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SOCIETYOF PETROLEUMENGINEERSOF AIME6200 NorthCentralExpressway ?~RSP~ 5544Dallas,Texas75206THIS PRESENTATIONIS SUBJECT,TOCORRECTION

The Equat ion for GeopressuredPredi cti on f rom Wel l LogsBy

Ben A. Eaton,MemberSpE-AIME,EatonIndustriesof Houston,Inc.@Copyright 1975American Institute of Mining Metaiiurgicai and Pet roieum Engineers Inc.

Thispaperwas preparedfor the 50thAnnualFallMeetingof the Societyof PetroleumEngineersof AIME, to be held in Dallas,Texas,Sept.28-Ott.1, 1975. Permissionto COPYis restrictedto an abstractof not morethan 300 words. Illustrationsmay not be copied.The abstractshouldcontainconspicuousacknowledgmentof whereand by wh~m thepaper ispresented. Publicationelsewhereafterpublicationin the JOURNALOF PETROLEUMTECHNOLOGYor the SOCIETYOF PETROLEUMENGINEERSJOURNALis usuallygrantedupon requestto the Editorof the appropriatejournalprovidedagreementto giveproper.creditis made.

Discussionof thispaper is invited. Threecopiesof any discussionshouldbe sentto the Society~f PetroleumEngineersoffice. Such discussionsmay be presentedat theabovemeetingand, with the paper,may be consideredfor publicationin one of the twoSPE magazines.ABSTRACT containinga springand a fluid,they simulathe compactionof claythatcontainedwater,This studyhas resultedin the development Overburdenstresswas simulatedby a piston,of fourequationsthatmay be used for the in Fig, 1. It was shownthatthe overburdenpredictionof geopressuredagnitudesfromwell stress$S, was supportedby the stressin thelog and drillingparameterdata. Equationsare spring,u, andthe fluidpressurefp. Thus,givenforuse withresistivityplots,conduc- long-acceptedequationof equilibriumwastivityplots,sonictravel-timeplots,end established.correctedd exponentplots. All equationshave the sametheoreticalbasis. s= d +p.. , e . . INTRODUCTION If Fig. 1 and Eq. 1 are studied,it is obviothatif S is increasedand the fluidis alloIn 1965f Hottmanand Johnsonlpresenteda to escape,dmust increasewhilep remainsamethodfor predictinggeopressuredagnitudesby hydrostaticpressure. However,if the fluidusingresistivityand soniclog data. This cannotescape,p muet alsoincreaseas S istechniquehas receivedwide acceptanceeven increassd.thoughthe predictionchartswere basedonly ondataconcerningTertiaryage sedimentsin the HubbertandRube publisheda compreheGulf Coast area. It was specificallypointed treatmentof thistheoryas relatedto sedi-out Knat thesetechniqueswere applicableonly mentaryrock compaction. They showedthat,ain areaswherethe generationof geopressuredis the overburdenstressis increasedas a resuprimarilythe resultof compactionin response of burial~the porosityof a givenrock isto the stressof overburden. decreased. Therefore,somefluidthatwas oin the poresof a givenformationwas laterIn 1972,thisauthorpresenteda theoryon squeezedout by compaction,In many suchcathe effectof overburdenstressgradientson thereis no escaperoute for the fluid,and tgeopressuredredictiontechniques@2 the fluidLecomesoverpressuredaccordingto1. Thishappensin many areas,end suchCompactioncausedby overburdenstresswas generatedoverpressuredzonesare oftencalldescribedclassicallyin a soilmechsnicsbook tabnormal~tressurezonesor geopressuredby Terzaghiend Peckin 194.83 w th a vessel ,Referencesand illustrationsat end of paper.

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TT.TF liYrTTfiTTflN9 ?if)U CWWRFSL.TTRF PRT llTf TTf)N FIW3M WTT.T,Tf)f% s

HottmsnendJohnsonrecognizedthe main Now, if we incorporatethe theoriesosignificanceof the precedingtheoryend Terzaghiend Peck3 andHubbertandRubey4developeda veryusefulrelationshipbetween by Eq. 1 is used,p/D is shownas followselectricallog propertiesand geopressured.They reasonedthat,sincerocks aremore SolveEqo 1 (S = d+ p)for p and dividearesistiveto electricalcurrentthan is forma- qusntitiesby depth,D, obtaining:tion water,swell compactedshalecontaininglesswater (becausethe waterhas escaped)is p/D = e/D - C5/D . . . . . . . ..more resistivethan a less compactedshalecontainingmore water (onein whichthe water oxhas not escapedto the samedegree). Also, theyreasonedthata sequenceof normallycompacted p/D = f(s/D, b/D)..o.o.o.c(~)sediments(inwhichwater is freeto escape)shouldhave a normallyincreasingresistivity If we combineEq. 7 firstwithEq. 4 andtrend. They substantiatedthis when they ratelywith Eq. 5, we find that the logpplottedresistivityfrom actualwell logs. Any etersare functionsof p/D,whichin turnresistivitydecreasefromthe well established functionof s/D and IS/D.normaltrendindicatesthe presenceof abnor-mallyhigh-pressuredzones. One empiricalrelationshipwas develtrial-and-errorfittingof data,and it pEmpiricaldata from well testsand logs the abnormalpressurebehaviordataof Howere usedto developa correlationof the pore smdJohnsonfairlywell. The equationispressuregradientas a functionof the resistiv-ity departureratio (seeFig. 2). A similaridea was used in conjunctionwith similarempir-icaldatato developa correlationof the pore P/D = s/D - 0.535 E i 3pressuregradientwith sonic-logtravel-timedeparturefromnormaltraveltimes (seeFig. 3). Eq. 8 reducesto the theoreticall?q,6wheNote thatin eachcorrelationonlyone lineis assumethatthe overburdenstressgradiedrawnandthe data pointsscatterconsiderably. equals1.0psi/ft,the resistivityratio1,0 (normalpressure),and the normalpor.Sucha scatterindicatesthatthe chancesoferrorin the pressurepredictionmagnitudeare pressuregradientequals0.L+65psi~ft.high when valuesare read fromthe be. TirnkoandFertljhave showna differentcorrelating p/D= 1*O - 0.535 (1)1*5curvethatmore accuratelypredictsthe magnit-udes of geopressuredin one localizedarea (eee = 0.465psilft . . . . , . . .Fig. 4). T& authortheorizedin 1972thatsuch scatterwas causedprimarilyby differencesin overburdengradients.THE THFDRY

The logdata and measuredpressuredatacc)rrelationsiscussedaboveshowthat thereisdefinitelya relationshipbetweenthe two.Ekpationsof thesecorrelationsmustbe of theform:

cf~Dis representedy the 0.535term.In simpleterms,normallycompactedmentshave a matrixstressgradientequaoverburdengradientminusthe normalporesuregradient.It was postulatedthenthatp/D andtl~evariablesthat controlthe log-derivgroups. In otherwords,the parametersdfrom log data sre dependentvariablespri

p/D - f (NormalR~h/ObservedR~h) . , . (2) controlledby the efistinfiore pressureentsand overburdenstressgradients. Ifand

p/D = f (Obsened~ t~h - Normal ~t~h).0.s. eooco O***. O (3)

= NormalR~h = f(p/D) . . .. . . . , (4)ObservedRshand

ObservedA tshNormal A tSh = f(p/D).. ..0., . . ...0 ,..00. ., (5

ie the case,correlationss~ch as thosedevelopedby HottmansndJohnsonshouldbexpendedto includethe effectof overbustressgradients. It couldbe -a?guedhaoverburdenstressgradientis constantfogivenarea and thereforeof no significaHowever,this is not truein areaswheretionand geopressuredare causedby incroverburdenloadswith deeperburial. Ovestressgradientsare functionsof burialin areassuchas the GulfCoast.

Overburdenstressesend overburdensgradientsmay be determinedby enymeansthe bulk densitiesof sedimentsfrom the

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--,. ., Q17RT A li ATflhTb >X4 J J J 4V me -.V.VLOtotaldepthare measured. Overburdenstressk relatedto bulk densityby the following

n( d /D) Normal =~- (P/D) Normal Squation:

/m- ~gD.. , , . . . . . . . . . .(10) It was alsoshownby Eq. 8 that for abnorpressuresituations~the matrixstressgradien3u1.kdensitiesare determinedeasilyby the use6

was approximatedby:)fdensitylogs. A cumulativeaveragingschemenaybe used to convertlGgbalk-densitydata to ( d /D)Abnormal=?urvesof overburdenstressgradientvs dept...l wosuchcurvesare shownin Figs. 5 and 6.

[1ObservedRsh 1*5

Notethatthe overburdengradientis not 0.535 ****. (1Normal RGhconstantwith depth.To developthe empiricalrelationship The constant,G. 535, i n Rq* 12 is reallythebetweenthe log resistivityparameter,the pore matrixst~~jgradient when S/D = 1.0,md (p/pressuregradient,and the overburdenstress normal= . Therefore,if the right-handgradient,we need considerabledataof the sideof Eq. 11 is substitutedinto%. 12?followingform: (1) logresistititydata, (2) replacingthe 0.535constanttthenmeasuredporepressures,and (3) log bulk-densitydata. Similarly,we need sonic-logdata ( d /13)Abnormal=to developthe shaleacousticparametercorrelation as a functionof pore pressuregradients [

s ]() ~o 1.5- (p/D)Norma ~ . (1snd overburdenstressgradients, 5 9

Such datawere not avtilablein 1972 but whereRo signifiesthe resistivityobservedinwere thoughtto be availableto severalinditid-uals withinlargeoil companies. If such data a clean shaleandRn is the resistivityat thesre availableand are plottedon chartssuchas samedepthon the normalcompactiontrendline(p/D)normalsi.mplymemsthe averagenormalthose shownin Figs.7 and 8, the theorysays pressuregradientof formationwatersin a givthatthe pointswill fall-along-S s~~fti g srea. This valueusuallyrangesbetween0.434differentoverbur~enstressgratientsSUKLISX to ~d 0.465 psiiftof depth.those shown.The linesshownin Figs.7 and 8 shouldbe If value..for anynormalpressuredsitua-tion sre used inFq. 13 as was done in Eq. 9,nearlycorrect,but thiscan be determinedonly resultwill be the same.with experimentaldata. However,two pointsoneach curveare fixed. One point is the end Pore pressuregradientsin any area cantrepresentingnormalpressuregradients(seeEq. be foundusing~s. 6 and 13. In fact,the tw9). The otherend pointof each curveshouldbethe extremecasein whichthe pore pressure equationsmay be combinedto givegradientequalsthe overburdenstressgradient.In this latterefireme,the matrixstress P/D=;-approacheszero. Therefore,the curvemust [~- pDl b 15 (approachthe valueof the overburdenat somelimitinglog parametervalue. One shouldnote that normalmatrixstress(whequalsthe term in bracketsabove)is reduced

THE THEORE? ICAL-EMPIRICALORE PRESSURE when abnormalpressuresexistand is reflecte&by (Ro/Rnbeing lessthan one. The term,PREDICTIONIQUATIONS (Ro/Rn)1 (whenit is lessthan 1.0),whenRecently,in 197L? Lme md Macph-0n7 multipliedwiththe normalmatrixstress(braetedterm in %. 14) resti ts i n the abnorm~publishedmuch data on this subject. The data matrixstressthat is lowerthannormal. Thisincluded: overburdenstressgradients,log is exactlyas it shouldbehavein abnorma3-resistivitydata,measuredpore pressuregradi- formationpressuresituations.ents,respectivewell.depthsfor eachpoint,andthe geologicage for eachdata set. These data The correctvalueof the exponenton thewere used to developthepore pressurepredic-tion equationsthat follow. resistivity-ratioermwas a greatquestionmauntill%. II+was ev~uated ~th MUChdataoIf one reviews.the precedingtheoryand Th~~ ~v~uation is shownin Table l?o. ltespeciallyMS. It 6T 8 and 9? i t Cm be seen where the valueof the exponentwas variedfrthatfor normalpressuregradientSituationsthe 1.2, 1.3, I . L, t o 1. 5. MeasuredformationPrmatrixstressgradientis givenby: sure gradients,calculatedformationpressure

gradients,and overburdenstressgradientsar

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4 THE EQUATIONSFOR GEWRESSURE PREDICTIONFROMWELL ILXX SPalso shown,as are the correspondingRo/Rnvalues. Resultsof the anaQsis shownin TableNo. 1 led this authorto what is believedto been excellentpore pressurepredictionequation.The equationis

6e

Formationpressuregradien~=eithernormal or abnormal(Psi/ft) =

p/D = 0.98- [98 -6~ (~) o= 0.98 - (0.515] (1..00)

= .98 - .515

= .465psi/ft

. ~-($-J-.)1920.I

= 9.0 ppg equivale~twhich is norm

overburden - Matrixstressgradient, At 17, 500t of depth$stressgradient eithernormalor abnozmal(Psi/ft) - (Psi/ft) e(15) ~o,h) 1s2 .[~) = 0.,,Note how this equationcorrespondswith Then,the verybasicEq. 6 for any pressur:ituationin sedimentaryrocks. P/D = 0.98- (o*SS) (fi,)In orderto understandbetterhow to useEq. 15 to predictformationpressures,the E .98 - 0.072followingexampleis used.

ExampleProblem1 I =.9C8psi/ftThe problemis to predictthe pressuregradientsexistingin the formationsin a welllocatedin SouthLouisisna,a verytroublesomedrillingarea.Solution

1. Evaluatethe electriclog from top tobottomfor conductivityor resistivityvaluesinthe cleanshales.2, Plot theseresistivityvaluesvs depthas shownin Fig. 9.3. Establishthe normalcompactiontrend.Use experienceand any knowndatato aid indrawingthe normalline.4. Calculatevaluesat variousdepthsfor

(Ro/Rn)l*.5. DetermineSID fromdensitydata

= 17.46ppg equivalent,

If one desiresto use the directcondtivitylog values,ratherthenlog resistiEq. 15 istrsnsformedas follows:

:=; -[ -(P,D)-J%)20.. Recently,it has been foundthatif one callatesendplotsthe correctedd exponentfrdrillingparameters,the resultingplot issimilarto a logresistivityplot. Therefthe followingequationwas developedfor gepressuredredictionfrom correctedd expondata.

J, Determine(p/D)nfromknownnory;t~gs Note the similaritybetweenEqs. 15 and 17suregradientsor water salinitydata.particularcase,S/D = O.$@psi/ft and (p/D)n.0.465psiift. Also,it has recentlybeendeterminedsonic-logdata can be usedto predictgeo-7. Use Eq. 15 to calculatepressure pressuremagnitudeswiiththe followingequgradientsof the variousRo points. At 8,5(20ftof depth,for example,Ro = 1.00sndRn . 1.(X3.Then, ~=;- [~- (pD)~ ~) 30 .

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SPE SEAL BEN A. EATON- ..-.Eq. 18 shouldbe validfor thepredictionof o = observedgeopressuredagnitudesfrom seismicdata also. n= normal

Each term of ~s. 15 through18 haveunits REFERENCESof psiift. 1, Hottman,C. E., and Johnson,R. K.: EstCONCLUSION mationof FormationPressuresfromLog-DerivedShalel%operties,J. Pet. Tech.The authorconcludesthatEqs. 15 through (June1965)717-722.18 are extremelyaccurate. Also concludedis 2. Eaton,B. A.: IATheoryon the Effectofthe factthatthe accuracyof eachequations OverburdenStresson Geopressuredredictabilityto predictgeopressuredradientmagni- FromWell lkgs,paperSPE 3?19presentetudedependson the qualityof the inputdata. SPE-AIMEAbnormalSubsurfacePore PressurThe methodsusedto establishnormaltrends Symposium,BatonRouge,La.,May 15-16,variesas much as the numberof peoplewho do 1972;J. Pet. Tech (Aug.1972)929-934.it. Generallyspeaking,however,if the equa- 3. Terzag~, Karl, and Peck,R. B,: Soiltionis usedwithknowledgeand care,it will Mechanic~in I&uzineringPractice,=predictgeopressuredradientmagnitudeswithin ~ey& Sons,Inc.,New York (1948)566.lessthan 0.5 ppg equivalent. 4. Hubbert,M. King, andRubey,W. W.: Rolof FluidPressurein Mechanicsof Over-NOMENCLATURE thrustFaulting,Part1,I;Bfll.fGSA (Feb1959)70.

C = conductivity- mill.imhos 5, Timko,D. J., Fertl,W. H.: Relationsd = con?ectedd exponent BetweenHydrocarbonAccumulationand Geo-D = depth,ft pressureand Its EconomicSignificance,f . function Pet. Tech. (Aug.1971)9z~-933*g = accelerationof gravity,cm/sec2p . formatio.1ressure,psi 6. Eaton,Ben A.: ItFractureradientPredicR . shaleresistivity,ohm-m tion snciIts Applicationin OilfieldOperS = overburdenstress,psi tions, J. Pe%.Tech. (Oct.1969)1353-1t = sonictraveltime,microsec/ft 7, Lane,RobertA., and MacphersonfLcuisA.PB= averagebulk densityof se&ents, gin/cc ~ARetiewof GeopressuredvaluationFroma= rockmatrixstress,psi I Well Logs - LouisisnaGd.fCoast~SPEPaper 5033presentedat the 49thAnnualFSubscript SF%AIME Meettig,Houston,Tex,fOtt, 6-9c . corrected 1974*sh = shaleB=bulk

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TA8LENUM82RIPOREPRSSSIJREFWIW2 CALCULATIONS

PorePressureGmdiencCa2cu2atow Page2FFG~Ft.

1.3 1.4 1.5Ro ~-G- Rn Ro

1.2 1.3 1.4 I l.s I * CalculatedJ@_ JL& J& ~ & FPGM Pa Rn Rn D Pai/Ft.* .777 .570.760 .937 .578.745 .585.739 .588.343 I .786.304 .954 .805.277 .819

I .808.837 .894 .567.553.559575 .810740 .400

.582 -1----194 I .780 .766,739 .565--1-7S6.792.756.792

.570.577.585.582 .695.722 .706

s339 I

.591

.570.577.585.591.508 .708.479 .959 .722.454 .735.428 .748.924 .497.887 .891 .513.878 .517.872 .520.813 .545.798 .894 .552.785 .557.772 .567.893 .511

.886 .891 .514.875 .519.866 .522.835 ,536,823 .894 .541.811 .547.799 .551.784 ,558.767 .895 .565.752 .572.736 .579

.565..553

.895717I

.568

+

.722 .706

.732524 r.918

.765.800 .566.573.580,748 .895-1-- .587.801.831574 .786+

.772 .758

.607 .586-i--479 .909 _-l-651.7001

.885.903

.616.896 .625.634.664

I .514

.559 .629E523 .861.559 .816 .496.-..>Ju H876 .867 .858.748 .732 .716 .894 .518.522.526.567.897 .574.581.588m

I.765.800 ,

.847 .531.835 .894 .536.824 .541.813 .545 6.684x

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Pore Preewre GradientCa3.culatow Page 3 Por.r.?=$ureGradientGalculations Page 4FPG_PsJFt.

.502

.511

.514

.523

.503

.587

.620

.497

.495

RO-ET.907

.833

.875

.875

.922

.904

.742

.857

.902

.889 .880.871

.803 .788 .774

.852 .841 .829

,852 .841 .829

.906 .897 .892

-H-886 .877 .8M.699 .678 .659++

.832 .818 .806

.884 .875 .866

1.5~Rn

.862

.760

.818

.818

.884

.859

.639

.793

.857

-1CalculatedFPCPsi/Ft.

h-.513.894 .516.520-H550.894 .556.562.568.528.892 .533.538.5.43

-

.528.892 .533.538.543

.505.892 .509.511.515

.514.894 .518.522.526

.598.907 .607.616.625

a

,540.907 .545.551.557.517.910 .521.525.529

.477

.548

.s91

.539

.562

.549

.593

.603

.608

.607

.917

.7.45

.714

.844

.847

.857

.745

.745

.750

1.2 1.3 1.4 L.5J& Ro ~ > &Rn r h h D.910 .893 .907

.886 .878.702 .682 .905.662 .643.668 .646 .905.624 .603.816 .803 .888.789 .776.818 .806 .889.792 .780.832 .828 .886.806 .794.702

.682 .941.662 .643.702 .682 .903.662 .643.744 .726 .938.709 .692.708 .688 .938.688 .650

CalculatedFPGPsi/Ft..505.512.515.519.596.60S.6M.622.611.621.631.642.543.548.554.560.541.547.553.558.536.542.547.552.607.616.626.635.607.616.626.635.589.598.605.613-1606.615.625.633

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Pore PreseuxeGradient Galculationa Page 6PorePressureGradiantCa2cu2ations

1 ,FPG 1.2 1.3 i 1.5~ Jt& ~ & RO &Ft. 2n .Rn Rn -iG- Rn

.708. 61S .750 .688 .6M .650 ~

.728.607 .768 .710 .691 .673

.558.68 .615 .532 .506 .482--

.604.678 .657 .579 .555 .532.668.635 .714 .645 .624 .603.564.679 .621 .538 .513 .490.746.554 .783 .728 .710 .693.752.619 .788 .734 .716 , .700.681. 62S .726 .660 .639 .618

- SI- r.938

.940

.940

.940

.937

.942

.940

.935

.936

3alculatedPPGPsz/Fc..606.61S.625.633+

.594.603.612.620

.675.687.700.711--l6S3.665.676.6874

.622.623.6L2.652.673,685.697.708.586.594.603.611

1

582.590.598.606.615.625.635.665

F?G 1.2 1.3& ~ & _&Ft. Rn Rn 7(U

.615.658 .667 .591

.668.655 71 645

.602.6:0 .655 L 577T6 1.5~r Rn.759 .744; .567 .545L

*

.553 .530

.875 .867

.676 .658

.155r .236

.93s

.938

.940

.930

.932

53 data po nce - =points m L.2 ZK OOJIJG~-7 poin~ on 1.3 t,4 potitson 1.4 ~110 pointsn 1 5 0

=3alculamd

FPGPsi/T. S64.571.578 I1585.647.658.622 I

-i

.633.643.653

.654.666.677.688,515.519.523.527

+

.598. .607.616.625

.828.839.849.858

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s

A*I 0*S5

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o

2

4

6

8

10

,2

,4

I6

I8

2%50 075

7

.

d I

+T_90 (OVERBURDEN STRESS QRAOIENT- FId/ft

Composite overburden stress gradient for allcompactedGulf coast formations.

0

00

D~ s>0 ~= .0 ~gL :eo ng ~zsg ggo y

~g a0

.00t

NORMA, R(~h} / OBSERVEO R{th)Fig. 7 - Shale resistivityparameter vs reservoirfluid pressure gradient.

0\

1

s\

4&00~I s~w0 ~

7\

8

9

\8007 075 08 005 09 095 IDOVERBURDEN STRESS QRADIENT - p i /ft.

n

Fig. 6 - Overburden stress gradient - Santa BarbcChannel, Calif.

045.0

0300- 100

0600=. - 120\=.gu.~ 0?006> - ,40gE

0800\ ~