SENSITIVITY OF A REACTIVE-TRACER BASED ESTIMATE OF THERMAL BREAKTHROUGH IN AN EGS TO PROPERTIES OF THE RESERVOIR AND TRACER

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1 PROCEEDINGS, Thirty-Seventh Workshop on Geotherml Reservoir Engineering Stnford University, Stnford, Cliforni, Jnury 3 - Februry 1, 212 SGP-TR-194 SENSITIVITY OF A REACTIVE-TRACER BASED ESTIMATE OF THERMAL BREAKTHROUGH IN AN EGS TO PROPERTIES OF THE RESERVOIR AND TRACER Mitchell. A. Plummer, Crl D. Plmer, Lurence C. Hull, Erl D. Mttson Orgniztion Idho Ntionl Lbortory P.O. Box 1625, MS228 Idho Flls, ID, 83415, USA e-mil: Mitchell.Plummer@inl.gov ABSTRACT Rective trcers provide potentil method for mesuring therml drwdown in geotherml system before significnt cooling occurs t the production well. Becuse rection rtes generlly hve strong temperture dependence, the conversion of rective trcer crried through reservoir is essentilly n indictor of reservoir temperture between the injection well nd the production well (Tester et l., 1987; Chrysikopoulos, 1993). With repeted tests, the rte of cooling my be estimted, which my provide criticl plnning dt. While severl recent studies hve suggested tht the sensitivity of this pproch to reservoir cooling is low, those nlyses were bsed lrgely on cooling behvior of isolted frctures. In this study, we exmine the sensitivity of successive rective trcer tests to reservoir cooling under vriety of conditions, nd illustrte how tht sensitivity reltes to the kinetic prmeters of rnge of compounds suitble for this ppliction. Notbly, while the mximum chnge in the reltive concentrtion between successive rective trcer tests in system cooling s n isolted frcture is pproximtely 35%, 1% difference could be mesured in system where cooling proceeds s it would for closely spced frctures, lthough the erly time sensitivity is ctully greter for the former system. To illustrte how this pproch my be used in n ctul system, we present results of our field test of two rective trcers t U.S. Geotherml Inc. s Rft River, Idho site. INTRODUCTION Geotherml reservoir mngement often requires injection of produced fluids to prevent them from entering shllow quifers nd surfce wters, to help extrct het from the subsurfce, nd to mintin pressures within the reservoir (e.g., Rose et l., 21). Knowledge of the time to therml brekthrough ssocited with these injected fluids is required for optiml mngement of the reservoir. While conservtive, rtificil trcers cn provide vluble informtion bout reservoir residence times nd flow pths (Behrens et l., 29), they provide little direct informtion bout therml brekthrough. It hs been proposed tht rective trcers tht degrde t rtes tht depend on temperture cn be used to estimte reservoir tempertures between the injection well nd the production well (Tester et l., 1987; Chrysikopoulos, 1993). With repeted tests, the rte of migrtion of the therml front cn be determined, nd the time to therml brekthrough clculted. While the bsic theory behind the concept of therml trcers hs been understood for some time, ective ppliction of the method hs yet to be demonstrted. Recently, Behrens et l. (29) indicted tht rective trcer brekthrough curves re not sensitive to chnges in the therml front nd therefore the suggested method lcks the sensitivity necessry to provide useful mesure of therml drwdown. In this pper, we explore the sensitivity of rectivetrcer brekthrough curves in EGS to reservoir nd trcer properties nd discuss lterntive trcer pproches tht could potentilly enhnce our bility to estimte therml brekthrough. THERMALLY REACTIVE TRACERS Rective trcers cn provide informtion bout the therml evolution of such system becuse chemicl rection rtes re temperture dependent. Rection rtes generlly increse with temperture nd the mount of conversion observed during trnsport between two wells should decrese s the reservoir cools. A second trcer test conducted some time fter n intil test should thus hve higher brekthrough curve concentrtions thn for the first test. Comprison of trcer tests conducted t different times cn provide informtion bout the corresponding chnge in reservoir, nd thereby id in predicting the working life of the reservoir.

2 To illustrte how rective trcers could be used to monitor the evolution of temperture in the system described bove, we consider the reltive rection rte long flow pth where the rection rte cn be described by pseudo first-order eqution of the form dcbs() t dt k( T) C ( t) Eq.1 bs where C bs is ctul concentrtion nd k(t) is the temperture-dependent rte coicient given by the Arrhenius eqution, E ( ) exp k T A RT (, f ) Eq.2 where T is the temperture in kelvins, R is the gs constnt, E is the ctivtion energy, is the operting time of the reservoir, nd f is the frction of the flow pth trveled. To illustrte the fundmentl sensitivity of rective trcers to the therml evolution of reservoir, we first consider trnsport under the simplified cse of piston-flow conditions, where concentrtion is ffected only by rection. For piston-flow trnsport of rective trcer undergoing first-order decy, the reltive trcer concentrtion, C = C bs /C with time, or equivlently, distnce, cn be obtined by substituting Eq. 2 into Eq. 1 nd integrting to yield C( t) exp A Eq.3 where, the therml rection time (Robinson nd Tester, 199), is defined by (, f ) exp E L RT (, f ) v f df Eq.4 nd L is the flowpth length (Tester et l., 1987). The sensitivity of the reltive concentrtion to men reservoir temperture cn be described by its derivtive with respect to n ective temperture of the frcture pth, T, where the ective temperture is the temperture needed to mtch the rective trcer concentrtion t the extrction well, ssuming constnt temperture long the flow pth: T E (, E ) Eq.5 R ln (,1) The sensitivity of the reltive concentrtion to T is function of tht prmeter, the kinetic prmeters A nd E, nd the residence time in the system, L/v: Eq.6 dc ( A, E, T ) dt L L E E A E exp A exp v v RT (, E ) RT (, E ) 2 RT (, E ) To illustrte how this sensitivity vries with the kinetic prmeters nd how it reltes to kinetic prmeters of compounds suggested for this ppliction, we clculted the sensitivity for trcer test tht INL conducted t U.S. Geotherml Inc. s geotherml reservoir in Rft River, Idho for rnge of A nd E vlues. The reservoir temperture t Rft River is pproximtely 14 C nd the trvel time between wells is pproximtely 2 dys. For rnge of vlues of A nd E encompssing esters nd mides tht Robinson nd Tester suggested s trcers, the results (Figure 1) demonstrte tht the mximum sensitivity is slightly greter thn 1% per degree chnge in T nd tht the mximum sensitivity is constrined to nrrow bnd running digonlly cross the figure. While the sensitivity plot identifies desirble vlues of A nd E for prticulr reservoir, the number of compounds suitble s rective trcers is limited, nd ech choice of E is explicitly tied to corresponding pre-exponentil fctor, A. In ddition, for clss of trcers with different substituents, E nd A re correlted becuse of the enthlpy-entropy compenstion ect (e.g., Lsg, 1998; Liu nd Guo, 21). The correltion of A with E for prticulr clss of compounds tends to be similr to the slope of the high sensitivity bnd illustrted in Figure 1. We illustrte this by showing regression lines for the ester nd mide hydrolysis dt of Robinson nd Tester (199) on the sensitivity plot for our hypotheticl reservoir with ph nd trvel time similr to tht t Rft River. Interestingly, the mide compounds, nd ssocited regression line, re locted precisely within the reltively nrrow bnd of mximum sensitivity for the system. While this is lrgely fortuitous circumstnce for ppliction of this pproch t Rft River, the clculted sensitivity does not vry strongly with temperture, ph, nd flow pth residence time nd those sme compounds my be s well suited to mny other systems. The slope of the high sensitivity bnd is primrily function of the reservoir temperture, decresing with incresing temperture. In contrst, chnging the residence time or ph ectively shifts the high sensitivity bnd upwrd or downwrd reltive to the entropy compenstion lines, while mintining the sme slope.

3 -1 s -1 ] ln(a )[L mol Esters -2.5 Amides Activtion Energy [kj mol -1 ] Figure 1. Log chnge in reltive concentrtion per degree chnge in ective temperture of flowpth, where the initil reservoir temperture is 14 C nd the residence time is 2 dys. Blue nd red lines illustrte the entropy-enthlpy compenstion ect for the second-order hydrolysis rections of some ester (blue symbols) nd mide (red symbols) trcers. The sensitivity given by eqution 6 gives insight into the preferred vlues of A nd E given prticulr reservoir temperture nd flow pth residence time, demonstrting tht prticulr reservoir hs good sensitivity only in reltively nrrow rnge tht is constrined to prticulr reltionship between A nd E. To trnslte this sensitivity to the ctul chnge in the reltive concentrtion tht might be expected s flow pth cools, we need n expression describing frcture cooling behvior, in order to estimte how the ective temperture of flow pth chnges over time. To illustrte the temperture chnges tht re likely to occur, nd the corresponding chnge in reltive trcer concentrtion s cooling progresses, we consider cooling of two types of systems, (1) cooling of single frcture without interference from surrounding frctures nd (2) cooling in system of prllel frctures where cooling fronts perpendiculr to the frcture fces overlp nd cuse more rpid cooling thn in the former cse. Previous discussions of therml trcer sensitivity hve considered only the therml evolution of flowpth through single isolted frcture, nd we begin with tht cse, where the reltive temperture s function of operting time, t op, nd distnce, x, is given by r x f () x erf f cp_ f bv rtop x/ v Eq.7 [Crslw nd Jeger 1959, Section 15.3, Cse III] where r = rock therml conductivity x = flowpth distnce trveled b = frcture perture f = crrier fluid density c p_f = fluid specific het v = velocity in the frcture r = rock therml diffusivity t op = operting time Following initition of pumping, therml drwdown in the frcture first occurs t the injection side of the frcture nd is not felt t the, production well until significnt portion of the frcture hs cooled (Figure 1). During this period, there is little or no discernible temperture chnge t the production well, so system opertion feedbck provides little or no informtion bout the therml evolution of the reservoir. Methods for mesuring cooling in the reservoir during this period, such s rective trcer tests, could provide dt criticl to long-term system opertion plnning. Tking 1% of the difference between the injection nd initil reservoir temperture s n rbitrry indiction of mesurble cooling t the production well, this implies, using Eq. 1, tht the operting time of interest for system interrogtion vi rective trcers is tht less thn t crit, where t crit x 1 r x v r bf cp_ f v Eq.8 Using t crit s the reference time for the system, we define dimensionless time, t D = t / t crit. The temperture profiles shown in Figure 2 represent dimensionless operting times rnging from.1 to 1. Temperture is plotted s reltive temperture, i.e., T rel TT T T res res inj Eq.9

Reltive temperture [-].8 injection temperture. Figure 3 lso illustrtes tht the ective temperture is significntly different from the men reservoir temperture, becuse it is dependent on the vlue of E..6.

4 Reltive temperture [-].8 injection temperture. Figure 3 lso illustrtes tht the ective temperture is significntly different from the men reservoir temperture, becuse it is dependent on the vlue of E..6.4 t =.1 tcrit t =.1 tcrit t =.25 tcrit.2 t =.5 tcrit t =.75 tcrit t = 1. tcrit Normlized flowpth distnce [-] Figure 2. Evolution of temperture in single frcture in hypotheticl geotherml system. Curves re given t t D =.1 to 1. The time t which therml brekthrough occurs in the production well is defined s t crit (t D = 1). Exmintion of temperture profiles t different times indictes tht cooling to the injection temperture is restricted to the zone immeditely djcent to the well, nd tht cooling is rpid t first but decreses s t crit is pproched. The shpe of the cooling curve convex, nd pinned to the injection temperture only very ner the injection well suggests tht the ective flow pth temperture does not chnge drmticlly until fter t crit is reched. A plot of ective reltive temperture, T, versus dimensionless time, (Figure 3) illustrtes this ect. The ective temperture chnges most quickly when t D is less thn.1, nd the totl chnge in temperture when t crit is reched is only 26% of the difference between the reservoir temperture nd Becuse the ective temperture depends on E, concentrtion chnges between trcer tests conducted t different times re gretest t the edges of the mximum sensitivity bnd where E is lrgest. For exmple, for difference in those tempertures of 1 C, the chnge in reltive concentrtion between rective trcer tests conducted t t D = nd t D = 1 is s shown in Figure 4. The mximum chnge for given vlue of A is pproximtely 3%-35%, nd occurs in the A - E bnd of gretest sensitivity illustrted in Figure 1. Assuming n initil rective trcer test is conducted t t D =, the increse in trcer concentrtion in successive tests, t t D >, vries with the evolving ective temperture nd the mximum chnge. The chnge in concentrtion is therefore lso function of A nd E. The generl behvior, however, is well illustrted vi isopleths of the chnge in reltive concentrtion s function of dimensionless time nd ctivtion energy, E (Figure 5). For the cooling of n isolted frcture, the chnge proceeds s does the ective temperture, more rpidly t first, before t D =.1, nd then t n essentilly constnt rte. While this ectively provides greter erly time sensitivity, the totl difference from the reltive. -.2 Reltive temperture chnge [-] C & J sol'n - ective T Porous medium sol'n - ective T C & J sol'n - men T Porous medium sol'n - men T Frction of criticl time [-] Figure 3. Temperture chnge, reltive to criticl time, for n isolted frcture (solid line) nd porous medium (dshed line). Red curves show men flowpth temperture; blck curves show ective flowpth temperture, s defined in Eq.5. Figure 4. Chnge in reltive concentrtion C2_mesh between t D = nd t D =1, when cooling proceeds s in n isolted frcture. concentrtion t t D = is lso only frction of the mximum vlue t t D = 1, so tht those concentrtion chnges might be hrd to mesure given the uncertinty ssocited with lbortory nlysis nd the reproducibility of the trcer test t different times.

Dimensionless time [-] Dimensionless time [-] As mentioned previously, discussions of the sensitivity of rective trcers to the therml evolution of reservoir hve been limited to cooling of isolted

5 Dimensionless time [-] Dimensionless time [-] As mentioned previously, discussions of the sensitivity of rective trcers to the therml evolution of reservoir hve been limited to cooling of isolted frctures, for which cooling occurs only extremely slowly. Figure 6 illustrtes how t crit, in yers, vries with frcture perture nd flow velocity. For ll frctures with perture less thn one mm nd residence time greter thn one dy, criticl times re t lest 1 yers. Becuse those re the expected conditions for nturl geotherml systems, nd premture cooling through some flow pths is known to occur, we conclude tht cooling in mny systems behves not s tht of isolted frctures but s collections of frctures tht re spced closely ( xyz ) ( xy z ) A B E [Kj/mol] Figure 5. Chnge in trcer concentrtion, from initil condition t time t D = to time t D =1, reltive to criticl time, for temperture chnge in n (A) isolted frcture nd for (B) highly frctured system with behvior similr to tht of porous medium. Clcultions re shown for plne representing ln(a)=5, s illustrted in the upper figure. Log criticl time [yers] Figure 6. Criticl time, t crit, in yers, for frcture crit.plot of perture nd residence time defined by, respectively, the ordinte nd bsciss, for therml properties typicl of hydrotherml systems. enough tht cooling fronts propgting through the rock overlp nd cuse more rpid cooling thn would occur for isolted frctures. To exmine cooling under these conditions, we consider the cse of infinite sets of prllel frctures of constnt spcing. The solution for the evolution of temperture profiles under those conditions ws described by Gringrten (1975). Applying tht solution nd clculting temperture profiles for hypotheticl frcture with therml properties identicl to those considered for the isolted frcture cse (Figure 7), we see tht cooling progresses quite differently for sets of closely spced frctures thn for isolted frctures. As the frcture spcing decreses, cooling progresses incresingly s shrp front nd the propgtion rte of the cooling front becomes incresingly constnt. In the extreme cse, where the spcing is such tht the time for trnsfer of het from the center of the mtrix to the fluid is equivlent to the time for fluid to flow pst the surfce the working fluid my be ssumed to be in equilibrium with the rock nd the cooling front moves through the frcture essentilly s step function. Under those conditions, the men temperture of the flowpth chnges t constnt rte nd the frcture is ectively cooled to the temperture of the injection fluid t t crit =1. Sets of frctures of intermedite spcing fll between these two extremes. The time to therml brekthrough, for prcticl purposes t crit, is proportionl to the frcture spcing (Figure 8), with endpoints ectively defined by the isolted frcture cooling scenrio nd the cooling of porous medium. While the cooling for the former cse my be hundreds of yers, the cooling front typiclly propgtes through porous medium t bout hlf the velocity of the fluid itself.

Criticl time [yers] Reltive temperture [-].8.6.4 t =.1 tcrit t =.1 tcrit t =.25 tcrit.2 t =.5 tcrit t =.75 tcrit t = 1. tcrit.2.4.6.8 Figure 7.

6 Criticl time [yers] Reltive temperture [-] t =.1 tcrit t =.1 tcrit t =.25 tcrit.2 t =.5 tcrit t =.75 tcrit t = 1. tcrit Figure 7. Evolution of temperture in single frcture in hypotheticl geotherml system. Curves re given t t D =.1 to 1. The time t which therml brekthrough occurs in the production well is defined s t crit (t D = 1). 15 Normlized flowpth distnce [-] 3) indictes tht very lrge chnges in the ective temperture occur during cooling of the flowpth. Under this scenrio, the reltive concentrtion difference between trcer tests conducted t t crit = nd t crit =1 (Figure 9) is 1% for reltively wide rnge of combintions of A nd E. Agin, these chnges occur most rpidly on the high E side of the high sensitivity bnd visible in Figure 1, becuse of the dditionl dependence of ective temperture on tht prmeter. We conclude tht the bsic sensitivity of the rective trcer pproch to monitoring therml evolution of the reservoir is sufficient in some cses for ppliction to systems where cooling behvior is best represented by tht of isolted frctures, but is much better for systems where cooling behvior is better represented by tht of sets of prllel frctures, prticulrly where the cooling front hs extended to pproximtely hlf wy long the flow pth Interfrcture hlf spcing, B [m] Figure 8. Criticl time s function of frcture spcing, for frcture perture of 1 mm, nd fluid velocity of 5E-3 m sec -1. Becuse the men temperture for flowpth in frcture tht is prt of set of closely spced frctures chnges much more thn tht of n isolted frcture, we expect tht the signl-to-noise rtio should be greter when rective trcers re used to monitor tht therml evolution. The ective temperture, however, is much more sensitive to even smll decreses in time t highest tempertures, so the ective temperture does decline to lower vlue thn tht provided by cooling of n isolted frcture until t D =.4 (Figure 3). Therefter, however, the ective temperture declines t n incresing rte nd t t D =.6, it declines to vlue lower thn would occur for n isolted frcture t therml brekthrough (t D =1). With the isolted frcture representing the end member with lowest signl-to-noise, ppliction to porous medium should represent the end member with highest signl-to-noise rtio. Exmintion of ective temperture for this type of cooling (Figure Figure 9. Chnge in reltive concentrtion between t D = nd t D =1, when cooling proceeds s in porous medium. CONCLUSIONS The ppliction of rective trcers s mens of mesuring therml drwdown hs long been proposed, but the sensitivity of the method hs been questioned. Previous discussions of the potentil sensitivity of the method hve, however, focused on mesuring temperture chnges induced by cooling of n isolted frcture. We demonstrte tht the sensitivity of the method is much greter for systems in which cooling is better represented one or more sets of prllel frctures, becuse of the greter cooling tht occurs long the pth before therml drwdown occurs t the production well. Rel frcture systems re likely to hve behvior somewhere between the end members represented by n isolted frcture nd porous medium. The equtions presented herein provide generl mens

7 of evluting the kinetic prmeters suitble for ppliction of rective trcers nd re illustrted using chrcteristics of the Rft River geotherml reservoir. Idho Opertions Office Contrct DE-AC7-5ID REFERENCES Behrens, H., I. Ghergut, M. Suter, T. Lich, 29. Trcer properties nd spiking results (from geotherml reservoirs. Proceeding of the Thirty Fourth Workshop of Geotherml Reservoir Engineering, Stnford, University, Stnford, CA, Februry 9-11, SGP-TR-187. Crslw, H.S., nd J.C. Jeger, Conduction of Het in Solids. Oxford University Press, Oxford, U.K., 51 p. Chrysikopoulos C. V. (1993) Artificil trcers for geotherml reservoir studies. Environmentl Geology, 22, 6-7. Lsg, A.C., Kinetic Theory in the Erth Sciences. Princeton University Press, 811 p. Liu, L., nd Q.-X. Guo, 21. Isokinetic reltionship, isoequilbrium reltionship, nd enthlpy-entropy compenstion. Chem. Rev., 11, Redden, G., M.Stone, K. Wright, E. Mttson, C.D. Plmer, H. Rollins, M. Hrrup, L. Hull, 21. Trcers for Chrcterizing Enhnced Geotherml Systems. Proceeding, Thirty-fifth Workshop on Geotherml Reservoir Engineering. Stnford University, Stnford, CA, Februry 1-3, 21, SGP- TR-188. Robinson, B.A. nd J.W. Tester, 199. Kinetics of lkline hydrolyisi of esters nd mines in neutrllybuffered solution. Interntionl Journl of Chemicl Kinetics, 22: Rose, P.E., W.R. Benoit, P.M. Kilbourn, 21. The Appliction of the polyromtic sulfontes s trcers in geotherml reservoirs. Geothermics, 3: Tester, J.W., B.A. Robinson, nd J. Ferguson, The theory nd selection of chemiclly rective trcers for reservoir therml cpcity production. Proceeding of the Twelfth Workshop of Geotherml Reservoir Engineering, Stnford, University, Stnford, CA, Jnury 2-22, SGP-TR-19. ACKNOWLEDGEMENTS Work supported by the U.S. Deprtment of Energy, Office of Geotherml Technologies under DOE

SENSITIVITY OF A REACTIVE-TRACER BASED ESTIMATE OF THERMAL BREAKTHROUGH IN AN EGS TO PROPERTIES OF THE RESERVOIR AND TRACER

PROCEEDINGS, Thirty-Fifth Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, California, February 1-3, 20 SGP-TR-188 SENSITIVITY OF A REACTIVE-TRACER BASED ESTIMATE OF THERMAL