A Thee-dimensional Coupled Themo-hydo Model o Enhanced Geothemal Systems S. N. Pandey* * Depatment o Applied Mechanics, Indian Institute o Technology Madas, Chennai 600036, Tamil Nadu, India S. N. Pandey, Depatment o Applied Mechanics, Indian Institute o Technology Madas, Chennai 600036, Tamil Nadu, India, Tel: +91 4422574074, Fax: +91 44 2257 4052, snpiitm@gmail.com Received: 15.07.2016 Accepted:22.09.2016 Abstact- A thee-dimensional numeical model o coupled luid low and heat tanse in EGS esevoi is investigated. The model consides a single uniom actue suounded by a thee dimensional low pemeable ock matix. The low is imposed on a actue plane, consisting o a doublet system. The pimay objectives o this pape ae to analyze the eects o injection tempeatue and mass low ates on heat extaction peomances. The study esults showed that o lowe injection tempeatue heat extaction ates om the esevoi ae highe. In case o highe injection mass low ate, enegy output inceased signiicantly. Howeve, ate themal beakthough the enegy output dops ae seen aste in compaison o lowe mass injection case. The aste enegy dop with the time ae esult o the slowe heat conduction inside the low pemeable ock matix pependicula to the actue. The pesent model neglected the actue apetue evolution even though tansmissivity eduction is obseved. The tansmissivity eduction is the esults o low esistance. The low esistance inside the actue is inceased due to the non-lamina low and cooling. The combined eect leads to ise the low impendence o the esevoi. These eects ae moe o the highe mass at the lowe injection tempeatue. Keywods Enhanced geothemal systems, Coupled pocesses, Themo-hydo eects, Heat extaction, low impedance. 1. Intoduction Themal enegy stoed inside the eath cust is known as geothemal enegy. Geothemal enegy is enewable, clean, ubiquitous, and has the potential o poviding base-load powe. Duing the last ou decades, geothemal enegy povides sustainable use o a lage vaiety o applications, such as heating/cooling o buildings using gound souce heat pump [1-3], desalination o wate, industial pocesses, mineal ecovey, and electicity geneation. Fom 2010 to 2014, the diect use o geothemal enegy inceased by 46.2% and eached 70,885 MWt [4]. The installed capacity o geothemal plants o electicity geneation also incease by 17% in the past ive yea (2010-2015) and eached 12.729 MW [5]. The IEA (Intenational Enegy Agency) epot says that by 2050, the shae o geothemal enegy expected to ise aound 3.9% o enegy o heat and 3.5% o electicity poduction [6]. Thee wee seveal studies in past on nonisothemal luid low and heat tanspot in geothemal esevoi [7-13]. Jiang et al. [14] modeled the low and heat tanse in EGS (enhanced geothemal system) esevoi. They consideed the esevoi as homogeneous poous medium. Local themal non-equilibium appoach was used. Howeve, esults o Jiang et al. [15] showed that tempeatue at poduction well was not much signiicantly aected when themal equilibium model assumption was used. Hadgu et al. [16] used FEHM (Finite Element Heat and Mass Tanse) to model the heat extaction in enhanced geothemal systems. Thei esults showed that actue oientation with espect to the well-pai plane has signiicant inluence on esevoi themal dawdown. Fox et al. [17] studied the eect o actue spacing on heat extaction peomances. Thei esult shows that enegy output inceased with deceasing actue spacing and inceasing numbe o actues in the esevoi. Kalinina et al. [18] examined the inluence o the heteogeneities in sand-stone esevois. They showed that the impact o heteogeneities on the heat extaction o tempeatue dop was insigniicant when the median actue spacing was small, but heat extaction inceased o lage median actue spacing. They also demonstated that the
heat extaction and tempeatue dop geneally depend on the hoizontal/vetical distibution o the pemeability ield and the actue spacing. The sensitivity analysis in single vaiable apetue actue was pesented in [19]. The esults o the study indicated that the heat tanse ate at the actue matix inteace was appaently aected by the actue apetue. Pandey et al. [20] studied the eect o coelation length on heat extaction om an EGS esevoi. The esult shows that with smalle coelation lengths, heteogeneity did not signiicantly inluence the tempeatue at the poduction well. But o lage coelation lengths, signiicant tempeatue vaiation at poduction well due to stong low channeling inside the esevois. The themo-hydo simulations in actue netwoks wae studied in [21]. They used EPN (equivalent pipe netwok) appoach to model the actue netwok. The pesent study develops a numeical model that ully couples the themo-hydo pocesses duing luid injection and heat extaction om actued EGS esevoi. The esevoi conside a single actue connects the injection and poduction wells. The assumption is applicable o geothemal esevoi dominated by a single actue/ault. The single actue also povide useul insights behavio o individual actues in a actue netwok inside the esevoi. The pesent numeical appoach and the insight om the simulated esults ae useul o geothemal esevoi engineeing due to the lack o inomation available om ield expeiments and expeience on long tem behavio o EGS-type geothemal systems. The tempeatue and pessue dependent luid popeties such as density, viscosity, enthalpy ae consideed to calculate the enegy output. Additionally, the eects o opeating condition o long tem peomances o EGS esevois ae also studied. 2. Govening Equations o Flow and Heat Tanse The govening equations o luid low though actue and the low pemeable ock matix can be expessed as [22-24]: 3 b Q P ρg 12 μf t k q P ρg (2) μ whee Q (1) (m 2 /s) is the apetue integated two-dimensional lux vecto, b is the actue apetue, P is the apetueaveaged pessue, P is the luid pessue in the ock matix, k (m2 ) is the ock pemeability,, and g ae the dynamic viscosity, density o the wate and gavitational acceleation espectively. In pesent simulations, the low ate nea the wells is high enough that non-lamina eects ae signiicant. To account o non-lamina eects, the expeimentally motivated appoach o Zimmeman et al. [25] is used. They poposed, 1 0. 00838Re. The Reynolds numbe o low is deined as Re ρ. F t The govening equations o heat tanspot though the actue and ock matix ae: b ρc c t whee p t p T T T conductivity, Q. λ T T Q. h b (3). T 0 q. h (4) is the tempeatue, h The subscipts is the enthalpy and and c p is the themal is the speciic heat. eeing o luid and ock, espectively. The local themal equilibium appoached is used o the heat tanspot. In the pesent model, the pemeability o ock matix is much smalle than actue, the heat tanspot though ock matix is only dominated by conduction (advection tem in eq. 4 is usually negligible). In eq. 3, T is the heat exchange tem which is coupled at the actue matix inteace. 3. Numeical Method The luid low and heat tanspot equations wee solved numeically by using FEHM code (Finite Element Heat and Mass Tanse) [26]. FEHM is a well-veiied CVFE (contol volume inite element) code, designed to solve consevation o mass, momentum and enegy equations (Eqs. 1, 2, 3 and 4) o non-isothemal single/multiphase low though poous media. The details o solving the govening equations and method is given in e. [27]. Simulations wee conducted in a actue matix system involving tanspot o luid in a highly pemeable hoizontal actue inside a 3-D geothemal esevoi. Fo modeling low and heat tanspot in actue, actue is consideed as an equivalent poous medium. The same appoach was ealie used o Themo-Hydo-Chemical modeling o geothemal system [9, 20]. 4. Computational Domain and Bounday Conditions The conceptual domain o geothemal esevoi is shown in Fig. 1. The size o esevoi is 1.5 km 1.5 km 1 km in the x, y and z diection. The computational domain extends om 2 km to 3 km below the gound. The actue in the esevoi is located 2.8 km below the top suace. The 1517
tempeatue gadient 0.70 O C/m is used to deine the initial tempeatue distibution inside the esevoi. Hence, the tempeatue o wate inside the actue is initially 226 O C, while along the vetical boundaies zeo heat (adiabatic) and mass lux (no low) bounday conditions ae speciied. The aveage initial tempeatue at the gound suace o esevoi is consideed 30 O C. The poe pessue inside the esevoi ollow the natual pessue distibution with the depth with an assumption o no egional low and tectonics activity. The initial pessue due to poe pessue gadient at the actue locations at a depth o about 2.8 km is about 28 MPa. Fo eicient and accuate solution o the coupled themohydaulic poblem, a nonuniom but stuctued computational mesh is used. The computational meshes along and ae shown in Figs. 2a and 2b, x y x z espectively. Since, the tempeatue and pessue gadients ae vey high below and above the actue (i.e. shap change in tempeatue and pessue poiles) vey ine mesh ae taken o 279.9 z 280. 1. Fo simila eason the computational mesh along plane is vey ine nea injection and poduction wells. x y Fig. 2. Mesh geneated in the study, (a) X-Y and, (b) X-Z diection. Table 2: Injection scenaios. Case No. T inj ( O C) m inj (kg/s) Fig. 1. Schematic diagam o a doublet geothemal heat extaction setup. Table 1: Input paametes o numeical simulation [20]. Paametes Value Initial actue apetue (m) 0.005 1 60 40 2 80 40 3 4 60 80 60 60 Resevoi pemeability (m 2 ) Density o ock (kg/m 3 ) Heat capacity o wate (J/kg/ o C) Heat capacity o ock (J/kg/ o C) Themal conductivity o ock (W/m/ o C) Themal conductivity o wate (W/m/ o C) 1 10 18 2500 4180 1000 2.5 0.60 5. Results and Discussion Fully coupled themo-hydo simulation o wate injection into a nondeomable actued geothemal esevoi have pesented o the opeational peiod o 20 yeas duations. To study the eect o injection mass low ate and tempeatue, ou cases have been consideed. These ae tabulated in Table 2. Two dieent values o ixed mass low ates (40 and 60 kg/s) and two dieent values o injection tempeatue (60 and 80 O C) ae consideed. The values esevoi paametes ae listed in Table 1. The esults 1518
petaining to cooling o esevoi with time and poduction tempeatue dawdown ae pesented. The heat extaction duing ciculation o wate in a doublet system can be expessed as ollows: E m h po h (5) inj moving away om the injection well and eaches the poduction well. Howeve the size o cold zone gows vey whee m is the poduction mass low ate, h inj and h po the enthalpy o wate at the injection and poduction well espectively. Howeve, due to incease o injection pessue, enthalpy o injected luid vaied om 277 kj/kg at beginning o injection to 292 kj/kg at end (20 yeas) o the poduction o Case 1 injection condition (40 kg/s and 60 o C). Since enthalpy is a unction o pessue and tempeatue ( ), and these eects ae consideed o h ( P, T) calculation o heat extaction. Fom the second law o themodynamics, convesion o heat to wok is ollow as: h h 1 T T (6) m po inj 0 po ae whee T 0 and T po ae the atmospheic tempeatue and the well head poduction tempeatue. Sanyal and Butle [28] poposed the ollowing elation, is used in this analysis to calculate the electic powe output based on an assumption that 45% o utilization eiciency o useul wok is conveted into electic powe: h 1 T T P 0.45m hpo inj 0 (7) po Fig. 3. The spatio-tempoal evolution o tempeatue poile at the actue plan ( 800 m) o injection condition ( 40 kg/s and T inj = 60 O C, (a) 0.5 yea, (b) 2 yeas, (c) 10 yeas, and (d) 20 yeas. m z whee T 0 is the atmospheic tempeatue. The wate low impedance I R (MPa/(kg/s)) is calculate as: I R whee Pinj Ppo (8) m P inj and P po ae the pessue at the injection and poduction well, espectively. The value o impedance paamete is invesely popotional to the actue tansmissivity. It is expected to be constant o nondeomable and noneactive esevoi. Howeve I R has been seen to incease even o themo-hydaulic modeling because incease o viscosity as the tempeatue o wate inside the actue deceases with time. The evolution o tempeatue ield and popagation o cold ont inside the actue ae shown in Fig. 3 ate 0.5, 2, 10 and 20 yeas om the beginning o injection o Case 1 injection condition. The tempeatue at the vicinity o the injection well dops vey ast. The cold ont (themal ont) Fig. 4. Velocity vecto plot at the actue plan ( z 800 m) o injection condition ( m 40 kg/s and T inj = 60 O C, (a) 0.5 yea, and (b) 20 yeas. 1519
slowly ate the aival o cold ont at poduction well. Since the heat tanse within the actue is advection dominated, the cooling is mainly dictated the low ield. The low ield is shown in Fig. 4 in the om vecto plot o apetue-integated lux ( ). The colou o aows epesents the elative Q magnitude o lux. Additionally lux is indicated as lage i the colou vaies om blue to ed. The cooling between the wells is aste than othe pats o the actue as the cold wate takes minimum time to each the poduction well when tavels linealy between wells. The lux vecto plots in Figs. 4a and 4b look vey simila. Since, the tansmissivity eduction caused by low esistance is vey small and evolutions due to T-H-M-C pocesses ae neglected. The tempeatue distibution within the actue suace ate 20 yeas o opeation o Case 1, Case 2, Case 3 and Case 4 ae pesented in Fig. 5. Among all the Cases, the moe tempeatue dop occued in Case 3 injection condition. This suggests that highe mass leads to highe advection inside the esevoi/actue and wate tavels a longe distance within the actue. In addition, tempeatue dop inside the esevoi is moe sensitive to injection tempeatue. Figs. 5a and b shows the esults o same injection mass low ate but dieent injection tempeatue. These igues suggests that highe tempeatue injection leads to lowe tempeatue dop inside the esevoi due to decease the tempeatue dieence between injected luid and esevoi ock tempeatue. This leads to less cooling inside the esevoi. Fig. 6. Tempeatue distibution in the esevoi matix ate 20 yeas along the vetical section at the plane ( y 0), (a) m 40 kg/s and T inj = 60 O C, (b) m 40 kg/s and T inj = 80 O C, (c) 60 kg/s and T inj = 60 O C, and (d) 60 kg/s and T inj = 80 O C. m m Fig. 7. The zoom views o tempeatue ields o Fig. 6. Fig. 5. Tempeatue ield ate 20 yeas at the actue plan ( z 800 m) o dieent injection conditions: (a) m 40 kg/s and T inj = 60 O C, (b) m 40 kg/s and T inj = 80 O C, (c) m 60 kg/s and T inj = 60 O C, and (d) m 60 kg/s and T inj = 80 O C. Fig. 8. Tempeatue distibution in the esevoi matix ate 20 yeas along the vetical section at the plane ( x 0), (a) m 40 kg/s and T inj =60 O C, (b) m 40 kg/s and T inj = 80 1520
m O C, (c) 60 kg/s and T inj = 60 O C, and (d) and T inj = 80 O C. m 60 kg/s Fig. 9. The zoom views o tempeatue ields o Fig. 8. Fig. 10. The tempeatue poile in vetical diection at injection point ate 20 yeas. The vetical tempeatue distibutions inside the low pemeable ock matix o Cases 1-4 ae shown in Figs. 6 and 8 (zoom view in igs. 7 and 9). Figs. 6 and 8 shows that the tempeatue dop inside the ock matix occued less than 100 m om the actue. Fo vey small value o matix pemeability, the heat tanse inside the inside the ock matix is only by the conduction. Compaing the all Cases, it is seen that slightly moe tempeatue dop occus in vetical diections o Case 3 because in this case the colde luid is injection with highe mass low ate. The tempeatue poiles along the vetical line passing though the injection well ae shown in Fig. 10 o Case 1-4. Nea the actue, almost linea tempeatue poile is obseved. Howeve appoximately 100 m away om the actue, the tempeatue poile match the initial geothemal gadient. In Fig. 11, the vaiation o poduction tempeatue, heat extaction ate, powe output and injectivity with time ae plotted. The ealy themal beakthough and aste Fig. 11. Compaison o esults to show the eect o dieent injection mass low ate and injection tempeatue on the vaiation o (a) tempeatue, (b) heat extaction ate, (c) electic powe output, and (d) low impedance. 1521
tempeatue dop at poduction well is caused by the slow heat tanse ate om the low pemeable ock matix at the inteace. Due to the aste cooling o actue by stong advection and slow conduction in the ock matix, the luid in actue did not get enough time to captue the heat om the low pemeable ock matix. But at late stage poduction tempeatue deceases slowly and heat tanse om the ock matix eaches steady state in pats o the actue. The tempeatue beakthough at poduction well occu ealy o highe mass low ate at lowe injection tempeatue. The heat extaction ate and electic powe output with time o all cases ae pesented in Figs. 11b-11c. Figs. 11b and 11c show that heat extaction ate and electic powe output is compaably moe o Case 3, due to highe mass injection at low injection tempeatue. Howeve, the lowe injection tempeatue help to extact moe enegy om the esevoi. Fo the highe injection tempeatue, heat extaction ate deceases due to the less tempeatue dieence between injected luid and ock/actue. Fig. 11d shows the evolution o the esevoi impedance (low impedance) with time o all injection scenaios. Fig. 11d shows that inceasing the mass low ate om 40 to 60 kg/s esults in a incease o low impedance. This is because o highe mass low ate inceased the low esistance. Fig. 11 d also shows that inceasing the injection tempeatue educes the lowing impedance. In this case low esistance is deceased due to lowe luid viscosity. 6. Conclusion In this study, a thee-dimensional coupled Themo-Hydo model o geothemal heat extaction has been pesented. Seies o numeical simulations compising o dieent injection tempeatue (T inj) and mass low ate ( m ) wee caied out to analyze thei eects on the heat extaction peomance, enegy output and low impedance changes om a actued geothemal esevoi. It was obseved that the injection tempeatue and mass low ate have a poound eects on tempeatue dawdown at the poduction well and cooling o actue/matix system. The esult o highe injection mass at lowe tempeatue shows aste dop o tempeatue at the poduction well and elatively ealy themal beakthough. But, in this case, moe heat extaction om the esevoi due to geate utilization o available esouce. The esults also showed that the low impedance ises due to the incease o viscosity as the esult o tempeatue dop inside the esevoi. The low impedance o esevoi was less o highe injection tempeatue. Howeve, in that scenaio both powe output and heat extaction ate deceased. Reeences [1] B. B., R. Saim, H. Benzenine, H. F. Oztop, ''Analysis o themal and dynamic compotment o a geothemal vetical U-tube heat exchange'', Enegy and Buildings, vol. 58, pp. 37-43, 2013. [2] B. D. P. Hepbun, M. Sedighi, H. R. Thomas, Manju, ''Field-scale monitoing o a hoizontal gound souce heat system'', Geothemics, vol. 61, pp. 86-103, 2016. [3] A. S. Kod and S. S Jazayei, ''Optimization and Analysis o a Vetical Gound-Coupled Heat Pump'', Intenational jounal o enewable enegy eseach, vol. 2 (1), pp. 33-37, 2012. [4] J.W. Lund, T.L. Boyd, ''Diect utilization o geothemal enegy 2015 woldwide eview'', Geothemics, vol 60, pp. 66-93, 2016. [5] R. Betani, ''Geothemal powe geneation in the wold 2010-2014 update epot'', Geothemics, vol. 60, pp. 31-43, 2016. [6] IEA-Technology Roadmap Geothemal Heat and Powe. Intenational Enegy Agency. http://www.iea.og/publications/eepublications/publicati on/geothemal_oadmap.pd. [7] M. Deo, R. Roehne, R. Allis, J. Mooe, Modeling o geothemal enegy poduction om statigaphic esevois in the Geat Basin'', Geothemics, vol. 51, pp. 38-45, 2014. [8] S. Finstele, Y. Zhang, L. Pan, P. Dobson, K. Oglesby, ''Micohole aays o impoved heat mining om enhanced geothemal systems'', Geothemics, vol. 47, pp. 104-115, 2013. [9] S.N. Pandey, A. Chaudhui, S. Kelka, VR Sandeep, H. Rajaam, ''Investigation o pemeability alteation o actued limestone esevoi due to geothemal heat extaction using thee-dimensional themo-hydochemical (THC) model'', Geothemics, vol. 51, pp. 46 62, 2014. [10] C. Rawal and A. Ghassemi, ''A eactive themopooelastic analysis o wate injection into an enhanced geothemal esevoi'', Geothemics, vol. 50, pp. 10 23, 2014. [11] Y. Zhao, Z. Feng, Z. Feng, D. Yang, W. Liang, ''THM (Themo-hydo-mechanical) coupled mathematical model o actued media and numeical simulation o a 3D enhanced geothemal system at 573 K and buied depth 6000 7000 M'', Enegy, vol. 82, pp. 193-205, 2015. [12] Y. Zeng, J. Zhan, N. Wu, Y. Luo, W. Cai, ''Numeical investigation o electicity geneation potential om actued ganite esevoi by wate ciculating though 1522
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