Study on wellbore fluid flow and heat transfer of a multilateral-well CO2 enhanced geothermal system

Applied Energy 249 (2019) 14–27

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Study on wellbore fluid flow and heat transfer of a multilateral-well CO2 enhanced geothermal system

T

⁎

Yu Shia, Xianzhi Songa, , Gaosheng Wanga, John McLennanb, Bryan Forbesb, Xiaojiang Lic, Jiacheng Lia a

State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing, Beijing 102249, China Energy & Geoscience Institute, University of Utah, Salt Lake City, UT 84108, USA c Sinopec Research Institute of Petroleum Engineering, Beijing 100101, China b

H I GH L IG H T S

and reservoir coupled fluid flow and heat transfer model is presented. • Wellbore characteristics of CO in wellbore are comprehensively analyzed. • Thermal of CO pressure work on wellbore temperature distribution is studied. • Effect insulation effect of central tube with three-layer structure is discussed. • Heat • Effects of wellbore sizes on CO fluid flow and heat transfer are studied. 2

2

2

A R T I C LE I N FO

A B S T R A C T

Keywords: Geothermal energy CO2 Enhanced geothermal system Wellbore fluid flow and heat transfer Heat extraction efficiency

Research efforts towards CO2 enhanced geothermal systems (CO2-EGS) are increasing due to potentially high heat extraction efficiencies. It is well known that CO2 properties are highly sensitive to the temperature and pressure and have noticeable effects on CO2-EGS heat extraction. Consequently, an understanding of wellbore CO2 fluid flow and heat transfer mechanisms is necessary when considering variable CO2 properties. In this paper, a coupled wellbore and reservoir fluid flow and heat transfer model is used to estimate multilateral-well CO2-EGS efficiency. The model is calibrated and validated by field data from the HGP-A well in Hawaii. Schematically, concentric tubulars are used allowing single well injection and production. Multiple cases are analyzed using this model. These include effects of CO2 pressure work on wellbore CO2 fluid flow and heat transfer, assessment of differences in heat extraction using varying wellbore sizes and central tubing insulation lengths, and evaluations of efficiencies under different injection-production well configurations. Results show that CO2 pressure work can induce a dramatic temperature reduction in the central tubing of the multilateralwell CO2-EGS. The majority of pressure loss occurs in the formation and central tubing. The optimized design suggests that a three-layer central tubing with a central diameter of 0.19 m will maximize heat insulation and heat extraction. The effect of annulus diameter on heat extraction is negligible. Also, a lower injection well configuration results in a higher outlet temperature, thermal power output, and lower pressure losses compared to an upper injection well configuration. These results provide significant suggestions for wellbore designs that can potentially optimize multilateral-well CO2-EGS efficiency.

1. Introduction As a renewable, sustainable, environmentally-friendly and abundant natural resource, geothermal energy is increasingly attracting global attention. Geothermal energy is widely used in electric generation, space heating, snow melting and green house heating applications [1].

⁎

In this paper, an enhanced geothermal system (EGS) with CO2 as the working fluid is considered for extracting high temperature geothermal energy for electric generation [2]. In 2000, Brown [3] proposed a CO2-EGS concept that uses supercritical CO2 instead of water as the EGS fracturing and working fluids. Subsequently, studies [3–11] have proven that CO2-EGS has several

Corresponding author. E-mail address: [email protected] (X. Song).

https://doi.org/10.1016/j.apenergy.2019.04.117 Received 12 January 2019; Received in revised form 9 April 2019; Accepted 16 April 2019 Available online 03 May 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature Ap cp,f cp,e cp,s EGS dp fD g h k p q Q1 Q2 R t T T1

T2 Te Tin Tout u

cross section area of tubing, m2 working fluid heat capacity, J/(kg·°C) surrounding formation heat capacity, J/(kg·°C) heat capacity of the solid part in the reservoir, J/(kg·°C) enhanced geothermal system hydraulic diameter of tubing, m Darcy friction factor gravitational acceleration, m/s2 convective heat transfer coefficient, W/(m2·°C) reservoir permeability, m2 pressure, Pa mass flow rate, kg/s heat flow rate between central tubing and annulus, W/m heat flow rate between annulus and formation, W/m thermal resistance, (m·°C)/W time, s temperature, °C working fluid temperature in central tubing, °C

working fluid temperature in annulus, °C original temperature of surrounding formation, °C inlet temperature at wellhead, °C outlet temperature at wellhead, °C working fluid velocity, m/s

Greek symbols ρf ρe ρs μf λca λce λe λf λs φ

working fluid density, kg/m3 formation density, kg/m3 density of the solid part in the reservoir, kg/m3 working fluid viscosity, Pa·s casing heat conductivity, W/(m·°C) cement heat conductivity, W/(m·°C) formation heat conductivity, W/(m·°C) working fluid heat conductivity, W/(m·°C) heat conductivity of the solid part in the reservoir, W/ (m·°C) reservoir porosity

operational factors on the GHE system’s performance. Zhang et al. [16] developed a quasi-3D line source model to predict the temperature and heat flux profiles of a GHE system. Xu et al. [17] proposed a simplified hydro-thermal model that described the fluid flow and heat transfer in industrial-scale EGS reservoirs. Wu et al. [18] presented a semi-analytical solution for the fracture number and spacing required to maximize the EGS lifetime. Furthermore, many numerical studies have also investigated the heat extraction efficiency of CO2-EGS. Pruess [4] conducted numerical simulations on a five-spot-well EGS that used CO2 and water as the working fluids. They found that the thermal power of the CO2-EGS was 50% higher than that of water-EGS when the mass flow rate of CO2 was four times of water. Further studies by Pruess [5] indicated that the open section of production well should be placed near the top of the reservoir so that buoyancy forces generated by CO2 could be fully utilized. Atrens et al. [10,11] found that under idealized conditions, the thermal power of CO2-EGS was equivalent to that of waterEGS. Luo et al. [6] studied the effects of injection mass flow rate, reservoir permeability, perforation position of wells on CO2-EGS efficiency. Cao et al. [8] pointed out that under the same operational conditions, the thermal power of a water-EGS was lower than that of

advantages. For example, the large compression and expansion capabilities of CO2 can generate large density differences between the injection and production wells that induce large buoyancy forces. This can significantly reduce the pumping energy required to circulate CO2 [4–8]. Additionally, CO2 is unable to dissolve and transport minerals, meaning no scaling and precipitation will occur [9]. Although CO2 has a low heat capacity and heat conductivity, it has high ratio of density to viscosity. Multiple case studies have shown that a CO2-EGS can have a comparable heat extraction efficiency to a water-based EGS [4–8,10,11]. In addition, due to high fluid losses in some geothermal reservoirs [12], a CO2-EGS can be considered beneficial for CO2 sequestration [13]. CO2 is selected as the working fluid in the EGS design in this paper based on its favorable fluid properties and heat extraction advantages. Simulation methods have been widely used to study geothermal development processes [14–18]. Zarrella et al. [14] used the numerical simulation tool CaRM to compare the long-term and short-term heat extraction efficiencies of helical-shaped and double U-tube ground heat exchanger (GHE) geothermal systems. Han and Yu [15] utilized COMSOL to simulate the influences of geological, design and

Fig. 1. Left is the schematic diagram of heat extraction for multilateral-well EGS [25] and right is the structure of central tubing wall that provides effective insulation. 15

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Fluid flow and heat transfer processes of CO2 in the central tubing and annulus are analyzed comprehensively. The effect of CO2 pressure work on the wellbore temperature is investigated. The insulating effect of the central tubing is studied. The effects of central tubing and annulus sizes on multilateral-well CO2-EGS efficiency are studied. The heat extraction efficiencies of upper injection and lower injection lateral-well configurations are compared. Results provide comprehensive explanations on the fluid flow and heat transfer of CO2 in the wellbore, and significant suggestions on wellbore design for a multilateral-well CO2-EGS.

CO2-EGS, but the service-life of the water-EGS was longer. Chen et al. [19] utilized a unified pipe-network method to simulate the heat extraction process of a CO2-EGS with complex fractures and displayed the promising potential of CO2 as the working fluid instead of water. Wang et al. [20] indicated that a CO2-EGS had a higher heat extraction and fluid loss rate than a water-EGS, especially in higher enclosing rock permeability, lower reservoir permeability or lower initial reservoir temperature systems. Wang et al. [21] developed a thermo-hydro-mechanical (THM) coupling model to simulate the heat mining and geological carbon sequestration of a three-spot layout of the practical EGS project. Guo et al. [22] utilized COMSOL to study the effects of fracture connectivity, fracture aperture and fracture permeability on the CO2EGS efficiency. Shi et al. [23] investigated the effects of rock deformation, rock mechanical properties, fracture quantity, fracture length and orientation on the multilateral-well CO2-EGS efficiency. Sun et al. [24] studied the heat transfer process of CO2 in the wellbore of a U-shaped closed loop geothermal system and stated that the pressure drop in the wellbore was dependent on the temperature profile. Pan et al. [7] pointed out that the pressure distribution in the wellbore had significant impacts on the CO2-EGS efficiency, and that the mass flow rate, injection temperature and production pressure should be appropriately optimized to ensure the stable production of CO2-EGS. The literature presented in the previous paragraph demonstrates the importance of fluid flow and heat transfer processes in the wellbore and their influence on heat extraction performance in a CO2-EGS. This is due to the sensitivity of CO2 properties to the wellbore temperature and pressure fluctuations. Most previous studies focused on the heat extraction process of CO2 in the geothermal reservoir and neglected wellbore effects. Sun et al. [24] and Pan et al. [7] provided meaningful conclusions related to the fluid flow and heat transfer processes of CO2 in the wellbore. However, further comprehensive theoretical analysis is still required. Therefore, there are opportunities for studying the effects of CO2 wellbore fluid flow and heat transfer on CO2-EGS efficiency. In a conventional EGS, a two well injection and production design is considered optimal for establishing a conductive thermal fluid flow network. The field design strategy is highly dependent on the specific characteristics of the target EGS. Therefore, careful evaluations and sensitivity studies are necessary to determine the optimum drilling and injection strategies to minimize drilling costs and maximize heat extraction. Previously, this group proposed a novel multilateral-well EGS using a single main wellbore to simultaneously inject and produce [25,26]. A schematic of this multilateral-well EGS process is illustrated in Fig. 1 [25]. Hydraulic fracturing, CO2 fracturing or N2 fracturing [27,28] was applied to create hydraulic fractures and re-activate naturally pre-existing fractures to form a stimulated reservoir volume (SRV) in the geothermal formation. The lateral wells enhanced connectivity between the wellbore and geothermal reservoir/fractures, thereby improving injection and production efficiency. A three-layer heat insulation central tubing [29] was designed to preserve heat of the working fluid in the central tubing (shown at the right of Fig. 1). The central tubing consisted of an inner casing, insulation layer and outer casing. The space between the inner casing and outer casing was occupied by air that acted as a beneficial heat insulator due to its ultralow heat conductivity properties. The structure of the insulated central tubing is simple and easy to construct at a low construction cost. The study [25,26] concluded that the heat extraction efficiency of a multilateral-well EGS was equal to or even better than a conventional dualwell injection-production EGS design. The previous studies [25,26] by this group analyzed temperature contours in the reservoir of a multilateral-well EGS and conducted sensitivity analysis on lateral well geometrical and operational parameters. However, wellbore fluid flow and heat transfer effects were not considered in the previous model. Therefore, this paper presents a wellbore and reservoir coupled fluid flow and heat transfer model for the multilateral-well CO2-EGS. The model is calibrated and validated by field data from the HGP-A well located in Hawaii. Based on the model,

2. Model development 2.1. Model assumptions In this study, CO2 was selected as the working fluid. The geothermal reservoir is assumed to be filled with CO2. Generally, under EGS conditions where the pressure and temperature are always above 7.38 MPa and 31.1 °C, CO2 is in a supercritical state. Thus, it is under single phase and single component fluid flow behaviour in the model. Because CO2 properties are highly sensitive to pressure and temperature, it is very important to accurately calculate CO2 rheologic properties [26,30]. In this paper, a CO2 equation of state developed by Span and Wagner (S-W EOS) [31] is used to calculate the density and heat capacity of CO2. Equations developed by Heidaryan et al. [32] and Jarrahian et al. [33] are utilized to compute the viscosity and thermal conductivity of CO2. These equations are selected due to their wide applicable range and high calculation accuracy. According to the literature [4–8,12,19], the fluid flow in the geothermal reservoir can be described by Darcy’s Law. Lastly, the reservoir rock is assumed to be homogeneous and isotropic.

2.2. Mathematical equations The fluid flow and heat transfer in the central tubing and annulus can be described by a non-isothermal pipe flow model. The model consists of mass conservation, momentum and energy equations. The mass conservation and momentum equations are as follows:

∂ (Ap ρf ) ∂t ρf

+ ∇ ·(Ap ρf u) = 0

(1)

∂u 1 ρf |u| u − ρf g = −∇p − fD ∂t 2 dp

(2)

where Ap (m ) is the cross section area of tubing and ρf (kg/m ) is the CO2 density. u (m/s) and p (Pa) represent the velocity and pressure, respectively. dp (m) and g (m/s2) denote the pipe hydraulic diameter and gravitational acceleration. In Eq. (2), the second term on the right indicates the pressure loss induced by the viscosity shear. The parameter fD represents the Darcy friction factor, which is calculated by Haaland model [34] and is expressed as: 2

3

1.11

1 e ⎞ ⎡ = −1.8log10 ⎢ ⎜⎛ ⎟ 3.7 dp ⎠ fD ⎣⎝

+

6.9 ⎤ Re ⎥ ⎦

(3)

where e (m) is the pipe surface roughness and is set as 0.046 m in this paper. Re represents the Reynolds number. The energy equations in the central tubing and annulus can be expressed by the following Eqs. (4) and (5), respectively.

ρf Ap cp, f

∂T 1 ρf Ap + ρf Ap cp, f u·∇T = ∇ ·(Ap λ f ∇T ) + fD |u| u2 ∂t 2 dp − Ap

16

T ∂ρ ρ ∂T

p

⎛ ∂p + u·∇p⎞ − Q1 ⎝ ∂t ⎠

(4)

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ρf Ap cp, f

∂T 1 ρf Ap + ρf Ap cp, f u·∇T = ∇ ·(Ap λ f ∇T ) + fD |u| u2 ∂t 2 dp T ∂ρ − Ap ρ ∂T

p

written as:

(ρcp )eff

⎛ ∂p + u·∇p⎞ + Q1 + Q2 ⎝ ∂t ⎠

where cp,f (J/(kg·°C)) and T (°C) represent CO2 heat capacity and temperature, respectively. λf (W/(m·°C)) denotes CO2 heat conductivity. The second term on the right of Eqs. (4) and (5) denotes the dissipated frictional heat. The third term on the right indicates the pressure work of CO2 induced by expansion [35]. The term Q1 (W/m) represents the heat exchange between the central tubing and annulus through the three-layer heat insulation structure, which can be expressed as

T1 − T2 R1

1 ln(d2/ d1 ) ln(d3/ d2 ) ln(d4 / d3 ) 1 + + + + πd1 h 2πλ1 2πλ2 2πλ3 πd4 h

(6)

(7)

Nu·λ f dp

(8)

where Nu is the Nusselt number, which is calculated by the Gnielinski equation [38]:

Nu =

(fD /8)·(Re −1000)·Pr 1 + 12.7 fD /8 (Pr 2/3 − 1)

(9)

where Pr is the Prandtl number. Q2 (W/m) represents the heat exchange between the annulus and the surrounding formation through the casing, which can be expressed as:

Q2 =

Te − T2 R2

(10)

∂t

⎡k ⎤ − ∇ ·ρf ⎢ (∇p + ρf g∇z ) ⎥ = 0 μf ⎣ ⎦

(17)

2.3. Model validation The finite element solver COMSOL is used to solve the previously described mathematical equations. The numerical solution should be compared with field data to validate its accuracy. However, no field data of this multilateral-well EGS are available for model validation. Therefore, the wellbore model and reservoir model are validated separately. Only validation of the non-isothermal pipe flow model in the wellbore is needed since the reservoir model has been verified in a previous study [25]. This wellbore model simulates the operation of the HGP-A well located in Hawaii [29,40,41]. The HGP-A well is a downhole coaxial heat exchanger geothermal system. Its wellbore structure includes a central tubing and annulus that is similar to the proposed multilateral-well EGS. The field data of the HGP-A well are compared with the simulation results shown in Fig. 2. It can be observed that the numerical results agree well with the field data even when there was a power failure during testing. Therefore, the multilateral-well EGS wellbore model is believed to be reliable.

(11)

(12)

where tD is the dimensionless time and tD = 2λet/(cp,eρe d6). cp,e (J/ (kg·°C)) and ρe (kg/m3) are the heat capacity and density of formation. In the geothermal reservoir, the fluid flow is assumed to obey Darcy’s Law [4–8,12,19] and is described by:

∂ (φρf )

(16)

where q (kg/s) is the mass flow rate of the working fluid. cp,f (J/(kg·°C)) is the heat capacity of the working fluid. The parameters Tout and Tin (°C) indicate the outlet temperature and the inlet temperature at the well head.

where d5 and d6 (m) are the inner and outer diameters of casing, respectively. d7 is the wellbore diameter. λca, λce and λe (W/(m·°C)) denote the heat conductivity of casing, cement and formation, respectively. f(t) is the transient heat conduction time function and expressed as [39]:

1.1281 tD (1 − 0.3 tD ), tD ⩽ 1.5 f (t ) = ⎧ ⎨ [0.4063 + 0.5 ln( t )](1 + 0.6/ tD ), tD > 1.5 D ⎩

λ eff = (1 − φ) λs + φλ f

P = qcp . f (Tout − Tin )

where Te (°C) denotes the original temperature of surrounding formation. R2 is formulated as:

f (t ) 1 ln(d6/ d5 ) ln(d7/ d6 ) R2 = + + + πd5 h 2πλ ca 2πλ ce 2πλ e

(15)

where ρs (kg/m ), cp,s (J/(kg·°C)) and λs (W/(m·°C)) represent the density, heat capacity and thermal conductivity of the solid component of the reservoir, respectively. In the reservoir model, the walls of the injection and production lateral wells are considered as boundaries that couple the fluid flow and heat transfer in the annulus, geothermal reservoir and central tubing. The temperature and pressure at injection lateral wells, production lateral wells, bottomhole of the annulus and central tubing, are regarded as the coupling data. The pressure and temperature at injection lateral wells are equal to the annulus bottomhole pressure and temperature. The pressure and temperature at production lateral wells are equal to the central tubing bottomhole pressure and temperature. The annulus bottomhole temperature is calculated from the wellbore model and set as the inlet temperature condition of the reservoir model. The average pressure of the injection lateral wells is computed from the reservoir model and set as the annulus bottomhole pressure condition. The average temperature and pressure of the production lateral wells are obtained from the reservoir model and set as the central tubing bottomhole temperature and pressure conditions. This setup allows full coupling of fluid flow and heat transfer between the annulus, central tubing and geothermal reservoir. The output thermal power is an important parameter required that indicates the heat extraction efficiency of a multilateral-well EGS. It is described as follows:

where d is the diameter shown in Fig. 1. λ (W/(m·°C)) denotes the heat conductivity of the three layers of the central tubing. h (W/(m2·°C)) is the convective heat transfer coefficient and is expressed as:

h=

(ρcp )eff = (1 − φ) ρs cp, s + φρf cp, f

3

where T1 and T2 (°C) are the temperatures of CO2 in central tubing and annulus, respectively. R1 ((m·°C)/W) is the thermal resistance [36,37] and is defined as:

R1 =

(14)

where (ρcp)eff and λeff are the effective volumetric capacity and the effective thermal conductivity, respectively, which are calculated by:

(5)

Q1 =

∂T + ρf cp, f u·∇T − ∇ ·(λ eff ∇T ) = 0 ∂t

(13)

3. A multilateral-well EGS case

where φ and μf (Pa·s) are the reservoir porosity and the fluid viscosity, respectively. k (m2) represents the rock matrix permeability. The item ρf g∇z indicates the effect of gravity. In this paper, a local thermal equilibrium model is used to describe the heat transfer in the geothermal reservoir. The energy conservation equation for the reservoir is

3.1. Computational model The computational model includes a 1D wellbore model and a 3D geothermal reservoir model, as shown in Fig. 3. The heat exchange 17

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simulations in representing a complex fracture network [42–45], which can efficiently forecast the production capability. The SRV is considered to be homogenous with a permeability that is the average permeability of the fractures and the rock matrix. Though the SRV model is simple, it is adequate to couple the wellbore model for predicting the CO2 wellbore temperature and pressure. The reservoir is a 1000 m × 1000 m × 1000 m cube and is located at a depth of 3000–4000 m. The SRV size is 500 m × 500 m × 500 m and is located at the center of the reservoir. The size of the reservoir is large enough to avoid boundary effects during the heat extraction period of interest [25]. The length and diameter of lateral wells are 150 m and 0.10 m. The vertical spacing between the injection and production wells is 400 m. Tables 1 and 2 list the parameters input in the 1D wellbore model and 3D reservoir model. 3.2. Initial and boundary conditions The CO2 temperatures in the central tubing and annulus are initialized at 40 °C for the 1D wellbore model. The annulus wellhead temperature and mass flow rate are set to 40 °C and 80 kg/s. The mass flow rate at the central tubing outlet remains constant at 80 kg/s. The temperature gradient of the surrounding formation is 0.05 °C/m with a ground temperature of 30 °C. The pressure at the annulus bottomhole is equal to the average pressure of the injection lateral wells which is calculated from the 3D reservoir model. The temperature and pressure at the bottom of central tubing are equal to the average temperature and pressure values of the production lateral wells obtained from the reservoir model. The initial temperature and pressure of the 3D reservoir model increase linearly from the surface along the boundary. The temperature and pressure at the top of the boundary are 190 °C and 30 MPa. The geothermal and pressure gradients are 0.05 °C/m and 5000 Pa/m. This model assumes that there is a cap rock above the reservoir. Therefore, the top boundary is considered to be insulated. A constant temperature condition is imposed on the bottom and side boundaries that utilizes the initial reservoir temperature. A no-flow condition is imposed at all boundaries. The mass flow rate of the injection lateral wells is fixed at 80 kg/s. The inlet temperature of the

Fig. 2. Comparison between simulation results and field data of HGP-A well [40,41].

between the annulus and formation in the 1D wellbore model is calculated by the term Q2 in Eq. (5). The heat exchange between the annulus and central tubing is obtained by Q1 in Eqs. (5) and (6). The temperature and pressure at the annulus bottomhole, central tubing bottomhole, and walls of the injection and production lateral wells in the 3D reservoir model are regarded as the data to couple the two models. The reservoir model consists of an enclosing rock, stimulated reservoir volume (SRV), six upper injection lateral wells, and six lower production lateral wells. The walls of the lateral wells are set as boundaries of the 3D reservoir model. The major focus of this paper is evaluation of CO2 wellbore fluid flow and heat transfer, rather than the heat extraction process in the geothermal reservoir. Therefore, to reduce the calculation complexity, the SRV is used to represent the fractured reservoir. The SRV model is widely used by numerical

Fig. 3. Schematic of the computational model. 18

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Table 1 Parameters of the wellbore model. Diameter (m)

Values

Heat conductivity (W/(m·K))

Values

Inner diameter of central tubing d1 Inner diameter of insulation layer d2 Outer diameter of insulation layer d3 Outer diameter of central tubing d4 Inner diameter of casing d5 Outer diameter of casing d6 Wellbore diameter d7

0.15 0.16 0.175 0.185 0.34 0.35 0.38

Central tubing inner layer λ1 Central tubing insulation layer λ2 Central tubing outer layer λ3 Casing λca Cement λce Formation λe Formation cp,e (J/(kg·°C))

43.5 0.026 43.5 43.5 0.7 2.4 900

Table 2 Reservoir model characterization properties. Items

Density (kg/m3)

Heat conductivity (W/(m·°C))

Heat capacity (J/(kg·°C))

Porosity (%)

Permeability (m2)

Enclosing rock SRV

2800 2700

3 2.8

1000 1000

1 15

10−18 2 × 10−15

injection lateral wells is equal to the annulus bottomhole temperature and is calculated from the 1D wellbore model. 3.3. Simulation mesh The meshing schemes are illustrated in Fig. 4. For the 1D wellbore, the edge is divided into 33 sections. For the 3D SRV, each lateral well is divided into 10 sections with triangular elements generated on the top surface. The mesh around lateral wells is refined. Next, the mesh on the top surface is swept along z-axis to the bottomhole surface to produce triangular prismatic elements. The number of sweep layers is 20. Finally, tetrahedral elements are generated for the enclosing rock using the free tetrahedral mesh method. Finer mesh is generated for the SRV compared to the enclosing rock since the heat extraction process mainly occurs in the SRV. To ensure that simulation results are mesh-independent, we investigate the outlet temperatures under various finite mesh numbers shown in Fig. 5. It can be observed that when the mesh number exceeds 50,000, the outlet temperature keeps nearly constant. Hence, a mesh scheme with around 60,000 elements is produced for the 3D reservoir domain and this results in an acceptable computational time and high accuracy. Lastly, a fully coupled solution approach is used to solve the mathematical equations in COMSOL.

Fig. 5. Outlet temperatures over 30-years production under various finite mesh numbers.

annular bottomhole temperature begins to noticeably decrease. The annulus wellhead pressure remains at 17.5 MPa during the entire production life whereas the annulus bottomhole pressure increases at the beginning of production and then remains constant at 44.5 MPa. This is due to CO2 accumulating in the formation around the injection lateral wells during the initial stages and leading to an increased bottomhole pressure. Fig. 7 plots the central tubing bottomhole and wellhead

4. Results and discussions 4.1. Analysis of temperature and pressure in wellbore Fig. 6 shows the annulus bottomhole and wellhead temperatures and pressures over 30-years of production. The annular bottomhole temperature decreases dramatically during initial production and then remains relatively constant. However, after 24 years of production, the

Fig. 4. Numerical meshing schemes. 19

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central tubing. The friction coefficients in the annulus and central tubing are similar. The CO2 density and heat capacity distributions along the annulus and central tubing after 30-years of production are shown in Fig. 10. The CO2 density increases gradually along the central tubing from the wellhead to well bottomhole, while the variation of CO2 density along annulus is very small. The CO2 density in the central tubing varies from 200 kg/m3 to 414 kg/m3, while the CO2 density in the annulus ranges from 812 kg/m3 to 869 kg/m3. Therefore, the large difference of CO2 density between the central tubing and annulus is believed to be the cause of differences in the pipe pressure losses. As a side note, Fig. 8 shows that the total pressure loss in the formation and central tubing is about 25 MPa. However, the pressure required to maintain circulation from pump is only 6.2 MPa. This is due to the CO2 buoyancy force generated by annulus and central tubing fluid density differences. It is found that the most efficient approach to minimize pressure loss in the central tubing is to increase the tubing size. Fig. 11 illustrates temperature distributions along the annulus and central tubing after 15 and 30 years. The annulus temperature increases linearly from the well head to bottomhole, whereas the temperature in the central tubing decreases dramatically from the bottomhole to surface. Fig. 12 demonstrates the output thermal power and heat flow rates between the central tubing, annulus and formation. The heat flow rate between the central tubing and annulus is very small and remains constant at about 0.77 MW, which validates the effectiveness of the central tubing heat insulation. Therefore, the central tubing temperature reduction is not caused by heat exchanges between the central tubing and annulus. This conclusion is further proven by calculating the outlet temperature assuming no heat exchange between the central tubing and annulus occurs (assuming the heat flow rate between the central tubing and annulus is 0 MW). The temperature results are shown in Fig. 13. The solid and dashed lines represent the central tubing wellhead temperature and bottomhole temperature. The outlet temperature is only 7 °C higher assuming no heat exchange compared to the base case. This scenario demonstrates that the heat exchanges between the central tubing and annulus have no correlation to the dramatic temperature reductions observed in Fig. 11. However, when pressure work is not considered (Fig. 13), the central tubing wellhead temperature reaches 271 °C (47 °C higher than the central tubing bottomhole temperature). The pressure work may be the cause of the large temperature reduction. This suggests that CO2 expansion from bottomhole to surface has a noticeable effect on the temperature distribution. Another challenge is determining why the central tubing’s wellhead

Fig. 6. Annulus bottomhole and wellhead 30-year production temperatures and pressures.

Fig. 7. Central tubing bottomhole and wellhead 30-year production temperatures and pressures.

temperatures and pressures over 30-years of production. The central tubing bottomhole and wellhead temperatures decrease gradually over time. After 24 years, the temperatures decrease rapidly due to thermal breakthrough in the geothermal formation. Thermal breakthrough indicates that the cooling region reaches the production lateral wells [25]. Also, the temperature difference between the central tubing wellhead and bottomhole is 78 °C. The reason for these large temperature differences will be discussed in the following sections. The central tubing bottomhole and wellhead pressure remain at 32.0 MPa and 11.4 MPa. From Figs. 6 and 7, the pressure difference between the annulus wellhead and central tubing wellhead is 6.2 MPa, which is the pressure required for a pump to maintain CO2 circulation. Fig. 8 compares pressure losses along the annulus, central tubing and formation to determine where the provided pump energy is consumed. The pressure losses along the central tubing and formation exceed 10 MPa, while the pressure loss along the annulus is close to 0 MPa. These pressure differences suggest that the pump energy is mainly consumed in the central tubing and the formation. The mass flow rates (80 kg/s) and hydraulic diameters in the annulus and central tubing are similar. However, the difference of pressure loss between the annulus and the central tubing is unexpectedly large. The annulus and central tubing frictional coefficients and CO2 densities are compared in an effort to explain these pressure differences. Fig. 9 illustrates friction coefficients at different production times along the annulus and the

Fig. 8. Formation, annulus and central tubing 30-year production pressure losses. 20

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Fig. 9. Annulus and central tubing friction coefficients at different times.

Fig. 11. Annulus and central tubing temperature distributions along the well length after 15 and 30 years.

Fig. 10. Annulus and central tubing CO2 density and heat capacity distributions along the well length after 30 years.

Fig. 12. Thermal power and heat exchange output between the central tubing, annulus and formation.

temperature is higher than the bottomhole temperature when pressure work is neglected. The solution is explained in Fig. 10. The CO2 heat capacity at the central tubing’s wellhead is 1470.55 J/(kg·K), which is noticeably lower than the central tubing’s bottomhole CO2 heat capacity. When the pressure work is omitted, there are negligible CO2 energy losses in central tubing. Thus, since the CO2 heat capacity at the wellhead is lower than the bottomhole CO2 heat capacity, the central tubing wellhead CO2 temperature should be higher than the associated bottomhole temperature. On the other hand, it can be concluded from Fig. 12 that before thermal breakthrough in the geothermal formation, the output thermal power of a multilateral-well CO2-EGS can be above 10 MW. The heat flow rate between the annulus and surrounding formation decreases significantly at the beginning of production and then remains almost constant at 0.58 MW. The initial high heat flow rate is caused by the large temperature difference between annulus and surrounding formation. This sharp reduction of high heat flow rate results in the dramatic decrease of annulus bottomhole temperature shown in Fig. 6.

4.2. Insulation of the central tubing In this section, the effect of the central tubing’s insulation length on multilateral-well EGS efficiency is studied. Fig. 14 shows the annulus and central tubing surface and bottomhole temperatures as a function of insulation length over 15 and 30-years production periods. As the insulation length increases, the annulus bottomhole temperature decreases and the central tubing wellhead temperature increases. When the entire central tubing is insulated, the outlet temperature improves significantly. Fig. 15 illustrates temperature distributions along the annulus and central tubing as a function of depth assuming various insulation lengths over 30-years of production. The temperature differences between the annulus and central tubing are minimal when no insulation is considered. There are multiple observations for the 1000 m case. The temperature profile at 1000 m depth has a discontinuity. No temperature reduction is observed within the insulation section (0–1000 m), whereas the region without insulation (1000–3300 m) exhibits a significant temperature drop. When the entire central tubing is insulated, the annulus temperature is significantly lower compared to the no insulation or insulation length of 1000 m cases. This suggests 21

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Table 3 The sizes of central tubing and annulus for different cases (unit: m). Cases

d1

d2

d3

d4

d5

d6

d7

1 2 3 4 5 6 7 8 9 10 11 12

0.15 0.16 0.17 0.18 0.15 0.15 0.16 0.17 0.18 0.17 0.18 0.19

0.16 0.17 0.18 0.19 0.16 0.16 0.17 0.18 0.19 0.18 0.19 0.20

0.175 0.18 0.19 0.20 0.17 0.17 0.18 0.19 0.20 0.19 0.20 0.21

0.185 0.19 0.20 0.21 0.18 0.18 0.19 0.20 0.21 0.20 0.21 0.22

0.34 0.35 0.37 0.39 0.35 0.38 0.34 0.35 0.36 0.34 0.34 0.34

0.35 0.36 0.38 0.40 0.36 0.39 0.35 0.36 0.37 0.35 0.35 0.35

0.38 0.39 0.40 0.43 0.39 0.42 0.38 0.39 0.40 0.38 0.38 0.38

that the central tubing should be completely insulated to maximize heat extraction efficiency. Fig. 13. Central tubing temperatures over 30-years of production assuming a base case, no heat exchange case, and no pressure work case.

4.3. Effect of wellbore size In this section, the effects of hydraulic diameters of the central tubing and annulus on multilateral-well EGS efficiency are investigated. The annulus hydraulic diameter is the difference between the inner and outer diameter. Table 3 lists the simulated tubing diameter cases. Cases 1 is the base case. Cases 2, 3 and 4 have large central tubing and annulus sizes. Cases 5 and 6 have the same size of central tubing, but different hydraulic diameters. Cases 7, 8 and 9 have the same size of annulus and different central tubing sizes. Cases 10, 11 and 12 have the same wellbore size as the base case, and variations in central tubing and annulus sizes. Fig. 16 illustrates the annulus and central tubing bottomhole and wellhead temperatures versus time. Fig. 17 shows the pressures after 30 years for cases 1, 2, 3, and 4. The annulus bottomhole and central tubing wellhead temperatures increase as the tubing size increases. However, the annulus bottomhole temperature changes are negligible. As the central tubing and annulus sizes increase, the pressure at the annulus wellhead remains nearly constant, while the central tubing wellhead pressure increases. For Case 4, the central tubing wellhead pressure is similar to the annulus wellhead pressure, which indicates that limited amount of pumping energy is required to circulate the injected CO2. Figs. 18 and 19 compare the tubing pressure losses and friction coefficients for cases 1, 2, 3, and 4. The pressure losses and friction coefficient decrease as both tubular sizes increase, but the variation trends in the central tubing are more noticeable compared to

Fig. 14. Annulus and central tubing bottomhole and wellhead temperatures as a function of insulation length over 15 and 30-years of production.

Fig. 15. Annulus and central tubing temperature distributions along the well depth over 30-years production assuming different insulation configurations.

Fig. 16. Cases 1, 2, 3, and 4 annulus and central tubing bottomhole and wellhead temperatures over 30-years of production. 22

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Fig. 17. Cases 1, 2, 3, and 4 annulus and central tubing pressures after 30-years production.

Fig. 20. Temperatures versus time at annulus bottomhole and central tubing wellhead for big size annulus.

improve outlet temperatures. Heat extraction efficiencies for Cases 5, 6, 7, 8 and 9 are studied to further contrast the importance of central tubing and annulus pipe size on multilateral-well CO2-EGS efficiency. Fig. 20 illustrates the tubing temperatures for cases 5 and 6. Both cases 5 and 6 exhibit nearly identical temperatures. Fig. 21 shows the annulus pressures, pressure losses and friction coefficients after 30 years for cases 5 and 6. The wellhead pressure comparisons are similar, whereas the pressure losses and friction coefficient for case 6 are lower. These results suggest that the annulus size has minimal effect on multilateral-well EGS efficiency. Fig. 22 plots the temperatures versus time for both tubing in cases 7–9. Fig. 23 shows the central tubing pressures, pressure losses and friction coefficients after 30 years for cases 7–9. As the hydraulic diameter of the central tubing increases, the wellhead temperature and pressure improve and pressure losses decrease significantly. The above studies advocate that a larger diameter central tubing is beneficial for multilateral-well EGS heat extraction efficiency. Thus, for the same wellbore size, if a larger diameter central tubing and a smaller diameter annulus are designed, the multilateral-well CO2-EGS efficiency may be dramatically enhanced. To demonstrate this hypothesis, the heat extraction efficiencies of cases 10–12 are compared. Fig. 24 plots the temperatures as a function of time at the annulus bottomhole and central tubing wellhead for cases 10–12. Fig. 25 shows the pressures and pressure losses after 30 years in the annulus and central tubing for cases 10–12. The outlet temperature for case 12 is 4.5 °C higher than case 10 and the central tubing pressure loss for case 12 is

Fig. 18. Cases 1, 2, 3, and 4 annulus and central tubing pressure losses after 30years production.

Fig. 19. Cases 1, 2, 3, and 4 annulus and central tubing frictional coefficients in after 30-years production.

variations trends in annulus. Based on these results, and according to the formula fq2/2dρAp2, an increase in tubing diameter is the key parameter in limiting pressure losses. It is also important to note that pressure work is mainly induced by the variation of pressure, meaning reduced pressure losses will alleviate pressure variation and reduce the pressure work. Therefore, increasing the central tubing diameter can

Fig. 21. Pressures, pressure losses and friction coefficients after 30 years in annulus for large diameter annuli. 23

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Fig. 25. Pressures and pressure losses after 30 years in central tubing for larger diameter central tubing and smaller diameter annulus.

Fig. 22. Temperatures versus time at annulus bottomhole and central tubing wellhead for big size central tubing.

validate that a larger diameter central tubing and small diameter annulus should be utilized in a multilateral-well CO2-EGS.

4.4. Comparison of different lateral-well configurations The previous study cited in this paper [25] detailed heat extraction efficiencies for upper injection and lower injection lateral-well configurations. That study used a geothermal reservoir model that assumed no wellbore fluid flow and heat transfer effects. The literature review concludes that wellbore thermal processes play an extremely important role in estimating multilateral-well CO2-EGS efficiency. Therefore, a more accurate comparison of heat extraction efficiencies for upper and lower injection lateral-well configurations has been conducted here based on a wellbore-reservoir coupled model. Fig. 26 is a schematic of the lower injection and upper production lateral-well configurations (the upper injection configuration is shown in Fig. 1). For the lower injection configuration, cooled CO2 is injected from the central tubing and lower injection lateral wells. After extracting heat from geothermal reservoir, the heated CO2 is produced from the upper production lateral wells and reaches the surface through the annulus. Additionally, the wellbore is insulated to minimize CO2 heat losses in the annulus. The outlet temperatures and output thermal power for the two lateral-well configurations are illustrated in Fig. 27. By using the lower

Fig. 23. Pressures, pressures losses and friction coefficients after 30 years in central tubing for large diameter central tubing.

Fig. 24. Temperatures with time at annulus bottomhole and central tubing wellhead for larger diameter central tubing and smaller diameter annulus.

2.451 MPa lower than case 10. For case 12, the pressure difference between the annulus and central tubing wellhead is only 0.13 MPa, which implies that additional energy is not necessary for maintaining multilateral-well EGS CO2 circulation. As a result, these cases further

Fig. 26. Schematic of lower injection and upper production lateral-well configurations. 24

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Fig. 27. Outlet temperatures and output thermal power with time for different lateral-well configurations. Fig. 29. Pressures with time for upper injection and lower injection lateral-well configurations.

Fig. 30. Pressure losses in annulus and central tubing with time for different lateral-well configurations.

Fig. 28. Temperature distributions along depth after 30 years for different lateral-well configurations.

well central tubing is much higher than the annulus tubing of lower injection configuration. This is due to pressure variations in the lower injection annulus being smaller than for the upper injection central tubing pressure variations (shown in Fig. 29). The pressure difference between the annulus bottomhole and wellhead for the lower injection configuration is 11.7 MPa, while the pressure difference between central tubing bottomhole and wellhead of upper injection configuration is 20.6 MPa. It can be seen from Fig. 30 that the pressure loss in the central tubing for the upper injection is much higher than the lower injection annulus pressure loss. It can be concluded from Fig. 29 that the pressure differences between the annulus and central tubing at the wellhead for the upper injection configuration and lower injection configuration are 6.2 MPa and 4.0 MPa. This suggests that the lower injection layout needs less energy to circulate CO2 than the upper injection scheme.

injection configuration, the outlet temperature and thermal power increase gradually with time over 25-years and then decline. This is because the production wells are located in the upper reservoir, whereas the CO2 is injected into the lower reservoir and flows up to the production wells. Consequently, the CO2 can be fully heated by the high temperature rock in the lower reservoir over 25-years. After that, the reservoir cooling region approaches the production wells and the production temperature declines. Also, both the outlet temperature and thermal power for the lower injection configuration are much higher than those for the upper injection configuration. For example, after 30 years, the outlet temperature and thermal power of lower injection configuration are 32.4 °C and 4.5 MW higher than those of upper injection configuration. Furthermore, thermal breakthrough in the lower injection configuration appears later than for the upper injection configuration. Therefore, we can conclude that the lower injection configuration has a higher heat extraction efficiency than the upper injection configuration. The temperature profiles, pressure, and pressure losses in the central tubing and annulus of the two lateral-well configurations are shown in Figs. 28–30. In Fig. 28, the temperature reduction in the upper injection

5. Conclusions In this paper, a coupled wellbore and reservoir fluid flow and heat transfer model is used to estimate multilateral-well CO2-EGS efficiency. 25

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The model is calibrated and validated with field data from the HGP-A well located in Hawaii. Multiple cases are analyzed using this model, considering the effects of CO2 pressure work on wellbore CO2 fluid flow and heat transfer, evaluating the differences in heat extraction using varying wellbore diameters and central tubing insulation lengths, and determining efficiencies for different injection-production well strategies. The key findings provide significant suggestions for multilateralwell CO2-EGS to obtain great heat extraction efficiency, which are as follows:

(Grant No. 2016YFE0124600 and 2018YFB1501804), the support provided from the Program of Introducing Talents of Discipline to Chinese Universities (111 Plan) (Grant No. B17045). References [1] Lund JW, Boyd TL. Direct utilization of geothermal energy 2015 worldwide review. Geothermics 2016;60:66–93. [2] Tester JW, Anderson BJ, Batchelor AS, Blackwell DD, DiPippo R, Drake EM, et al. Impact of enhanced geothermal systems on US energy supply in the twenty-first century. Philos Trans Roy Soc London A: Math, Phys Eng Sci 2007;365:1057–94. [3] Brown DW. A hot dry rock geothermal energy concept utilizing supercritical CO2 instead of water. In: Proceedings of the 25th workshop on geothermal reservoir engineering. Stanford University, pp. 233–8. [4] Pruess K. Enhanced geothermal systems (EGS) using CO2 as working fluid—A novel approach for generating renewable energy with simultaneous sequestration of carbon. Geothermics 2006;35:351–67. [5] Pruess K. 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• CO

•

• •

•

•

2 pressure work has a significant effect on the temperature distribution in the wellbore and induces a dramatic temperature difference between the central tubing at the wellhead and bottomhole. This means that a small pressure variation can alleviate the temperature reduction in the central tubing. Therefore, reducing pressure losses in the wellbore is a very efficient approach for improving the outlet temperature and heat extraction efficiency of a multilateral-well CO2-EGS. Also, the CO2 pressure work should be considered to accurately estimate the multilateral-well CO2-EGS efficiency. The pressure loss in a multilateral-well CO2-EGS occurs mainly in the formation and the central tubing. The central tubing pressure loss differs significantly from that in the annulus. These losses are mostly attributed to CO2 density differences in the central tubing and annulus. In addition, it is found that the difference of CO2 density in the central tubing and the annulus induce a buoyancy force that provides energy needed to maintain CO2 circulation. The three-layer central tubing design that is suggested has a significant heat insulation effect. As the insulation length increases, the outlet temperature improves significantly. These results point to a completely insulated central tubing for an optimal heat extraction efficiency. The hydraulic diameter of the central tubing has a significant effect on the heat extraction efficiency of the multilateral-well CO2-EGS, whereas the annulus hydraulic diameter does not. As the hydraulic diameter of the central tubing increases, the pressure losses decrease significantly, and the central tubing wellhead pressure and temperature improve dramatically. When the hydraulic diameter of the central tubing is increased sufficiently, the central tubing wellhead pressure is close to the annulus wellhead pressure, which indicates that additional energy is not needed for maintaining CO2 circulation. Therefore, for the same wellbore diameter, a larger diameter central tubing and a smaller diameter annulus should be considered for a multilateral-well CO2-EGS. Compared to the upper injection configuration, the lower injection configuration has a higher outlet temperature and output thermal power, with reduced pressure loss. Thermal breakthrough for the lower injection configuration occurs later than for the upper injection configuration. Therefore, a lower injection and upper production configuration is more appropriate for a multilateral-well CO2EGS. The simulation results shed light on the importance of CO2 wellbore fluid flow and heat transfer processes in multilateral-well CO2-EGS. In future studies, based on the presented numerical model, operational multilateral-well EGS parameters, such as inlet temperature, injection mass flow rate and production pressure, will be considered and optimized to obtain greater heat extraction efficiencies. Comparisons of heat extraction efficiencies, with the inclusion of wellbore effects, of multilateral-well water-based EGS and CO2-EGS will also be compared.

Acknowledgements The authors would like to acknowledge the National Natural Science Funds for Excellent Young Scholars of China (Grant No. 51822406), National Key Research and Development Program of China 26

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