Scuola di Ingegneria Industriale e dell’Informazione
Analytical modelling of a Coaxial Borehole
Heat Exchanger for geothermal applications
Relatore:
Prof. Andrea Lucchini
Correlatore:
Dr. Patrick Verdin
Tesi di Laurea di:
Ambruso Alessio
Matr. 875547
SCHOOL OF WATER ENERGY AND ENVIRONMENT Energy Systems and Thermal Processes
Master of Science
Academic Year 2017 - 2018
ALESSIO AMBRUSO
Analytical and CFD modelling of water flow boiling in a coaxial borehole heat exchanger
Supervisor: Dr Patrick Verdin September 2018
This thesis is submitted in partial fulfilment of the requirements for the degree of MSc
© Cranfield University 2018. All rights reserved. No part of this publication may be reproduced without the written permission of the copyright owner.
I am grateful to my supervisor Prof. Andrea Lucchini, who helped me with great expertise to develop the analytical model since my time in Cranfield. My gratitude goes also to my Cranfield supervisor Prof. Patrick Verdin, for the support and the availability in the first months of thesis.
Thanks to my friends, who made this year in Cranfield wonderful, and the thesis mates in IMEC. Sharing is caring. Many thanks to Gemma for the optimism and encouragements throughout the thesis period, from England to the sunny Barcelona. And finally, last but by no means least, a very special thanks goes to my family, whose support from distance in time of difficulty has been as effective as having everyone by my side.
I più caldi giacimenti geotermici in Islanda sono estremamente attrattivi per il loro potenziale in termini di generazione di potenza. Avviato 20 anni fa, l’Iceland Deep Drilling Project si propone di esplorare sistemi geotermici ad alta temperatura in prossimità di camere magmatiche. Dopo il fallimento del pozzo IDDP-1, sito in Krafla, abbandonato dopo aver perforato una sacca magmatica a 2 km di profondità, l’uso della tecnologia a pozzo chiuso per produrre vapore surriscaldato in prossimità di camere magmatiche non è stata ancora esaminata. Basandosi su una geometria coassiale (Coaxial Borehole Heat Exchanger), questa tesi implementa una procedura in cui un modello analitico di scambio termico contribuisce a valutare il comportamento del sistema geotermico. Il modello è stato sviluppato per stimare le proprietà termofisiche dell'acqua che scorre nel pozzo, compresa la transizione di fase, nonché il profilo di pressione. Inoltre, la regione del pozzo interessata da ebollizione satura è stata analizzata con simulazioni numeriche basate su una mesh assialsimmetrica. Tre casi, basati su diverse portate massiche, sono stati testati per valutare la robustezza del modello. I risultati evidenziano che la procedura analitica, che include un modello di transizione di fase, può fornire una stima realistica dell'andamento della temperatura nello scambiatore geotermico ed evidenzia una buona efficienza termica per la geometria in esame. Infine, le prestazioni in termini di produzione di potenza dello scambiatore sono state valutate teorizzandone l’installazione in un ciclo Rankine geotermico, del tipo a vapore secco, evidenziando la competitività della soluzione per applicazioni di piccole-medie dimensioni. Questa opportunità, tuttavia, è influenzata da una limitazione della portata massica ammissibile e da una significativa sensibilità alla distribuzione del gradiente geotermico.
Parole chiave: Ebollizione convettiva, Scambio termico, Energia geotermica, Produzione di potenza, Scambiatori geotermici
The hottest geothermal fields in Iceland are extremely appealing in terms of electricity production potential. Started 20 years ago, the Iceland Deep Drilling Project aims at exploring high-temperature geothermal systems close to magmatic chambers. After the failure of the IDDP-1 Krafla open well, abandoned after drilling into magma at a 2-km depth, the use of closed pipe technology to produce superheated steam has not been assessed close to magmatic chambers. Based on a coaxial deep borehole exchanger geometry, this thesis implements a procedure in which an analytical-empirical heat transfer model contributes at assessing the behaviour of the geothermal system. The analytical model has been developed to estimate the thermophysical properties of water flowing in the well, including the two-phase transition, as well as the pressure profile. In addition, the location along the well where the saturated boiling occurs is investigated with numerical simulations based on an axisymmetric mesh. Three cases, based on different mass flow rates, were tested to assess the robustness of the empirical methodology. It is shown that a comprehensive analytical procedure, with the inclusion of a boiling model, can provide a realistic assessment of the temperature trend in the borehole heat exchanger and highlights a satisfactory heat transfer behaviour for the geometry. Finally, the power production potential of the solution has been assessed implementing the heat exchanger in a geothermal dry-steam-like Rankine cycle, highlighting the competitivity of the solution for small-medium size applications. This opportunity, however, is affected by a limitation of the admissible mass flow rates and a significant sensibility to the geothermal gradient distribution.
Keywords: Boiling Flow, Heat Transfer, Geothermal Energy, Power Production, Geothermal heat exchangers
Analytical modelling of a Coaxial Borehole Heat Exchanger
for geothermal applications
Alessio Ambruso
A B S T R A C T
The hottest Icelandic geothermal fields are extremely appealing in terms of electricity production potential. The long-lasting Iceland Deep Drilling Project aims at exploring these sources, but after the failure of the IDDP-1 Krafla open well, abandoned after drilling into magma at a 2-km depth, the use of closed pipe technology as a feasible alternative has not been assessed yet. This thesis aims at building a model to predict the performances of a coaxial borehole heat exchanger for superheated steam production, to feed a dry-steam like Rankine cycle. The analysis includes a study of the boiling region and a sizing of the plant, highlighting the possibility of competitive power production rates. The outcomes of the thesis should be weighted, in future research, with the limitations of the CBHE geometry: namely a low admissible mass flow rate and a high sensitivity to the reservoir temperature profile.
Nomenclature
𝐴 Cross flow area [m2]
𝑏 Geothermal grad. [ºC/km] 𝑐𝑝 Specific heat [J kg-1 K-1] ℎ Heat tran.coeff. [W m-2 K-1] ℎ̂ Specific enthalpy [J kg-1] 𝐻𝑙𝑜𝑠𝑠 Head loss [m] 𝐿 Length [m] 𝑚̇ Mass flow [kg s-1] 𝑝 Pressure [Pa] 𝑃 Wetted perimeter [m] 𝑄̇ Thermal power [W] 𝑇 Temperature [ºC] 𝑈 Global HT coef.[W m-2 K-1] 𝑣 Velocity [m s-1] 𝑥 Axial coordinate 𝑊̇ Mechanical power [W] 𝛼 Mass quality 𝜂 Electrical efficiency 𝜌 Density [kg m-3] Indexes boil Boiling c Convective cycle Power cycle ext External f Liquid phase g Vapour phase geo Geothermal h Hydraulic head Wellhead
inlet Inlet of the CBHE ins Insulant
int Internal l Liquid
NcB Nucleate boiling
o Only
pump Plant pump sat Saturation sec Section TP Two-phase turb Turbine v Vapour Acronyms
CBHE Coaxial Borehole Heat exchanger IDDP Iceland Deep Drilling
1.
Introduction and literature review
For several years, a vast amount of studies has been held to favour the spread of renewable energy systems, e.g. to reduce the erosion of natural resources. Among several technologies, geothermal energy proved to be a reliable source for electric power generation. The geothermal potential of Earth was estimated up to 46 TW, summing the contribution of the crust and mantle lithosphere to the overall geothermal heat flux. Despite this potentiality,
the worldwide installed capacity stands at 12.64 GWel, 0.3% of the world electricity demand.
Nowadays the focus is on pursuing a faster growth of the sector by exploiting deep geothermal resources.
Some locations of the world are particularly suitable for the purpose. Iceland, for instance, is the country with the deepest penetration of geothermal power production, with a 30% share in the sector (Huenges and Ledru, 2011). This scenario proved out to be attractive for energy-intensive businesses, generating the impulse of a deeper utilisation of the existing reservoirs. Therefore, the government's interest has recently been focused on the investigating unconventional high-temperature geothermal systems (240-340 °C), which could potentially lead to very high energy generation rates. Several plans of this kind are gathering the attention of the scientific community in the past years, the most notable of which was the Iceland Deep Drilling Project (IDDP), whose operations are set in Krafla (Northern Iceland). In 2009, a government-business consortium started to dig a deep geothermal well, named IDDP-1, with the purpose of extracting highly valuable supercritical geothermal fluids, unlocking a specific rated power one order of magnitude greater than a conventional power plant installed in the same field (Elders et al., 2014) The drilling failed irreversibly at a depth of 2 km, due to magmatic intrusion. The well was then converted to
a subcritical dry-steam source for a 30 MWel Rankine cycle.
The IDDP-1 incident, while showing that magma may be met, although rarely, at shallower depths than previously deemed possible, opened a profitable scenario for power production purposes. The US Department of Energy, in the context of the “Magma Energy Program”, advocated for several years the employment of downhole heat exchangers for extracting, in a controlled manner, high-enthalpy energy from magma in the form, for instance, of superheated steam. The shift from an open-well configuration ‒ allowing geothermal fluid to rise through it ‒ to a closed-well set-up, not permitting mass exchange with the reservoir and with a recirculation the working fluid, presents several advantages. These are, namely, avoiding the production of brines, and eliminating the post-treatment equipment for the geothermal steam.
The most common downhole heat exchanger solution is called Coaxial Borehole Heat Exchanger (CBHE). This geometry has gathered rising interests from research and engineering areas on geothermal systems, being a promising solution for sustainable and carbon-free heating. For several years, the CBHEs has been exploited, in a limited number of cases, in the ground-coupled heat pump systems for heating and cooling buildings. The implementation of a CBHE in a geothermal reservoir for power production purposes is limited by: the water boiling temperature, the phase change enthalpy and the common geothermal temperature gradient (24-48 °C/km). These limitations can be potentially overcome considering the exceptional conditions in the Icelandic Krafla field, where the local
geothermal gradient reaches peaks of 190-200 °C/km. Preliminary calculations suggest that a CBHE installed in the Krafla field, where the IDDP-1 experiment failed, could produce superheated water vapour from injecting ambient temperature water at its inlet.
The CBHE item consists in two coaxial pipes inserted in a well. Water is injected in the external annulus, between the well casing and the internal shell (Alimonti et al., 2018). During the downward flow, the fluid heats up. At the bottom-hole, the fluid introduced in the annulus rises back towards the wellhead. If enough thermal power is provided, the fluid can undertake phase transition in its downward flow. The gap between the two pipes is filled with insulating material to reduce the heat exchange between upward and downward flow. Figure 1 displays a schematic layout of the CBHE as well as a sectional view.
The CBHE can be analytically modelled in a valid way using the electrical analogy to account for conduction across the walls and employing heat transfer correlations to calculate the variation of the thermophysical properties (temperature, pressure, etc.) of the flow. This thesis aims at implementing a model following this principle, including also an analytical characterisation of the boiling region, using boiling models available in the literature. In addition, the possibility of a numerical characterisation of the two-phase transition has been considered.
Figure 1 Coaxial borehole heat exchanger. Section and schematic view (Alimonti and
Soldo, 2016)
Numerical modelling of boiling flows represents one of the hardest challenges for Computation Fluid Dynamics (CFD), due the discontinuity of the thermal properties through the liquid-vapour interface and the related mass exchange. A further trial lies in the difficulty of validating the data coming from simulating complex systems like the CBHE geometry with the surrounding geothermal field. A large variety of numerical models have been developed for open well configurations, including also a treatment of the surrounding porous zone, while the performance of a CBHE used as a water boiler has never been assessed. To sum up, the main limitation of the numerical approach for treating boiling flow in a closed well geothermal application is that it needs to be calibrated to the specific case and geometry. A numerical model with ANSYS Fluent has been built with the purpose of coupling the analytical approach with a numerical assessment of the position, length and exchanged thermal power of the two-phase region.
2.
Modelling the Coaxial Borehole Heat Exchanger
The system described in this work is a CBHE geometry proposed in several publications (Alimonti et al., 2018; Alimonti and Soldo, 2016; Nian and Cheng, 2018), with an axial length (depth) of 2070 m, and an external diameter of 0.24 m. The geometric parameters and operating conditions are put on display in Table 1.
Figure 2 Schematic layout of the CBHE geometry and, on the right, its conceptual regions
Table 1 Geometric parameters and operating conditions of the wellbore system Parameter Value Parameter Value
𝑳 2070 m Bottom hole temperature 𝑇bot 400 °C
𝑳𝐢𝐧𝐭 2069 m Wellhead temperature 𝑇head 10 °C
𝑹𝒓𝒆𝐭𝐢 50.8 mm Geothermal gradient (𝑏) 188.41 K/km 𝑹𝐚𝐧𝐢 113.3 mm Inlet pressure 𝑝inlet 10 bar 𝒕𝐞𝐱𝐭 8.9 mm Inlet water temperature (𝑇inlet) 46 °C
𝒕𝐢𝐧𝐭 10 mm External pipe conductivity 16.27 Wm-1K-1
𝒎̇ 0.5-1-2 kg/s Internal pipe conductivity (𝑘ins) 0.03 Wm-1K-1
The temperature boundary condition applied to the rock formations surrounding the well is a linear gradient:
𝑇geo(𝑥) = 𝑏 · 𝑥 + 𝑇head
based on a simplification of the Krafla reservoir conditions and neglecting time-varying temperature trends. The inlet temperature and pressure where chosen for a realistic power production assessment, aiming to limit the dimension of the condenser and pump installed in the power cycle. The analytical model is constituted by 4 interconnected sub-models for
the zones numerated in Figure 2 and representing: (1) subcooled liquid region; (2) boiling,
or two-phase transition, region; (3) superheated vapour region and (4) riser. The thermal properties of water (both liquid and vapour) were obtained with the Steam Tables script for MS Excel (Holmgren, 2007). The riser was assumed to be adiabatic to made feasible an
2.1 Governing equations
The conservation of mass (continuity) equation is:
𝑚̇ =𝜌𝐴𝑣= constant
The mechanical energy equation, assuming steady state and one-dimensional flow, provides the Bernoulli’s equation:
𝑝1 𝜌1𝑔 + 𝑣12 2𝑔 + 𝑥1 = 𝑝𝜌2 2𝑔 + 𝑣22 2𝑔 + 𝑥2+ 𝐻loss [m]
The pressure head loss due to friction can be evaluated with:
𝐻loss = 𝑓 𝑣1
2
2𝑔∆𝑥𝐷ℎ
The steady flow energy balance for an infinitesimal section of the annular channel is:
𝑑𝑞 ̇← = 𝑚̇[ℎ̂(𝑥 + 𝑑𝑥) − ℎ̂(𝑥)] = −𝑃 · 𝑈(𝑥)[𝑇(𝑥) − 𝑇
geo(𝑥)]𝑑𝑥
2.2 Single-phase zones
An iterative procedure was set up to evaluate the variation of the thermal properties with the bulk temperature of the subcooled water and superheated vapour in the annulus, and hence estimate: (1) where the liquid reaches the saturation conditions and (2) the conditions of vapour at the bottom of the CBHE. The well was divided into 1 m long sections i, and the iterative procedure for each section was based on the following convergence criterion (which is an energy conservation balance):
∣𝑚̇𝑐𝑝,𝑖(𝑇𝑖− 𝑇𝑖−1) − 𝑈𝑖𝐴sec(𝑇̅geo𝑖− 𝑇bulk,𝑖)∣ < 𝜀
2.3 Boiling region and related models
2.3 Boiling region and related models
To characterise the two-phase transition. the main parameter to be studied is the convective
two-phase heat transfer coefficient (ℎ𝑇𝑃), which univocally binds the wall temperature 𝑇𝑤
and the heat flux 𝑞 ̇ in a specific location along the borehole. These parameters influence the
trend of the mass quality 𝛼 in the boiling region:
𝛼 =𝑚̇ 𝑚̇𝑔
𝑓+ 𝑚̇𝑔
The heat transfer coefficient is a combination of two mechanisms, nucleate boiling and forced convection. The variety of analytical models proposed is commonly based on a power-law type function that merges the two contributions:
ℎ𝑇𝑃 = [(ℎ𝑐)𝑛+ (ℎ𝑁𝑐𝐵)𝑛]1 𝑛⁄
A selection was made among the most used correlations, as displayed in Table 2.
Table 2 Boiling models with the related empirical correlation
Chen ℎ𝑇𝑃 = 𝐹ℎ𝑐+ 𝑆ℎ𝑁𝑐𝐵 Steiner ℎ𝑇𝑃 = [(ℎ𝑓𝑜𝐹𝑇𝑃)3+ (ℎ𝑁𝑐𝐵,𝑜𝐹𝑁𝑐𝐵)3]1 3⁄ Liu ℎ𝑇𝑃2 = (𝐹ℎ𝑓𝑜)2+ (𝑆ℎ𝑁𝑐𝐵)2 Shah 𝐶𝑜 > 1 ℎ 𝑁𝑐𝐵/ℎ𝑓 = {230 𝐵𝑜 0.5 if 𝐵𝑜 > 3 · 10−4 1 + 46 𝐵𝑜0.5 if 𝐵𝑜 < 3 · 10−4 0.1 < 𝐶𝑜 < 1 ℎ𝑁𝑐𝐵⁄ = 𝐹 𝐵𝑜ℎ𝑓 0.5 exp(2.74 𝐶𝑜−0.1) 𝐶𝑜 < 0.1 ℎ𝑁𝑐𝐵⁄ = 𝐹 𝐵𝑜ℎ𝑓 0.5 exp(2.47 𝐶𝑜−0.15) Where 𝐶𝑜 = (1−𝛼𝛼 )0.8(𝜌𝜌𝑔 𝑓) 0.5 and 𝐵𝑜 = 𝑞 ̇ 𝐺ℎ̂⁄ 𝑓𝑔
The length of the region is obtained with a procedure like the one of the single-phase regions,
carried out until reaching a unitary mass quality 𝛼 = 1. From the 𝛼 profile it is possible to
estimate the two-phase pressure gradient using the separated flow model (Collier and Thome, 1994).
3
Results
3.1 Temperature profiles
This thesis investigates three scenarios in which the injected mass flow varies from 0.5, 1
and 2 kg/s. Figure 4 displays the temperature profile of the working fluid in the annular
channel and the geothermal gradient. The profile highlights:
• The subcooled region (the bulk temperature increases with the same trend of the
geothermal gradient);
• The boiling region (it is marked by a flat temperature profile determined from the
saturation conditions, 𝑇sat(𝑝)). Figure 5 shows a close-up;
• The superheated vapour region (the newly formed vapour phase departs from
The temperature profile in the single-phase zones was estimated also using a model furtherly simplified from the analytical one. Its functional form, which derives from an infinitesimal energy balance, is:
𝑇 (𝑥) = 𝑇ℎ𝑒𝑎𝑑+ 𝑏𝑥 + (𝑇𝑖𝑛𝑙𝑒𝑡− 𝑇ℎ𝑒𝑎𝑑+𝑏𝑚̇𝑐ℎ𝑃 ) · exp (−𝑝 ℎ𝑃𝑥𝑚̇𝑐
𝑝) −
𝑏𝑚̇𝑐𝑝
ℎ𝑃
which makes evident that the initial temperature difference between the geothermal gradient
and the bulk fluid temperature fades exponentially reaching 𝑇geo(𝑥) − 𝑇(𝑥) = 𝑏𝑚̇𝑐𝑝⁄ for ℎ𝑃
𝑥 ≥ 5𝑚̇𝑐𝑝/ℎ𝑃. The same trend is visible in the superheated vapour region, where the
temperature of water departs from saturation conditions and exponentially approaches the geothermal slope.
The pressure trend in the whole CBHE is displayed in Figure 6, as it was obtained from the empirical model. This trend impacts on the local saturation temperature, which in turns determines the location of the onset of saturated boiling, where the bulk fluid temperature reaches saturation (Figure 7). Table 3 summarises the main results.
Figure 4 Temperature profile in the annular channel
Figure 5 Close-up on the boiling and superheated vapour regions
Table 3 Notable results from the empirical model Parameter 2 kg/s 1 kg/s 0.5 kg/s 𝑥𝑙,𝑠𝑎𝑡 1842 1831 1824 𝑥𝑣,𝑠𝑎𝑡 (Chen) 1940 1899 1870 𝐿𝑠𝑎𝑡 (Chen) 98 m 68 m 46 m 𝑄̇boil 1767 kW 890 kW 447 kW 𝑇 (𝑥 = 2069) = 𝑇oulet 391.8 °C 394.2 °C 395.1 °C 3.2 Boiling models
Regarding the boiling models employed, the length of the boiling region differs up to 10 % from one model to another, taking the Chen model as a reference, while the discrepancy is up to 40 % for the Shah’s correlation results. Shah’s model incorporates the suppression of convective boiling for low mass qualities, thus leading to a less steep trend of the cumulative
thermal power exchanged in the phase transition, as displayed in Figure 8. Despite this drawback of the Shah’s model, all the four models predict with satisfactory accuracy (∆𝑄̇boil < 2 %) the thermal power transferred in the phase transition compared to the
theoretical value 𝑄̇boil (calculated from the enthalpic balance, Table 3).
Figure 6 Pressure profile in the CBHE Figure 7 Visualization of the saturation temperature and bulk fluid temperature
The cumulative curves in Figure 8, although highlighting a slight discrepancy in terms of
boiling region length, essentially converge to the same 𝑄̇boil value. Finally, a series of
sensitivity analyses show that 𝑚̇ > 5 𝑘𝑔/𝑠 or 𝑏 < 171.5 ºC/km would imply partial
evaporation. The phase transition could furtherly proceed in the riser, moving along an isenthalpic line, but this occurrence has been discarded from the present study. This case, however, could be accurately predicted introducing a different empirical model, whose development has been handed over to future improvements of this work. Moreover, loosening
the hypothesis of adiabatic riser (and then introducing an insulant conductivity of 𝑘ins =
0.03 W m−1K−1) evidenced a reasonable share of thermal power dispersion from riser to
annulus.
Figure 8 Cumulative thermal power transmitted to the working fluid in the boiling region, computed with the four boiling models (case 𝒎̇ = 𝟐 𝒌𝒈/𝒔)
3.3 Numerical model
Figure 9 Temperature profile in the simulated case
power production potential of the well. The simulations were performed with an
axisymmetric mesh and analysing a simple case study, the one of 𝑝inlet = 35 𝑏𝑎𝑟 and 𝑇eva =
242 °𝐶, held neglecting the static head contribution to the pressure pattern in the well. A complete solution of the multiphase flow is beyond the aim of the thesis, that is determining the trend of the thermal and flow properties along the CBHE and assessing its power production potential. To the purpose of this work, empirical correlations were used to determine with sufficient accuracy the section along the well in which boiling occurs, along with the pressure drop in the multiphase region. The numerical simulations, although performed with a model and a mesh not particularly refined, highlighted a reasonable accordance with the analytically determined boiling region length and thermal power exchanged. The exclusive use of the analytical model, even with discrepancies between correlations, allowed to obtain these outcomes without the necessity of a refined mesh and numerical boiling simulation. These final aspects were left to future scenarios, whether a more precise definition of the flow boiling pattern was required.
4
Preliminary sizing of the Rankine power cycle
One of the scopes of this thesis is assessing the power production potential of a CBHE with a geometry and thermal boundary conditions as close as possible to the one in the Krafla geothermic field. The analytical model developed in this thesis and the results exposed in Chapter 6 can provide an estimation of this possibility.
Figure 10 displays the layout of the power cycle. The configuration set as example in this thesis derives from the dry-steam power plant configuration, used in medium power applications when a dry steam geothermal reservoir is available. The state of the art plants processes on average 20-25 kg/s of geothermal steam, with a range of power outputs from
10 to 60 MWel. However, the layout investigated in this thesis differs from the conventional
geothermal power generation systems due to the presence of a CBHE, exploiting the function that in conventional Rankine cycles is performed by the boiler and by the pump. Following the cycle displayed in Figure 10, liquid water, coming from the condenser, is pumped (a) and injected in the annular channel. It exchanges thermal power with the surroundings (b), undertakes a complete phase transition while being pressurised. The superheated vapour rises through the internal pipe and enters a lamination valve (c) that regulates the turbine
inlet pressure. After being expanded in a steam turbine (d), the vapour is condensed (e), closing the loop.
Figure 10 Process flow diagram of the power cycle
Figure 11 displays the thermodynamic points of the cycle obtained after a preliminary sizing of the components of the cycle. Table 4 summarises the results. The energy conversion (electrical) efficiency of the cycle positively meets the average values of the medium size dry-steam geothermal plants, like the ones installed in Tuscany, Italy (DiPippo, 2016), as
well as the rated power per mass flow unit 𝑊̇net/𝑚̇. The value of the isentropic efficiency of
the turbine 𝜂is,turb has been referenced as well to medium size dry-steam applications.
Finally, it was deemed reasonable to estimate the number of CBHE units to achieve a net power output fitting in the range mentioned beforehand for the dry-steam power plants.
Considering 𝑊̇net,target= 25 MWel led to the results displayed in the last row of Table 4.
Table 4 Results from the sizing of the power cycle
Parameter 2 kg/s 1 kg/s 0.5 kg/s 𝑄̇𝑡𝑜𝑡←[kW] 5373 2704 1358 𝑊̇eng,pump [kW] 2.577 1.288 0.644 𝜂is,pump 0.8 0.8 0.8 𝑊̇alt,turb [kW] 1413 709.4 355.3 𝜂is,turb 0.75 0.75 0.75 𝑊̇net [kW] 1368 686.9 344.0 %𝑊̇eng,pump 0.19% 0.19% 0.19% 𝛼𝑇𝐷,𝑜𝑢𝑡𝑙𝑒𝑡 0.84 0.84 0.85 𝜂cycle 25.46% 25.40% 25.33% 𝑁𝐶𝐵𝐻𝐸 19 37 73
Figure 11 T-s diagram [𝒎̇ = 𝟐 𝒌𝒈/𝒔]
5
Conclusions and future scenarios
The model was developed to produce a realistic estimation of the location of the boiling region along with the temperature profile in the annular channel, with the final goal of assessing how the CBHE geometry could fit in a conventional medium size Rankine cycle. The model was built on strong hypotheses, such as the adiabatic rising channel, with the aim of achieving an analytically-treatable procedure to determine a realistic trend of the notable thermal properties in the heat exchanger, as well as the thermal power transferred to the working fluid.
The procedure highlighted a boiling region occupying a significant portion of the length of the annulus and providing a great contribution to the thermal power transmitted to the fluid, with minor variations with the boiling model employed. The CBHE geometry proved to be efficient in terms of exploitation of the geothermal gradient to heat up the working fluid from subcooled liquid to superheated vapour conditions. The conditions reached in the bottom-hole revealed a satisfactory power production potential. The sizing of the cycle evidenced that installing a reasonable number of CBHE units to feed a single medium-power steam turbine could overcome the limitation of a low mass flow rate admissible for the CBHE (to avoid partial boiling in the annulus). The trends obtained in this context are comparable to recent dry-steam power plants in terms of specific power output and conversion efficiency. The numerical simulations implemented proved to be too simple to provide a characterisation of the phase distribution in the boiling region. However, this occurrence is not relevant to the aim of describing the phase transition only in terms of length and thermal power transmitted, about which the numerical approach provided results in line with the analytical ones.
The future developments of this work could include a technical-economic analysis about implementing CBHE in a power cycle for exploiting conditions different to the one of the Krafla field, also considering time-varying geothermal temperature profiles. Furthermore, it deserves to be assessed how the analytical model could be furtherly developed by including a more sophisticated boiling model, incorporating for instance experimental results. In turn, it is left to future scenarios determining how a numerical model could be useful for the characterization of the phase transition and the general optimisation of the cycle.
Aknowledgments ... i
Sommario... iii
Abstract ... v
Extended summary ... vi
Table of contents ... xvii
List of figures ... xxi
List of tables ... xxv
Nomenclature ... xxvii
List of abbreviations ... xxx
Introduction ... 1
1.1 Aims and objectives... 2
1.2 Outline of the Thesis ... 3
Literature review ... 5
2.1 The Iceland Deep Drilling Project (IDDP) ... 5
2.1.1 The concept ... 5
2.1.2 The IDDP-1 at Krafla ... 6
2.1.3 The IDDP-2 and future activities ... 8
2.2 Borehole heat exchangers ... 8
2.2.1 General background on deep borehole heat exchangers (DBHE) ... 9
2.2.2 Geometry and properties of coaxial BHE ... 9
2.2.3 Performance of CBHE ... 10
2.3 Geothermal energy: power plant technologies ... 11
2.3.1 Dry-steam geothermal power plants ... 12
2.4 Power generation applications for the CBHE ... 13
2.5 Available numerical models ... 16
2.5.1 Heat transfer simulation of DBHE ... 16
2.5.2 CFD modelling of flow boiling ... 17
2.5.3 CFD applied to geothermal reservoirs ... 18
2.6 Summary of the review and gap in the literature ... 19
Flow boiling in annular channels ... 21
3.1 Physical quantities describing flow boiling in an annulus ... 24
3.2 Boiling models ... 28
3.2.2 Steiner-Taborek correlation ...31 3.2.3 Liu-Winterton correlation ...33 3.2.4 Shah correlation ... 34 3.3 Pressure gradient in two-phase flow ... 36 3.3.1 Homogeneous and separated flow models ... 36 3.3.2 Separated flow estimation of pressure gradient in the two-phase region of the annulus ... 37
Empirical model ... 39 4.1 Definition of the problem: geometry and conditions ... 40 4.2 Algorithms for the computation of the physical properties ... 42 4.2.1 Governing equations ... 44 4.2.2 Analytical sub-model for the subcooled liquid region ... 47 4.2.3 Simplified calculus method: an analytical function ... 53 4.2.4 Analytical sub-model for the two-phase region ... 57 4.2.5 Analytical sub-model for the superheated vapour region ... 60 4.2.6 Evaluation of the flow properties in the riser ... 60 CFD preliminary model and its outcomes ... 65 5.1 Numerical model ... 66 5.1.1 Governing equations and multi-phase model ... 66 5.1.2 Geometry and mesh ... 67 5.1.3 Properties of fluids and materials ... 69 5.1.4 Boundary conditions ... 71 5.1.5 Solver and solution settings ... 71 5.2 Results of the simulations ... 73 5.3 Considerations about using a numerical model for this case study ... 76 Results from the empirical model ... 79 6.1 Comparison of the simplified model with the empirical one ... 80 6.2 Temperature profiles ... 83 6.3 Sensitivity analysis on the geothermal gradient ... 88 6.4 Boiling models ... 89 6.4.1 Pressure profile in the boiling region ... 98 6.5 Pressure profile ... 100 6.6 Velocity and density tendencies ... 104 6.7 Heat flux and single-phase heat transfer coefficient ... 107 6.8 Assessment of the adiabatic riser hypothesis ... 109
6.9 Admissible range of mass flow ... 111 Preliminary sizing of the power cycle ... 113 7.1 Cycle layout ... 113 7.2 Sizing of the components ... 115 7.2.1 Condensate pump ... 115 7.2.2 Coaxial borehole heat exchanger ... 116 7.2.3 Lamination valve ... 117 7.2.4 Turbine ... 117 7.2.5 Results and plots ... 117 7.3 Efficiency and general performance of the cycle ... 120 Conclusions and future work... 125 8.1 Future scenarios ... 126 References ... 129 Appendices ... 133
List of figures
Figure 2-1 [above] Location of Iceland and Krafla’s field on the Mid-Atlantic Ridge
(Friðleifsson, Elders and Albertsson, 2014) ... 7
Figure 2-2 [left] Simplified outline of the IDDP-1 well, in which the two alternative paths, drilled after the magma intrusions, are highlighted (Axelsson, Egilson
and Gylfadóttir, 2014) ... 7
Figure 2-3 Coaxial borehole heat exchanger. Cross section and schematic view
(Alimonti and Soldo, 2016) ... 10
Figure 2-4 Dry-steam geothermal power plant process flow diagram (Moya, Aldás
and Kaparaju, 2018) ... 13
Figure 2-5 Direct cycle configuration (Mokhtari et al., 2016) ... 15 Figure 2-6 Organic Rankine Cycle binary layout (Mokhtari et al., 2016) ... 15 Figure 3-1 Development of two-phase flow in a vertical pipe (Collier and Thome,
1994) ... 23 Figure 4-1 Schematic layout of the geometry of the CBHE studied in this project 40 Figure 4-2 Layout of the zones of the analytical model ... 43 Figure 4-3 Visualisation of the infinitesimal section of the annular channel used to
define the energy balance ... 46 Figure 4-4 Schematic layout of a section (generically named section i) used for the
iterative procedure to determine the subcooled liquid region ... 47 Figure 4-5 Flow diagram displaying the algorithm followed to determine the bulk
temperature at the outlet of section i ... 48 Figure 4-6 Electrical resistance analogy for heat transfer between rock and water
flowing in the pipe ... 51 Figure 4-7 Infinitesimal control volume and variables used to determine the
temperature profile function ... 53 Figure 4-8 Representation of the result of the differential equation for three different
inlet temperatures ... 55 Figure 4-9 Flow diagram displaying the iterative procedure to determine the
properties of boiling water in section i ... 59 Figure 4-10 Layout of the sections of the pipe with the corresponding indexes ... 61
Figure 4-11 Flow chart of the iterative procedure used to estimate the pressure drop along the riser ... 62 Figure 4-12 Sensitivity analysis for the pressure drop iterative method ... 63 Figure 5-1 Schematic representation of the meshing criteria ... 68 Figure 5-2 Close-up of the finer mesh, wellhead zone ... 69 Figure 5-3 Close-up of the finer mesh, bottom-hole zone ... 69 Figure 5-4 Temperature profile in the simulated case ... 74 Figure 5-5 Close-up on the boiling region for the simulated case ... 74 Figure 5-6 Tendency of vapour volume fraction in the annular channel ... 74 Figure 5-7 𝜷 contours in two notable positions along the boiling region [CFD-Post] ... 75 Figure 6-1 Temperature profile of the flow in the annular channel (𝒎 = 𝟐 𝒌𝒈/𝒔) 79 Figure 6-2 Temperature profile obtained with the simplified model ... 82 Figure 6-3 Bulk temperature profile in the downward annular channel for the three
mass flow cases investigated ... 83 Figure 6-4 Visualization of the saturated liquid condition and thw ... 85 Figure 6-5 Trend of the bulk fluid temperature in the boiling and superheated vapour
regions ... 86 Figure 6-6 Close-up on the onset of boiling ... 87 Figure 6-7 Temperature profile in the first 100 m of the annular channel ... 87 Figure 6-8 Temperature profiles associated to 𝒃𝒍𝒊𝒎 = 𝟏𝟕𝟏. 𝟓 °𝐂/𝐤𝐦 ... 88 Figure 6-9 Saturated boiling heat transfer coefficient, plotted against the mass
quality (𝒎 = 𝟐 𝒌𝒈/𝒔) ... 90 Figure 6-10 Saturated boiling heat transfer coefficient, plotted against the axial
coordinate of the annular channel (𝒎 = 𝟐 𝒌𝒈/𝒔) ... 90 Figure 6-11 Saturated boiling heat transfer coefficient, plotted against the mass
quality (𝒎 = 𝟏 𝒌𝒈/𝒔) ... 91 Figure 6-12 Saturated boiling heat transfer coefficient, plotted against the axial
Figure 6-13 Saturated boiling heat transfer coefficient, plotted against the mass quality (𝒎 = 𝟎. 𝟓 𝒌𝒈/𝒔) ... 92 Figure 6-14 Saturated boiling heat transfer coefficient, plotted against the axial
coordinate of the annular channel (𝒎 = 𝟎. 𝟓 𝒌𝒈/𝒔) ... 92 Figure 6-15 Cumulative thermal power transmitted to the working fluid in the
boiling region computed with the four boiling models, case 𝒎 = 𝟐 𝒌𝒈/𝒔 ... 95 Figure 6-16 Volume fraction variation in the boiling region with the four boiling
models used (𝒎 = 𝟐 𝒌𝒈/𝒔) ... 96 Figure 6-17 Heat flux profiles in the boiling region with the four boiling models used
(𝒎 = 𝟐 𝒌𝒈/𝒔) ... 96 Figure 6-18 Pressure gradient in the two-phase region, case 𝒎 = 𝟐 𝒌𝒈/𝒔 ... 99 Figure 6-19 Pressure gradient in the two-phase region, case 𝒎 = 𝟏 𝒌𝒈/𝒔 ... 99 Figure 6-20 Pressure gradient in the two-phase region, case 𝒎 = 𝟎. 𝟓 𝒌𝒈/𝒔 ... 99 Figure 6-21 Complete pressure profile in the coaxial heat exchanger... 100 Figure 6-22 Frictional (fr) and static head (gr) pressure gradient contributions
subcooled liquid region ... 102 Figure 6-23 Frictional (fr) and static head (gr) pressure gradient contributions
superheated vapour region ... 102 Figure 6-24 Pressure decrease trend in the riser, plotted with the gravity and
frictional contributions (𝒎 = 𝟐𝒌𝒈𝒔) ... 103 Figure 6-25 Pressure decrease trend in the riser, plotted with the gravity and
frictional contributions (𝒎 = 𝟏𝒌𝒈𝒔) ... 103 Figure 6-26 Pressure decrease trend in the riser, plotted with the gravity and
frictional contributions (𝒎 = 𝟎. 𝟓𝒌𝒈𝒔) ... 103 Figure 6-27 Velocity profile of subcooled liquid region for the 3 cases ... 104 Figure 6-28 Velocity profile of the superheated vapour region for the 3 cases ... 105 Figure 6-29 Density profile of subcooled liquid region for the 3 cases ... 106 Figure 6-30 Density profile of the superheated vapour region for the 3 cases ... 106 Figure 6-31 Heat flux and heat transfer coefficient profiles, subcooled liquid ... 107 Figure 6-32 Heat flux and heat transfer coefficient profiles, superheated vapour . 107
Figure 6-33 Thermal power transmitted from the rising fluid to the descending flow in the annular channel, compared to the one effectively transmitted from rock to fluid in the adiabatic riser model ... 111 Figure 6-34 Close up on the boiling region for the high mass flow cases ... 112 Figure 7-1 Process flow diagram of the power cycle ... 114 Figure 7-2 Relevant thermodynamic plots of the power cycle, from top to bottom T-s, h-s and p-h [𝒎 = 𝟐 𝒌𝒈/𝒔]... 119
List of tables
Table 3-1 Nucleate flow boiling coefficient at normalised conditions ... 32 Table 4-1 Geometric parameters and operating conditions of the wellbore system 40 Table 4-2 Pressure drop variability with riser temperature and number of sections ... 63 Table 5-1 Resolutions of the meshes used for the independence study ... 69 Table 5-2 Properties of solid materials ... 70 Table 5-3 Settings used for the properties of liquid and vapour phases ... 71 Table 5-4 Mass-flow inlet and pressure-drop outlet boundary conditions ... 71 Table 5-5 Solver settings ... 72 Table 5-6 Key results of numerical simulations ... 73 Table 6-1 Simplified model and empirical model comparison, liquid region ... 81 Table 6-2 Key results of the temperature profiles obtained with the analytical
approach ... 84 Table 6-3 Heat transfer coefficient's notable values for the four boiling models
investigated ... 93 Table 6-4 Length of boiling region for the four boiling models ... 94 Table 6-5 Notable results of the pressure analysis in the boiling region ... 98 Table 6-6 Key result from pressure profiles ... 101 Table 6-7 Module and percentage variation of subcooled water velocity ... 104 Table 6-8 Module of superheated vapour velocity in the annular channel,
accompanied by percentage change and corresponding pressure drop ... 105 Table 6-9 Reynolds dimensionless number in notable sections of the annulus ... 108 Table 6-10 Notable result from the sensitivity analysis for the adiabatic riser
assumption ... 110 Table 6-11 Results on the sensitivity analysis for the admissible range of mass flow ... 112 Table 7-1 Thermodynamic points of the power cycle, 𝒎 = 𝟐 𝒌𝒈/𝒔 ... 118
Table 7-2 Thermodynamic points of the power cycle, 𝒎 = 𝟏 𝒌𝒈/𝒔 ... 118 Table 7-3 Thermodynamic points of the power cycle, 𝒎 = 𝟎. 𝟓 𝒌𝒈/𝒔 ... 118 Table 7-4 Results from the sizing of the power cycle ... 121 Table 7-5 Power cycle parameters and energy conversion efficiencies for selected
Nomenclature
Latin symbols
𝐴 Flow area [m2]
𝐴an Flow area of the annular channel [m2]
𝐴sec External surface of a section in which the annulus is discretised [m2]
𝑐𝑝 Specific heat capacity at constant pressure [J kg−1K−1]
𝐷ane External diameter of annular pipe [m] 𝐷𝑒 Equivalent diameter [m]
𝐷ℎ Hydraulic diameter [m]
𝐷rete External diameter of return pipe [m] 𝐹 Reynolds number factor [1]
𝑓 Moody’s friction factor [1] 𝐺 Mass velocity [kg s−1m−2]
ℎ Convective heat transfer coefficient [W m−2K−1] ℎ𝑐 Single-phase forced convection coefficient [W m−2K−1]
ℎ𝑁𝑐𝐵 Nucleate boiling convection coefficient [W m−2K−1]
ℎ𝑇𝑃 Convective two-phase heat transfer coefficient [W m−2K−1]
ℎ̂ Specific enthalpy [J kg−1]
ℎ̂𝑓𝑔 Latent heat of vaporisation [J kg−1]
𝑘 Thermal conductivity [W m−1K−1]
𝑘ins Thermal conductivity of the insulated internal pipe [W m−1K−1]
𝐿 Length of the wellbore [m] 𝐿int Length of the return pipe [m]
𝐿sec Length of a section in which the well was analytically discretised [m]
𝑚̇ Mass flow rate [kg s−1] 𝑀𝑀 Molar mass [kg kmol−1]
𝑁𝑢 Nusselt Number [1] 𝑝inlet Inlet pressure [bar]
𝑃 Wetted perimeter [m] 𝑃𝑟 Prandtl Number [1] 𝑞 ̇ Heat flux [W m−2]
𝑅 Thermal resistance [K W−1] 𝑅𝑒 Reynolds Number [1]
𝑅ane External radius of annular pipe [m] 𝑅ani Internal radius of annular pipe [m] 𝑅rete External radius of return pipe [m] 𝑅reti Internal radius of return pipe [m] 𝑆 Chen’s suppression factor [1]
𝑇bot Geothermal temperature of the surroundings at the well-end [°C]
𝑇𝑓 Bulk fluid temperature [°C]
𝑇geo Geothermal temperature of surroundings at a specified 𝑥 [°C]
𝑇head Geothermal temperature of the surroundings at the well-head [°C]
𝑇inlet Inlet water temperature [°C]
𝑇sat Saturation temperature [°C]
𝑇𝑤 Wall temperature [°C]
𝑡ext Thickness of the external annular pipe [m]
𝑡geo Geothermal gradient [°C/m]
𝑡int Thickness of riser [m]
𝑈 Overall heat transfer coefficient [W m−2K−1] 𝑢av Average velocity across the flow area [m s−1]
𝑢̂ Specific internal energy [J kg−1]
𝑥 Axial coordinate of the coaxial heat exchanger [m] 𝑋𝑡𝑡 Martinelli coefficient [1]
Greek symbols
𝛼𝑣 Void fraction [1]
𝛼 Mass quality, vapour volume fraction [1] 𝜇 Dynamic viscosity [Pa s]
𝜌 Density [kg m−3] 𝜎 Surface tension [N m−1]
𝜑𝑓𝑜2 Two-phase frictional multiplier [1]
Subscripts
an Annular channel
boil Relative to the boiling region 𝑓 Saturated liquid conditions
𝑓𝑜 Liquid-only, total flow assumed liquid 𝑔 Saturated vapour conditions
geo Geothermal
𝑔𝑜 Vapour-only, total flow assumed vapour head Well-head
inlet Inlet of the coaxial borehole heat exchanger
𝑤 Wall
Indices and operators
∆ Difference
∇ Nabla operator 0 Initial iteration 𝑖 ∈ 𝐼 Index set
List of abbreviations
BHE Borehole Heat Exchanger
CBHE Coaxial Borehole Heat Exchanger CFD Computational Fluid Dynamics DBHE Deep Borehole Heat Exchanger EGS Enhanced Geothermal Systems HE Heat exchanger
IDDP Iceland Deep Drilling Project RANS Reynolds Averaged Navier-Stokes UDF User defined function
Introduction
For decades, different studies have been held to develop sustainable and renewable energy systems capable of reducing the environmental impact of greenhouse effect, global warming, devastation of natural resources and air pollution. Among a wide variety of technologies, geothermal energy proved to be a reliable and environmental friendly source for electric power generation (Huenges and Ledru, 2011).
The Earth’s geothermal potential lays back to when the planet was formed, and it is continuously restored at about 80% by the radioactive decay of the materials of crust and mantle (potassium, uranium) and 20% by the thermal power from the Earth’s interior, such as volcanic activity ad solar radiation absorbed by the surface of the planet (DiPippo, 2016). The total thermal power production within the crust and mantle lithosphere due to these two mechanisms is 46 TW. However, despite this outstanding potential, the global contribution of geothermal energy in terms of power generation potential is relatively modest. Indeed, the International Energy Agency (IEA, 2015) estimated that the worldwide installed capacity stands at 12.64 GWe, being only the 0.3% of the overall electricity demand. The International Energy Agency has suggested drawing up plans to undertake the engineering-focused challenge of accomplishing a faster growth of the sector. Reaching considerable depths is a basic requirement to exploit deep geothermal resources, but the experience gained so far by implementing sophisticated deep geothermal projects has disclosed some technical and economic challenges.
Due to a naturally enhanced geological activity, Iceland leads the world in terms of geothermal energy exploitation and diffusion. Ground heat pumps warm nearly 90% of households, while about 30% of power production is geothermal (Huenges and Ledru, 2011). Hence, the country is broadly supplied by sustainable and low price primary energy. This scenario proved to be alluring for energy-intensive businesses, triggering a virtuous cycle in which an ever-increasing utilisation of the existing reservoirs is required. Therefore, the government interest is lately focused in exploring unconventional high-temperature (240-400 °C) geothermal systems potentially capable of very high power generation rates (Elders et al., 2014). Several plans of such kind are gathering the attention of the scientific community in the past years, the most notable of them being the Iceland Deep Drilling Project (IDDP), whose operations are set in Krafla (Northern Iceland). Although the variety of systems capable of producing electricity is extremely vast (DiPippo, 2016), the main distinction lays in the interface between the working fluid and the geothermal reservoir. If the well is open to the surroundings and geothermal fluids rise through it, the system operates in an open-well configuration (Huenges and Ledru, 2011). On the contrary, if the well does not allow mass exchange with the reservoir, but the working fluid is simply heated by the surroundings and recirculated in the system, the configuration is called closed-well (DiPippo, 2016).
1.1
Aims and objectives
The work developed in this thesis aspires at exploring, in a preliminary and simplified way, the feasibility of a power production system whose performances have never been investigated before.
The aim of this master’s thesis is to build a comprehensive model of a closed-well system suitable for the conditions of an Icelandic plant (well IDDP-1 in Krafla) and assess its performance through an analytical-empirical model built for this purpose. Since boiling is expected to occur at some location along the well, a set of analytical heat transfer methods, organically constituting an empirical model of the well, will be used to understand the behaviour of the two-phase transition. Moreover, the master’s thesis aims at investigating the location along the well where saturated boiling occurs and delineate the trends of the main thermophysical properties, in the optic of evaluating the power production potential of the designed system. Finally, a further target of this work is conducting a preliminary sizing of a power cycle
exploiting the coaxial heat exchanger as a water boiler, along with testing the model for different mass flow rates to assess the robustness of the methodology.
1.2
Outline of the Thesis
The structure of the thesis can be summarised as follows. After these introductory pages, a review of the published literature (Chapter 2) is carried out summarising the current state of the knowledge in the field of the thesis. Chapter 3 contains a focus on the boiling transition, with an overview of boiling two-phase flows and a review of the boiling models implemented in this thesis. The results of these chapters will be used to delineate the boundary conditions of the system and its geometry, as well as familiarising with the possible ways of building the analytical model. Chapter
4 contains the methodology applied in the study of this thesis, along with a detailed description of the sub-parts of the analytical model, while Chapter 5 illustrates the preliminary numerical analysis of the phase transition region. The results of the empirical model are presented in Chapter 6, while in Chapter 7 a preliminary sizing of the related power cycle is carried out. The conclusions of the findings of this thesis are summarised in Chapter 8.
Literature review
This Chapter presents an organic summary of the published literature about the topic of this thesis. The first purpose is delineating the case study used for the boundary and geometric conditions of the wellbore system. These have been identified with the Krafla geothermal field in Northern Iceland, where the Iceland Deep Drilling Project based its operation to assess the feasibility of exploiting its extreme temperature conditions for power production purposes. After a focus on the chronology of the project, the literature review unfolds covering the geometrical characteristics of the borehole heat exchanger and its applications to geothermal energy extraction. Finally, the state of the art methods to numerically describe geothermal wellbores are presented.
2.1
The Iceland Deep Drilling Project (IDDP)
2.1.1The concept
The IDDP is a long-term plan, held by a government-industry joint consortium, based on investigating the performance of unconventional geothermal fields with a focus on their power production potential. In particular, the Project aims at studying the environmental impact associated to exploit these reservoirs and assess the technical and economic value related to the geothermal operations (Friðleifsson, Elders and Albertsson, 2014). The consortium was established in 2000 between three major Icelandic energy companies (HS, LV and OR) and the National Energy
Authority of Iceland. From the beginning, the focus has been on investigating the drilling for supercritical geothermal power sources, believed to produce, given the steam volumetric flow rate, electric power an order of magnitude higher when compared to conventional fields (Elders et al., 2014).
Between 2006 and 2007 the operations were based in Krafla (Northern Iceland). The three power companies of the joint committed to drill three fully cased wells in three different Icelandic localities, Krafla included. These wells were designed to reach a depth of 3.5-4.0 km.
Hydrous supercritical systems are associated to great depths, typically under an oceanic plaque due to the hydrostatic gradient. The water column naturally creates a significant pressure in the rock formations below oceans, establishing the conditions necessary for the presence of supercritical fluids. However, some evidences show the presence of hydrothermal supercritical fluids in relatively shallow formation in the Icelandic mainland. This stimulated the possibility of deliberately exploiting natural supercritical fluids for power production purposes over controlled conditions. In particular, the IDDP concept aimed at extracting supercritical fluids following a thermodynamic path to obtain mono-phase superheated steam at the well outlet (Friðleifsson, Elders and Albertsson, 2014).
2.1.2 The IDDP-1 at Krafla
Following the collapse of a 3.1 km deep geothermal well in the Reykjanes locality in 2005, the operator of the Krafla geothermal field offered IDDP the deepening of a planned well. Hence, from 2006, the IDDP operations were based at that location (Friðleifsson, Elders and Albertsson, 2014). The Krafla high-temperature geothermal field is located in North-eastern Iceland, in an area geologically characterised by the presence of an active volcano incorporating a large magmatic caldera at 5 to 8 km depth. On its ground a geothermal power plant is currently producing 60 MWe (Ármannsson et al., 2014).
In 2009, the consortium started to dig the first deep geothermal well of the Project under the name of IDDP-1. The well, located in the Northern Leirbotnar field in the Krafla area, was attempted in the proximity of the Krafla volcano on a 40 km2 geothermal field, the same where the 60 MWe power plant is located (Elders et al., 2014). The initial design consisted of a large diameter well with five concrete casing strings, with the diameter progressively reducing until the final value of 8.5 inches
(0.216 m), reaching a depth of 4500 m, approximately 500 m below the expected boundary of the supercritical fluid zone (Elders et al., 2014; Thórhallsson et al., 2014).
In spring 2009, the drilling of the IDDP-1 progressed fairly well until 2 km depth, where the drilling bit got progressively stuck, causing the collapse of part of the borehole. The drilling assembly got irreversibly snagged twice, at a depth of 2093 and 2096 m, causing the consecutive drilling of two side paths (Elders et al., 2014). Nevertheless, in June 2009 the drilling problems found their explanation and the digging of the exploratory borehole had to be unexpectedly aborted at a depth of 2104 m. As a matter of fact, the encounter of a 900 °C rhyolitic magmatic intrusion caused the magma to flow into the borehole and quench into glass, thus filling the last 10 m of the hole (Ármannsson et al., 2014; Thórhallsson et al., 2014).
Figure 2-1 [above] Location of Iceland and Krafla’s field on the Mid-Atlantic Ridge
(Friðleifsson, Elders and Albertsson, 2014)
Figure 2-2 [left] Simplified outline of the IDDP-1 well, in which the two alternative paths, drilled after the magma intrusions, are highlighted (Axelsson, Egilson and
Consequently, the IDDP consortium decided to complete the project converting the well to a subcritical configuration: 2072 m of vertical depth (just above the contact zone with magma) and a slotted liner to allow the upward flow of the subcritical fluids. During 2011, this well produced 10-12 kg/s of dry superheated steam at a temperature of up to 450 °C, capable of generating 25-35 MWe if fed to a thermodynamic cycle.
2.1.3 The IDDP-2 and future activities
The construction of a second deep geothermal well within the IDDP consortium was planned to begin in 2010 in Reykjanes, south-western Iceland. The failure of the IDDP-1 attempt and a national economic crisis jeopardised the project, however, the power company HS Orka committed in realising the IDDP-2 well to favour the scaling-up of a pre-existent geothermal power station in the area.
After a 7-year hiatus from the IDDP-1 failure and the consequent pause of the IDDP activities, the drilling of the long-lingered second well started in August 2016 in the designed Reykjanes field and was completed by February 2017 at 4659 m depth. The samples collected from the borehole highlighted the presence of supercritical fluids (Iceland Deep Drilling Project, 2017). During 2018 the well has been subject to a series of tests and logging requiring water and tracer injections, while the power production pilot testing is due to occur in 2019 (Science Applications Group of Advisors, 2018).
2.2
Borehole heat exchangers
The IDDP-1 incident showed that magma may be met at shallower depths than previously deemed possible (Ármannsson et al., 2014). The encounters with magma in a geothermal well, apart from the Krafla case, proved to be extremely rare but, nevertheless, potentially profitable for power production purposes. The US Department of Energy, in the context of the “Magma Energy Program”, advocated for several years the employment of downhole heat exchangers for extracting, in a controlled manner, high-enthalpy energy from magma in the form, for instance, of superheated steam (DiPippo, 2016).
After a national-size study, the Long Valley Caldera of California was deemed the suitable site in the US for digging into magma. However, the project of a 6 km deep well never reached light due to funding issues. Nevertheless, Krafla is a much more
alluring location to test the concept of energy from magma, albeit the issues faced with the IDDP-1 project (Elders et al., 2014), using deep borehole heat exchangers.
2.2.1General background on deep borehole heat exchangers (DBHE)
The concept of Deep Borehole Heat Exchanger has gathered rising interests from research and engineering areas on geothermal systems, being a promising solution for sustainable and carbon-free heating. For several years, this solution has been broadly exploited in the ground-coupled heat pump systems for heating and cooling buildings. In these contexts, the boreholes are dug at shallow depths (40-150 m) (Fang et al., 2018).
Lately, the concept has arisen in another technical sector: power production through direct use of geothermal energy. In these applications, the wells may go down to 2000 m below the ground level (Fang et al., 2018). One of the main advantages of this “closed-well” solution is that production of brines that need to be subsequently reinjected is avoided. Reinjection is complicated and expensive due to drilling and maintenance of further wells, as well as increasing pumping costs (Alimonti and Soldo, 2016).
2.2.2Geometry and properties of coaxial BHE
The most commonly used solutions are coaxial BHE, U-pipe HE and double U-pipe BHE (Nian and Cheng, 2018). Being the solution employed in this thesis, the coaxial borehole heat exchanger deserves a deeper focus.
The geometrical concept of the coaxial borehole heat exchanger is elementary: it consists of two coaxial pipes inserted in a well and usually made of stainless steel. A working fluid is injected in the external annulus, between the well casing and the internal shell (Alimonti et al., 2018). During the downward flow, the fluid exchanges heat from the surrounding ground and raises its temperature. At the bottom-hole, the fluid introduced in the annulus rises back towards the wellhead; this is helped also by the density gradient, since the hot and less dense fluid near the bottom of the well tends to spontaneously surge due to buoyancy. The gap between the two pipes is filled with insulating material in order to reduce the heat exchange between upward flow and downward flow (Holmberg et al., 2016). Figure 2-3 displays a schematic layout of the CBHE as well as a sectional view.
Figure 2-3 Coaxial borehole heat exchanger. Cross section and schematic view
(Alimonti and Soldo, 2016)
To increase the thermal resistance (i.e. lower the thermal forestall), the thermal conductivity of the internal well (commonly called riser) has to be reduced, or, alternatively, the wall thickness of the central pipe has to be increased. Clearly, the less invasive solution in terms of alteration of the geometry is the first (Fang et al., 2018). The CBHE is generally provided with a double walled heavily insulated steel pipe (Nian and Cheng, 2018). According to published studies, the choice of material for the return tube should to be determined considering thermal properties, structural strength, and economical prospects, including transport and installation (Holmberg et al., 2016).
The extracted fluid can be used for producing thermal power or, alternatively, electrical power via a Rankine Cycle (Alimonti et al., 2018). The outer pipe of the downhole coaxial heat exchanger has a thin wall and is highly conductive. Consequently, its thermal resistance is often negligible in the published models (Yekoladio, Bello-Ochende and Meyer, 2013).
2.2.3 Performance of CBHE
The coaxial setup is generally deemed the most advantageous configuration, but is the least used as it has a higher installation and construction cost compared to single or double U-tube configurations (Sliwa and Rosen, 2017). The coaxial system is the preferred for deep configurations, such as the ones relative to power production purposes. One of the argumentations for these inclinations is merely geometric: the
CBHE exploits a larger fraction of the borehole area as flow area, with the only exclusion of the thickness associated to the internal and external walls (Alimonti et al., 2018). Moreover, this setup involves smaller pressure drops if compared to other configurations (Sliwa and Rosen, 2017)
Published literature indicates, however, that such a design is the least advantageous in terms of efficiency. The values determined for the effective thermal conductivity are lower than those of a BHE with U-tubes. These results depend however on the fact that the efficiency of coaxial design is heavily dependent on the characteristics of the flow (velocity, Reynolds number) and the internal tube parameters, such as dimensions, material and thickness, which influence thermal losses in the annulus (Sliwa and Rosen, 2017).
A further benefit of having a closed system is that the water or the heat carrier fluid is kept clean from contaminants which may accumulate, for instance, in heat exchangers. The use of water as a thermal vector also reflects the intention to use a slightly higher operation temperature, compared to conventional BHE installations that work with fluid temperatures often less than 0 °C under peak load conditions (Holmberg et al., 2016).
2.3
Geothermal energy: power plant technologies
After defining the geometry of the CBHE, the following purpose of this literature review is illustrating the current situation of the geothermal power production field, with the aim of researching which plant configuration could integrate a CBHE installed in a high-temperature reservoir. The researchers generally agree by individuating three configurations that embrace the majority of installed capacity:
1. Dry-steam plants exploit vapor-dominated reservoirs. The geothermal steam is directly expanded in a turbine driving an alternator. Electricity is generated following a conventional water Rankine cycle.
2. Single-flash plants are the preferred layout when the mixture produced at the wellhead is liquid-dominated. A cyclone pressure vessel separates the steam-brine mixture in two distinct phases, liquid and vapour. The latter is expanded in turbine generating electrical power. The liquid is reinjected back in the reservoir through dedicated wells. Double-flash plants include a second flashing process applied to the liquid stream leaving the primary separator,
thus allowing to reach 25% more power output from the same geofluid conditions.
3. Binary plants are widely used for low or intermediate temperature hydrothermal reservoirs (120-150 °C). The geothermal fluids extracted from the well preheat and evaporate the working fluid flowing in a Rankine cycle, by transferring heat through a dedicated preheater and evaporator. The binary cycle operates commonly in an Organic Rankine Cycle (ORC) setup (DiPippo, 2016; Moya, Aldás and Kaparaju, 2018).
Flash power plants (single and double) have a share of 62% of the overall installed capacity (41% single, 19% double and 2% triple flash), followed by dry-steam (23%) and binary plants (15%) (Moya, Aldás and Kaparaju, 2018). Considering this framework, the CBHE could be employed to retrofit a dry-steam plant, by substituting the production well and eliminating the necessity of a reinjection well. It must be highlighted that the cycle configurations described above exploit geofluids, while the CBHE would constitute a mass transfer barrier from the reservoir to the cycle itself. A power cycle exploiting superheated vapour from a CBHE, hence, would have few analogies with the layouts describing beforehand. For the purpose of this thesis, the necessity of a reference cycle layout where to fit a CBHE geometry was solved by considering a simple dry-steam layout, deprived from the injection well, the steam treatment components and the control valves. Chapter 7 includes a preliminary analysis of a dry-steam like power cycle coupled with the CBHE geometry investigated in this thesis.
2.3.1 Dry-steam geothermal power plants
Geothermal dry-steam plants are installed in many locations worldwide, the two largest being the dry-steam reservoirs in Larderello, Italy, and in The Geysers, USA. These plants are referred as the most efficient among the high enthalpy layouts (DiPippo, 2016). This configuration exploits vapour-dominant mediums at high temperatures, directly feeding a condensation thermal cycle (Rankine) without regeneration, with the purpose of maximising the power extraction from steam. A typical plant layout is shown in Figure 2-4, and it is similar to the single-flash layout, with the cyclone-flash replaced by a particulate remover. The extracted vapour flows through a centrifugal separator which precipitates the solid particles contained in it (rock bits, dust). Therefore, the vapour is expanded in turbine until the condensation temperature, and the produced water is reinjected in the reservoir.
Figure 2-4 Dry-steam geothermal power plant process flow diagram (Moya, Aldás and
Kaparaju, 2018)
The condensation heat is rejected in the environment through direct contact (evaporation tower) or surface-type (shell and tube) units. About 70% of the geothermal capacity in Italy is concentrated in the Larderello geothermal field (Tuscany). The installed capacity in the field amounts to 600 MWel, spread in 22 dry-steam plant units. The rated power range for the single plants vary from 10 to 60 MWel. The most newly installed plants produce 20 MWel. The Geyser reservoir in California, in turn, is the largest reservoir exploited by dry-steam plants. It consists in 26 units with an installed capacity of 1477 MWel. The largest plants can generate up to 113 MWel (DiPippo, 2016).
2.4
Power generation applications for the CBHE
The closed loop concept, constituting the concept of the borehole heat exchanger, can be ideally applied, in deep geothermal applications, to access the opportunity of exploiting abandoned dry or hydrothermal reservoirs (Falcone et al., 2018). However, only a few of BHE have been successfully implemented across the world, not always with a positive outcome. Since 1994, a 2300 m deep CBHE is in operation in Weggis, Switzerland, for district heating and heat pump applications. The riser is vacuum-insulated and the bottom well temperature is 78 °C on average, allowing a production of 220 MWhth/y. A similar well is installed in Weissbad, Switzerland: with a depth of 1200 m the downhole temperature reached is 45 °C, again suitable only for heating
