Resistivity Logging of Natural Basalt

8/6/2019 Resistivity Logging of Natural Basalt

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Proceedings Eighth Workshop Geothermal Rese rvoir EngineeringStanford University. Stanford, California. December 1982SGP-TR-60RESISTIVITY LOGGING OF FRACTURED BASALT

V. Stefansson, G. Axelsson and 0 . Sigurdsson

OrkustofnunGrensdsvegi 9Reykjavik, IcelandI"

he electric log has been used for abouthalf a century as a tool for s tudyingthe formations penetrated by a borehole.A t early stage, comprehensive studies ofsedimentary rock es tab lish ed thedependence of formation re s is t i vi tyfa ct or upon poros ity. Archie (1942)pioneered this ef for t by suggest ing h iswell-known empi rical formula co rr el at in gthe formation fac tor and porosity. Eversin ce, Archie's law has been a ce nt ra lpoint in in te rpre ta t ion methods fore l e c t r i c a l l og s.Desp ite the simple empir ical dependanceof rock conductivit y on porosity asexpressed by Archie's law, th er e doesnot ex is t a s imple the ore t ica lexplanation for this phenomenon.Mathematical modeling t o prove theval id i ty of an Archie type re la t ionsh iphas been ca rr ie d out by Greenberg andBrace (1969) , Shankland and Waff (1974)and Hadden (1976) . However, a l l modelsdepend on si mp li st ic geometricalassumptions of pore space di st r ib uti on sand the degree of reali sm can bedispu ted .During the l a s t decade, inves t igat i onson geothermal re se rv oi rs haveaccentuated the ro le of f ractu res inres erv oir physics. Various types ofgeophysica l logs have been applie d inorder t o dis t in gui sh between fracture dand int erg ran ula r reservo irs. One ofthe s t rong candidates for th at is th ee l e c tr i c lo g (Towle 1962, Aguilera 1974and 1976). The main r eason f o r t ha t i sthe fact that the exponent i nArchie's law seem t o be 1.0 in the caseof f ra ctu re d rock (Brace and Orange1968 ), where a s a va lu e of 2.0 seems t obe va li d fo r non-fractured rock (Braceet.al. 1965).

Consider an idealized model forf r ac tu r ed r ock in o rde r t o e s t ima te t hee f f e c t s o f f r ac tu res onr es i s t i v i ty - po r os i ty r e l a t i ons . Th i smodel is presented in f igure 1 andco ns is ts of cubes representing the rockand th e spac ing between th epara1 elepipeds representing waterf i l l e dfr ac tu re s. Simil ar models have beenpres ente d bef ore (Towle 1962, Agui lera1974 and 1976, Hirakawa and Yarnaguchi1981), but the pres ent approach issomewhat different.The following parameters a r e used i n themo d e l :Pw = r e s i s t i v i t y of water i n poresand f ractures43 = r e s i s t i v i ty of r ock mat rixe - por osit y of rock matrix( r e l a t i v e t o m t r i x v olume

only)x = len gth of each matrix cube,f r a c t i o n1 -X Width of f r ac tu r es , f r ac t ion

It i s convenient t o in t roduce lumpedresistances in approximating th er e s i s t i v i ty o f t he model as i s shown inf i g u r e 1. Thus the resis tance of anunit cube is approximately given by

and the re si s t iv i t y of the model i sp t R ( 2 )

Ref er r ing t o f i gu r e 1(3 )

I n t h i s paper a simple lumped doubleporosity model is s tud ied i n o r de r t oFurthe r, t he r e su l t s of r e s i s t i v i t y andpor os i ty l ogg ing in I ce l and ic basa l t i s

( 4 )x PWes t imate the e f f e c t s o f f r ac tu r es on t h e R2 =-es i s t i v i ty - po r os i ty r e l a t i onsh ip . X2presented, and it is shown that the 1 ( 5 )PWi s t r i bu t ion o f po r os i ty i n t hese rocks R3 =-re dominated by fractures. 1-x*

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IFigure I

IFigure 1 Schemat ic f i ure of thedouble porosity Ael and theequva len t r e s i s t i v i ty ca l cula t edfor each unit cube.

and the re si s t iv i t y of the f racturedrock is according t o equat ion 1

whereF = P/P, ( 9 )

Equation 8 is somewhat sim ple r tha n th eone pr es en te d by Hirakawa and Yamaguchi(1981), but gives similar results.The s a m e approach can be used t oestimate th e formation fac tor for modelswi th e i t he r ve r t i ca l f r ac tu r es only o rhorizonta l fra ctu res only. Omitt ing th ede ta i l s of the der iva t ion one obtainsf o r ve r t i ca l f r ac tu r es on ly :

Equation 8 is used t o estimate theformation re si s t iv i t y factor for thedouble po ros ity model. Here it isassumed t h a t

The use of an exponent of 2 is supportedby the results of Brace and Orange(1968b). From their experiments withdif fe ren t rock samples, saturated withbri ne and measured a t 4 kbar t o c lose upmost of th e crack por os ity , an exponentof 2 dependence of re si st iv it y uponresi dual poro sity was obtained. Thesere su lt s were confirmed by the s imulat ionst ud ie s of Shankland and Waff (1975).Equation (12) has been recognized as anempiric al law in th e petroleum indu stryand is va li d for normally cementedsandstone.The re la tio ns hi p between the poro sitygnd the formation fa ct or according t oequation 8 i s presented i n f igures 2 and3. The results for hor izontal f ractureonly (equation 11) ar e presented inf igu r e 4 .

In troducing the f rac ture porosi tytJf = 1 - x3 (7 )

an ar e s i sp r o s>proximation for the formation:ivi ty factor for the doublei ty model is obtained as:

Figure 2 Relation between formationr e s i s t i v i t y f a c t o r and t o t a lporosi ty as calculated from thedouble po ro si ty model. Curve Br ep resen ts ve r t i ca l f r ac tu r e on lywith ma t r i x porosi ty equal t o zero .Other curves a re for cases whereboth ver t ical and hor izo ntalf r ac tu r es a r e p r esen t.

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i E uations 8, 10 and 11 can be combinedwfth Archie's l a w (Archie 1942)VerlicoI ond horizOnlol froslurel

where

i s t h e to t al porosity. The doublepor osit y model in the presence ofve rti cal and horizon tal frac tur es, when$bf 0 and ot


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4 ) Assuming th a t the ra t i o of ver tkca lt o h o r i zo n t a l f r a c t u r e s is a s i n t h emodel of figure 1 with to t a l poros i tyand for mat ion fa ct or known fromgeoph ysical logging dat a, one canes t imate roughly the re la t ive importanceof fracture- and ma t r i x poro sity by theuse of th e approximate model pre sen tedabove.BESISTIVITY-WROSITYBELATIOWSPPBBASALTExtensive geop hysic al logging has beenperformed in sev er al. deep ( 2 km )bo re ho le s in Icel and . Among th eparameters observed were r e s i s t i v i t y(16" and 64" normal) and po ro si ty(neutron-neutron) . Examples ofr e s i s t i v i t y ( fo rm at io n r e s i s t i v i t yfac tor ) poros i ty c ro ssp lot s from twoboreholes in bas a l t ic environment arepresented in f igures 5 t o 7. Thesefi gu re s show only few, but represe nta-tive examples.

JHDBY-9000 G Ax@ZOO 1067 11% J F O". 5

D o l r l t . 1800-18701 \

Figure 5 R e s i s t i v i t y - poros i tyc r o s s p l o t f o r D o l e r i t e a t 1 90 0 -1970 m depth in w e l l KJ-16 i n t h eKraf l a high temper ature geothermalf i e l d . The b e s t l i n e a r f i t t o theda ta po in t s is shown along with i t sc o r r e l a i o n c o e f f i c i e n t.

m1.500

LOO0

2 . 500

).ax,m

Well KJ-16 is a produc t ion hole dr i l le din sid e the Krafla geothermal area(StefSnsson 1981) in the neovolcaniczone of Ice la nd . The IRDP-hole(Fr idl e if sson e t . a l 1982, Robinsone t .a l . 1982) is dr i l l e d in a pproximately10 My o ld b a s a l t p i l e i n E as te rnIce land. The pore water re s i s t iv i t y( Pw ) is f a i r l y well known, a s a func t ionof dep th, fo r th e IRDP-hole, whichenables the es t imation of the formationr e s i s t i v i t y f a ct o r ( f i g u r e s 6 and 7 ) .A rather good correlation betweenr e s i s t i v i t y and p o r o s i ty is seen for theexamples in f igures 5 t o 7 . Are la t io nsh ip of the form P = apW$" has been f i t t ed t o thes e da ta andt h e results ar e presented in the

F Oum6

a2.-

2.00

I.so

I m0

Figure 6 Formation re s i s t iv i t yf a c t o r - p o r o si t y c r o s s p l o t forBa sa lt d ike s in the de p th in te rv a l1360-1500 m i n t h e IRDP hole inEastern Iceland.m:Dd::bY50Tz Flqui. 7

0.600 I .ax,,zT I1 \ + + + :\r*-0.93

0!.W

t.m

I Q

I m*,

Figure 7 Formation re s i s t iv i t yf a c t o r - p o r o si t y c r o s s p l o t f o rBa sa l t f lows in the de p th in te rva l1700-1800 m i n t h e IRDP hole inEastern Iceland.

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f igures . An equa t ion of this form hasa l so been f i t t e d t o da ta from o the rin te r va l s , not presented here , andweighted average for th e exponent ca lcula ted for the two di f fe ren ta reas . The res ul ts a r e presented int a b l e I.

t m >-Kraf l a 1.02 2 0.07 205 m out of(0-1 My) 2 x 1300 mI RDP 1.10 & 0.04 430 m out of(-10 My) 1100 m


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These results a r e i n good agreement withreEUlt6 for ba sa lt from Rawaii (Kell cret .a l, 1974) and res ult 8 from .theAtla nti c Ridge a t 23'N (KirkpatrickRow do we int erp re t an exponent c l o s e t o 1.0 1 This indicates,according t o the double poro sity modelpresented before and the results ofBrace and Orange (1968a), that fracturescon sti tut e an important part of theporosity for the basalt6 studied.However, we can not determine, on th ebas is of the values for alone, howimportant fractures are in the overa l lporosity . According t o the doubleporos i ty model an exponent of 1.0 ispossible, even though matrix porosity isconsiderable.

1979)

A more complete int erp ret ati on offormation re s i s t iv i t y fac tor-poros itycross-plots can be attempted on theba si s of th e double por osi ty model. Themodel can be used t o estimate there la ti ve - importance of fract ure- andmatrix p or os it y when t he por e waterr e s i s t i v i t y is known. We w i l l take asexamples th re e cross -plo ts from theIRDP-hole present ed i n fi gu re s 8 to 10.The two extremum cases ($b = 0 andQf = 01 , for vertical and horizontalfractur.es, as well as one or two linesfor const ant k-rat ios ar e superimposedon these cross -plo ts. We se e from t hef igures tha t these da ta can beint erpr eted on th e bas is of the doubleporosity model. A n in te rpre ta t ion oftha t kind is of course approximate,requires an exact knowledge of the valuefor and is limit ed by th e underlyingassumption of fra ctu re orientation.r n 2 r , o Y ; ; ; &

looVJFigure 8 Relation between formationre s i s t iv i ty f ac tor and to ta lporosity for Basalt f low6 in thedepth interval 0-300 m i n t h e IRDPhole in Eastern Iceland.superimposed ar e lines fo r the twoextremum cases $b = 0 ana $f = 0and one l in e for constant rat iobetween fr ac tu re poro sity andmatrix porosi ty.

2.m

I .m

I.m

0.mDI'

Figure 9 Relatio n betweenformation re s i s t iv i t y fac tor andto ta l poros i t y for Basa l t f lows inth e depth in te rv al 1500-1600 m inthe IRDP hole in Eastern Iceland.Superimposed ar e li ne s for t he twoextremum cases $ = 0 and = 0along wi t h a t i ne for constan tra ti o between fra ctu re porosity andmatrix porosity.

Figure 1 0 Relation betweenformation res is t ivi ty fac tor andto ta l poros i tv for Basalt dikes I nthe depth in ti rv al 1700-i 1800 m I nthe IRDP hole in Eastern Iceland.Superimposed ar e li ne s for th e twoextremum cases ob = 0 and Qf - 0along with l in es for constant ra t i obetween fr ac tu re por os ity andmatrix porosity,

Using figure 3 we can estimate roughlythe ra t io of f r ac ture - t o mat rixporosity . For th e cases from th eIRDP-hole presented i n f igure s 8 to 10the following resul ts are obta ined( tab le 11):

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-n t e r v a l 6 f+-- .-

0-300 mBasalt flows -0.71500-1600 mBasalt f lows =0.51700-1800 mBasalt dikes =0.2-0.3

The apparen t decrease in f r ac t ureporos i ty wi th dep th i s noteworthy, butth e underlying assumptions mentionedabove shoul d be kept in mind. Ad ec r ease in f r ac tu r e p o r o s i ty co uld b eth e r e su l t of i n c rea s in g p r e ssu re w i thdepth c losing up some f r ac tu r e s . Th i seffect could on the other hand alsore su l t f rom changes in f ra c tu reor i en t a t i on wi th dep th.To conclude t h i s d iscus sion we p r esen tone example for a n o n -b asal t i c u n i t i nf i g u r e 11, where formation re s i s t iv i t yf ac to r - p o r o s i ty c r o ssp lo t f o r ad i o r i t e (55% S i 0 ) u n i t from t h eIRDP-hole is shown. Here w e see ar e l a t io n sh i p which is q u i t e d i f f e r e n tfr om th e r e l a t io n sh i p s f o r t h e b as a l tp resen ted above. In te rpre t ing th e datai n f i g u re 11 accor d ing t o th e doublepor osi ty model we f i n d t h a t f r a c t u r ep o r o s i ty sho uld b e in s ig n i f i ca n t i n t h i sd i o r i t e u n i t.

O.Oo0 0.600 I .ow I2:600 \1

Figure 11 Relation betweenf or ma t io n r e s i s t i v i t y f ac to r andt o t a l p o r o s i t y f o r 10 m t h i c kDiorite formation a t 1710 m depthi n t h e IRDP hole in EasternIceland. Superimposed are l i n e sfor the two extremum cases * b = 0and + f = 0. The d a t a p o i n t s f a l lc l o s e t o and para l le l w it h t h e l i n e= 0 i n d ic a t in g t h a t f r a c t u r eg r o s i t y is n e g l i g i b l e .

w9.500

2.ow

I,600

I ,000m

CONCLUSIONA lumped double por os it y model has beens tu d ied in o r d e r t o estimate t h e e f f e c tof f r a c t u r e s on r e s i s t i v i t y - p o r o s i tyr e l a t io n s . I t is found tha t ther e l a t io n sh i p be tween r e s i s t i v i t y an dp o r o s i ty f o r f r ac tu r ed rock is i ngen era l no t simple and depends both onth e amount of ma tr ix po ros ity as w e l l asth e fr ac tu re ori ent ati on. However, whenf ra c tu res dominate over matr ix poros i tythe exponent is close t o 1.0.R es i s t i v i t y - p o r o s i ty r e l a t io n s have b eendetermined fo r la rg e amount of ba sa lt icformat ions in Ice land . An exponentc l o s e t o 1. 0 is found in a l l casesinvest iga ted . This is i n t e r p r e t e d asf r a c t u r e s c o n s t i t u t e a considerab le parto f t h e p o r o s i t y o f t h e b a s a l t s . I n th eIRDP-hole i n Easte rn Icel and it is foundt h a t t h e r a t i o o f f r a c t u r e p o r o s i t y t oto t a l p o r o s i ty d ec r ease s w ith d ep th .I n c o n t r a s t t o th e exponent of 1.0 foundfor b as a l t i c fo rmat ions i n Ice land , manyin ter b edd ed f o r ma t ion s in t h e b as a l t i cpi l e reve al an exponent of approximately2.0. This is i n t e r p r e t ed as matrixp o r o s i ty d om in ates f r ac tu r e p o r o s i ty inth ese ca se s .The s tudy of res is t iv i ty - poro si t yr e l a t io n sh i p p r e sen ted d em on s t ra t e s t h a ttommon geophysical log s can dis tin gui shbetween fra ctu red and porous res erv oir s.

W e thank Rafnragnsveitur Rfkis ins-Kriif luvirkjun for permiss ion t o u se d a t af rom th e Kraf la f ie ld .

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Resistivity Logging of Natural Basalt