ScienceDirect. Heat transfer and fluid transport of supercritical CO 2 in enhanced geothermal system with local thermal non-equilibrium model

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1 Available online at ScienceDirect Energy Procedia 63 (2014 ) GHGT-12 Heat transer and luid transport o supercritical CO 2 in enhanced geothermal system with local thermal non-equilibrium model Le Zhang a, Feng Luo a, Ruina Xu a, *, Peixue Jiang a, Huihai Liu b a Beijing Key Laboratory or CO2 Utilization and Reduction Technology, Key Laboratory or Thermal Science and Power Engineering o Ministry o Education, Department o Thermal Engineering, Tsinghua University, Beijing , China b Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Abstract The heat transer and luid transport o supercritical CO2 in enhanced geothermal system (EGS) is studied numerically with local thermal non-equilibrium model, which accounts or the temperature dierence between solid matrix and luid components in porous media and uses two energy equations to describe heat transer in the solid matrix and in the luid, respectively. As compared with the previous results o our research group, the eect o local thermal non-equilibrium mainly depends on the volumetric heat transer coeicient ah, which has a signiicant eect on the production temperature at reservoir outlet and thermal breakthrough time. The uniormity o volumetric heat transer coeicient ah has little inluence on the thermal breakthrough time, but the temperature dierence become more obvious with time ater thermal breakthrough with this simulation model. The thermal breakthrough time reduces and the eect o local thermal non-equilibrium becomes signiicant with decreasing ah The The Authors. Published by Elsevier by Elsevier Ltd. This Ltd. is an open access article under the CC BY-NC-ND license ( Selection and peer-review under responsibility o GHGT. Peer-review under responsibility o the Organizing Committee o GHGT-12 Keywords: Enhanced geothermal system; CO 2; local thermal non-equilibrium 1. Introduction In recent years, with the accelerated reduction o ossil uels and the greenhouse eect brought by the utilization o ossil uels, it is urgent to develop renewable low carbon-emitting energy. The enhanced geothermal system (EGS) is aimed to extract geothermal energy rom the hot dry rock (HDR) artiicial racture reservoir at a depth rom 3km to 10km by circulating the heat transmission luid low through the reservoir. Field scale numerical simulation o * Corresponding author. Tel.: ; ax: address: ruinaxu@mail.tsinghua.edu.cn The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( Peer-review under responsibility o the Organizing Committee o GHGT-12 doi: /j.egypro

2 Le Zhang et al. / Energy Procedia 63 ( 2014 ) geothermal reservoir is a very important tool to evaluate the heat extraction perormance with heat transmission luid. Brown proposed a novel CO 2-EGS concept using supercritical CO 2 instead o water as heat transmission luid to extract geothermal energy rom hot dry rock [1]. Many studies have shown that CO 2-EGS system not only produces greater power due to the avorable transport properties o CO 2, but also sequestrates carbon and minimizes water loss due to working luid losses at large depths [2-4]. The geothermal reservoir is always treated as porous media in the extensive simulations o EGS heat extraction perormance. There are two models to describe the luid low and heat transer in the porous media: local thermal equilibrium model (LTE) and local thermal non-equilibrium model (LTNE). The LTE model assumes there is no temperature dierence between the solid matrix and luid, however, the LTNE model describes the heat transer in porous media with consideration o temperature dierence. Shaik et al [5] investigated the eects o heat transer between rock matrix and luid and racture connectivity in naturally ractured geothermal system and showed that the heat transer coeicient has a proound eect on the economic potential o a geothermal reservoir. Jiang and Chen [6-7] develop a novel three-dimensional transient model with local thermal non-equilibrium model or the study o the subsurace heat exchange process in EGS. The studies showed that the results o local thermal non-equilibrium model has scarcely any dierences rom that o local thermal equilibrium model and the parameter has very little eect on the production temperature. However, the heterogeneity o permeability o dierent layers and the racture zone are not considered in the studies. Thereore, it is very important to develop numerical modeling with local thermal nonequilibrium model to predict the heat extraction behaviors o CO 2-EGS system with racture zone and heterogeneity layers. The present work is a continuation to our previous work [4]. This paper presents a numerical model to simulate heat transer and luid low o supercritical CO 2 in EGS with two wells ater conditions at the European EGS site at Groβ Schonebekc using the CFD (computational luid dynamics) code FLUENT 6.3. This study compares the results o local thermal non-equilibrium model with that o local thermal equilibrium model, which has been presented in the paper o Luo et al [4]. And it shows that the eect o local thermal non-equilibrium on the heat extraction depends on the volumetric heat transer coeicient. Nomenclature porosity density o luid, kg/m 3 viscosity o luid, Pa thermal conductivity o luid, W/m K E internal energy o luid, J/kg velocity vector, m/s P pressure, Pa density o rock, kg/m 3 thermal conductivity o rock, W/m K C ps isobaric speciic heat, J/kg K k permeability, m 2 C inertial low resistance actor h internal convective heat transer coeicient between the rock matrix and luid, W/m 2 K a the speciic surace area, m Numerical approach This study numerically simulates CO 2 low and heat transer in 3D CO 2-EGS system with a reservoir with ractures over a 25 year period, based on the parameters o the European EGS site at Gro Schonebekc. The modeled reservoir shown in igure 1 was divided into ive layers and two hydraulic racture regions around the wells. The characteristic parameters o the reservoir and the hydraulic and thermal properties o reservoir rock were taken rom Luo s study [4].

3 7646 Le Zhang et al. / Energy Procedia 63 ( 2014 ) Fig.1. Schematic diagram o a doublet CO 2-EGS [4] The reservoir was modelled as porous media, and the laminar low and heat transer in the reservoir were solved by Navier- Stokes equation and local thermal-equilibrium model. The governing equations are listed as ollowed. Continuity equation: ( V ) 0 t (1) Momentum equation: ( V ) 2 T 1 ( VV ) P ( ( V V VI)) g ( V C V V ) t 3 k 2 (2) Energy equation o luid: ( E ) T 2 ( V( E P)) ( T V( V V VI)) ha( Ts T) t 3 (3) Energy equation o rock matrix: Ts (1 ) scps ((1 ) s Ts) ha( Ts T) t (4) Where is the luid density, is the luid viscosity, is the luid thermal conductivity, V is the velocity vector, P is the pressure, E is the internal energy o luid per kilogram, is the solid matrix density, is the solid thermal conductivity, C ps is the isobaric speciic heat, k is the permeability, C is the inertial low resistance actor, is the porosity, h is the internal convective heat transer coeicient between the rock matrix and luid. a is the speciic surace area. The main low channel in EGS is the racture with aperture o mm magnitude. According to the previous research, layer 4 is the main heat transer path because o the largest permeability. So the speciic surace area o layer 4 is assumed as 0.001, while the speciic surace area o other layers is calculated by porosity, listed in Table 1. s s

4 Le Zhang et al. / Energy Procedia 63 ( 2014 ) Table 1. Speciic surace area o the reservoir in each layer. Fracture region Layer 1 Layer 2 Layer 3 Layer 4 Layer 5 a According to the existing results, the injection rate o CO 2 is 20 kg/s. The injection temperature o CO 2 lowing in the reservoir is 70. Luo et al suggested that placing the injection well peroration only in layer 3 with the production well perorated only in layer 2 gives the longest thermal breakthrough time and the greatest cumulative heat extraction rom the reservoir beore thermal breakthrough. This study numerically simulates the unsteady heat transer and luid transport o CO 2 in the geothermal reservoir with ractures and layers or 25 years utilization lietime with FLUENT sotware. The PISO (Pressure-Implicit with Splitting o Operators) algorithm, which is suitable or transient calculation especially with large time step, was used to couple the pressure and velocity. And PRESTO! (PREssure Staggering Option) scheme was used or pressure discretization and second-order discretization scheme was used or advection and energy terms. 3. Results and discussion This study is aimed to investigate the eect o local thermal non-equilibrium on the heat extraction o EGS ractured reservoir. ah is a parameter which describes the heat transer between the rock matrix and luid. The larger ah enhances the rock matrix-luid heat exchange in the reservoir and generally diminishes the rock-luid temperature dierence. When the volumetric heat transer coeicient ah tends to ininity, the temperature dierence is zero, which is called local thermal equilibrium model. The CO 2 temperature at the reservoir outlet through the reservoir with LTE model and LTNE model are shown in Fig. 2. From the Fig. 2, it is concluded that the results o LTNE model with nonuniorm ah has little dierence rom that o LTE model. The eect o local thermal non-equilibrium is not important or this simulation model. The case with constant ah in dierent layers indicates that the uniormity o ah has little inluence on the thermal breakthrough time, but the dierences o temperature become more obvious with time ater thermal breakthrough. Fig. 2. CO 2 temperature variation with time or dierent models Fig. 3 and Fig. 4 show the temperature distributions in the reservoir along a slice linking the injection and production wells ater 9.5 years o CO 2 injection or various ah and constant ah in dierent layers with local thermal non-equilibrium model. As shown in Fig. 3, the temperature dierences between rock matrix and luid in the dierent layers are very dierent. The temperature distributions o rock matrix and luid in layer 4 are almost the same, while the temperature dierence between rock matrix and luid in layer 5 is signiicant. This is because that the speciic surace area a o dierent layers varies greatly. For example, the speciic surace area a o layer 5 is smaller 5 orders o magnitude than that o layer 4, so the eect o local thermal non-equilibrium is more remarkable in layer 5. It

5 7648 Le Zhang et al. / Energy Procedia 63 ( 2014 ) should be noted that the injection CO 2 mainly low through the layer 4 channel because o largest permeability, and the eect o local thermal non-equilibrium o the whole reservoir depends on the eect o local thermal nonequilibrium o layer 4. The luid low and heat transer in the layer 5 has little impact on the production temperature at the reservoir outlet. This is the reason that the results o LTNE model with non-uniorm ah has little dierence rom that o LTE model. When ah is uniorm and equals 1 in the reservoir, the temperature dierences o rock matrix and luid in dierent layers are all small, and the eect o local thermal non-equilibrium can be ignored, shown in Fig. 4. (a) Solid temperature distribution (b) Fluid temperature distribution Fig. 3. Temperature distribution in the reservoir along a slice ater 9.5 years o CO 2 injection with ah is various in dierent layers (a) solid temperature distribution (b) luid temperature distribution (a) Solid temperature distribution (b) Fluid temperature distribution Fig. 4. Temperature distribution in the reservoir along a slice ater 9.5 years o CO 2 injection with constant ah=1 in dierent layers (a) solid temperature distribution (b) luid temperature distribution Three another cases with ah values o 0.1, 0.01, 0.001, respectively, are simulated or the urther study o the eect o local thermal non-equilibrium on the luid low and heat transer in the rock matrix o EGS. The CO 2 temperature variations in 25 years or dierent ah are presented in Fig.5. The thermal breakthrough time is reduced to 6.5 years, 0.8 years, 0.5 years when ah equals 0.1, 0.01, 0.001, respectively. Fig. 6 shows the temperature distributions o rock matrix and luid in the reservoir along a slice linking the injection and production wells ater 9.5 years o CO 2 injection or various ah with local thermal non-equilibrium model. The temperature dierence becomes larger and the eect o local thermal non-equilibrium becomes signiicant with decreasing ah. It shows the eect o local thermal nonequilibrium on the CO 2-EGS heat extraction mainly depends on the volumetric heat transer coeicient ah. Thereore, the accurate prediction o volumetric heat transer coeicient ah is very necessary to predict the heat extraction rate and operation lietime o a given CO 2-EGS reservoir.

6 Le Zhang et al. / Energy Procedia 63 ( 2014 ) Fig. 5. CO 2 temperature variation with time or dierent ah in the reservoir (a) Solid and luid temperature with constant ah=0.1 (b) Solid and luid temperature with constant ah=0.01

7 7650 Le Zhang et al. / Energy Procedia 63 ( 2014 ) (c) Solid and luid temperature with constant ah=0.001 Fig. 6. Temperature distribution in the reservoir along a slice ater 9.5 years o CO 2 injection with constant ah in dierent layers (a) ah=0.1 (b) ah=0.01 (c) ah= Conclusions This study presents a numerical model o CO 2-EGS with racture zones and dierent layers with two wells to study the eect o local thermal non-equilibrium on the heat transer and luid transport o supercritical CO 2 in enhanced geothermal system. This study is a continuation o our previous research. As compared with the previous results o our research group, the eect o local thermal non-equilibrium has a proound eect on the production temperature at reservoir outlet and thermal breakthrough time o a given EGS reservoir. The eect o local thermal non-equilibrium becomes signiicant with increasing ah. Moreover, the uniormity o volumetric heat transer coeicient ah has little inluence on the thermal breakthrough time, but the temperature dierences become more obvious with time ater thermal breakthrough. The thermal breakthrough time reduces and the eect o local thermal non-equilibrium becomes signiicant with decreasing ah. The accurate prediction o volumetric heat transer coeicient ah is very necessary to predict the heat extraction rate and operation lietime o a given CO 2-EGS reservoir. Acknowledgements This work was supported by International Science & Technology Cooperation Program o China (2012DFG61510), the National Key Technology Research and Development Program o the Ministry o Science and Technology o China (2012BAC24B01) and the Research Project o Chinese Ministry o Education (No A). Reerence: [1] Brown DW. A Hot Dry Rock geothermal energy concept utilizing supercritical CO2 instead o water. In: Proceedings o the Twenty-Fith Workshop on Geothermal Reservoir Engineering, Stanord University, 2000; [2] Pruess K. Enhanced geothermal systems (EGS) using CO2 as working luid a novel approach or generating renewable energy with simultaneous sequestration o carbon. Geothermic 2006; 35: [3] Pruess K. On production behavior o enhanced geothermal systems with CO2 as working luid. Energy Conversion and Management 2008; 49: [4] Luo F, Xu RN, Jiang PX. Numerical investigation o luid low and heat transer in a doublet enhanced geothermal system with CO2 as the working luid (CO2-EGS). Energy 2014; 64: [5] Shaik, A.R., Rahman, S.S., Tran, N.H., Tran, T., Numerical simulation o luid-rock coupling heat transer in naturally ractured geothermal system. Applied thermal engineering 31: [6] Jiang, F.M., Luo, L., Chen, J.L., A novel three-dimensional transient model or subsurace heat exchange in enhanced geothermal systems. International communications in heat and mass transer 41: [7] Chen, J.L., Luo, L., Jiang F.M., Analyzing heat extraction and sustainability o EGS with a novel model. Journal o earth science and engineering 3: