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Modelling an unconventional closedloop deep borehole heat exchanger (DBHE): sensitivity analysis on the Newberry volcanic setting
Geothermal Energy volumeÂ 9, ArticleÂ number:Â 4 (2021)
Abstract
Alternative (unconventional) deep geothermal designs are needed to provide a secure and efficient geothermal energy supply. An indepth sensitivity analysis was investigated considering a deep borehole closedloop heat exchanger (DBHE) to overcome the current limitations of deep EGS. A T2Well/EOS1 model previously calibrated on an experimental DBHE in Hawaii was adapted to the current NWG 5529 well at the Newberry volcano site in Central Oregon. A sensitivity analysis was carried out, including parameters such as the working fluid mass flow rate, the casing and cement thermal properties, and the wellbore radii dimensions. The results conclude the highest energy flow rate to be 1.5Â MW, after an annulus radii increase and an imposed mass flow rate of 5Â kg/s. At 3Â kg/s, the DBHE yielded an energy flow rate a factor of 3.5 lower than the NWG 5529 conventional design. Despite this loss, the sensitivity analysis allows an assessment of the key thermodynamics within the wellbore and provides a valuable insight into how heat is lost/gained throughout the system. This analysis was performed under the assumption of subcritical conditions, and could aid the development of unconventional designs within future EGS work like the Newberry Deep Drilling Project (NDDP). Requirements for further software development are briefly discussed, which would facilitate the modelling of unconventional geothermal wells in supercritical systems to support EGS projects that could extend to deeper depths.
Introduction
Geothermal energy is an ideal candidate to dominate the energy industry in the foreseeable lowcarbon future. Holding a good reputation at providing a constant supply of heat and/or electricity, this mature baseload technology could aid the climate crisis by significantly reducing carbon emissions.
Conventional deep geothermal methods have been utilised to provide power production from natural hydrothermal reservoirs with these desired characteristics: a large heat source, highly permeable, sufficient supply of injected water, impermeable layer of cap rock, and a reliable recharge system (DiPippo 2015). Generally, these sites are unique and restricted by location, severely limiting the true potential of geothermal energyâ€”according to the International Energy Agency, this resource could generate 1400 TWh per year by 2050 while avoiding 800 Mt of CO_{2} (IEA 2011). This largely untapped resource demands alternative solutions to compete in the renewable energy market, specifically exploiting unconventional methods to extract heat, notably from petrothermal sources where permeability and/or porosity are lacking (Falcone etÂ al. 2018). There are significant research gaps for deep unconventional methods where the geothermal gradient is larger than the mean value of 25â€“30Â°C/km (Olasolo etÂ al. 2016). In an Enhanced Geothermal System (EGS), cold water is injected at high pressure into the subsurface to stimulate fractures, hence creating an artificial reservoir (Olasolo etÂ al. 2016). The first EGS project was in Los Alamos (New Mexico), previously defined as a Hot Dry Rock (HDR) project due to lack of natural water saturation in basement rocks (Olasolo etÂ al. 2016; Breede etÂ al. 2013). EGSs are currently under technical review as they are associated with the risk of inducing seismic activity (Lu 2018). Examples of abandoned EGS projects due to induced seismicity are the Basel project in Switzerland (Lu 2018) and the Pohang project in South Korea (Kim etÂ al. 2018). Fundamental research and development on Supercritical EGS (SEGS) is ongoing, such as Icelandâ€™s IDDP projects (Reinsch etÂ al. 2017), the Japan BeyondBrittle Project (Muraoka etÂ al. 2014), and the DESCRAMBLE project in Italy (Bertani etÂ al. 2018). SEGSs involve drilling deeper into regions of partial melt past the brittleâ€“ductile transition zone to achieve a larger flow temperature at the bottom of the wellbore (Cladouhos etÂ al. 2018). Here, the fluid is expected to reach a supercritical state, with no clear distinction between the liquid and vapour phases; for pure water, this corresponds to temperature and pressure conditions above approximately Tâ€‰=â€‰374 \(^{\circ }\text {C}\) and Pâ€‰=â€‰22.1 MPa (Sudarmadi etÂ al. 2012; Dobson etÂ al. 2017). The development of SEGSs relies on ultrahightemperature technology, capable of withstanding bottomhole temperatures of 430â€“550Â \(^{\circ }\text {C}\), typical of supercritical environments (Lu 2018). The IDDP1 well yielded superheated steam at a temperature of 452Â \(^{\circ }\text {C}\) and pressure of 140 bar, corresponding to an electricity generation potential of 35 MWe, while in 2017, the IDDP2 successfully reached supercritical fluids at 426Â \(^{\circ }\text {C}\) and 340 bar at a depth of 4659 m (DEEPEGS 2018). However, IDDP1 drilling was abandoned after hitting a magma intrusion at 900Â \(^{\circ }\text {C}\) at 2100 m and the first flow test of IDDP2, conducted in December 2019, encountered delays (DEEPEGS 2018, 2019). Overcoming the challenges posed by these unique resources could potentially unlock a five times greater energy content and a factor of ten times electricity generation potential associated with supercritical fluids at 400Â \(^{\circ }\text {C}\) compared with EGS technology at 200Â \(^{\circ }\text {C}\) (Cladouhos etÂ al. 2018).
Before initiating an indepth numerical investigation of unconventional designs into supercritical geothermal systems, this study presents a foundation for potential usage of this gamechanging technology. In this study, an unconventional deep borehole heatexchanger (DBHE) design is accommodated into the NWG 5529 openloop well, to investigate its energy performance and potential usage for EGS projects in subcritical environments. It could also aid the development of unconventional designs in supercritical environments when a much greater depth is requiredâ€”see Borehole settings in Newberry field for details on the current case study investigated.
The conventional BHE design was conceived for shallow depths and lowtemperature gradients, for heating and cooling applications (AcuÃ±a etÂ al. 2011; Beier etÂ al. 2013; Holmberg etÂ al. 2016). Some DBHE sites already exist, including two deep boreholes in Weissbad and Weggis in Switzerland, at depths of 1.2 km and 2.3 km, respectively (Kohl etÂ al. 2000, 2002).
The modelled DBHE involves pumping cold fluid down the outer annulus, such that hot fluid rises to surface up the inner tubing via a thermosiphon effect (natural convection) or through the use of pumps (Tang etÂ al. 2019). The DBHE design was previously modelled in the Villafortuna abandoned oil well in Italy (Alimonti etÂ al. 2016), the KTB deep borehole project setting in Germany (Falcone etÂ al. 2018), and the IDDP1 well in Iceland (Renaud etÂ al. 2019). Replacing the current NWG 5529 well with a DBHE would not only mitigate the risks of induced seismicity, but also prevent fluid losses and contamination to the surrounding environment, as the working fluid is not in direct contact with the surrounding rock (Wang etÂ al. 2019). Installation costs can also be reduced by decreasing the boreholes thermal resistance via a thermally enhanced outer pipe in groundcoupled heat pump systems (Raymond etÂ al. 2015). A heatconducting filler of graphite could also be implemented around the DBHE design to enhance downhole heat transfer (Falcone etÂ al. 2018).
Former DBHE studies have relied upon numerical or analytical methods to discretise the geothermal system into elements within a grid (Alimonti etÂ al. 2018). A research code T2Well/EOS1, recently developed at Lawrence Berkeley National Laboratory for simulating coupled wellborereservoir processes involved in geothermal systems, was adopted in this study to model appropriate subcritical conditions in the Newberry volcano area.
Borehole settings in Newberry field
This study focuses on the Newberry Volcano EGS project in Central Oregon. This site was one of the first to consider heat extraction from a volcanic source, in addition to developments in hydroshearing stimulation techniques to mitigate induced seismicity and adapting a thermally degradable zonal isolation material to isolate fractures from intended stimulated zones (Cladouhos etÂ al. 2016). FigureÂ 1 shows the two wellbore locationsâ€”NWG 5529 and NWG 4616â€”along the western flank of the volcano.
From Fig.Â 1, the NWG 5529 was drilled down to 3067 m with a bottom well temperature of 331Â \(^{\circ }\text {C}\) (Cladouhos etÂ al. 2016), at subcritical conditions (100Â \(^{\circ }\text {C}\) <â€‰Tâ€‰<â€‰374Â \(^{\circ }\text {C}\) and 0.1 MPa <â€‰Pâ€‰<â€‰22.1 MPa) (Asl and Khajenoori 2013), and plans to deepen the NWG 4616 well to 4877 m are in place to transition into supercritical environments (Cladouhos etÂ al. 2018). It is important to note that the wells NWG 5529 and NWG 4616 are openloop designs whereby the pumped working fluid is in direct contact with the reservoir.
A low average flow rate of 3.2 kg/s was obtained from an NWG 5529 stimulation test, compared to expected conventional EGS flow rates of 50â€“60 kg/s (Cladouhos etÂ al. 2016; MIT 2006). As a result of this and of the potential risk of induced seismicity, the DBHE design was chosen for this study. To ensure realistic wellbore properties for the synthetic DBHE in the Newberry settings, casing radii dimensions from existing sites defined previously (Weissbad and Weggis) were applied in this study. See "Sensitivity analysis" section for details.
Methods
The DBHE was modelled into the Newberry geothermal system with a 2D axisymmetric MESH adopting T2Well/EOS1 (Pan and Oldenburg 2014). The model setup is described below.
Mathematical model
T2Well/EOS1 is an integrated wellborereservoir numerical simulator to simulate nonisothermal flows of multiphase fluids (steamâ€“water) in both domains simultaneously (Pruess etÂ al. 2012). T2Well was previously used to model various contexts, such as heat extraction in a closedloop system with supercritical CO_{2} as the working fluid (Higgins etÂ al. 2016) and for a gas storage blow out (Pan etÂ al. 2018). The equation of state (EOS1) was utilised, representing one nonisothermal water component under twophase conditions (Pruess etÂ al. 2012). The applied thermodynamic equations within the reservoir are similar to those used in other TOUGH2 family code and are defined in TableÂ 1.
Equation (1) depicts the general mass and energy conservation equation with \(M^{\text{m}}\), \(F^{\text{m}}\), \(M^{\text{E}}\), and \(F^{\text{E}}\) in Eqs.Â (2)â€“(5) representing the mass accumulation, mass flux, energy accumulation, and energy flux terms, respectively (Renaud etÂ al. 2020). The phase velocity \(u_{\text{ph}}\) in Eq.Â (6) is solved by adopting a 3D multiphase Darcy flow for a heterogeneous porous media.
The key equations for the wellbore used in T2Well/EOS1 are defined in TableÂ 2. EquationÂ (7) depicts the conservation equation in partial derivative form, with \(M^{\text{E}}\) defined in Eq.Â (8) and \(F^{\text{E}}\) in Eq.Â (9) representing the energy accumulation and flux terms, respectively (Renaud etÂ al. 2020).
The driftâ€“flux model (DFM) is used in solving the twophase momentum conservation equation in the wellbore. A relationship is assumed between the gas velocity (\(u_{\text{G}}\)) and the volumetric flux of the mixture (j):
The liquid velocity \(u_{\text{L}}\) can then be calculated from j and the drift velocity \(u_{\text{d}}\) as:
The drift velocity is thus calculated as (Pan etÂ al. 2005):
The velocities \(u_{\text{G}}\) and \(u_{\text{L}}\) within the mixture are then solved with \(u_\text{d}\) to obtain the momentum conservation equation; simplified to Eq. (13) (Pan etÂ al. 2011; Akbar etÂ al. 2016):
TableÂ 3 defines the remaining parameters from the driftâ€“flux model, extracted from Pan and Oldenburg (2014). The mass and energy conservation equations are solved using the Newtonâ€“Raphson iteration process (Pruess etÂ al. 2012).
Newberry case study
The DBHE was modelled into the Newberry geothermal system by replacing the NWG 5529 well with the unconventional closedloop design. The DBHE model built with T2Well/EOS1 is based on an experimental study from Morita etÂ al. (1992b), whereby the measured and computed pressure and temperature values were verified with the HGPA well site in Hawaii (Morita etÂ al. 1992b). The original completion diagram from Morita etÂ al. (1992b) was altered to account for the increase in depth from 879.5 m to the NWG 5529 wellbore depth of 3067 m (Cladouhos etÂ al. 2016). A 2D axisymmetric grid representation of the design is presented in Fig.Â 2; note that Casg1(A.) is the inner casing separating the outer annulus and the inner tubing and Casg2(B.) is the external casing separating the outer annulus and the cement, Ceme1(D.). FigureÂ 2 highlights key elevation depths for each section to account for these changes. The bottom of the well reached an elevation of âˆ’â€‰1267 m.
The Newberry geothermal area was defined according to the thermalâ€“hydrologicalâ€“chemical model adopted from Sonnenthal etÂ al. (2012). Four geological zones are highlighted in Fig.Â 2 with their thermodynamic properties in TableÂ 4, obtained from Sammel etÂ al. (1988), Sonnenthal etÂ al. (2012). Thermodynamic wellbore properties are also defined in TableÂ 5, incorporated from Morita etÂ al. (1992a), Falcone etÂ al. (2018).
Referring to Fig.Â 2, water was injected into the outer annulus at a temperature of 12 \(^{\circ }\text {C}\) with an imposed mass flow rate \({\dot{m}}\). The top boundary condition of the reservoir model was set with a surface temperature of 12 \(^{\circ }\text {C}\) and a surface atmospheric pressure of 1 bar (Sonnenthal etÂ al. 2012). As shown in Sonnenthal etÂ al. (2012), it was assumed in the model that the surface pressure and temperature values were constant at elevation +â€‰1600 m, neglecting the pressure and thermal losses in the water table defined between +â€‰1800 and +â€‰1600 m. The default pressure for the boundary condition on the DBHE was set to 3 bar (as shown by \(P_{\text{i}}\)) to prevent effects from local vacuum conditions reaching the lower limit of the code. Only heat flow was considered between the wellbore and reservoir to reflect the closedloop design, excluding fluid flow.
T2Well numerical validation
Experimental validation
The experimental data from a DBHE in Hawaii set at the depth of 879.6 m were used to validate the T2Well model (Morita etÂ al. 1992b). The pressure and temperature distribution in the first 12 h showed a good match between measured values and simulations, as illustrated in Fig.Â 3. Model properties and details can be found in Renaud etÂ al. (2020).
Numerical discussion
A DBHE with graphite on the wellbore was numerically investigated using FEFLOW (Falcone etÂ al. 2018). While authors in Falcone etÂ al. (2018) used constant water properties, T2Well uses the pressure and temperaturedependent thermophysical properties based on models suggested by the International Formulation Committee (IFC 1967). As stated in Tang etÂ al. (2019), Sui etÂ al. (2019), constant fluid properties seem to generate errors in the pressure losses calculation and heat produced in DBHEs. The produced water temperature and heat flux were underestimated for a DBHE of 6100 m (Alimonti and Soldo 2016) and overestimated by 11% in a DBHE of 3500 m (Hu etÂ al. 2020). These errors occurred due to not accounting for specific heat capacity and density changes within the DBHE. Compared with constant water properties, these changes would increase the total heat energy while decreasing the temperature of the return fluid.
The same deep geothermal system was modelled based on the KTB deep borehole project, reaching a reservoir depth of 8000 m (Falcone etÂ al. 2018), using T2Well/EOS1. While a 3D model was considered in Falcone etÂ al. (2018), the T2Well model used in this work is an axisymmetric RZ mesh centred on the wellbore. Graphite is implemented with a thermal conductivity value of 300 W/mK and an assumed porosity of 1%.
The T2Well grid contains 1030 elements. The maximum radial extension of the model is 1 km. The bottom of the DBHE was set at a depth of 7000 m. Water was injected in the annulus at the flow rate of 304.8 \(\text {m}^{3}\)/day (\(\sim\)â€‰7 kg/s). The reservoir was assumed to be fully saturated water. The surface temperature was set to 15 \(^{\circ }\text {C}\), with an initial temperature gradient of 40 \(^{\circ } \text{C}\)/km. The bottom temperature is 330 \(^{\circ } \text{C}\). The graphite filled the surrounding of the DBHE from the depth of 4400 and 7200 m instead of the cement or grout. The value of casing materials is 900 J/kgÂ K and the wall roughness is 2.5\(\times 10^{5}\) m. The thermal properties of the rock and DBHE sections applied in the model can be found in Seyidov (2016), Falcone etÂ al. (2018). FigureÂ 4 describes the water temperature at the surface of the DBHE compared to the FEFLOW results.
From this case study, the temperature obtained at the surface of the DBHE was lower than previously described in Falcone etÂ al. (2018), suggesting the potential overestimation of the water temperature using constant water properties due to changes in the specific heat value (Song etÂ al. 2018). As stated by Hu etÂ al. (2020), the temperaturedependent properties as calculated in T2Well/EOS1 must be considered for longterm performance evaluation of DBHE.
Sensitivity analysis
TableÂ 6 summarises the parameters investigated in this study: mass flow rate of water \({\dot{m}}\) (kg/s), thermal conductivity \(\lambda\) (W/mK) of the casings and cement (see Fig.Â 2), and the wellbore inner \(r_{\text{i}}\) (m) and outer \(r_{\text{o}}\) (m) radii dimensions for the annulus and tubing. All parameter changes were referenced against a basecase scenario from Morita etÂ al. (1992b).
The working fluid velocity \(u_{\text{F}}\) at the bottom of the well was explored for values 3 kg/s \(< {\dot{m}}<\) 9 kg/s (see "Mass flow rate" section).
An insulated inner casing is advantageous for preventing heat losses between the inner tubing and the outer annulus, hence maximising the extracted energy flow rate at the outlet (Falcone etÂ al. 2018; Song etÂ al. 2018). Therefore, the effectiveness of an insulated inner casing as inner tubing for the DBHE was investigated by adjusting \(\lambda\) (W/mK) of Casg1, whilst \({\dot{m}}\) was fixed at 5 kg/s. Note 46.1Â W/mK was chosen as an upper limit to explore the heat transfer through the design when all three casing properties are identicalâ€”Casg2â€‰=â€‰Casg3 at \(\lambda = 46.1\, {\text{W}/{\text{mK}}}\)â€”(see "Inner casing properties" section).
Fixing Casg1 at \(\lambda = 0.01038\, {\text{W}/{\text{mK}}}\) and \({\dot{m}}= 5\, {\text{kg}/{\text{s}}}\), the outer casing thermal conductivity \(\lambda\) was adjusted based on quoted values in TableÂ 6. The casing properties extracted from the Weissbad DBHE and the NWG 5529 well were explored here (see "Outer casing properties" section).
Fixing \({\dot{m}}\), Casg1 and Casg2 properties to the basecase values quoted in TableÂ 6, the thermal conductivity \(\lambda\) parameter for various cements was explored. The use of a heat conducting filler for enhanced heat transfer (graphite flakes positioned laterally and parallel to one another) was also investigated (Falcone etÂ al. 2018) at \(\lambda =\) 300Â W/mK (see "Cement properties" section).
Four wellbore radii cases were investigated: annulus reduction (Case1), annulus increase (Case2), tubing increase (Case3), and tubing reduction (Case4) against the basecase radii dimensions from Morita etÂ al. (1992b). Again, the mass flow rate was fixed at \({\dot{m}} =\) 5 kg/s. Case1 involved an annulus reduction by 1.27, incorporating \(r_{\text{i}} =\) 0.0629 m from the Weggis plant (Kohl etÂ al. 2002). Case2 involved an annulus increase by 1.33 by implementing \(r_{\text{i}} =\) 0.1061 m from the Weissbad well (Kohl etÂ al. 2000). Case3 values were chosen, so the tubing increase factor was equal to that of Case2 (1.33). Case4 tubing reduction by 1.22 was influenced by \(r_{\text{o}} =\) 0.0365 m tubing dimension from the Weggis well (Kohl etÂ al. 2002). For all radii changes, the annular space between \(r_{\text{i}}\) and \(r_{\text{o}}\) remained constant at 0.0092 m and 0.0192 m for the annulus and tubing, respectively. The crosssectional area ratio between the annulus and tubing was also explored, by adopting Eqs. (14) and (15), respectively:
Here, \(r_{\text{i},\text{A}}\) is the inner annulus radii, \(r_{\text{o},\text{T}}\) is the outer tubing radii, and \(r_{\text{i},\text{T}}\) is the inner tubing radii. See "Radii" section for more details.
The heat transfer down the outer annulus and up the inner tubing was investigated for each parameter change and compared to the basecase scenario from Morita etÂ al. (1992b), as shown in TableÂ 6. For each parameter change, the temperature T \((^{\circ }\text {C}\)) and pressure P(MPa) vs. elevation (m) were investigated over a total simulation time of 30 years. In addition, the simulated energy flow rate of the wellbore \(q_{\text{Th}}\) (MW) was also extracted from the output file. A review on the energy flow rate for the closedloop DBHE vs. openloop NWG 5529 wellbore was explored and concludes this study. The energy flow rate is estimated for the NWG 5529 wellbore by adopting Eq. (16):
where \(\Delta T = T_{\text{o}}  T_{\text{i}}\), \(T_{\text{o}} = 94\) \(^{\circ }\text {C}\) representing the first flow back temperature recorded at the outlet point of the NWG 5529 wellbore (Cladouhos etÂ al. 2016) and \(T_{\text{i}} =\) 12 \(^{\circ }\text {C}\) is the surface temperature of the Newberry environment (Sonnenthal etÂ al. 2012). \(c_{\text{P}} = 4200\, {\text{J}/{\text{kg}}}\,^{\circ }\text {C}\) is assumed a constant for pure water properties. See Energy flow rate comparison between DBHE and NWG 5529 section for details.
ResultsÂ and Discussion
Mass flow rate
FigureÂ 5 shows the temperature and pressure distributions along the DBHE for varied \({\dot{m}}\). TableÂ 7 highlights key thermodynamic properties from Fig.Â 5 and the simulation output file: \(\Delta T\) between inlet \(T_{\text{i}}\) and outlet \(T_{\text{o}}\) points, energy flow rate \(q_{\text{Th}}\), and the working fluid velocity \(u_{\text{F}}\) at the bottom of the wellbore:
From Fig.Â 5, it appears that an increase in \({\dot{m}}\) results in a lower bottom well temperature (32 \(^{\circ }\text {C}\) for 9 kg/s in comparison to 73 \(^{\circ }\text {C}\) for 3 kg/s). This decrease is observed in response to an increase in working fluid velocity (4.42 m/s vs. 1.51 m/s), leading to a shorter residence time. An increased \({\dot{m}}\) up the tubing results in a lower outlet temperature (34.5 \(^{\circ }\text {C}\) for 9 kg/s in comparison to 71.4 \(^{\circ }\text {C}\) for 3 kg/s)
A slight gain in temperature up the tubing is also observed (a 2.48 \(^{\circ }\text {C}\) increase for 9 kg/s in comparison to a 2.06 \(^{\circ }\text {C}\) decrease for 3 kg/s). This could be due to a higher pressure reduction up the tubing (\(\Delta P = 43.7\) MPa for 9 kg/s vs. \(\Delta P = 29.4\) MPa for 3 kg/s).
A mass flow rate value of 9 kg/s displays the highest \(q_{\text{Th}}\) compared with 3 kg/s and yields the largest \(\Delta {T}\) up the tubing. Ideally, \(\Delta {T}\) should be minimised up the tubing to enhance the systems efficiency by extracting more heat from the surrounding formations. A balance between efficiency and energy flow rate should be achieved. Due to 9 kg/s causing too high of a friction loss up the tubing and inducing higher pumping costs as shown by an increased inlet pressure (15.9 MPa as opposed to 1.62 MPa for 3 kg/s), and 3 kg/s yielding the lowest energy flow rate (1.14 MW), 5 kg/s is considered the bestcase scenario with minimal \(\Delta {T}\) up the tubing and an energy flow rate of \(q_{\text{Th}} =\) 1.46 MW.
Inner casing properties
FigureÂ 6 shows the temperature and pressure distributions along the DBHE for varied \(\lambda\) in Casg1. TableÂ 8 summarises key thermodynamic properties extracted from Fig.Â 6 and from the simulation output file: \(\Delta T\) between inlet \((T_{\text{i}})\) and outlet \((T_{o})\) points and the energy flow rate \(q_{\text{Th}}\).
\(\Delta T\) down the annulus is seen to increase, while \(\lambda\) increases in Casg1 (\(\Delta T =\) 39.2 \(^{\circ } {\text{C}}\) for \(\lambda =\) 0.01038 W/mK compared with \(\Delta T =\) 216 \(^{\circ } {\text{C}}\) for \(\lambda =\) 46.1 W/mK). This is in agreement with Fourierâ€™s law of heat conduction (Nuclearpower.net 2019) via an increase in heat transfer from the reservoir into the wellbore. The inlet pressure remains approximately constant at 5 MPa due to the constant mass flow rate of 5 kg/s imposed. In addition, the outlet pressure remains constant at 0.3 MPa. Using a thermal conductivity \(\lambda>\) 0.01038 W/mK, the temperature up the tubing significantly reduces as a result of low thermal insulation between the annulus and tubing (Song etÂ al. 2018). For maximum efficiency, \(\Delta T\) should be minimised to follow an isothermal process to surface. In fact, \(\lambda =\) 46.1 W/mK is considered the worstcase scenario when all casing properties are identical and thermal insulation is at its lowest.
A higher \(\lambda\) yields a smaller \(\Delta T\) between the inlet and outlet points and hence a smaller energy flow rate \(q_{\text{Th}}\) (0.830 MW vs. 1.46 MW), again due to poor thermal insulation. Therefore, minimising the thermal conductivity in Casg1 (\(\lambda =\) 0.01038 W/mK) is the bestcase scenario to achieve maximal bottomhole T and preventing significant cooling of the fluid up the tubing.
Outer casing properties
FigureÂ 7 displays the temperature and pressure distributions along the DBHE for varied \(\lambda\) in the outer casing. The first three parameter changes result in nearly identical temperature and pressure profiles. Therefore, two cases were compared: \(\lambda =\) 0.01038 W/mK for the inner Casg1 only (red), and for all casings (green). TableÂ 9 highlights key thermodynamic properties from Fig.Â 6 and the output file: \(\Delta T\) between inlet \(T_{\text{i}}\) and outlet \(T_{\text{o}}\) points, the inlet \(P_{\text{i}}\) and outlet \(P_{\text{o}}\) pressure points and the simulated energy flow rate \(q_{\text{Th}}\) for these two cases.
When all casings are insulated at \(\lambda =\) 0.01038 W/mK, a lower bottomhole temperature (17.2 \(^{\circ } \text{C}\) vs. 50.4 \(^{\circ } \text{C}\)) is observed in addition to a lower outlet temperature (\(T_{\text{o}} =\) 17.8 \(^{\circ } \text{C}\) vs. \(T_{\text{o}} =\) 50.0 \(^{\circ } \text{C}\)). This is due to insufficient heat transfer between the reservoir and wellbore. \(\Delta T\) between the inlet and outlet points decreases approximately by a factor of 6 (6.92 \(^{\circ } \text{C}\) vs. 38.9 \(^{\circ } \text{C}\)) and hence results in a reduction in \(q_{\text{Th}}\) (0.785 MW vs. 1.46 MW) as the water fails to gain significant temperature down the annulus when all casings are insulated. Therefore, to ensure an efficient thermal recovery, the bestcase scenario is observed when only the inner casing is insulated at \(\lambda =\) 0.1038 W/mK compared to all casing. This is because Casg1 is most sensitive to \(\Delta T\) up the tubingâ€”as seen in "Mass flow rate" section above.
Cement properties
FigureÂ 8 shows the temperature and pressure distributions along the DBHE for varied \(\lambda\) cement properties (Ceme1 and Ceme2 in Fig.Â 2). Key thermodynamic properties extracted from Fig.Â 8 and from the simulation output file are summarised in TableÂ 10: \(\Delta T\) between inlet \(T_{\text{i}}\) and outlet \(T_{\text{o}}\) points, and the simulated energy flow rate \(q_{\text{Th}}\).
The bottomhole temperature down the annulus increases from 50.4 to 60.9 \(^{\circ } {\text{C}}\) for \(\lambda =\) 0.99 W/mK and \(\lambda =\) 300 W/mK respectively. Hence, \(T_{\text{o}}\) increases as a result of an increase in \(\lambda\) within the cement, suggesting that this parameter change enhances the amount of heat transfer between the reservoir and working fluid. In particular, this heat transfer is hindered when \(\lambda\) is lower than that of the reservoir, as identified in Song etÂ al. (2018). As \(\lambda\) predominantly affects T and not P (as seen in "Inner casing properties" section), the pressure distribution along the DBHE shows similar results for all parameter changes. Referring to TableÂ 10, \(\lambda\) is maximised in conjunction with \(q_{\text{Th}}\), with a percentage increase of \(14.4\%\) comparing conventional cement with a graphite heat conductive filler (1.67 MW for \(\lambda =\) 0.99 W/mK vs. 1.46 MW for \(\lambda =\) 300 W/mK). While the use of graphite significantly empowers the heat transfer in the DBHE design, its use as a cement additive is an unproved concept. Therefore, \(\lambda<\) 3.52 W/mK parameters are deemed more reasonable as bestcase scenarios, because conventional cement falls into the region of 0.2 \(< \lambda<\) 3.63 W/mK (Ichim etÂ al. 2016).
Radii
FigureÂ 9 shows the temperature and pressure distributions along the DBHE for varied radii. Two key scenarios were analysed: varying the inner annulus radius (Case1 and Case2) and increasing the tubing radii by a factor of 1.33 (Case3). Each scenario was then compared to the original basecase radii from Morita etÂ al. (1992b), with a constant mass flow rate \({\dot{m}} =\) 5 kg/s. TableÂ 11 highlights the key thermodynamic properties from Fig.Â 9 and the output file for each scenario, respectively: \(\Delta T\) between inlet \(T_{\text{i}}\) and outlet \(T_{\text{o}}\) points, the inlet \(P_{\text{i}}\) and outlet \(P_{\text{o}}\) pressure points, the simulated energy flow rate \(q_{\text{Th}}\), and the working fluid velocity \(u_{\text{F}}\) at the bottom of the well. The crosssectional area values for the annulus (\(\sigma_{\text{A}}\)) and tubing (\(\sigma_{\text{T}}\)) are also quoted along with their ratio (\(\sigma _{\text{A}}/\sigma_{\text{T}}\)).
Concerning the annulus comparison in TableÂ 11, the bottomhole temperature decreases from 50.4 to 48.8 \(^{\circ } \text{C}\) alongside an inner radius reduction (Case1) and increases to 52.3 \(^{\circ } \text{C}\) alongside an inner radius increase (Case2). This occurs due to variation in the annulus crosssectional area (0.0291 \(\text {m}^{2}\) vs. 0.00621 \(\text {m}^{2}\)). For Case2, the annulus crosssectional area decreases the working fluid velocity down the annulus. This leads to a longer residence time and hence enhanced heat transfer within the wellbore, as discussed in Nalla etÂ al. (2005). \(T_{\text{o}}\) also shows this trend, decreasing from 50.0 to 48.5 \(^{\circ } \text{C}\) for Case1 and increasing to 51.8 \(^{\circ } \text{C}\) for Case2.
\(P_{\text{i}}\) is seen to slightly increase from 4.97 to 5.90 MPa for an inner annulus radius reduction (Case1) and decrease from 4.97 to 4.87 MPa for an inner annulus radius increase (Case2) due to changes in the crosssectional area ratio (3.09 vs. 14.5). Therefore, to impose a constant \({\dot{m}}\), the return pressure will decrease as a result of this increased crosssectional area ratio for Case2. Both Case1 and Case2 reach an equal bottomhole pressure of 33.1 MPa which results in \(P_{\text{o}} \approx\) 0.302 MPa for both cases. This occurs due to the constant crosssectional area witnessed in the tubing (0.00201 \(\text {m}^{2}\)).
\(q_{\text{Th}}\) increased from 1.46 to 1.50 MW alongside an inner annulus radius increase (Case2) and slightly decreased to 1.43 MW for an inner annulus radius reduction (Case1). The former is influenced by an increase in the working fluid velocity and crosssectional area as discussed previously. In addition, there is a decrease in frictional pressure down the annulus (254 Pa/m vs. 3.04 Pa/m in Fig.Â 10), and hence an increased heat transfer and increased \(\Delta T\) between the inlet and outlet points. Therefore, a radii increase in the annulus (Case2) is the bestcase scenario here for maximal energy flow rate.
Case4 (tubing reduction by 1.22) failed to run for \({\dot{m}} = 5\) kg/s due to a change in pressure into the wellbore that exceeded the limits of the software, 1000 bars (Renaud etÂ al. 2018). For a constant \({\dot{m}} = 5\text { kg/s}\), at time tâ€‰=â€‰0, the pressure seen at the bottom of the well was \(0.25\times 10^{8}\) Pa, but below the DBHE in the surrounding formation, the pressure reached \(1\times 10^{9}\) Pa, i.e., 1000 bars. Therefore, a detailed comparison between Case3 and Case4 could not be achieved. Instead, an inner tubing radius increase (Case3) was compared with respect to the original radiiâ€”referring to Fig.Â 9 and TableÂ 11.
A slight increase in temperature down the annulus from 50.4 to 50.9 \(^{\circ } \text{C}\) is seen for an inner tubing radius increase (Case3). This occurs due to a decreased upward velocity in the tubing (1.41 m/s vs. 2.48 m/s), leading to enhanced heat loss from the tubing into the annulusâ€”see Fig. 11. In addition, the outlet temperature has slightly decreased (49.6 \(^{\circ } \text{C}\) vs. 50.0 \(^{\circ } \text{C}\)) when the crosssectional area in the tubing increased. Down the annulus however, the working fluid velocity has increased (0.446 m/s vs. 0.363 m/s), in addition to an increase in frictional pressure (50.6 Pa/m vs. 23.7 Pa/m).
To maintain the imposed mass flow rate \({\dot{m}} =\) 5 kg/s at the inlet point, the inlet pressure for Case3 has decreased (\(P_{\text{i}} =\) 1.35 MPa vs. 4.97 MPa) following an increase in the working fluid velocity at the inlet point described above. In addition, the increased frictional pressure down the annulus (50.6 Pa/m vs. 23.7 Pa/m) consequently slows down the working fluid velocity in the tubing (1.41 m/s vs. 2.48 m/s) and a reduced inlet pressure is witnessed. Despite this ratio yielding a factor of 2 lower than that of the original radii (3.16 vs. 6.83), this loss in \(P_{\text{i}}\) is due to a slight reduction in the annulus crosssectional area (0.0112 \(\text {m}^{2}\) vs. 0.0137 \(\text {m}^{2}\)) and the reduced working fluid velocity witnessed in the tubing.
\(q_{\text{Th}}\) is seen to be nearly identical at 1.46 MW for Case3 and the original radii. It can be inferred that when the inner tubing radius increases, there is little influence on the value of \(q_{\text{Th}}\) apart from a slight heat loss up the tubing. On the contrary, adjusting the tubing will affect the inlet pressure and hence the costs associated with the imposed energy flow rate. To avoid high energy consumption associated with a high injection pressure, a tubing reduction (Case3) could be considered a viable option for future designs to sustain a good energy flow rate.
In comparison, adjusting the annulus radii heavily influences the extent of heat transfer down the annulus. For an increased annulus radius, the heat transfer down the annulus increases and offers a higher \(q_{\text{Th}}\) from an increased bottomhole temperature. The bestcase scenario concluded here is for a radius increase in the annulus (Case2) to increase the energy efficiency of the system. However, according to Nalla etÂ al. (2005), adjusting the radii can incur high drilling costsâ€”from the analysis, a tubing reduction (Case3) could be suggested as an alternative.
It is worth noting that the assumption of a constant wellbore radius along the wellbore is only a preliminary step, as wells are conventionally drilled with decreasing diameter sections at increasing depths (Nalla etÂ al. 2005). However, keeping a constant radius for the entirety of the wellbore depth simplifies the model, as experimented in Morita etÂ al. (1992b).
Energy flow rate comparison between DBHE and NWG 5529
Assuming an average flow rate of 3.2 kg/s, and \(\Delta T = 94\)âˆ’â€‰12â€‰=â€‰\(82\,^{\circ } {\text{C}}\) obtained from the first NWG 5529 flow back test (Cladouhos etÂ al. 2016), in addition to \(c_{\text{P}}= 4200\text { J/kg} \,^{\circ } {\text{C}}\) for pure water, the energy flow rate obtained at the wellhead of NWG 5529 is approximately \(q_{\text{Th}} = 1.10\text { MW}\). Comparing this to the DBHE results at 3 kg/sâ€”\(q_{\text{Th}} = 1.14\text { MW}\)â€”it can be inferred that the DBHE offers a slightly higher energy flow rate at the wellhead compared to the NWG 5529 openloop well with a percentage increase of 3.44%. It is important to note that this comparison is an estimate, and in reality, \({\dot{m}}\) and \(c_{\text{P}}\) will vary considerably with depth.
A comparison between the two designs is also interpreted by assessing the bottomhole temperature at a fixed depth of 3067 m. Assuming no major temperature losses up the tubing (Â± 5 \(^{\circ } {\text{C}}\)), the temperature at the wellbore bottom can be regarded as the temperature at the outlet point.
The highest bottomhole temperature observed in this sensitivity analysis without significant heat loss up the tubing is 73.4 \(^{\circ } {\text{C}}\) for 3 kg/s in the \({\dot{m}}\) parameter change, whereas the conventional openloop NWG 5529 wellbore reached a static bottomhole temperature of 331 \(^{\circ } {\text{C}}\) (Cladouhos etÂ al. 2016). Both examples are at a fixed depth of 3067 m. Taking \(\Delta q_{\text{Th}} = 0.956  (0.200) =\) 1.16 MW as the simulated energy flow rate between the wellbore bottom and the inlet point for 3 kg/s, a comparison can be made with that obtained in the conventional NWG 5529 well.
Assuming constant parameters \({\dot{m}} = 3\text { kg/s}\), \(c_{\text{P}} = 4200\text { J/kg} \,^{\circ } {\text{C}}\) for pure water and \(\Delta T = 331  12 = 319\) \(^{\circ } {\text{C}}\), then \(q_{\text{Th}} = 4.02\text { MW}\) for the NWG 5529 wellbore in comparison to \(q_{\text{Th}} = 1.16\text { MW}\) for the DBHE design. This concludes that the closedloop DBHE design offers an energy flow rate output approximately a factor of 3.5 lower than that of the conventional design.
However, the highest energy flow rate obtained in the \({\dot{m}}\) analysis was for 9 kg/sâ€”yielding \(\Delta q_{\text{Th}} =\) 1.45â€‰âˆ’â€‰(âˆ’â€‰0.614) = 2.06 MW for a bottomhole temperature of 32.1 \(^{\circ } {\text{C}}\) in comparison to \(q_{\text{Th}} =\) 12.1 MW for the NWG 5529 wellbore at a fixed \({\dot{m}} =\) 9 kg/s. This yields an energy flow rate drop for the DBHE of approximately a factor of 5.84 lower in comparison to the static NWG 5529 bottomhole temperature of 331 \(^{\circ } {\text{C}}\).
These mass flow rates were chosen for comparison, because, according to Cladouhos etÂ al. (2016), similar values were obtained for an initial flow test (9.5 kg/s down to 5.7 kg/s after 1 h, with an average flow rate 3.2 kg/s).
The estimate of \(q_{\text{Th}}\) for NWG 5529 carries some uncertainty, especially when defining \(c_{\text{P}}\), because phase changes will occur with depth and the specific heat capacity will change. In the T2Well/EOS1 software, these phase changes are taken into account, so the simulated energy flow rate values will carry accuracy. Nevertheless, it can be inferred that the closedloop design is associated with a lower heat extraction potential compared to that of an operating EGS (assuming the EGS is successful)â€”especially when the closedloop design offers lower wellhead temperatures, according to Alimonti etÂ al. (2018).
However, a DBHE solution for the current NWG 5529 well would not require stimulation to create an artificial reservoir, and hence, less energy consumption is initially used up. This energy consumption for the current NWG 5529 could outweigh the lower heat extraction potential seen from the DBHE design, hence bringing forward potential benefits for accommodating the DBHE design in this setting from this numerical study. Furthermore, the DBHE is a closed system, which enables easy monitoring and prevents fluid losses and pipe corrosion/blockage. For EGS projects where unexpected failures occur, the DBHE design could be an effective alternative. For example, an EGS site at Rosemanowes in Cornwall failed to create artificial fractures and suffered fluid loss of 70%â€”leading to project abandonment in 1991 (Lu 2018). EGS activities in Cornwall, UK are ongoing and having the DBHE as a backup option could be beneficial, especially if drilling does not meet expectations.
While supercritical depths in the Newberry reservoir could not be modelled in this study due to software limitations, numerical wellborereservoir modelling will need to be further developed by adopting a supercritical equation of state (EOS1sc), see, for example, Croucher and Oâ€™Sullivan (2008), Battistelli etÂ al. (2020), to assess the true thermal potential in these ultrahigh temperature environments, notably targeted in the NDDP and IDDP projects.
It is also worth noting that only the thermal energy flow rate was quantified in this study. In fact, the overall net thermal capacity and total efficiency of the system should be investigated, considering the pumping power required for fluid circulation. Other future work entails:

The return flow pressure at the bottom of the wellbore should be validated with another experimental study or Multiphysics software.

Exploring a variety of working fluids, including water with salinity, carbon dioxide (Sun etÂ al. 2019), or isobutane as a supercritical fluid (Wang etÂ al. 2019).

Investigating more complex unconventional DBHE designs, such as an artificial geyser concept (Heller etÂ al. 2014).

Investigating the effects of anisotropic reservoir permeability/porosity on DBHE thermal recovery.

An economic analysis in the Newberry environment could also benefit the suitability of the DBHE design.
Conclusion
An indepth sensitivity analysis was performed with reference to a basecase DBHE design from Morita etÂ al. (1992b), and was modelled into the NWG 5529 Newberry environment.
The bestcase scenarios that offered maximal thermal efficiency was: \({\dot{m}}=\) 5 kg/s, an insulated inner tubing for Casg1 of \(\lambda =\) 0.01038 W/mK, maintaining a high \(\lambda\) for the outer casings (Casg2, Casg3) and the cement layers (Ceme1, Ceme2) and increasing the inner annulus radius (Case2), with a resulting thermal output \(q_{\text{Th}} =\) 1.50 MW.
Each parameter change offered some interesting insights. Altering the mass flow rate influenced the working fluidâ€™s velocity and its residence time down the annulus. An insulated inner tubing limits heat losses and minimises \(\Delta {T}\) up the tubing. The outer casing properties do not significantly affect the heat transfer inside the wellbore, but should not be insulated to ensure sufficient heat transfer occurs between the reservoir and wellbore. The cement properties lead to a higher \(q_{\text{Th}}\) when \(\lambda\) was maximised and the use of graphite flakes in a conductive filler as opposed to conventional cement appears to be an efficient, though unproved concept, yielding a percentage increase in energy flow rate of 14.4% (\(q_{\text{Th}} =\) 1.67 MW). Adjusting the radii dimensions will affect the residence time of the working fluid, similar to the sensitivity analysis conducted for varying the mass flow rate.
An energy flow rate comparison was made between this study and the conventional NWG 5529 EGS well. The results showed that the DBHE was a factor of 3.5 and 5.84 lower when assuming constant mass flow rates of 3 kg/s and 9 kg/s, respectively. While the DBHE design has a lower heat extraction and efficiency compared to the conventional EGS designs, the initial energy consumption to stimulate an artificial reservoir is not needed and could be an ideal candidate for future EGS projects where issues like induced seismicity, fluid losses, and contamination are mitigated. Future EGS projects should, therefore, consider the DBHE as an alternative design in situations where drilling may achieve original projects expectations.
Further work is needed to fully quantify the potential of the DBHE concept. The use of Multiphysics software and/or experimental data will be useful to validate the uncertainties in the pressure losses from the return fluid at the wellbore bottom. In addition, a variety of working fluidâ€™s and unconventional DBHE designs should be explored. Numerical wellborereservoir modelling tools will need to be further developed for supercritical environments, using the IDDP and NDDP projects for initial verification and calibration.
Availability of data and materials
The datasets generated and/or analysed during the current study are available in the Enlighten repository https://doi.org/10.5525/gla.researchdata.1111.
Abbreviations
 \(\kappa\) :

Index for the working fluid
 V :

Volume (\(\text {m}^{3}\))
 n :

Outward normal vector
 \(\Gamma\) :

Surface area of well side (\(\text {m}^{2})\)
 \(M^{\kappa }\) :

Mass accumulation term
 \(F^{\kappa }\) :

Key mass/energy transport terms
 \(q^{\kappa }\) :

Key source/sink terms
 \(\phi\) :

Porosity
 S :

Local saturation of phase
 \(\rho\) :

Density of phase (\(\text {kg/m}^{3}\))
 X :

Mass fraction of water in phase
 u :

Velocity of fluid (m/s)
 c :

Specific heat capacity (\(\text {J/kg}\,^{\circ } {\text{C}})\)
 T :

Temperature \((^{\circ } {\text{C}})\)
 U :

Specific thermal energy in the phase
 \(\lambda\) :

Thermal conductivity (W/mK)
 h :

Specific enthalpy in phase (kJ/kg)
 k :

Permeability (\(\text {m}^{2}\) or Darcy)
 \(\mu_{\text{ph}}\) :

Phase viscocity of the fluid (PaÂ s)
 P :

Pressure (Pa)
 g :

Gravitational acceleration (\(\text {m/s}^{2}\))
 z :

Elevation in well (m)
 \(\theta\) :

inclination angle of wellbore \((^{\circ })\)
 \(\sigma\) :

Crosssectional area of wellbore (\(\text {m}^{2}\))
 \(C_{0}\) :

Profile parameter
 j :

Volumetric flux of mixture (m/s)
 K :

Function to smooth transition of drift velocity from fluid stages
 \(K_{\text{u}}\) :

Kutateladze number
 \(m(\theta )\) :

Inclination of wellbore
 \(\gamma\) :

Slip between two phases
 f :

Apparent friction coefficient
 \({\dot{m}}\) :

Mass flow rate (kg/s)
 r :

Horizontal radii dimension (m)
 \(\Delta {T}\) :

Change in temperature up tubing or down annulus \((^{\circ } {\text{C}})\)
 \(q_{\text{Th}}\) :

Energy flow rate (MW)
 ph:

Phase
 L:

Liquid phase
 G:

Gaseous phase
 R:

Rock properties
 a :

Absolute permeability
 r,Â ph:

Relative permeability of a certain phase
 d:

Drift velocity
 c:

Characteristic velocity
 m:

Mixture
 A:

Annulus
 T:

Tubing
 i:

Inlet
 o:

Outlet
 i,Â A:

Inner annulus
 o,Â T:

Outer tubing
 i, T:

Inner tubing
 F:

Working fluid at wellbore bottom
 DBHE:

Deep borehole heat exchanger
 EGS:

Enhanced geothermal system
 SEGS:

Supercritical enhanced geothermal system
 NDDP:

Newberry Deep Drilling Project
 IDDP:

Icelandic Deep Drilling Project
 HDR:

Hot dry rock
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Acknowledgements
I would like to acknowledge Dr. Xiaolei Liu for initial assistance in T2Well/EOS1 software manipulation.
Funding
This research is supported by the UK Engineering and Physical Sciences Research Council (EPSRC) [Grant number EP/R513222/1].
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TR assisted in numerical validation section and general advice on journal layout. LP and TR assisted in T2Well/EOS1 software manipulation. All authors read and approved the final manuscript.
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Doran, H.R., Renaud, T., Falcone, G. et al. Modelling an unconventional closedloop deep borehole heat exchanger (DBHE): sensitivity analysis on the Newberry volcanic setting. Geotherm Energy 9, 4 (2021). https://doi.org/10.1186/s40517021001850
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DOI: https://doi.org/10.1186/s40517021001850
Keywords
 Closedloop deep borehole heat exchanger
 EGS
 NDDP
 T2Well
 EOS1