UPPTEC ES13006
Examensarbete 30 hp
2012
Jules Verne or Joint Venture?
Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student
Abstract
Jules Verne or Joint Venture? Investigation of a Novel
Concept for Deep Geothermal Energy Extraction
Henrik Wachtmeister
Geothermal energy is an energy source with potential to supply mankind with both heat and electricity in nearly unlimited amounts. Despite this potential geothermal energy is not often considered in the general energy debate, often due to the perception that it is a margin energy source bound to a few locations with favorable geological conditions. Today, new technology and system concepts are under development with the potential to extract geothermal energy almost anywhere at commercial rates. The goal of these new technologies is the same, to harness the heat stored in the crystalline bedrock available all over the world at sufficient depth. To achieve this goal two major problems need to be solved: (1) access to the depths where the heat resource is located and (2) creation of heat transferring surfaces and fluid circulation paths for energy extraction.
In this thesis a novel concept and method for both access and extraction of geothermal energy is investigated. The concept investigated is based on the earlier suggested idea of using a main access shaft instead of conventional surface drilling to access the geothermal resource, and the idea of using mechanically constructed ‘artificial fractures‘ instead of the commonly used hydraulic fracturing process for creation of heat extraction systems. In this thesis a specific method for construction of such suggested mechanically constructed heat transfer surfaces is investigated. The method investigated is the use of diamond wire cutting technology, commonly used in stone quarries.
To examine the concept two heat transfer models were created to represent the energy extraction system: an analytical model based on previous research and a numerical model developed in a finite element analysis software. The models were used to assess the energy production potential of the extraction system. To assess the construction cost two cost models were developed to represent the mechanical construction method. By comparison of the energy production potential results from the heat transfer models with the cost results from the construction models a basic assessment of the heat extraction system was made.
The calculations presented in this thesis indicate that basic conditions for economic feasibility could exist for the investigated heat extraction system.
ISSN: 1650-8300, UPPTEC ES13006
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ACKNOWLEDGMENTS
I would like to express my sincere gratitude to my supervisor Professor Peter Lazor at the Department of Earth Sciences, to my reviewer Therese Isaksson at the Department of Engineering Sciences and to my examiner Kjell Pernestål at the Department of Physics and Astronomy at Uppsala University for indispensable support and guidance throughout this project.
I also want to thank Professor Jefferson W. Tester at Cornell University for introducing me to the warm community of geothermal energy research. A special thanks to Dr. John Garnish, former director of geothermal programs of the European Commission, for his advice and encouraging correspondence. Gratitude also goes to Dr. Tony Batchelor, chairman and managing director of GeoScience Ltd. and EarthEnergy Ltd., for providing much valuable information.
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CONTENTS
1 INTRODUCTION ... 7
1.1 Background ... 7
1.2 Purpose of study ... 8
1.3 General assumptions and delimitations ... 9
1.4 Methodology ... 9
2 THEORETICAL FRAMEWORK ...11
2.1 The geothermal resource ...11
2.2 Concepts of energy extraction ...14
2.3 Description of the investigated concept ...21
2.4 Modelling of fractures and heat transfer ...23
3 ANALYTICAL MODEL FOR ESTIMATION OF HEAT TRANSFER ...25
3.1 Introduction ...25
3.2 Estimation of the temperature distribution ...27
3.3 Thermal and electric power ...29
3.4 Thermal and electric energy ...29
3.5 Validation of the analytical model ...30
4 RESULTS FROM THE ANALYTICAL MODEL ...32
4.1 Base case parameter values ...32
4.2 Base case initial study ...33
4.3 Outlet temperature at different initial rock temperature ...37
4.4 Outlet temperature at different flow velocity ...39
4.5 Outlet temperature at different rock thermal conductivity ...41
4.6 Optimal power and energy production ...44
4.6.1 Introduction ...44
4.6.2 Optimal thermal energy production...44
4.6.3 Optimal electric energy production ...47
5 RESULTS FROM THE NUMERICAL MODEL ...50
5.1 Introduction ...50
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5.3 Comparison of results from the analytical and the numerical model ...55
6 CONSTRUCTION OF HEAT EXCHANGE SURFACES ...59
6.1 Introduction ...59
6.2 Diamond wire cutting...59
6.3 Wire cut cost parameters ...63
6.4 Total cut cost by selected parameter values ...64
6.5 Total cut cost by Monte Carlo simulation ...65
6.6 Additional cut cost model ‘Quarry model’ ...67
6.7 Power production installation cost ...70
7 DISCUSSION ...72
8 CONCLUSION ...78
9 FURTHER RESEARCH: UNDERGROUND THERMAL ENERGY STORAGE ...79
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NOMENCLATURE
ηC Thermal efficiency Carnot -
ηTRI Thermal efficiency triangular -
ηREAL Thermal efficiency real -
T0 Temperature ambient K
TH Temperature heat source K
T(x,z,t) Temperature distribution function °C
Tr,0 Initial rock temperature °C
Tw,0 Water inlet temperature °C
Tout Water outlet temperature °C
w Half fracture width in x m
H Fracture height in z m
L Fracture depth/length in y m
A Area of rock fracture interface one side (A = HL) m2
U Water flow velocity m/s
ṁ Water mass flow rate kg/s
ṁ/A Area normalized water mass flow rate kg/m2 s
kr Thermal conductivity rock W/m K
ρr Density rock kg/m3
cp,r Specific heat capacity rock J/kg K
Α Thermal diffusivity rock m2/s
kw Thermal conductivity water W/m K
ρw Density water kg/m3
cp,w Specific heat capacity water J/kg K
β Dimensionless parameter -
t Time of the production phase S
Pth Power thermal W
Pel Power electric W
Eth Energy thermal J
Eel Energy electric J
Pavg,th Average thermal power per fracture area W/m2
Pavg,el Average electric power per fracture area W/m2
kthd Thermal drawdown -
D Distance between parallel fractures m
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1
INTRODUCTION
1.1
BACKGROUND
During this last century we have seen an incredible global economic development and a significant increase in living standards. This fast development has been based on the abundance of cheap and highly effective energy sources – the fossil fuels.
Today we know that our development has occurred on the expense of our environment. We are also aware of the fact that oil is running out. We have already begun to see consequences of these conditions: climate change, rising fuel prices and the impact of energy security in international relations. To change these current developments, regardless of motivation, new sustainable energy sources are necessary.
In everyday life we rarely think about what exists under our feet. Not often do we reflect on the fact that Earth is a rotating orb of melted rock with a core temperature of 6 000 degrees Celsius and with just a thin layer of solid crust to walk on. The large amounts of energy stored and produced in the Earth’s interior is an energy source not often considered but with a practically endless potential.
This thesis investigates a novel concept for extracting deep geothermal energy. The concept is based on ideas presented in the report ‘Man-made Geothermal Energy Systems – MAGES’ published by the International Energy Agency (IEA) in 1979. These ideas have been further developed by the two researchers active in this project: Henrik Wachtmeister (author of this report) and Christoffer Källberg (author of the associated report). With new technology and knowledge available today ideas suggested 30 years ago might be possible to realize.
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symmetrical artificial fractures transferring heat from the surrounding rock to the working fluid.
During the research process Dr. John Garnish and Dr. Tony Bachelor, both active in the MAGES project at the time, kindly pointed out that a proposal regarding a shaft based system was put forth as long ago as in 1904 by the prominent Anglo-Irish engineer Sir Charles Parsons, inventor of the steam turbine among many things. In the beginning of the 20th century Parsons (1904) addresses the British Association for the Advancement of Science and proposes the idea of constructing of a 12 km deep shaft for steam and power generation. In a following address, published at the end of the Great War, Parsons (1919) comments the immense horror and destruction seen in past years. He also identifies the remarkable technological development during the war, and its integral role in it. Furthermore he recognizes the fundamental significance of energy sources for both political and social stability as well as for military power. He concludes that the power of the British Empire, and its ability to survive the war, was primarily based on its early development of coal and its following employment of oil. Foreseeing the inevitable exhaustion of coal reserves Sir Parsons returns to the geothermal idea presented in 1904, stressing the importance of deploying new energy sources for both economic development and for peace. In his calculations the proposed 12 km deep shaft could be constructed at a cost equal to the monetary cost of just a single day of the Great War, pinpointing the skewed allocation of human efforts.
1.2
PURPOSE OF STUDY
The purpose of this thesis is to investigate and evaluate a specific method for mechanical construction of heat transferring surfaces for deep geothermal energy production systems. To evaluate the method the two following key questions need to be answered:
What is the energy production potential of a system constructed with the investigated method?
What is the cost of constructing a system with the investigated method?
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1.3
GENERAL ASSUMPTIONS AND DELIMITATIONS
This investigation is a theoretical estimation of the performance of an ideal system based and conducted on the premise that the system is possible to construct. The study is based on the assumption that shaft construction to required depths is technically achievable. Furthermore, remote control and large scale implementation of wire saw technology is assumed. These main assumptions require technology and methods not developed or proved today.
Several practical aspects have been disregarded. The impact of the extreme conditions at depth in terms of temperature, pressure and rock stresses is not treated. Structural integrity of the artificial fractures is assumed.
The study only investigates the heat extraction system. The results from this study, if positive, must therefore in addition be able to cover the access cost and all other disregarded costs for economic feasibility of a complete system concept. Furthermore, since the study only looks at the possible performance of an ideal energy extraction system, pumping, conversion and other losses are not included. The cost estimate of the construction method is based on basic cost parameters identifiably for surface applications. Possible additional cost for underground and remote control application is disregarded.
This being said, the construction of a shaft based concept must not necessary be considered insurmountable. The deepest shaft today is 3.9 km in depth, and is located in the South African TauTona gold mine (SPG Media Group PLC 2009). New shaft construction technologies are under development that could make required deep shafts possible, as example described by Chadwick (2010) and Ferreira (2005). It is also possible to assume an alternative scenario where the proposed extraction system is constructed in already existing locations, for example in abandoned mines as proposed by Hall, Scott, & Shang (2011) and Rodriguez & Diaz (2009).
1.4
METHODOLOGY
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To examine the construction cost of the heat extraction system a cost model for diamond wire cutting was developed in a qualitative manner together with experts from the diamond wire industry. Total cut cost were derived from identified cost parameters by two methods: (1) selected parameter values and (2) Monte Carlo simulation. The qualitative model derivation was complemented with a quantitative analysis of wire performance parameters by examining proprietary data from 35 different stone quarries.
The feasibility of the energy extraction concept was investigated by comparing the estimated potential energy production with the estimated construction cost of the system.
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2
THEORETICAL FRAMEWORK
2.1
THE GEOTHERMAL RESOURCE
The heat within Earth originates from the creation of the planet and is also continuously produced by decay of radioactive isotopes. The crust is cooled by space through the atmosphere. The temperature difference between the hot interior and the cold crust has established the ‘geothermal gradient’, the temperature distribution with respect to depth. The geothermal gradient at near surface conditions has a global average of 25-30 °C/km but can be several times higher in high-grade geothermal regions (Henkel 2006). In Figure 1 temperature at depth is given for four different geothermal gradients.
Figure 1.Temperature at depth at four different geothermal gradients.
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When looking at ways of using geothermal energy the continuous heat flow (60 mW/m2) is not of main interest. The real potential of geothermal energy lies in extracting the massive amounts of stored heat in Earth’s rock masses. The term ‘heat mining’ is often used to describe this concept, a comprehensive account is given by Armstead & Tester (1987). Energy is extracted by cooling a specific volume of rock, this volume loses its temperature during extraction and after the extraction period production moves on and a new volume is mined. The cooled rock mass will slowly regain its initial temperature due to heat conduction by the surrounding rock supported by the continuous heat flow from the core.
To assess the scale of the heat resource in rock the following estimation can be made: a volume of 1 km3 of granite rock with temperature 200 °C contains about 160 TWh of thermal energy. Extracting 10 % of that energy, cooling it from 200 to 180 °C, yields 90 MW of thermal power during 20 years. Extracting 50 % of the heat in place, cooling the rock from 200 to 100 °C, yields 450 MW of thermal power. See Figure 2 for a schematic representation of scale.
Figure 2. Estimation of the geothermal resource.
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The energy extracted comes in the form of hot fluid, most common water is used as working fluid. Energy in form of hot water can be transformed into electricity in steam cycles, using ordinary steam turbines and electricity generators. The efficiency of this conversion is limited by the Carnot efficiency. According to DiPippo (2007) the triangular cycle is more realistic to use for binary geothermal plants since geothermal hot water is not a non-isothermal heat source. Also other efficiency losses need to be taken into account resulting in a real efficiency of thermal to electrical power of approximately 0.58 of the ideal triangular, see Equation 1, 2 and 3.
(1)
(2)
(3)
T0 is the ambient temperature and TH the temperature of the heat source, both in Kelvin. In Figure 3 thermal efficiency is presented as a function of fluid temperature (the heat source) according to Equation 1, 2 and 3. As seen in Figure 3 the conversion efficiencies for thermal power to mechanical and electric power is low for the temperature levels associated with geothermal energy. For large scale electricity production high mass flows are therefore necessary.
Figure 3. Thermal power conversion efficiencies.
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2.2
CONCEPTS OF ENERGY EXTRACTION
Several ways of extracting energy from deep impermeable crystalline rock has been proposed. The goal of these different concepts is the same, to harness the heat stored in the crystalline bedrock available almost everywhere on Earth at sufficient depth. To achieve this goal two major problems need to be solved:
Access the depths were the heat resource is located
Create heat transferring surfaces and fluid circulation paths
Some concepts have more spectacular solutions to these problems than others. As an example, according to Gringarten et al. (1975), in the 70’s scientist in both the United States and in the Soviet Union were considering the use of sequentially fired and controlled nuclear explosives to create highly fractured underground rock systems for water circulation and energy extraction.
The most developed and successful concept so far is the use of conventional deep boreholes for access and hydraulic fracturing for creation of heat transfer surfaces. These concepts are referred to as Enhanced Geothermal Systems (EGS), also the earlier name Hot Dry Rock (HDR) is used. Drilling to depth up to 12 km has been achieved (Kola Superdeep Borehole, Soviet Union 1989), and drilling to 6 to 8 km is regular procedure in the oil and gas industry. Hydraulic fracturing is also a technology with roots in the oil industry. It is a rock breaking process where water is pumped down the borehole at high pressure. The high fluid pressure opens preexisting joints and creates new ones in the rock system surrounding the injection borehole. Depending on geology and the preexisting rock formations and stress fields the results of hydraulic fracturing differs. The results of the fracture process are measured by seismic instruments at the surface.
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in France (Geothermie Soultz 2012), and the Cooper Basin project in Australia (Geodynamics Ltd. 2012).
The development of EGS looks very promising but one remaining obstacle is the risk and uncertainty associated with both drilling and hydraulic fracturing. Conventional drilling to required depths is complicated and expensive and can sometimes fail leading to new additional boreholes adding large unexpected costs to the projects. The creation of the reservoir, and its productivity and lifetime, is also related to uncertainties. These obstacles among others were identified by IEA (1979) and were partly the reason why an alternative option was considered: the use of shafts for access and the use of mechanically constructed surfaces for heat extraction at depth. Such a system would be closed in regard to fluid circulation and controllable in regard to power production. Also the idea of shafts in combination with underground boreholes was considered.
According to Dr. John Garnish (personal communication, 2012), former director of geothermal programs of the European Commission and involved in the MAGES project at the time, the purpose of the MAGES study was to ‘brainstorm’ and consider all possible concepts for heat extraction from deep rock formations. The idea of a shaft based concept had at that time not been subject of any preceding study. The concept was therefore treated only in a very theoretical way.
In the final MAGES report by IEA (1979) some key positive properties of a shaft based concept were identified as well as the many difficult and unknown practical aspect of such a system. The major obstacle being the cost of a shaft deep enough and the extreme working conditions at the relevant depths. The principal advantage of a shaft system is that it yields access to the heat resource and enables implementation of controllable methods for construction of heat transfer surfaces. Also, machines and personnel can work at depth, installations can be maintained, repaired and refined. A main shaft from which several smaller shafts and boreholes can be constructed eliminates the need of multiple boreholes all the way from the surface. A surface borehole can only handle a limited mass flow, and is therefore limited in potential power production, a single shaft can handle large mass flows by large diameter pipes. A system based on a main access shaft, even though initially very expensive, can be further expanded even under production. It is assumed in report that a shaft access concept may be more cost effective for large scale systems due to the need of only one access path, not several surface boreholes.
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decided to develop the EGS concept. Within a few years the research was concentrated to a single cite, Soultz, primary due to the high cost of deep drilling and the need of necessary scale. Even after this concentration of effort it was not until 2005 that the system produced electricity. According to Garnish it had been difficult enough to continue to get funding from the various national bodies for the Soultz project, under no circumstances could funding have been obtained for the far more challenging shaft concept, an no attempt was made to do so either.
In the MAGES project (IEA 1979) the idea of constructing artificial fractures mechanically was considered among other options as a mean of extracting energy. By constructing heat transfer systems from design predictability and controllability can be achieved eliminating the risk associated with contemporary hydraulic fracturing concepts. In this thesis a specific technical method for constructing such artificial fractures is considered. The method investigated is the use of diamond coated wire technology, a stone cutting method normally used in stone quarries. A diamond wire saw creates a channel in the rock – an artificial fracture – with width of around 11 mm. Diamond wire cuts can be executed in several ways and in almost any kind of geometry. For heat transfer purposes extremely large cuts are necessary for any substantial energy production potential. The artificial fractures must therefore be constructed by several sub cuts. The heat extraction concept is described further in chapter 2.3, details about diamond wire cutting is given in chapter 6.
EGS concepts can be referred to as open systems since the fluid flows freely in the rock structure between injection boreholes and production boreholes. The shaft based concept can be referred to as a closed system with fluid circulating in constructed paths and channels. Except of shaft based concepts there are another additional type of closed system: borehole heat exchanger systems. These concepts consist of boreholes only, either a single borehole or multiple boreholes. A single borehole concept, 14 000 m in length, is proposed by Schulz (2008). Another concept is developed by Norwegian company Rock Energy AS and is described by Moe & Rabben (2001). In this later concept two main boreholes are drilled from the surface. At depth a system of several heat extracting boreholes are drilled with directional drilling technology between the two first main boreholes creating a underground closed heat exchanging system.
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described in more detail by Hämmerle (2012). The GTKW concept came to the author’s attention at a late stage in the research process. The original concept investigated in this report was developed in parallel with GTKW and without knowledge of its existence. This is interesting since the two research groups, although considering different heat extracting methods, has reached similar conclusions and identified several similar important aspects in many questions.
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Figure 5. Example of HDR/EGS concept with surface boreholes and hydraulic fracturing (Tester et al. 2006).
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Figure 7. Example of shaft concepts. Geothermietiefenkraftwerk (GTKW), an Austrian shaft concept with heat exchanger system based on tunnels and multiple boreholes, depth 6 000 m (Ehoch10 Projektentwicklungs GmbH 2012).
The GTKW heat extraction method is based on a tunnel system with multiple intersecting boreholes for fluid circulation. According to Hämmerle (2012) the power output from such boreholes is in the range of 150 to 250 W per m borehole at relevant depths. The GTKW concept is planned to be deployed in the scale of gigawatts. Hämmerle (2012) describes a plant consisting of a 6 000 m deep shaft, 25 km of tunnels and 40 000 km of heat extraction boreholes. This system is estimated to produce 10 000 MW thermal and 1 000 MW electrical power. The estimated construction cost is 13 billion euro.
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2.3
DESCRIPTION OF THE INVESTIGATED
CONCEPT
Figure 9 to Figure 12 shows schematic representations of the herein investigated concept. A main access shaft gives access to the heat resource. A system of smaller construction shafts and tunnels and necessary boreholes for cutting are established at depth. From this system diamond wire cutting is used to create channels with large heat transferring surfaces. The channels are constructed in modules creating separated large ‘artificial fractures’. Further construction and expansion of the system is possible, in all directions, at the same time as the first modules are producing energy.
Figure 9. Schematic representation of the investigated concept: Main access shaft and mechanically constructed heat transfer surfaces with diamond wire saw technology.
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Figure 10. A system of smaller construction tunnels and shafts are established at depth. From this system necessary boreholes for wire cutting are drilled. Wire saws cuts channels between tunnels and boreholes creating large heat transfering surfaces (red color in picture).
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Figure 12. Multiple channels or artificial fractures can be constructed next to each other at suitable distance on the same level. The main shaft can continue deeper, with establishment of new channel systems on deeper levels. Further construction and expansion can be performed while the first part of the system is producing energy.
2.4
MODELLING OF FRACTURES AND HEA T
TRANSFER
Several authors have created models to study the heat transfer problem between injected water and rock formation at depth. Two of the earliest works in this area was done by Gringarten et al. (1975) and Wunder & Murphy (1978). The heat transfer problem addressed in these works, and the analytical model of heat transfer in rock developed, has been developed further by Tester et al. (2011).
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3
ANALYTICAL MODEL FOR ESTIMATION OF
HEAT TRANSFER
3.1
INTRODUCTION
The analytical heat transfer model was adapted from earlier works by Gringarten et al. (1975), Wunder & Murphy (1978), Armstead & Tester (1981) and Tester et al. (2011).
The model describes a geometry representing a single rectangular vertical fracture of constant width that separates two masses of homogeneous, isotropic, impermeable rock. The rock is assumed to extend horizontally to infinity. Initially the system is at uniform temperature. During heat extraction water is injected uniformly at the bottom of the fracture and is flowing upwards to the outlet at constant mass flow rate. The heat transfer process to be solved is a coupled problem of heat conduction in the rock and forced convection in the fracture. With a set of assumptions and boundary conditions the heat transfer equations in this geometry can be treated analytically for any case with uniform fluid flow and fixed inlet temperature. The model geometry is given in Figure 13.
Figure 13. Geometry of analytical heat transfer single fracture model in three dimensions.
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Figure 14. Analytical model in two dimensions.
The geometry seen in Figure 2 is used for solving the heat transfer problem. It represents the half-width fracture w and one of the two the surrounding rock masses with temperature distribution T(x,z,t). All constituent model parameters are presented in Table 1.
Table 1. List of analytical heat transfer model parameters.
T(x,z,t) Temperature distribution function °C
Tr,0 Initial rock temperature °C
Tw,0 Water inlet temperature °C
Tw,H Water outlet temperature °C
w Half fracture width in x M
H Fracture height in z M
L Fracture depth/length in y M
A Area of rock fracture interface one side (A = HL) m2
U Water flow velocity m/s
ṁ Water mass flow rate kg/s
ṁ/A Area normalized water mass flow rate kg/m2s
kr Thermal conductivity rock W/mK
ρr Density rock kg/m3
cp,r Specific heat capacity rock J/kgK
α Thermal diffusivity rock m2/s
ρw Density water kg/m3
cp,w Specific heat capacity water J/kgK
β Dimensionless parameter -
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Initially at t = 0 the whole system is at uniform temperature Tr,0, the initial temperature of the surrounding rock. During the production phase water is injected at z = 0 at constant temperature Tw,0 and constant flow velocity U. The water flows upwards to the outlet at z = H. The model is based on the following assumptions:
The variation of water temperature in x-direction in the fracture is neglected. The fracture aperture is very small in relation to fracture height, w << H.
The heat transfer resistance at the rock-water interface is neglected. The water temperature is equal to the rock temperature at x = 0 for every z.
Heat conduction in z-direction is neglected both in the fracture and in the surrounding rock mass.
Heat conduction in y-direction is neglected both in the fracture and in the surrounding rock mass.
Density and specific heat capacity is constant for both water and rock. Thermal conductivity of rock is constant.
Single phase flow in in the fracture is assumed.
Under these assumptions heat transfer only occurs by conduction in the rock in x-direction and by forced convection in the fracture in z-direction. In this manner fluid dynamics equations can be disregarded altogether.
3.2
ESTIMATION OF THE TEMPERATURE
DISTRIBUTION
The time dependent heat conduction in x-direction within the rock is described by the differential equation
(4)
Where α is the rock thermal diffusivity, i.e. the ratio of thermal conductivity kr and the product of density ρr and specific heat capacity cp,r of rock
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The boundary conditions at the rock-fluid interface gives
|
(6)
The initial rock temperature gives the initial condition
( ) (7)
The far field rock temperature gives the boundary condition
( ) (8)
The constant water temperature at the inlet gives the following additional boundary condition ( ) (9)
The analytical solution to Eq. 4 under the boundary conditions Eq. 6-9 is based on the solution of a classical transient heat transfer problem. The solution is presented in (Tester et al., 2011). ( ) ( ) [ √ ] (10) where (11) Outlet temperature
With z = H and x = 0 Eq. 10 can be simplified to give the outlet water temperature Tout at the end of the fracture
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3.3
THERMAL AND ELECTRIC POWER
Thermal power
The available thermal power from the artificial fracture system is calculated from the temperature and mass flow of the fluid at the fracture outlet.
The thermal power Pth is calculated by
̇( ) (13) Where the mass flow ṁ is
̇ (14)
Electric power
Potential electricity production is calculated from thermal power using ideal Carnot conversion efficiency according to
̇( ) (
) (15)
For Carnot efficiency T needs to be in Kelvin.
3.4
THERMAL AND ELECTRIC ENERGY
Thermal energy
To assess the produced thermal energy over time the following integral needs to be solved
∫ (16)
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Electrical energy
To assess the produced electric energy over time the following integral need to be solved
∫ (17)
This integral is solved numerically in MATLAB.
3.5
VALIDATION OF THE ANALYTICAL MODEL
The analytical model was based on the same mathematical solution as presented and used by Tester et al. (2011). Use of the same input parameter values should yield the same result in both analytical models. This was investigated and confirmed. Figure 15 is the same as presented by Tester et al. (2011) and shows outlet temperature at four different locations along a 500 m long and 0.06 m wide fracture. Results from both the analytical model and the numerical TOUGH2 model are presented.
The same input parameters values were used in our analytical model and in our numerical COMSOL model. These results are presented in Figure 16. The results from our analytical model and the analytical model by Tester et al. (2011) should be identical in this particular case; this is confirmed by results shown in Figure 15 and Figure 16. The results from our COMSOL model and the numerical TOUGH2 model should be similar; this is also confirmed by results shown in Figure 15 and Figure 16.
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Figure 15. Model validation: Outlet temperature at four locations along a fracture according to Tester et al. (2011).
Figure 16. Model validation: Outlet temperature at four different locations along same fracture according to developed models, analytical model in black and numerical COMSOL model in red.
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4
RESULTS FROM THE ANALYTICAL MODEL
The analytical heat transfer model was implemented in MATLAB. A base case of parameter values was selected for the model. The base case set of parameter values is referred to as just the 'base case’.
The model solves the temperature distribution in the system over time. The main output from the model is water outlet temperature Tout from the fracture over time. From outlet temperature thermal power, electric power, produced thermal energy and produced electric energy can be calculated.
To facilitate comparison between different fracture systems and model setups average power per fracture area is calculated for each case. Average power is calculated from the aggregated thermal and electric energy production, according to Eq. 16 and 17, divided on total production time (30 years) and fracture area (1 000 000 m2), see Eq. 18 an 19.
(18)
(19)
Three major studies are presented in this report, preceded by an initial study of the base case. 0. Initial study of base case
1. Outlet temperature at different initial rock temperature 2. Outlet temperature at different water flow velocity 3. Outlet temperature at different rock thermal conductivity
All studies were based on the base case, altered parameter values are reported in each study.
4.1
BASE CASE PARAMETER VALUES
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Table 2. Base case parameter values for analytical heat transfer model.
Tr,0 150 Initial rock temperature °C
Tw,0 20 Water inlet temperature °C
w 0.0055 Half fracture width in x m
H 1000 Fracture height in z m
L 1000 Fracture depth/length in y m
A 1 000 000 Area of rock fracture interface one side (A=HL) m2
U 0.005 Water flow velocity m/s
ṁ 55 Water mass flow rate kg/s
ṁ/2A 2.75e-05 Area normalized water mass flow rate kg/m2s
kr 2.9 Thermal conductivity rock W/mK
ρr 2700 Density rock kg/m3
cp,r 1050 Specific heat capacity rock J/kgK
α 1.02e-06 Thermal diffusivity rock m2/s
ρw 1000 Density water kg/m3
cp,w 4184 Specific heat capacity water J/kgK
t 30 [years] Time of the production phase s
4.2
BASE CASE INITIAL STUDY
The model solves the temperature distribution in the system at position and time x, z and t. The water flow path, the fracture, is located at x = 0. The rock extends in x-direction. Initial rock temperature is 150 °C and water inlet temperature at x = 0, z = 0 is 20 °C. The water flow velocity U is 0.005 m/s and constant during the whole production period. The water mass flow depends on the geometry; at water flow velocity 0.005 m/s and fracture geometry of 0.011 x 1000 x 1000 m the water mass flow equals 55 kg/s.
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Figure 17. Temperature distribution in rock and water at three time instances. From left, t = 1, 15 and 30 years.
The scale of Figure 17 does not give a complete picture of the temperature field at the interface between rock and water. In Figure 18 the temperature distribution at t = 30 years is shown at a different scale, x = 0-10 m into the rock. The color coding representing temperature is the same as in Figure 17.
In Figure 18 we can see the effect of the boundary condition that states that the rock and water has the same temperature at the interface x = 0 m. Since the water flow velocity is low, in the base case 0.005 m/s, this assumption is realistic.
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Figure 18. Temperature distribution at rock water interface.
In Figure 19 the water temperate along the fracture in z-direction is shown at a specific point in time, t = 30 years. We can see that at constant flow velocity the temperature rise of the fluid is linear along the fracture in z-direction.
Figure 19. Water temperature along fracture height.
The most interesting output from the model is water outlet temperature over time. In Figure 20 we can see how the outlet temperature drops with time and ends at 76 °C after 30 years of production. The outlet temperature is constant only for a short period of time. Thermal power is proportional to the outlet temperature and could be described by the same curve but with different y-axis unit. In the beginning at 150 °C the system produces 30 MW, at the end at 30 years the power has dropped to 13 MW according to Eq. 13.
z [m] 1000 76 77 78 80 82 84 86 88 90 91 93 95 950 74 74 76 78 80 82 84 86 87 89 91 93 900 71 71 73 75 77 79 81 83 85 87 89 91 850 69 69 71 73 75 77 79 81 83 85 86 88 800 66 66 68 70 72 74 76 78 80 82 84 86 750 63 63 65 67 70 72 74 76 78 80 82 84 700 61 61 63 65 67 69 71 73 75 77 79 81 650 58 58 60 62 64 66 68 71 73 75 77 79 600 55 55 57 59 62 64 66 68 70 72 74 76 550 52 52 54 57 59 61 63 65 67 69 72 74 500 49 50 52 54 56 58 60 63 65 67 69 71 450 46 47 49 51 53 55 58 60 62 64 66 68 400 44 44 46 48 50 53 55 57 59 61 64 66 350 41 41 43 45 48 50 52 54 57 59 61 63 300 38 38 40 42 45 47 49 51 54 56 58 60 250 35 35 37 39 42 44 46 49 51 53 55 58 200 32 32 34 37 39 41 43 46 48 50 53 55 150 29 29 31 34 36 38 41 43 45 47 50 52 100 26 26 28 31 33 35 38 40 42 45 47 49 50 23 23 25 28 30 32 35 37 39 42 44 46 0 20 20 22 25 27 29 32 34 36 39 41 43 0 0,1 1 2 3 4 5 6 7 8 9 10 x [m] 0 200 400 600 800 1000 20 30 40 50 60 70 80
Height position in f racture [m]
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Figure 20. Outlet temperature over time.
Heat conduction in the surrounding rock is the limiting factor for heat transfer to the flowing water. In the beginning of the process cold water is in contact with rock of high temperature. The temperature difference that drives heat conduction makes the heat transfer process fast. With time when the temperature gradient decreases the heat transfer slows down.
From this first study we can conclude that changing the water flow velocity will change the behavior of the system and the outlet temperature. A higher initial rock temperature will also naturally yield higher thermal power. Changing the material properties of the rock, such as the thermal conductivity will also have effect on the system. In the next three studies these aspects will be investigated.
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4.3
OUTLET TEMPERATURE AT DIFFERENT INITIAL
ROCK TEMPERATURE
The effect of different initial rock temperature was investigated. Four different rock temperatures was studied: 100, 150, 200 and 250 °C. Assuming global average geothermal gradient of 30 °C/km, these temperatures can be expected at the depth of 3300, 5000, 6700 and 8300 m. As stated earlier and seen in Figure 21 the outlet temperature drops with time
Figure 21. Outlet temperature at different initial rock temperature.
At constant flow rate the ratio between outlet temperature and initial rock temperature is the equal for each case. This ratio is called thermal drawdown. It depends only on the flow rate and effective heat transfer area. It scales directly with the area normalized water mass flow rate ṁ/2A, where A is the total fracture area (1 000 000 m2) and 2A is the total effective heat transfer surface area since the artificial fracture consist of two rock surfaces (Tester et al. 2011).
(20)
In these four cases the thermal drawdown is about 0.5 according to Eq. 20. From Eq. 13 and 15 thermal and electrical power is calculated. The integral of these functions Eq. 16 and 17 gives the produced energy. The results from these calculations are presented in Figure 22.
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Figure 22. Power and energy at different initial rock temperature.
As seen in Figure 22 the magnitude of power and produced energy depends fully on the temperature of the rock resource. High rock temperature means deeper depths, which means higher access costs. It can be assumed that a certain depth exists related to an economical optimum for a system with a certain geothermal gradient and a certain exponentially rising drilling or excavation cost. In chapter 7 such an optimum will discussed further.
Table 3 shows the average power per fracture area of the four cases according to Eq. 18 and 19.
Table 3. Average power at different initial rock temperature.
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The average thermal power per fracture area varies in these four cases between 12 and 34 Wth/m
2
. Note that the average thermal power per heat transferring surfaces is half of that (1 m2 of fracture consist of 2 m2 of heat transferring surface). From this it is possible to conclude that very large heat transferring surfaces are needed to maintain any substantial power production. It is also possible to conclude than such heat transferring surfaces must be able to be constructed fast and at a low cost to make a system with artificial fractures economically viable.
4.4
OUTLET TEMPERATURE AT DIFFERENT FLOW
VELOCITY
The effect of different water flow velocity was investigated. Figure 23 shows the outlet temperature over time at four different flow velocities, U = 0.04, 0.01, 0.005 and 0.001 m/s. The initial rock temperature is 150 °C in all four cases.
Figure 23. Outlet temperature at different flow velocity.
Naturally it is possible to maintain a high outlet temperature over time with a low fluid flow velocity as in the case U = 0.001 m/s. In our base case with fracture dimensions 2w = 0.011 m, H = 1000 m and L = 1000 m this velocity equals a mass flow of ṁ = 11 kg/s.
Increasing the flow velocity to U = 0.005 m/s gives a mass flow of ṁ = 55 kg/s, at this rate the outlet temperature begins do drop with time and after 30 years it is 76 °C. Increasing the
40
flow velocity further enhances this effect, U = 0.01 m/s yields ṁ = 110 kg/s and Tout = 49 °C. Finally U = 0.04 m/s yields ṁ = 440 kg/s and Tout = 27 °C after 30 years of production. The increased velocity and mass flow has a substantial effect on power and energy production. At 0.01 m/s (440 kg/s) the initial thermal power is almost 240 MW (out of the chart scale in Figure 24) but decreases very fast due to the fast decrease in rock temperature, after only 5 years the outlet temperature has dropped under 40 °C. It is apparent that an optimal flow velocity exists for any specific set of fracture parameters and desired output application.
Figure 24. Power and energy at different flow velocity.
High flow velocity yields higher amounts of produced thermal energy, but since the high flow is at low temperature the energy is not as usable as in the case with higher temperatures and lower flow velocities. This effect is seen in the amount of potential electric power. We can see that electric power drops fast and even below the low fluid flow cases. The Carnot efficiency, the ability to transfer heat to mechanical work, is dependent on temperature of the working medium. The fast drop in temperature leads to lower potential electric power which
41
leads to lower amounts of produced electric energy. In the last plot in Figure 24 we can clearly see than an optimal flow velocity for maximal production of electric energy exists. In these four cases the third case at 0.005 m/s (55 kg/s) yields the highest production.
In chapter 4.6 optimal flow for thermal and electrical power will be investigated further. The average power from the four simulations above is presented in Table 4.
Table 4. Average power at different flow velocity.
Initial rock temperature Flow velocity Mass flow Final outlet temperature Average thermal power Average electric power [°C] [m/s] [kg/s] [°C] [W/m2] [W/m2] 150 0.001 11 149 6.0 1.8 150 0.005 55 76 19 4.4 150 0.010 110 49 23 3.8 150 0.040 440 27 26 1.8
4.5
OUTLET TEMPERATURE AT DIFFERENT ROCK
THERMAL CONDUCTIVITY
The effect of material and thermodynamic properties of different rock was investigated. In the base case the rock is assumed to be granite with the following constant properties: specific heat capacity 1050 J/kg K, density 2700 kg/m3 and thermal conductivity 2.9 W/mK. These values are based on the values used by Tester et al. (2011). Since rock is a non-homogenous material its properties varies according to composition and physical aspects.
Specific heat capacity and thermal conductivity are temperature dependent. Thermal conductivity decreases with higher temperature while specific heat capacity increases with higher temperature. Vosteen & Schellschmidt (2003) reports a difference of 3.5 to 1.0 W/mK and Maqsood, Hussain Gul, & Anis-ur-Rehman (2004) 3.5 to 1.5 W/mK for different granite samples.
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Since there are many variables that effect material and thermodynamic properties of granite rock we modeled a range of thermal conductivity of 2.0 to 4.0 W/mK. This interval will include most of the variable aspects due to varying chemistry and porosity.
In Figure 25 outlet temperature during production period of 30 years is presented at four different values of thermal conductivity of rock. Lower thermal conductivity yields as expected lower outlet temperature and higher thermal drawdown ratio.
Figure 25. Outlet temperature at different thermal conductivity.
Earlier we stated that heat transfer is limited by the heat conduction in the rock and that conduction decreases with lower temperature gradients in the system. As seen in Figure 25 higher thermal conductivity of rock mitigates this effect, but the heat conduction in the rock mass is still the limiting factor for heat extraction.
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Figure 26 shows power and produced energy at the four different values of thermal conductivity. Average power is presented in Table 5.
Figure 26. Power and energy at different rock thermal conductivity.
If comparing the two cases 2.0 W/m K and 4.0 W/mK the amount of produced thermal energy is 25 % higher in the latter case. This in turn has significant impact in the produced electrical energy where the difference between the two cases above is 44 %.
Table 5. Average power different rock thermal conductivity.
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4.6
OPTIMAL POWER AND ENERGY PRODUCTION
4.6.1 INTRODUCTION
In chapter 4.3 we concluded that the temperature of the rock resource is the most important aspect of heat mining operations. We also concluded that an optimal depth exists if drilling or excavation costs increase exponentially width depth. Since the rock temperature is related to the local geothermal gradient and depth, and since depth is related to the cost of drilling or excavating and the construction of the whole production system an optimization of these conditions exceeds the scope of this report.
In chapter 4.4 we concluded that and optimal water flow exists for a certain fracture system with a certain initial temperature and during a certain production period. In the follow chapters this optimal flow will be investigated.
In chapter 4.5 we concluded that higher thermal conductivity yields higher power and energy production. The material parameters will not be investigated further in the optimization context.
4.6.2 OPTIMAL THERMAL ENERGY PRODUCTION
As concluded earlier an optimal water flow velocity exists for a particular fracture system and output usage. If the system is to be used for district heating only, with no electricity production, the limiting factor is the lowest acceptable outlet temperature from the system. This lowest acceptable temperature can depend on the cost of heat exchangers or the technical limitations of the district heating distribution system.
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Figure 27. Outlet temperature at 30 years at different flow velocity.
In Figure 28 the outlet temperature at the optimal flow rates found in Figure 27 is presented. The outlet temperature drops faster at the higher flow velocities as seen earlier. After half the production time the outlet temperature is almost the same for the four cases.
Figure 28. Outlet temperature at optimal flow for thermal energy production.
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In Figure 29 power and energy for these four cases are presented. The cases with higher flow velocity and mass flow yields higher power even though the temperature reaches the same magnitude in the latter part of the production period.
Figure 29. Power and energy for optimal thermal energy production flow velocity.
As seen in Figure 29 and Table 6 high initial rock temperature enables higher mass flow which leads to a higher power and energy production. In the case with initial rock temperature of 250 °C a mass flow of 143 kg/s is possible while still fulfilling the condition of outlet temperature of 60 °C after 30 years. This system has an average power per fracture area of 42 W/m2.
Table 6. Average power at flow for optimal thermal energy production.
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The condition of outlet temperature of 60 °C after 30 years is only an assumption to make it possible to find an optimal flow. Limiting condition could be chosen in several ways. Water with 60 °C temperature is still valuable and could be used for example together with heat pumps to utilize more of the available heat (Henkel 2006).
4.6.3 OPTIMAL ELECTRIC ENE RGY PRODUCTION
The available power for electricity production, the exergy content in the fluid flow, depends on the outlet temperature. The dependence is exponential due to temperature dependent conversion efficiency. Higher temperatures yields higher Carnot efficiencies and a larger part of the thermal energy can be converted into mechanical and electric energy. The efficiencies for converting thermal power to electric power are low for the temperature intervals in question for geothermal energy. At Tout = 150 °C the Carnot efficiency is ηc = 0.31, at Tout = 76 °C it is ηc = 0.16. Real world geothermal plant efficiencies are even lower, see Figure 3. (DiPippo, 2007)
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Figure 30. Optimal flow velocity for electricity production.
Figure 31. Power and energy at optimal flow velocity for electricity production.
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At optimal flow and with initial rock temperature of 250 °C it is possible to produce an average electric power per fracture area of 12 W/m2. The outlet temperature is in this case still high at 30 years, 125 °C, and still contains useful energy.
Table 7. Average power at flow for optimal electricity production.
Initial rock temperature Flow velocity Mass flow Final outlet temperature Average thermal power Average electric power [°C] [m/s] [kg/s] [°C] [W/m2] [W/m2] 100 0.0044 48.4 59 11 1.8 150 0.0046 50.6 83 18 4.3 200 0.0048 52.8 102 26 7.6 250 0.0051 56.1 125 33 12
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5
RESULTS FROM THE NUMERICAL MODEL
5.1
INTRODUCTION
A numerical model of a single fracture with surrounding rock was created in the simulation software COMSOL Multiphysics. The model is described in detail by Källberg (2012). The numerical single fracture COMSOL model describes the same geometry as the analytical model and uses the same base case parameters values. The COMSOL model is more refined and uses built-in coupled physical processes and parameters dependencies.
The same three major studies done with the analytical model was done in the numerical COMSOL model.
Outlet temperature at different initial rock temperature
Outlet temperature at different flow velocity
Outlet temperature at different rock thermal conductivity
The results from these studies are presented by Källberg (2012). In chapter 5.3 the results from the numerical COMSOL model is compared with the results from numerical model presented earlier in this report.
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5.2
COMSOL MULTIPLE FRACTURE MODEL
A multiple fracture model was developed in COMSOL in order to study how heat extracting fractures affect each other and at what distance. Geometry and mesh of the model is presented in Figure 32 together with the regular single fracture model. The model describes three fractures by using mid-plane symmetry. Five different fracture distances were modeled, D = 125, 100, 75, 50 and 25 m. To the far right (and far left according so symmetry) 200 m of bulk rock surrounds the fracture system, on top and below 100 m of rock surrounds the fracture. The outlet temperature in the middle fracture was measured.
Figure 32. Mesh and geometry of numerical COMSOL models: single fracture model (left) and multiple fracture model (right).
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constant water flow velocity of 0.005 m/s, initial rock temperature 150 °C and production time of 30 years. Material properties of water and granite were also the same as in the base case with the addition of definition of thermal conductivity of water kw = 0.6 W/mK (not used in analytical model).
Figure 33. Temperature distribution at 30 years, from left D = 125, 100, 75, 50 and 25 m.
In Figure 33 temperature distribution in rock and fracture after 30 years is shown. At fracture distance of 125 m (left) unaffected rock mass still exists between the two fractures. At 100 m the cold wave around the middle fracture looks similar to the cold wave of the single fracture at the same time.
At fracture distance 75, 50 and 25 m the rock mass surrounding the middle fracture has been cooled significantly compared to the case of a single fracture.
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Figure 34. Single fracture model and multiple fracture model with D = 100 m.
In Figure 35 the outlet temperature during 30 years is presented for fracture distance D = 100, 75, 50 and 25 m. The result from the single fracture model for the same parameters is also presented in the graph for comparison.
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Figure 35. Outlet temperature in central fracture at different fracture distances.
In this particular case and geometry a fracture distance of 100 m leads to a final outlet temperature only 3.5 % lower than of a single fracture. At D ≥ 125 m the multiple fracture model gives the same outlet temperature results as the single fracture model.
These findings correspond to the thermal penetration estimate presented by Armstead & Tester (1987) which state that in a conductive controlled environment the thermal penetration depth can estimated by
√ (21) where
t Time s
αr α = kr / ρr cp,r Thermal diffustivity rock m 2
/s
kr 2.9 Thermal conductivity rock W/m K
ρr 2700 Density rock kg/m3
cp,r 1050 Specific heat capacity rock J/kg K
Figure 36 shows the thermal penetration according to Eq. 21. After 30 years the cooling at the fracture surface has affected the initial rock temperature over 60 m into the rock mass.
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Figure 36. Theoretical estimation of thermal penetration depth.
From this it is possible to conclude that fractures at the distance of around 120 m or closer will affect each other during the time studied. At this distance the effect is low which makes it possible to place fractures at closer distances without having a significant loss in outlet temperature. As seen in the COMSOL model a distance of 100 m does not reduce the outlet temperature significantly.
The thermal penetration depth is of importance in construction design and economical optimization of an artificial fracture heat exchanger system.
5.3
COMPARISON OF RESULTS FROM THE
ANALYTICAL AND THE NUMERICAL MODEL
The results from the analytical model implemented in MATLAB were compared with the results from the numerical COMSOL model for the same set of input parameters.
The first study shows outlet temperature over a production time of 30 years at four different initial rock temperatures at constant flow 0.005 m/s.
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Figure 37. Comparison of model results: Outlet temperature at different initial rock temperature.
As seen in Figure 37 the temperature results from the COMSOL model are consistently higher than the results from the analytical MATLAB model. At the start, before thermal breakthrough, the outlet temperature is constant and therefore equal in the two models. When thermal breakthrough occurs and the outlet temperature begins to drop the difference between the two models start to increase. At the end of the production period the difference decreases slightly.
In Table 8 the outlet temperate at 30 years and 15 years are shown. At 30 years the COMSOL results are 2.4 to 3.5 % higher than the analytical model. At 15 years the difference in outlet temperature is between 2.4 to 3.7 %.
Table 8. Comparison of results: Outlet temperature at different initial rock temperature.
Tr,0 100 150 200 250 °C
30 years Numerical COMSOL 56.2 79.0 100.6 122.6 °C Analytical MATLAB 54.7 76.3 98.0 119.7 °C
Difference 1.5 2.7 2.6 2.9 °C
Difference 2.7% 3.5% 2.7% 2.4% 15 years Numerical COMSOL 68.9 99.2 128.3 157.6 °C
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A probable cause for this difference between the two models is the heat conduction dimensional setup. The analytical model is based on an energy balance that neglects conduction in z-direction (height), heat conduction occurs only in one dimension, in direction. The COMSOL model calculates heat conduction in two dimensions, both in x-direction and z-x-direction. The COMSOL model also has two additional surrounding rock masses on top and bottom to withdraw heat from. Tester et al. (2011) find similar differences between the analytical model and the numerical TOUGH2 model and the same conclusion was made.
The second study shows the outlet temperature at four different flow velocities at constant initial rock temperature Tr,0 = 150 °C. The results are shown in Figure 38. The outlet temperature from the analytical model and the numerical model differ in the same manner as seen in the earlier study. The numerical COMSOL model yields consistent higher outlet temperature.
Figure 38. Comparison of model results: Outlet temperature at different flow.
The third and final comparison study shows the outlet temperature at four different values of rock thermal conductivity at constant initial rock temperature Tr,0 = 150 °C. The results are shown in Figure 39. The outlet temperature from the analytical model and the numerical model differ in the same manner as seen in above, the numerical COMSOL model yields consistent higher outlet temperature.
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Figure 39. Comparison of model results: Outlet temperature at different thermal conductivity.
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6
CONSTRUCTION OF HEAT EXCHANGE
SURFACES
6.1
INTRODUCTION
The concept investigated in this report is based on the use of diamond wire cutting as construction method for the heat transfer system. In this chapter the capabilities, limitations and costs of diamond wire cutting are investigated.
Two cost models are presented, the first model represents a future automated or semi-automated implementation specially adjusted for the construction method. The model is used with both selected parameter values and with Monte Carlo simulation of parameter values. The second additional model represents diamond wire cutting performed today in stone quarries. The ‘Quarry model’ takes additional time dependent parameters into account, most significantly work costs.
Finally in chapter 6.7 the construction cost is compared with the power production of the fracture system which enables an estimation of the economic viability of the system.
6.2
DIAMOND WIRE CUTTING
A diamond wire saw is basically a motor that rotate a flywheel that drive a loop of diamond coated wire. The diamond wire is abrasive and grinds its ways through the rock. The wire is tensioned by the machine moving slowly along a track. The wire rotates in its path grinding the rock and creates a slit between two flat rock surfaces.
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Figure 40. Diamond wire cutting in stone quarry (Pellegrini Meccanica 2012).
There are two main types of cutting methods and setups, the wire loop can be either pulled or pushed. The most effective and straight forward way is cutting by pulling the wire. The wire is passed through boreholes and by pulleys to create a closed loop around the cut area. The wire machine is then tensioning the loop while at the same time rotating and driving the diamond wire around in its path.
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Figure 41. Diamond wire cutting by pulling (Pellegrini Meccanica 2012) (Wachtmeister 2012).
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Figure 43. Setup (left) and finished blind cut (right) (Wachtmeister 2012).
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6.3
WIRE CUT COST PARAMETERS
To assess the cost of diamond wire cutting the wire life time and wire cutting speed is of importance. These aspects can vary a lot depending on the rock composition, diamond wire composition, rock stress, skill of the operator etc. The cost of the wire itself is naturally a critical parameter. Also the power of the machine and the price of electricity (or diesel) to drive it have impact on the total cut cost.
The cost related parameters and their value range presented in Table 9 were developed together with Arne Hallin, Scandinavian representative of TYROLIT Schleifmittelwerke Swarovski K.G., a leading manufacturer of diamond wire. Wire data in form of recorded wire wear and cutting speeds from 35 different quarries was also examined.
The first cost model developed represent cutting cost for a future application of the above described concept with construction of large underground heat transferring surfaces. This entails the assumption of large scale implementation of the cutting process with full or semi full automation. Operator work cost and capital cost for machines and equipment is not included in this first model.
Table 9. Wire cut cost parameters.
Normal Low High Unit
NC L H
Wire cost WC 550 350 1000 SEK/m
Cut speed CS 10 5 15 m2/h
Wire lifetime WL 15 10 20 m2/m Machine power MP 75 50 100 kW Electricity cost EC 1 0.5 2 SEK/kWh
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6.4
TOTAL CUT COST BY SELECTED PARAMETER
VALUES
A model was developed to assess the total diamond wire cutting cost per area (SEK/m2) by modeling the different cases of the parameter values set up in Table 9. Based on the normal cost case (NC) each parameter was changed to its lowest (L) and highest (H) value each at a time. This generates a cloud of possible cut cost levels based on the selected parameter values, see Figure 45.
Figure 45. Cut cost cases with selected parameter values.
By picking the ‘best’ value for each parameter an additional optimal case was created with total cut cost of 20 SEK/m2. Based on the discussion of future cost development an additional optimistic case was created. This case is based on cut speed of 40 m2/h, wire life time 25 m2/m and wire cost of 200 SEK/m. The total cut cost for the future case is 8.9 SEK/m2.
Table 10. Three wire cut cost scenarios.
Normal Optimal Future Unit
NC OPT FOPT
Wire cost WC 550 350 200 SEK/m Cut speed CS 10 15 40 m2/h
Wire lifetime WL 15 20 25 m2/m Machine power MP 75 75 75 kW Electricity cost EC 1 0.5 0.5 SEK/kWh
Total cut cost 44 20 8.9 SEK/m2
NC WC-L WC-H CS-L CS-H WL-L WL-H MP-L MP-H EC-L EC-H 0 10 20 30 40 50 60 70 80 90 100
Cut cost case
