2nd Law Analysis Research Articles

Advanced Cascaded Recompression Absorption System Equipped with Ejector and Vapor-Injection Enhanced Vapor Compression Refrigeration System: ANN based Multi-Objective Optimization

Although traditional compression absorption refrigeration cycle (CARC) addresses the respective limitations of the Absorption Refrigeration Cycle (ARC) and Vapor Compression Refrigeration (VCR) systems while harnessing their individual strengths. But this arrangement faces challenges related to power wastage, insufficient thermal energy absorption, and high compressor power requirements. To address these issues, in this study, an advanced RAC (Recompression Absorption System) is integrated with enhanced VCR incorporated with ejector to develop advanced proposed Ejector-Compression Recompression Absorption cycle (E-CRAC) and Ejector enhanced Vapor-Injection Compression Recompression Absorption Cycle (EI-CRAC). A computational model is developed in the Engineering Equation Solver (EES) employing energy, mass, and exergy conservation principles to conduct a thorough 1st and 2nd law analysis. An Artificial Neural Network (ANN) model, combined with a Genetic algorithm, enabled multi-objective optimization to pinpoint optimal operational conditions. The COP of the proposed systems is nearly three times higher than the traditional CARC system, showing an improved efficiency in cooling operations. Additionally, EI-CRAC and E-CRAC demonstrate near 10% and 20% COP enhancement, as well as 15% and 25% increase of Exergy efficiency over benchmark basic CRAC respectively. Furthermore, the research highlights the sensitivity of these systems to various operating conditions, such as pressure drop across ejector nozzle, evaporator temperature, condenser pressure, absorber temperature etc., emphasizing the need for precise control to maximize efficiency. The results of this detailed theoretical thermodynamic analysis with optimization provide a comprehensive understanding of the proposed systems while offering valuable insights for further scope of improvements.

System Design, Optimization and 2nd Law Analysis of a 100 MWe Double Reheat s-CO2 Power Plant at Full Load and Part Loads

Super-critical Carbon dioxide (s-CO2) power plants are considered to be efficient and environmentally friendly compared to the traditional Rankine cycle-based steam power plants and Brayton cycle-based gas turbine power plants. In this work, the system design of a coal-fired 100 MWe double reheat s-CO2 power plant is presented. The system is also optimized for efficiency with turbine inlet pressures and the recompression ratio as the variables. The components needed, mass flow rates of various streams and their pressures at various locations in the system have been established. The plant has been studied based on 1st and 2nd laws at full load and at part loads of 80%, 60% and 40%. Operating parameters such as mass flow rate, pressure and temperature have considerably changed in comparison to full load operation. It was also observed that the 1st law efficiency is 53.96%, 53.93%, 52.63% and 50% while the 2nd law efficiency is 51.88%, 51.86%, 50.61% and 48.1% at 100%, 80%, 60% and 40% loads, respectively. The power plant demonstrated good performance even at part loads, especially at 80% load, while the performance deteriorated at lower loads. At full load, the highest amount of exergy destruction is found in the main heater (36.6%) and re-heaters (23.2% and 19.6%) followed by the high-temperature recuperator (5.7%) and cooler (4.1%). Similar trends were observed for the part load operation. It has been found that the recompression ratio should be kept high (>0.5) at lower loads in order to match the performance at higher loads. Combustion and heat exchange due to finite temperature differences are the main causes of exergy destruction, followed by pressure drop.

Artificial intelligence approach for energy and entropy analyses of NiFe2O4/H2O nanofluid flow in a tube with vortex generator

The base purpose of the study is to examine the influence of vortex generator geometry and nanofluid on thermo-hydraulic and irreversibility behavior by using a numerical and predictable approach under a laminar flow regime. The selection of an original magnetic nanofluid, the handling of forced convection in a tube including a vortex generator with the artificial neural network approach, and the 2nd law analysis of thermodynamics reflect the novelty of the study. In this context, it was explored numerically for heat transfer and flow profiles of NiFe2O4/H2O flowing with 1% volume fraction in a tube with different vortex generator geometries. This study has been carried out with the solutions under constant heat flux conditions of 2000 W/m2 along the tube. The analyzes have been applied in the range of 500≤Re≤2000. The Laminar model and single-phase approach in all analyses have been taken into account. Heat convection coefficient, pressure drop, and entropy generation were analyzed for the smooth tube and tube with wave ratio (WR=h/w) of 2, 3, and 4. Levenberg-Marquardt as train algorithm and Learngdm and Tansig as transfer function was used as the MLP network model in the present study. As a result, The highest heat transfer ratio, pressure drop, frictional entropy, and total entropy values are obtained for the tube with a wave ratio of 2. The highest deviation rates between the predicted and numerical results for WT1 and WT2 cases (the supreme among all cases) have been seen as 4.67% and 1.73% for the heat convection coefficient and pressure drop values, respectively.

Experimental study and analysis of a novel layered packed-bed for thermal energy storage applications: A proof of concept

This paper presents a study carried out as part of commissioning and testing of world’s first grid-scale 150 kWe Pumped Heat Energy Storage (PHES) demonstration system. The system employs two novel layered packed-bed thermal stores. The present study experimentally investigates one of the stores designated as “hot thermal store”, which has an energy storage density of 1072 MJ/m3 and stores heat at 500 °C and 12 bar. The layered store is an enhancement of a normal packed-bed store and offers a higher degree of thermal stratification. Experiments show that layering results in about 64 % reduction in pressure loss along with yielding considerably narrower thermocline. Round-trip efficiency, storage capacity and utilisation were calculated based on 1st Law analysis considering both simple and layered mode operation at nominal design conditions. Two cycle control scenarios were considered: time-based and temperature-based. In the time-based scenario, the store shows nearly similar performance in both modes. However, in temperature-based scenario, layered mode outperforms. During cyclic operation, layered mode outperforms as it reaches steady-state in merely 3rd cycle, without any loss in efficiency, capacity and utilisation; simple mode yields competitive efficiency but capacity and utilisation deteriorate after each successive cycle and steady-state is achieved in 20th cycle. 2nd Law analysis was additionally performed to gain insight into various losses and their impact on the performance.

Conceptual design and performance evaluation of a novel cryogenic integrated process for extraction of neon and production of liquid hydrogen

Novel integration of a hydrogen liquefaction process and cryogenic rectification of air is presented. The thermodynamics analysis including the 2nd Law and sensitivity analysis regarding this process are conducted. The proposed cryogenic process can produce 111.3 kg/s of nitrogen and 42 kg/s of oxygen with argon. In addition, this process produces more than 132 × 103 tons of liquid hydrogen and 751 tons of crude neon per year. Moreover, as the number of the used compressor is very fewer than of the conventional process, the required power consumption of the proposed cryogenic plant is almost low. Based on the exergy analysis, using expanders, providing the requested refrigeration condition by solar heat exchangers and proper streams, and integrating two processes with the similar operating condition, the exergetic efficiency of the cycle is more than 70 %. The sensitivity analysis of operating parameters such as pressure, temperature, reflux ratio, and the number of stages of column presents their the importance of them on the recovered neon, oxygen, and nitrogen. Moreover, the production of cryogenic liquids is more sensitive to operating pressure and temperature than the reflux ratio and the number of stages.

Thermodynamic limits of atmospheric water harvesting

We use 2nd law analysis to obtain the maximum and practical efficiency for common open system atmospheric water harvesting methods. We apply this metric with supercomputing to map performance globally and suggest key system variables for improvement.

Numerical Investigation of a modified Kalina cycle system for high-temperature application and genetic algorithm based optimization of the multi-phase expander's inlet condition

As an alternative to the conventional steam Rankine Cycle, Kalina Cycle has witnessed a growing interest over the past years for high-temperature applications (A working fluid temperature of 500°C at the turbine inlet). However, the possibility of implementing an additional multi-phase expander on the weak ammonia-water solution loop of the Kalina cycle was hardly analyzed in the available literatures. In this research, two novel Kalina cycles (Kalina cycle-12A and Kalina cycle-12B) have been presented by integrating a multi-phase expander in addition to the turbine installed downstream of the Kalina evaporator. For Kalina cycle -12A, this additional multi-phase expander is positioned downstream of the Kalina separator and on the weak ammonia-water solution loop for Kalina Cycle-12B. A detailed mathematical model based on the thermodynamic laws has been developed to solve and optimize the Kalina Cycles. The influence of critical decision parameters, specifically the ammonia concentration on working fluid and evaporation pressure, were investigated. The optimization was performed based on the objective to maximize the net power output from the multi-phase expander under steady-state operating conditions. When the performance of the proposed Kalina cycles was compared with the conventional Kalina Cycle-12, both of them demonstrated superior performance, i.e., net power output and peak thermal efficiency increased by a maximum value of 3.23% for the proposed Kalina Cycle-12A cycle and 3.94% for the proposed Kalina Cycle-12B cycle. In terms of second law efficiency, Kalina Cycle-12A is 3.68 percent more efficient than Kalina Cycle-12, while Kalina Cycle-12B is 4.04 percent more efficient. Furthermore, 2nd law analysis also reveals, maximum destruction of exergy occurs at the condensers of the cycles.

On small-scale liquefaction of natural gas with supersonic separator: Energy and second law analyses

Under certain conditions supersonic separators promote superior natural gas conditioning over traditional routes. An instigating possibility consists in using supersonic separators to obtain liquefied natural gas that exhibits global growth. This work analyses natural gas liquefaction through a low-scale process using realistic non-isentropic supersonic separator whose design was proposed in the literature. Results are compared with other compact adiabatic expansion routes like the Joule-Thomson and turbo-expander, all starting from natural gas at (298.15 K, 80 bar) and reaching saturated liquefied natural gas at (115.4 K, 1.25 bar). The objective was to demystify the notion that 100% liquefaction per pass is possible with supersonic separator by obtaining the maximum liquefaction fraction per pass for the three compact routes and unveiling whether supersonic separators lead to a less power intense, technically, thermodynamically and economically superior short-scale liquefaction process. To this end, a HYSYS Unit Operation Extension was created to simulate supersonic separators with rigid-geometry, following expected physical behavior and satisfying the 2nd Law of Thermodynamics. Results include a 2nd Law analysis of processes leading to thermodynamic efficiency and liquefaction lost work. Supersonic separator route reached the highest Net Present Value of all routes but was somewhat outperformed by turbo-expander route in terms of power consumption, thermodynamic efficiency and lost power.

Vaporization and caloric studies on yellow lead oxide PbO

The vaporization of pure yellow PbO(c) to provide reference data for lead titanate and other lead oxide containing compounds was investigated at temperatures of 810–1040 K. Thermodynamic quantities of sublimation and reaction enthalpies, and entropy were derived from the partial pressures of gaseous Pb, PbO, and O2 over pure yellow lead oxide. The experimental sublimation enthalpy of Pb from PbO(c) was ΔsubH930K0(Pb)=(206±5)kJmol−1, ΔsubH298K0(Pb)=(215±5)kJmol−1 and for PbO was ΔsubH930K0=(223±3)kJmol−1, ΔsubH298K0=(236±3)kJmol−1. The enthalpy, entropy and Gibbs energy of the following reactions were determined by 2nd and 3rd law analysis at T = 930 K:TableΔrHT0 kJ mol−1ΔrST0J mol−1 K−1ΔrGT0 kJ mol−1PbO(c) = PbO(g)223 ± 395 ± 1137 ± 4PbO(c) = Pb(g) + 0.5O2(g)312 ± 6136 ± 1186 ± 5PbO(g) = Pb(g) + 0.5O2(g)86 ± 240 ± 150 ± 2Data base dependent adaptation to 298 K are given in the tables below. Heat capacity measurements under constant pressure (Cp(T)0) by Dynamic Scanning Calorimetry (DSC) in the temperature range 298–1100 K resulted in two complex polynomial equations (see tables). The Cp(T)0 values increased to a maximum at T = about 750 K from (47.6–50.12) J mol−1 K−1 and decreases to 48.4 at the phase transition of Tc = 1006 K. Beyond the transition, Cp(T)0 becomes linear and nearly constant with ≅ 48.5 J mol−1 K−1 at 1100 K. Even the low values of entropy, ∆trsST0 = (0.045 ± 0.001) J mol−1 K−1 and enthalpy, ∆trsHT0 = (0.045 ± 0.002) kJ mol−1, and the peak shape of the phase change in the Cp(T)0 function suggest that the transition can be classified as a first order one. This phase transition was not published so far. The enthalpy and the entropy values were calculated from the Cp(T)0 polynomials and from the vaporization studies.

Thermoeconomic analysis of a hybrid PVT solar system integrated with double effect absorption chiller for cooling/hydrogen production

A novel solar-based combined system which is consisting of a concentrated PV, a double effect LiBr-H2O absorption chiller, and a Proton Exchange Membrane (PEM) is proposed for hydrogen production. A portion of the received energy is recovered to run a double effect absorption chiller and the rest is turned into electricity, being consumed in the PEM electrolyzer for hydrogen production. The thermodynamic and thermoeconomic analyses are performed to understand the system performance. A parametric study which is implementing Engineering Equation Solver (EES) is carried out to assess the influence of main decision parameters on the overall exergy efficiency and total product unit cost. The 2nd law analysis shows that PVT with exergy destruction rate of 76.9% of total destruction rate is the major source of irreversibility. Furthermore, in the cooling system, Cooling Set (CS) has the highest exergy destruction rate due to the dissipative components. Exergoeconomic results demonstrate that in cooling set with the lowest value of exergoeconomic factor, the cost of exergy destruction and loss has the major effect on the overall cost rate. Furthermore, results of the parametric study indicate that by decreasing PV cell’s temperature from 100 °C to 160 °C, the total product unit cost is decreased by about 1.94 $/GJ.

Proposed 2nd Law of Thermodynamics: An assertive statement

Generally, the 2nd Law is stated in negative, passive terms, in a way that says what cannot happen, or what the best possible outcome could be, or what is an inevitable (e.g., inopportune) consequence. Granted, there has been productive usage of the exergy concept, to do ‘2nd Law Analysis’. Granted, there are statements saying that a consequence of every process is the generation of entropy. And there have been many efforts aiming to use an entropy statement to do ‘2nd Law Modeling’ – to predict the path of processes. While there have been specific successes, there are issues. For example, in some instances a success depends upon an extremization that maximizes the entropy generation (or the rate thereof), while in other instances, minimization. Though there may be criteria for determining whether maximization or minimization is appropriate in a particular application, the need for such a criterion points out a weakness. Proposed here is this: Every process is a consequence of a cause, and to assertively predict the path of a process is to determine consequences of a cause. Entropy production is not a cause but only a consequence. The 2nd Law statement to be proposed herein employs a common measure of cause, namely Gibbs' available energy, and how the expenditure of that cause ensues in a process. Therein lies an underlying principle for modeling the process path (whether macro, nano, bio or micro).Three rudimentary examples of the application of this ‘2nd Law principle’ for modeling processes are presented in this paper; one for a transient ‘heat transfer’ process, one for a ‘mechanical’ process, and a third for a combined thermal and pneumatic process. It is shown how available energy provides a key to modeling processes of different ‘types’ – heat transfer, mechanics, pneumatics. Heretofore each type required distinct ‘principles’ (and courses of study). To show the authenticity of the results obtained with this ‘2nd Law modeling’, they are compared with results obtained with the ‘traditional’ models.

2nd law analysis of Portuguese municipal solid waste gasification using CO2/air mixtures

Urbanization, mainly caused by population growth and industrialization, is causing serious environmental problems. Municipal solid waste (MSW) is one of the major challenges facing the world today. In Portugal the growing volume of MSW has become a central problem for municipalities, due to lack of space and the high costs to solve it. Gasification is starting to be considered as a possible alternative when dealing with municipal wastes. However, first is necessary to overcome some concerns related to the process, such as tar mitigation and carbon dioxide emissions.The presented study focuses on a second law analysis conducted on Portuguese MSW gasification using carbon dioxide and air mixtures. To do so, a previously developed numerical model, validated using data from a semi-industrial plant, was used to assess carbon dioxide injection. First, influence of operational conditions on syngas exergy values was studied. Exergy values increased close to 6% when equivalent rate was increased from 0.15 to 0.25, steadily dropping with further increase. On the other hand, exergy values appear to steadily increase with carbon dioxide addition (14% when increased from 0 to 1) and reactor temperature (40% when increased from 700 to 900°C).Then, the influence of temperature and CO2/MSW ratio on exergy efficiency, tar efficiency and carbon dioxide conversion was investigated. Results showed that both parameters have a positive effect on exergy efficiency. Conversely, CO2/MSW ratio and gasification temperature lead to decreases in both tar exergy efficiency and in carbon dioxide.

Potential of Exergy Efficiency Improvement of Coal Power Plants in Sri Lanka: a Case Study

In the context of energy utilization it is required to harvest maximum possible potential from the available energy sources. Therefore analysis, monitoring and optimization of available energysources and in particular those related to power plants are major requirement in the sector. Generally the energy performances of power plant are evaluated using criteria based on 1st law of thermodynamics. However, subsequent development in the field of thermodynamic studies in particular the exergy analysis was identified as a useful method to design, evaluation, optimization and improvement of power plant performance. It is based on 2nd law of thermodynamics. In this study, it is aimed to find out the potential of exergy efficiency improvement opportunities in coal power plants through exergy flow analysis. A methodology was developed to estimate exergy flows in coal power plants and efficiencies of major equipment in power plant employing 2nd law or exergy analysis. This was done according to general equations which are used in thermodynamics. As a result, set of equations pertaining to the thermodynamics behaviours was established to analyse exergy flows in coal power plants. The methodology was then applied to unit 01 of Lak Vijaya power station (LVPS) in Sri Lanka as a case study. In the process, thermodynamic properties of water-steam cycle of LVPS unit 01 under both design and actual calculation were used to evaluate exergy values of critical states of the cycle as well as the resulting exergy flows and related efficiencies of major equipment. Boiler was identified as the major exergy destruction equipment in power plant and consequently it has less exergy efficiency. Hence boiler sub system was analysed to identify potential of exergy efficiency improvement in coal power plants. The main parameters of boiler were used to identify the exergy flow behaviours of the boiler. An economic analysis was also done for the boiler to identify the benefits. Not only steam generating cost saving in power plant but also reduction of hazardous CO2 emission calculations were carried out.

Panel I: Connecting 2nd Law Analysis with Economics, Ecology and Energy Policy

The present paper is a review of several papers from the Proceedings of the Joint European Thermodynamics Conference, held in Brescia, Italy, 1–5 July 2013, namely papers introduced by their authors at Panel I of the conference. Panel I was devoted to applications of the Second Law of Thermodynamics to social issues—economics, ecology, sustainability, and energy policy. The concept called Available Energy which goes back to mid-nineteenth century work of Kelvin, Rankine, Maxwell and Gibbs, is relevant to all of the papers. Various names have been applied to the concept when interactions between the system of interest and an environment are involved. Today, the name exergy is generally accepted. The scope of the papers being reviewed is wide and they complement one another well.

Thermodynamic assessment of active cooling/heating methods for lithium-ion batteries of electric vehicles in extreme conditions

The battery cooling/heating with active methods is required for EVs (electric vehicles) in the extreme temperature conditions. This work presents a new active battery cooling/heating method based on PCS (phase change slurry) cycle. Two typical often used active cooling/heating methods so-called the direct cabin air blow and refrigerant circulation are also illustrated in detail. The thermodynamic assessment is conducted on these battery active cooling/heating methods with both of 1st Law and 2nd Law analysis. The variations of extra thermal load to the vehicle air-conditioning system are investigated as changes of ambient temperature, humidity and thermal load for the direct cabin air blow method. The simulation results show that the direct cabin air blow method causes more extra thermal load to the air-conditioning system without considering the cabin ventilation effect. The PCS cycle method performs higher exergy efficiency than that of using refrigerant circulation method.

Novel two-step thermochemical cycle for hydrogen production from water using germanium oxide: KIER 4 thermochemical cycle

Abstract This paper proposes a novel two-step thermochemical cycle for hydrogen production from water using germanium oxide. The thermochemical cycle is herein referred to as KIER 4. KIER 4 consists of two reaction steps: the first is the decomposition of GeO2 to GeO at approximately 1400–1800 °C, the second is hydrogen production by hydrolysis of GeO below 700 °C. A 2nd-law analysis was performed on the KIER 4 cycle and a maximum exergy conversion efficiency was estimated at 34.6%. Thermodynamic analysis of GeO2 decomposition and hydrolysis of GeO confirmed the possibility of this cycle. To demonstrate the cycle, the thermal reduction of GeO2 was performed in a TGA with mass-spectroscopy. Results suggest GeO2 decomposition and oxygen gas evolution. To confirm the thermal decomposition of GeO2, the effluent from GeO2 decomposition was quenched, filtered and analyzed. SEM analysis revealed the formation of nano-sized particles. XRD analysis for the condensed-filtered particles showed the presence of Ge and GeO2 phases. The result can be explained by thermodynamic instability of GeO. It is believed that GeO gas disproportionates to ½Ge and ½GeO2 during quenching. 224 ml hydrogen gas per gram of reduced GeO2 was produced from the hydrolysis reaction.

Performance Evaluation of an Oxy-coal-fired Power Plant

Power generation systems based on the oxy-coal combustion with carbon dioxide capture and storage (CCS) capability are being proposed and discussed lately. The proposed systems are evolving and various alternatives are to be comparatively evaluated. This paper presents a proposed approach for performance evaluation of a commercial scale power plant, which is currently being considered for ‘retrofitting’ for the demonstration of the concept. System components to be included in the discussion are listed. Evaluation criteria in terms of performance and economics are summarized based on the system heat and mass balance and simple performance parameters such as the fuel to power efficiency and brief introduction of the 2nd law analysis. Cases are selected for comparative evaluation, based on the site-specific requirements. With limited information available, preliminary evaluation is attempted for the cases.

Solar hydrogen production via a two-step water-splitting thermochemical cycle based on Zn/ZnO redox reactions

The production of hydrogen from water using solar energy via a two-step thermochemical cycle is considered. The first, endothermic step is the thermal dissociation of ZnO(s) into Zn(g) and O 2 at 2300 K using concentrated solar energy as the source of process heat. The second, non-solar, exothermic step is the hydrolysis of Zn(l) at 700 K to form H 2 and ZnO(s); the latter separates naturally and is recycled to the first step. Hydrogen and oxygen are derived in different steps, thereby eliminating the need for high-temperature gas separation. A 2nd-law analysis performed on the closed cyclic process indicates a maximum exergy conversion efficiency of 29% (ratio of ΔG 298 K °| H 2+0.5 O 2→ H 2 O for the H 2 produced to the solar power input), when using a solar cavity-receiver operated at 2300 K and subjected to a solar flux concentration ratio of 5000. The major sources of irreversibility are associated with the re-radiation losses from the solar reactor and the quenching of Zn(g) and O 2 to avoid their recombination. An economic assessment for a large-scale chemical plant, having a solar thermal power input into the solar reactor of 90 MW and a hydrogen production output from the hydrolyser of 61 million-kWh/yr, indicates that the cost of solar hydrogen ranges between 0.13 and 0.15$/kWh (based on its low heating value and a heliostat field cost at 100–150$/m 2) and, thus, might be competitive vis-à-vis other renewables-based routes such as electrolysis of water using solar-generated electricity. The economic feasibility of the proposed solar process is strongly dependent on the development of an effective Zn/O 2 separation technique (either by quench or by in situ electrolytic separation) that eliminates the need for an inert gas. The chemical aspects of the reactions involved and the present status of the pertinent chemical reactor technology are summarized.

The solar thermal decarbonization of natural gas

The endothermic decomposition of natural gas into a carbon-rich condensed phase and a hydrogen-rich gas phase, using concentrated solar energy as the source of high-temperature process heat, is considered as a model reaction for conducting a 2nd-law analysis of a solar decarbonization process in which carbon is removed from fossil fuels prior to their use for power generation. The theoretical maximum closed-cycle exergy efficiency, defined as the ratio of the Gibbs free energy change of the reaction to the solar power input, can be as high as 35% for a black-body solar cavity-receiver/reactor operating at 1500 K and under a mean solar flux concentration ratio of 1000, and decreases to 21% if the products exiting the solar reactor are quenched without recovering their sensible heat. Four technically viable routes are examined for extracting power from the chemical products of the solar decomposition of CH 4: (1) carbon is sequestered and only H 2 is used in a fuel cell; (2) carbon is used to fuel a conventional Rankine cycle and H 2 is used in a fuel cell; (3) carbon is steam-gasified to syngas in a solar gasification process and the syngas further processed to H 2, which, together with H 2 from the CH 4-decomposition reaction, is used in a fuel cell; and (4) carbon serves as a reducing agent of ZnO in a solar carbothermic process for producing Zn and CO that are further converted via water-splitting and water-shifting reactions to H 2 for use in a fuel cell. The open-cycle energy efficiency, defined as the ratio of electric power output to the thermal energy input (solar + heating value of reactants), exceeds 65% for the 3rd and 4th power generation routes. Both of these routes offer a net gain of 40% in the electrical output and, consequently, an equal percent reduction in the corresponding specific CO 2 emissions, vis-à-vis the direct use of CH 4 for fueling a 55%-efficient combined Brayton–Rankine cycle. For route nr. 1, the energy penalty for avoiding CO 2 emissions amounts to 30% of the electrical output. Nomenclature C mean solar flux concentration ratio (dimensionless) EGF ratio of the electric output of the process to that obtained when using same amount of CH 4 to fuel a 55%-efficient combined Brayton–Rankine cycle HHV high heating value ( kJ mol −1) I normal beam insolation ( kW m −2) Irr heat exchanger irreversibility associated with heat exchanger ( kW K −1) Irr quench irreversibility associated with quenching ( kW K −1) Irr reactor irreversibility associated with solar reactor ( kW K −1) LHV low heating value ( kJ mol −1) ṅ molar flow-rate ( mol s −1) p pressure (bar) Q heat exchanger heat transferred by heat exchanger (kW) Q FC heat rejected to the surroundings by fuel cell (kW) Q HE heat rejected to the surroundings by heat engine (kW) Q quench heat rejected to the surroundings by quenching (kW) Q reactor, net net power absorbed by solar reactor (kW) Q reradiation power re-radiated through reactor's aperture (kW) Q solar solar power input through reactor's aperture (kW) W FC work output by fuel cell (kW) W HE work output by heat engine (kW) ΔG Gibbs free energy change ( kJ mol −1) ΔH enthalpy change ( kJ mol −1) ΔS entropy change ( kJ mol −1 K −1) η absorption solar energy absorption efficiency η Carnot efficiency of a Carnot heat engine operating between T H and T L η heat exchanger heat recovery factor by heat exchanger η HE efficiency of heat engine η exergy, max maximum exergy efficiency of an ideal system η exergy, Closed − Cycle exergy efficiency of closed-cycle system η exergy, Open − Cycle exergy efficiency of open-cycle system σ Stefan–Boltzmann constant (5.6705×10 −8 W m −2 K −4)