Procdings World Gothrmal Congrss 25 Antalya, Turky, 24-29 April 25 Th Hall Plot Analysis of a Watr Injction Tst Affctd by Gothrmal Rsrvoir Rspons I. Mtin Mihcakan,* Elif I. Altinay,* and Ibrahim Kasap** *Ptrol v Dogal Gaz Müh. Bol., Madn Fak., Istanbul Tknik Univ. Maslak Istanbul 34469, Turky / mihcakan@itu.du.tr **Midas Müh. Müm. Tic. Ltd., Gnclik Cad. No. 127-1, Anittp, Ankara 657, Turky Kyords: Gothrmal, Kizildr, Injction Tst, Hall Plot Analysis, Rsrvoir Fill Up, Carbon Dioxid. ABSTRACT Watr injctivity into gothrmal rsrvoirs is discrnd by atr injction tsts conductd in injction lls and may continu for ks. Th volution of an injctivity tst and th rsponsiv variations in rsrvoir proprtis may b ascrtaind by th stady-stat Hall-plot analysis. Thus th fficincy of injctivity may b valuatd by such analysis mthod, in a continuous mannr. A variabl-rat and long-trm atr injction tst, that as conductd in a rinjction ll in Kizildr gothrmal fild, as attmptd to b assssd by th Hall plot analysis. Th prsnc of fr carbon dioxid gas, prior to th commncmnt of atr injction, is claimd to b dtctd in th rsrvoir. At a crtain stag in injction opration, th rsrvoir fill-up and subsqunt dissolution of fr carbon dioxid in atr ar also rcognizd. 1. INTRODUCTION Various rasons may rquir th injction of surfac atrs or th rinjction of producd gothrmal atrs, hich turns out to b disposal atr, into gothrmal rsrvoirs, in a continuous mannr. Prior to an injction or rinjction opration th atr injctivity, i.., th rat of accptanc of injctd atr by th rsrvoir rock, for an injction ll is xamind by conducting an injction tst. Such tsts may covr a tim span in th ordr of svral ks or months. On of th controlling factors that affct th ntranc and propagation and, thus, th injctivity of cool injction atr into th hot rsrvoir rock is th rsistanc xhibitd by th formation ithin f mtrs around th llbor. Th majority of th forc applid to driv injction atr into th rsrvoir rock is usd up in this rgion of rsistanc. Essntially, th skin ffct and th ffctiv prmability to injctd atr around th llbor prompt such rsistanc. In th cas of fracturs or fissurs xist and xtnd out from th llbor, th forc or nrgy dissipatd for driving th injctd fluid in ould b much lor in this rgion. Th diffrnc in tmpratur of th injctd and rsrvoir atrs lads to th propagation of a tmpratur front in th rsrvoir, during an injction tst. Chmical intractions, inducd by tmpratur diffrncs, btn th cool injction atr and th hot rsrvoir rock may caus th prcipitation of som of th dissolvd minral spcis ithin or ithout th rgion of rsistanc, dpnding on th advancmnt of cool atr front in th rsrvoir. Basd on th volution of an injction tst, th variations in rsrvoir proprtis that may mrg as th rduction in absolut prmability as ll as in th ffctiv prmability to cool atr may rsult in a dcras in atr injctivity. 1 Watr injctivity is also controlld by th total volum of atr that can b injctd into a gothrmal rsrvoir and, in turn, is limitd ith th fractur gradint and th por volum or liquid storativity of th rock. Onc th rsrvoir is filld ith atr, th nforcmnt of mor atr into th formation lads to a rmarkabl incras in rsrvoir and injction prssurs, du to th lo comprssibility of liquid atr. Th prolongd injction undr ths conditions ill vntually caus th uncontrolld fracturing of th rock or furthr xpanding th xisting fracturs. Nithr of ths occurrncs is a dsird consqunc. Prformanc analysis and intrprtation for atr injction oprations in gothrmal filds may bcom rathr difficult hn th injction llhad prssurs and th obsrvationll bottom-hol prssurs ar usd. Misintrprtations ar possibl, spcially, hn th rsrvoir rspons to atr injction is attmptd to b prcivd from th monitord injction llhad prssurs or rats in tim. Thus, th mthod of analysis that uss th monitord tst data has paramount importanc for a rliabl valuation of atr injctivity and for th fficint application of th injction opration. Th Hall plot analysis is a simpl mthod and is dvlopd to liminat such difficultis in valuating th prformanc of a atr injction ll. In this ork th Hall plot analysis is applid to valuat a producd atr rinjction tst, conductd in KD-1A ll in Kizildr gothrmal fild in Turky. It is invstigatd hthr th dtrmination of variations in prmability or skin factor could b dtrmind by th Hall plot analysis, as th tmpratur front propagats during th variabl-rat and long-trm atr injction tst. Th injction llhad prssurs ar usd and convrtd to bottom-hol prssurs in th analysis. In th convrsion calculations th frictional nrgy losss and th variation of atr dnsity ith th chang of tmpratur ith dpth ar takn into account. Th rcordd prssur and tmpratur data, of hich th lattr is rcordd at to diffrnt dpths, at th obsrvation ll KD-1, is incorporatd in th analysis in ordr for a bttr comprhnsion of th rsrvoir rspons. 2. HALL PLOT ANALYSIS Injction tsts mployd to dtrmin atr injctivity and long-trm injction fficincy may last as long as svral ks or months. Th transint prssur analysis mthods,.g., falloff tsts, injction tsts, tc., may not b adquat for valuating th variations in rsrvoir charactristics and injction fficincy that occur during th long-trm tst. Inadquacy is inhrnt to th ssntials of transint prssur analysis mthods that stimat rsrvoir proprtis at on point in tim, hras th Hall plot is a continuous monitoring mthod for that purpos (Bull, t.al.199). Th Hall plot analysis is a stady-stat mthod, originally dvlopd to analyz th atr injction ll prformanc in atrflooding applications in oilfilds (Hall, 1963). Hall
plot prmits monitoring th atr injctivity and injction fficincy continuously and provids mans to idntify th variations in som rsrvoir proprtis that occur ovr th xtndd priod of an injction tst (Hall, 1963). Hall plot mthod has som advantags, such as th smoothing ffct on th rcordd prssurs ovr tim and th us of llhad prssurs, hich can b asily convrtd to bottom-hol prssurs using th knon tchniqus. On of th major difficultis in th analysis of an injction tst ariss from th variations ncountrd in th injction llhad prssurs and rats. Such difficultis can b ovrcom by mploying th Hall plot analysis, in hich Darcy s la for th stady stat flo of singl-phas fluids in a ll cntrd in a circular rsrvoir is usd : k h f q = 18.665 B µ ( p p ) [ Ln( r r ) + s]... (1) hr, r is th radius xtnding from llbor to th front of th cool atr bank, i.., th intrfac of injctd cool atr and th hot rsrvoir atr, rsrvoir prssur at this front, and p f is th bottom hol injction prssur. For a stady-stat vrtical flo, th bottom-hol prssur can b xprssd in trms of llhad (or tubing had) prssur, p tf, prssur drop du to intrnal frictional in flo, p f, and fluid had in ll, (ρg) D, as follos. p f [( g ) g c ] D p f = ptf + ρ... (2) Although p f in Eqn.2 varis ith varying injction rat, th magnitud of its variations is at a ngligibl lvl. Hall intgratd th both sids of Eqn.1 ith rspct to tim : t k h q dt = 18.665B µ [ Ln( r r ) + s] t ( p ) f p dt... (3) hr th lft-hand sid dscribs th volum of cumulativ atr injction, W, and th right hand sid givs th total variation in rsrvoir prssur during th corrsponding injction tim, t, in days If surfac (or llhad) prssurs ar dsird to b usd in practic, thn, Eqn.2 is substitutd into Eqn.3, and aftr rarranging Eqn.4 is obtaind. t {( p p + [( g) D / ]) p } dt m W hr tf f ρ g c =... (4) H 18.665B µ mh = k h [ Ln( r r ) + s]... (5) Not that m H is th slop of th straight lin obtaind hn th cumulativ variation in prssur diffrnc in lapsd tim on th lft hand sid of Eqn.4 is plottd against th cumulativ volum of injctd atr, W. Th slop (m H ), although assumd to b constant, incrass ith incrasing radius of xpanding cool atr front, r. Th validity of this assumption for constant Ln (r /r ) and p is xplaind by Hall (1963), considring th fact that th rat of incras in r is constant and indpndnt of changs in skin factor or in ffctiv prmability. As illustratd in Figur 1, th slop (m H ) of Hall plot may hav mislading valus hn ithr llhad prssurs (p tf ) or bottom-hol prssurs (p f ) ar usd alon in Hall intgral on th lft-hand sid of Eqn.4. Thus, in ordr for obtaining a ralistic slop and for 2 smoothing th calculatd data, Hall intgral is suggstd to b usd in th form of ( p p ) dt. Hall Intgral, bar. day 2 16 12 8 4 m H1 f m H2 p f dt p tf dt (p f - p ) dt 5 1 15 2 25 3 35 4 Cumulativ Watr Injction, 1 m 3 Figur 1 : Comparison of Hall intgration mthods that diffr in slops in squntial stags of injction. In all thr Hall plots in Figur 1, th initial straight-lin sctions ith th slop of m H1 rprsnt th tim intrval, in hich any variation in ffctiv prmability (k ) or skin ffct (s) has not bn ncountrd yt, during th atr injction in a gothrmal ll. Th slops (m H2 ) of th scond straight-lin sctions of th curvs incras ith dcrasing k and incrasing s, as a rsult of formation damag or any othr ffct of similar natur. If a stimulation ffct taks plac during th injction opration, thn th slops (m H2 ) ould dcras ith incrasing k and dcrasing s. Data collction for th Hall plot analysis is inxpnsiv, sinc th rcording of injction llhad prssurs and rats ith rspct to tim is sufficint. As statd by Bull, t.al. (199), a major disadvantag of Hall plot analysis is th simultanous prsnc of to unknons, transmissibility (kh/µ) and skin ffct (s), in th slop trm. Th valu of transmissibility ould chang only if a significant chang in viscosity or ffctiv prmability occurs. Any chang in ffctiv prmability around th llbor ould caus a chang in skin ffct and, in turn, th slop changs. In this cas, th rlation btn th slops of to sctions on a Hall plot in Figur 1 may b givn as follos. k h s2 = s1 18.665 B µ ( m m ) H1 H 2... (6) hr th subscripts 1 and 2 rprsnt th first and scond straight-lin sctions of th plot, rspctivly. Any formation damag occurrd during atr injction may b dtrmind by calculating s 2 in Eqn.6, hich rquirs th valu of s 1 b knon from anothr tst, such as falloff, injction or intrfrnc tst. If th skin around th injction llbor is constant and th ffctiv prmability far aay from th llbor changs during atr injction opration in a gothrmal rsrvoir, thn th transmissibility (or flo fficincy) trm for th scond straight-lin sction in Hall plot, in Figur 1, can b obtaind from th ratio of slops, as follos. mh1 mh2 ( k h / µ ) 2 =... (7) ( k h / µ ) 1 Th valu of (k h/µ ) 1 trm for th first straight lin is rquird to b obtaind from anothr tst, as in th cas of dtrmining skin ffct for th scond straight lin, abov.
3. REINJECTION APPLICATION IN WELL KD-1A Saturatd hot atr and stam has bn producd from to rsrvoirs in Kizildr gothrmal fild sinc 1968. By th mid 197 s, rinjction of ast producd atrs back into th uppr rsrvoir as considrd, mainly for ast atr disposal, supplmntal hat xtraction, and maintnanc of rsrvoir prssur. A pilot rinjction tst as conductd at th ll KD-1A, in 1976 (Kasap, 1976), to invstigat th atr injctivity and injction fficincy. Dtaild information on th vindication of rinjction attmpt and a gnral ovrvi of Kizildr gothrmal fild may b found in lshr (Satman, t al, 2). During th 29-k long injction opration th avrag injction rat as approximatly 83 tons pr hour ith ± 1 prcnt fluctuations, and th injction atr tmpratur varid btn 3 C (33 K) and 42 C (315 K),dpnding on th prvailing tst conditions. Figur 2 illustrats th bhavior of llhad prssur and injction rats, rcordd at ll KD-1A. Th ll KD-1, 68 mtrs aay from th injctor, as chosn as th obsrvation ll and its donhol tmpraturs, at th dpths of 5 and 53 mtrs, and bottom-hol prssurs r monitord as sn in Figur 3. Not that th ll KD-1 as drilld to a total dpth of 54 mtrs until a fractur ntork as ncountrd hr th mud circulation as lost at th dpths of 53 to 535 mtrs. Wllhad Prssur, bars 14 13 12 11 1 9 8 7 6 Wllhad Prssur Injction Rat 5 1 15 2 25 3 Tim, k Figur 2 : Variation of llhad prssur and injction rat ith tim for th injction ll KD-1A. Bottom Hol Prssur, bars 64 62 6 58 56 54 52 Obsrvd Prssur, bars T @ 53 m, C T @ 5 m, C 5 1 15 2 25 3 Tim, ks Figur 3 : Don-hol tmpraturs, at th dpths of 5 and 53 mtrs, and bottom-hol prssurs monitord at th obsrvation ll KD-1. As sn in Figur 2, in th first 7 ks, th llhad prssur incrass from 7 bars (.7 MPa) to 9 bars (.9 MPa) as th injction rat incrass from 75 tons/hr to 9 tons/hr. During th sam tim fram, both th bottom hol prssur and tmpratur at 53 mtr dpth in ll KD-1 13 97 91 85 79 73 67 61 55 199 198 197 196 195 194 193 Injction rat, tons/hour Don Hol Tmpratur, o C 3 Mihcakan, Altinay, and Kasap incras ith som oscillations to 57 bars (5.7 MPa) and 198.5 C (472 K), rspctivly, as sn in Figur 3. From 7th to 12th ks, th injctor llhad prssur drops don to 8 bars (.8 MPa), and th injction rat oscillats around 9 tons/hr, implying a slight dcras in formation rsistanc to th injctd atr around th llbor and a good hydraulic communication in btn th to lls. In othr ords, no scaling inducd prmability rduction occurs about th injctor, during this 5-k intrval. In th obsrvation ll, hovr, th prssur and tmpratur at th dpth of 53 m drop 4.5 bars and 4.5 C, rspctivly, yt th tmpratur at 5-m dpth drops only 1 C. Such tmpratur rspons at th obsrvation ll indicats th arrival of injctd atr front through th alrady dtctd fractur ntork at th dpth of 53 mtrs in th obsrvr. Thrfor, it can b statd that th fractur ntork dos not xtnd up to th dpth of 5 mtrs and 1 C cooling at this dpth is mrly du to th conductiv hat transfr, hil th cooling at th dpth of 53 m is du to primarily convctiv and scondarily conductiv hat transfr. Btn th 12th and 15th ks, injction rat sharply drops from 89 tons/hr to 75 tons/hr, but llhad prssur incrass 3 bars to a lvl of 11 bars (1.1 MPa), as shon in Figur 2. Bottom-hol prssur at th obsrvation ll promptly rsponds to follo a similar trnd (Figur 3) and incrass 6 bars to a lvl of 59 bars (5.9 MPa). Th tmpratur at 53 m dpth at KD-1 incrass only 1.5 C by th conductiv hating of th rock, sinc th coolr atr flo toard th obsrvation ll is mitigatd ith th rapidly dcrasing injction rat. Th tmpratur at 5 m also rsponds to th allviatd flo of injctd atr by minor oscillations around 197.7 C. Tan (1984) attributs such suddn incras in prssur to th plugging up of formation by prcipitatd silicat (SiO 2 ), yt, dos not provid any xplanation for th subsqunt incras in injction rat along ith th furthr incras in bottom-hol prssur aftr th 15th k. Tan s argumnt for formation prmability rduction as th rsult of silicat prcipitation contradicts ith th incras in injction rat. Th argumnt is basd only on th obsrvd silicat scaling, ith a thicknss of 2 to 4 millimtrs, on th innr alls of both th surfac injction-atr flo conduits and llhad quipmnt (Kasap 1976). Considrabl amount of silicat prcipitation out of atr in th injction facilitis, in fact, lads to th injction of atr ith lo silicat contnt and, thus, furthr contradicts ith th Tan s argumnt. If any solids prcipitation took plac ithin th rsrvoir, thn th injctor KD-1A ould hav xprincd a prssur ris much arlir than did th obsrvr KD-1. Yt, such rspons is not sn in Figurs 2 and 3. Consquntly, th injction rat and prssur bhavior btn 12th and 15th ks should actually b considrd as a good xampl for th rsrvoir fill up by injctd atr. It is knon that th long trm dpltion of lor rsrvoir causd th formation and th subsqunt vrtical migration of a fr gas phas, consisting of ssntially carbon dioxid and som atr vapor, into th uppr rsrvoir in Kizildr fild. Aftr th arrival of injctd atr at th obsrvation ll, on th 6th k of opration, it is mor likly that th furthr injction is filling up th rsrvoir hil comprssing th fr gas phas. Th sharp incras in bottom-hol prssur, shon in btn th solid arros in Figur 3, may b attributd to th disprsion of fr gas phas in liquid atr upon comprssion. Simultanously th dclin in injction rat is lssnd (Figur 2) as th volum of disprsd gas phas is rplacd by sloly incrasing volum of atr. Sinc th cool injction atr fills up th rsrvoir at a lo rat and
arms up, th tmpratur at 53-m dpth incrass ith oscillations, and th tmpratur at 5-m dpth around ll KD-1lvls off, as sn in Figur 3. Th rsrvoir fill up sms to b compltd by th nd of 15th k. Aftr th 15th k, th injction rat incrass about 1 tons/hr and rmains constant at th lvl of 85 tons/hr. Th llhad prssur follos th sam trnd ith on k dlay, thn incrass 2 bars and rmains constant at 13 bars (1.3 MPa), until th 21st k., as in Figur 2. Th bottom hol prssur at th obsrvation ll rsponds to th rat incras ith to-k dlay and rapidly riss up to a pak of about 61.7 bars and, thn, rapidly drops don to 58.2 bars, until th 22nd k, as shon in Figur 3. According to th authors of this papr, such prssur and rat bhavior rsmbls ithr th nlargmnt of xisting fracturs or a small scal fracturing in an alrady prssurd up formation. It is ll knon that onc th fracturing is startd, its propagation dos not rquir as much prssur as for initiating th fractur. Bottom-hol prssur bhavior, btn th 17th and 22nd ks in Figur 3, sms to b an indicator for such occurrnc, hich may b intrprtd as th comprssion of injctd xcssiv atr until th start of fracturing or fractur nlargmnt on th 19th k. Within th sam tim fram, th injction llhad prssur in Figur 2 riss up to th highst lvl of 13 bars and rmains constant. Probably th fractur nhancmnt as not so xtnsiv to rlax th systm and to caus a drop in llhad prssur. In th man tim, both tmpratur rsponss at th dpths of 5 and 53 mtrs (Figur 3) support this intrprtation by maintaining thir bhavior ith minor oscillations btn th 15th and 22nd ks. Aftr th 22nd k, both th injction rat and llhad prssur bgin to dclin (Figur 2) and th bottom hol prssur starts rising, sinc th rsrvoir is alrady filld up and dos not accpt additional atr blo th gradint for gnrating n and substantial fracturs. Evntually, th rinjction opration as stoppd at th nd of 29th k. 4. EVALUATION OF TEST PRESSURE DATA Th prssur data rcordd at th injction and obsrvation lls ar valuatd in ordr to stimat svral rsrvoir proprtis and to apply Hall plot analysis on th injction tst. Initially th llhad prssurs, p tf, ar convrtd to bottom-hol prssurs, p f, according to Eqn.2, so that th Hall intgral in ( p p ) dt form could b valuatd. f 4.1 Calculation of Injction Bottom-Hol Prssurs For calculating th bottom-hol prssur at ach injction rat, th llbor is dividd into 12 imaginary sctions ith qual sction hight of 45 m, xcpt th last sction. Last sction has th hight (or dpth intrval) of 35 m. Th dnsity, tmpratur, frictional prssur losss, and prssur of atr ar calculatd itrativly for th bottom of ach sction. Sinc th injction atr has rathr lo TDS of approximatly 5 ppm, dnsity calculations ar basd on ordinary atr assumption. Watr dnsitis at prvailing tmpraturs, btn 2 C and 2 C, and at prssurs, btn 1 bar and 6 bars, ar dtrmind using th data xtractd from th Stam Tabls in SI Units (199). Th xtractd data is plottd as in Figur 4, for practical us. Mor accurat stimation of dnsity is obtaind using th folloing quation, hich is fittd by linar rgrssion to th plottd data in Figur 4 (Altinay, 22). 5 4 3 2 ρ = C 1 p + C2 p + C3 p + C4 p + C5 p + C6... (8) Dnsity of Liquid Watr, kg/dm 3 Dnsity of Liquid Watr, kg/dm 3 1.1.999.997.995.993.991.989.987.985.983.99.98.97.96.95.94.93.92.91.9.89.88.87.86 2 o C 25 o C 3 o C 35 o C 4 o C 45 o C 5 o C 6 o C 5 1 15 2 25 3 35 4 45 5 55 6 Prssur, bars To Phas Rgion 7 C 8 C 9 C 1 C 125 C 15 C 175 C 2 C 5 1 15 2 25 3 35 4 45 5 55 6 Prssur, bars Figur 4 : Dnsity of liquid atr plottd as a function prssur and various tmpraturs, using th data from Stam Tabls in SI Units (199). In Eqn.8, th dnsity (ρ) at a particular tmpratur is in kg/dm 3 and is dpndnt on prssur (p) in bars. Constants of A to F ar th rgrssion cofficints, tabulatd in Tabl 1, and ar to b multiplid by th numbr in parnthsis just blo th titl of that particular constant at th top of th its prtinnt column. Itrativly calculatd atr dnsity in ach sction is usd to stimat both th frictional prssur losss and th bottom prssur for th particular sction. Tabl 1 : Dnsity of liquid atr plottd as a function prssur and various tmpraturs, using th data from Stam Tabls in SI Units (199). T ( C) C1 ( 1 12 ) C2 ( 1 9 ) C3 ( 1 8 ) C4 ( 1 6 ) C5 ( 1 5 ) C6 ( 1 1 ) 2-6.852 1.273-5.431 1.1412 3.8972 9.9817 25-7.8467 1.,1825-6.3649 1.4768 3.99 9.976 3 6.8655.97455 4.9347-1.111 5.6449 9.9554 35-3.6339.57126-3.246.76921 3.6726 9.9398 4 3.852-5.725 3.336-7.8416 11.992 9.925 45-1.2932 1.879-9.425 1.9218 3.993 9.918 5-3.6339.57126-3.246.76921 3.6726 9.8798 6-9.932 1.4686-7.1927 1.284 3.7427 9.8317 7-9.932 1.4686-7.1927 1.284 3.7427 9.7777 8-1.346 1.8938-9.1132 1.5874 3.8424 9.7176 9-1.922 1.8514-1.831 2.5111 2.7938 9.6528 1-1.5633 2.8329-18.674 5.4317-1.9372 9.5859 125 2.7342-4.6916 29.343-8.664 14.246 9.3865 15-1.7798 2.9962-19.35 5.5479-1.329 9.175 175 5.6712-9.7354 62.738-18.782 32.258 8.952 2-13.597 25.831-188.84 66.135-12.99 8.765 4
As sn in Figur 4, th dnsity of injctd atr is a function of its prssur and tmpratur. It is a knon fact that th tmpratur of injction atr varis along th ll dpth, as a rsult of thrmal nrgy xchang btn th arth and atr in th ll. Thus, th folloing quation proposd by Ramy (1962) is usd to calculat an avrag atr tmpratur for ach imaginary sction in th ll. Ti z A ( z t) a z + b a A+ [ T ( t) + a A b].... (9) = hr T i is th tmpratur of injction atr in C at dpth z and tim t, T is th llhad tmpratur of injction atr in C, t is th tim sinc th start of injction, a is th local gothrmal gradint in C/m, A is th tim function, b is th gothrmal surfac tmpratur in C, and z is th dpth from th top of ach sction in mtrs. Hr th tim function, A, is dfind as (Ramy, 1962), [ λ + r U f () t ] qm c p pi A =... (1) 2 π rpi U λ hr q m is th injction mass flo rat in kg/d, c p is th spcific hat of atr at constant prssur in J/kg C, λ is th thrmal conductivity of arth in W/m C, and r pi is th innr radius of injction pip in mtrs. Th dimnsionlss transint hat transfr function for arth, f (t), is stimatd using th folloing xprssion. r () po f t = Ln. 29... (11) 2 α t hr r po is th outr radius of injction pip in mtrs, α is th thrmal diffusion cofficint of arth in m 2 /d, and t is th tim lapsd sinc th start of injction. Th ovrall hat transfr cofficint, U, in W/m 2 C pr unit dpth in Eqn.11 is dtrmind from 1 1 1 Ln ( rpo / rpi ) Ln ( r co / rci ) = + +... (12) U 2 π h rpi λ p λc hr r pi and r po ar th innr and outr radii of injction pip, and similarly r ci and r co ar th innr and outr radii of cmnt, rspctivly. Thrmal conductivity cofficints for th injction pip and cmnt ar dsignatd as λ p and λ c and ar slctd as 43.3 and.865 W/m C, rspctivly. Sinc th silicat prcipitation in surfac flo lins as significant, th silicat scaling on th injction pip alls is thought to b ngligibl and, thus, omittd in th calculation of ovrall hat transfr cofficint, U. Th thrmal convction (film) cofficint of atr, h, is stimatd in W/m 2 C for ach imaginary sction in th ll using th Dittus-Boultr quation (Çngl, 1998). 2 r n pi h.8 Nu =.23 R Pr =... (13) λ hr th Nusslt numbr, Nu, is calculatd using th Prandtl numbr, Pr, of 4.87, and th Rynolds numbr, R, hich is itrativly calculatd for ach flo rat and atr dnsity in th particular ll sction. Not that th por n of th Prandtl numbr is.4 for hating and is.3 for cooling of floing atr. Obtaind Nu valus ar usd to stimat h for th λ =.618 W/m C of atr. As sn in Figur 5, th point valus of h dcras slightly, as atr cools don by loosing thrmal nrgy to th coolr surroundings until th dpth of 135 mtrs, and incrass non-linarly as atr hats up by gaining thrmal nrgy from th arth, blo that dpth. Figur 5 also implis that th highr th injction rat th gratr th thrmal film convction cofficint of atr, h, ithout a rmarkabl chang in its dpth dpndnt profil. Dpth, m 5 1 15 2 25 3 35 4 45 5 q = 75 tons/h q = 8 tons/h q = 85 tons/h q = 9 tons/h 45 46 47 48 49 5 51 52 53 54 Thrmal Convction (Film) Cofficint, kw/m 2 o C Figur 5 : Variation of thrmal convction cofficint, h, of injction atr ith ll dpth. For th minimum and maximum injction rats R is found to b varying btn 16.4 1 4 and 2.5 1 4. Sinc th Rynolds numbr, R, is a function of atr dnsity, hich varis ith tmpratur and prssur, Eqn.2 and Equations 8 through 13 ar solvd conscutivly by itrating on dnsity, tmpratur and prssur. Itrations ar continud until th calculatd tmpratur, dnsity, and prssur of injctd atr at th bottom of ach imaginary sction did not chang byond th slctd margins of rror. Th chang in atr dnsity, ρ, along th ll for various injction rats (q) and llhad prssurs (p tf ) is shon in Figur 6. As xpctd, for th sam llhad prssur th highr th injction rat th highr th dnsity of injctd atr. Similarly, for th sam injction rat th gratr th llhad prssur th highr th injctd atr dnsity. It sms that th llhad prssur has mor ffct than th injction rat on th injctd atr dnsity, particularly in th lor or dpr parts of th ll. Dspit th continuous incras in prssur in squntial ll sctions, atr dnsity incrass to th dpth of about 35 m and, thn, dcrass to th dpth of 53 m. Such dnsity bhavior implis that, blo th dpth of about 35 mtrs, th volumtric xpansion of atr du to its thrmal nrgy gain from arth is gratr than th volumtric comprssion of th sam atr by th fluid had abov. Dpth, m 5 1 15 2 25 3 35 4 45 q = 75 tons/h ; ptf = 7 bars q = 75 tons/h ; ptf = 11 bars q = 85 tons/h ; ptf = 11 bars q = 85 tons/h ; ptf = 13 bars 5 55 998.8 999. 999.2 999.4 999.6 999.8 1. Dnsity of Injctd Watr, kg/m 3 Figur 6 : Changs in atr dnsity ith ll dpth for various injction rats and llhad prssurs. 5
Onc th injction atr dnsity is dtrmind in a sction, th had of atr for that sction is calculatd and addd on to th sction top prssur to obtain th sction bottom prssur. Th sam calculation stps ar rpatd for ach sction, until th bottom-hol injction prssur is obtaind. Th gravitational acclration of arth, g, is dtrmind to b 9.792 m/s 2 (CRC, 1991) for Kizildr fild, hich is about 18 m abov sa lvl at th latitud of 37 53 and th longitud of 28 23. Thus th ratio of g/g c in Eqn.2 is dtrmind to b.9983. Σ[(p f -p ) t], bar.d 12 1 8 6 4 m H1 =.22842 bar.d/m 3 m H2 =.43224 bar.d/m 3 Upon th dtrmination of variation of atr dnsity ith dpth th frictional prssur loss, p f, in ach sction is stimatd using modifid Darcy-Wisbach formula, p f f L 5 rpi 2 qm g c 7 = 1.9167 1... (14) ρ in hr f is th Moody friction factor obtaind itrativly from Colbrook quation, L is th sction lngth in mtrs, ρ is th dnsity of atr in kg/m 3, g c is th convrsion factor of 9.86 kg m m/s 2 kg f. Eqn.14 is modifid in th sns that it is drivd for mass flo rat, q m, in tons/h and its cofficint is spcific for th Kizildr fild. Th injction atr tmpratur at th llhad, although varis btn 2 C and 42 C during th tst, is assumd to b constant at an avrag valu of 35 C. It is found that such variation in modrat injction atr tmpratur has a ngligibl ffct on th calculatd bottom-hol injction prssurs, particularly at shallo dpths. For instanc, at th dpth of 53 mtrs, th prssur of atr at 2 C is only.3 bars gratr than that of at 4 C. Should th rror in prssur masurmnts, committd by using th convntional gaugs at th tim of injction in 1976, is considrd, it ould b concivabl that lss than.2 bar diffrnc in bottom hol prssur calculations is vry minor and, for all practical purposs, dos not affct th rsults. For gratr injction dpths, th variations in injction atr tmpratur should b takn into account in th bottom-hol injction prssur calculations. 4.2 Estimation of Avrag Rsrvoir Prssur Avrag rsrvoir prssur around th injction ll prior to th injction opration is stimatd to b approximatly 54.5 bars at 53-mtr dpth. Th stimatd prssur is calculatd basd on th rsrvoir prssur of 46.2 bars, obsrvd at th dpth of 43 mtrs bfor injction. Th dnsity of rsrvoir atr usd in calculations is stimatd as 872.7 kg/m 3 for th TDS of 5 ppm and th stam fraction of 11 prcnt at surfac prssur and tmpratur (Ugur, 1996). As sn in Figur 3, th bottom-hol prssur at th KD-1 obsrvation ll had bn fluctuating around 54 bars, arly in th opration. This obsrvation ll prssur, rcordd bfor th ffct of injctd atr as flt, confirms th avrag rsrvoir prssur stimatd at th injction ll. 5. HALL PLOT ANALYSIS OF REINJECTION TEST Th Hall plot analysis is applid using Eqn.4 to valuat th rinjction tst conductd in ll KD-1A. Bottom-hol prssurs that ar convrtd from llhad prssurs ar mployd in th analysis. As shon in Figur 7, th valus of Hall intgral in bar day ar plottd against th volum of cumulativ atr injction in 1 m 3. Th Hall plot xhibits to straight lins, of hich th scond lin dviats from th first lin aftr th 12th k of injction. 6 2 5 1 15 2 25 3 35 Cumulativ Watr Injction, km 3 Figur 7 : Hall plot for th Wll KD-1A rinjction tst. Th slops of th first and scond straight lins, indicatd by solid circls, ar dtrmind to b m H1 =.22842 and m H2 =.43224, both ar in bar day, rspctivly. Th slop of th scond lin bing almost tic that of th first lin may b intrprtd as th incras in skin valu, from s 1 to s 2, aftr th 13th k of injction, hn Eqn.6 is considrd. Th othr intrprtation may b th dcras in prmability, from k 1 to k 2, if Eqn.7 is considrd. Eithr occurrnc is possibl to tak plac in-situ hn th solids prcipitat as th mixing zon of th injctd and rsrvoir atrs mov aay from th llbor. Hovr, th rat, prssur, and tmpratur obsrvations at both lls do not indicat such formation damag, until th nd of th 13th k of injction, as xplaind in sction 3 abov. 5.1 Dtrmination of Rsrvoir Proprtis In ordr to hav an ida about th transmissibility, kh/µ, btn th to lls, a simpl intrfrnc tst analysis is prformd using th injction rats and obsrvation ll prssurs rcordd until th injctd atr arrivs at th obsrvation ll KD-1 on th svnth k. Dcras in prssurs du to th cooling ffct of injction ithin that priod is ignord and th typ-curv matching tchniqu is applid in th intrfrnc tst analysis (Earloughr, 1977). Th transmissibility, kh/µ, btn lls KD-1A and KD-1 is dtrmind as 528.3 md m/mpa s. A skin factor of s 1 = 5.85 is calculatd by substituting th stimatd transmissibility in Eqn 5, for first straight lin bhavior in Figur 7. Such a lo skin factor is rgardd as th confirmation of a fractur ntork xists around th obsrvation ll. Not that a fractur ntork as dtctd by a rmarkabl mud loss hn th bottom part (535-54 mtr intrval) of KD-1 as drilld. Th fractur ntork is prsumd to xtnd to th injction ll, bcaus th apparnt llbor radius, r a, calculatd by Eqn.15 for th injction ll is found to b 39 mtrs and sms to support this prsumption. ra s r =... (15) Satman (1988) also hypothsizs th xistnc of a fractur ntork of 12 fracturs around th injction ll, basd on th rsults of hat-flo modl calculations. Consquntly, it is dcidd that a fractur ntork is xtnding from ll KD-1A to KD-1 ithin th dpth intrval of 53-54 m and is acting as an fficint flo conduit. Th skin factor, s 2, for th scond straight lin bhavior in Figur 7 is calculatd using Eqn.6 and found as 5.35. Sinc both skin factors ar not vry diffrnt from ach
othr, it can b statd that th rinjction opration has not causd a significant minral prcipitation inducd plugging of fracturs in th formation. Th lattr skin factor is usd in Eqn.15 to valuat th chang in th apparnt llbor radius and found as 24 mtrs, implying a minor plugging (if thr is any) in th formation. Typ-curv matching paramtrs of th intrfrnc tst analysis ar furthr usd to stimat th rsrvoir storativity as φhc t =.958 m bar 1. Sinc th ffctiv formation thicknss (h), through hich th injctd atr flos, is unknon, nithr th ffctiv prmability (k ) nor th porosity (φ) ithin th fracturd systm can b stimatd. 5.2 Analysis of Rsrvoir Fill-Up Though th combind rsults of Hall plot and intrfrnc tst analyss indicat a minor damag in rsrvoir, th rat, prssur, and tmpratur rsponss at both lls do not support such thsis. It is clar from Figur 3 that th injctd atr brakthrough at th obsrvation ll occurs aftr th injction of 85,565 m 3 of atr as of th 7th k. Thn, cooling and subsqunt prssur dclin taks plac around th obsrvation ll until th 12th k, during hich an additional 82,116 m 3 of atr is injctd. If thr r a significant minral prcipitation inducd plugging in th rsrvoir, injctd atr brakthrough and subsqunt cooling ould not hav occurrd in thos 12 ks. Evn if significant plugging had occurrd, th injction llhad prssur ould b xpctd to ris slightly, instad of staying constant at 8 bars, as sn in Figur 2. Thus, th prssur, rat, and tmpratur bhavior obsrvd in both lls is attributd to th filling up of th rsrvoir btn th 7th and 12th ks. Existnc of fr carbon dioxid (CO 2 ) ith atr in th uppr rsrvoir as dtctd hn th lls compltd in th uppr rsrvoir producd fr CO 2 gas. Thrfor, until th nd of 12th k, fr CO 2 gas had to b somhat comprssd and som of it had to b dissolvd in injctd atr, as th liquid-vapor systm trid to rach quilibrium. In th man tim, continuous hating up of th injctd atr must hav affctd th progrss of CO 2 dissolution or libration in th cours to th obsrvation ll. As th rsrvoir is filld up th injction rat dcrass but th injction prssur stays constant, as th cooling coms to an nd and prssur starts rising around th obsrvation ll. As markd by th solid arros in Figur 3, btn th 12th and 15th ks th prssur at both lls ris sharply but th tmpratur around th obsrvation ll incrass ith oscillations. Such rsrvoir rspons is attributd to th rsrvoir fill up so that th injctd additional atr is no mor floing ith as toards th obsrvation ll but forcing th fr CO 2 to dissolv in atr. In othr ords, th injction of 28,745 m 3 of atr, btn 12th and 15th ks, starts raising th fr atr lvl (or th liquid atr saturation) in th rsrvoir as th fr CO 2 gas is forcd to b disprsd in atr. At this point a comprssibility calculation is prformd to valuat hthr th sharp incras in prssur as th rflction of th comprssion of fr CO 2. Th changs in volum and prssur btn th solid arros in Figur 3 ar usd and th comprssibility of fr CO 2 is calculatd to b c cd =2.48 1 2 bar 1 at approximatly 195 C. Satman and Ugur (22) dclard c cd =2.49 1 2 bar 1 at 2 C. Such rsult is considrd as a good vidnc for th fill up scnario hypothsizd in this study, yt a matrial balanc calculation is attmptd for furthr support of this scnario. 5.3 Matrial Balanc Calculations If thr r fr CO 2 phas ithin th fractur ntork, bfor its complt disprsion in atr prior to th 16th k, thn, stimating th saturations of both atr and CO 2 phass at th tim of brakthrough should b possibl. Th injctd volums of atr during th 3 squntial injction stags of 1st to 7th k, 7th to 12th k, and 12th to 15th k ar usd in a matrial balanc calculation for this purpos. In th third stag, btn th 12th to 15th ks, th volum of injctd atr, V 12-15 = 28,745 m 3, should b qual to th volum of comprssd and disprsd CO 2 in atr. In th scond stag, btn th 7th to 12th ks, th volum of injctd atr, V 7-12 = 82,116 m 3, should b qual to th volum of xpandd CO 2 du to cooling ffct of injctd atr. Th sum of ths volums should yild th volum of fr CO 2 in th rsrvoir, V cd = 11,861 m 3, at th tim of brakthrough on th 7th k. Th volum of atr injctd until th brakthrough, V, is 85.565 m 3. Thus, at th tim of brakthrough, th saturations of atr and fr CO 2 phass ar calculatd from, S Scd V V + Vcd =... (16-a) Vcd V + Vcd =... (16-b) and atr and CO 2 saturations around th obsrvation ll ar obtaind as S =.436 and S cd =.564, rspctivly. Using ths saturations th total comprssibility of th fluid systm, c t, is stimatd from th xprssion of c t S c + Scd ccd + c f =... (17) hr th formation comprssibility, c f, is ignord sinc its magnitud is insignificant compard to that of th atr and fr CO 2 comprssibility. Th comprssibility of Kizildr rsrvoir atr is dtrmind to b c =2.648 1 2 bar 1 at th brakthrough tmpratur of 197 C (Satman and Ugur, 22). Not that th Kizildr rsrvoir atrs ith a TDS of 5 ppm contain only about 1.5 prcnt dissolvd CO 2. As a rsult th total systm comprssibility is stimatd as c t = 1.681 1 2 bar 1 at th tim of brakthrough. Substituting th total comprssibility in th storativity, φhc t, of.958 m bar 1, obtaind by th intrfrnc tst analysis, yilds φh = 5.7 m. Th product of φh is for th fractur ntork, through hich th injctd atr and CO 2 gas flos. Sinc th distanc, r bt, travld by th injctd atr until brakthrough, for a radial systm, can b xprssd as rbt = V B... (18) π φ h Solving Eqn.18 rsults in r bt = 72 mtrs, hich is only 4 mtrs diffrnt than th surfac distanc btn th lls KD-1A and KD-1. Thus, th rsults obtaind by matrial balanc application sm to b accptabl and confirming th rsrvoir fill up, considring th lack of information on th actual distanc and th gomtry of fractur ntork btn th to lls at th dpth of 53 to 54 mtrs. Consquntly, th slop chang in Hall plot hr indicats ssntially th rsistanc to flo causd by th rsrvoir fill up. Evn if thr r any formation damag, it as minor and could not b dtctd from Hall plot in this cas. 7
5.4 Fractur Enhancmnt As as discussd prviously in Sction 3, th start of a short-trm incras in injction rat and a rapid but finit incras in injction prssur aftr th 15th k is thought to rflct ithr an nlargmnt of xisting fractur ntork or a small scal hydraulic fracturing in th alrady filld up formation (Figur 2). Th rapid incras and subsqunt rapid drop in obsrvation ll prssur aftr th 16th k, in Figur 3, supports such intrprtation. Normally th ffct of such fractur nhancmnt is xpctd to b sn as a dcras in slop in th Hall plot, starting from th 21st k or aftr th cumulativ atr injction of 25, m 3. If Figur 7 is carfully inspctd, although vry slight, a dcras in slop may b sn. Yt such claim ould b spculativ, if th comprssibility of atr ith high CO 2 contnt, th assumption of constant rsrvoir prssur in Hall intgral, and th rror in prssur masurmnts ar takn into account. Thus, it can b statd that th limitd but rapid incras in injction rat, prior to th rapid jump in obsrvation ll prssur, rflcts a minor nhancmnt or fracturing in th fractur systm around th obsrvation ll. Th fractur nhancmnt must b rathr minor, so that it did not caus a distinct chang in th Hall plot slop. 6. CONCLUSIONS Hall plot analysis is applid to a rinjction tst conductd in ll KD-1A in Kizildr gothrmal fild to invstigat th possibl changs in rsrvoir proprtis. Th chang in slops of Hall-plot straight lins alon implis damag in th rsrvoir. Hovr, incorporating th prssurs and tmpraturs, monitord at th obsrvation ll KD-1, in intrprtation indicats rsrvoir fill up ith th injctd atr. An intrfrnc tst analysis, prformd by using th injction rats and obsrvation ll prssurs, provids mans to quantify th transmissibility and storativity of rsrvoir. Th rsults of matrial balanc calculations, hn combind ith that of th intrfrnc tst and Hall plot analyss, rvals that th rsrvoir fill up causd th slop chang in th Hall plot and maskd th variation, if thr r any, in rsrvoir proprtis. Intrprtations also confirm th prviously dtctd prsnc of fr carbon dioxid gas phas ithin th fractur ntork in rsrvoir. 1. Hall plot analysis can b usd to valuat th injction prformanc, rsrvoir proprtis, and rsrvoir rspons in long trm atr injction tsts applid in gothrmal lls, ith th rquirmnt of at last rsrvoir transmissibility and storativity obtaind from anothr typ of tst, such as an intrfrnc tst. 2. Rsrvoir fill up, hich should occur in a long trm injction tst, may mask th possibl variations in rsrvoir rock proprtis and, thus, may lad to mislading intrprtations if th Hall plot analysis rsults ar usd alon. 3. Hall plot and intrfrnc tst analyss togthr may hlp dtcting th fractur ntork, if ssntially all fluids in th systm saturat and flo through th fractur systm. 4. A minor fractur nhancmnt cannot b dtctd by Hall plot, unlss th fractur nhancmnt causs a distinct dcras in th slop of Hall plot. 5. In th convrsion of injction llhad prssurs into th bottom-hol prssurs, th variations in injction atr dnsity ought to b dtrmind by taking th salinity and th incrasing tmpratur and fluid had into account. Particularly in lls dpr than 6 mtrs, th accurat stimation of injction atr dnsity can mak significant diffrnc in calculatd bottom-hol prssurs. NOMENCLATURE A : tim function, m a : local gothrmal gradint, C/m B : formation volum factor of atr, m 3 /sm 3 b : gothrmal surfac tmpratur, C c cd : comprssibility of carbon dioxid, bar 1 c f : comprssibility of formation, bar 1 c p : spcific hat of atr at constant prssur, J/kg C c t : total comprssibility, bar 1 c : comprssibility of rsrvoir atr, bar 1 f : Moody friction factor, dimnsionlss f (t) : arth transint hat-transfr function, dimnsionlss h : rsrvoir thicknss, m h : thrmal convction cofficint of atr, W/m 2 C L : flo distanc, m m H : straight lin slop in Hall plot, bar d/m 3 Nu : Nusslt numbr, dimnsionlss Pr : Prandtl numbr, dimnsionlss p obs : obsrvation ll bottom-hol prssur, bar p tf : injction llhad prssur, bar p f : bottom-hol injction prssur, bar p : avrag rsrvoir prssur, bar q : volumtric injction rat of atr, m 3 /d q m : mass injction rat of atr, tons/h R : Rynolds numbr, dimnsionlss r : xtrnal radius of th injctd atr front, m r ci : innr radius of cmnt, m r co : outr radius of cmnt, m r pi : innr radius of injction pip, m r po : outr radius of injction pip, m r : llbor radius, m r a : apparnt llbor radius, m S cd : carbon dioxid gas saturation, fraction S : rsrvoir atr saturation, fraction s : skin factor, dimnsionlss TDS : total dissolvd solids, ppm T i : tmpratur of injction atr at any z and t, C T : llhad tmpratur of injction atr, C t : tim, hours (or days) U : ovrall hat transfr cofficint, W/m 2 C/m V cd : volum of carbon dioxid at brakthrough, m 3 V : volum of rsrvoir atr at brakthrough, m 3 W : cumulativ atr injction, m 3 z : dpth, m Grk Lttrs α : thrmal diffusion cofficint of arth, m 2 /d p f : frictional prssur loss, bar λ c : thrmal conductivity cofficint of cmnt, W/m C λ : thrmal conductivity of arth, W/m C λ p : thrmal conductivity cofficint of pip, W/m C µ : viscosity of atr at injction tmpratur, mpa s µ r : viscosity of atr at rsrvoir tmpratur, mpa s ρ : dnsity of injctd atr, kg/dm 3 ρ r : dnsity of rsrvoir atr, kg/dm 3 8
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