Master of Science Thesis KTH School of Industrial Engineering and Management

Energy Technology TRITA-ITM-EX 2018:11 SE-100 44 STOCKHOLM

Modelling and simulation for optimizing a deep, closed-loop

geothermal heat exchange system

Bechara HAGE MEANY

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Master of Science Thesis TRITA-ITM-EX 2018:11

Modelling and simulation for optimizing a deep, closed-loop geothermal heat exchange

system

Bechara HAGE MEANY

Approved

2018-02-15

Examiner

Björn Palm

Supervisor

Willem Mazzotti

Commissioner

Contact person

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Abstract This thesis examines the potential of deep geothermal closed-loop installation for the heat supply of the Swedish city of Karlskoga. The thermal behavior of 5.5 km depth bi-directional wells is investigated through a numerical model in Comsol Multiphysics, the development of which is explained here in detail, including geometry, meshing, physics, and results.

Under the local geological conditions, according to current knowledge on drilling technology, and given the assumptions taken in this study, it was found that there are multiple configurations, including curved boreholes, which allow the construction of a closed-loop engineered hydrothermal system partially satisfying the local heat demand of Karlskoga.

The first tried configuration results in the estimation that, after 10 years of operation, 2.82 MW power could be extracted with an outlet temperature of 62.4 °C, while the second model results in 6.51 MW and 56.3°C, with the total drilling length of each model’s borehole system being respectively 20.5 and 42.5 km. The thermal response of these systems is studied over a span of 100 years and estimated to be mostly a radial diffusive mechanism.

Sammanfattning Detta examensarbete undersöker potentialet med djupa och slutna geotermiska anläggningar till värmeförsörjningen av Karlskoga. Det termiska beteende av 5.5 km djupa böjda borrhål utredas genom ett numeriskt modell i Comsol Multiphysics, vars utveckling förklaras här i detalj, inklusive geometrin, meshen, fysiken och resultaten,

Under de lokala geologiska förutsättningarna, med den befintliga kunskapen om borrteknik och de antaganden som togs i studien, det hittades att fler konfigurationer, inklusive böjda borrhål, tillåter byggandet av ett slutet geotermiskt system som delvis täcker värmebehovet av Karlskoga.

Den första simulerade konfigurationen resulterar i ett uppskattat effektuttag av 2.82 MW efter 10 år drift, med vattentemperatur på 62.4 °C. Den andra konfigurationen visar en högre effekt på 6.51 MW fast en lägre temperatur på 56.3°C efter samma drifttid. Den totala borrlängden är av 20.5 km och 42.5 km för den första respektive den andra konfigurationen.

Den termiska responsen av dessa system studeras under en spännvidd av 100 år och uppskattas vara främst radiell.

Acknowledgement I just want to leave a big thank you note to my supervisors, Willem Mazzotti and Oskar Dahlin, who accompanied me through the whole project. I also want to express my gratitude to the Energeotek AB team who made this wonderful experience possible.

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Table of Contents Abstract ........................................................................................................................................................................... 3

Sammanfattning ............................................................................................................................................................. 3

Acknowledgement ......................................................................................................................................................... 3

Table of Figures ............................................................................................................................................................. 5

1 Introduction .......................................................................................................................................................... 6

1.1 Context.......................................................................................................................................................... 6

1.2 Objectives ..................................................................................................................................................... 6

2 Background ........................................................................................................................................................... 7

2.1 Geothermal Energy ..................................................................................................................................... 7

2.2 Previous Work ............................................................................................................................................. 9

3 Part 1: Methodology ......................................................................................................................................... 14

3.1 COMSOL ................................................................................................................................................... 14

3.1.1 Geometries ........................................................................................................................................ 14

3.1.2 Meshing ............................................................................................................................................. 17

3.1.3 Material Properties ........................................................................................................................... 19

3.2 Model and Assumptions .......................................................................................................................... 21

3.2.1 Physics and equations ...................................................................................................................... 21

3.2.2 Boundary Conditions ...................................................................................................................... 22

3.3 Validation.................................................................................................................................................... 23

3.3.1 Validation of the assumptions ....................................................................................................... 23

3.3.2 Validation of model ......................................................................................................................... 24

4 Results: ................................................................................................................................................................ 27

4.1 First Model: single inlet/outlet and three absorption wells ................................................................ 27

4.1.1 Thermal study ................................................................................................................................... 27

4.1.2 Power and temperature curve ........................................................................................................ 30

4.1.3 Influence of Mass flow and Temperature .................................................................................... 31

4.1.4 Lifetime .............................................................................................................................................. 32

4.1.5 G-function ......................................................................................................................................... 33

4.2 Second Model ............................................................................................................................................ 34

4.2.1 Symmetry ........................................................................................................................................... 34

4.2.2 Power and temperature curves ...................................................................................................... 35

4.2.3 Heat demand optimization ............................................................................................................. 36

4.3 Discussion and comparison ..................................................................................................................... 38

5 Conclusion and future work ............................................................................................................................ 40

6 References........................................................................................................................................................... 41

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Table of Figures Figure 1: Example of EGS Power plants in Europe (Shyi-Min, 2017) ................................................................. 6 Figure 2: Estimate of temperature in Europe with depth ( at A 1km, B 2km, C 3km, D 4km, E 5km, F 7km, G 10km) (Limberger, et al., 2013) ............................................................................................................................... 7 Figure 3: Lindal Diagram (Lindal, 1973), Geothermal heat applications ............................................................. 8 Figure 4: Example of an EGS (Moe, 1999) ............................................................................................................... 9 Figure 5: Examples of Geothermal Wells as heat exchangers (Law, et al., 2014) ............................................. 10 Figure 6: Temperature decline at the bottom of the U-tube with different heat extraction rates (Law, et al., 2014) .............................................................................................................................................................................. 10 Figure 7: Geometrical values of Gardemoen EGS(Moxnes, et al., 2012) .......................................................... 12 Figure 8: Parameters for Gardemoen calculations (Moxnes, et al., 2012) .......................................................... 12 Figure 9: Pump specifications for Gardemoen EGS (Moxnes, et al., 2012) ...................................................... 12 Figure 10: Temperature versus accumulated depth, closed loop EGS simulation Holmberg. (2016) .......... 13 Figure 11: Geometrical design of the first model ................................................................................................... 15 Figure 12: Geometrical design of the second model ............................................................................................. 16 Figure 13: Radial temperature profiles surrounding a cylindrical cavity with a constant wall temperature (Holmberg, 2016) ........................................................................................................................................................ 18 Figure 14: The three different sizes of the mesh represented here in Model 1 ................................................. 18 Figure 15: Thermo-physical properties of the rock (granite) as function of temperature in Kelvin. ............ 19 Figure 16: Water flow path in the wells represented in the numerical model 1 ................................................ 20 Figure 17: Thermo-physical properties of the heat transfer fluid (water) as function of temperature in Kelvin ........................................................................................................................................................................................ 20 Figure 18: Temperature gradient, 25°Cper kilometer ............................................................................................ 23 Figure 19: Impact of geothermal gradient on the results, at 5, 10 and 20 years’ time, Normalized to 0.075 W/m2 at their respective time. .................................................................................................................................. 24 Figure 20: Relative difference between local temperature after 100 years and undisturbed rock temperature is plotted on the graphs, at the bottom, side, back and front of the outer volume, from top left to bottom right, respectively. ........................................................................................................................................................ 25 Figure 21: From left to right, temperature and normalized heat flux vector field at 1000m depth and 3509m depth after 100 years’ time at the outlet borehole. ................................................................................................. 26 Figure 22: Isothermal lines and heat streamlines at 3509m depth after 100 years of the outlet borehole. ... 26 Figure 23: Temperature profile around the outlet borehole at 3509 m depth at different times. .................. 27 Figure 24: Isothermal contours on a vertical cross-section. 100 years simulation, 48 degrees inlet at 45kg/s massflow. ...................................................................................................................................................................... 28 Figure 25: Heat flux streamlines. 100 years simulation, 48 degrees inlet at 45kg/s massflow. ....................... 29 Figure 26: Temperature along the boreholes at different depths after 1 to 100 years ..................................... 30 Figure 27: Outlet temperature and outlet power for a constant mass flow and inlet temperature of 45kg/s and 48degC ................................................................................................................................................................... 30 Figure 28: Temperature and power curves, same results as figure 30, but shown with the log of time ....... 31 Figure 30: Temperature and Energy stored in the rock. The Temperature (left plot) is taken from the lowest point at the borehole wall. .......................................................................................................................................... 33 Figure 31: G-function as function of time in years represented in a logarithmic scale .................................... 34 Figure 32: Simplification of the second model domain using symmetry ........................................................... 34 Figure 33: Model 2, Outlet temperature and Power as function of time for a constant mass flow of 45 kg/s, a constant inlet temperature of 48°C and from 2 to 8 boreholes modelled ...................................................... 35 Figure 34: Power in MW at 10 years’ time as function of the number of boreholes ....................................... 35 Figure 35: Karlskoga average heat demand throughout a year (Data given by Energeotek AB.) .................. 36 Figure 38: Usage of the ground as heat storage, injection of heat during summer (Bär, et al., 2015) ........... 38 Figure 39: Usage of the ground as heat storage, extraction of heat during winter (Bär, et al., 2015) ............ 39

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1 Introduction

1.1 Context Awareness of anthropogenic climate change has been rising exponentially over the past few decades, as well as the many consequences and ramifications it can have for the globe and life it inhabits. To mitigate said consequences, and in an effort to avoid the worst case scenarios, considerable labor is now being invested towards reducing greenhouse gas emissions by moving away from conventional combustion of fossil fuels as a source of energy, those fuels being replaced with renewable energy sources.

Geothermal energy is one such renewable energy source. It exists in abundance across the globe, and can be utilized to provide clean energy for heating and cooling purposes and /or electricity production.

Geothermal energy is a mature and proven technology. However, there is room for improvement: nowhere is it being used close to full capacity. As of today, the exploitation of deep geothermal energy as an energy source is primary confined to areas with naturally-occurring hydrothermal systems and volcanic activity (Lund, et al., 2016). However, it is entirely thinkable to exploit geothermal energy in any point in the globe, even those with the lowest temperature gradients, by artificially engineering hydrothermal systems. Said EGS can provide a way for geothermal energy to grow outside its geographical constrains. While these have not been fully developed and proven commercially viable at the present time, they are currently being researched and studied by this work and similar others such as Holmberg (2016).

As a matter of fact, EGS technology has seen ample development by multiple agents with an aim towards the valorization of low-temperature geothermal potential reached with deep boreholes in specific areas, such as, in central Europe, the area of the Rhine Graben between France and Germany, with a pilot plant in Soultz-sous-Forêts (France), as well as other EGS plants that were built in Landau (Germany), and Rittershoffen (France) which are presented in Figure 1.

Figure 1: Example of EGS Power plants in Europe (Shyi-Min, 2017)

1.2 Objectives The aim of the project is to study the behavior of fracture free, closed-loop EGSs in the specific conditions of the Baltic Shield, establishing a tool for decision makers and investors to help them determine the energetic and economic viability of such installations. The Baltic Shield has a heat gradient that is among the lowest in the globe, and, for the most part, an impermeable and uniform granite bedrock. This study is performed through thermal modeling and simulations of several EGS with different geometries, followed by a parametric study of different design and operation variables on the performance of the EGS. This study focuses on the development and simulation of a model for one specific case: the potential construction of an EGS in Karlskoga in collaboration with Energeotek AB, a startup focusing on providing geothermal solutions in the heat and power generation field. Numerical results are obtained by calculation though finite-element method (FEM) simulations in software COMSOL Multiphysics® (COMSOL®).

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2 Background

2.1 Geothermal Energy The Earth’s mantle and crust contains radioactive elements that are constantly decaying, emitting radiation that becomes heat (Gando, 2011). This process added to the heat coming from the Earth’s core entails a drop in temperature from the core to the surface. From a practical perspective, the temperature inside the Earth’s crust is seen to increase linearly with depth. This phenomenon is called the geothermal gradient.

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Figure 2: Estimate of temperature in Europe with depth ( at A 1km, B 2km, C 3km, D 4km, E 5km, F 7km, G 10km) (Limberger, et al., 2013)

As seen in Figure 2, ground temperatures in continental Europe reach values over 100°C that can be used for heat generation, as one reaches below a few kilometers depth. Sweden is of particular interest in this study; there, approximatively 80 to 120 °C is reached at 5km depth. This does not come off as a particularly impressive or favorable scenario for geothermal energy, if compared to how the temperature gradient is in Iceland for example. Nevertheless, there are many low-temperature applications in which a geothermal heat plant could provide an economically and ecological advantage. Figure 3 lists such applications for a wide

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range of temperature gradients. In the case of Sweden, where ground temperatures are estimated to go as far as 120 degrees Celsius at 5km, usages range from fish farming and space heating to greenhouse farming.

Figure 3: Lindal Diagram (Lindal, 1973), Geothermal heat applications

There are many different ways to exploit geothermal energy, and in this report we will only focus on EGS, it is a power generating system that differentiates from the rest because it does not need the presence of natural phenomena like convection or permeable rocks. The strategy is to drill a set of boreholes that connect underground, thereby forming a basic heat exchanger. Water is injected under pressure through the wells; it heats up along the wells’ length through the borehole surface, and comes out again. Heat is then extracted for whatever purpose is appropriate, such as for the generation of electrical power and/or for used directly in a variety of applications, one of the most well-known and sought-after being district heating. For instance, Figure 4 shows a schematic example of an engineered geothermal system, where water is injected at 45°C and recovered at 75°C. The extraction takes place down to 5 km deep, and, at this depth, the temperature is assumed to be 110°C. Such a heat plant could produce as much as 1.6 MW of heating power.

If the extraction temperature is high enough, it is also possible to produce electrical power, either with a closed-loop organic Rankin cycle (ORC) or with a conventional turbine. ORC geothermal power plants have seen development in central Europe as mentioned in part Context1.1.

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Figure 4: Example of an EGS (Moe, 1999)

2.2 Previous Work This section recounts and describes results from similar studies and other relevant research, giving an overview of the technological state of the art and the theoretical knowledge base that serve as grounding and context for this study itself.

In Sweden, geothermal wells are commonly used in small applications, such as local heating of houses. These wells are usually quite shallow, being designed for different purposes than the one presented in this report. However, looking at some results is helpful to understand the overall heat transfer mechanisms that one finds in underground heat exchangers; it provides preliminary understanding of the EGS that is to be modelled.

In Figure 5 three different types of geothermal wells are shown. Out of these three variations of the technology, the closed U-Tube type of borehole heat exchanger is the most similar to a closed-loop EGS. The system is fairly simple; cold water is injected in one of the tubes, heats up along the way down and comes back up through the U-tube at a higher temperature.

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Figure 5: Examples of Geothermal Wells as heat exchangers (Law, et al., 2014)

In Law’s study (2014) simulations are run using the U-tube geometry. Different but constant heat extraction rates are imposed to the well. The evolution of the return temperature with time is shown in Figure 6. The study establishes that the higher the extraction rate, the quicker the ground temperature drops, and how this in turn leads to a drop in temperature of the return water (Law, et al., 2014).

Figure 6: Temperature decline at the bottom of the U-tube with different heat extraction rates (Law, et al., 2014)

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This provides the first indication of a fact that this report returns to multiple times: that while the heat in a certain volume of soil is a renewable resource, it replenishes itself much slower than what would be considered a practical exploitation rate. This gives such thermal power plants a specific horizon of usage depending on the intended purpose and the required temperature. Such a horizon can be expanded or controlled through recharging of the system. One could imagine that re-injecting hot temperatures into the ground recharges part or all of the energy previously extracted. This can thus provide a more sustainable heat source, where heat is extracted during winter time (high demand) and re-injected during summer (low demand). However, even without reinjection of heat, said horizon can be easily in the order of magnitude of decades; a reasonable time-frame for a large scale project.

There are many studies of co-axial heat exchangers, some of them as deep geothermal heat exchangers. These studies look promising as it was found that it is possible to provide for 69% of the energy consumption of an office building with a 2.5 km deep co-axial heat exchanger (Huchtemann, et al., 2013).

Such systems have been approached with similar strategies as the one of this study, namely using numerical simulations to model the system performance. These results serve as a guideline and the response of this study’s heat exchanger are estimated to show better results, although the construction of the EGS is more challenging and likely more costly (Le Lous, et al., 2015). Others are looking into reconverting old abandoned boreholes into heat exchangers. It was found that a 2302 m deep borehole heat exchanger plant could provide 200 kW of heat capacity (Kohl, et al., 2002).

Another study deals with the heating of an airport in Oslo, Gardemoen (Moxnes, et al., 2012). In this study, an EGS is sized in order to provide heating for the airport.

The geometry of the underground pipes is very similar to Figure 4. Namely, it consists of a closed circuit in which the descending borehole fans out and is sub-divided into multiple smaller boreholes, also known as cross wells, diverging from each other in order to secure a larger effective volume of ground that can be depleted of its heat. To further increase the distance covered and the volume of ground exploited relative to the maximum depth of the borehole, the cross wells are inclined. The cross wells then converge again, collecting the heated water towards the ascending vertical borehole, through which the hot water is pumped back up into the thermal station. The latter usually mainly consists of a heat exchanger that can be used to whichever purpose the consumer deems fit, given high enough temperature levels. Heat pumps could be used in case of too low temperature levels obtained from the underground installation.

The geometrical values of the projected Gardemoen plant are gathered in Figure 7. Notably, the borehole is shown to be 5 km deep. The engineered system involves no less than twenty-one cross wells, each of them two kilometers long and inclined by 40° inclined.

The modeling and calculations were done with “Geocalc”, a spreadsheet developed at the Department of Energy and Process Engineering at NTNU. It is specifically designed for geothermal plants with two drilled vertical wells and a drilled sub-surface heat exchanger. The parameters and requirements of their calculations are presented in Figure 8. The inlet fluid is water, which comes in at 55°C and returns with a temperature gain of 27°C and a pressure loss of 7 bar. The exploitation time horizon for their study is set to ten years. Notably, the type of rock and the temperature gradient are functionally identical to the ones in our own study’s chosen location, which positively impacts the study’s relevance and comparability to our own.

Such a power plant has an average heat production of 10 MW at 82 C° with a required pumping head of 7 bar as seen in Figure 9.

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Figure 7: Geometrical values of Gardemoen EGS (Moxnes, et al., 2012)

Figure 8: Parameters for Gardemoen calculations (Moxnes, et al., 2012)

Figure 9: Pump specifications for Gardemoen EGS (Moxnes, et al., 2012)

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The last study which is referred to in this project is another Norwegian study (Holmberg, 2016). This study is of particular importance because similar simulations were done; it is thus used for comparison and validation of the results

Figure 10 shows a typical temperature profile along the length of the system. In this example, the water enters the system at 60 °C and returns at 90 °C. The temperature drops near the entrance and exit of the wellbores; adding insulation to those sections could increase the efficiency of the system by reducing heat losses. According to Holmberg (2016) these are most prominent during the first years of operation, and are mostly important for smaller systems.

Figure 10: Temperature versus accumulated depth, closed loop EGS simulation Holmberg. (2016)

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3 Part 1: Methodology

3.1 COMSOL

3.1.1 Geometries

The aim of this project is to study a closed-loop EGS for a possible installation in Karlskoga, Sweden, to provide 15 MW of thermal power at 90°C during winter. The geometrical design of the EGS for such power plant is critical to maintain the production requirements. Ultimately, the EGS design is tailored to the geological conditions of the location.

Achieving exploitable temperatures in the Baltic shield requires drilling below 5 km distance, where the temperature of the ground is estimated to be around 100°C. Thus, the depth of the geothermal heat exchanger investigated in this project is set to 5.5 km.

Current drilling technology also dictates which type of geometries can be utilized for the boreholes. Current drilling technology enables the drilling of bi-directional wells, with curvatures radius of minimum 1910 m. For practical and cost-related reasons, the surface part of the design (inlet and outlet holes) should preferably be confined to a limited area.

These parameters have led to two designs for the geometry of the underground pipes. The geometry of the first model is represented in Figure 11, while Figure 12 shows the design used for the second model. Finally, Table 1 gathers the values of the design parameters.

Both designs can be divided in three fundamental parts:

1. The inlet wells are straight boreholes, which begin at the surface, and are inclined with respect to the vertical axis. The fluid entering the inlet wells is colder and is led into the absorption wells.

2. The absorption wells are curved, bi-directional boreholes that connect the inlet and outlet wells. It is through these wells that most of the heat is absorbed from the ground: they are the core of the heat exchanger.

3. The outlet wells are straight vertical boreholes that are drilled directly from the surface and meet the absorption wells at the bottom, collecting all of the hot water and leading it upward to the surface.

The first model or model 1, as shown in Figure 11, consists of a single inlet, a single outlet, and three absorption wells. The inlet well is straight, and angled at the surface. The inlet borehole then diverges into three different bi-directional absorption wells. At maximum depth, the three absorption wells gather again.

This is the point at which the outlet well meets the absorption wells, collecting the circulating water for extraction.

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Figure 11: Geometrical design of the first model

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Figure 12: Geometrical design of the second model

In the second model a different approach is taken, the design has multiple inlets and one outlet. Each inlet well is identical and starts with an angled straight well, that turns into a bi-directional well becoming again straight at the target depth in order to maximize the heat uptake where the temperature is the highest. The number of inlet wells is modular and Figure 12 shows an example with 8 inlet wells.

The second model, or Model 2, builds upon the first model to develop a different variant of the same approach. Instead of having one inlet splitting into multiple absorption wells deeper in the ground, the inlet and absorption wells are one and the same in this model. All the inlet wells nevertheless converge at the maximum depth where the single vertical outlet well is met.

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Variables  Model 1  Model 2  Description 

Zmax  5500 [m]  5500 [m]  Max depth outlet well 

RS  1909.9 [m]  1909.9 [m]  Bidirectional drilling radius 

L  0 [m]  1500 [m]  Straight distance at the bottom 

num  3  1‐12  Number of absorbtion wells 

Beta  18 [deg]  360/num [deg]  Separation Angle between Wells 

Hx  1617.2 [m]  2317.2 [m]  x coordinate at max depth inlet well 

Hz  2574.1 [m]  2207.2 [m]  z coordinate at max depth inlet well 

H  2806.1 [m]  3200.2 [m]  Length of straight section of Inlet Well 

D  500 [m]  500 [m]  Separation between inlet and outlet wells at surface 

Alpha  32.14 [deg]  46.39 [Deg]  Angle Inlet Well 

R_in  0.16 [m]  0.16 [m]  Radius inlet well 

R_out  0.16 [m]  0.16 [m]  Radius outlet well 

r1  0.11 [m]  0.11 [m]  Radius Absorbtion well 

Table 1: Geometrical design parameters of the boreholes

3.1.2 Meshing

This work employs a Finite Element Analysis method (FEA) to simulate the behavior of the system and extract the resulting data that is to be analyzed and mined for information. The system is divided into a number of discrete small elements, the behavior of which is predicted in a simplified way as a succession of discrete states in which short periods of time separate one state from the next. In general, the smaller the elements and the leaps in time, the higher the precision of the model. There are some requirements for the convergence of the simulations, notably the time steps need to be smaller than a certain value that depends on the size of the mesh.

However, smaller elements and time steps require higher processing power. In areas of the system where not much change happens over time and space, or where what happens is not critical or relevant to the final sought result, this processing power would be wasted. Therefore, the mesh will be designed to be finer and denser where the most important changes happen. On the opposite, it will be coarser and contain fewer elements in the areas where very little change occurs.

Accordingly, the meshed volume has been divided into three regions, with Figure 14Error! Reference source not found. providing a graphic representation of how this division was implemented in Model 1, and Figure 13 a graph extracted from Holmberg (2016) used to define the different sizes of the three regions:

1. The primary or inner region is the area closest to the borehole, where heat conduction, and therefore temperature gradients, are the highest. Temperature in this area changes significantly as the radius increases outward from the tube, and this temperature profile is quickly and intensely affected by the temperature and mass flow of the circulating fluid in the borehole. Therefore, the mesh in this area needs to be especially fine. It is the inner cylinder shown on the right section of Figure 14Error! Reference source not found., surrounded by the intermediate region.

2. The secondary or intermediate region is the volume between the primary and the general domain of the numerical model. Figure 13 shows that this volume only needs to encompass a radius between 150 and 200m away from the point of heat exchange, with temperatures beyond that distance remaining negligibly affected under the system lifetime. Therefore, this 150m-radius cylinder-shaped volume around each borehole is considered to be the “heat resource” or “exploited volume”

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from which the system obtains its energy, while the rest remains undisturbed. This is an area where important changes happen, but where these changes are far less intense than in the primary region, thus being attributed a less dense finite element mesh. The secondary region is shown in all three illustrations of Figure 14.

3. The third or outer region is the rest of the volume of simulated soil in the area where the boreholes are drilled. As no changes are expected to happen in it, its mesh can be allowed to be very coarse, with very large elements, without any cost in terms of the precision of the final results. This region serves mainly to set the right boundary conditions. It is the parallelepiped shown on the left illustration of Figure 14, surrounding the intermediate region.

Figure 13: Radial temperature profiles surrounding a cylindrical cavity with a constant wall temperature (Holmberg, 2016)

Figure 14: The three different sizes of the mesh represented here in Model 1

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3.1.3 Material Properties

3.1.3.1 Rock

The ground material in which the boreholes are drilled is assumed uniform and composed of granite. Its relevant thermo-physical properties are presented in Figure 15. Given the temperature range involve in the simulations, the material has a thermal conductivity that decreases with temperature, a heat capacity at constant pressure that linearly increases with temperature, and a density that is not temperature-dependent. The influence of the porosity of the rock was not included in this study.

This granite is the material in which the heat is stored, and it is through direct contact with it that this heat is extracted by the circulating fluid.

Figure 15: Thermo-physical properties of the rock (granite) as function of temperature in Kelvin.

3.1.3.2 Heat Transfer Fluid

In conventional EGS the heat transfer fluid is water mixed with minerals from the rock, mostly salts (brine). Constant recirculation in the subterranean circuit (as shown in Figure 16) in direct contact with the granite is bound to load the circulating fluid with diverse salts, eventually turning it into a brine of sorts. The effects of this change and any other geochemical reactions are not considered in this study. The circulating fluid is thus treated as fresh water, with the properties that are shown in Figure 17.

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Figure 16: Water flow path in the wells represented in the numerical model 1

Figure 17: Thermo-physical properties of the heat transfer fluid (water) as function of temperature in Kelvin

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3.2 Model and Assumptions

3.2.1 Physics and equations

3.2.1.1 Conduction in the Granite

Fourier’s heat equation in solid may be written as

.

where

is the density of the rock

is the heat capacity at constant pressure of the rock

is the heat flux in the rock

is the thermal conductivity of the rock

T is the temperature of the rock

Q is the heat sources in the rock

Note that all bold characters refer to vectors and non-bold to scalars.

The first, time-dependent term on the left of the equation, denotes the thermal power that is stored in or extracted from the rock per unit volume. It is proportional to the rate of temperature change over time. The second term refers to the spatial rate at which heat is conducted across the rock via temperature gradients. The third term refers to the heat sources or sinks in the rock itself like heat generated by radioactive decay or chemical reaction. In short, these equations derive from the first principle of thermodynamics, the conservation of energy: the changes in stored heat caused by temperature changes in the granite over space and time add up to the heat that the granite intrinsically generates or loses.

3.2.1.2 Thermal pipe flow

The momentum and continuity equations may be expressed as:

∙2

| |

∙ 0

where

u is the fluid velocity

ρ is the density

P is the pressure

is the Darcy friction factor

F is the volume force terms, Gravity

A is the cross section

is the hydraulic diameter of the pipe

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The Navier-Stokes momentum equation is also a conservation law, with, on the left-hand side, a time-dependent term and a term that depends on space variation, both relating to the velocity, acceleration, and momentum of the fluid. It should be noted that the second term, which is similar to convection, involving the spatial velocity gradient, turns out to be negligible for the purposes of this study’s calculations, as we assume an incompressible fluid and piecewise-constant cross section, which from the continuity equation means that div(u)=0. In the model, only the tangential component of this equation with regard to the pipe, is considered.

The solution to the Navier-Stokes equation system is a field of flow velocity, applying Newton’s second law to fluid motion in a dissipative system. The right side terms then describes the following: the first term denotes the effect of hydrostatic internal forces (the spatial changes in fluid pressure), the second describes the pressure drop due to viscous shear friction because of the fluid viscosity, and the last one represents the effect of volume forces, of which the only one relevant in in this case is gravity.

The following is a formulation of the energy conservation equation, for an incompressible fluid in a pipe:

. . Ak2

| |

is the fluid heat capacity

T is the fluid temperature

is the transverse component of the fluid velocity

is the normal vector along the transversal direction

k is the thermal conductivity of the fluid

is the heat transferred along the walls of the pipes

It is similar to the Navier-Stokes Momentum Conservation Equation seen above, but instead of looking at the momentum, it describes the energy conservation. On the left-hand side, as expected, are a “temporal variation” term and a “convection” term. On the right-hand side is the friction heat dissipated due to the viscous friction and conduction, and, finally, the heat exchange outside of the wall.

3.2.2 Boundary Conditions

The top surface temperature is set as the yearly average atmospheric temperature, which is considered constant (see Table 2). The inlet temperature is that at which the water is delivered into the system, this temperature was considered both constant in some simulations, and variable in others in such a way that the heat extraction rate was imposed. The geothermal heat flux in the ground represents the rate at which heat enters the defined simulation domain: the natural heat coming from the center of the Earth, which contributed to create with radioactive decay of elements the temperature gradient in the first place. The surface roughness is used by the model to determine viscous behavior, convection rates and losses due to surface friction. The surface roughness was taken as 1 cm, a rough approximation describing a coarse rock-fluid interface.

Variables  Model 1  Model 2  Description 

Tamb  5 °C  5 °C  Surface Temperature Tin  48 °C  48 °C  Inlet Temperature 

mflow  45 kg/s  45 kg/s  Mass Flow qground  0.075 W/m2  0.075 W/m2  Heat Flux in the Rock Srough  0.01 m  0.01 m  Surface Roughness inside the wells 

Q  ‐  15 MW  Heat extraction (overrides inlet temperature 

Table 2: Boundary Conditions

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3.3 Validation

3.3.1 Validation of the assumptions

3.3.1.1 Materials

Granite is chosen as a type of rock due to being extremely common: the main and often only constituent of the bedrock in the Baltic Shield (SGU). While it is possible for there to be sand pockets or layers of other materials, rock fractures, changes in porosity, or property shifts between different types of granite in the same substrate, for the purposes of this work, the material is considered uniform and homogenous. Note, however, that its properties are temperature dependent as described in section 3.1.3.1

3.3.1.2 Temperature gradient and Boundary Conditions

The temperature gradient in this work is taken to be a constant 25°C per km. This is a simplification as fractures, porosity, and humidity circulating through the rock, local anomalies such as volcanic activities or higher concentrations of radiogenic elements as well as the material being otherwise heterogeneous, may cause the flow of temperature over distance to vary. Nevertheless, in this model, the system is assumed to have a constant temperature gradient in its undisturbed state, as shown in Figure 18.

Figure 18: Temperature gradient, 25°C per kilometer

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Figure 19: Impact of geothermal gradient on the results, at 5, 10 and 20 years’ time, Normalized to 0.075 W/m2 at their respective time.

It should be noted, however, that the geothermal temperature gradient is easy to adjust in the model. As Figure 19 shows, the difference in the power extracted and in the outlet temperature is easily calculated by a simple proportional coefficient. It should be noted that the graph does not show the temperature gradient directly, but the geothermal heat flux. The two values are directly proportional within the considered range of geothermal heat flux, the thermal conductivity being the proportional constant.

More precisely, Figure 19 shows a parametric approach, in which one considers the behavior from high to low gradient, normalizing all the results with the highest value 0.075 W/m2 or 25°C/km for the given thermal conductivity. The normalization was done by dividing the power and outlet temperature achieved at the studied geothermal gradient by the power and outlet temperature achieved with a 0.075 W/m2 geothermal flux, for a given time.

Therefore, as the graph shows, a geothermal gradient of 0.045 W/m2 yields 30% of the energy extracted compared to a geothermal gradient of 0.075 W/m2. However, the temperature gain remains 80% as compared to the simulation with the highest geothermal heat flux.

Notably, the graphic shows that the timescale does not significantly influence the behavior of the normalized temperature and power curves shown in Figure 19. That means that for the time scales studied here, the geothermal gradient and time are separate variables. Thus one could use these results to estimate the performance of an EGS under different temperature gradient conditions without redoing complex numerical analysis studies.

3.3.2 Validation of model

In this context, what is meant as validation is a verification of the coherence of the simulation results and their consistency with the stated assumptions.

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3.3.2.1 Size of the ground

The size of the ground needs to be large enough to encompass all the physical changes during the time of the study. Thus the changes in temperature at the boundaries of the studied volume where studied, If the model would show appreciable changes in the state of the border would mean that the system would not be represented in its totality and it would be necessary to consider a larger simulation domain.

Figure 20 shows the temperature variation in percentage after 100 years at the bottom, side, back, and front of the volume. At first sight of the plots shows a variation of colors between regions, a glance at the legends shows that the differences are of the order of one hundredth of a percent, that is to say, entirely negligible.

Figure 20: Relative difference between local temperature after 100 years and undisturbed rock temperature is plotted on the graphs, at the bottom, side,

back and front of the outer volume, from top left to bottom right, respectively.

3.3.2.2 Mesh

Figure 21 shows two transversal cuts around the extraction cylinder, showing a color map of the temperatures and a vector field of black arrows representing the bi-dimensional heat flow. The plot on the left shows the situation at a thousand meters’ depth, while the other is set at a depth that is closer to the bottom, at 3.5 km. These graphs illustrate the direction of the heat flux vector at different depths, showing that at shallower depths heat is going out of the borehole, i.e. heat is lost, as opposed to larger depths where heat is going in the borehole.

The temperature change is mostly confined to the inner part of the intermediate area, represented by the larger cylinder in Figure 21 and negligible near its outer boundary.

Figure 22 shows the isothermal lines and heat streamlines at the same depth as Figure 21’s right plot. The plot demonstrates a clear radial symmetry around the central axis, as expected.

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Figure 21: From left to right, temperature and normalized heat flux vector field at 1000m depth and 3509m depth after 100 years’ time at the outlet

borehole.

Figure 22: Isothermal lines and heat streamlines at 3509m depth after 100 years of the outlet borehole.

3.3.2.3 Transient simulations

Figure 23 shows radial temperature profiles of the rock around the vertical outlet borehole. The borehole is in the middle of the figure, where the sharpest temperature changes occur, and is surrounded by rock material. Every color-coded curve corresponds to a different simulation time with the unit ‘a’ standing for years.

The blue curve is the first chronologically, and shows an increase in temperature in and around the borehole. The temperature keeps increasing until it reaches 140°C shown by the green curve in the graph. After that the trend abates and reverses; the temperature eventually decreases further on.

This initial temperature increase is due to the initial conditions. At time zero, the temperature of the rock and water in the borehole is at every point equal to the undisturbed ground temperature at that depth. The surface temperature is 5°C, and at the bottom 140°C.

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Therefore, initially, what is observed is said water at 140°C that is coming up through the outlet borehole. The time scale at which this phenomenon happens is negligible compared to the length of the study, namely 0,001 years compared to 100 years. Therefore, this phenomenon has a negligible influence on the later stages of the system and can be ignored for the purpose of this study.

Once the quasi-steady-state conditions in the borehole are settled. In the center, where the borehole is, the temperature is that of the borehole wall. This is due to the operating physics with the software COMSOL Multiphysics. A numerical approximation is done by the program, where the boreholes are 2-D lines. The temperature of the rock converges then to the temperature calculated at the borehole wall when approaching the line in question. To get the temperature of the fluid, the program calculates it using known empirical calculations of the heat transfer coefficient. Then, as distance from the borehole increases, the measured temperature starts converging towards the undisturbed temperature.

Figure 23: Temperature profile around the outlet borehole at 3509 m depth at different times.

4 Results

4.1 First Model: single inlet/outlet and three absorption wells

4.1.1 Thermal study

Figure 24 is a cross-section of the model domain, cutting through the centermost of the three absorption wells as well as the outlet well. The color lines are isothermal lines; one may notice their distortion around the borehole. Isothermal lines going down in the vicinity of the borehole means that the temperature inside the borehole is lower than outside, thus heat is going into the fluid, on the opposite isothermals going up in the vicinity of the borehole means that the temperature inside the fluid is higher than in the rock, thus heat is going out of the system The sharpness of the drop of the isothermal lines is an indicator of the heat flux intensity, one can see that it is at the bottom of the system where the heat flux is the greater. Although heat is lost in the top part of the underground system, heat is extracted through most of the borehole length.

Figure 25 is similar to Figure 24, but with an added top layer of red-colored heat streamlines. One can approximatively see the points where the streamlines are not going into the borehole anymore, and instead go tangent. At these points, the water in the borehole does not extract any heat: the temperature inside the

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borehole and in the rock is identical. In the sections below these points, the water in the borehole gains heat as shown by the streamlines flowing into it from higher temperature levels, while in the sections above, it loses it as the streamlines flow out. This happens when the temperature inside the water is hotter than the surroundings, so heat is lost instead of gained as the water moves along the borehole. Whereas, in the former case, the water is colder than its environment, so heat goes flows out of the rock and into the water.

This transition point is therefore a good reference as to how far to extend a potential added insulation around the boreholes, as it is the furthest distance at which the insulation ceases to be useful

Figure 24: Isothermal contours on a vertical cross-section. 100 years simulation, 48 degrees inlet at 45kg/s massflow.

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Figure 25: Heat flux streamlines. 100 years simulation, 48 degrees inlet at 45kg/s massflow.

Figure 26 shows the temperature along the borehole at different times and in two different graphs. In the first one on the left, temperature is plotted as function of depth. In the second one, on the right, the same temperature is plotted as function of the cumulated length along the heat exchanger. It shows how temperature changes dramatically over a very short distance at the heat absorption wells. As indicated by their name, this is where most of the heat is absorbed. The water also absorbs some heat and gains temperature along the inlet and outlet wells, although heat is lost in the upper part of these wells too.

It is also possible to see how the temperature profiles change with time: the temperature gain in the absorption wells grows smaller and smaller as the rock around the wells cools down and the amount of available energy to be harvested diminishes.

It should be noted that it is similar to the plot shown in Figure 10. The latter resulted of applying an analytic Simulink model to a very comparable situation. Although different parameters entail different outputs, the similarity of the results tips the scales in favor of this model’s validity.

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Figure 26: Temperature along the boreholes at different depths after 1 to 100 years

4.1.2 Power and temperature curve

In this section, the thermodynamically response of the ground from the fluid perspective. In Figure 27 and Figure 28 Simulations were run with constant inlet temperature of 48C° and 45 kg/s mass flow for a hundred years, the outlet temperature of the fluid and the outlet power is plotted on the graphs, the power was taken as the difference between inlet and outlet temperature times the mass flow and heat capacity of the water at every instant. Figure 28 shows the same results as Figure 27, the difference being that the time scale was set to logarithmic to have an idea of how these values evolve during the first instants of operation.

These figures show that at constant inlet temperature and mass flow the outlet temperature and power one can produce from such a system decays over time in a quasi-stationary way, slowly reaching its steady state. Outlet temperatures go from 70C° after 1 month, 64C° after 1 year, 62 C° after 10 to 60 C° after 100. The values at ten years of operation were taken as reference for comparison, in this case 62,40C° and 2,82 MW.

Figure 27: Outlet temperature and outlet power for a constant mass flow and inlet temperature of 45kg/s and 48°C

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Figure 28: Temperature and power curves, same results as figure 30, but shown with the log of time

4.1.3 Influence of Mass flow and Temperature

Figure 29 allows one to compare the outlet temperature and power output for different given inlet temperatures of the fluid. In all results so far in this report, the inlet temperature has been set to 48°C. This Figure shows what happens if this parameter is instead set as 10, 30, 50 or 70°C. All the presented results are taken after 10 years of continuous operation under the same regime.

Figure 29: Influence of inlet temperature on the outlet power and outlet temperature

Figure presents the variation of the same two parameters with regards to the mass flow. Until now, the latter was set as 45 kg/s for all the presented simulation results, whereas it is varied between 15 and 60 kg/s for the results shown this figure.

Figure 28 shows that a lower inlet temperature allows for higher power extraction while delivering a lower return temperature. The tradeoff looks linear.

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Changing the mass flow has the opposite impact. Lower mass flows result in higher outlet temperature but lower power, and vice-versa.

On an intuitive level, this can be explained thusly. Let us postulate a specific volume. There is a pipe running through the middle, though which water is run to extract heat. Lower mass flows yield lower heat extraction rates. On the other hand, higher mass flows result in a higher heat extraction rate, this also means that the temperature in the rock would decrease faster as more heat is extracted from it. However, the higher the mass flow, the bigger the volume of water that the heat that one is extracting is diluting in, so the outlet temperature of the water is lower.

At constant mass flow and variable inlet temperature, the difference in power is then due to the difference in temperature between the rock and the water. The bigger this difference is, the more heat flows from the hot source to the cold. However, the starts with a lower amount of energy, resulting in a lower amount of energy at the outlet, which means a lower outlet temperature.

Figure 30: Influence of mass-flow in the outlet power and outlet temperature

4.1.4 Lifetime

Figure 30 shows the simulated borehole wall temperature at 5.5kmand net energy balance under 100 years of heat extraction followed by 800 years of recovery. The inlet temperature and mass flow are kept constant under the heat injection period, and then left to rest for 800 more years without any circulation. The left figure is the temperature of the borehole wall at the deepest point of the EGS, and the right is the energy change in the rock, it is the difference between the initial value and the current value of the heat capacity at constant pressure times the density and temperature of the rock. This was calculated for the volume inside the intermediate mesh i.e. at 160 meters’ radius from the borehole.

The energy drop looks linear, lasting 100 years, with 45kg/s as a mass flow rate. Subsequently, the heat extraction is stopped and the ground naturally recovers. The plots show that, although the temperature lost returns over 300 years to 95% of its original value at max depth, the energy initially stored in the rock takes much longer to be replenished: after 800 years of recovery it’s only come back to 60% of what it was.

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Figure 29: Temperature and energy stored in the rock. The temperature (left plot) is taken from the lowest point at the borehole wall.

4.1.5 G-function

The following equation defines the function called G. It was initially defined for cases where the initial temperature and borehole wall temperature are uniform. Traditionally used in GSHP systems, here we have adapted it to this study, taking an average of the values in question. It involves the following factors:

2π⋅

is the average temperature at the borehole wall interface.

is the average undisturbed temperature of the ground through the borehole length

q is the average heat extraction rate in W/m

k is the average rock’s conductivity over the length and temperatures of the system.

The G function is non-dimensional as are the parameters it depends on; namely time over a characteristic time of the system. The plot in Figure 31 over a period of 1000 years. The G function is plotted in blue, for a system operating with a constant mass flow of 45kg/s, and a constant heat extraction rate of 0.5MW. This is guaranteed by regulating the inlet temperature.

Traditionally, this G function is used in simple, shallow, straight boreholes. Within that limited context, this is a robust tool used for dimensioning installations.

The G function represents how the system reacts to a power step. A linear G function corresponds to radial 1-D heat transfer, one dimensional analytical solutions could be used to describe transient heat transfer in the vicinity of the borehole (Cimmino, et al., 2014).

However, after the initial linear phase of G, thermal interaction of neighboring boreholes, in our case absorption wells, and radial-axial 2-D heat transfer mechanisms dictate the behavior of the system and the increasing slope of the G function. Finally when the steady state is reached and he borehole field and ground are in equilibrium, the G function becomes constant (Cimmino, et al., 2014).

The plot in Figure 31 shows that, for this system, the G function is pretty linear with regard to the logarithmic time between the 0.01 years and 10 years, one can also see that between year 10 and 100 the deviation from this linear trend is inferior to 10%, after 100 years the trend changes more significantly and the ILS approximation is no longer accurate. This is due to other heat transfer mechanisms that come into play such as interaction between boreholes and radial-axial heat transfer as mentioned above.

Although this means is that it is possible to approach this modeling problem, for the same geometry, with an analytic estimation that is reasonably accurate, this simpler approach would have limitations in flexibility, when generating different scenarios with different boundary and initial conditions, as well as not adaptable to more complex scenarios, for example one that considers groundwater flow.

G-functions for infinite line source problems are also presented in Figure 31, for wells with a diameter equal to the one used for the absorption wells and for the inlet/outlet wells. It is shown that the first years of operation the system acts as an infinite line source of diameter equal to the absorption wells.

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Figure 30: G-function as function of time in years represented in a logarithmic scale

4.2 Second Model Model 2 is designed with a variable number of heat-absorption boreholes radially distributed around the center, where they converge in one single return borehole. In Figure Figure 12, an example of 8 absorption boreholes was presented.

4.2.1 Symmetry

A model with multiple boreholes can more easily become excessively large and, thus, time-consuming for COMSOL to calculate. The way to avoid this is to take advantage of symmetry to reduce the size of the simulated domain. For instance, Figure 32 shows a configuration with eight wells, along with all the resulting symmetry planes, which are drawn here in red lines. The resulting representative domain which was selected to be the simulation domain is the red triangle highlighted in the lower area of the graph.

Figure 31: Simplification of the second model domain using symmetry

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The black triangle area seen in Figure 31 is removed from the modelled domain because this space is too distant from the borehole for there to be any perceptible changes within the relevant timescale of 100 years for a longer simulations time, a larger domain is also needed to account for the change in temperature of those areas. The final simulation domain is portrayed on the right side of Figure 32.

4.2.2 Power and temperature curves

Thereafter, Model 2 is tested for several numbers of boreholes, namely every 2 boreholes from 2 to 8 items in total, with a constant inlet temperature of 48°C and a constant mass flow of 45kg/s. Note that the model domain is adapted to the number of borehole simulated.

Figure 33 shows, on the left, the evolution of the outlet temperature with time, and, on the right, the evolution of power with time for all different scenarios.

It is conspicuous that the resulting outlet temperature is independent of the number of boreholes we get if they are all identical, because they are far enough from each other that they interact very little, with the only interference happening at the bottom.

Figure 32: Model 2, Outlet temperature and Power as function of time for a constant mass flow of 45 kg/s, a constant inlet temperature of 48°C and

from 2 to 8 boreholes modelled

As shown in Figure 34, the power obtained increases with the number of boreholes. While the relation is not directly proportional, it is practically linear, because the thermal interaction between boreholes is weak. Per borehole, the power extracted in these conditions after 10 years is about 1.63 MW.

This power per borehole ratio is nonetheless not constant; it slowly decreases as the number of boreholes grows. The more boreholes, the larger the thermal interference, which in turn affects the power extracted. Furthermore, the longer the time, the larger the radius of affected ground around the borehole and, thus, the larger the overall thermal interaction. This effect does however not become significant within 100 years, which is the timespan of interest as it is assumed the technology to become obsolete after this point.

Figure 33: Power in MW at 10 years’ time as function of the number of boreholes

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4.2.3 Heat demand optimization

The city of Karlskoga has provided its average monthly heat demand, summarized in the graph and table contained in Figure 35.

The key highlights are as follows: the average power demand is about 15MW during winter and then drops by late spring to reach its lowest level of 3 MW during August in the summer. Afterwards, the heat demand sharply increases until reaching its maximum average value of 15 MW in October.

In order to match this heat demand in the developed numerical model, the boundary conditions are changed as follows: instead of having a constant inlet temperature, which was previously set to 48°C, the inlet temperature will vary as needed so that, with a constant mass flow, the right amount of heat is extracted, as given in Figure 35. The energy balance comes from the energy conservation of the fluid cycle,

. . ∆ we come then to .

. Note that this assumes that the heat demand can be covered

regardless of temperature levels obtained from the EGS. This could correspond to a case in which a heat pump is used to provide heat to the district heating network. Note, however, that the amount of heat provided by the heat pump to the district heating network would be even higher than the amount of heat extracted from the ground in that case. As would one need to know the energy performance of the heat pump (COP) to be able to recalculate the provided heat, this is not investigated further in this study.

Figure 34: Karlskoga average heat demand throughout a year (Data given by Energeotek AB.)

Model 2 with six boreholes was studied to see how it satisfies the demand of Karlskoga shown in Figure 35. The results shown in Figure 36 are obtained with a 60kg/s mass flow over 10 years. The oscillations can be seen in the extracted power, which results in the variation of the inlet temperature in red.

When there is a drop in power, the difference between inlet and outlet temperature decreases as well, while when the power increases, the difference between outlet and inlet temperature also increases. It is apparent here that over the course of ten years the average outlet temperature slowly decreases with time, meaning that the heat resource is depleting.

If one increases the number of boreholes, leaving the same heat power extraction profile as input, the difference between inlet and outlet temperature will be smaller in average and the average level of temperatures will be higher, because there is a bigger effective volume of ground to take this power from.

To increase the outlet temperature, one needs to either increase the total length of the system, or use the mass flow as control as well, lower mass-flows result in higher outlet temperature.

Likewise, if the number of boreholes is reduced from 6 to 4 but the heat extraction profile remains at the same levels, that would increase the temperature difference between inlet and outlet, leading to lower inlet and outlet temperatures.

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This can only be done to some extent, until inlet temperature becomes too low to satisfy the heat demand. For example, low outlet temperatures are harder to find an application for, and if a heat pump is used to increase the temperature of the fluid, lower outlet temperatures lead to more work required from the heat pump to get the same end temperature.

Figure 36: Model 2, with imposed heat extraction equal to Karlskoga heat demand, 6 boreholes and 60 kg/s mass flow.

Figure 37 shows the performance of four individual Model 1 plants under the heat demand of Karlskoga. As previously discussed, Model 1 consists of a system with the inlet borehole branching off into 3 absorption wells which then gather at the bottom into the return borehole. Instead of increasing the number of boreholes in a single plant, the number of power plants is increased to four, so that each covers one fourth of Karlskoga’s heat demand. Alternatively, this means that only one fourth of the city heat demand is covered by the EGS Model 1.

That is what is seen in the graph: the power only reaches a fourth of the initial 15 MW of average power extraction. Accordingly, the yearly average is not 11.67 but one fourth of that value, which is 2.92 MW. The response of the system when changing the boundary conditions is different, mainly because the geometry is different.

With more information about the district heating requirements (delivery temperature and flow rate) we could have taken that into account and it would have been possible to determine optimum and required temperature levels for the system. However, without these pieces of information, it is only possible to provide a spectrum of plausible scenarios that can later be used together with information about requirements in order to design such an EGS coupled to a district heating network.

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Figure 37: Model 1 with imposed heat extraction at 1/4 of Karlskoga heat demand and 30 kg/s mass flow.

4.3 Discussion and comparison Results from previous section lead to imagine that such systems could provide enough power to be

used in low temperature applications such as district heating. It was seen that with the appropriate control on the inlet temperature the requirements in power of the city of Karlskoga could be met. If on top of that a control on the mass flow and coupled with a heat pump to bring the outlet temperature up, these deep closed loop geothermal systems could be a viable alternative for heat production. Furthermore, heat could be re-injected into the ground during summer when the energy consumption is low to restore the temperature and energy of the rock and thus have a longer lifetime on the system and also a more performant system during winter time, as seen in Figures 38 and 39.

 

Figure 35: Usage of the ground as heat storage, injection of heat during summer (Bär, et al., 2015)

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Figure 36: Usage of the ground as heat storage, extraction of heat during winter (Bär, et al., 2015)

The table portrayed in Table 3 gathers the main geometrical parameters of the model, the main pumping requirements and operating temperatures and mass flow, as well as power and temperatures extracted. It also does the same thing for similar studies from the literature review, such as the Oslo report Gardermoen (Moxnes, et al., 2012) and the study done by Henrik Holmberg (2016). Furthermore, it contains empirical data from an actual operating deep geothermal power plant in Soultz Sous-Forêt, enabling a comparison between the type of EGS presented in this report and more conventional geothermal power plant.

Specifications  Model 1  Model 2 Literature Holmgren 

Soutlz 

 

Total Length of the system [m]  20520  42535.2  14698.53  20000 

Total length of absorption wells [m]  12214  24234.4  6000  ‐ 

Number of absorption wells  3  4  3  ‐ 

  Pressure difference In/Out [bar]  3.62  17.43  3.4  ‐ 

Mass‐flow per inlet well [kg/s]  45  45  25  35 

Volume Flow per inlet well [m^3/s]  0.05  0.05  0.025  0.35 

Pump Efficiency  0.5  0.5  0.7  ‐ 

Pump Power [kW]  32.95  174.33  12.14  ‐ 

Number of pumps  1  4  1  2 

  Average Temperature Gradient [degC/km]  25  25  20  40 

Temperature Outlet [degC]  62,40 (10 years)  56,30 (10 years)  50 (10 years)  175 

Temperature Inlet [degC]  48  48  40  70 

Thermal Power [MW]  2,82 (10 years)  6,51 (10 years)  1 (10 years)  13 

Power per meter drilled [W/m]  137.56  153.05  68.03  650 

Pressure drop per meter drilled [Pa/m]  1.76  4.10  2.31  9.5 

Table 3: Comparison of the models, other similar studies and an operating EGS (Held, et al., 2014) .

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5 Conclusion and future work In this study, different models where developed, Model 1 was designed as a single inlet and outlet deep closed loop heat exchanger with branching into three absorption wells, similarly Model 2 was also a deep closed loop heat exchanger, with multiple inlets and one shared outlet. These designs were studied for a project developed by Energeotek AB, where the aim was to install such systems in the city of Karlskoga to cover totally or partially its district heating demand.

It was seen that it is possible to use such systems to provide variable heat loads using the mass flow and inlet temperature as control parameters, in this case for the district heating of Karlskoga.

It was found that deep geothermal heat exchangers can be a viable tool to exploit underground heat, the two geometries studied yield different results. Model 1 was found to have higher return temperatures, namely62,4 C° compared to 56,3 C° in Model 2, both after 10 years of operation time. Model 2 was found to had a more efficient power extracted per meter drilled of 153,05 W/m as compared to 137,56 W/m for Model 1. Although these values might seem low compared to other EGS currently in service, like in Sloutz- sous-Forêts, with 650 W/m, it is important to keep in mind that this model considers only pure conduction in the rock, and the underground conditions in Soultz-sous-Forêts are not the same, as temperatures are higher there. Moreover, the installation in Soultz-sous-Forêts is a different kind of EGS which is based on water extraction and recirculation through fractures. In reality the picture is much more complex, porosity in the rock allows for natural fluid convection that can influence the heat transfer mechanisms. Thus it is important to further examine and broaden this study, notably include convection mechanisms in the rock, but also consider using a larger reservoir volume and heat transfer surface by for instance using hydraulic stimulation to widen the cracks in the rock and fracture the volume around the boreholes, thus improving the heat transfer mechanisms.

The next challenges lie in the technical and economic feasibility of such immense projects. There is still much room for development regarding our drilling capabilities at those depths. A pending question is for example, how one can actually complete a closed system. At best, all currently-existing deep geothermal power plants have wells connected through hydraulically-induced fractures or channels. One of the challenges is thus in how to connect the wells directly.

Then, from an economical point of view, the competitiveness of this method should be assessed and compared to other types of EGS, as well as other sources for the generation of heat.

Development of new materials could prove handy for the insulation of the higher levels to reduce the heat losses and innovative design could improve heat transfer mechanisms at the target depth.

Further research could be done on the control mechanisms for this type of power plants and the applicability of pre-existing control technology in thermal plants and shallow borehole. For example how such EGS interacts with a heat power plant, hence the need for dynamic system simulations.

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