A downhole heat exchanger for horizontal wells in low-enthalpy geopressured geothermal brine reservoirs

Geothermics 53 (2015) 368–378

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A downhole heat exchanger for horizontal wells in low-enthalpy geopressured geothermal brine reservoirs Yin Feng 1 , Mayank Tyagi ∗ , Christopher D. White 2 Craft & Hawkins Department of Petroleum Engineering, Louisiana State University, United States

a r t i c l e

i n f o

Article history: Received 22 August 2012 Accepted 16 July 2014 Keywords: Low-enthapy geothermal resource Downhole heat exchanger Force convection Binary power plant Organic rankine cycle

a b s t r a c t Geothermal energy is a clean, renewable energy resource that is widely available and reliable. Improved drilling and heat conversion systems make geothermal energy an increasingly attractive alternative. Downhole heat exchangers (DHEs) can accelerate the development of geothermal energy by reducing the capital cost and the risk of microquakes or subsidence. However, low-enthalpy geothermal resources are difficult to develop economically because of low heat extraction efficiency. In this study, a coaxial DHE concept is proposed to exploit forced convection driven by a downhole pump inside a horizontal wellbore. Two configurations of the proposed design are introduced, each having different flow paths for working and reservoir fluids. One system – which circulates working fluid through the inner-most tubing in the coaxial arrangement has better thermal exchange efficiency of about 29%, and is evaluated by coupling it to a simple model for a binary power generation plant and a geothermal reservoir simulator. Thermodynamic analysis evaluates the DHE performance for electricity generation. A field case study of the Camerina A reservoir (Vermillion Parish, Louisiana) demonstrates a net power of about 350 kW can be generated by a turbine even after 30 years of production. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction Geothermal energy is attractive due to its enormous potential (MIT Report, 2006; Cutright, 2009), renewability (Rybach, 1999, 2007), availability (U.S. DOE, 2005), low emission potential (Bloomfield et al., 2008), and low levelized costs (Cutright, 2009). According to Cutright (2009), with improvements in technologies including drilling, completion, and binary cycle power plants and relatively high petroleum prices, geothermal energy is becoming an economically viable alternative. Nonetheless, many challenges remain. High capital requirements have impeded geothermal resource development in the past. The required investment could be 3000–4000 per kW for hydrothermal resources, in which 47% is invested in the power plant and 42% is spent on drilling wells (U.S. DOE, 2009). Hydraulic fracturing, reinjection, depletion, and thermal stresses may induce seismicity or subsidence in the formation (Majer, 2009). Produced brine needs to be reinjected rather

∗ Corresponding author. Tel.: +1 2255786041. E-mail address: [email protected] (M. Tyagi). 1 Now at Department of Petroleum Engineering, University of Louisiana at Lafayette, United States. 2 Now at Department of Earth and Environmental Sciences, Tulane University, United States. http://dx.doi.org/10.1016/j.geothermics.2014.07.007 0375-6505/© 2014 Elsevier Ltd. All rights reserved.

than disposing to surface waters to avoid any environmental impacts (John et al., 1998). Water disposal further increases capital and maintenance costs. Because of high capital costs, geothermal projects must provide sustained power over many years (Rybach, 2007). A downhole heat exchanger (DHE) reduces construction costs by eliminating surface facilities and dedicated injectors for brine disposal (Lund, 2003). The proposed single-bore DHE configuration avoids surface handling of geofluids and disturbs the reservoir chemo-poromechanical equilibrium minimally to further reduce the risks of any associated geomechanical problems. Several designs for downhole heat exchangers have been proposed. However, downhole heat exchangers in vertical wells may perform poorly because of the poor thermal coupling between the wellbore and the formation and the absence of free convection in the reservoir (Nalla et al., 2004). In another coaxial design with two concentric annuli between the tubing, an inner insulated casing and the outer casing in a vertical configuration (Alkhasov et al., 2000), hot water was injected through the tubing and working fluid was injected into the outer annulus and returned to the surface through the middle annulus. Wang et al. (2009) proposed a single-well EGS configuration with a thermosiphon, in which thermally induced density differences between the wellbore and reservoir fluids drive convection. The heat extraction efficiency was further enhanced by free convection in fractures. Feng et al.

Y. Feng et al. / Geothermics 53 (2015) 368–378

(2011) included natural convection in their model for heat extraction with a DHE in a horizontal well. The DHE was approximated as a line sink with a linearly varying temperature along the well, and the DHE burial location and its length were optimized. This paper introduces a DHE design for saturated geothermal reservoirs to improve heat extraction and sustainability. The proposed design uses forced convection through the horizontal wellbore heat exchanger. One benefit is that the forced geofluid circulation delivers more heat to the DHE, enlarges the thermal extraction volume and increases the profitable life of the geothermal project. The forced convection within the DHE also increases heat exchange efficiency between the working fluid and the reservoir fluid.

2. Proposed downhole heat exchanger configurations The DHE design that is proposed in this article exploits improvements in directional drilling and well completions. Horizontal or deviated wells can access geofluids from the highest enthalpy region of a geothermal reservoir. Current completion techniques and downhole equipment make a coaxial DHE possible in a horizontal section of the well, and an electric submersible pump can be placed inside the wellbore to drive the geofluid and increase heat exchange to the working fluid. A deviated well exits the overburden and follows a (nearly) horizontal path within the reservoir. A coaxial DHE is placed inside the horizontal section of the wellbore, and forms three fluid pathways (Fig. 1). Two paths circulate the

369

working fluid, and the third path is used to transport the geofluid between production and re-injection completion intervals. The proposed design can be configured in two ways: the geofluid can travel through the tubing (geofluid through tubing, indicated as G, Fig. 2a); or the working fluid can be injected through the tubing (working fluid through tubing; indicated as W, Fig. 2b). The return path for the working fluid is insulated to reduce heat loss to the working fluid injection path. In either configuration, the geofluid is injected into the reservoir away from the heat exchanger using the pressure head from a downhole pump.

2.1. Geofluid through tubing: description and analysis The geofluid enters the tubing through a cross-over at the heel of the deviated wellbore (the end nearest the wellhead or the dog-leg kickoff location), flows through the heat exchanger, and is reinjected into the reservoir at the wellbore toe, some distance away from the DHE. Radial paths in the cross-over (Fig. 3) allow geofluid to enter the tubing from the reservoir; the tubing insulation should decrease heat transfer between the hot, returning working fluid and the relatively low temperature, injected working fluid. The axial holes at different azimuthal locations could provide paths for the working fluid to flow into the outer annulus and out of the inner annulus of the coaxial DHE. The working fluid is injected into the outer annulus (Annulus II), and exchanges heat from the reservoir via conduction as it flows along the DHE length. The outer casing (Casing II) and surrounding

Fig. 1. Schematic of wellbore paths and DHE cross-section (Tyagi and White, 2010).

Fig. 2. Schematics of two configurations for the DHE: (a) G and (b) W.

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with two boundary conditions: Ta1 (L) = TL Tt (0) = Te For Eq. (6), the analytical solution is Ta1 = C1 + C2 erx

(7)

where r= Fig. 3. Schematic of a cross-over to provide radial/axial distribution of fluid in different flow paths of DHE.

cement should be designed to maximize conduction. The working fluid reverses direction and returns through the inner annulus (Annulus I) at the well toe (that is, the end of the horizontal section furthest from the wellhead). In the return flow path, the working fluid is heated by the geofluid flowing inside the tubing. The inner casing (Casing I) could also be insulated to decrease heat losses between the flow paths of working fluid. For typical rates and dimensions for geothermal reservoir completions, convection controls the rate of heat exchange in the wellbore, and the timescale for intrawellbore heat transfer is much faster than for the reservoir. For the small time intervals used to compute DHE performance, one can therefore, assume steady state conditions in the reservoir and derive simplified heat transfer equations. Tubing :

˙ g Rat Ta1 = cg m

dT t + Tt dx

dT a1 Ta1 − Tt = Rat dx

Innerannulus :

˙w cw m

Outerannulus :

dT a2 Te − Ta2 ˙w cw m = Rfa dx

(1) (2)

Ta2 (x) =

Ti + (e

− 1)Te

ex/cw mw Rfa

Ti + (eL/cwf m˙ wf Rfa − 1)Te eL/cw mw Rfa

C2 =

TL − Te ˙ wf r + erL − 1 Rat cwf m

Thus, the working fluid temperature at the outlet of the DHE (crossover end) is: Tout = Ta1 (0) = C1 + C2

(8)

2.2. Working fluid through tubing: description and analysis As indicated in Fig. 2b, the geofluid circulates through the outer annulus (Annulus II) driven by a downhole pump. The working fluid is injected into the DHE from the tubing and returns through the inner annulus (Annulus I). The tubing is insulated to reduce heat losses from the output to the input working fluid stream. Based on the similar assumptions to the configuration, G, the analytical solution is derived as follows. Inner annulus: dT a1 Ta1 − Ta2 = Raa dx

(9)

Outer annulus:

(4)

˙ gf cgf m

dT a2 Te − Ta2 Ta1 − Ta2 = + Rfa Raa dx

(10)

By combining above two equations, we have a second-order ODE (notice that B2 − 4AC is always greater than zero for positive mass flow rates). AT a1  + BT a1  + CT a1 + Te = 0

(11)

where ˙ gf cwf m ˙ wf A = Raa Rfa cgf m ˙ wf + Raa cwf m ˙ wf − Rfa cgf m ˙ gf B = Rfa cwf m C = −1 with two boundary conditions: Ta1 (L) = Ti Ta2 (0) = Te For the above-stated equation, an analytical solution can be obtained by assuming constant thermal properties and applying the boundary conditions.

(5)

where L is the length of DHE and TL is the working fluid temperature at the end of Annulus II. Second step: By combining Eqs. (1) and (2), we have the expression for Ta1 : ˙ gf cwf m ˙ wf Ta1  + (cwf m ˙ wf − cgf m ˙ gf )Ta1  = 0 Rat cgf m

C1 = TL − C2 erL

(3)

and, TL =

and, the integration constants are:

˙ wf cwf m

˙ R, A and  indicate temperature, specific thermal where T, c, m, capacity, mass flow rate, thermal resistance, cross-sectional area, and density respectively. The subscripts g, w, t, a1, and a2 represent geofluid, working fluid, tubing, inner annulus and outer annulus, respectively. The lumped thermal resistances (e.g., Rat ) are defined in Appendix A. An analytic solution for heat exchange in a DHE can be derived with three further assumptions: (1) the casing separating the inner and outer annuli is a perfect insulator; (2) material properties such as heat capacity and conductivity are constant; and (3) the reservoir temperature Te remains constant at these time scales (this assumption can be relaxed later, see Section 5). The solution is in terms of ratios of exponential functions shown as follows. First step: By integrating Eq. (3) with the boundary condition of Ta2 (0) = Ti , the expression of Ta2 temperature vs. distance x is obtained as: ˙ wf Rfa x/cwf m

˙ gf − cwf m ˙ wf cgf m ˙ gf cwf m ˙ wf Rat cgf m

(6)

Ta1 = C1 er1 x + C2 er2 x + Te where r1 = r2 =

−B + −B −



B2 − 4AC 2A



B2 − 4AC 2A

(12)

Y. Feng et al. / Geothermics 53 (2015) 368–378 Table 1 Baseline parameters for sensitivity study.

371

(a) geofluid through tubing

(b) working fluid through tubing

150 temperature °C

geofluid in tubing

Reservoir properties Rock density Heat conductivity Temperature

−3

2700 kg m 1.9 W m−1 K−1 149 ◦ C

DHE geometry Length (baseline) Outer casing OD, ID Inner casing OD, ID Tubing OD, ID Heat conductivity

305 m 21.91, 19.37 cm 16.83, 15.36 cm 12.70, 10.86 cm 45 W m−1 K−1

Working fluid (n-butane) properties Density Heat conductivity Specific thermal capacity Viscosity Injection temperature Mass flow rate

582 kg m−3 0.107 W m−1 K−1 2763 J kg−1 K−1 1.7 × 10−4 Pa s 32 ◦ C 5.25 kg s−1

Geofluid (water) properties Density Heat conductivity Specific thermal capacity Viscosity Mass flow rate

1000 kg m−3 0.519 W m−1 K−1 3182 J kg−1 K−1 1.1 × 10−4 Pa s 2.34 kg s−1

geofluid in outer annulus

120 90

wo rk

work in

g, in

ner

60 kin wor

30 0

g flu

id in

r oute

ulus ann

100 200 length (m)

300

ing

flui d

in i

nne

r an

nul us working fluid in tubing

0

100 200 length (m)

300

Fig. 4. Temperature variation along flow path in the DHE for different configurations [lines: analytical solution; symbols: numerical solution].

3. Parametric sensitivity study Several sensitivity studies examine the DHE performance and use the operating conditions in Table 1 as a baseline. Heat exchanger length, working fluid mass flow rate, and geofluid mass low rate are varied here. 3.1. Exchanger length

and, integration constants are: C1 = ˛ C2 =

Ti − Te ˛er1 L + er2 L

The outflow temperature of the working fluid in the DHE increases with the DHE length, because a longer DHE provides a larger heat exchange area: as length quadruples from 152.5 to 610 m, the outlet working fluid temperature increases by 22 ◦ C for configuration G and by 30 ◦ C for W (Fig. 5).



Ti − Te ˛er1 L + er2 L

 ˛=



˙ wf r2 1 − Raa cwf m



3.2. Working fluid mass flow fate

˙ wf r1 − 1 Raa cwf m

Then, the working fluid temperature at the outlet of the DHE is: Tout = Ta1 (0) = C1 + C2 + Te

(13)

2.3. Comparison of heat extraction rates for different configurations The numerical solution for flow and heat transfer within the reservoir is coupled to the DHE using discretized versions equations (Eqs. (14) and (15) are for the configuration, W). The assumed working fluid is n-butane (Dolan and Sage, 1964; Carmichael et al., 1963; Kay, 1940), pure water properties are used for simplicity, and rock properties are summarized in Table 1. The thickness of the insulation is assumed to be negligible. Inner annulus: ˙ wf cwf m

Ta1,i − Ta2,i Ta1,i+1 − Ta1,i−1 = Raa 2x

(14)

3.3. Geofluid mass flow rate

Outer annulus: ˙ gf cgf m

Te,i − Ta2,i Ta1,i − Ta2,i Ta2,i+1 − Ta2,i−1 = + Rfa Raa 2x

The rate of heat extraction by the working fluid in the DHE is out − T in ). Therefore, for a given injection temperature, a ˙ w cw (Tw m w reduction in the outlet temperature alone does not determine the overall exchanged heat. As the mass flow rate increases from 2.63 to 10.5 kg s−1 , the outlet working fluid temperature decreases by 35 ◦ C for configuration G and by 67 ◦ C for configuration W (Fig. 6), thus lowering the specific enthalpy carried by the exiting working fluid. However, with increasing working fluid flow rate, the total enthalpy extraction rate increased by 0.57 MW for G and by 0.63 MW for W. The heat extraction rate is about 7% higher for configuration W compared to G for working fluid flow rates between 4 and 15 kg s−1 . For working fluid mass flow rates above 24 kg s−1 , the heat extraction rate for configuration G is about 1% higher than for configuration W. However, the higher parasitical load of pumping at higher rates and the lower binary cycle efficiency for lower exiting working fluid temperatures might well offset such minor gains (MIT Report, 2006), and the configuration, W, is thus chosen for further analysis (Fig. 7).

(15)

The working fluid temperature at the DHE outlet (crossover end, at the heel of the well) of configuration G (113 ◦ C) is lower compared to the exit temperature for W (122 ◦ C), implying a lower amount of heat extracted for configuration G (Fig. 4). Furthermore, in configuration G, heat extracted from the rock and geofluid are 54 and 46%, respectively. However, for the W configuration, the corresponding percentages are 37.5 and 62.5%. The difference in enthalpy extraction leads to a geofluid reinjection temperature of 40 ◦ C for W, compared to 76 ◦ C for G.

A higher geofluid mass flow rate can also increase the exiting fluid enthalpy rate by increasing the convective heat transfer coefficients between the outer annulus and the outer casing (and thus the reservoir, increasing conductive heat transfer to the well) and between the geofluid and the returning working fluid (that is, between the inner annulus and the tubing). However, the power requirements for the downhole pump in this geofluid flow path could also be high, especially for low permeability geothermal reservoirs. A fourfold increase in the geofluid mass flow rate (from 1.17 to 4.68 kg s−1 ) increases the outlet working fluid temperature by almost 50 ◦ C for both configurations, and the enthalpy rate

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Fig. 5. Temperature variation for three heat exchanger lengths. (a) For configuration G, the working fluid is warmed in the annulus by convection. For longer DHE lengths, further heating of the working fluid occurs only near the brine inlet near the heel of the well. (b) For configuration W, the tubing is insulated so that there is no warming of the working fluid until it reaches the toe of the well and reverses into the inner annulus.

temperature (°C)

120

90

working fluid in inner annulus

(a) configuration G, geofluid through tubing 150

brine

in tu

(b) configuration W, working fluid through tubing ⋅ kg s−1 m w

bing

⋅ kg s−1 m w 2.63

2.63

br in

5.25

60

e in

out

5.25

er a

nnu

lus

10.5 10.5

g workin

30

ou fluid in

ulus ter ann

workin g

fluid in

inner

annulu

s

working fluid in tubing

0

50

100

150 200 length (m)

250

300

0

50

100

150 200 length (m)

250

300

Fig. 6. Temperature variation for three working fluid mass flow rates [10.5, 5.25 and 2.63 kg s−1 ].

increases by about 70% (Fig. 8). The heat extraction rate increases ˙ ≈ 5 kg s−1 and H˙ ≈ 1 MW for both configurations, rapidly until m before reaching a plateau of approximately 1.6 MW at flow rates of ca. 20 kg s−1 . Parasitic power requirements, injectivity, and productivity in complex well completions might make it difficult to achieve very high geofluid rates (Fig. 9). 4. Thermodynamic analysis for the power generation with a downhole heat exchanger

(states 6–7). n-butane is then condensed (states 7–8) and is injected into the DHE. The thermodynamic analysis uses equations from Appendix B (Yari, 2010) and procedures from Appendix C (Dipippo, 2008). The assumptions are: (1) the power plant is operating at steady state; (2) pressure losses in surface pipes and the condenser are negligible; (3) kinetic and potential energy changes within the surface facilities are negligible. Enthalpy and entropy are estimated from an n-butane thermodynamic chart. The exergy rate is ˙ w [h − h0 − T0 (s − s0 )] . E˙ = m

Binary power plants are more efficient for low- or medium- temperature resources (Dipippo, 2008), and are included in the analysis by coupling a thermodynamic model of the binary power plant with the DHE (Fig. 10). The working fluid is n-butane in this organic Rankine cycle (Lakew and Bolland, 2010). This analysis uses the working fluid through the tubing (W) configuration. The working fluid is injected into the tubing as a liquid (state 1), and remains in the liquid phase through the DHE (states 2–4). The pressure decreases along the return path in the inner annulus, and drops below the vapor pressure (state 5), so that n-butane vapor flows to the surface to drive the turbine and generate electricity

Results are summarized in Table 2. The turbine outlet pressure of 0.3 MPa ensures that the working fluid remains in the vapor phase. A pump may be required to increase pressure from state 8 to state 1. The net power generated by the turbine is 357 kW. If the isentropic efficiency of the feed pump is assumed to be 75% and the working fluid mass flow rate is 5.25 kg s−1 , the electrical power for a pump will be about 1.1 kW. The turbine efficiency using exergy analysis is approximately 88% and the fluid pump efficiency remains around 100%. The overall thermodynamic efficiency for the DHE is about 29%.

Y. Feng et al. / Geothermics 53 (2015) 368–378

373

Table 2 Thermodynamic properties with state numbers referring to Fig. 10. State no.

Temperature T (◦ C)

Pressure P (MPa)

Enthalpy h (kJ/kg)

Entropy s (kJ/kg◦ K)

Exergy rate E˙ (kW)

0 1 2 3 4 5 6 7s 7 8

25 32 32 32 110 110 110 61 67 32

0.1 0.4 13.2 13.2 13.1 1.85 1.43 0.3 0.3 0.3

328 −23 −16 −16 188 431 453 386 396 −23.2

5.32 4.02 3.97 3.97 4.57 5.27 5.36 5.36 5.39 4.02

0 191.1 306.1 306.1 438.4 619 593.7 241.9 247.8 189.9

W 1.6 G

⋅ heat extraction rate H (MW)

⋅ heat extraction rate H (MW)

1.5

1.0

0.5

1.4 W 1.2 G 1.0

0.8 0.0 0

10 20 30 ⋅ (kg s−1) working fluid flow rate m w

40

0

Fig. 7. Heat extraction rate against working fluid flow rate.

The downhole heat exchanger is evaluated using the properties of a potential geothermal resource in the geopressured brine reservoir, the Camerina A sand near the Gueydan Salt dome in

temperature (°C)

120

90

working fluid in inner annulus

(a) configuration G, geofluid through tubing

br in

(b) configuration W, working fluid through tubing 4.68

e in

tub

⋅ kg s−1 m w

br

ing

⋅ kg s−1 m g

in

e

in

ou

2.34

4.68

te

ra

nn ul

us

2.34 1.17 1.17

wor k

60 wor

king

in fluid

r oute

ulus ann

30

ing

fluid

in in

ner

ann ulu

s

working fluid in tubing

0

50

100

150 200 length (m)

250

20

Fig. 9. Variation of rate of enthalpy extraction for varying woking fluid rates. At low working fluid rates, performance is identical, as both configurations heat the working fluid to very near the reservoir temperature and the extracted enthalpy varies linearly with the working fluid rate. The working fluid through the tubing (W) configuration performs slightly better in the transition range, until both systems plateau for rates greater than ca. 20 kg s−1 .

5. Field case study – Camerina A

150

5 10 15 ⋅ (kg s−1) geofluid flow rate m g

300

0

50

100

150 200 length (m)

250

Fig. 8. Temperature variation along flow path in DHE for different geofluid (brine) mass flow rates [4.68, 2.34 and 1.17 kg s−1 ].

300

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Y. Feng et al. / Geothermics 53 (2015) 368–378

Fig. 12. Sketch of the x–z plane for the computational Camerina A model.

Table 3 Parameters for the computational model.

Fig. 10. Schematic of a binary cycle with a DHE. The circled numbers correspond to the states in Table 2. The geofluid flow path is from a to b.

Reservoir Rock density Heat conductivity Geothermal gradient Permeability Porosity Dip angle Thickness Width × length

2700 kg m−3 1.9 W m−1 ◦ C 28 ◦ C km−1 200 mD 0.20 5◦ 100 m 2000 m × 2000 m

Geofluid Density Heat conductivity Specific thermal capacity Viscosity

1000 kg m−3 0.649 W m−1 ◦ C−1 3726 J kg−1 ◦ C−1 3 × 10−4 Pa s

Reservoir simulations use a geothermal simulator (Feng, 2012) based on the open-source Cactus computational toolkit. The numerical procedure is similar to the approach of Feng et al. (2011), which examined natural convection and modeled the DHE as a linear heat sink with the geofluid inlet at one end and the geofluid outlet at the other end. After each timestep, the geothermal reservoir simulator updates the reservoir temperature and thus the boundary condition for the heat transfer for the DHE (i.e., Te ). In contrast to Feng et al. (2011), steady-state DHE equations (presented in this article) are used to couple the heat exchange between the well and reservoir, because convection-driven temperature evolution in the DHE is much faster than in the reservoir (Fig. 12). The Camerina A reservoir is idealized as an inclined rectangle. The bounding shales are modeled as 200 m thick layers above and below the permeable reservoir interval, which is 100 m thick. The bounding layers contribute heat to the reservoir by conduction only. The average temperature in the reservoir is 142 ◦ C. This study varies the distance between the DHE and geofluid injection completion and the dip angle to assess DHE performance for analogs of the Camerina A reservoir. The parameters corresponding to the simulation are summarized in Table 3 (Gray, 2010). 5.1. Reinjection distance

Fig. 11. 100 ◦ C isotherm map of the study area (Szalkowski and Hanor, 2003).

Vermillion Parish, Louisiana (Fig. 11). According to Gray (2010), salt domes in South Louisiana may serve as heat conduits that increase the temperature of relatively shallow saline aquifers, increasing their potential as a geothermal resource; the Camerina A sand is an example of such a reservoir. Kehle (1972) estimated temperatures for the Camerina A to be between 128 and 160 ◦ C, implying that the Camerina A is a low-enthalpy geothermal reservoir.

In configuration W, the hot geofluid enters the outer annulus and transfers heat to the working fluid in the inner annulus, and is then injected into the reservoir at the geofluid outlet. The relatively cool injected geofluid flows through the reservoir, displacing hot geofluid toward the DHE geofluid inlet and also regains some heat from the reservoir rock. If geofluid injection is moved farther from the DHE, the geofluid residence time increases, which heats the geofluid longer and increases the thermally swept volume of the reservoir. The injection interval can also be extended to decrease the work required for reinjection (Fig. 13). The working fluid exit temperature falls by 15–20 ◦ C over the 30-year project life (Fig. 14). The working fluid temperature is relatively stable after the first 5 years. The proposed configuration uses insulated tubulars to transport the working fluid to the surface, and the analysis assumes zero heat loss so that the DHE

Y. Feng et al. / Geothermics 53 (2015) 368–378

375

Fig. 13. Downhole heat exchanger with an offset geofluid injection interval. This configuration transports the cooled brine further from the geofluid inlet, delaying thermal breakthrough. The parametric study used an offset of 500 m, with an injection interval of 500 m. Fig. 15. Working fluid temperature variation vs. time for different dip angles and geofluid flow directions, where DA represents dip angle; U and D are defined as up dip and down dip, respectively.

This temperature difference is equivalent to 36 kW of thermal power and about 11 kW of electricity. As production continues, the temperature difference increases, which indicates that offsetting the injection interval improves sustainability. 5.2. Dip angle

Fig. 14. Working fluid temperature variation vs. time for different reinjection distance, where RD is defined as reinjection distance.

working fluid outlet temperature is equal to the binary power plant inlet temperature. The state of this fluid is used to compute power output (Appendix C). After 30 years, the working fluid temperature at the outlet of the DHE with a 500 m offset injection interval is about 2.5 ◦ C higher than the zero-offset case (Fig. 14).

The performance of DHE in geothermal reservoirs with various dip angles is also analyzed. The dip angle in Camerina A varies between 1.2◦ and 28◦ (Gray, 2010), and the comparison considers three dip angles (0◦ , 5◦ , and 28◦ ) and two directions of geofluid reinjection injection-production configurations. In the downdip configuration, geofluid is trasported downward from the production interval to the production inverval via the DHE, offset, and injection interval. The flow direction is reversed for the updip configuration: injection is at the updip end of the well. The downdip fluid is hotter, so that the updip configuration will access higher-temperature fluid for the DHE. Fig. 15 shows a comparison of the above-stated scenarios starting with the same temperature baseline in the permeable layer. Up

Fig. 16. Temperature contours of the 2D x–z plane in the middle of the 3D system (y = 1000 m) containing the DHE [top: 0◦ ; middle: 5◦ ; bottom: 28◦ and left: down dip; right: up dip], where the solid line represents the DHE section and the geofluid is reinjected through dash line further away.

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dip scenarios can extract more heat from the geothermal reservoir because the hotter geofluid is produced inside the wellbore and brought in contact with the DHE. Schematics for each scenario are shown in Fig. 16 where the solid line represents the location of DHE inside the wellbore and the dashed line denotes the extended wellbore section for the reinjection of the cooler geofluid further away from the DHE. Although updip injection has higher heat extraction rates for the modeled rates and project life, downdip injection may have advantages for different reservoir, well, or project parameters. The injected geofluid is cooler and thus denser, so that gravity provides a downward driving force. In downdip injection the density contrast transports the cooled geofluid away from the the heat exchanger inlet, whereas in updip injection the density contrast transports the cooled geofluid downdip toward the heat exchanger inlet. This free convection in the reservoir could delay thermal breakthrough and prolong economically viable production for some projects.

tubing and the Annulus I, both conduction and convection modes are considered, and the thermal resistances are the results of parallel connection of both conduction and convection effects. The following equation represents the overall thermal resistance:

6. Conclusions

where

A downhole heat exchanger is proposed to eliminate surface handling of produced geofluids, lower injection costs, and reduce risk of induced seismicity. With the advances in directional drilling technology and improvements in the well construction tubulars, a long coaxial heat exchanger can be placed in the horizontal section of wellbores. Placing the heat exchanger near the reservoir improves heat exchange efficiency and minimizes heat losses. Of the two downhole heat exchanger configurations examined in this article, the configuration injecting the working fluid through the innermost flow path (the tubing) has a higher heat extraction rate than the configuration with produced geofluid flowing through the tubing. A field case study evaluates downhole heat exchangers using the reservoir properties of the Camerina A geothermal reservoir. A coupled wellbore-reservoir simulation models heat extraction for the designed operation life of 30 years. Injecting cooled geofluid into the same reservoir through a completion offset away from the heat exchanger increased heat extraction rates for the designed project life while producing about 350 kW through the operation.

Rat = +

1 + Rcond,tubing (1/Rcond,t ) + (1/Rconv,t ) 1 (1/Rcond,a1 ) + (1/Rconv,a1 )

(A.1)

where the subscripts t, tubing, a1, cond, and conv represent inside tubing, tubing, Annulus I, conduction and convection. Due to the high flow rates inside the pipes, the overall heat transfer is dominated by convection. Rcond magnitude is larger compared to Rconv due to the flow inside the tubing and the Annulus I. The above-stated equation can be further simplified as: Rat = Rconv,t + Rcond,tubing + Rconv,a1

(A.2)

1 1 1 = = dti ht Nut kt dti (Nut kt /dti ) rto 1 ln(rto /rti ) Rcond,tubing = dr = 2rktubing 2ktubing rti 1 1 1 dc1i − dto = = Rconv,a1 = dto ha1 Nua1 ka1 dto dto (Nua1 ka1 /dc1i − dto ) Rconv,t =

A.2. Annulus I–Annulus II Similar to tubing-Annulus I, for Annulus I-Annulus II, we have Raa = Rconv,a1 + Rcond,c1 + Rconv,a2

(A.3)

where 1 1 1 dc1i − dto = = dc1i ha1 Nua1 ka1 dc1i dc1i (Nua1 ka1 /dc1i − dto ) ln(rc1o /rc1i ) = 2kc1 dc2i − dc1o 1 1 1 = = = dc1o ha2 Nua2 ka2 dc1o dc1o (Nua2 ka2 /dc2i − dc1o )

Rconv,a1 = Rcond,c1 Rconv,a2

Acknowledgments

A.3. Annulus II-formation

Authors would like to acknowledge the support provided through a grant from the Department of Energy, Geothermal Technologies Program (DOE-GTP) (DE-FOA-000336) award. The authors thank the Center for Computation & Technology (CCT) and the Craft & Hawkins Department of Petroleum Engineering (Louisiana State University) for the computational resources provided to conduct this research. One of the authors (CDW) thanks Chevron for the support provided through a professorship.

A significant difference for Annulus II-formation thermal resistance compared to other resistances is that the heat transfer from the formation to casing II may not be dominated by convection due to the slower flow rates in the porous media. The following thermal resistance equation shows the contributions from various components:

Appendix A. Concept of thermal resistance

where

By employing thermal resistance definitions (Bauer et al., 2010), the overall thermal resistance can be divided into three components: tubing-Annulus I, Annulus I–Annulus II, and Annulus II-formation. A.1. Tubing-Annulus I The thermal resistance between tubing and Annulus I can be further divided into three serially connected heat transfer processes: inside the tubing, on the tubing, and in the Annulus I. On the tubing surface, heat transfer happens in the conduction mode. In the

Rfa = Rconv,a2 + Rcond,c2 +

1 (1/Rcond,b ) + (1/Rconv,e )

(A.4)

1 1 1 dc2i − dc1o = = dc2i ha2 Nua2 ka2 dc2i dc2i (Nua2 ka2 /dc2i − dc1o ) ln(rc2o /rc2i ) Rcond,c2 = 2kc2 ln(re /rc2o ) Rcond,e = 2ke de − dc2o 1 1 1 Rconv,e = = = dc2o ha2 Nue ke dc2o dc2o (Nue ke /de − dc2o ) Rconv,a2 =

Nu (Nusselt number) presents the ratio of convective heat transfer to conductive heat transfer across the fluid boundary layer (hL/kf ). The following two correlations are used for the calculations presented in this study:

Y. Feng et al. / Geothermics 53 (2015) 368–378

A.4. Gnielinski correlation (Gnielinski, 1976) Nu =

377

where f is the Moody friction factor (Eq. (C.2) proposed by Chen (1979)), d represents pipe diameter, v is velocity, and gc is conversion factor (32.17(lbm − ft)/(lbf − s2 )).

(f/8)(Re−1000)Pr 1+12.7(f/8)0.5 (Pr 2/3 −1)



for 0.5 ≤ Pr ≤ 2000, 3000 ≤ Re ≤ 5 ×106

1 = 2log f

A.5. Dittus–Boelter correlation (Dittus and Boelter, 1930)



 2

5.0452 ε/d − log() 3.7065 Re

with Nu = 0.023Re0.8 Prn for 0.7 ≤ Pr ≤ 160, 10, 000 ≤ Re where n = 0.4 for heating of the fluid and 0.3 for cooling, f is the friction factor, Re is the Reynolds number describing the ratio of inertial forces to viscous forces (vL/), and the Prandtl number, Pr, represents the ratio of momentum diffusion to thermal diffusion (cp /k). Appendix B. Equations for thermodynamic analysis Energy and exergy balances (Kanoglu and Bolatturk, 2008) for any control volume at steady state with negligible kinetic and potential energy changes can be expressed, respectively, as: ˙ = Q˙ + W



˙ = E˙ heat + W

˙ out hout − m



E˙ out −





˙ in hin m

E˙ in + I˙

(B.1) (B.2)

where the subscripts in and out stand for the inlet and outlet states, ˙ are the input net heat and work, h and I˙ represent enthalpy Q˙ and W and the rate of exergy destruction, respectively. E˙ is defined as: E˙ heat =



1−

T0 T



Q˙

(B.3)

The specific flow exergy is: e = h − h0 − T0 (s − s0 )

(B.4)

The power generated by the turbine in the cycle is: ˙ t =m ˙ wf (h6 − h7 ) W

(B.5)

where h7 = h6 − (h6 − h7s )

(B.6)

The power consumed by the pump in the cycle is: ˙ fp = m ˙ wf (h1 − h8 ) W

v(P1 − P8 ) h1 − h8

(B.7)

(B.8)

The exergy efficiency for the turbine is: ex,t =

˙ t W E˙ 6 − E˙ 7

(B.9)

and for the pump: ex,p =

E˙ 1 − E˙ 8 ˙ p W

(B.10)

Appendix C. Procedures for thermodynamic analysis (1) For a given injection pressure P1 and temperature T1 , s1 and h1 can be read from a n-butane thermodynamic property chart. (2) Assuming no heat loss due to the tubing insulation i.e. T2 = T1 and P2 = P1 + Phydraulic − Pfriction , s2 and h2 can be read from the chart. The frictional pressure gradient is represented by: 2

dP fv  =− dz 2gc d

(ε/d) 2.8257

+

 7.149 0.8981 Re

(C.3)

where ε is the pipe roughness and Re is the Reynolds number (vd/). (3) T3 remains same as T2 due to the tubing insulation, and P3 is calculated based on friction loss. Then, s3 and h3 can also be obtained accordingly. (4) T4 is calculated from the DHE simulator while adding frictional pressure losses i.e. P4 = P3 + Phydraulic − Pfriction , and s4 and h4 are then read from the thermodynamic chart. (5) T5 remains same as T4 due to the tubing insulation. P5 becomes the n-butane vapor pressure at T5 (Eq. (C.4) presented by Kay (1940)). (read from the chart for the thermodynamic state corresponding s5 and h5 ). logP10 =

−1654.1 + 1.7047logT10 − 1.988 × 10−5 T T

(C.4)

where P is in psi and T is in ◦ R. (6) P6 = P5 − Phydraulic − Pfriction and T6 = T5 (read from the chart for the state corresponding to s6 and h6 ). (7s) Assume an isentropic process where s7s = s6 and P7 is the design outlet pressure for the turbine. For this thermodynamic state, h7s and s7s can be read from the chart. (7) For a given turbine isentropic efficiency (t = (h6 − h7 )/(h6 − h7s )), the true state h7 can be calculated. Now, the s7 can be calculated for the values of h7 , P7 , and T7 . (8) For a given pump isentropic efficiency (p = (h1s − h8 )/(h1 − h8 ) = (P1 − P8 )/(h1 − h8 )), h8 is calculated by using the friction pressure losses as P8 = P7 − Pfriction . T8 and s8 can now be read from the chart corresponding to the calculated thermodynamic state. References

with the efficiency as: p =

1.1098

=

(C.2)

(C.1)

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