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Historical development and current state-of-the-art
Feher (1967) has firstly revealed the versatility of Brayton cycle by proposing a cycle that operates over the critical point of the working fluid. In his opinion, the supercritical CO2 (SC-CO2) Brayton cycle has potential to overwhelm the Rankine steam cycle in similar conditions (high turbine inlet temperature and pressure). Meanwhile, Angelino (1969) performed an extensive review of various configurations of SC-CO2 Brayton cycles, which highlights the potential cycle efficiency improvement during the cycle configuration modification.
The dissertation of Dostal et al. (2004) is considered to be the first SC-CO2 industry feasibility investigation with integration of cycle efficiency enhancement and machinery sizing. Thanks to his study, the benefits of higher cycle efficiency and smaller turbomachinery components of SC-CO2 Brayton cycle are revealed and quantified. From then, worldwide studies focus on its fundamental aspects as well as technical limitations of the crucial components, such as turbomachinery and heat exchangers, see Table 1.3. Rather than roughly describing past work in the area of SC-CO2 power cycles, this dissertation organizes numerous studies in different categories.
The Table 1.3 lists various studies regarding different industrial applications. They are classified according to their investigation area and industrial application. Meanwhile, many of cited papers have been supported by the existing test facilities, detailed in Table 1.4. Notably, a scaled up test loop of 1 MWe has been under preparation with the SunShot initiative funding (DOE, 2015) in order to better assess existing technical risks in the industrial adoption.
Firstly, it can be concluded that this cycle has no discrimination on different application fields. SC-CO2 Brayton cycle can be integrated in nuclear, concentrate solar power (CSP) and fossil application, (see Tables 1.3 and 1.4). The main difference between these various applications is the diverse industrial constraints such as the heat source temperature, the cooling technology and its temperature. For example, in desert dry regions where water resource is highly limited, the dry air cooling is favorable, resulting in higher cooling temperature hence decreases the cycle efficiency. CSP application with tower/central receiver technology can reach maximum temperatures of 773 K-1273 K (Chacartegui et al., 2011; Ma and Turchi, 2011); while parabolic technology can only reach a inlet turbine temperature of 673 K-773 K (Singh et al., 2013a). An advanced Generation IV nuclear reactor (Dostal et al., 2004) can heat the inlet turbine temperature to 1153 K, whereas a medium temperature nuclear reactor (Jeong et al., 2011a) and sodium-cooled fast reactor (Moisseytsev and Sienicki, 2009) can reach reactor outlet temperature of 823-923 K. For pulverized coal-fired plant application carried byMecheri and Le Moullec (2015), SC-CO2 Brayon cycle has a maximum temperature of 893 K, which corresponds to the condition of actual advanced ultra supercritical steam (USC-steam) boiler technology. For an application of IGCC, the SC-CO2 leaving the boiler can theoretically achieve 1477 K and 30 MPa, (Weiland and White, 2018).
Motivation for integrating SC-CO2 Brayton cycle into pulverized coal-fired
Figure 1.6 shows a simplified process flowsheet of a current state-of-the-art pulverized coal-fired plant. It is composed of three main blocks: boiler, electricity generation and flue gas treatment blocks. The power cycle applied in the coal-fired plant is a Rankine cycle with a superheating (Hirn cycle) and reheating. Firstly, the pulverized coal is injected with preheated air in the boiler where the combustion takes place. The heat is then recovered by the water (steam) circulating in the boiler and transforms the steam to its supercritical phase. In the electricity generation block, the working fluid is feeding the turbines at different pressure level (HP/IP/LP turbines) in order to generate electricity (conversion of the mechanical rotating energy to electricity through the alternator). The last block, purification block, serves to denitrify, desulphurise and remove dust from the combustion flue gas before it is released to the atmosphere.
The current average cycle efficiency (cycle) of applied ultra-supercritical (USC) steam Rankine cycle is around 47%-pts, with steam parameters of 30 MPa/873 K/893 K. The condition of superheated steam is beyond its critical point (647 K and 22.1 MPa). It is recalled that in Table 1.1, the overall plant net efficiency within the lower heat value (LHV) consideration (LHV plant) of 45%-pts is listed. The difference is due to the consideration of the boiler efficiency in the overall plant efficiency. Along this dissertation, the boiler block is considered as a heat source, but its inside structure as well as the coal combustion are not considered in the power cycle study.
Under the context of growing energy demands and sustainable development, current studies on pulverized coal-fired plant focus on developing more efficient power plants. By considering a higher steam temperature (over 873 K), hence higher pressure, (Weitzel, 2011; LeMoullec, 2013a; Wang et al., 2014b; Long et al., 2017) a theoretical improvement of 5%-pts on cycle efficiency is foreseen. Relatively expensive materials (high-nickel alloys) are then necessary to be considered (Thimsen, 2014) in order to bear the steam at such extreme conditions. Meanwhile, Wang et al. (2014a) focus on the coal-fired plant retrofit in “Boiler block” and “Electricity generation block”. Cycle configuration/architecture improvement (i.e., Boiler block and Electricity generation block) is demonstrated to be another potential solution in efficiency enforcement.
Material and key component development
More experimental tests and numerical research are identified to leapfrog several technology gaps. For example, suitable materials for high-temperature and high pressure plant design are still under development and long-term material data of CO2 are also necessary considering the erosion phenomena in some component, (D. Hofer , 2016; Brun et al., 2017). The need in component development such as turbomachinery and heat exchangers is also highlighted by D. Hofer (2016): the technology gap in turbomachinery relies in the development of advanced seals and the transient management; while finding cost-effective heat exchangers (compromise between size, performance, pressure drops, costs) is identified as the key feature to support the industrialization of SC-CO2 Brayton cycle.
The aforementioned material and component development are important features for the future commercialization of SC-CO2 Brayton cycle. Nevertheless, this thesis does not intend to bring forward their state-of-the-art but rather applied current published studies as assumptions.
Other modifications of the Van der Waals EoS attractive term
Besides the previously introduced cubic EoS, some other important efforts have been proposed in the dedicated literature to the modification of EoS attractive terms. The Schmidt- Wenzel and the Patel-Teja EoS (Schmidt and Wenzel, 1980; Patel and Teja, 1982) have the same repulsive term as the Van der Waals EoS but different attractive terms. In fact, in the Schmidt- Wenzel EoS, universal parameters are replaced by parameters that depend on !. The Patel and Teja EoS involves a third parameter (noted c in Table 2.2). Both EoS have a component specific critical compressibility factor. Unfortunately, the predicted component specific critical compressibility factor deviates notably from the experimental critical compressibility factor. However, these modifications allow to have a better reproduction of the saturated liquid density on specific temperature ranges. For more details the reader is referred to their papers.
Equation of state expressed in terms of Helmholtz energy
Instead of considering generalized equations, adjustable (parameterizable) equations of state developed for CO2, especially those expressed in terms of Helmholtz energy are also reviewed in this report. In 1994, Pitzer and Sterner (1994) have developed an equation of state for pure CO2 involving 10 functional terms of residual Helmholtz energy and 28 adjustable coefficients. Another equation, the Span Wagner (SW) EoS, Span and Wagner (1996), is currently known as one of the most accurate equations of state available for pure CO2, (Kim, 2007;Mazzoccoli et al., 2014; Yu et al., 2015). In their equation, the residual Helmholtz energy involves 42 functional terms with 188 adjustable coefficients. Kim (2007) simplified the SW EoS by decreasing the number of functional terms to 30. Their improvement leads to a more accurate representation in the vicinity of the critical point but the model is less accurate than the SW EoS in the liquid and vapor phases.
Representation of the critical region
Equations of state (e.g., cubic and SAFT type) do not accurately represent all the state variables (properties) in the vicinity of the critical point with a similar accuracy. Since our study includes this region; this chapter intends to evaluate the capacity of various EoS to predict properties in the critical region. As a matter of fact, near the vapor-liquid critical point of a substance, some non-classical behaviors are observed. For example, the experimental shape of the critical isotherm in the (cv, P) (cp, P) planes and the variation of the isothermal compressibility factor are significantly different from predictions by classical cubic EoS, (Poling et al., 2001). From a molecular point of view, that is because the molecular correlations are much longer ranged and fluctuate differently in this region. However, the classical theory of critical region in most of the EoS corresponds to a mean-field approximation, which neglects the local inhomogeneity (fluctuations) in density.
To overcome this deficiency, considerable studies have been done to develop equations that bridge two regions, from the “classical” region (classical behavior that occurs sufficiently far away from the critical point) to the “non-classical” critical point region. One approach is to use the crossover functions developed by Sengers and coworkers (Tang and Sengers, 1991; Anisimov et al., 1992; Kiselev, 1998), which are only applicable in the vicinity of a critical point. Such functions consider the long-scale fluctuations in density near the critical region in order to link the two regimes. However, their original method does not cover all conditions, recent efforts have led crossover functions applicable to subcritical, supercritical and critical regions by considering crossover functions as patch functions.
In this case, the crossover function is extended into a larger application range and is applied to cubic EoS (ex: Peng-Robinson EoS, Patel-Teja EoS) or SAFT type EoS outside the vicinity of the critical point, (Kiselev, 1998; Lee et al., 2007; Sun et al., 2005; Behnejad et al., 2015; Hu et al., 2003). Results show that this approach yields better property profiles in the critical region in comparison with the original cubic or SAFT EoS.
Table of contents :
CHAPTER 1 – Introduction
1.1 Challenge in the energy sector
1.1.1 General context
1.1.2 The role of coal
1.2 Power cycle
1.2.1 Definition
1.2.2 Power cycle classifications
1.3 Supercritical CO2 Brayton cycle
1.3.1 Motivation for integrating SC-CO2 Brayton cycle into pulverized coal-fired plant
1.3.2 Technology improvement and this dissertation
CHAPTER 2 – Thermodynamic model choice for CO2
2.1 Equation of state
2.1.1 Cubic equation of state
2.1.2 Virial equation
2.1.3 Equation of state expressed in terms of Helmholtz energy
2.1.4 SAFT equation
2.1.5 Representation of the critical region
2.2 Discussions and Selection of EoS candidates
2.3 Methods
2.3.1 Selection of properties for the comparison
2.3.2 Comparison steps
2.4 Results and discussion
2.4.1 Critical density
2.4.2 MAPE investigation of six candidate EoS
2.4.3 Graphic representation of SW EoS in the entire region of interest
2.4.4 Comparison of the SW EoS with the unused experimental data sets
CHAPTER 3 -Modeling and design of recuperated SC-CO2 Brayton cycle.
3.1 Process description of a recuperated SC-CO2 Brayton cycle
3.2 SequentialModular Simulation
3.3 Methodology for the design of components
3.3.1 Estimation of the UA product in the recuperator R1
3.3.2 Turbomachineries
3.3.3 Sensitivity analysis
3.4 Results and discussions
3.4.1 Process simulation results : influence of the thermodynamic model choice on cycle efficiency and other cycle performance indices
3.4.2 Influence of the thermodynamic model choice on component design
3.4.3 Sensibility analysis
CHAPTER 4 – Superstructure optimization of SC-CO2 Brayton cycle
4.1 Process synthesis
4.2 Optimization-based process synthesis
4.3 Optimization-based process synthesis procedure
4.3.1 Modeling of the superstructure
4.3.2 General mathematical problem formulation
4.4 Results
4.4.1 Preliminary comparison of the feasible and the infeasible approach
4.4.2 Superstructure Optimization of SC-CO2 Brayton cycle
4.4.3 Result validation by six Non Linear Problem optimizations
4.4.4 Sensitivity analysis
CHAPTER 5 – Energy and economic optimization based synthesis: SC-CO2 Brayton cycle for coal-fired plant application
5.1 Superstructure in industrial conditions
Contents xv
5.2 Mono-objective superstructure optimization of SC-CO2 Brayton cycle
5.2.1 General mathematical problem formulation for energy mono-objective optimization
5.2.2 Results
5.2.3 Sensitivity analysis
5.3 Techno-economic analysis of SC-CO2 Brayton cycle
5.3.1 Economic Approach adopted by EDF R&D for SC-CO2 Brayton cycle
5.3.2 LCOE result of the two best energy optimization results
5.4 Multi-objective superstructure optimization of SC-CO2 Brayton cycle
5.4.1 General mathematical problem formulation for energy aspect optimization
5.4.2 Results and discussions
CHAPTER 6 – Conclusion and perspectives
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