutrjactto pub
on reviewby EditorialCommitteesof tha Society
ofPatrolaumEnglr@ere,Parmtalbn to copyISroatrictuf to an abatmctofM morethan300words,Illumratkmsmeynotbac@@, Thaabstr-:t shouldcontaincorwpic,ousacknowledgment
of Marc and by whom Ifw papa lapmsenlsd. Writs Librarian, SPE, P,O, Son8S333S,FNchardsen,TX KOS3-3S3S,U.S.A.Tale% 1S3245SPEl)T.
ABSTILMX
This paper deseribes a new )abora?cr--
tcchnique to evaluate the properties of a naturally
~ low permeability ewe sample, We
speeifleallydetermine (1) the porosityof the mam
(2) the permeabilityof the matrix (3) the effective
width of the kturea, and (4) the permeabilityof the
fhemrea.
Newlaboratoryequipmenthas been designed
and eonstmted to conduct pressure pulse tests in
either a homogeneousor a fkaemed cwe sample,
Analyticalsolutionshavebeendevelopedto modelgas
flowin a fraetud coresampleduring a pressurepulse
test Amwltomatichistorymatchingprogramhas been
developedto analyzethe Morstory measuredpressure
transientdata using the analyticalsolutions,The new
teehnique has been used to measure the matrix and
fracture properties in tweive naturally fractured,
DevonianShaleems,
The techniquewe developedin this research
is new to the p2,mleum industry, 02r laboratory
equipmentis unique,and the analyticalsolutionshave
not been published in the literature, With this
teehnique,weean measurematrixpropertiesas lowas
10-9 rnd, This is a significant step forward in
permeability measurement beeauae the lowest
permeability that most existing laboratories can
measureisabout 104 millidarcies.
INTRODUCTION
Oil and gas preduetion from naturally fractured
reservoirs is an important source of energy
throughouttheworld.Petroleumengineersneedto
improve their understanding of naturally fractured
reservoirsto betterpredietoil and gas flow rates and
resews. The poroaities and permeabilitieaof the
matrix and tictures are key an meters used in
reservoir simulation modeis to P Act the
performanceof naturallyfracturedreservoirs.
The moat reliable and direet way to
determine the formation properties is to cut a core
from the reservoirand to measure the propeties in
the laboratory. However, conventional laboratory
methodscannot be used to measure the matrix and
fracturepropertiesin a naturally fracturedcore. If a
core sample eonta m a natural fmcture, existing
laboratorymethmts can only measure the effeetive
permeability of the core sample. The effective
permeabilitywill be the thicknessweightedaverage
permeabilityof the matrix and the fractures. The
speefic properties of the matrix and the natural
fractures can not be distinguished using existing
laboratorytechniques.
In 1990,Kamathefal, 1 first showedthat the
pressufetransientlxhvior of a pressuretransienttest
in a fractured core was different from that in a
homogeneous core if the equipment is properly
designed Theycalculatedthe pressure responsesfor
homogeneousand fractured cores using a finite
differencemodel,Theyconductedmeasurementswith
an ti~cirdly split sandstonesampleandmatchedthe
experimentaldata with numericalsolutionsto obtain
the fractureandmatrixproperties,
Hopkins et al , 2 conducted an extensive
numerical study on the laboratory pressure pulse
testing for evaluating low permeability, naturally
fractured core samples, They performed sensitivity
Referencesand illustrationsat endof paper,
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THEMEASUREMENTFMATRtXANDFRACTUREROPERTiES
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studies varying key parameters including core
geometry,fracture properties, matrix propwtiesand
vesselsizes. lhey also investib3tedthe effixts of the
positionof a fkactureand the numberof fracturesin a
cm sampleon the essure transientbehavior.
In this research wehavedevelopedJ unique
Iaboratoxyechniqueto determine(1) the porosityof
thematri%(2) the permeabilityof the matri~ (3) the
effective width of the iiactures, and (4) t.iw
permeability~fthe fractures,in a naturallyfractured,
low permeability core sample. A pressure pulse
methodis used in the new techniquewith gas as the
flowing medhru. With our new technique,we can
measure matrix permeabilities as low as 10-9
millidarcies, This technique a so enables us to
analyze homogeneouscores that have permeabilities
toolowto measurewithconventionalmethods.
PAUNCXPLES
Figure : is a schematicdiagram for the pressurepulse
measurement.Thecoresampleis loadedin the rubber
sleeve of a core holder with which a confhdng
pressurecanbe appliedaround the sampleand a pore
pressurecanbe applied insidethe sample.There is an
upstmun vohune (Vu)at one end and a downstream
vohune(V~)at theotherendof thesample.
To conducta pressurepulse tes. q confking
prcaus (pC)is appliedfromoutsideof thesa...,. Ad
a system pressure (@ is applied in the upstream
volume,thedownstreamvolumeand the porespaceof
the sample,The threevolumesare filledwithgas and
the pressure in the system is allowed to reach
equilibriumbeforethe test. To start the test, a small
volumeof gas is quicklyinjectedinto Vuto genera:: a
pressurepulse in the upstreamvolume.As gas flows
fromthe upstreamvolumethrough thecore sampleto
he downstreamvolume,the pressurein Cudecreases
and thepressurein Vdincreases.Thepressuresin the
upstream volume and the downstreamvolume are
recordedas a imctionof timeandanalyzedafterwards
todeterminethe propertiesof thecoresample,
Fig, 2 presentsthe comparisonbetween the
pressure transient cwves for a fractured core and a
homogeneous core, Fig, 2 shows that for the
homogeneouscore, the upstreamvolumepressure(pU)
decreasesand the downstreamvolume pressure (pd)
increases with time until they reach the final
equilibrium pressure, For the fractured core,
p
decreasesandPd increaseswith time during the early
portion of the test, As time progresses,PMand pd
comwrgeto a same pressurecalled the convergence
pressure, The time at which pu and Pd starts to
converge is called the convergence time Atler the
convergence time, the pressures in Lhe upstream
volumeand the downstreamvolumedecreasetogether
until theyreachthe finalequilibriwnmsmre.
Quaiitativeiy,the time required to reach the
convergencepressureis dominatedoythe conductivity
of the fracturq the time requiredto reach the final
equiiibiiumprewwreis dominatedby the permeability
of the matrix, and the magnitude of the fiuat
equilibriumdimensionlesspressure is dominated by
the porosityof the matrix. Therefore,we should be
abie to determine these parametersby analyzing the
laboratorymeasuredpressurepulsetest data. Although
therearemanywaystodo this, the mostaccurateway
is to match the experimentaldata with tht iinalyticat
soiutions.
ANALYTICAL SOLUTIONS
Physical hfodcis
Toderivethe anaiyt.icaiexpressionthat describesgas
flow in a hctured core sampie, we first need to
simpli~ the
system
into an idniized physicalmodei.
We can then study the gas flow behavioi in the
simplifiedmodei. Fig. 3 illustrates the shapes and
dimensionsof a real core sample=4 the simplified
model.The real sampleis a cyiinderwith length L,
anda diameterD. There is a fmcturerunningthrough
the middleof the cylinder.The fracturehas a width
h~a iengthW,anda depthL. The simpiifkd modeiis
a paraileiepipedwith iength
L,
width
W,
and height
h,,,+h~ The fracturein the simpiitledmodei has the
same dimensions as tiwt in the real core. The
simplifiedmodeihas the samecress xxtional area as
that ofthe realsample.
Fig 4 illustratesgas flow in the simpiitied
modelduring a pressurepulse test, At time zero, the
uwssurein the downstreamvolume,the fracture,and
the matrix is at the initial systempressure(@, and
the pressurein the upstreamvoiume is at the puke
pressure(PPUI).Whentime is greaterthan zero, gas
flowsfromthe upstreamvoiumeinto the fractureand
the matrix, Somegas flowsthroughthe fractureinto
the downstreamvoiumeand some flowsthrough the
fracture into the matrix, Gas sise flows from the
downstreamvolun?:into the matrix.
Our objective is to derive the analytical
expressions describing the pressuw transient
behaviors in the upstream voiume and the
downstreamvoiumefor the physiwdmodeidescribed
above. To do this, we first neei to estab%h a
diffusivity equation in the matrix, a diffusivity
equationin the fracture,a materialbalanceequation
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SPE2S898 NING,X.,FAN,J,,HOIXNTCH,,A.,andLEE,W.J.
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in the upstream volume, and a material baianee
equation in the
dwnstmm volume. Since the
boundaryconditionsof the differentialquatiom are
rciam we need to solve the systemof differential
cquaticms simultaneously to obtain the analytical
solutions.
Early Time Approximate Solution
The differentialequation systemsand the definition
of the dimensionlessParametersare resented in the
~anot be written in expiic +form, thereforewe need
to make assumptions to obtain the approximate
solutions.If the transmissibilityof the matrix is much
smah than that of the fracture, i . e., ~~m
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THEMEASUREMENTFMATRIXANDFRACTUREROPERTIES
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~ N.4T &by ~c~D CORES
SPE25898
Equations1- 3am valid a+y at the early timeof the essure puke teat.At the late time, the solution
willnotapplybecausethe assumptionthat thegasflowintothe rnmrixfromthe xdirection doesnot interferewith
the@flow fromthez-directionis notvalid.
Late Time Approximate Solution
The approximateexpressionfor the pressuresin the upstreaLvolume(or the dowmnreamvohune)at the
latetimeofa pressurepulsetestis obtaiwi as follows:
PppDe
~=
[r)
. ...... ,.,., .............4.................s...... .....................(4)
~th *KA
+ C&,
w
Eq. 4 ean be
invertedinto realtimedomainas foilows:
PpDe =
PPPDS
where,yn are the rootsof
tarlyf=-
&CV
, ........................(6)
/Kh@n
Eqs, 4-6 are validonlyat the late timesofp~essurepulsetest,
In deriving the mudytieal soiutions, we
assumedthat the core samplehad a singie fracturein
the middle,But the reai coresamplesused in pressure
puisetestmayhavea fractureawayfromthemiddieof
the core or have muitipie fff ;tures. We ean still
descrih these core sampies using the simplified
physicalmodeiswithappropriatemodifieations3,
Comparison Between the Anaiyticai soiution and
Numerical Simulation
We have deveioped a l:~ite difference modei to
simulatethe pressurepulsetcs, to checkthevalidiiyof
the analytical soiution, Table 1 summarizes the
~fs of the~~ SSMpleand theequipmentused
inboththe numericaiad theanalyticalmmieisforthe
exampleeaieuiationsina fracturedcore,
....................(5)
Table 1ParametersUsedin ComparisonCalculations
fora FracturedCore
CoreLength 2.0 in
CoreWidth
1,5in
MatrixThickness
1,1781in
FractureWidth
0.01 in
MatrixPermeability
1.0x 1W5md
FracturePermeability
10.0md
. SystemPressure
I
1000psi
PulseRessure
40psi
7
~ Fiuid
I
iieiium
I
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Fig. 5 presents the
simulation and the analytical
resuhs of numerical
solution. The dashed 12. A data acquisition system including a data
acquisitionboardanda pert>iudwmputer.
DATAANALYSES
Sensitivity
Study on Pressure Transient Curves
To develop the data analysis method, we first
conductedsensitivitystudies to investigatethe effects
of matrix and ftacture propertieson the shapesof the
pressure transient curves. The core and equipment
**K~eters used in these calculationsare summarized
in Table2.
Table2 ParametersUw.din SensitivityStudies
.
lines representthe numericalsimulationand the So :d
lines represent the analytical solution. The figure
shows that *Ae finite diffemce modjl and the
analytical solutionagree very wdl at the early time.
The slight difference between the ~urnerical
simulationand the analyticalsolutioiiat the iate time
is probablycausedby the roundofferrors in the finite
differencesimulation,
Laboratory Equipment
We have designed and conmwted laboratory
equipmentto conductpressurepdse measurementsin
either fractured or homogenmus, low permeability
cores.Fig. 6 is a schematicdiagramof the laboratory
equipment we designed and constructed in this
research.The equipmentincludesthe followingmain
components:
1.
2.
3.
4.
5.
6.
7,
8,
9,
An insolation chamber that houses the criticat
componentsto preventthe testfrombeingaffected
bythechangesin ambienttemperature;
A core holder that holds core samples during a
pressurepulsetest;
A gas accumulatorthat suppliesgasto the system,
A referencepressureaccumulatorthat providesa
constant reference pressure for the differerv:al
pressuretransducers;
A pressure regulator that controls the system
pressure,and generatesthe pressurepulse in the
upstreamvolumeat the beginningofa test;
A hydraulic pump that provides the confining
pressureto thecoreholder;
Tubing and valves to connect the different
components;
Two differentialpressure transducersto measure
the diffixentialpressuresin the upstreamvolume
and the downstream volume relative to the
referencepressure;
A referencepressure transducer to
me sl ie
the
pressurein the referencevolume;
10, A cottfhting pressure transducerto measure the
pressureof theconfiningfluid;
11, A thermal couple to measurethe tcmpemturein
the upstreamvolume;and
55
, CoreLength(L)
2,0 in
CoreWidth(W)
1,5in
MatrixThickness(h.)
1.1781in
Fracture Width(hd _0.0001in
MatrixPermeability(km)
10-5,10+, 10-7,
10-8,md
Fracturel%meability(k~
1, 10, 100,
1,000md
MatrixPorosity($ ~)
2%4% 8%
16?40
Fracture Porosity($ ~
10? 50+ 0
UpstreamVolume(Vti)
3.0 cc
DownstreamVolume(V~)
2,0 cc
Ftuid Helium
, SystemPressure(pi)
1,000psi
~ PressurePulse(Pm,,I)
40psi
Fig, 7 presentstheeffit ofmatrixporosityon
the shape of the pressure transient curves,
Dimensionlesspseudopressurefor matrixporositicsof
2%, .Wq8%, and lL% are plotted versus time, with
otherparametersbeingconstant,Thefigureshowsthat
as matrix porosity increases, the final equilibrium
pressuredecreases,
Fig. 8 presents the etlxt w matrix
permeabilityon the shape of the pressure transient
curves. Dimensionless pscudopressurcs for matrix
pcrmcabiliticsof 10-5$104, 10-7, and 10-8 md are
plotted versus time, with other parameters being
constant, Fig, 6,2 shows that as matrix permeability
increases, the tim~ required to reach the final
cquilibriurnpressuredecreases,
Fig, 9 presents the effect of fracture
pcmtcabili~ on tic shape of the pressure transient
curies, Dimensionless pseudopmsums for fracture
Pemi:abiliticsof 1, 10, 100,and 1000md are plotted
versus;ime,withotherparametersbeingconstant,Fig.
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INNATURALLYtUCTUREDCORES
SPE25898
6,3 showsthat as fkacturepermeabilityincreases,the
convergencetime &cremes
ti,cause the rate of gas
flow from the upstream volume to the downstream.
volume is dominated by the condrmivity of the
fracture,
Fig. 10presents the etl%.tof porosityin the
fkactureon the shape of the pressuretransientcurves.
Dimensionlesspseudoprwures for fractureporosities
of 10% and
5 WO are
plotted versus time, with other
parametersbeing constant, We can see that the two
pressure transient cwves essentially lie together,
indicatingthat the changein fractureporositydoesnot
affixt the shape of pressure transient curves
signifkantly. This is becausethe pore volumeof the
fracture is negligible as compared wkh the pmre
volume of the matrix the upstream volume, or the
downstreamvotiume,
The conclusionsfrom the sensitivitystudies
can be summarizedas follows:
1.
2,
3.
4,
Thefinal equilibriumpresnureis dominatedby the
matrixporosityof thecoreSarnplc,
The time required to reach the final equilibrium
pressm is
dominated
by hematrix permeability
of thecoresample;
The time required for the upstream and the
downstreampressurestoconvergeisdominatedby
the fractureconductivity;and
The si~ageof the Dressuretransientcurvesare not
sensitiveto theporosityof the fmcture,as long as
the pore votumeof the fractureis much smaller
than the total systemvolume.
Automatic History Matching Program
Basedon the sensitivitystudies,wchavedcvclopcdan
automatichistorymatchingprogramto determinethe
matrix and fracture properties,The history matching
program matches the Iaboratoty measured prcssurc
transient data with the analytical solution. An
optimizationroutineis usedto find Ihccombinationof
the unknown variables that yields the best match
betweenthe laboratorydataand theanal~licalsolution.
The programcm determinethe followingparameters:
1,Matrixporosity;
2,Matrixpermeability,
3, Fracturepertmxtbiiity;and
4. Effectivefracturewidth.
The effective fracture \vidth and fracture
permeability are dctcnnined usiog the fracture
Conduaivity (k
fhf )
and the relation between the
w dth of an open slot and its permeabilityas shown
bellow:
kf
=54.4 xl(?h; , .,.,,.,..,, .,..,..,.,.
(7)
where,kis in millidarciesand ,:~isn inches.
Byusing this equation,we are assumingthat
the fracture porosity is essentially 1000A.T xwcfore,
the fracturewidth obtainedthis way is the etfective
heightas if the fkactureis completelyot-~ The actual
fracture height should be greater h..
is value
becausethe fizx~res are usually partially ,illed with
minerals
andior
other cementing materials,
Accordingly,theactualfracturepcnneahilityshouldbe
less than the value given by the history matching
programwhich is determinedbased on the effective
fracture width. Howmer, the fracture conductivity
(kA$ given by
the
history matching program should
k correct because the early time pressure transient
dataaredominated6ythefractureconductivity.
RESULTSOF MEASUREMENTS
ARerthe laboratoryequipmenthad been cxtstructed
and calibrated,we first tested the equipment using a
homogeneous Berea Sand core sample. We then
created a fracture in the sampie and perfrtned
measurementsin the artificially fractured sample to
test the accuracy and the repeatability of the
measurements,After the equipmenthad been tested.
we performed pressure pul~ measurements with
hvehc naturallyfracturedDevonianShalecores.
Measurements with a HomogeneousBerea Sand
Core
To test our new laboratory equipment, wc fiI$(
performedseveralpressurepulsemcasiircmcntswith a
homogeneousBerea Sand core sample from WCII
AshlandFMC tIO.The laboratorymeasuredpressure
transient data were analyzed using the history
ma chingprogram The porosityof the sample was
determinedto be6,8 I
,4?40
which is the sameas lhat
measuredby the Coro Laboratoriesusing a helium
porosimcler,The Wrmcabilitywas dctcrmincd o be
0,0010*0,0001 md,
Mcastmcmcntswith the Artificially Fractured Core
Afterthe measurementsusing homogcncou$core, .w
artificiallycrackedthecore intotwopartsand then put
the parts back together,
We performed wvcral
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pressurepulse tests in the artificiallyfracturd core.
The results of data analysisfor the fiaetured sample
along with those for the homogeneoussample are
tabulatedinTable3.
Table3 ResultsofMeasurementswith
BereaSandCore 4
I Homogeneous
Fractured
Sample
I
Samnie
Porosityof Mntrix 6,8M).4 6.514.4
Permeabilityof ] O.OO1OMMM610,0013* ~
Matrix (red)
I
O.NM1
Efkctive Widthof NIA
3,0M.06
Fracture(j@
Permeabilityof
NIA 760330
Fracture(red)
I
I
I
Table 3 showsthat the pnrosityof the matrix
determined with the
rtitlci lij fracthd
sample is
veryC1OSCo that measumdwith the samecoresample
beforethe fhcture is created.This exampleindicates
that the new techniquedoes yield the correctmatrix
porosity,The permeabilityof the matrix determined
fromthe fractmd sampleis slightlyhigher than that
determinedbeforethe fkacmrewascreated.
To check the repeatabilityof the prwsure
pulsemeasurements,wegraphedthe pressuretransient
c~rvesfim two wparate tests togetherin Fig. 11. In
this figure, dimensionless pressures were graphed
versustime,with the solid lines representingthe data
fromtestNo,3 and thesquaresrepresentingthedata
fromtestNo. 4. Wecansee that the pressuretransient
data fromthe twote~tslie together,Threfore, we can
conclude that the measurements with the new
%uiprnentare repeatable.
Measurements with Naturally Fractured Devonian
Shale ~OtW
Using the new technique developed in this
rese=xh, we %ve performed measurements using
twelveDevonianShale cores. The samples are from
weil FMC 69whichwas eompletcdin the Devonian
Shale fcmnation of the Appalachian. Tke well is
heated in Ashlandfieldin easternKentucky,For the
12DevoNanMale coresampleswe test@ a pressure
pulsetestlastedfor 14to 30hours,Sincethe test time
is very long, any leaks from the equipment during a
pressurepulse test can cause significanterrors in the
results of measurement.Leak eompensatkmmethods
have been developedto correct the raw pressure
transientdata3,The correctedpressuretransient data
were then analyzed using the history matching
progmm to dc:ermine the matrix and fracture
properties.
Table 4 summarizes the mults of
measurementswith the 12DevonianShale cores.We
can seefmm Table 4 that the matrix porositiesrange
from 1.5?40o 4,5?4%he matrix permeabiliticsrange
ftom 4X10-9 to 8xIW8 millidarcies, the fracture
pcrmeabilitiesrage from 8 to 2%6 millidarcies,and
the effective fracture width rages from 0.3 to 5.5
microns.To our knowledge,no laboratoryI?chnique
hasbeenpublishedtomeasureperrneabiliticsas lowas
10-9millidarcies,
Table4 ResultsofMeasurementswithDevonianShaleCoresfromWellFMC 69
Core Matrix
flatrix Fracture
Fracture
Numberof
Name
Porosity Permeability
width
Permeability
Major
(Ye) (red) ( ~m)
(red)
Fractures
.
5A 2.53
8,14x 10-9
0,99
75,2
10
8C 4,44
4.05
X1O-8 1.09
99,3 4
16C 2.05
4.56x 109
1.00
83,7
9
18?3 4.26
2,14X 10-8
2.42
492,1
3
21D 3439
4.91x 10-9
1,13
108,3
9
22A 2,27
5.89X
1W9
0.39
13,1
,$?
23B 1.86
1,17x 10-8
1.81 277,5
4
27A 3.10
2.00x 10-8
0,47
18,7
5
29B 1,59
5,87
X
10-8
0,76
48,1 1
31B 3,18
4,30x 10-8
5,52 2566.0
1
,
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THE MEASUREMENT OF MATRIX AND FRACTURE PROPERTIES
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SPE 25898
Noticethat the fkacturepermeabilityand the
effectivefracture width are determined assuming
thatthefracturesreopen wuh a pormity of 100Yo.
The actual fracture width could be greater than the
value given here because the fractures may contain
minerals and arnenting materials and may not be
completelyopen.Thefhcture conductivity(k ~ is the
~a we actuallymeasureand shouldbe correct
forall coresamples,
As an example, Fig, 12 presents the
experimentaldata ano the resultsof historynw chfor
core 5A. This core contains 10 major ikactures
running through it, The gasporosityof the matrixwas
determinedtobe 2,53% thepermeabiliooftLe matrix
be 8,14 x 10-9md, the av-mge fracturepermeability
be752 m~ and tlwaverageeflbctivefracturewidthbe
0,99 microns. Fig, 12 shows that the laboratory
measumd pressure trrmaientdata and the analytical
solutionmatchwell,
Corn- ofMatrixmrodtie8Mea8urad
with
Duferent Method8
Tocheck thewmracy of the
measurementswith our
ncwtechniqw theendtrims of thesarne Devonian
Shale co- were sent to the Core Laboratoriesin
Houston to measure the porositieswith a difkrent
method.At* Core bboratori~ the end trims were
crushed into srnali pieces. Oil and water were
exracted fkoin the crushed pieces, The bulk volume
was measurd using the Archimedes principle. The
grain volume was measumd with helium using the
Boyleslaw.The total porosi~ of the matrixwasthen
determined ftom the grain volume and the bulk
volume,From the total porosityand the amountof oil
and gasextractedfroma
core
sarnplc,we can compute
the gasporosityof themairix.
Table 5 presents the comparisonbetweenthe
natrix porosity to gas measured in our Iaboratov
using the newmethodand tiose measuredbythe Core
Laboratcms, For most core samples,the gas porosity
values mewured in our laboratoryare Nightly lower
than thoseobtainedby the Core Laboratoriesbecause
we conducted the measurementsat a net confinihg
pressureof about 3000 psi while Core Lab measured
the poroaitieaat the atmosphericpressure, For core
Sarnpl- with theextremelylowmstrix perrncabilities,
the agreement between the two laboratoriesis very
good. Therefore, we can conclude that our new
Iabwstorytechniquecan estimatethe matrix porosity
accurately,
Table5 CorsparisonBetweenthe PorositiesMeasured
byTM and ThoseMeasuredbyCorrLab
I GasPorosity
byTAMU@ GasPorosity
Core
3000psiNet
byCoreLab@
Name
Stress
AmbientStress
5A 2,53 1,93
8C 4.44 4.51
~6C
2,05 2.51
18B
4.2t. 4,92
27A
3.10 3,57
29B 1.59 0,43
3lB
3,18 0.39
33B
3,91
4.14
39A
1,73
3,72
CONCLUS1ONS
The followingconclusionsare pertinentbased on
workcompletedin this research:
the
1.
2.
3,
4,
A newlaboratov techniquehas beendevelopedto
measure the pr&wrties-of the matrix ti the
fracturts simultaneouslyin a naturaily fmcturwL
low permeabilitycore, Matrix pennealilities as
low as 10-9 millidarciescan be measuredwith
thistechnique.
A set of new analytical solutions describinggas
fSown fracturedcoresduringa pressurepulsetest
hasbeendevelcpcd.Theanalyticalsolutionsagree
with finitediffwme simulation,
Laboratory equipment has been designed and
constructed to
perform
pressure pulse
measurements in either a homogeneous or a
fractured core sample, The laboratory meastmd
pressuretransientdata and the analyticalsolution
matchwell,The resultsof measurementswith the
newequipmentare repeatable.
An automatichistoiymatchingprogramhas been
5,
562
developed to analyze the laboratory mdaaured
pressure transient data using the analytical
solutionsto determine(a) the matrix porosity,(b)
the matrix permeability, (c) the fractute
permeability,and (d) theeffectivefracturewidth,
trix ndfiwure propertiesof twelvenaturally
fractured Devonian Shale cores have been
rnwured succea@ly using the new technique.
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7/25/2019 [Holditch] SPE 025898 (Ning) Measurement of Matrix and Fracture Prop Naturally Frac Cores
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SPE 25898
NIbKi, X., FAN, J,, HOLDtTCH, S, A,,
and
LEE, W, J,
9
The matrix porositiesdeterminedusir: the new
techniquecomparefavorablywith thosemeasmd
by the Core Laboratoriesusing the crushed end
trims fromthe samecores,
NOMENCLATURE
A
~ d
Cy
Ctm
Ctu
,~u)
hj
hm
h
me
k
4
Lm
Le
Pd
Pj
Pi
Pm
ppD
Ppd
PpDti
gG
Ppl%?
PpDe
PpDf
PpDf
PpDm
PpDm
PpDu
Pplh
Crosssectionalarea of c o[~ sample,tt2,w
Tots compressibilityin downstreamvolume,
l/psia
Totalcompressibilityhr fracture,l/psia
Totalcompressibilityin matrix, l/psia
Total compressibility in upstream volume,
l/psia
Dimensionlessgroupin Lapkwedomain
Widthof fracture,ft
mch~ of ~~~ R
Eq\Jvalentmatrixthicknessas definedin Eq,
4.41, a
Permeabilityof fracture,md
Permeabilityoftnati md
LengthofcoreSamp eft
Length of Me time equivalent model as
defkd in Eq. 4.42,ft
Pressurein bwnstmm volume,psia
Pmsure in tlacture,psia
Initial systempressure,psia
pressurein matrix,psia
Dimensionksspseudopressure
pseudopressure in downstream volume,
psia2/cp
Dimensionlesspseudopressurein downstream
volume
Dimensionlesspseudopressurein downstream
volumein Laplacedomain
Dimensionlesspseudopressurein equivalent
volume
Dimensionlesspseudopressurein equivalent
volumein Laplacedomain
Dimensionlesspseudopressuren fracture
Dimfmiordess pseudopressurein fracture in
Laplacedomain
Dimensionlesspseudopressuren matrix
Dimensionless pseudopressurein rnatzix in
Laplacedomain
Dimensionless pseudopressure in upstream
volume
Dimensionless pse~opressure in upstream
Pseudopressure in equivalent volume,
psia2/cp
Pseudopressuren fracture,psia2/cp
Pseudopressureat initi: condition,psial/cp
Pseudopressuren matrix, sia2/cp
?
Pseudopressurepulse,psia T
Eqttivalentpseudopressurep~lse,psia2/c
5
seudopressuren upstreamvolume,psia Icp
Pul= pressure,psia
Pressurein upstreamvolume,psia
Time,sec
Dimensionlesstime
Laplacevariable,dimensionless
Downstreamvolume,ft3
Equivalentvolumeas definedinEq. 4.40,ft3
Porevolumeof the fracture,ft3
Porevolumeof the matrix, f13
Upstreamvolume,ft3
Widthofphysicalmodel,fl
Distanceinx-direction,fl
Dimensionlessdistancein x-direction
Distancein zdirection, ft
Dimensionlessdistancein zdireetimr
Fractureto upstreamvolumestorativityratio,
dimwiotdess
Pore volume to upstream volume storativity
ratio,dimensionless
Porosity,fraction
~omsifyof fmcmm,
f~ction
Porosityof matrix,fraction
Downstream volume to upstream volume
storativityratio,dimensionless
Matrixaspectratiosquared,dimensionless
Equivalent length to actuai Icngth ratio,
dimensionless
Equivalent height to actual height ratio,
dimensionless
Matrix to fracture transmissibility ratio,
dimensionless
Viscosity,cp
Ti~,ie
averaged
viscosity+omprcssibiiity
product,cp/psia
Time averaged viscositycompressibility
productin downstreamvolume,,,,,,.,cp/psia
=Time averaged viscosity-compressibility
productin equivalentvolume. ,.,,,.,,,cp/psia
~Cf f Timeaveragedviscosity+ompressibility
productin fracture,cp/psia
volumeinLaplawdoItin
563
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THE MEASUREMPIT OF MATRIX AND FRACTUKE PRCFERTIES
IN NATURALLY FIUCTURED CORES
SPE 25898
Timeaveragedviaco$ity.compressibility
produ~tin matri~ cp/paia
Timeaveragedviscosity-compressibility
productat referencepre5iure,cp/psia
Timeaveragedviscosity-compressibility
productin upstreamvolume,cp/psia
VissosityN referencepressure,cp
Matrixto fracturestorativityratioas defined
in Eq,4,32, dimensionless
Downstreamvolumeto referenceviscOsity-
compressibilityratio,dimensionless
Equivalentvolumeto referenceviscosity-
compresaibilityratio, dimensionless
hcture to referenceviscosity-mnpressibilily
ratio,dimensionless
Matrixto referenceviacoaity-mpressibility
ratio,dimensionless
Upstreamvolumeto referenceviacosity-
compreasibilityatio,dimensionless
Rootsof Bq 6, dimensionless
Fquiva entvolumeto rture volumeratio,
dimensionless
REFERENCES
1.
2.
3,
Kamath,J,, %yer, R, E,, and Nakagmva,F N ,:
Characterize.Jn of Core Scale Heterogeneities
UsingLaboratoryPressureTransient paperSPE
20575 presented at the 65th Annual Technical
Conference and Exhibition of the Society uf
petroleumEngineers held in Ncw Orleans, LA,
Sep.23-26,1990,
Hopkins,C,W,,Ning,X,, andLancaster,D, E,:
Reservoir Engineering and Treatment Design
Technology =
A Numerical
Investigation of
LaboratoryTransientPulseTestingfor Ewdusting
Low Permeability, Naturally Fractured Core
Samples, a Topical Report (Jan, = June 1991)
submitted to Gas Research Institute, 8600 West
Biyn Mawr Avenue, Chicago, IL 60631, GRI
contract No, SOS6*23-1446, Recipients
Aaxssion No,GRI.91/03S0,
Ning, X,:
The Mettsurcmcnt of Matrix and
Fracture Properties in Naturally Fractured Low
PerrneobiMy Cores Using a Pressure Pulse
Mtth&
Ph.D. dissertation TI..WS A&M
University,CollegeStation,TX, (Dec. 1992)
ACKNOWLEDGMENT
The authorsacknowledgeMeridianOil, GRI, and the
PetroleumEngineering DepartmentC?Texas A&M
Universityfor the
financial supportto thb
resear:h,
APPENDIX
rz this appendix,we present the differentialquation
systemsdescribinga pressurepulse test in a ikactured
sore sample,
Detaih+d derivations have &en
documentedbyNing3arxicannotbe includedheredue
to the spacelimitation,
Partial Differential Equatioo System
By applyingthe continuityequationand Dar@s law,
wc get the system of differential equations for a
pressurepuke test (refertoFig. 4) as follows:
Thediffusivityequationforgas flowin the fractureis
,
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7/25/2019 [Holditch] SPE 025898 (Ning) Measurement of Matrix and Fracture Prop Naturally Frac Cores
11/15
*
.
SPE25898
NTNGPX., F/lB , J., ItU21iC H, S, A,, andI.EE, W, J,
11
The initialconditionis
Ppm (~.o) = Ppi, (A.6)
The boundaryconditionsare
Ppnr(W)=Ppd(O
, ,,,,.,,,,,,,,,,.,,,,(A,7)
Ppn+) = Ppj+,i), o.c.o,..,,..A,9)
[
ppm
and -
az ,=0 = 0
. ,,,4,,,,, ,,,,,,.,,,,,,.(A,1O)
The differential equation for materialbalance in the
downstreamvolumeis
.....(A. {)
The initialconditionis
Ppd (o)= Ppi
,.,,,.,,,,,,., ,, .,, ,.,,,,,,
(A,12)
The differenualequation for materialbalance in the
upstreamvolumeis
[ , [ 3..:
,,,,,,(A,13)
The initialconditionis
Ppu(O =
Ppp
,,, ,,, ,,, ,,, ,,, ,,,,,,, ,,,,,,
(A,14)
In Eqs, A,l, A,5, A,ll and .4,13,
pCt is
a
t~
averaged vixosity-compressibility product
~[b;~hisdcfin~
3S
where, j = j
m u d e
with
J= inthefracture,
m = in thematrix,
u = in theupstreamvolume,
d = in thedownstreamvolume,and
e = in theequivalentvolume,
The integrand (~f ) is evaluatedat the VOIUmetdC
averagepressurein the correspondingvohe at time
r,
Definition of DimensionlessParameters
To simpii@the differential equations into
dimensionless fo~ we define the following
dimensionlessparameters:
J?knensionlesspseudopressure:
Ppj - Ppi
PpDj =
j F d, $ m, u,
Ppp - Ppi
(A 16)
Dimensionlessime:
7,324 x10-8kft
11)=
,
,,,,,,,.,,,,,(A,17)
$jq)l?
Dimensionlessdistances:
x&
1.
,
,1,.,, ol, ,,l,l, t,.,,, ,,, ,,, ,
,4,,,,,,,
(A,18)
Matrix to fracturestorativityratio:
@f~@f
566
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12
THE MEASUREMENT OF MATIUX AND FRACTURE PROPERTIES
LNNATURALLY FMCTURED CORES
,
SPE 25898
Matrixto fracturetransmissibilityratio:
~ =
Ld L
kf hf
) .,,*,,.,.,,.,,,..,,,,,,,I. ,,,.,,
A,21)
Matrixaspectratiosquare+;:
Fracture to upstreamvolumestorativityratio:
Jfcq
a =
vu%
v ,,,., .,, ,, ., ,. ,,, ,. ,, ,., ,. . . . . . . ..
(A,23)
DowWmam volume to upstreamvolumestorativity
ratio(originallydefinedinChapter111):
~= j %J
,..,~., ,,..,,,.,,~,,~ .O,.. ..,,,.
(A.24)
u
Viscosityomprcaaibilityatios:
q
{j= ~,
j *J m, u,,d, e , (A.25)
where, j= in thefkture,
m-inthematri%
u-
in the upstreamvolume,
d= in Medowns-m volume,and
e = in the late timeequivalentvolume,
Using these dimcnsionkxs parameters, we
can rewrite the differential equation system
describing gas flow in fractured cores in
dimensionlessform, If wcassumethat at early times,
gas flow into the matrix fkomthe upstreamvolume
and the dwn streamvolumedoes not interferewith
that flom the fracture,wecan solvethedimcndonlcss
equations to obtain the early time approximate
analyticalsolutionsas shownin E+, 1and 2,
Late Time Equkkn: M~Ael
At the late timeof a pressurepulse test, gas
flows into the matrix fkomboth the x-directionand
the zdircdon, We needtosimplifythe flow pattern
intoonedirncnsionaloobtaincxplieitsolutions,We
firstnoticethat if thstransmissibilityf thematrixis
muchsrnailerhanthatwtheMure, thepressuren
the upstreamvolurns,the downstreamvoiunw,and
the fracturewill be essent.iailyhe sams at late time.
The p=~ in tke
VOhiMU
demeases
as gas flows
into thematrix,
Fig, 13 illustrates the concept we use to
simpli$ the twodimensional flow pattern into an
equivalentorudimcnsional flowpPIem at late time
of pressure oulss test, The upstream volume, the
downstra volume and the pore volume of the
fractureare lumpedintoan equivalentvoiumc(Vc),
ve=~u+vd+vj , ,,,,,,,,,,,,.,,,,,,,,(A,26)
The original ma&ix that takes gas flow from two
dimensionsis turned into an equivaieat matrix that
takesgas flowonlyin the z-direction,The cquivaicnt
matrix
shouidhavethe samevoiume md the same
exposureareaas the rsai matrix, To satis&theso
requirements,hethicknesshme)andthe iength(Le)
of theequivakntmatrixaredefinedasfollows:
Equivalentmatrixheight:
Equivalentmatrixlength:
Le=L+hm , ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
(A,28)
An equivalent pseudopressure pulse as
definedin Eq,A,29needso beusedin theequivalent
syslcmto obwin the sameIatctimeprmsurctransient
behavioras that in theoriginaisystem,
P w e
v
%pp
,,, , ,,, , , ,, , , , , , , , ,
(A,29)
e
Wecan nowestablishthe parliai differential
equationand itsboundaryconditionsfor the late time
cquivaicntmodelas foilows:
ThegoverningequationforgM flowin the equivalent
matrixis
560
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SPE2S89S
NDKl,X.,FAN,J, HOLDITCH,A.,sndLEE,W,J,
13
The
initialonditionis
Ppm(w =
Pp/
,,, ,,,(31)
The
boundaryconditionsare
ppm(*~j) = PFe}
,,,,,,,,,,,,,,,,,,(A,32)
ant
[1
+
=
, ,,,,,,,,.,,,,,,,,,,,,,(A,33)
z =()
The material balance equation in the eqvivalcrtt
volumeis
.,,,,.,,,,,.,,,,,,, ,,.,,,.,,,,,.,,,,,, ,,,,,,,,,,,,.,,,,,,
(A,34)
with initial condition
Ppe (0)= Pppc.
,,,,,,,,.,.....,,,.,,,,....
(A.35)
To simpl~ thepartialdiffcrentiatequation
~em for the equivalentsystemntodimensionless
fo~ w need to
fbnhcr defi-?
the following
dimensionlessparameters:
Dimensionlesspseudopressure+n the equivalent
volume:
Ppe - Ppi
PpDe =
* o.itl14,., o,,ot.,
A,36)
Ppps -
Ppi
Equivalentlengthto actualIcngthratio:
K/=+
, IO,o,t.., oo,, ,,,,,,, ,,o,,., ,, .11,,
(A,37)
4
Equivalent matrix k.ight to actual matrix height
ratio:
h
Kh =
h
, ,,$,. O OO ,, ,$ .,, ,.,,,,,,,,,,
(A438)
Equivalentvolum~tofrsctux porevolumeratio:
+
,,, ,,, ,,, ,,, ,, .,. ,,, .,, ,,s .4,,,,, i .. ..
(A,39)
J
By rewriting the differential equation in
dimensionlessformand applyingLaplacetransforms,
the analytical expression for the pressures in the
upstreamvolume(or the downstreamvolumebecause
they are the same at late time) can be obtained as
shownin Eq, 4,
I
Upsmln
Volume
1.0
. . . . . . . . .
........
. . . . ] ~f)nlt)gcnctjus
... ,
~;,q
*,
Frwlurd
~ 0,s
pu
*,,
1
~,,
,,
006
(i
k
b
\,
(),4
I
,,
,
,/
0,2
,;
,8
0,0
,,
10
10 10
a
10 104 10$
TimL(ucc)
Figure2 ComparisonBctwccnPrcssuroTmnsicntCurves
for Homogcna.wsandFrxturcd Cores
Figure 1 Schcmm,icDiagram for PressurePulseTest
667
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THE MEASUREMENT OF MATRIXAND FRACTURE PROPERTIES
14 IN NATURALLY FIMCTURED CORES
4
D
v
V?Ou
imi2
w
T ,ure 3 Simplified
Model for a Fractured Core Sample
z
t
0
L
4
x
?-
.-. Numerical Simulation
halyticd Solution
\
-~1~
1
10
la-) lIXM 10
Time (SCC)
m
Reference
,
SPE25898
n
86 K
Gas
M
ha AcquisitionSystem
1= System Pressure Transducer
2 = UpstzeamDiffimrniat
PressureTrarsdm
3 = DownstreamDifferential
PressureTnmducez
4 = Cod-king PressureTmnaduc
Figure6
SchematicDiagram of theLaboratoryEquipment
)Y;wc 4 Open-End Model forGasFlow in FracturedCores
. gurc5 ComparisonBctwccn the Analytical Solution
afld LtreFinite Diffc~nce Simulation
568 Figure8 Effectof Matrix Pimrwabilityon Presure Transient Curves
i.0
~
f= 10%
kt=ltX)md
~ 0,8
pu
km= IE-6 md
:
3
& 0.6
2
~
Qm.2%
g
0.4
Omd%
~ 0m=8%
2 o,~
m=161
10 10 101 102 103 104 10s :
Time (w+
Figure 7 Efffcct of Mmix Porosity M Presure Transient Curves
Of: 10%
kf = 100 md
klm = 4%
km=lE-5 km=lE.6m=l E-7
I
I I
I
101 100 101 102 IOJ lf)~
I
I
10J
106 1
Time
SC4
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15/15
Q
9
SPE25898 NING, X., FAN, J. , HOLDITC~ S. A., and LEE, W. J.
15
10} 10 lot 102 10 104 Id 106
Tm (See)
F:gurc 9 Effect of FracturePermeabilityori PresureTransientCurves
1 ~
kf.lood
km= lE.6 md
., 0.8-
@m= 4%
.
=
~
-?
~ 0.6-
,,
~
+
0.4-
3
.:=
- 0.2-
Of=lO%
Kl 0f=50%
1 1
10 101 102 103 104 10 106
Time
SC4
Figure 10Effect of FracturePorosityonPresureTransientCurves
Om = 2.53%
km= 8.14E-9 MCI
~ 0.8-
hf = 0.99
pm
kf= 75,2 d
i
& 0.6-
3
z
~ 0.4-
~
E 0,2-
CI Expcrirncntsl Dats
AImlytid solution
0.0-
1o 10 10 102 103 104
1(? 1(
Tm (Kc)
Figure 12The Match Betweenthe ExperimentalData
and theAnalytical Solution
for Core 5A
z
t
*
hmi2
4
44.4~ *
Vd +
. . . . . . .. .. . . . . .
. . . . . . . .
v v-
T v
t vu
-9
*
-
hm12
+
*
o L. x
z
t
u
hn2e 2 .
.
4 4
4 4
hme12 :
0
tip
Figure 13EquivalentModel for Late Time PressureFWe Test
l
1 10
100 1(XM
Time(SCC)
Figure 11RepeatabilityTest with theArtilicitdly
FracturedBereaSandCore 4
569