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WORKSHOP

ON

GEOTHERMAL RESERVOIR ENGINEERING*

Paul Kruger and Henry J. Ramey, J r .

Stan f o rd Geo the rma 1 ProgramStan fo rd Un ivers i t y

Stan fo rd , Ca l i fo rn ia

Workshop Report

December 15- 17, 1975

J;Conducted under Grant No. NSF- AER-72-03490 sponsored by the RANN programof the Nation al Science Foundation.

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TABLE OF CONTENTS

Page

Summary of the Workshop - P. Kruger . . . . . . . . . . . . . . . . . . 1 

Rapporteur Reports

Reservoir Physics - P. A. Witherspoon . . . . . . . . . . . . . . . 4 Well Test ing - H. J. Ramey, J r . . . . . . . . . . . . . . . . . 6 Field Development - G. Frye . . . . . . . . . . . . . . . . . . . . 8

Model ing - J. W. Mercer . . . . . . . . . . . . . . . . . . 12Wel l St imulat ion - M. Nathenson . . . . . . . . . . . . . . . . . . 9

Overv iews

A Programmatic View of Geothermal Reservoir Engineering - R. Corye l l 16The B i r t h o f Geothermal Reservoi r Engineering - H. J. Ramey, J r . . . 20

Reservoir Phvsics

Summary Description o f Research Ac t i v i t i es - D. R. Kassoy . . . . . .Heat and F l u i d Flow Experiments t o Measure Geothermal Rese rvoi r

Physical Parameters - W. E. Brigham . . . . . . . . . . . . . . . An Attemp t t o Cor re la te Kh D i s t r i b u t i o n w i t h Geo logical S t ruc tu re

2326

o f Lard ere l lo Geothermal F ie l d - R . C e l a t i , G. Ner i , F . Perus i n i ,and P. Squarci . . . . . . . . . . . . . . . . . . . . . . . . . 37

Fl ui d Flow i n Geothermal Reserv oirs - J . C . M ar t i n . . . . . . . . . 42

Fr act ur e Flow i n Geothermal Reser voirs - G. Bodvarsson . . . . . . . 4 5Reservoir Factors Determining th e Fra ct ion o f Stored EnergyRecoverable from Hydrothermal Convection Systems - M. Nathenson . 50

U t i l i z a t i o n o f G r av i me t ri c D ata f o r E s ti m at i on o f Hydrothermal

Reservo i r Charac ter i s t ic s i n the East Mesa Fi e ld , Imper ia l Val ley ,

C a l i f o r n i a - T, Meidav, R. James, and S. Sanyal . . . . . . . . 52E f f e c t s o f R e i n j e c t i o n - C. F. Tsang and P. A. Witherspoon . . . 62

 An I n v e s t i g a t i on o f Screeni ng Geothermal Product ion We1 1s from

Land Surface Subsidence Ass ocia ted w i t h Geothermal EnergyProduct ion - S. K. Garg . . . . . . . . . . . . . . . . . . . . . 65

Well Test ing

Pressur e and Temperature Bu ild up i n Geothermal Wells - M. S. G u l a t i . 69Well Log Anal ysis and Well T est ing i n the Heber

Geothermal Field - L . Mann . . . . . . . . . . . . . . . . . . . 7 4

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Geothermal Wel l Test i ng at Roosevel t KGRA, Beaver County, Ut ah -D . C. Har ban . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Shel l ' s Acti vi ty i n  The Geysers Area - E. L. Fehl berg . . . . . . . . 84Water Entry Bel ow SteamProducti on:

 The Geysers - G. Frye . . . . . . . . . . . . , . . . . . . . . . 89An I nter f erence Test i n Al f i na Geothermal Fi el d (Northern Lat i um,

I t al y) - A. Barel l i and G. Manett i . . . . . . . . . . . . . . . 93Horner Method Appl i ed to Bui l d- Up Tests on Traval e 22 Wel lA. Barel l i , R. Cel at i , G. Manett i , and G. Neri . . . . . . . . . 101

Study of a Geothermal Fi el d i n the Asal Act i ve Vol cani c R i f t Zone(French Terr i tory of Af ars and I ssas, East Af r i ca) -A. C. Gri ngarten and L. Sti el t j es . . . . . . . . . . . . . . . . 113

J . F. Kunze, L. G. Mi l l er , and R. C. Stoker . . . . . . . . . . . 117

Proj ect , I daho -  T. N. Narasi mhan and P. A. Wi therspoon . . . . . 124

A Case Hi story at

-

Raf t Ri ver Geothermal Reservoi r Engi neeri ng and Wel l St i mul at i on -

I n i t i a l Resul t s of Reservoi r Product i on Test s, Raf t Ri ver Geothermal

Fi el d Devel opment

An Approach to Geothermal Devel opment - R. A. Woodi ng . . . . . . . . 126Geopressured Geothermal Reservoi r Engi neeri ng Research at the

Uni versi ty o f  Texas - R. M. Knapp, M. H. Dorf man, 0. F. I sokrari 130SDGEE Pi oneeri ng Geothermal Test Work i n the I mperi al Val l ey of

Southern Cal i f orni a - G. L. Lombard and J . M. Nugent . . . . . . 135Ni l a nd Reservoi r Moni tor i ng and Eval uat i on Operati ng Program-

T. C. Hi nr i chs . . . . . . . . . . . . . . . . . . . . . . . . . 143East Mesa Reservoi r -  T. L. Goul d . . . . . . . . . . . . . . . . . 146

 The PG&E Geysers Power Pl ant - A Ut i l i ty Company' s Vi ewpoi nt -L. J . Woi t ke . . . . . . . . . . . . . , . . . . . . . . . . . 153Geothermal Reservoi r Pressure Requi rements f or Product i on -

J . T. Kuwada . . . . . . . . . . . . . . . . . . . . . . . . . . 156On t he Opti mal Rate of Geothermal Energy Extract i on - C. R. Scherer . 161Economi c Model i ng f o r Geothermal Reservoi rs and Power Pl ants -

C. H. Bl oomst er . . . . . . . . . . . . . . . . . . . . . . . . . 167

We1 1 St i mul at i onPhysi cal Model s o f St i mul ated Geothermal Reservoi rs

-P . Kruger

. . .I69

Hydr aul i c- Fracture Geothermal Reservoi r Engi neer i ng - H. D. Mur phy . 1 7 4Model Experi ments i n Hydraul i c Fracture - J . Dundur s . . . . . . . . 178Anal yt i cal St udy of Crack Growth and Shape by Hydraul i c Fractur i ng

of Rocks - T. Mura, L. M. Keer, and H. Ab6 . . . . . . . . . . 180Control of Si l i ca Scal i ng - H. L. Barnes and J . D . Ri mst i dt . . . . . 185Predi cti ng Expl osi on- Generated Permeabi l i t y around

Geothermal Wel l s - C. R. McKee and M. E. Hanson . . . . . . . . . 192i i

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Model in g

Summary o f ou r Research i n Geothermal Res erv oir S im ul at io n -C. R. Faust and J . W . Mercer - . . . . . . . . . . . . . . . . .

The Pr in ce to n Geothermal Research Program - George Pinder . . . . . .

Numerical Calculat ion o f Mult iphase F l u id and Heat F low i nHydrothermal Reservoirs - J. W. P r i t c h e t t . . . . . . . . . . . .Methods o f So lu t i on o f th e Equations f o r Convection i n Porous

Media, w i t h Geothermal Ap pl ic at io ns - R. A. Wooding . . . . . . .A Hele-Shaw Model of Heat Convec tion i n Porous Media under

Geothermal Conditions - H. W . Shen . . . . . . . . . . . . . . .Numerical and Analyt ical Studies on Heat and Mass Tra nsf er i n

Volcanic Isl and Geothermal Rese rvoirs - Ping Cheng . . . . . . .Research on Numerical Modeling o f L i q u i d Geothermal Systems -blichael Sorey . . . . . . . . . . . . . . . . . . . . . . . . . .Fin i te E lement So lu t ion o f Geothermal Energy Ex tr ac ti on -

Z. P. Ba?ant, S . Nemat-Nasser, and H. Ohtsubo . . . . . . . . . .Numerical Model in g of Hydrotherma l Reacti ons i n Geothermal

Reservoirs - C . G . Sammis . . . . . . . . . . . . . . . . . . . .Progress Report on a Mathematical Model of a Paral lelepiped Reservoir

w i t h No Penetrat ing Wel lbore and Mixed Boundary Conditions -A. B a r e l l i , G . Manet t i , R. Celat i , and G. Ner i . . . . . . . . .

Serge Bories . . . . . . . . . . . . . . . . . . . . . . . . . .

Fract ure and Pore Perme abi l i ty - P. W. Kasameyer andR. C . Schroeder . . . . . . . . . . . . . . . . . . . . . . . . .

Fundamental Study o f Changing o f Phase i n Porous Ma te ri al s -

Thermal Depletion of Liquid-Dominated Geothermal Re serv oirs w i t h

Geothermal Energy fro m a Bor ehole i n Hot Dry Rock - A Pre l im inaryThe Use o f General S e n s i t i v i t y Theory t o Analyze the Geothermal

Study - D . Sharma and T. Maini . . , . . . . . . . . . . . . . .Reservo i r Mode l' s S en s i t i v i t y t o the Permeab i l i t y Funct i ons -R. W .  Atherton . . . . . . . . . . . . . . . . . . . . . . . . .

198199201

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1 NTRODUCTION

 Although geothermal energy was f i r s t co nverted t o e l e c t r i c i t y more

than 70 years ago, u n t i l recen t l y l i t t l e pub l i c demand fo r i t s widespreaduse existe d. Geothermal energy has been considered an a t t r a c t i v e a l t er n at e

source o f energy f o r more than a decade i n many developed as we ll as un-developed countr ies and th e in t erna t ion al awareness o f t he growing d e f i c i t

o f f os s i l fue l s has sparked acce le ra ted in t e res t i n de te rmin ing na t iona lresources and u t i l i z a t i o n technologies.  As o f 1976, t he t o ta l wo r l dgenerat ing capac i ty fo r generat ing e l e c t r i c i t y from geothermal resources

i s about 1100 MW (equal t o t h at o f one modern nuclear power p la nt ) and

more than 3/4 o f i t i s produced at on ly two s i tes , The Geysers i n Cal i fo rn i aand the Tuscany f i e l ds i n I t a l y .

Many problems have been identified which beset the rapid development

of geothermal resources, cover ing the e n t i r e " fue l cyc le" f rom exp lo ra t ion

through conversion and residu als co nt ro l . The major problem i s th e i n -f l e x i t y o f natura l geothermal resources which occur i n a wide va r i e t y o f

hydrogeolog ic, thermal , and chemical qu al i t ie s . U t i l i z a t i o n must bedesigned to f i t the spe c i f i c chara c te r i s t i cs o f i nd iv idu a l resources.

S ince the thermal e f f i c i en c i es f o r convers ion t o e l ec t r i c energy a re very

low even for the t w o known highest qual i ty hydrothermal resources, i n-

du st r i a l development awaits grea ter economies i n resource exp lo ra t i on and

eva lua t ion , energy ex t r ac t i on , and u t i l i z a t i o n technologies. To compoundthe problems, development i s occu rr i ng i n an era of increased p ub l i c aware-

ness about i n s t i t u t i o n a l and environmental concerns.  As a resul t , aformidable arr ay o f legal , soc ia l , and regulato ry problems a ls o requi resreso lu t ion .

 As the developnent o f a geothermal in du st ry proceeds, these manyproblems are be ing evaluated genera l ly by the sector o f the nat iona l

economy th at has had experience i n solv i ng s im i l ar problems fo r oth erresources. The ex pl or at io n fo r geothermal resources has been undertaken

largely by the energy resource companies that use subsurface geosciences

and the d r i l l r i g as t h e i r mode o f ope ra t ion . Conv ersi on t o e l e c t r i c i t y ,

present ly the major u t i l i z a t i o n o f geothermal resources, has been under -

t ak en by t he p r i v a te and pub l i c u t i l i t y i ndus t r y. And t he i n s t i t u t i o na lproblems are wi t h i n the domain o f the several l e v e ls o f p u b l i c a d m i n i s t r a t i o n

ranging from the Federal government t o county and township agencies.

I t can be assumed t ha t as th e p ub l i c demand fo r energy t o be supp li ed

by geothermal resources increases, accommodations between suppliers,regu la to rs , and the pub l i c w i l l be achieved. I t can also be assumed thatadequate technology w i l l be dev e loped t o u t i l i z e "commercial" resources for

bo th e l e c t r i c a l and d i r ec t t he rm al app l i c a t i ons .concern i n th e acce ler ate d development o f a geothermal ind ust ry i s t hed e f i n i t i o n o f what c o n s t i t u t e s a "commercial" resource.

po in t of v iew, a "commercial" resource i s one from which a su f f ic i en t amountof geothermal resource can be ext ract ed t o se l l t o a w i l l i n g buyer a t a

pr of i t ab le pr ic e over some reasonable per i od of t ime.

in s t i t u t io na l d i f f i c u l t i e s , i s underway. Recent es timates by the U. S .

Thus, th e major area for

From a pragmatic

Explora t ion fo r geothermal resources, i n sp i t e o f t he aforement ioned

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Geological Survey in di ca te a l ar ge number of po te nt ia l areas of geothermal

resources i n the U. S. alo ne. The assessment o f "commercial" v i a b i l i t y o ft hes e resources i s t he d i f f i c u l t t as k , due i n pa r t t o t he sm al l number ofe x i s t i n g o p e ra t i on a l f i e l d s , and a l s o i n p a r t to t h e e m pi r i ca l h i s t o r y ofgeothermal power p la nt development, wi th i n s t a l l a t i on of generat ing capac i ty

by one smal l u n i t a t a t ime. I t i s c le ar f rom the many publ ished forecasts

o f t he po te nt ia l f o r geothermal energy, ranging over orders o f magnitude,

t h a t th e ac tu al resources (beyond the 1,000 t o 2,000 MW p robab l y ex i s t i nga t the one U. S . loc at i on) ar ee ss en t i a l ly unknown. For undeveloped f ie ld s ,uncer ta in t ies e x i s t abou t the thermal q ua l i t y o f the resource , the hea t

and f l u i d e x t r a c t i o n c a p a b i l i t y , t h e p ro ba bl e t i me h i s t o r y o f d e l i v e r a b i l i t y

and lo ng ev it y, and the syste matic s f o r optimum development of the re sourceshould i t prove t o be "commercial." A l l o f the aspects may be consideredt o f a l l under t he c atego ry o f "Geothermal Reservoir Engineering," t h e t o p i cof t h i s Workshop.

Geothermal re se rv oi r en gin eer ing has been an ada pti ve branch of

engineering; much o f th e n ome ncl atu re and methodology have come f r o m t he

o i l and gas ind ust ry, f rom hydrology and hydrogeology, from the m inera lin du st r i es , and from the bas ic physi cal , chemical , and nuclear sciences.

I n add i t i on t o t he ex tens i ve e f f o r t s c a r r i ed ou t by t he ope ra to rs i n under  -s tand ing s pec i f i c r es e rv o i r c h a r a c t e r j s t i c s , a national focus has developedon th i s important segment o f the geothermal " fue l cyc le ," i n v o l v in g u n i v e r s i t i e s ,

in du st ry , and the Federal government.

of geothermal r es er vo ir engi neeri ng were supported by the Nat ional Science

Foundation and the U. S%. Geo log ica l Survey. The Surv ey's program has beenpr im ar i l y an in-house program di re ct ed a t d esc rib ing what a geothermal

resource i s . Many co nt r i bu t i on s have been made i n the c la ss i f ic at io n andmo de ll in g of hydrotherma l conve cti ve and geopressured systems. TheNati onal Science Foundation du ri ng i t s tenure as lead Federal agency for

the accelerated development o f geothermal resources i n i t i a t e d a s e r i e s ofg ran ts t o un iv er s i t i es and research corpora t ions t o b r i n g v ar i ou s d i s c i p l i n e s

together t o bu i l d t h i s b ranch o f sc ience and technology known as geothermal

reservo i r eng ineer ing . Adm in i s t r a t i on has inc luded such researc h i n i t s ov e ra l l program. S im i l a ref fo r t s are underway i n o th er geothermal cou ntr ie s .

Ea r l y e f f o r t s t o deve lop t he t ec hno log ies

The newly-formed Energy Research and Development

The purpose of th e Workshop convened her e a t Stan ford t h i s December,

1975, i s two- fo ld. F i r s t , the Workshop was designed t o br in g toget herresearchers ac t i ve i n the var ious phys i ca l and mathematical branches oft h i s new l y-em erging f i e l d so t h a t t h e p a r t i c i p a n t s c ou l d lear n about t he

very many studies underway and share experiences through an exchange of

research r es ul t s. The second purpose was t o prepar e these Proceedings of

the Workshop so tha t the i n tegr a ted in fo rmat ion cou ld be d isseminated t o

the geothermal community re spons ib le f o r th e development , u t i l i z a t i o n ,and reg u la t i on aspects o f th e in dus t r y .

Dur ing the o rgan iza t ion o f th e Workshop some seventy t o ei gh ty re -searchers ac t i ve i n the NSF program, the U . s . Geol ogic al Survey, and i nun i ver s i t y , i ndus t ry , and ERDA na t i ona l l abo ra to r i es were i de n t i f i e d bythe Program Commit tee. In v i ta t i on s t o them and severa l in d i v i du al s i n

na t ions a c t i v e i n th i s new f i e l d were extended.i n the p rogram cons is ted o f res erv o i r physics (s tud ies to evaluate the

The major areas covered

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physical processes occurr ing

used i n sp ec i f ic and gener ic

c h a r a c t e r i s t i c s o f a reservodevelopment o f producing f i eenergy recovery from marg ina

i n geothermal systems), we1 1 tes t ing ( techniquesf i e l ds t o de te rmine the vo lumet r i c and ex t r ac t i ve

r), f i e l d development (methods f o r t he optimumds) , we1 1 st imulat ion ( techniques for improv ing

hydrothermal and dry geothermal resources) ,and model 1 ing (mathematical methods t o study geothermal re ser voi rs ).

The Workshop resulted i n , t h e p res en ta t i on o f 50 technical papers,summaries o f which ar e included i n these Proceedings. We hope th at thesesummaries and the Rapporteur reports of the f ive sess ions w i l l prove va luableto our col leagues i n indu str y, academic in st i t ut io ns , and especgovernment agencies respon sible f o r an accelerate d ord er ly deve

our geothermal resources.

I wish t o acknowledge the ass is tance of the Program CommiP. Kruger, M. Nathenson, H. Ramey, P. Witherspoon), the session

a l l y t o t he

opment o f

tee (R. Cory e l l ,Rapporteu rs

(P. Witherspoon, H. Ramey, G. Frye, M. Nathenson, J. Mercer), o ur collea guesfrom France, I t a l y , and New Zealand, whose pa r t ic i pa t io n enrich ed our pro -

gram, th e stude nts i n ou r S ta nf or d Geothermal Program (P.  Atkinson, H. Chen,

A. Hunsbedt, and M. Kuo) who ass ist ed i n th e workshop executio n, and th eNational Science Foundation for i t s suppo rt and encouragement.

Paul KrugerStan fo rd Un ivers i t y

December 18, 1975

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RAPPORTEURS' REPORTS

SESSION 1 - RESERVOIR PHYSICS - Paul A. Witherspoon

Session I on Reservoir Physics included ni ne papers covering a wide

v a r i e t y o f t o p ic s .

underway a t th e Un iv er si ty o f Colorado, where attempts ar e being made t o

cha rac ter ize and model the var ious processes th at occur i n geothermal

sys tems. The importance o f f au l t s i n co n t ro l l i n g the convec t i ve mot ion

w i t h i n geothermal systems i s being examined from a number o f st and poi nts ,

and t h e e f f e c t o f a r e a l i s t i c v a r i a t i o n i n v i s c o s i t y on co nv ec ti on i n por ous

bodies has revealed t ha t the conv ect ive mot ion i s un l i ke the symmetricc l a s s i c a l p r o f i l e s t h a t r e s u l t f ro m a f l u i d o f c o ns ta nt v i s c o s it y .

ab le e f fo r t i s be ing made t o deve lop a better understanding of the East Mesa

geothermal system i n the Impe rial Va l ley .

Kassoy summarized t h e r e s e a r c h a c t i v i t i e s c u r r e n t l y

 A cons ider  -

Brigham reviewed the labo rat ory inv est iga t io ns cur re nt ly underway at

Stanford U ni ve rs i t y t o develop a fundamental understanding of non- isothermalb o i l i n g t w o-phase f l ow i n porous media. One o f the c r i t i c a l problems i s howthe norma l l y immob ile l i q u i d sa tu ra t ion s vapor i ze w i th p ressure reduc t ion

under non- i so thermal condi t ions.r e l a t i v e

temperature dependent pro pe rt y o f rocks. Labora tory measurements have

revealed th at the temperature ef f e c t on per meab i l i t y depends on the na ture

o f the sa tu ra t ing f l u i d , whereas

b i l i t y seems t o be independent o f the na tu re o f the sa tu ra t ing f l u i d . The

ob j ec t i ve o f t h i s work has been t o s imu l taneously measure the e f f ec t o f

thermal and mechanical stre sses on pe rm ea bi l i ty . Brigham al so summarized

the advances t h a t have been made i n severa l d i re c t io ns i n model ing geothermalf l u i d p ro du ct io n.

Recent work on the effect of temperature on

perm eabi l i ty suggested th at absolute per meab i l i t y was a l so a

the ef fe c t o f con f in ing pressure on permea-

Manett i summarized some rece nt work t h at has been ca rr ie d out i n I t a l y

t o c o r r e l a t e t h e kh d i s t r i b u t i o n w i t h g eo l o gi c a l s t r u c t u r e a t L a r d e r el l o .

Data from about 50 we l l s i n d i f f e r en t pa r t s o f La rde re l l o were ana ly zed byback-pressure and pressure build- up methods. Good agreement between t he khvalues fo r any given we l l was on ly p oss ibl e when the s ki n- ef fe ct was taken

into account.

between a reas o f h igh t ra nsm iss iv i t y and the var ious s t ru c tu ra l h ighs w i th in

the Larder e l lo f i e l d . The permeab i l i t y i s be l ieved to reach i t s maximum

values a long the c res ts because te c t on ic a c t i v i t y has r esul ted i n a maximum

of f r a c tu r i n g and f i s s u r i ng a t s uch l oc a t i ons .

 A co rr el at io n o f these re su l t s shows a good correspondence

Mart in presented a rev iew o f an ana lys is tha t he has made on internal

s team dr iv e i n geothermal re ser vo i rs that are produced by pressure deplet ionw i t h no water i n j ec t i on . He compares the pressure- temperature behavior of

geothermal systems and shows how they di f f e r depending on the i n i t i , a l condi-t i on s . He concludes tha t under ce r t a i n cond i t ions on ly a r e l a t i v e l y sma ll

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amount o f t he heat i n i t i a l l y c onta ined i n a geothermal reservoir w i l l beproduced during pressure deplet ion.

and hot water occurs dur in g dep let ion , more o f the t o t a l heat can be produced

by completing we l l s h ig h i n the res erv o i r t o enhance steam product ion and

suppress water production.

Where gra vi t y segregat ion o f the steam

Bodvarsson reviewed the a na ly si s th at he has been making of the “macro-permeabi l i ty ” th at pre va i l s i n igneous rocks because of f r ac tu re condi t ion s.From an ana l y t i c a l ex press i on f o r f l ow t o a ho r i zon ta l f r a c tu re i n te rs ec t i nga borehole, he has analyzed the f lo w condi t io ns th at ex is t i n f ra c tu red

reservo i rs . Th is approach has been used i n Icel and t o develop methods f o rtes t in g we l l s , es t imat ing rese rvo i r permeab i l i t y , and eva lua t ing the resu l t s

of wel l st i mul at i on. Bodvarsson al so discussed how the isot ope chemistry ofgroundwaters i n i ce land has been used t o lo ca te areas o f recharge.

Natnenson sumar i zed inv est iga t io ns t hat he has made t o est imate thef r ac t i on of s tored energy i n hydrothermal convect ion systems t ha t i s recover  -

able. He has analyzed two poss i b le methods f o r ex t rac t in g energy: (a) b o i l i n gthe water i n the system t o produce steam and (b) nat ura l and a r t i f i c i a lrecharge o f c o ld water t o recover res erv o i r heat by a sweep process. I t

appears th at th e re s t r i c t e d range of po ro si ty , temperature, and recharge over

which the b o i l i n g method w i l l work l i m i t s i t s app l i c a t i on t o ra the r s pec ia lcases such as vapor -dominated systems. The f r a ct i o n o f stored energy th at

may be recovered i s c r i t i c a l l y dependent on the average l i qu id sa t u ra t ion .I n us ing recharg ing co ld water t o dr iv e hot water t o produc ing wel l s , conduc-t i o n can be analyzed t o a f i r s t approximat ion by superpos i t i on on to the move-

ment o f the temperature f r on t . Another fac to r i s t he r o t a t i o n of t h e i n i t i a l l y

v e r t i c a l in te rf ac e between co ld and ho t water. These processes can be com-

b in ed q u a l i t a t i v e l y t o y i e l d an e st i ma t e of energy recovery.

Meidav presented a review o f a method o f usi ng gr av im et r i c data t oest imate hydrothermal re se rv oi r ch ar ac te ri st ic s a t the East Mesa geothermal

f i e l d i n C a l i f o r ni a . S i x p o s i t i v e g r a v i t y anomalies are assoc ia ted w i thabnormal ly hig h temperature gra die nts i n the I mperial Val ley , and one o f

these anomalies i s a t East Mesa. The expl anat ion f o r these observed ef fe ct si s d e n s i f i c a t i o n o f the s hal low sediments by depos i t i on of temperature-se ns i t iv e mine rals i n the upward r i s i n g plume o f geothermal waters. An

excess mass o f about 10 b i l l i o n tons of matter i s be l ieved t o have been

deposite d a t East Mesa which would have requ ir ed an upwe ll i ng o f an estima ted

2.5 t r i l l i o n tons o f thermal wa te r . Assuming a per iod o f 50,000 years wasrequ i red leads t o the conc lus ion th a t the ve r t i c a l permeab i l i t y ranges f rom

0.6 t o 60 m i l 1 i da rc ies . A 1 though surf i c i a l evidence o f geothermal a c t i v i t yi s absent at East Mesa, t h i s ana lys is sheds l i g h t on the very la rg e underground

movements of thermal waters th at are p oss ibl e when hydrogeologi cal c ond it ion s

do not favor out f lo w t o the sur face.

Tsang summarized an ana ly s is he has re c e n t l y made on screenin g geo-the rmal p roduc t ion we l l s f rom the e f f ec ts o f re i n je c t i on . In the norma lmethod o f re in je c t in g co ld water i n t o a geothermal res erv o i r , breakthrough

eve ntu al l y occurs depending on several f act ors . I n the s implest case of adoublet , one product ion and one i n j ec t i on we l l , th is breakthrough t ime can

be lengthened conside rabl y by plac in g a screenin g we ll between the two w el l s

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so as t o in ter cep t the shor tes t stream l in e . By producing water from the

screening wel l , not on ly can breakthrough be delayed, but a s i gn i f ic an t

increase i n energy recovery can al so be achieved.f e a s i b i l i t y s t u d y o f the e f f e c t s of screening has no t yet been made.

A de ta i l ed econcmic

Garg rev iewed the work t ha t he and h i s co l leagues ar e carry ing out i n

an ef f o r t t o mathemat ica l ly model land sur face subs idence assoc iated wi th

geothermal energy prod ucti on. Thi s i s p o t e n t i a l l y a serious problem,p a r t i c u l a r l y f o r l iq ui d-domi nate d geothermal systems. The th eo r et ic al model,

developed wi t hi n the framework o f t he Theory o f In te ra ct in g Continua,

descr ibes th e thermomechanical response o f the r ock and f l u i d compositemat er i a l i n terms o f the i so l a t ed components. The s t re ss - st ra in equat ions

fo r t he rock m a t r i x a re coup led w i t h t he d i f f us i on equa ti ons f o r t he f l u i d .

The mic roscale de ta i l s o f the p o r e / f r a c t u r e network i n the rock are ignored,bu t t he f l u i d p res su res and t he s t res s f i e l d i n t he roc k m a t r i x a re per  -mi t t ed t o assume d i s t i n c t va lues wi th in each computat ional reg ion fo r thecomposite. Al though most o f th e requir ed ma te ri al pr ope rt i es can be

obtained from standard la bor ato ry t es ts on cores, i t should be noted that

the rese rvo i r behav ior i s f re que nt l y governed by f ra c tu res , format ion

inhomogeneit ies, and othe r lar ge scale feature s such as fa ul ts . It, the re-fo re , becomes impor tant t o supplement the la bo ra to ry measurements by su i ta bl ef i e l d d a t a .

subsidence problem was pr esen ted. An example o f some p r e l im ina r y r e s u l t s i n mode ling a hypo the t i ca l

SESSION 1 1 - WELL TESTING - Henry J. Ramey, J r .

Data f rom n ine d i f f e r en t f i e l d t es t s were p resented . This one f a c tsets t h i s session apart f rom a l l prev ious meetings o r workshops.

cases considered ranged from vapor t o l i quid -dominated reservoirs, and l i q u i d -dominated systems ranged from low t o h igh s a l i n i t y systems. The types of

we l l te st s included pressure bui ldu p and drawdown, and inter fer enc e tes t i ng . As a r e s u l t , i t appears the s ta te o f development and application o f the tech-nology i s good. App l ic at i on o f e x i s t in g petro leum engineer ing and ground-water hydrology theories were shown t o reveal the need for new solut ions,

however. Problems ident i f ied inc lude:

The f i e l d

1 . New so lut i on s f o r t r ans i en t we l l t es t i n g (both i n te r f e rence and i nd i v i d-ual wel l tes ts) i n hot aqui f ers which conta in a carbon d i ox id e gas cap.

The so lut ions should cons ider e i th er product ion of hot water f rom down-s t r uc t u re we l l s , and p roduc t ion o f carbon d iox id e from u p s t r u ct u r e o r

gas-cap wel ls . What pro per t ie s are detected i n such tests?

2 . New sol ut i ons are needed fo r p ar t i a l ly - p e n e t r a t i n g w e l l s i n a t a l lsteam column supported by boil ing of a deep l i qu id in te r face . A l ltypes o f t es ts should be evaluated.

3 . Stud ies shou ld be aimed a t the re su l t s o f f l as h in g i n the rese rvo i r rockand re su l t in g non-condensable gas evolution.

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 Anothe r f i n d i n g was t ha t there hasn't been much supported research i nthe area o f wel l t es t analy s is . Work to date has invo lved most ly a re t rea ding

o f ex i s t i ng i n fo rm a t i on . Sme work has been underway as a  j o i n t p r o j e c t byENEL of I t a l y and personnel o f the Sta nfor d Geothermal Program.During the presen tat i ons, a plea f o r f i e l d data was made and several

pa r t ic ip an ts responded (Roger Stoker o f the Raf t River Pro jec t , and Al a i nGringarten concerning data from the Afars and l ssas T e r r i t o r y ) .

Sign i f icant f ind ings were made as a res u l t of the p resen ta t ion of muchf i e l d d at a. I t i s c le ar tha t geo therma l reservo i rs a re f u l l y responsive t o

a l l p e r t i n e n t l aws of physics. A c a re fu l s tudy o f f i e l d performance resul tswill of te n ind ica te important fac t or s which should be inc luded i n computers imul at ion models. F i e l d data presented a t the workshop ind ica ted : (1) th er e

are we ll t es ti n g equipment needs, and (2) ther e were important recent f ind ing sas a r e s u l t o f a p p l i c a t i o n o f new instr umen ts. One need f o r new equipmentconcerned running pressure recorders in to very h ig h ve lo c i ty s team we l l s whi le

producing. There i s a need f o r pres sure and temperature re cord ers which canwi ths tand bo th h igh v i b r a t io n and h igh tempera tu res. F l u i d p roduc t ion ra tes

on the order o f one m i l l i o n pounds per hour were c i te d i n several cases!

Very in t e re s t i ng ear th t i d e e f f ec ts were c i te d as measured w i t h high-p rec i s i on qua r tz c r y s t a l p res s ure reco rde rs i n t he Ra ft R i v e r p ro j ec t .

Pressur es were measured t o 0.001 p s i . This h igh prec is ion represents a majorstep forward. However, th e dev ice i s l i m i te d t o upper temperatures i n therange of 300°F t o 3 5 O O F . The Hewlett-Packard system was used i n the Raf tRiv er pr oj ec t. However, the Sperry-Sun s ta in less capi l lary tube system has

been used a few times, and i t appears t ha t a combina t ion o f the cap i l l a ry tubew i t h a qua rt z det ect or i n an ins ula ted chamber a t the surface might haveimmediate use i n some geothermal wells.

Fi na l l y, several important observat ions from the Geysers F ie ld were made.Burmah ha5 observed water entry below a steam entry i n two separate wel ls .

Water samples were obtained, and i t appears t h a t t he f i r s t s i g n i f i c a n t i n f o r  -

mati on on the deep l i q u i d in t er f ac e pos tu la te d by Ramey, Bruce, and White may

have been obta ined . Another i mpor tant obs erv ati on was reporte d f r o m the cur  -ren t She l l we l l d r i l l i n g a t the Geysers. Hydrogen su l f i d e concen t ra t ions as

high as 3000 ppm were observed. Th is p a r t o f th e w e ll was plugged and thewel l s idet racked. Both the Burmah and Shel l wel l s are i n the eastern po r t io n

of the Geysers Field.

Throughout the discussions of var ious f i e l d w e l l t e s t s , i t becameobvious th at most re po rt er s considered presence o f f r ac tu re s common t o geo-

thermal reser vo i rs . As a r es ul t i t appears that a " h o l i s t i c " approach via

w e l l te s t in g was us ua l l y necessary. Most f i e l d tes ts were character ized bya dear th of c onv en t i ona l e l ec t r i c log and core da ta . Wel l tes t ana ly s is i san important technology th at has la rg el y been neglected to date. Because of

the po ten t ia l impor tance o f t h i s techno logy , one ma jo r f i nd in g o f the work-

shop was i d e n t i f i ca t i o n of the need f o r more work i n t h i s a rea .

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SESSI O N 1 1 1 - FIELD DEVELOPMENT - G. A. Frye

The auth ors pr esent a matur ing approach t o f i e l d development., As men-t ioned i n the opening sess ion, the b i r t h o f geothermal res erv o i r engineer ing

i s accompl ished and th i s session r e f l e c t s ea rl y chi ldhood development. Many

auth ors express a cauti ous optimism about geothermal energy po te nt ia l. Consi-derat ions about opt imal energy extract ion rather than concerns about economical

p roduc t i on re f l ec t t h i s optimism. Several t imes the authors express the needf o r engineering design data and improved cor re la t i on s from geophysics and we l l

tes t in g. Even though the geothermal energy f i e l d i s re la t i ve ly young i n t h eUnited States, comments such as I would have done i t d i f f e r e n t l y i f I had t odo i t over again," in di ca te development of geothermal res erv oir e ngineering.

Spec i f i ca l l y the d iscuss ion sess ions a f te r the p resen ta t ions re f lec ted

the needed development o f hi gh temperature, hi gh res ol ut io n too ls f o r

great er conf idence and shor t er observat ion per iods. Rein j ect io n w i l l beextremely dependent on ani so tr op ic featu res o f the r ese rvo ir found by these

too ls. Hinr i chs discussed Magma's e f f o r t s in Imperial County t o o b t a i n datafo r es ta bl is hi ng opt imum prod uct io n and in je ct io n techniques. He then i n t r o -duced M r . James Nugent o f San Diego Gas and Electric Company (SDGEE:) whopresented the e f f o r t s o f SDGEE and now alon g w i t h ERDA on the geothermal t e s t

f a c i l i t y associated w it h the Magma we l l s. I n some cases the geophysical

analyses o f economic f i e l d s can be expanded t o new pros pect s. Wooding, w h i l e

recommending t h i s approach, cau ti one d t ha t the same geophysics d o n ' t neces-s a r i l y y i e ld the same wel l te s t . More co rr e l a t io n between wel l t es t data and

the geophysical data are required.the Bureau of Reclamation has assigned t o lntercomp. The i n i t i a l phase of

t h is assigment invo lves analys is o f cur ren t geophysical data in cons ider at ion

of f i v e we ll s on East Mesa operated by the Bureau o f Reclamation.

phases of t h i s study concern reserves, f i e l d development and i n j e c t i o n .

lntercomp i s al so working w i t h Republi c Geothermal on the no rt h end o f East

Mesa.

Gould present ed th e t as k TRW Systems and

Later

 Anothe r t h r u s t o f t he d iscuss ion expressed conc ern about t he length o ft im e and i n i t i a l c a p i t a l investment th at ch aract er ize e l ec t r ic a l power produc-t i o n from geothermal energy.

Woitke discussed PGEE's r e l a t i o n s h i p w i t h steam developers.The Geysers development i s t y p i c a l o f Burmah's experience.were two items now causi ng some concern or d el ay i n f i e l d development a t TheGeysers.

t i o n , PGEE has made additional commitments t o abate ex is t ing p lan ts be fo re

development i s expanded.

concern about ce rt ai n Federal leasing r egu lat ion s. Unless these concerns are

reso lved in a t i me ly manner, power p la nt co ns tr uc ti on may be delayed.ments such as th e need t o opti mi ze th e cost per ki lo wa tt - ho ur and r io t maximizet o t a l energy recovery r e f l e c t th i s concern. Kuwada caut ioned in h i s presenta-t i o n t ha t some opt imal f i e l d development f o r energy may not minimize product i on

Whi le no t sp ec i f i c a l l y f i e l d development,

The schedule f o r Also presented

The f i r s t was a s ta tus repor t on H2S abatement. Since th is presenta-The second item expressed an investor-owned u t i l i t y ' s

Com-

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P o l l a r d (1975) has als o i nve st ig dte d the inf luen ce o f the ground surface oncrack shape and s t a b i l i t y and the deformat ion o f t he ground surface dur in g

subsurface crack ing. Dundurs ( t h i s vo lume) i s model ing f ra c tur es by d r i l l i n gf i n e ho le s i n t o a block of epoxy r es in , cementing tubes i n t o the holes and

supply ing mercury under pressure t o form hyd rau l ic f ra ctu re s.

exper iments was f or a c rack propagat ing pa ra l l e l t o an ex is t i ng pressur izedcrack a t a d is tance l ess than the s i ze o f t he f i r s t cra ck. The second cr ac k

turned and jo ined the f i r s t crack. The j o i n t was on the side (n ot t i p ) o fthe f i r s t c rack and was o f a very small s ize . F u rt h er p r e s s u r i z a t i o n o f t h esecond crack enlarged the f i r s t c rack but the second crack d i d not expand.Byerlee, Lockner, and Weeks (1975) have s tud ied hydrau l i c f rac tur es i n sand-stone a t conf in ing pressures to 1000 bars and d i f fe rent ia l s t resses t o 4000

bars. A t high i n j e c t i o n r a t e s , hydr au l i c tens ion f r ac tu res were formed, buta t low in je ct io n rates, shear f r act ur es were formed.

One o f the

Murphy ( t h i s volume) i s a na l yz i ng t h e h ea t t r a n s f e r t o a c i r c u l a r c ra ckwhose f rac tur e gap w id t h var ies across the c rack fo r the l i m i t in g case o f nomechanism fo r po ro si ty generat ion, so t h a t heat i s t r a n s f e rr e d t o t he c r a ckon ly by con duc tio n. The cr ac k i s assumed open so t ha t t he fo rmu la fo r f l ow

re si sta nc e i n a t h i n channel can be used and the con duction problem i s solvedto prov id e a kerne l for t he s o l u t i o n o f t h e f l u i d f l o w e qu at io n ( i n c l u d i n gbuoyancy) and energy equat ion i n th e crack. McFarland (1975) has solved

several problems fo r heat t ran s f er and f l u i d f low inc lud i ng buoyancy i n a

crack . The f low i n c i rc u l ar cracks o f e l l i p t i c a l cr oss se ct io n i s ;alved f o rcases i n which the crack i s e i t h e r p a r t l y f i l l e d w i t h porous m at er ia l o r i sopen. The cr ac k may co nt ra ct or re ta in i t s shape. Baiant , Nemat-Nasser, andOhtsubo ( t h i s volume) are us ing f i n i t e e lement methods to so lve fo r the i n i t i a -

t i on and extens ion o f f ra c tur es i n h o t d r y r o c k and f o r t he c i r c u l a t i o n o f

water and heat t ra nsf er i n the f ra ctu re d zone. I n an example, th ey compareana l y t i c a l and numer ical so lu t i on s f o r t he temperature d i s t r i bu t i on f o r wate r

f lowing i n a stream tube and gaining heat by conduction from the surroundingrocks.

The p rogress o f f i e l d s tud ies t o develop the ex t r ac t i on o f energy us ing

hy dr au l i c fr ac tu re s has been rec en tl y descri bed by Smith, Aamodt, Po tt er , and

Brown (1975). A w el l d r i l l e d t o a depth of 2928 m has a bottom-hole tempera-t u r e of 197°C. Various fr ac tu r in g experiments have been performed. Forexample, w i t h a packer set a t 2917 m y a s in g le hy drau l i c f r ac t ure was createda t a surfa ce pumping pressure o f 120 bars wi th a calculated crack radius of

57 m .temperature of 2 0 3 O C (H. D. Murphy, Written Commun., 1976;  Aamodt, 1976).These two wells have been connected by what i s thought t o be a system ofhydrau l i c f rac tu res .

A second we l l recen t l y d r i l l e d t o a depth o f 3060 m has a bottom-hole

The second sti mu la ti on techn ique disc ussed a t t he workshop was t he

creat ion o f Permeabi l i t y by exp los ions .

1975) propose tha t the p erme abi l i t y i n the f r ac tu r d zone beyond the ca v i ty

where r i s d i s tance f rom t t ie shot point . ,co l leagues are look ing a t v a r i o u s , a s p e c t s o f heat and mass tran sfe r. rel eva nt

McKee and Hanson ( t h i s vollume andshould scale as l / r5 f o r a spher i ca l b l as t and l / r5 f o r a c y l i n d r i c a l b l a s t

Kruger ( t h i s volume) and Ihis

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t o s t im ula ted res e rv o i r s .to ry model o f a rubbl e chimney t o study th e processes o f in-p la ce b o i l i n g ,

moving f l a sh fr on ts , and two-phase f low. The i n i t i a l rock loading has a h ighporos i ty and permeabi l i ty so th at pressure gradients needed t o dr iv e the f l o wa re s ma ll . The system i s i n i t i a l l y f i l l e d w i t h l i q u i d w at er . As i t i s pro-duced f rom the top, e i th er no recharge o r recharge o f co ld or h ot water i s

added from the bottom. Plans are underway t o scale these experiments t of i e l d - size systems.

measure heat and mass transfer rates from a sphere of porous material i n ab at h o f c i r c u l a t i n g f l u i d t o check i f heat t ra nsf er rat es ar e enhanced by

mass d i f fus ion.

i s such a s l o w process tha t heat t ra nsf er ra t es are not a ffec ted.Kruger, and Umana have been looking a t the propert ies of radon as a d iagnos t i cfo r reservo i r s tud ies .

releasing radon i s p ropo r t i ona l t o the exposed surface area, i t may be possible

t o r e l a t e radon measurements t o th e increase i n surfac e area caused by stimu-

l a t i on . S ince f i e l d da ta a re no t av a i l ab l e for s t imu la ted reservo i rs ,

measurements are being made on production from natu ral systems t o develop

interpret ive techniques.

Hunsbedt, Kruger, and London have b u i l t a labo ra-

Kuo, Brigham, and Kruger desc ri be ano the r experiment to

Resu lts i nd ic a te tha t mass t rans fe r by mo lecula r d i f fu s i on

Stoker,

Since the emanating power of a r ock ma te ri al f o r

Barnes and Rimstidt ( t h i s volume) ar e studying e q u i l ib r iurn chemist ryo f s i l i c a s o l ub i l i t y and k i ne t i c s o f t he dominant react i ons . Data ob ta i nedw i l l be usefu l f o r suggest ing ways t o manipulate wel ls i n order t o preventscale formation during the f l ow o f ho t water i n we l l s and pipes. Sammis( t hi s volume) discusses t he model ing o f chemical rea ct i ons i n geothermal

res ervo irs . Natural f l u i d s i n hydrothermal convect ion systems have long

aqu if er residence t imes a t hi gh temperatures so tha t they tend t o be i n

chemica l equ i l i b r ium wi th t he i r hos t rocks. The in j ec t io n o f co ld wate r in to

a natura l o r s t imulat ed geothermal rese rvo i r w i l l p ro vi de a f l u i d t h a t i s no ti n e qu i l i b r i u m l ea di ng t o p o s s i b i l i t i e s o f d e p o si t io n , s o l u ti o n , and redeposi-t i o n depending upon the i n i t i a l d isso lved - s o l i ds c on tent o f t he f l u i d and i t ssubsequent temperature history. Summers, Winkler, and Byerlee (1975) havefound s i gn i f i c an t permeab i l i t y reduc tions i n f l owing water th rough g ra n i t e

a t hi gh temperatures, and Charles and Valagna (1975) d es cr i be a l t e r a t i o nproducts i n the f l o w of water through monzogranite a t high temperature. Theres u l t s o f these and f u r th er s tud ies must be in tegra ted i n t o models o f f l u i d

i n j e c t i o n p rocesses i n o rd e r t o assess p o t e n t i a l d i f f i c u l t i e s .

REFERENCES

 Aamodt, R. L., 1976, Hy dra ul i c fr ac tu r i ng i n and communication between twoadjacent wel lbores: EOS Trans.,  Am. Geophys. Union, v. 57 ( i n p re ss ).

Byerlee, J., Lockner, D . and Weeks, J., 1975, Tension fractures and shearf rac tu res p roduced dur ing hydrau l i c f rac tu re : EOS Trans., Am. Geophys.Union, v. 56, p . 1060.

Charles, R. W . and Balagna, J. P., 1975, Monzo-grani te a l te ra t i on i n a hydro-thermal system: EOS Trans.,  Am. Geophys. Union, v. 56, p. 913.

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Kruger, Paul and Otte, Carel , 1973, Geothermal energy- resources, production,s t imu la t i on : S tan fo rd , CA., Stanford Univ. Press, 360 pp.

McFarland, R. D., 1975, Geothermal re se rv oi r models--crack plane moldel:Los Alamos Sc i . Lab. Report LA-5947-MS, 18 pp.

McKee, C. R. and Hanson, M.E., 1975, Explos ive ly c reated permeabi l i t y f romsingle charges: S O C . Petroleum Engineers SPE 5414, 7 pp.

P o l l a r d , D. D., 1975, On the in te ra ct io n between the ground surface andh y d r a u l i c f r a c t u r e s : EOS Trans., Am. Geophys. Union, v. 56, p. 1060.

Secor, D. T., Jr. and Pol lard, D. D. , 1975, On the s t a b i l i t y o f 0pe.n h y d r a u l i cf r a c t u r e s i n t h e E a r t h ' s c r u s t :NO. 1 1 , pp. 510-513. Geophysical Research Letters, v. 2,

Smith, M. C.,  Aamodt, R. L. , Pot ter , R. M., and Brown, D. W . , 1975, Man-madegeothermal r es er vo ir s: Un it ed Nat ion s Symposium on th e Development and

Use o f Geothermal Resources, 2nd, San Francisco, 1975, Proc.( i n p r es s) .

f l u i d f l o w t hr ou gh h o t g r a n i t e :

Summers, R., Winkler, K., and Byerlee, J., 1975, Perm eab i l i ty changes duri ng

Tbmasson, J. and Tho rst ein sso n, T., 1975, Use o f in je c t io n packer for hydrother  -mal wel l s t imu la t i on i n Ice land [abs .] : U.N. Symp. on Development and Use

of Geothermal Resources, 2nd., San Francisco, abs. no. V I - 4 5 .

EOS Trans., Am. Geophys. Union, v. 56, 1060.

SESSION V - MODELLING - James W. Mercer

The goa l o f t h i s r epo r t i s t o summarize the present s ta tus of: geothermal

The geothermal model l ing e f f o r t presented a t t h i s workshop i srese rvo i r mode ll i ng , and t o i nd i ca te the fu tu re goa l s o f geothermal1 model l ingresearch.

ca tegor i zed i n F ig . 1.  The major subdi v is ions ar e model l ing of nat ur al geo-thermal systems and mo de ll in g o f produ cin g geothermal systems. These two

subdivisions were chosen because, i n general , they emphasize two d i f f e r e n t

v iewpoints. Model l ing of nat ur al geothermal systems i s usua l ly done i n the

v e r t i c a l c r o s s- sect ion and emphasis i s placed on examining f r e e convectio n i no r de r t o g a i n i n s i g h t i n t o t h e n a t u r a l ( p r e - exploi tat ion) behavior and forma-

t i o n o f geothermal reservo i rs . Model l ing o f producing geothermal systems i susu al ly done i n the areal p lane.

t i on e f fec ts i n o rder t o reproduce observed f i e l d cond i t i ons , and hope fu l l yp r e d i c t f u t u r e f i e l d c o nd i ti o ns .

subdivided further as shown i n Fig. 1 .  

This approach emphasizes simulat ing exploi ta -

Model l ing associated wi th product ion can beThese div is ions w i l l be discussed la te r.

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Geothermal Modelling

1I

 ModellingI

 Modelling

 Natural Systems Producing Systems

I I IPorous Fractured Subsidence Hydrothermal

Reservoir Re servoir React ionsPerformance Performance

Single- phase+Two-Phase(Hot- Water) (Steam - Water)

Figure 1.--Status of Geothermal Modelling.

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Researchers involved w i t h t he model l i ng o f nat ura l geothermal systems

inc lude ( i n t he o rder o f t h e i r p res en ta t i ons ) :P . Cheng and M. Sorey. D r . Wooding considers analyt ical and f in i te - d i f f e r e n c etechniques appl ied t o fr ee convect ion. For reasons o f economics, he genera l l yr es t r i c t s h i s models t o two d imensions. To examine the three-dimensionalaspects of the problem, he i s co l l ab or at in g w i t h D r . Shen, who i s using phys-ical model 1 ing (Hele-Shaw ce l l models) t o examine fr ee convect ion. The phys i-cal models developed by D r . Shen are a ls o be ing used t o ve r i f y the numer ica lmodels. D r . Cheng uses f i n i t e - di f f er en ce techniques t o examine the f re e con-ve ct io n associated w i t h vo lc an ic is la nds, such as the Hawai ian Is la nds. He

has a l so developed anal y t ic a l so l u t i ons f o r f re e convect ion caused by var ioustypes of magmatic intrusions. D r . Sorey examines the heat and mass transferassoc iated wi th var ious hot spr ing geometr ies .based on an int egr ate d f i n i te - difference scheme.

R. A. Wooding, H. W . Shen,

He uses a numerical method

I t i s i n t e r es t i ng t o no te t ha t a l l o f t he above models c ons ide r s i ng l e -A lo g i ca l ex tens ion o f t h i s work would be t o inc ludephase (hot-water) f low.

the vapo r phase. Such a two-phase, cross-sectional model could a i d i n t e s t i n gthe various hypotheses concerning vapor -dominated geothermal systems. Alt houg h

such a model was n ot present ed a t t h i s workshop, Dr. T. Lasseter (who wasin v i te d t o the workshop but could n ot a t tend ) has cons idered t h is problemusin g a model based on int egr ate d f in i t e - d i f fe rence techn iques .

Researchers involved w i t h th e mod ell in g o f pr oducing geothermal systemsinc lude ( i n the o rde r o f t he i r p res en ta t i ons ) : C. R. Faust, J . W. Mercer,G . F. Pinder, W. G. Gray, J . W. P r i t c h e t t , 2 . P. Bafant, S . Nemat-Nasser,H. Ohtsubo, C. G. Sammis, A. B a r e l l i , R. C e l a t i , G. Manet t i , G. Ner i , S . Bor ies ,and T. Main i . Drs. Faust and Mercer have developed finite - element and f i n i t e -di f f eren ce models f o r s imul at in g product ion o f geothermal r eserv o i rs . These

models can treat s ingle - and two-phase (steam-water) f low, and are capable o fsimulating the conversion of a compressed-water regi on t o a two-phase region.

Drs. Pinder and Gray have concentrated o? theoret ical equat ion developmentand computer code implementation (using finite - e lement techniques) f o r mu l t i -phase flow (steam-water), subsidence, and f low i n fr ac tu re media. O i r . P r i t c h e t thas developed a finite - di f f er en ce model f o r mul t iphase f lo w and heat t ran sport .

I t i s proposed t ha t t h i s model be coupled w i th a co ns ol id at io n model developedby S . K . Garg i n order t o s imulate subsidence and induced se ismic ac t i v i t y .Drs. Bafant, Nemat-Nasser and Ohtsubo use finite- element techniques t o examinethe fo rmat ion of f rac tu res (bot h hy dr au l i ca l l y and ther mal l y induced) and the

subsequent f l ow of water i n the f rac tur es. D r . Sammis examines rock-wateri n te rac t i ons us i ng f i n i t e - di f f er en ce and experimental techniques. He considersd i s s o l u t i on and p rec i p i t a t i on reac t i on and a l t e ra t i on reac t i on e f f ec t s on:

( 1 ) re ac t i on heat (chemical energy), ( 2 ) changes i n per mea bi l i ty and po ro si ty ,and (3 ) changes i n the thermodynamic p ro pe rt ie s of water. Drs. Barel 1 1 ,Cel a t i , Manet t i and Ner i examine ana ly t i ca l l y the p ressure h i s t o r y o f a pa r t i a lpene t ra t ing we l l i n a ho t-water reservo i r . D r . Bor ies i s a t t emp t i ng t o de te r  -mine exper imental l y the hea t t rans fe r coe f f i c ie n t s between f l u i d and rock i n

a porous system undergoing conversion from single - t o two-phase f low. F i na l l y ,D r . Main i uses ana ly t i ca l so lu t ions to examine downhole heat exchange.

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 Ano ther paper, which does no t f i t d i r e c t l y in to the scheme i n F ig . 1 ,but which encompasses a l l o f the mod ell ing work, was giv en by R.  A ther ton on

general s e ns i t i v i t y theory .

d i f f e ren t i a l equa t i ons , a s e n s i t i v i t y ana lys is may be performed on bo th equa-

t i o n parameters and boundary co nd it io ns t o determine i n which space domainsthey are important.

By appropr ia t e ly mod i fy ing a g iven se t o f pa r t ia l

Be fo re d iscuss ing fu tu re goa ls o f mode l l i ng , i t should be noted that

ther e were oth er papers which de al t i n par t wi th model l ing; however, they w i l lbe included in the othe r rappo rteurs ' repo r ts .

Re tu rn ing to F i g . 1 , i t i s evident from the papers presented that model-l i n g of porous res er vo ir performance, both s in gle - and two-phase, i s a t anapp l i ca t ion s tage . However, mode l l i ng o f f rac tu red rese rvo i r per fo rmance ,subsidence and hydrothermal reactions needs further research and development

b ef or e f i e l d a p p l i c a t io n s o f t h i s t yp e ar e p os s ib l e.presented include: (1) incorp orat e a we1 lb or e model and/or near-we1 l bo remodel with a reservo i r model , (2) inc lude the equat ion o f s t a t e f o r s a l i n ewater, ( 3 ) coup le th e re se r vo ir model w i t h a management model, (4) performfu r t he r s e ns i t i v i t y ana l y s i s , and (5) include more rock-water in te rac t ion .

Extensions o f the models

One of the most importan t po in ts made a t t h i s workshop i s the need forpeople i n model l ing t o work more c lo se l y w i t h people do ing labo rato ry and

f i e l d work, i n order t o determine what data ar e needed and what assumptions

are va l i d . Some o f the con tr i but ion s f rom laborator y work inc lude: ( 1 ) thermale f fec ts on re la t i ve and abso lu te permeabi l i t y , (2) the rma l e f fec ts on d isper  -s ion, ( 3 ) chemical r eac t io n ra tes, (4) ca p i l l a r y p ressure e f f ec t s , and (5) heatt rans fe r ra tes between f l u i d and rock . Cont r ibu t ions from f i e l d work inc lude :

( 1 ) dete rmina t ion o f permeab il i t i e s and poros i t i e s , (2) reservo i r boundar iesand thickness , (3) i n it i a l pressure and temperature/enthal p y d i s t r i b u t i o n s ,and (4) reservo i r geology.

I t i s the op in ion of t h i s rapporteur t hat the most important goal for geo-thermal model l ing ind i cate d a t t h i s workshop, i s the need t o make f i e l d ap pl i -

cations, and i f these app l i ca t i ons a re t o be success fu l, i t i s essen t ia l t o havegood communication between people doing mod ell in g and people doing w el l te st in gand f i e l d work.

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A PROGRAMMATIC V IE W OF GEOTHERMALRESERVOIR ENGINEERING

R i t c h i e B. Corye l lNat ional Science Foundat ion

Washington, D. C. 20550

I w i l l make my remarks b r i e f i n the i n t er es t o f g et t i ng on w i t h thesc i en t i f i c sub jec t o f th i s workshop, wh ich I l i k e t o regard as t he scienceof geothermal reservo i rs .

w i t h th e science or technology o f how t o f i nd and how t o assess the energy

po t en t ia l o f these rese rvo i rs (a lb e i t imposs ible t o make a clean separa t ion

between the re l a te d technolog ies) ; but ra t her our purpose i s t o focus on

the behavior o f res erv oir s under th e st imulu s of prod uct i on and commerciale x t r a c t i o n o f h ea t.

To be more s p e c i f i c, we are not concerned here

A t NSF we feel t h i s i s a hi gh ly opportune moment t o convene such a groupas t h i s . Many research and development e f f o r t s ar e now underway i n t h i s

area, and many have reached th at po in t where si gn if ic an t re su lt s have beenachieved and where new data and new ques tion s ar e being generated a t a ra pi d

pace.

e f f o r t s were i n i t i a t ed th rough the NSF Geothermal Program.)( I n a moment I w i l l rev iew the recen t h is to ry of how many of these

Therefore, NSF i s pleased t o support Stanford Univ ers i ty i n sponsor ingt h is workshop, and i n behal f o f the Foundat ion I want t o welcome you here.We have at tempted t o gather those who ar e cur re nt ly ac t i ve i n geothermal

re se rv oi r engineeri ng research and who are i n the for ef ro nt of new knowledgeand exper ience o f th i s rap id l y expanding f ie l d .

I n t h i s o b j e c t i v e , I t h i n k D r . Paul Kruger and hi s colleagues a t Stanfordhave succeeded admirably . The response t o workshop in vi ta ti on s, I understand,

has been enthusiastic and almost 100% i n acceptances . Some request!; t o a t-

tend had t o be discouraged, no t because the people are not smart enough and

not because they lac k a le g i t i ma te in te re st i n the subject area and f ind ing s

of th e workshop.

s i z e so as t o enable f r u i t f u l and spontaneous exchange of ideas among th eac t i v e res ea rc he rs i n t he f i e l d .

Rather, attendan ce had t o be cons trai ned t o a manageable

Because the re i s a wide community o f in te re st i n these matters:, 1 haveasked Stanford t o prepare a re po rt summarizing the papers, discussions and

f in din gs o f these thr ee days. They have agreed t o do t h i s, and the re po rt

w i l l be made av ai la bl e to a l l who are int ere ste d. Furthermore, I f u l l yexpe ct t o see numerous confe renc es and symposia i n t h e coming year devotedt o t h i s and othe r areas o f geothermal science. These meetings, a t whichmany o f you w i l l present papers, w i l l prov ide ample oppor tun i t y fo r thed i f f u s i o n o f new and cur re nt knowledge t o th e whole community of te ch ni ca land commercial in te re st .

I want t o extend a spec ial welcome t o the workshop pa rt ic ip an t s who

have come here from other countries.

c ount r y t o pa r t i c i pa te i n t h i s workshop, bu t we l ook w i t h an t i c i pa t i on t o

You are not only welcome i n our

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st rengthen personal and profes s iona l re l at i ons hip s wi th you that w i l l beo f m utual ben e f i t i n ou r r esea r ch e f f o r t s i n t he f u t u r e .

Now, i t may i n t e r e s t you t o know how some o f th e U. S . e f f o r t s we r es t ar t ed . The f i r s t p r o j e c t t o be i n i t i a t e d by NSF was r i g h t here a t

Stanford. Paul Kruger i n St an fo rd 's C i v i l Engineer ing Department had someideas about ta ppi ng steam ou t o f a ru bb le chimney created by an underground

exp los ion i n hot rock, and he wanted t o expl ore th e thermal and mass t ra ns-

fe r processes t o be expected i n such a s i tu at i on and t o f i n d ways t o e x t r a c t

th e heat. Henry Ramey, o ver i n th e Petroleum Engineering Department,

wanted answers t o quest ions o f fundamental behavior o f ho t water and steamth at had ar ise n i n h i s con sul t in g p ra ct i ce a t The Geysers and out o f h i sex tens ive exper ience i n ho t water f lo od i ng and o ther thermal s t i mu l a t io n

methods i n o i l r ese r vo i r s . Th is p r o jec t was s t a r t ed i n Ju l y 1972.

Take a l ook at F ig ure 1 , and see how the f und ing has progressed a t

NSF i n t h i s impor tant area. Our funding i n reserv oir engineer ing research

has peaked i n FY 1975 as i n every area o f t he NSF Geothermal Program, I t

i s i n t e r e s t i n g t o n o te i n r e tr o sp e c t, t h a t 20% of the $13.4 m i l l i o n t o t a linvestment i n geothermal energy by NSF over a f ive- yea r p er io d has beendevoted t o rese rvo i r eng ineer ing.

ra te i n the ear ly p er iod than d i d the program as a who le , bu t fo l lowin g

t he f o r m a t ion o f ERDA i n FY 1975, I t has become a l ar ge r f r a ct i o n of t h ewhole. Thi s increased r e l a t i v e emphasis der ive s from ou r po l i c y t o f ocus,no t on the eng ineering app l ic a t ions , no t on the u t i l i z a t i o n technology and

t he p i l o t p lan t s and t he demons tr a ti on p lan t s , and no t on t he i ns t i t u t i on a l

and non- t echn ica l ba r r i e r s t o u t i l i za t i on , bu t r a t he r on t he fundamental

sc ience prob lems i nh ib i t in g t he fu l l es t deve lopment o f the resource ,

Cl ea r l y, problems concerning r es er vo ir phenomena comprise a si gn i f i ca nt

pa rt o f t h i s concern fo r new fundamental knowledge, and the NSF program i smoving i n t ha t d i r ec t i on .

The investment grew a t a somewhat le ss er

F i na l l y , f o r a word on ou r cu r r en t l y ac t i v e p r o jec t s , each o f wh ich

w i l l be repor ted a t t h i s workshop, p lease look at f i g u r e 2.  Here I havel i s t e d t h e g ra nt ee i n s t i t u t i o n s , the research area of each pro je ct , the

pr i nc ip a l inves t iga to r , and the cumula tive fund ing through FY 1975. Thes t a t us o f t he r esea rch r epr esent ed on t h i s l i s t w i l l u nf ol d i n t he t h r e edays ahead o f us.

I t i s go ing to be a very s t i mu l a t i ng th ree days , as no t on ly the NSF

research i s descr ibed bu t a ls o tha t o f t he U. S . Geological Survey, i nt he ERDA l a b o r at o r i e s, i n t h e f i e l d and i n l ab o r a t or i e s o f p r i v a t e U. S .companies, and i n fo re i gn cou nt r i es w i t h ac t i ve geothermal programs andwho are represented here today.

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1972 1973 1974

235

FY1975

rl9"FY

1976

Figure 1 .   Reservoir Engineering Support i nt h e Geothermal Energy Program ofThe National Science Foundation.

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Nat i onal Sci ence Foundati on

GEOTHERMAL ENERGY PROGRAMRESERVOI R ENGI NEERI NG PROJ ECTS

Pr i nci pal Fund i ngI nst i tut i on Res ear ch I nvest i gator 5) t h ru FY75Stanf ord U.

Penn State U.

Pr i nceton U.

Col orado U.

Sys tems Sci ence

U. of Hawai i *

Northwestern U.

l aboratory experi ments i nheat and mass t ransf er

l aboratory exper i ment s i nreservoi r chemi st rynumer ca1 mode 1 i ng ofWai rakei f i el d by f i ni teel ement method

numeri cal model i ngprobl ems by f i ni t edi f f erence methods

numeri cal model i ng ofSal t on Sea f i el d byf i ni t e di f f erencemet hods

numeri cal model i ng ofcoastal aqui f er probl em

rock mechani cs probl emsi n st i mul at i on of geo-thermal reservoi rs

Henry Ramey, J r . $ 586,700Paul Kruger

Hugh Barnes,Wayne Bur nhamGeorge Pi nder

Davi d Kassoy

 J ohn Pri t chett

P i ng Cheng

Hans Weer t man

402 000

249, 500

248, 300

378)000

61, 100

213, 900

* Transf erred to ERDA under Hawai i Geothermal Proj ect

Fi gure  2

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 THE BI RTH OF GEOTHERMAL RESERVOI R ENGI NEERI NG

Henry J. Ramey,  J r .Pet rol eumEngi neer i ng Department

Stanf ord Uni versi t ySt anf ord, CA 94305

 The term"reservoi r engi neer i ng' ' arose wi thi n t he f i el d of study ofthe devel opment of gas and o i l reservoi rs. One def i ni t i on of reservoi rengi neer i ng i s the appl i cat i on of sci ent i f i c pr i nci pl es to the drai nageprobl ems ar i si ng dur i ng devel opment and producti on of o i l and gas reservoi rs.Al though many i mportant physi cal l aws concerni ng reservoi r mechani cs wereestabl i shed dur i ng the f i rst hal f of thi s cent ury, r eservoi r engi neer i nghas f l our i shed mai nl y si nce the end of Wor l d War i l .  The Combi nat i on ofthe recogni t i on of i ncreasi ng energy requi rements i n a r api dl y i ndustr i al -i zi ng worl d and the rel ease of t rai ned manpower f ol l owi ng Worl d War I Iabet ted the devel opment of the f i el d of reservoi r engi neer i ng. I n the1940' s and 1950' s oi 1 recovery processes such as underground combust i on

of oi l and oi l recovery by st eamand hot water i nj ect i on recei ved greatattent i on. The modern devel opment of geothermal reservoi rs al so beganto accel erate about that t i me. The pi oneer i ng geothermal devel opment i nLarderel l o, I t al y, began t he massi ve j ob of rebui l di ng the devastat i on ofWorl d War I I . New Zeal and began the i mpor t ant devel opment of geothermalpower i n the Wai rakei steamf i el d, and the Magma- Thermal Power Companydevel opment of the Geysers i n Cal i f orni a, USA, f ol l owed t hereaf ter .

Neverthel ess, i t was not u n t i l the ear l y 1960' s that petrol eumreservoi r engi neer i ng pr i nci pl es were f i rst appl i ed to geothermal reservoi rprobl ems. I t appears t h a t the f i rst such st udy was conducted by Whi t i ngand Ramey i n t he mi d 960' s ( Whi t i ng and Ramey, 1969). As a resul t ofthi s work, Cady began an exper i mental st udy of the i mportance of capi l l ary

pressure on boi l i ng w t hi n porous medi a i n 1967 ( Cady, 1969) , a l i ne ofst udy whi ch cont i nues to thi s date,of a geothermal f i el d was presented by Ramey i n 1968 concerni ng the GeysersGeothermal Fi el d i n Cal i f orni a.

A second reservoi r engi neer i ng study

Al though reservoi r engi neer i ng pr i nci pl es were wi del y known for 20years pri or to appl i cat i on to geothermal reservoi rs, the bi r t h of geothermalreservoi r engi neer i ng appears to date to the ear l y 1960' s.say that geothermal reservoi rs were not subj ect to sci ent i f i c study cl osel yrel ated to modern reservoi r engi neer i ng.i nvest i gat i on were more cl osel y al i gned to the f i el ds of geol ogy, geophysi cs,hydrol ogy, and geochemi st ry.

 Thi s i s not to

I t appears th a t the types of

 The reason for t hi s si tuat i on appears to l i e i n a mi sunderst andi ngconcerni ng pet rol eum reservoi rs.geothermal resources, i t was remarked that because pet rol eum reservoi rswere al ways cl osed pool s and geothermal systems were al ways act i ve hydro-thermal syst ems, there was nothi ng appl i cabl e wi thi n the fi el d of pet rol eumreservoi r engi neer i ng. The concl usi on that geothermal systems were l argehydrothermal syst ems subj ect to nat ur al "recharge" al so had an ef f ect.

I n one st at e publ i cat i on concerni ng

I t

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had been theorized that geothermal systems could be se

developed properly. I t was only necessary t o d i sc ove r

ra te (both hea t and f l u i d ) and p roduce a t t ha t ra te t o

system which would never deplete. I t now appears thatsystems can recharge a t t he phenomenal r at es re qu ir ed

genera t ion.

f - regenerat ing i f

the natura l recharge

have a steady- statefew i f any natura lo r e l e c t r i c power

The remark that petroleum reservoi rsswere always closed pools i sincor rec t as we l l .

t o water recharge ( i n f l u x) was publ ished i n 1930. The word " res e rv o i r  "

i s now used i n t he same sense as a "thermodynamic system.'' I t i s p o s si b l et o have t ranspor t in to and out o f the system, o f course. Let us then tu rnto geothermal r es er vo ir engineering as a new f i e l d of study.

The f i r s t s tudy o f o i l reser vo i r performance sub jec t

 Although many o f t he p r i n c i p l e s o f r es e r v o i r physics invo lved i n non-

i s otherm al o i l p roduc t ion by f l u i d i n j ec t i on ( o i l p roduc t ion by underground

combust ion and steam inject ion) are reasonably wel l understood, i t i s n ot

su r pr i si ng t h a t some problems appear t o remain fo r geothermal res e rv o i r

phys ics. For t h i s reason, Cady (1969) st ud ie d geothermal system beha viorw i t h t he phy s ic a l model p r i o r t o 1969.pressure might reduce the vapor pressure o f l i qu i d wa te r t o a s ubs tan t i a l

degree was res pon sib le f o r th e Cady study.  Although vapor pressure suppres-

s i on was n o t n o t ic e d i n Cady's work w i t h an unconsolidated sand core, hedi d make the sur pr is in g observat ion t ha t an isothermal dry steam zone could

develop w i t h i n a few inches above a two-phase bo i l i n g zone which fol l owed

th e vapor pressur e curve f o r water as pressure decl ined.

c a p i l l a r y p r e s s u r e e f f e c t s upon bo i l in g cont inues a t Stanford.

A s p e c u l a t i o n t h a t c a p i l l a r y

A search for

Unfo r tuna te l y , i t i s d i f f i c u l t t o sca l e a l l important physicalparameters between th e f i e l d and the lab orat ory. Many important physic al

phenomena have been discover ed by thorough ana ly si s o f f i e l d performance

data. However, f i e l d data f o r geothermal systems are not re ad i l y ava i la b le .In reservo i r eng ineer ing i t appears t h at the re i s no hope of ev e r phy s i c a l l y

ex am in i ng t he res e rv o i r d i r ec t l y . I t i s n o t l i k e l y t h a t we s h a l l m ine o rexhume many res erv o i r s . Thus, the re sp on s i b i l i ty o f the res erv o i r engineer

usu al l y inv o lves a two-step process: ( 1 ) t o make and in terpret ind i rectmeasurements o f the qua n t i t a t i v e cha rac te r i s t i cs o f the rese rvo i r , and( 2 ) t o employ t h i s in fo rmat ion and bas ic phys ical p r i nc i p le s t o fo recas tthe behav io r o f the re servo i r under any po t en t i a l l y use ful p roduc t ion

scheme. The second ste p assumes t ha t a l l ba sic physi cal p r in ci pl es areknown. Here in l i e s the need f o r much f i e l d and la bora tory exper imentalwork. Even i n the much o l de r f i e l d o f petro leum reservo i r engineer ing,i t i s cl ea r th a t much remains t o be discovered concerning bas ic ph ysi calp r i n c i p l e s .

(1962) and Ramey (1971).

-See recent d iscuss ions o f res erv o i r engineer ing by Wyl l i e

Ramey po in te d ou t th a t such important inf orm ati on as can be determined

by di r e c t measurement on re se rv oi r samples (cores) of te n leaves much t o be

d es ir ed . The d i f f i c u l t y w i t h c o re a n a l y s i s i n fo r ma t io n l i e s i n r e l a t i n g

i t t o the reservo i r . Indeed, as W y l l i e has po in te d out , why should weassume that the reservo i r i s l i k e the minuscule volume o f rock samplestaken out of the r es er vo i r and d iscarded? Many i mpo rta nt computations

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and decis io ns are reached, nevertheless, upon the basi s o f qu an t i ta t i ve

information derived from core samples.

By now, in te rp re ta t i on o f in fo rmat ion der ived from cores should bewel l es tab l ished and s tandard ized. I t i s no t ! There i s no consensusof proper methods o f handl i ng core data.

t ha t t he approach t o r es e rv o i r eng inee r i ng be ho l i s t i c ( t ha t t he dete r  -

minat io ns be made i n wholes, no t i n par ts - - fo r example, t h at "whatmat te rs i s the rock u n i t and no t samples o f a rb i t ra ry s i ze tha t may

have been taken from i t"). He c i t e d pre ssur e bu il du p and drawdown

tes t i ng . Determini ng t he c ha rac te r i s t i c s o f the reserv o i r by in - s i t umeasurements using we ll s as th e i np ut and ou tp ut f lo w faces of th er e s e r v o i r "core" makes a great deal o f sense. Reservoir s imu lat ion byd i g i t a l computer i s another highly popular technique that embodies theh o l i s t i c approach. We at tempt t o genera te a de ta i led 'desc r i p t ion o f ar e s e r v o i r to match a l l known performance data. I f the matching i s suc-ce ssf ul , we assume th at a reasonably accurate model o f the actu al res er vo ir

system i s available and employ i t to forecast behavior under various

ope rat iona l schemes. To re st at e t h i s s i tu at io n, performance matchingc ons i s t s o f developing an n-dimensional mathematical reservoir mode.1th at responds t o model f l u i d product ion as t he proto type responds t oac tua l f l u i d p roduct ion . The "response" involved usually means pressure

response.

incl ude both f l u i d and energy, and response t o includ e pressure, temperature,

enthalpy, qu al i t y , and composi t ion. The b i r t h of geothermal reservoirengineer ing i s accomplished, and we aw ai t th e development of t he c h i l d .

W y l l i e made an eloque nt pl ea

I n t he case o f geothermal systems, we gene ral ize product ion t o

References

Cady, G. V . 1969. Model Studies o f Geothermal F l u i d Produc tion. Ph.D.d i s s e r ta t i on , S tan ford Un i v e rs i t y , S tanfo rd , Ca l i f o rn i a .

Ramey, H. J., J r . 1971. Reservoi r Engineer ing i n the 70's and 80%.Jou rna l of Petroleum Technology, p. 33.

Ramey, H. J., J r . 1968.  A Reserv oir Engineering Study o f the GeysersGeothermal Fi el d. Submitted as evidence, Reich and Reich, P et it io ne rs

v. Commissioner o f I n t e r n a l Revenue, 1969 Tax Court o f the U.S., 52.T.C. No. 74, 1970.

Whit ing, R. L., and H. J. Ramey, Jr. 1969.  App l i c a t i on o f Material andEnergy Balances t o Geothermal Steam Pro duct ion . Jou rna l o f PetroleumTechnology, v. 21, pp. 893-900.Wy l l i e , M. R. J. 1962. Res erv oir Mechani cs--Sty l ized Myth or Potent ia lScience? Journa l o f Petroleum Technology, pp. 583-588.

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SUMMARY DE S CRI P T I ON OF RESEARCH A C T I V I T I E S

D . R. KassoyMechanical Engineering Department

Un ivers i t y o f Cc lo rado

Bou1der, Colorado 80302The bas ic goa l o f the Un ive rs i t y o f Colorado Geothermal Research

Program has been t o assess, cha ra ct er ize and model the myriad o f phy sica l

processes oc cur ri ng i n th e geothermal environment. While develop ing anunderstanding o f the fundamental nat ure of these phenomena we can construct

a comprehensive model o f t he s t ruc tu re o f a gi ve n geothermal system. Sucha re su l t should p rove use fu l i n the in te rp re t a t io n o f su r face geophysicalmeasurements and for th e gener al development o f a geothermal f i e l d . Our

studies spanning the range from heat and mass tr an sf er process i n hydro-

thermal convect ion anomalies t o t he po ssib le appearance of di la ta nc y duet o l a rge ra tes o f l i q u i d w i thdrawa l , a re car r ie d ou t by a d ive rse group of

engineers , geophys ic is ts geolog i s ts , seismo logist s and expe rts i n computa-t i on . Much o f the e f f o r t has been car r i ed out wi t h the cooperat ion of the

geothermal group a t Systems, Science and Software, La Jo ll a , Ca li fo rn ia .

The fo l l owi ng summary o f a c t i v i t i e s prov ides an ext remely b r i e f

de sc ri pt io n o f t he ongoing research programs, t h e i r purpose and whenappropr ia te , the re su l ts obta ined .

Phys ica l Character izat ion

Black" ) has ca r r i ed ou t a subsurface study o f the Mesa anomaly i n theImperial Val ley . His stu dies have shown th at :

There i s a cap o f low ve rt i ca l per meab i l i ty composed of a la rg e

f r a c t i o n o f c l a y - l i k e m ate r i a l .Below the cap are r e l a t i v e l y compacted, sandy s tr at a w i th

s i gn i f i c an t pe rm eab i l i t y .

Fra ctur ing i n deeper rock layers , presumably assoc iated wi t h

s e i s m ic ac t i v i t y i nc reas es v e r t i c a l pe rm eab i l i t y .

In te rs ec ti ng f a u l t zones near two we ll s have produced a chimney

o f pa r t i c u l a r l y h i gh v e r t i c a l pe rmeab i l it y . Subs tan t ia l upwe ll i ng

of hot water from depth occurs here as we l l as long the l in ea r

fau l t zone to the southeast.

The r is ing hot water spreads l a t e r a l l y , m o s t l y t o the southeast

as the f a u l t zone in te rse c ts re la t i ve ly permeable hor i zon ta laqu i fe rs .

Reduced sa l in i ty o f water a t depth compared t o th at i n upper le ve ls(0-800m) imp1 i e s grea te r c i rc u l a t io n and less evapor i tes i n thedeeper zone.

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R inehar t (2 ) has cons idered the presence of fa u l t i ng i n geothermalareas. He has concluded t h a t :

(A)  Almost a l l p roduc t i ve geothermal ar eas a re associated w i t hfa u l t i ng . Many o f these a re pa t te rns o f r in g f ra c tu r es

assoc ia ted w i th ca lderas wh i l e o thers a re l i n ea r fea tu res

assoc ia ted w i th r i f t zones.

(B) Fau l t zones ac t as condu i ts fo r the f low o f hea ted f l u i d f romdepth. They can a f f e c t the supply o f sur face water t o the

system a t depth.

Mechanical Models

R i r ~ e h a r t ' ~ )has suggested a po ss ib le ph ys ic al mechanism for t heobserved cy c l i c va r ia t io n i n f l ow ra tes and water ta b le leve l assoc ia ted

wi th sa tu ra ted porous media sub jec ted t o tempora l a l te ra t ion s i n i n - s i t u

st re ss due t o te ct on ic and t i d a l f orces . Making reasonable assumptions,he argues th at a so l i d bloc k supported by a saturat ed porous material cou ld

move as much as seve ral cen tim ete rs due t o pe ri od ic mechanical loa din g.Th i s im pl i es t ha t t he e f f e c t i v e pe rm eab i l i t y o f

a l t e r e d s u b s t a n t i a l l y .

Archambeau(a) i s cu r re n t l y deve lop ing non ldue t o i r r ev e r s i b l e po re c o l l aps e . i ncl uded i s

tu ra l rock fa i l u r e ( induced se i smic i t y ) due t o dh igh lev e ls o f e f f ec t i ve s t ress as pore p ressure

Heat and Mass Transfer

rac tu re reservo i rs can be

nea r models o f suibs idence

h e p o s s i b i l i t y of s t r u c -l a t anc y res u l t i ng f r o mi s reduced.

Kassoy and Zebib(4) examined the e f f ec t o f a rea l s t i c v is c oi j i tyv a r i a t i on on t he ons et o f c onv ec t i on i n a hor izonta l porous s lab.

' leight i on . The r o l l pa tt e rns d i s p l ay re l a t i v e l y h igh v e l o c i t i e s and lai rge

tempera tu re g rad ien ts a t depth un l i ke th e symmet ri c c l ass i ca l p r o f i l e s .

C r i t i c a l Ray-numbers a re d ras t i ca l l y reduced w / r to the cons tan t p roper ty ca lcu la -

K a s ~ o y ( ~ )has considered convective f l o w i n a nar row v e r t i c a l s a tu ratedporous sl o t as a model o f mass tr an s f e r i n a fa u l t zone. The mass f l o w ra tes ,resu l t i ng par t l y f rom convec t ion due to p re sure head and par t l y fromnatu r a l convec tion, a re o f t e agn itu de 10 kg/day over an area 0.5 km2when the perme abi l i t y i s 10- Icm5 .

Garg e t a l . (6) have computed t he fl ow pa tt er n and temperature var ia---t i o n i n a ho r i z on ta l aqu i f e r when f l u i d i s in t roduced f rom an in t er sec t i ngv e r t i c a l f a u l t zone i n whi ch t h er e i s ho t f l u i d r i s i n g from depth.so lu t i on shows the development o f a conf in ed nat ur al convect ion c e l l i n t heaqu i fe r . Hence, i n the model cons idered la te ra l sp i l l a ge from the f a u l tzone does no t re su l t i n s imp le th rough f low i n the aqu i fer .

The

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Kassoy and Zebi b( b) have extended thei r work to three- di mensi onalcontai ners more r epresentati ve of geothermal areas i n hi ghl y f ractured rockof vol cani c or i gi n. The resul ts al so port ray l i near convecti on pat terns i nnarrow vert i cal f aul t zones, and may be used to expl ai n the prese c ofperi odi cal l y spaced hot spr i ngs al ong 1 i near f aul t zones.shown that nat ur al convect i on i nstabi l i t i es can enhance the vert i cal f aul tzone f l ow descri bed above.

Kas ~oy~~'has

Kassoy ( d ) has extended hi s anal ysi s to i ncl ude l at eral spi l l age i ntoi ntersecti ng hori zontal aqui f ers. The pressure and temperature di st r i bu-t i ons are remi ni scent of those f ound i n the Mesa geothermal anomal y. Li neari nst abi l i t y at cri t i cal a Rayl ei gh number l eads t o superi mposed cl osed rol l s.

 These mi ght be used to expl ai n the pai r of hot spots at the Mesa anomal y.

Nayf eh( 7) et a l . have exami ned two- t emperature model s of f l ow i nporous medi a. They concl ude that f or most geothermal appl i cati ons thef l u i d and sol i d are i n l ocal thermal equi l i br i um.

--

 There has been a maj or ef f ort to devel op useful descri bi ng equat i onsfor thermal l y act i ve def ormabl e porous medi a contai ni ng two phase f l ui dswi th concent rat i on gradi ent s. Thi s work i s summari zed i n Ref s. 6 and 8.

REFERENCES

1. H. T. Bl ack - A Subsurf ace St udy of the Mesa Anomal y, I mperi al Val l ey,Ca. CUMER* 75- 5.

2.  J . S. Ri nehart - Faul t i ng i n Geothermal Areas. CUMERa 75- 12.3 . J . S. Ri nehart - Model f or Long Peri od Earth  Ti dal Def ormati ons.

 To appear as a CUMER report .4. D. R. Kassoy, A. Zebi b - "Var i abl e Vi scosi ty Eff ects on the Onset of Con-

vect i on i n Porous Medi a, " to appear i n  The Physi cs of Fl ui ds ,_I

& CUMER: ; 75-4.5. D . R. Kassoy - "Heat and Mass Transf er i n Model s of Undevel oped GeothermalFi el ds , " to appear i n Proceedi ngs o f the UN Geothermal Symposi um, San

Franci sco, 1975 - al so CUMER 75-7.

6. S. K. Gar g et a l . - "Si mul at i on of Fl ui d- Rock I nteracti ons i n a GeothermalBasi n, " S S S T - 7 6 - 4 7 3 4 Syst ems, Sci ence and Sof t ware, La J ol l a, Ca.

7 . A. H. Nayfeh --et a l . - "Heat Exchange i n a Fl ui d Percol ati ng Through PorousMedi a, ' l Proc. SO~.Eng. Sci . Meeti ng, Aust i n,  Texas, Oct . 1975.8.  T. R . Bl ake, S. K. Garg, "On the Speci es Transport Equat i on for Fl ow i n

Porous Medi a, " submi t ted to Water Resources Research (1975) .ACUMER ref ers to Mechani cal Engi neer i ng Report , Uni versi ty of Col orado.(a) - (d ) - Ongoi ng r esearch act i vi t i es.

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HEAT AND FLUID FLOW EXPERIMENTS TO MEASUREGEOTHERMAL RESERVOIR PHYSICAL PARAMETERS

W i l l i a m E . Brigham

St an f o r d Un ive r s i t y

Stanford, CA 94305

BENCH-SCALE MODELS

The te st o bje ct iv es and apparatus involved i n the bench-scale models

were presented i n Progress Report No. 1 (Ref. 1 ) . I n b r ie f , t hese exper i -ments were designed t o te s t fundamental concepts f or nonisothermal b o i l i n g

two-phase f l ow throu gh porous media. Thi s work i s aimed a t t he en t i r eres erv oir , w hi le the chimney model deals most d i r e c t l y wi th the wel lbo reand near -wel l re ser voi r cond i t io ns. The combinat ion should be broadlyuseful i n the new f i e l d o f geothermal rese rvo i r engineer ing .

The term "geothermal reservoir engineer ing" i s an adaptat ion of ' 'pe tro -

leum reservoir engineer ing," the branch of engineer ing which deals wi th

assessment, and pla nni ng, o f optimum development o f petrol eum re se rv oi rs .Fo r t una t e l y , t he r e i s much that i s use f u l fo r geothermal engineer ing i n the

l i t e r a t u r e o f o i l r ecover y. O i l recovery by steam inject ion (Ref. 2) andunderground combustion (Ref. 3) present some o f the impor tant features ofnonisothermal two phase f l ow which appear per t i ne nt t o geothermal re se rv oi rs .

In add i t io n , there i s a cons iderab le body o f use fu l da ta on the proper t i es

of rocks and f lu id s as a fun ct i on o f temperature and pressure.

these data ar e summarized i n Reference 4.one spec i f i c s tudy o f the f low o f s ing le-component (water) two-phase (thusnonisothermal) f lo w i n porous media (Ref. 5 ) . I n pa r t ic u l a r , t here was noin for mat io n on the important phenomena involv ed when normally immobile