PREDICTION OF THERMAL BREAKTHROUGH FROM TRACER TESTS. G. Michael Shook

Transcription

1 PROCEEDINGS, Tenty-Fouth Wokshop on Geothemal Resevoi Engineeing Stanfod Univesity, Stanfod, Califonia, Januay 25-27, 1999 SGP-TR-162 PREDICTION OF THERMAL BREAKTHROUGH FROM TRACER TESTS G. Michael Shook Idaho National Engineeing and Envionmental Laboatoy Idaho Falls, ID ABSTRACT A method of pedicting themal beakthough fom tace test analysis is pesented. Because the atio of fluid velocity to themal velocity is a constant, any vaiations in fluid flo ae identically eflected in the themal font, even in heteogeneous media. A vaiable tansfomation is pesented hich facilitates compaison beteen tace effluent concentations and tempeatue histoies. An example demonstates the success of the method in pedicting the onset of themal decline in a heteogeneous poous media. INTRODUCTION Reinjection of spent geothemal fluids has become a standad esevoi management stategy ove the past decade. Reinjection seves not only to maintain esevoi pessue, but also inceases enegy extaction efficiency ove the life of the esouce. Of couse, since the spent fluid is fequently much coole than the fluid in situ, these benefits depend stongly on locating injection in such a fashion that shot-cicuiting ithin the esevoi does not occu. While optimizing an injection stategy to avoid pematue themal beakthough is sometimes iteative, a popely designed tace test can be used to tace flo paths ithin the esevoi, and to pedict the timing of themal beakthough. Vaious eseaches have examined the popagation of a themal font in single-phase, poous medium (e.g., Bodvasson, 1972; Woods and Fitzgeald, 1993). These studies have shon that, due to the themal inetia of the ock volume, the themal font lags behind the fluid font by a constant facto elated to the volumetic heat capacity. In homogeneous media, then, one ould expect a shap tansition fom fa-field tempeatue to injection tempeatue behind the injection font. In heteogeneous media, hoeve, mixing of the injected fluids ith in situ fluid esults in both an ealie and moe gadual decease in poduction tempeatue. Such pematue themal beakthough have been obseved in vaious geothemal esevois, including Beoae (Benoit and Stak, 1993) and The Geyses (Beall et al., 1994). Themal beakthough leads to a host of opeational poblems, including plant output unning belo design, the added cost of makeup ells, and/o modifications to field opeations. Tace testing has become a standad tool fo tacing flo ithin a geothemal esevoi (e.g., Beall et al., 1994; Kocabas et al., 1996; Rose et al., 1997). By injecting a finite slug of tace ith injectate, fluid flo paths and mean esidence times of injectate can be estimated. Knoledge of the flo field povides a means of identifying poblems ith and optimizing injection. Though numeical simulation, one may futhe pedict the onset of cooling in poduced fluids. This pape demonstates that a finite injection (slug) tace test can be eadily analyzed and used to pedict themal beakthough of a tempeatue font in single-phase, heteogeneous poous media. Equations descibing consevation of mass and enegy ae shon and discussed. It is the fom of the combined equations that indicate ho tace test analysis can be used to pedict tempeatue declines. Tansfomations that allo convenient compaison beteen pedicted and simulated tempeatue changes ae shon, and an example of the method is given. CONSERVATION EQUATIONS Fo a single-phase fluid in poous media, the consevation of mass and enegy can be expessed (Woods and Fitzgeald, 1993) as: ρ ϕ + ( ρ u ) = (1) t

2 ( ρc T) p ϕ + ( ρ uc pt) = ( K T) (2) t hee ρ C = ϕρ C + ( 1 ϕ) ρ C p p If e assume incompessible ock and constant heat capacities (both ock and fluid), and also neglect conduction of heat as a second ode effect (Woods and Fitzgeald, 1993), e can combine Eqns. 1 and 2 to obtain an expession that descibes the velocity of the themal font in the poous medium: T t + u ϕ ϕρ C p ϕρ C + (1 p p ϕ) ρ C p T = (3) Fom Eqn. 3, the velocity of the tempeatue font is etaded elative to the fluid velocity by a value that is elated to the volumetic heat capacities: v v T vt = u ϕ = ϕρ C p ϕρ C + (1 p ϕ) ρ C p (4) In fact, the etadation tem in Eqn. 4 is not a constant, as liquid density changes as a function of tempeatue. It has been found, hoeve, that the use of liquid density at the aveage tempeatue ((injected + initial)/2) seves vey ell in hat follos, and does make the etadation tem constant. One impotant aspect of Eqn. 3 is that no assumption of homogeneity as made in the deivation. That is, even is the pesence of vaiations in pemeability and poosity, the atio of fluid-to-tempeatue velocities is a constant. Futhemoe, in the absence of dispesion, a chemical ave moves at the same velocity as the bulk fluid velocity. This implies that vaiations in the fluid (o tace) velocity ill be identically eflected in the themal velocity (ith the appopiate shift in time fom Eqn. 4). Thus, if e ae able to monito the fluid font via a tace test, e can pedict the velocity of the tempeatue font. VARIABLE TRANSFORMATIONS In a conventional tace test, a slug of tace is injected, folloed by clean injectate. Due to heteogeneity and non-paallel flo lines, the tace mixes, so that the oiginal shap tace font is smeaed out. Effluent tace concentations ae oiginally lo, incease to some maximum that is typically much smalle than the injected concentation, and again fall to zeo. Tempeatue, on the othe hand, deceases monotonically fom the initial tempeatue (T I ) to the injected tempeatue (T J ). What e seek is a tansfomation, such that the tansfomed vaiables exhibit simila (monotonic) behavio. We have found empiically that the folloing vaiable tansfomations povide an appopiate means of compaing tace concentations and tempeatues. Fo the pedicted tempeatue histoies, plot nomalized tace ecovey (T P ) vs. pseudotime (t*): t q( C( Tp ( t) = (5) q( C( dτ dτ (1 ϕ)ρc p t* = t 1 + (6) ϕρ C p Fo obseved tempeatue histoies, plot dimensionless tempeatue (T D ) vs. time (t): T D T ( t) T = T T J I I (7) As is shon belo, these tansfomations povide the means of pedicting themal beakthough fom a tace test. In the folloing example, a tace test is simulated and analyzed as discussed above. We then pedict a themal histoy at each ell, and compae that ith the simulated themal histoy. EXAMPLE OF THERMAL BREAKTHROUGH PREDICTION A tace test as simulated in a to-dimensional, heteogeneous poous medium. A andom pemeability field as geneated, ith a mean pemeability of 1 md. Pemeability as assumed to be log-nomally distibuted and uncoelated, ith a standad deviation of 18 md. The domain as assumed to be 2m by 2m aeally and 5m thick, and as modeled ith a 4 by 4 by 1 gid. Poosity as assumed to be a unifom.5. Initial pessue and tempeatue ee 14 kpa and 175 o C, espectively, and domain boundaies ee taken as closed. A single injecto as placed at the appoximate cente of the gid, and fou poduction ells ee placed thoughout the domain. No attempt as made to place these ells; athe, they ee located in a somehat haphazad fashion. Well

3 locations and the pemeability field ae given in Figue 1. Othe popeties fo this example ae summaized in Table 1. Fom the static initial condition, tace as injected at a ate of 1 t/h fo 5.88 days, afte hich injection as sitched to fesh ate. Injection tempeatue as taken as 35 o C. The fou poduction ells ee poduced against a bottomhole pessue of 9 kpa. Tace effluent histoies ae given in Figue 2, and tempeatue histoies ae given in Figue 3. A speadsheet pogam as used to numeically integate the tace etun cuves ove time fo each ell. The values at each time ee then nomalized by cumulative tace ecovey (on a pe-ell basis); these ae the pedicted tempeatues. Othe vaiables to be plotted follo simply fom Eqns. 5-7 above. The pedicted and simulated tempeatue histoies ae given in Figues 4-7 fo each of the poduction ells. The excellent ageement obseved in each of the ells clealy indicates the validity of this appoach in pedicting themal beakthough fom tace testing. SUMMARY AND CONCLUSIONS Tace tests can be analyzed and used to pedict themal beakthough in single-phase, poous media. Even in heteogeneous media, if themal conductivity and dispesion can be neglected as second ode effects, the themal font moves at a constant velocity elative to the fluid flo font. By analyzing a tace esponse cuve (hich also moves ith the bulk fluid font velocity), velocity and tavel time of the themal font can be estimated. An empiical tansfomation of the tace data povides a elatively simple means of pedicting themal beakthough, as shon in an example. Futhe ok is equied to make this method moe obust. Fist, the vaiable tansfomations noted above ee obtained empiically; it is likely thee is a mathematical eason hy they ok so ell. Also, this analysis has been esticted to single phase flo in poous media. Futue ok on this poject ill extend these esults to multi-phase flo and factued media. ACKNOWLEDGMENTS Funding fo this ok as povided by the U.S. Depatment of Enegy, Office of Enegy Efficiency and Reneable Enegy, Geotheaml Technology Division, unde contact # DE-AC7-94ID The autho also ishes to thank J.L. Renne and K.K. Bloomfield fo thei evie of the manuscipt, and J.L. Boe fo he help ith the gaphics. NOMENCLATURE C Tace concentation in effluent (f.) C p Rock specific heat (J/g o C) C p Liquid specific heat (J/g o C) K Themal conductivity (W/m o C) q Mass flo ate of ell (kg/s) t Time (s) t* Pseudotime, as defined in Eqn. 6 T Tempeatue ( o C) T D Dimensionless tempeatue as defined in Eqn. 7 T I Initial tempeatue ( o C) T J Injected tempeatue ( o C) T p Pedicted dimensionless tempeatue (fom tace analysis) u Dacy velocity of liquid phase (L/t) v Intestitial velocity of liquid phase (L/t) v T Velocity of themal font (L/t) ϕ Poosity ρ Liquid density (kg/m 3 ) ρ Rock density (kg/m 3 ) REFERENCES Beall, J.J., M.C. Adams, and P.N. Hitz, 1994, R-13 Tacing of Injection in The Geyses, Tans. Geothemal Resouces Council, 18, pp Benoit, W.R. and D. Stock, 1993, A Case Histoy of Injection at the Beoae, Nevada Geothemal Resevoi, Tans. Geothemal Resouces Council, 17, pp Bodvasson, G., 1972, Themal Poblems in Siting of Reinjection Wells, Geothemics 1(2), pp Kocabas, I., G. Axelsson, and G. Bjonsson, 1996, Intepetation of the Retun Pofile of a Tace Test in the Thelamok Geothemal Field, Iceland, Poc. 21 st Wokshop on Geothemal Resevoi Engineeing, Stanfod Univesity, Stanfod, Ca., pp Rose, P.E., K.D. Appeson, S.D. Johnson, and M.C. Adams, 1997, Numeical Simulation of a Tace Test at Dixie Valley, Nevada, Poc. 22 nd Wokshop on Geothemal Resevoi Engineeing, Stanfod Univesity, Stanfod, Ca., pp Woods, A.W. and S.D. Fitzgeald, 1993, The vapoization of a liquid font moving though a hot poous ock, J. Fluid Mech, 251, pp

4 Table 1. Summay of esevoi and numeical popeties fo example poblem. Dimensions 2m x 2m x 5m Poosity.5 (V p = 1, m 3 ) Pemeability mean =1 md, log-nomally distibuted Rock heat capacity 1 kj/kg o C Themal conductivity 2. W/m o C Initial conditions: Pessue 14 kpa Tempeatue 175 o C Bounday Conditions no-flo, insulated Gid 4 x 4 x 1, unifom gid Time step size 4 day maximum P 1 P IN J E C T 3. P 3 P D ista n c e (m e te s) Log of Pemeability F ig u e 1. P e m e a bility fie ld fo e x am ple sim u l ati o n o f a tac e te st.

5 Figue 2. Tace concentation histoies fo example poblem. 1.E-1 1.E-2 Well P3 Well P4 Well P2 1.E-3 Well P1 Tace Mass Faction 1.E-4 1.E-5 1.E-6 1.E-7 1.E Figue 3. Tempeatue histoies fo example poblem. 17 Well P1 15 Well P3 Well P4 Well P2 13 Tace Mass Faction

6 Figue 4. Pedicted vs. Tempeatue Histoies, Well P pedicted Figue 5. Pedicted vs. Tempeatue Histoies, Well P2 1.9 pedicted

7 Figue 6. Pedicted vs. Tempeatue Histoies, Well P3 1.9 pedicted Figue 7. Pedicted vs. Tempeatue Histoies, Well P4 1.9 pedicted