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Fractured Reservoir Modeling
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FracturedReservoirModeling
SS2014Dr.RainerMller
Whatisafracturedreservoir?Thebehavior,capabilityofstorageandmovementoffluidsandgasesinrocksisgenerallycontrolledbytheproportionofopenspaces(pores,interstices)intherockmatrix.Thisattributeofrocksisdescribedasporosity.Theporesmaybeinterconnectedorisolated.
absolute porosity Pt =(bulkvolume solidvolume)/bulkvolumex100effectiveporosityPe =interconnectedporevolume/bulkvolumex100
Aswell,thematrixpermeability thecapabilitytotransmitfluidsorgases iscontrolledbytheeffectiveporosity.
Primaryporosityisdevelopedduringsedimentation.Inclasticrocks,theprimaryporositycorrespondsatalargeextendtotheintersticesbetweengrains,andiscontrolledbythegrainsize,theroundnessandthepackageofthegrains.
TypesofPorosity
Secondaryporosityorinducedporosityistheresultofgeologicalprocessesactingafter theformationofrocks.Possiblecausesare: Fundamentaljointpatternbylossofwater), thedissolutionofsoluteprimarycomponents (pressuresolution,stylolites)or
dolomitization inlimestones and thetectonical formationoffractures.
Porositymaybedistinguishedintoeffective(open)andineffective(closed)porosity.
Vuggy porosityisaspecialtypeofsecondaryporosity,duetotheirregual dissolutionofof largercomponents,suchasfossilsincarbonaterocks.
Whatisafracturedreservoir?Fracturesmayincreasetheeffectiveporosityofrocksbyinterconnectingtheprimary(matrix)porosityand(inconsequence)thepermeability(fracturepermeability).So,theymaysupporttheflowofhydrocarbonsreservoirs,thus,theproductionrate.Insomehydrocarbondepositsfractureassemblagesaretheleadingfactorsofthedeposits.Thesedepositsarecalledfracturedreservoirs.
Therefore,theknowledgeoftypesoffractures,theirbehaviorandtheiroriginisofmajorimportancefortheexplorationandproductionofhydrocarbons.
Ontheotherhand,astheformationandopeningoffracturesdependonpressure,theclosureofopenfractureduringextractionofhydrocarbonscoulddowngradeflowrates.
TheUseofFracturesinPetroleumReservoirsFracturespresentbothproblemsandopportunitiesforexplorationandproductionfrompetroleumreservoirs.Manypetroleumreservoirsweregeneratedinhighlyfracturedrocks,wherefracturepropertiessuchasdensityandorientationarecrucialtoreservoireconomics.Thisaspectappliesespeciallytocarbonatereservoirs.Inmostcasesthefracturesareusuallyimportantofpermeabilityratherthanporosity.Matrixporositystoresthehydrocarbons,andfracturesprovidepermeablepathwaysfortheirtransport.Theobjectiveofhydrocarbonexplorationinfracturedreservoirsistofindareasofintensefracturing,orsweetspots.(CommitteeonFractureCharacterizationandFluidFlow1996)
Fracturedhydrocarbonreservoirsprovideover20%oftheworldoilreservesandproduction.Examplesoftheprolificfracturedpetroleumreservoirsare:
1) theAsmari limestonereservoirsinIran,2) thevugular carbonatereservoirsinMexicoand3) thegroupofchalkreservoirsoftheNorthSea.
Thesereservoirsproducemorethanfivemillionbarrelsofoilperday;theircommonfeatureisalonglifespan,whichcouldlastseveraldecades.
Thereisalargenumberofotherfracturedhydrocarbonsreservoirsofverydifferentfeaturesfromtheabovereservoirs. TheAustinchalkfield, theKeystone(Ellenberger)fieldinTexa,and theTempa Rossa fieldinItalyThosedepositshaveverylowporosities.
Ontheotherhand,theaveragematrixporosityoftheEkofisk chalkfieldintheNorthSeaisaround35%.
FracturesinPetroleumReservoirs:Examples
UnconventionalGasReservoirs
Inthelastyears,majoreffortshavebeentargetedonunconventionalgasreservoirs,suchasshalegasortightgasorcoalbedmethane.Thesedepositsarecharacterizedbyverylowpermeabilitiesandadsorptionofgasintotherockmatrix.Inthiscase,fracturesarenotonlyusedfortheproductionofgasbutalsoartificiallygeneratedbythetechniqueofhydraulicfracturing(orabbreviatedasfracking).
Tectonicfracturesarenotrandomlydistributedintheearthscrustbutrigidlycontrolledby
typesofrocks,theircomposition,rheologyandthickness, typesoffractures, locationanddepth, density, filling(aretheyopenornot)andtypeoffilling orientationsand the(originalandactual)stressfield.
Theyareconcentratedatdistinctzones(zonesofweakness,fracturezones).Theirorientation(strike,dip)isstrictlycontrolledbyorientationandtypeoftheactingstressfieldduringthetimeofformationofthefractures.
Whatshouldweknowaboutfractures?
Whatarewegoingtotalkabout?
Basicdefinitionsandtypesofthedifferentfractures
Measuringandreconstructionoffractures
Methodsofrepresentationoffractures(roses,stereographicprojection)
Factorscontrollingtheformationandpropagationoffractures
(Stressfields,Mohrcircle)
TypesofGeometricalElementsinGeology
Planes
Lineations
TypesofPlanesinGeology1)PrimaryPlanes
areplanes,whicharegeneratedduetotheprocessofformationoftherocks.Beddingplanes(stratificationplanes):
areresultofsomekindofinterruptionorchangeofthesedimentationprocess areoriginallyorientatedparalleltotheearthsurface(horizontal) showawiderangeofdifferenttypes,combinations(beddingtypes)andgeometries areaffectedbylatertectonicalinfluences(fractures,folds,pressuresolution) maybedistinguishedfromotherplanesbyobservationofchangesofmaterial
TypesofPlanesinGeology1)Beddingplanes:Examples
left:parallelbedding(flatbedding)ofsandstone siltstoneintercalations
right:irregularbeddingplanesofthickbeddedlimestones
TypesofPlanesinGeology1)Beddingplanes:Examples
left:ripplebeddinginsandstone
right:laminationinmudstones
TypesofPlanesinGeology2)Metamorphicfoliation,cleavage
Foliationissecondary,tectonicallycontrolledtypeofplanesinrocks,commonlydevelopedinfinegrainedshalesandleadingtorocks,whicharecalledschist.Foliationorschistosityorcleavageisareactionofrocks,whichwereexposedtoextremetectoniccompression.
Penetrativeaxialplanecleavageinfoldedschists Complexfoldingofmetamorphicfoliationinamphibolites
TypesofPlanesinGeology3)Fractures
Fracturesaresecondaryseparationplanesoftectonicorigininrocks,whichmaybesubdividedintothreetypes:
a) Joints
b) Fissures
c) Faults
TypesofPlanesinGeology3a)Joints
Jointsarecommonandfrequentfracturesinanytypesofrocks.
Jointsareseparationplanes,cracks,inrockswithoutanyvisible(oremeasurable)verticalorhorizontaldisplacement.
Inthesenseofviewoffracturemodelling,theyareofmayorimportance.Differenttypesanddifferentoriginsofjointsareknown.
Plumosestructures:areindicatorsforcrackpropagationonjoints
Differentintersectingsetsofjoints
TypesofPlanesinGeology3b)Fissures,tensiongashes
Fissuresarejointlikefractureswithameasurablehorizontaldisplacementnormaltotheorientationoftheplane.Itmeans,thatfissuresare(originally)openstructures,whichareofmayorimportanceforthemigrationandthetransportofliquidsandgas.Inmanycasesfissuresare(secondarily)filledwithmineralprecipitationslikegypsum,calciteorquartzorevenraremineralslikeores(veins).Tensiongashesare(normallysmallscaled)structuresasaresultoftensionalstress.
TypesofPlanesinGeology3c)Faults
Faultsareseparationplanesinrocksshowing(megascopically)visibleandmeasurabledisplacement.Thedisplacementmaybeobservedby:
Setofthreenormalfaultsdisplacingalimestonelayer(Alps,fromRamsay)
thedisplacementofmarkerbeds, by striations along the fault plane or by dragging of the nearby beds.
Strikeslipfaultinlimestones (LeinetalRift,Mller)
Typesoflineationsingeology:(primary)sedimentarylineations
Manynontectonical,primarytypesoflineations,especiallyinsedimentology,areknown,whichprovideuswithinformationabouttransportdirectionsandsourcesofsedimentarymaterial.
Flutecasts,striationmarks,groovecastsarethebestknownstructuresofthistype.However,eveninigneousrockslinearalignmentofneedleshapedmineralsservesasindicatorofflowdirectionsandinfluxmechanismsofmelts.
Flutecastsonadownsidedbeddingplaneofoverturnedgreywackesequences,Harz
Typesoflineationsingeology:FoldaxisFoldaxis(hingelines)aretheconnectinglinesoftheinflexionpointsofafold,atwhichtheconcavityofthelimbsreverses(eitheranticlineaxisorsynclineaxis).Foldaxisarethemostimportantgeometricalelementtodescribetheorientationandtypeoffolds.
Typesoflineationsingeology:Foldrelatedlineations
Fishmouthstructurebetweenboudins inmarbles;Matreishearzone,Austria.
Mullionstructureinaalternatingsequenceofgreywackes andslates,Eifel(RAMSAY)
Typesoflineationsingeology:Intersectionlines
Infoldedrocks,theintersectionlineationsbetweenfoldrelatedplanescorrespondtotheorientationofthefoldaxis.Intersectionsofplanesofthesameorder(suchasbeddingplanes)arecalledlineations.Intersectionsofplanesofdifferenttype(andorigin),forinstancebeddingplanes(s0)andcleavage(s1)arecalledlineations.
Pencileshapedpiecesofslates,formedbyaobtuseanglebetweenbeddingandcleavage(lineations).Thelongaxisofthepencilsrepresenttheorientationoffoldaxis.
Typesoflineationsingeology:Mineralstretching
Typesoflineationsingeology:Mineralgrowth
Newformingorrecrystallized needleshapedmetamorphicmineralsoraggregatesofmineralsundercontinuouscompressional stressconditionsaregrowingparalleltotheminorstressaxis.
Needles Platyshapedminerals
Typesoflineationsingeology:Striation
Vertical striations and crescentlike edges indicate, that the (upper) hanging-wall block was displaced vertically downwards, resulting in a normal fault.Jurassic limestones, French Jura, (diameter of the picture: 1m), Photo: Mller
Striationsarescratchmarksonfaultplanes,formedbythetectonicaldisplacementprocessofthetworigidblocksalongthefaultplane.Theyareofmajorimportance,astheydemonstrateustherelativeandabsolutedisplacementdirection.
Wheredoesstructuralinformationcomefrom?
a) superficialoutcrops:
Advantages: easilyaccessible,lowcostsexposedin3dimensionsatlargeextensionslargenumbersofdatamaybecollectedrelativetemporalandspatialrelationsofdifferentelementsandgenerationsmaybedistinguished
Problems: transferofsuperficialinformationtothedepth
b) Drillings:informationonfracturesmaybeobtaineddirectlyfromcores,fromvideorecordingsofthedrillholeorfromspeciallyprocessedlogsorcombinationsoflogs,producing3Dimages.
Advantages: informationmaybeobtaineddirectlyfromthelocationofinterest
Problems: highcost,verylimitedrageofinformationinspace,limitednumberofdataorientationandmeasurementofelementsisdifficult
Wheredoesstructuralinformationcomefrom?
b) Seismics:interpretationsofresultsofseismicexplorationin2Dand3D
Advantages: informationmaybeobtainedregionalscaleundgreatdepth
Problems: highcost,limiteddetaileddissolution,minorstructuresdifficulttoanalyse,orientationandmeasurementofelementsisdifficulttoanalyse,
Wheredoesstructuralinformationcomefrom?
Typesofstructuraldata,tobecollected
Spatialorientationofthefractures: eachkindofstructuralmodelingdependsbasicaly ontheorientationofthefracturepatterninastatisticalpointofview.Forrepresentationandanalysisofthedataspecialmethodsasrosediagramsandstereographicrepresentationareneeded.
Analysisoftype,relationsandoriginofthefractures: usingjoints:observationofgenetically,temporallyandspatiallyrelatedjoints(setsofjoints).usingfaults:observationofthetypeoffaults,kinematicsanddimensionofdisplacement.
Spatialrelation,densityofthefractures: veryimportantfortheinterpretationoftheroleofaspecialsetofjointsaspathwayforthemigrationoffluids.Thenumberofjointsofaspecialorientationhastobecountedandbereferredtoanormalizeddistance.
Openingandfillingoffissures
MeasuringtheOrientationofPlanes
StrikeN
Dip direction
horizontal plane
Dip angle
Strikedescribestheorientationofan(imaginary)horizontallineonaninclinedplane(tothenorthdirection).Strikeisspecifiedbetween0and180.
Dipdirectionistheorientationofthelineofsteepestpossibledipangleonaninclinedplane(tothenorthdirection),normaltostrike.
Dipangleistheanglebetweentheplaneinquestionandan(imaginary)horizontalplaneindipdirection.Dipangleisspecifiedbetween0and90.
GeologicalCompass
Brunton compass
GeologicalCompass
GermanMiners Compass
GeologicalCompass
GermanClar Compass
Notationof structural data:planes070/40SE 160/40 N070E,40SE125/10NE
010/80W
170/05W
30/10NW
160/80W110/50NE
140/10SW
050/15NW
000/40W090/50N
180/90
035/10
280/80
260/05
300/10
250/8020/50
230/10
320/15
270/40
000/50
090/90
N055E,10NE
N010E,80W
N010W,05SW
N030E,10NW
N020W,80W
N070W,50NE
N050W,10SW
N050E,15NW
N000,40W
N090E,50N
N000,90
MeasuringtheOrientationofLineations
N
Trenddescribestheorientationofan(imaginary)horizontalprojectionofthelineationtothenorthdirection).Trendisspecifiedbetween0and180.
Plungedirectionisthedirectionoftheinclinationofthelineation(tothenorthdirection),paralleltothetrend.
Plunge(angle)istheanglebetweenthelineationinquestionandthe(imaginary)projectionofthelineationtoanhorizontalplaneinplungedirection.Plungeisspecifiedbetween0and90.
horizontal plane
Plunge (angle)
Notationofstructuraldata:lineations
130/40SE 130/40 S050E,40015/80NE
15/10NE
140/42NW
050/30SW
100/54NW170/80N
010/20N
030/13SW
014/50S140/00
065/14SW
015/80
015/10
320/42
230/30
280/54350/80
010/20
240/13
194/50
140/00
245/14
N015E,80
N015E,10
N040W,42
50,S030W
80,N54W
10,N80N
10,N020E
60,S13SW
S014W,50
N040W,00
S65W,14
ClassificationofFaults
ClassificationofFaults
Normalfaults
Reversefaults
Strikeslipfaults:G:sinistralI:dextral
CombinationsofNormalFaults
TypesofReverseFaults
Reversefault:dip>45 (~65)
Thrustfault:dip
Exercise:Determinationoftypeanddisplacementoffaults
Quantitativedeterminationofdisplacementratesoffaults(1)
Todeterminethedisplacementrateof(verticallydisplaced)faultsingeologicalmaps,twotriangularrelationsmaybeused.Thefirstgeometricalconstructionisexecutedalongasectionverticallytothefaultplanewiththecomponents:
s =(apparent)horizontalwidthofdisplacement(=horizontalcomponentofw)(heave),t =verticalwidthofdisplacement(=verticalcomponentofw)(throw),w =(real)widthofdisplacement(slip)
Quantitativedeterminationofdisplacementratesoffaults(2)
Usingthethrowt,theformertrianglemaybecombinedwithasecondtrianglearrangedverticallytothebeddingofdisplacedrocks,whichusesanapparenthorizontalrateofdisplacementsh (strikeseparation).Thestrikeseparationsh canbemeasuredalongalineofstrikebetweenthesameplaneofadisplacedlayer.
tan(bedding)=t/sh;t=sh *tan(bedding)
sin(fault)=t/w;t=w*sin(fault);w=t/sin(fault)
cos(fault)=s/w;s=w*cos(fault);w=s/cos (fault)
tan(fault)=t/s;t=s*tan(fault);s=t/tan(fault)
Quantitativedeterminationofdisplacementratesoffaults(3)usingtrigonometricfunctions
Exercise:QuantitativedeterminationofdisplacementratesoffaultsCalculatedisplacementratesandcompletethesketchesofmaps,assumingpureverticaldisplacement
Scale1:10000
Joints
Definitions: Jointtrace:intersectionlinebetweenajointplaneandanyotherplane. Jointset:isasetof(moreorless)parallelorientatedandgeneticallyrelatedjoints. Jointzone:section,inwhichajointsetofspecificorientationareconcentrated
(comparedtoitssurroundings). Jointsystem:theentiretyofthejointsetsofdifferentorientationsinaregion,
whichmaybeconsideredasgeneticallyrelatedtothesamestressconditions.Thosejointsetsmaybesymmetricallyorientated,forexampleorthogonallyorientatedjointsorconjugatesetsofjoints.
Jointpattern:theentiretyofalljointsofareregion,whichmaybecomprisedofseveraljointsystemswithgeneticallyandtemporarydifferentorigin.
Jointsarefractureswithoutvisibleormeasurabledisplacementinrocks
SystematicjointsJoints,whicharegeometricallyregular(parallel,orthogonal)(jointsystems)intheirarrangementarecalledsystematicjoints.
Lessregularjointsarecallednonsystematicjoints.Theyarenormallyofaminorscaleandofirregular,randomorientations.Nonsystematicjointsmaybeoriginatedbylocalvariationsofrheologicalparameters.Theycanhardlybepredicted.
NonsystematicJoints
Joints
Manyjointsystemsexhibitregionallyconsistentpatternsoforientations,whichareobservedtopersisteventhroughoutthestratigraphicsection.
Insedimentaryrocksasystematicperpendicularorientationofjointstothebeddingplanesiscommonlyobserved,frequentlyshowinganorthogonalarrangement oftwosetsofjoints.Thissocalledfundamentaljointsystemseemstobegeneratedalreadyduringearlydiagenesis.Sometimes,theorientationofthesystemcorrespondstotheaxisofthebasin.
Therefore,thearrangementofjointsinsedimentsfrequentlyshowsrelationstotheshapeofthesedimentarybasin.
Mostobservationsonjointsimply,thattheyhavebeenformedundertensilestressconditions.Nevertheless,compressiveregimenisthecommonstateofstressintheearthscrust(load!),therefore,effectivestress,controlledbyfluidpressure,playsanimportantroleinjointformation.
Joints
Thespacingofjointsinsedimentarylayersiscontrolledbytheelasticbehaviorandthicknessofthebeds.Therefore,spacingdiffersinmanysequencesfromlayertolayer.TheelasticbehaviorofrocksisdescribedbytheYoungmodulus,whichisameasureoftheirstiffnessanddescribestherelationbetweentensilestressandstrain.
Fissures,tensiongashes
Fissuresareopenstructures,combinedwithextensionalstressconditions.Theyarearrangedintypicalorientationstotheappliedstressfieldandthecorrespondingmajorstructures(faults).
Mineralfibers(gypsum,calcite,quartz)infissurescrystallizeparalleltotheminorstressaxis3Photo:RODRIGUES etal.(2009):J.Geol.Soc.;166:.695709
Representationofstructuraldata
Structural datasets normally involve the following features: they represent the 3-dimensional orientation of planes or lineations, they include normally a large number (several tens or hundreds) of samples, they include different types of structural elements (bedding, faults, joints),
whose geometrical relations are known and must be verified.
Please note: Directional data, expressed by strike and dip, can not be treated statistically as two independent values, but are 3-D vectorial data ! For statistical analysis of gravity centers of orientation and their variation, special complex methods of vector analysis are required.
These large and complex directional datasets must be interpreted and represented in a 3-dimensional system.Two methods are in use: Rose diagrams and stereographic projection (Schmidt Net)
RosediagramsInrosediagrams(only)thetrendofstructuralelementsisusedfortheconstructionofadirectionalhistogramshowingthefrequencyofdataofcertaindirectionalclasses,representedina360 or180 circle(rose).Itisfrequentlyusedforsteeplydippingjointsetsorotherdatainwhichthedipangleisnotimportant.
Rosediagrams:ExampleData: Orientations of 64 joints
10/48 E 94/80 S 63/74 NW 154/68 SW 14/68 ESE 07/56 E 149/70SW 59/80NW12/68 E 109/88 N 163/67 NE 17/81 ESE 90/80 S 12/66 E 94/73 S 13/83 E01/81 W 06/78 E 62/85 NW 149/70SW 16/77 E 04/68 E 150/75SW 80/59N06/60E 91/81 S 64/75/NW 155/69/SW 15/68 ESE 08/77W 148/76SW 60/60 SE12/49 E 93/80 S 69/74 NW 151/68 SW 13/68 ESE 06/56 E 147/70SW 61/80NW12/83 E 111/88 N 161/67 NE 20/81 ESE 89/80 S 15/66 E 91/73 S 09/83 E03/84 W 10/78 E 65/85 NW 151/70SW 19/77 E 02/68 E 152/75SW 79/59N07/66E 94/81 S 59/75/NW 148/69/SW 13/68 ESE 11/77W 146/76SW 66/66 SE
Rosediagrams:Differenttypes
Rosediagrams:Resultsoftheexample
max = 26.98%
0
90
180
270
90
0
bung Kluftrosen.pln Datasets: 63
Interval: 10
Interval: 10
max = 33.33%
Rosediagrams:Resultsoftheexample
Analysis of the example data using TectonicsFP
Applicationofjointdiagrams
Stereographicprojection(SchmidtNet)
Theintersectionoftheelementwiththespheressurfaceleavesatraceinformofacirclesegment(plane)orapoint(line).
Thesecondmethodofrepresentationofdirectionaldataismuchmoremeaningful,howevermoredifficulttounderstand,touseandtointerpret.
Inthiscase,planesorlines,areconsideredtobearrangedwithinina(imaginary)sphere,passingthroughthecenterofthesphere.
Thepositionofthetraceorthepointoneithertheupperorthelowerhemisphereisprojectedtoaplanepassingthroughthecenterofthesphere.
Polar(normal)or azimuthal Projektion
The projection may be polar (a) or azimuthal (b).
Polar projection is applied as the so called polar net.Longitudes are represented as straight lines; latitudes as circles with differing radii.
For the Schmidt net azimuthal projection is used.Latitudes and longitudes are +/- curvilinear segments of a circle; equator and N-S-axis are represented as straight lines.
TypesofProjection
Spherical surfaces may be projected as: equal angle (Wulf net, Mercator), equal length or equal area (Schmidt net).
Equal angle projection is used for the correct representation of angular relations, for example the angles between crystal planes in crystallography.
The Schmidt net projection is of equal area type. Equal area relations are needed for a statistical analysis of the population density of representing point on the surface of a sphere.Equal angle relations are represented without distortion along great circles.
Stereographicprojection(SchmidtNet)
Model Projection
SchmidtNettop:polar(normal)projectionbottom:azimuthalprojection equalareaprojection
Net
SchmidtNetN
S
EW
NW NE
SESW
Equator
greatcircles(meridians)
smallcircles
1020
3040
Transparency Layer
PreparationoftheNet:
Fixapinfromthebacksidethroughthecenterofthenet
Fixatransparencylayer
Orientatelayersparallel
Markcenter(cross)
Markoutercircle
MarkNPosition
N
Representationofaplane(70/20NW)asgreatcircle
Preparethetransparencylayer
Rotatethelayerwith70 counterclockwise
Count20 onequatorfromoutsidetocenter
Markthecorrespondinggreatcircle
Rotatethelayerbacktoorigin
N
Representation of lineations Example: (70/20NE)
Preparethetransparencylayer
Rotatethelayerwith70 counterclockwise
Count20 alongNScenterlinefromNtocentertocenter
Markthecorrespondingpoint
Rotatethelayerbacktoorigin
N
Inthepetroleumprospectionfield1highflowrateshavebeendetectedintheverticaldrillhole DH1atadepthof1000m,obviouslycontrolledbytheintersectionoftwonormalfaultzones.Theirorientationsare:Fault1:125/35Fault2:156/551)Locatethepossiblecorridor,inwhichthisintersectionzonecouldcrosstheprospectoffield2andselectapossibledrillinglocation.2)Atwhichdepththefavorableflowratesaretobeexpected?
Exercise:Determinationofahighpermeabilitypathwaybytwointersectingfaults
Point counting: Statistical evaluation of structural data
One of the most typical applications of stereographical projection of structural data is their statistical evaluation. The scope of these procedures is the determination of the center(s) of gravity of a cloud of poles.The mathematical calculation of those parameters is complex. Orientational data in a 3-D space are vectors; their evaluation requires methods of vector analysis.Actually, some of those operations can be performed using special tectonic programs.A manual analysis is quite simple but time consuming.It is performed using a so called counting net (see next slides).
AnalysisofSchmidtnetdata
AnalysisofSchmidtnetdata
4Klassierung: 1 Punkt2 - 3 Punkte4 - 5 Punkte5-10 Punkte
0 00
00000 0
00
0
0
0 0
0
0
0
0
0
0
0 0
0
0
0
0
0
0
0
0
0 0 0 0 0
0
0
0
0
0
00
0
0
0
0
0
00 00
0
0
0 0
0 0
0
0 0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1 1
13
32
2 3
1
1
1
1
1
1
1
2
1
1
43
3
2
910
109
3
4 4
4
4
8
56
33 12
4
AnalysisofSchmidtnetdata
bung Kluftrosen.plnDatasets: 63
Max. value: 15.6%at : 101 / 69
Contours at:1.00 3.00 6.00 9.00 12.0
AnalysisofSchmidtnetdata:ExampleTectonicsFP
RepresentationofFaultsusingStereographicProjection.
.usingtheANGELIER method Example:reversefaultplane:200/80striation:270/60
StressandtheDeformationofRocks
Inacoordinatesystem,thestateofstressofasinglepointinasolidcanbeexpressedbythreeprinciplestressaxis,whichareorientatednormaltoeachother:
1 =inthedirectionofthemajorstress,2 =inthedirectionoftheintermediatestress,3 =inthedirectionoftheminorstress,
Stress isameasureoftheintensityandorientationoftheforcesperunitareaonadeformablebodyonwhichinternalforcesact.Deformationorstrainisthereactionofrockstostressandisdescribedbytherelationbetweenaninitialandfinalplacementofasolidexposedtostress.
StateofStressonaPlane
Thestateofstressonasinglepointonaplanewithinthesolidcanbedescribedby anormalstresscomponentn and two(perpendicular)shearstresscomponents1 and2
Onplanesperpendiculartooneofthethreeprinciplestressaxis,theshearstresscomponentsarezero.
Themaximumshearstressactsonaplane,thatbisectstheanglebetweenmaximumandminimumprinciplestress:
max =(1 3);
Thecorrespondingmaximumnormalstressequalsto:
n max =(1+3);
ANDERSONS TheoremofFaulting.
states,thatonahorizontalearthssurface,thereisnoshearstress,whichcouldcausemassdisplacement.Asaconsequence,oneoftheprincipalstressaxesmustbearrangednormaltotheearthssurface,thetwootheraxeshavetobeparalleltothesurface.Thisconceptleadstothreeprinciplestateofstresssituationsintheearthcrust:
1vertical:dilatation,normalfaults
3vertical:compression,reverse,thrustfaults
2vertical:compression,strikeslipfaults
Case1:
Case2:
Case3:
Stress:DefinitionsandUnits
Thestresstensormaybedecomposedintotwocomponents:MeanStress..
isthemeanvalueofthestressstate:m =(1+2 + 3)/3;
andrepresentstheisotropicpartofthestress
DeviatoricStress.isthedifferencebetweenaprinciplestressandthemeanstress:
i=i m;whichisresponsibleforalmostallcompressivedeformationalfeatures.
TheunitforstressisPa(Pascal)=N/mCompressivestressesareconsideredtobepositive!
1bar=105 Pa10bar=1MPa (megaPascal)=106 Pa
Pressureat5kmoceandepth:500bar=50MPa100MPa =1Kb(Kilobar)=1000bar
Pressureat30kmdepthofthecrust:approx.10kbar=1Gpa =109 Pa1atm (atmosphere)=1,0133x105 Pa
1kg/cm2 =0,9807bar
Lithostaticpressure..(orLoad)actsnormaltotheearthssurfaceandiscontrolledbytheloadoftherockpile,whichisdepth(inm)bydensity(atanaverageof2,5g/cm)bygravitationalconstantof9,82msec.LithostaticpressureisalsoexpressedasverticalstressvExample:Rockpileof5000m,density:2,5g/cm500000cmx2,5g/cm=1250000g/cm=1250kg/cm1250kg/cmx0,9807=1225bar=1,225Kb1,225KB=122,5MPa
HydrostaticPressure..(confining,geostatic,fluidpressure)isthehydrostaticpressureofawatercolumninaspecificdepthduetotheforceofgravity:pfluid =depth[m]x0,1[g/cm](1000mx0,1=100bar=10MPa)Hydrostaticpressurehasthesamemagnitudeinthreedirections(confining).Internalporefluidpressurereducestheeffectivestrengthactingonthesolid.
EffectiveStress.isthedifferencebetweenmeanstressandfluidpressure:
3)3(
3321
*3
*2
*1* fluid
m
P
Stress:DefinitionsandUnits
TheMohrDiagramTheMohrdiagramisaveryimportanttoolforrepresenting,analyzingand,aboveall,understandingthestateofstress,actingonaplaneofanyorientationinastressedsolidmaterial(givenbytheprincipalstressaxes1,2,3).WewillconsiderMohrdiagramoperationsintwodimensionsonly.
Example:Aplaneinahomogeneouslystressedcube.Itsnormalincludesanangle (=shearangletheta)with1.
Thestateofstressactingonthegivensurface,definedbytheshearangle,canbydividedintotwocomponents:Thenormalstressn isactingnormaltotheplaneTheshearstress isactingparalleltotheplane,resultinginasheardisplacementalongtheplane
1 n A
A= ( cos+ sin)cos
3 n B
B = ( sin+ cos)sin
2321 sincos n
cossin)( 31
;2cos)2
()2
( 3131 n
;2sin)2
( 31
Trigonometricrelationsdeductedfromthediagram
solved for n:
solved for :
converted into:
PlottingtheMohrDiagramTheMohrdiagramrepresentsthestateofstressofamaterialusingn asxaxisand asyaxis.Thestressonasinglepointonaplaneplotsasapoint(n ,).Compressivestressplotsontheright,tensilestressontheleftsideofthediagram.Thestatesofstressofallpossibleplanesofagivenstressfieldarearrangedonacirclewithacenterofthemeanstress andaradiusofthedeviatoricstress.1 and3 plotonthecircleintersectionwiththexaxis.Theshearangle(2)isrepresentedbytheangleofalinebetweenthecenterandtherepresentingpointofaplane.Planesperpendicularto1 and3 (with=90)havenoshearstress.Maximumshearstressoccursat=45.Thelargerthedifferencebetween1 and3 (deviatoricstress)thelargeristheshearstressonagivenplane.
TheMohrDiagram:Exercises
1) Theprinciplestresses1 and3 aregivenwith80Mpaand45Mparespectively.1 isorientatedhorizontallyinEWdirection,3 vertically.Whatisthestateofstress(n, )onafractureplanestrikingNSanddippingwith30 totheE?
Solution:=60,2=120max=17,5Mpaat =45nmax =62,5MPan =53,75MPa =15,15MPa
2) Thestateofstressismeasuredin2slotsofamine.Thefirstdips32Eandhasanormalcompressivestressn of57Mpaandashearstressof12Mpadowndip.Theseconddips84Eandhasanormalcompressivestressnof40Mpaandashearstressof3Mpa.Whatisthestateofprinciplestressesandtheirorientationinthisregion?
Solution: Constructthetworepresentingstresspoints,Bisectorlineinterferingthexaxisresultsinthecenter ofthecircle:1=66,5MPa,3=40MPa
TheMohrEnvelope:GatheringExperimentalData
Triaxial testingapparatus(fromSUPPE 1985:152)
Piston
Resultofatriaxial testofacylindricalshalesample(Inst.ofGeology,TUClausthal)
TheMohrEnvelope:ResultofanExperiment
Mohrdiagramofthefractureexperimentataconfiningpressureof50Mpa.Thediagramrepresentsthreedifferentstatesofdeformation.Therockprobefailedataloada of750(800load 50confiningpressure)Mpa (fromSUPPE 1985:152).
longitudinalstrain:
Stressstraindiagramofthetests(fromSUPPE 1985:152).Thenearlylineartrendisaresultoftheelasticbehaviorofthesample.
0
0 )(l
lll
common confining pressure c
TheMohrEnvelope
Mohrdiagramfordiabase sampleswithincreasingconfiningpressuresatroomtemperature.Eachcirclerepresentsthestateofstressatfailureatadifferentmeanstress.Therockstrengthincreaseswithmeanstress,dependingondifferentconfiningpressures.Thelocusofstressstates,thatboundsthefieldsofstableandunstablestresses,iscalledtheMohrenvelope(fromSUPPE 1985:153)
TheMohrEnvelope
ThreefieldsoffracturedevelopmentarerepresentedintheMohrenvelope. Thetensilefieldisrepresentedbyafixedtensilestrength T0.Onlyonedirectionofpossible
fractures,perpendiculartothedirectionofmaximumtensilestress,exist.Typicalvaluesoftensilestrengthare5to20Mpa.
TheMohrEnvelope
ThetransitionaltensilefieldislocatedbetweenT0 and1 >|5T0|andischaracterizedbyarapidnonlinearincreaseinmeanstrengthwithincreasingconfiningpressure.Mohrcirclesaretangenttotheenvelopeattwopoint;twoconjugateddirectionsoffracturesmayexist.Mostjointsareformedinthetensiledomain.
TheMohrEnvelope
TheCoulombfracturebehaviorrepresentsthelinearincreaseofshearstrengthcorrespondingtoincreasingconfiningpressure,characterizedbyaslopeoftan.
Theangleiscalledangleofinternalfriction. Itstangentiscalledcoefficientofinternalfriction,whichisamatterconstant. Athighconfiningpressureandincreasingtemperatures,strengthincreaseonlyslowlyat
ductilebehavior.
2)Ina6000mdeepdrillhole,thefollowingparametershavebeendetermined: Averagedensityoftherocks:2,7g/cm Densityoffluids:1,1g/cm Directionofh (usingbreakouts):150/00 h =0,5v H =0,8v Jointset1:330/60 Jointset2:60/60
Problems:a) Calculatetheprinciplestressesb) ConstructtheMohrdiagramrepresentingthestateofstressatthebottomofthedrillhole.c) Determinemeanstressanddifferentialstressd) Determinemeanstressandeffectivestresse) Drawasketchofthestateofstress,itsorientationandthesituationofthejointinthe
boreholef) Bytriaxialtestingexperiments,theMohrenvelopeoftherocksintheboreholehavebeen
determined.Willthejointsfailornotbythegivenparameters.g) Ifthejointwillnotfail,howcouldwetriggerthefracturegeneration?
TheMohrEnvelope:Exercise
Solution:
v =1 =159MPaH=0,8V =2 =127MPah =0,5V =3 =79,5MPaCenter=(1+ 3)/2=119,25MPapfluid =66MPa =38,06MPamax=40,5MPaMeanstress:121,8MPaEffectiveStress:55,8MPa
Onthebaseofexperimentaldataofthestateofstressandstraininrocksestimationstothefollowingproblemsmaybefound:
Themagnitudesofn and atthemomentoffailureoftherocksarerelatedtoeachother.TherelationisdescribedbyBYERLEEs law:Withincreasingnormalstressincreasescriticalshearstress:
crit =0,6 n to0,85 n inregionsofmoderatestress.
Thereare3possibilitiesintheearthscrust:1. 1 =2 =3 : thereisnoshearstressT2. 1 >2 >3: therearetwoplanesofmaximumshearstress
intersectingparallelto2 .Shearstressesachievetheirmaximumsymmetricallyto1 and3 withashearangleof45,resultingin(potentially)conjugatedfractures.
3. 1 =2 or2 =3: resultsinaninfinitenumberofplanesofmaximumshearstress
TheMohrDiagram:Consequences
Determinationofdifferentialstresses(1 3) DeterminationoftensilestrengthT0 ofrocks Determinationoftheangleofinternalfriction,whichiscontrolledbythegradientofthe
Mohrenvelope(mostly30) Determinationofthecoefficientofinternalfriction =tan(mostly0,55 0,85,inclays0,3
0,4) Estimationoftheinfluenceoffluidpressurepfluid anditsrelationtolithostaticpressurev,
whichismoreorless0,4inrespecttothedensitiesof1,0g/cmofwaterand2,7g/cmofrocksinopensystemsintheuppercrust.
Estimationaboutthepossiblestrainregimeandbehaviorofrocks(tensile,compressive,ductile)
Estimationaboutpossibleorientationsoffracturesinrocksaccordingtoanexistingorpreexistingstateofstress
Reconstructionofapreexistingorientationofstateofstressandthepositionofstressaxisusingaexistingfracturesystem
Simulationofconditions,underwhichtheformationoffracturescouldbesupported(hydrofracking)orimpeded,i.e.bycontrollingfluidpressure.
TheMohrDiagramWhatkindofinformationcanbederivedfromit?
TheOriginofJoints(fromSUPPE 1985)IntheMohrdiagramtheprincipledomainofjointgeneratingconditionsisthetensileortransitionaltensileregimen.Tensilefracturesformperpendiculartothedirectionofthemaximumtensilestress(between5and20Mpa).Transitionaltensilebehaviorisexhibitedabovetheleasttensilestrength.
Theequationforjointformationis: 0*3
*1 24)( T
0*3
*1 4)( T
0*1 3T
Forjointformation,themaximumdeviatoricstressequals:
whichisthelimitofthemaximumdeviatoricstressforatensileeffectivenormalstresstangentbytheshapeoftheMohrenvelope.
Fortruetensilejoints,themaximumeffectivestressislimitedto3timesthetensilestrength
Problem:Verticalstressisduetothegravitationalloadcompressive.Therefore,therequirementsfordeepformationofjointsare:
smalldeviatoricstressesand highfluidpressurerations
TheDepthofJointFormation(fromSUPPE 1985)
)1(3 0
gT
z
Usingtheaboveequationandtheequationforlithostaticpressure,maximumdepthofformationofjointcanbecalculatedas:
Forrockswithnormaltensilestrengthbetween2to10MPa,theformationofjointsislimitedto1or2kmofdepth,assuminglowfluidpressures(lowsalinities).
with: =meanrockdensityg=gravitationalconstant=fluidpressureratio
TheSpacingofJoints(from SUPPE 1985)Jointsperpendiculartobeddingisanimportantstructuralfeatureinsediments.Jointspacingiscontrolledby: rocktype:jointsaremuchmorecloselyspacedincoalthaninsandstones thicknessofthebeds:jointsaremorenumerousinthinbedsthanininterlayeredthickbeds
ofthesamerocktype. somejointsmaybelimitedtosinglebeds,otherspassthroughmanybeds.Considerapileofsedimentaryrocks,eachwiththicknessesd1,d2dn.andeachwithdifferentelasticconstantsE1,E2 En.anddifferenttensilestrengthT1,T2Tn,whereEistheYoungsmodule:
1 1 2 2 n nE E .......E
l
E
Thebedshaveundergonecompactionandareinthesamestateofstress.Thehorizontalstressandstraininalayeristhen:
Ifthesebedsareuniformlystretchedbyastrainx ,thenewhorizontalstress,generatedineachofthenlayerswillbedifferent: 1 1 1 xE
2 2 2 xE Asaconsequence,uniformstrainwillgeneratebedparallelnormalstress,whichwillbedifferentineachlayerofcontrastingelasticproperties.
and soon.
TheSpacingofJoints(fromSUPPE 1985)
Inthefieldweobserve,thatthespacingofjointscorrespondstothelayerthickness.ThesocalledGRIFFITH theory,states,thatthestressreleasearoundanewformedjointaffectsonlyaradiusofaboutonecracklength.Inconsequence,stressreleaseaffectsonlyashortdistancearoundthenewformedcrack,therestofthebedwillremaininanearfailuretensilestresscondition.Smallincreasesofstrainwillformnewjoints,sothatalayerwillbejointedin(moreorless)uniformdistancesequaltoitsthickness.Furthermore,stressreleaseinonedirectionmayinfluencethemagnitudesof 2 and3.Asaconsequence,theorientationofthenewformedjointschangeorthogonally.