Development of a code for the design and optimisation of Organic Rankine Cycles for power generation

i Equation Chapter 1 Section 1 Proyecto Fin de Máster Ingeniería Industrial Development of a code for the design and optimization of Organic Rankine Cycles for power generation Dpto. Ingeniería Energética Escuela Técnica Superior de Ingeniería Universidad de Sevilla Autor: Jaime Víctor Hernández Campo Tutor: David Tomás Sánchez Martínez Co-tutor: Francesco Crespi Sevilla, 2020 iii Proyecto Fin de Máster Ingeniería Industrial Development of a code for the design and optimization of Organic Rankine Cycles for power generation Autor: Jaime Víctor Hernández Campo Tutor: David Tomás Sánchez Martínez Co-tutor: Francesco Crespi Dpto. de Ingeneiría Energética Área de máquinas y motores térmicos Escuela Técnica Superior de Ingeniería Universidad de Sevilla Sevilla, 2020 v Proyecto Fin de Máster: Development of a code for the design and optimization of Organic Rankine Cycles for power generation Autor: Jaime Víctor Hernández Campo Tutor: Co-tutor: David Tomás Sánchez Martínez Francesco Crespi El tribunal nombrado para juzgar el Proyecto arriba indicado, compuesto por los siguientes miembros: Presidente: Vocales: Secretario: Acuerdan otorgarle la calificación de: Sevilla, 2020 El Secretario del Tribunal vii Agradecimientos En el terreno personal, un agradecimiento inconmensurable a mis padres Francisco Manuel Hernández Aja y María Esperanza Campo Font, cuyo apoyo ha sido y continúa siendo fundamental en cada paso. Sin olvidar jamás a los amigos que he hecho en el camino, a través de los cuales he crecido. En lo académico, el correspondiente al Dr. David Sánchez por brindarme el brillante privilegio de realizar este singular trabajo en un entorno incomparable como es el grupo de investigación del CREALab del Politecnico de Milán. En el cual encontré enormes ayudas personificadas en el profesor Alberto Guardone y su alumna de doctorado, Camilla Conti. Así como a Francesco Crespi, por su soporte técnico y dedicación en la materialización de este documento. Las contribuciones de cada una de estas personas han sido cruciales para lograr este objetivo. A mi tierra, a mis orígenes Jaime Víctor Hernández Campo Sevilla, 2020 ix Abstract The aim of the present work is the parametric optimization of Organic Rankine Cycles (ORC) for its main application to medium-low temperature generic sources. For this purpose, a Matlab® [1] computational code has been developed, in which design parameters, mass flow ratios, cycle configuration and fluid selection (including mixtures) are simultaneously optimized to offer the best combination of variables for the maximization of the efficiency. Given its extraordinary reliability the reference thermodynamic database of the choice has been REFPROP® [2] v.9.1. The results accomplished por pure fluid configurations show great adaptability to previous validated optimization studies. Whereas, those for mixtures support the theoretical evidence that there is a significant efficiency growth to be accomplished when combining organic pure fluids into binary zeotropic mixtures. The main improvements of the present work with respect to previous ORC optimization studies are, in one hand the emphasis on looking for the most suitable mathematical method for optimization of variables, previous works lack more exhaustive considerations when choosing the theoretical nature of algorithm, for this purpose multiple algorithms had been put to test running the same model, concluding that heuristic and stochastic algorithms provide more accurate results in the job of converging to global optimal. In the other hand, regarding the specifics of ORC optimization, the goal of this work is to first develop a reliable computational tool for the analysis and optimization of ORC and then verificate it in orther to expand its performance to include the analysis of binary zeotropic mixtures, which is the ultimate objective of this study. It is a fact that the actual global situation calls for renewable and robust solutions for the energy production, these being one of the main reasons why there is a susbstantional increase of industries interest regarding the ORC technology. Aiming to represent a humble contribution to the promising future, this work pretends to create an enlighting tool for the study of different ORC configurations and potential scenarios in the upcoming energy production world. xvii Notation T Temperature (ºC) p Pressure (bar) h Enthalpy (KJ / Kg) s Entropy (KJ / Kg K) Δ𝑇𝑝𝑝,𝑃𝐻𝐸 Pinch point temperature difference at primary heat exchanger Δ𝑇𝑝𝑝,𝑟𝑒𝑐 Pinch point temperature difference at recuperator Δ𝑇𝑎𝑝,𝑐𝑜𝑛𝑑 Approach temperature difference at condenser outlet Δ𝑇𝑎𝑝,𝑐𝑜𝑛𝑑 ∗ Approach temperature difference at condenser inlet Δ𝑇𝑠𝑐,𝑐𝑜𝑛𝑑 Subooling temperature diference in condenser Δ𝑇𝑠𝑐,𝑒𝑣𝑎𝑝 Subooling temperature diference in evaporator 𝜂𝑖𝑠,𝑡𝑢𝑟𝑏 Isentropic turbine efficiency 𝜂𝑖𝑠,𝑝𝑢𝑚𝑝 Isentropic pump efficiency 𝜂𝑚𝑒𝑐−𝑒𝑙𝑒𝑐,𝑡𝑢𝑟𝑏 Electromechanic turbine efficiency 𝜂𝑚𝑒𝑐−𝑒𝑙𝑒𝑐,𝑝𝑢𝑚𝑝 Electromechanic pump efficiency 𝜂𝑔𝑒𝑎𝑟 𝑏𝑜𝑥 Gear box efficiency 𝑣𝑞𝑚𝑖𝑛 Min vapor quality 𝑃𝑖𝑛,𝑡𝑢𝑟𝑏 Inlet turbine pressure ∆𝑇𝑎𝑝,𝑃𝐻𝐸 Approach temperature difference at PHE ∆𝑇𝑝𝑝,𝑃𝐻𝐸 ∆𝑇𝑎𝑝,𝑐𝑜𝑛𝑑 Pinch point temperature difference at PHE Approach temperature difference at condenser ∆𝑇𝑝𝑝,𝑐𝑜𝑛𝑑 ∗ Modified pinch point difference at condenser ∆𝑇𝑝𝑝,𝑟𝑒𝑐 Pinch point difference at recuperator 𝑊𝑛𝑒𝑡 󰇗 Net work output 𝑄𝑖𝑛 󰇗 Net heat introduced 𝜂𝑐𝑦𝑐𝑙𝑒 Cycle efficiency 𝜀𝑟𝑒𝑐 Recuperator effectivity 𝜂𝑝𝑙𝑎𝑛𝑡 Plant efficiency 𝜂𝑙𝑜𝑟𝑒𝑛𝑡𝑧 𝜂𝐼𝐼 𝑚𝐻𝑆−𝑊𝐹 󰇗 𝑚𝑊𝐹−𝐶𝑆 󰇗 𝑃𝑖 PHE 𝑇𝑎𝑚𝑏 T𝑙𝑖𝑚𝑖𝑡 𝑇𝑟𝑒𝑖𝑛𝑗𝑒𝑐𝑡𝑖𝑜𝑛 𝑙𝑖𝑚𝑖𝑡 𝜎 Lorentz efficiency Second law efficiency Mass flow ratio of hot source fluid to working fluid Mass flow ratio of working fluid to cold fluid Cycle point i Primary Heat Exchanger Ambient temperature Limit temperature fro REFPROP accuracy Reinjection limit temperature Standard deviation xix Introduction Over the last recent years, the attention on ORC technology has been constantly growing, this can be explained by the multiple interests gathering around this field that makes it extremely convenient for the energy sector. In one hand there is the global concern on reducing the consumption of fossil fuels as well as the emissions of several contaminating gases (carbon dioxide, green house and pollutants mainly) that are permanently contributing to the severely damaged environment. Attending this issue, ORC systems contribute by making use of renewable heat sources as solar [3-5], geothermal [6-8], biomass [9] and waste heat recovery from combustion engines [11-14]. Although the latest application is not directly renewable, the use of ORCs has proven to efficiently recover a large amount of the profitable wasted heat generated from power production industry (50- 60% of waste heat) thus making a substantial contribution to reduce the fossil fuel consumption of primary engines as well as diminishing the damage of emissions by lowering the temperature of exhaust gases. Even though steam cycles will probably persist as the most competitive technology for high temperature heat sources, it occurs that when sources are below the 150-170°C range (typical of most common renewable sources) water should be throttled to such low pressures that a very poor thermodynamic efficiency results, thus its performance at low-grade sources has no comparison to ORCs, which presents significant number of preferable reasons: • Remarkably better cycle and heat recovery efficiencies due to a much favorable thermodynamic cycle shape, even with simple layouts. • Low turbine mechanical stress due to low peripheral speed leading to low turbine RPM that allow the direct drive of the electric generator without gear reduction. • No erosion of blades thanks to the absence of moisture in the vapor nozzles (dry expansion). • Excellent partial load behavior, been able to variate flow and temperature conditions while maintaining 90% of cycle efficiency at 50% load. • Reduced volume flow rates with low enthalpy drops in the expander, allowing for higher isentropic efficiencies, reduced size designs and more competitive manufacturing costs Moreover, given the extraordinary adaptability of ORC and the increasing restrictions on working fluids, they are also suitable due to its capability to constrain the design for the use of fluids with low GWP, ODP and high security standards while still performing competitive efficiencies. On the other hand, there are various economic advantages that are closely related to the previous reasons to justify the potential of ORCs, the most important is the reduced costs of the heat source and its maintenance, either if it comes from geothermal brines, waste heat recovery (WHR) or practically any renewable field, this since the nature of organic fluids brings the opportunity of exploiting low-medium heat sources ranging a wide set of temperatures (50 – 350°C) which is commonly the spectrum for most of the cases, in consequence the heat source of the cycle is available at a low cost either in a naturally renewable way or taking advantage of industries waste. In addition, a lot of financial incentives are arising coming from both private and public initiatives which make the exploitation even more competitive and attractive for its investment and rapid development. For all these reasonings ORC technology has proven to be one of the most promising technologies to convert medium-low grade heat into power [15 -17]. This study pretends to approach the parametric optimization of ORC focusing on the best attainable combination of thermodynamic performance and fluid selection to conclude which are the best design variables at each potential scenario. xxi 1 1 REVIEW OF THE STATE OF THE ART OF OPTIMIZATION PROCESSES his optimization review intends to be and over all view of the history in ORC optimization along with the parallel evolution of organic fluids in this technology. 2.1. Origins Even though the principles of ORC are well known since the 60’s decade, where the first binary cycle was built in 1967 in Kamchatka (operated with CFC-12), it has not been until the early 90’s that the optimization of this technology started to take relevance in the power generation community, with a special focus on the fluid selection. This mainly due to the need of improving plant efficiencies and the increasing restrictions arising from the Montreal Protocol, Vienna, 1987 [19] which banned the production and usage of CFCs (and later HCFCs) as a consequence of the study made by Chemistry Novel prices Mario Molina and Frank Sherwood Rowland (1995) about the ozone depletion reasons. This along with the improvements in the component technology (heat exchangers, expander, pump) and the growing complexity of fluids, boosted ORC as one of the most promising technologies to reduce contamination and exploit medium-low grade sources. 2.2. State of the art Given the exponential growth of ORC technology over the last decades and the wide number of different approaches written about its optimization, it seems imperative to collect a chronological review of the start of the art for ORC optimization to get a deep understanding of which are the present and future needs of the field. Regarding the initial approaches to ORC optimization, it is important to notice that, although the technology can cover a wide range of renewable applications (i.e. biomass, solar, ocean thermal and more) most of the commercial applications and hence the research efforts are focusing on two main branches, geothermal heat sources and waste heat recovery (WHR). Invernizzi et al. [20] pointed the preference of HFCs (hydrofluorocarbons) as the auspicious R245fa or n-Pentane, over traditional CFCs (chlorofluorocarbons) and HCFCs (hydrochlorofluorocarbons) in the optimization of a geothermal brine (100 – 300°C) with the plant exergy efficiency as objective function and evaporation pressure as variable. Constraining the cycle to be subcritical, the results showed the existence of optimal temperature ranges for each fluid and the convenience of choosing fluids with a critic temperature above the heat source temperature. Hettiarachchi et al. [21] followed the path of geothermal heat sources optimizing the ratio of total heat transfer area to total net power with the Powell Method [22] (gradient descendent algorithm) and compared the results among a set of three different fluids, Ammonia, R123, n-Pentane and PF5050. The best scenario for lowtemperature geothermal brine was a plant efficiency of 8.0 % for an evaporating pressure of 38.7 bar and Ammonia as working fluid. T Review of the state of the art of Optimization processes 2 Wei et al. [23] considered the optimization of HFC-245fa (1,1,1,3,3-pentafluoropropane) only, for its application to WHR and studied the ORC reactions to disturbances in the design parameters with respect to the nominal value. Conclusions were that increasing the exhaust flow rate or temperature lead to a better exploitation of heat source hence an improvement on system efficiency and power output. Moreover, the optimal performances were met in cycles with subcooled condensers, in which the subcooling conditions at the outlet were in the range of 0.5-0.6K. Finally, it was acknowledged that there is a strong dependency between the drop of net power output and high sink temperatures, whose rise can diminish the cycle performance up to a 30% from the nominal value. Whilst the previous works focused on subcritical configurations primarily, Saleh et al. [24] considered supercritical configurations in comparison to subcritical for 31 pure fluids (alkanes, fluorinated alkanes, ethers and fluorinated ethers). The thermodynamic screening was conducted with BACKONE equation of state [25] for low-temperature geothermal brines in the arch of 30-100°C and the elected objective function was the thermal efficiency. Conclusions evidenced that, superheating is effective for subcritical configurations only if an Internal Heat Exchanger (IHE) is included and at the contrary, supercritical cycles suffer a decrease of thermal efficiency when superheating. Also, most of the selected fluids with a low critical temperature turned to find their optimal in subcritical configurations while those with higher critical temperature were supercritical, this infers that for heat sources above the range limit of 100°C, supercritical configurations are to be expected. The highest thermal efficiencies were found for high boiling temperature fluids with overhanging saturated vapor lines in subcritical configurations including IHE. Dai et al. [26] optimized 10 working fluids under sub-critical conditions emphasizing the dependence of this on the saturated vapor line shape (T-s diagram), hence on the turbine work output of ORCs, distinguishing between those with a negative slope in the saturated vapor curve (i.e. wet fluids), and those with non-negative slope (i.e. dry fluids). This difference is clearly represented in Fig. 1. The software of the choice to perform the thermodynamic simulation was Fortran and REFPROP® 6.01 for the thermodynamic properties calculation. Optimization was carried out for the Exergy efficiency by means of the genetic algorithm [27] which is a great option to avoid non-global optimal solutions. Results show that, for the chosen set of fluids and temperature range (80-135°C), the lower the exhaust temperature of waste heat the higher the exergy efficiency for dry fluids, and no IHE is needed under this scenario, since it would reduce the cycle performance in recovering the waste heat in the effort of maintaining the work output. R236EA fulfills all this requirement having the highest efficiency with the lowest exhaust temperature within the tested fluids. Figure 1. Classification of organic fluids attending to their saturation shape in the T-s diagram. 3 Development of a code for the design and optimization of Organic Rankine Cycles for power generation Continuing in the search for better performances in the promising transcritical range, Schuster et al. [28] studied the potential of supercritical ORCs. They analyzed the performance of several working fluids by means of the exergy efficiency and compared the mediums for sub- and supercritical cases. Optimization variables were, evaporation temperature and inlet temperature for subcritical and supercritical scenarios respectively. It turned out that supercritical configurations acquire higher plant efficiencies as result of the corresponding better exergetical efficiencies. The work agreed to previous studies pointing that the thermal efficiency (or cycle efficiency), as defined in Eq. (1), is not the best choice as optimization objective function, given the fact that increasing the thermal efficiency usually leads to a decrease in the heat recovery rate. This is proved analyzing the shape of the organic fluid’s curve in the T-Q diagram, showing that at higher live vapor temperatures less heat is transfered and the system efficiency declines. It is rather useful to set the plant efficiency Eq. (2), as the objective function for optimization and comparison purposes. Plant efficiency improvements are directly linked with the reduction of both exergy losses and exergy destruction, hence the optimal plant efficiencies are found by looking for the lower exergy losses. Results evidenced that, for generic heat sources with temperatures around 210°C, the best fluids for subcritical cases are R245fa and iso-butene with evaporation temperatures of 140°C approximately, whilst for supercritical scenarios the most convenient combinations are either R365mfc or isopentane with inlet temperatures around 180°C, achieving plant efficiencies of 13.2% (subcritical) and 14% (supercritical). Rashidi et al. [29] conducted the parametric optimization of a regenerative ORC. Exergy efficiency, specific work and thermal efficiency were selected as the objective functions to optimize the thermal parameters for different expansion pressures by using Engineering Equation Solver (EES). In the look for a good optimization approach they made a particular combination of two algorithms in a two stages optimization, firstly, according to the data achieved from the parametric analysis the artificial neural network (ANN) is applied, then, in the next stage the artificial bees colony (ABC) is run to optimize the specific network, thermal efficiency and exergy efficiency outputs from ANN. Ongoing, the cycle configuration was not simple either since it had two feedwater heaters, three pumps and a three stages turbine, thus the selected optimization variables were the pumps output pressures for the sake of simplicity. Conclusions present R717 as the fluid with the highest performance. Roy et al. [30] decided to apply the screening criteria based on the parametric optimization between R- 123 (HCFC family) and R-134a (HCF family) for regenerative supercritical ORCs. A Matlab® code was developed to optimize system and second law efficiencies, turbine work output and irreversibility ratio with respect to turbine inlet temperature (TIT) and expansion pressure incrementations under several heat source temperatures. Unlike any previous ORC optimization study, the thermodynamic properties at constant pressures were calculated via MBWR (Modified Benedicte Webbe Rubin) equation of state and standard text [36]. Analysis were carried for fixed heat source temperatures (FHST) as well as for variable heat source temperatures (VHST) in subcritical case. Conclusion were that increasing TIT for R-123 in the range 165-250°C and with pressures between 25-27 bars provides better results for all objective functions, thus resulting in higher efficiencies, turbine work output and lower irreversibility ratios. The method used by Wang et al. [31] applies a multi-objective parametric optimization, in which two objective functions are weighted by means of coefficients and applied as a single objective function into the annealing algorithm, the first being the heat exchanger area for unit of power output and second the heat recovery. Code was written in MATLAB for the optimization of condensation an evaporation pressures, water cooling velocities and the selection of the fluid from a set of 13 working fluids and WHR temperatures in 100- 220°C. The results acknowledged that for WHR temperatures ranging from 100°C to 180°C R-123 is the best choice, however if the exhaust temperatures are over 180°C (up to 220°C) the best suitable fluid is R-141b. Also, they noticed that the objective functions values drop with the growth of pinch point in the evaporator, and the optimal value for this parameter is found to be 15°C. Finally, settled a lower bound for ORC feasibility of 100°C, below that limit ORC technology does not acquire profitable performances. System Modeling 10 Although there are several design parameters, losses coefficients and efficiencies depend on the equipment choice (technology, quality and maintenance) therefore not strictly relevant for the case of cycle design optimization, meaning that the intersecting parameters for this purpose are the so called “Cycle defining parameters” which are shown in Table 3. It is important to mention that, whilst the present work focuses on the optimization of 𝑃𝑖𝑛,𝑡𝑢𝑟𝑏 and ∆𝑇𝑎𝑝,𝑃𝐻𝐸 in order to optimize the objective function which is the plant efficiency, the developed code is flexible to optimize any other combination of two of the cycle defining parameters. In that case 𝑃𝑖𝑛,𝑡𝑢𝑟𝑏 and ∆𝑇𝑎𝑝,𝑃𝐻𝐸 will have to be a fixed value. Fig 4. Shows the mentioned Design Parameters in the corresponding subcritical (a) and supercticial (b) T-s diagram. Figure 4 a). Design parameters in subcritical T-s. Figure 4 b). Design parameters in subcritical T-s diagram. Concerning heat exchangers it is convenient to mention that there is a minimum pinch point temperature required during heat exchanges between fluids, this is because there is a crucial necessity to avoid the mathematical solutions in which the working fluid reaches a temperature higher than the hot source at any isentropic state. For this study the corresponding minimum pinch point differences for the primary heat exchanger and the recuperator (if applied) are taken from various literature and shown in previous Table 1. TABLA 2. CYCLE DEFINING PARAMETERS Paramter Definition 𝑃𝑖𝑛,𝑡𝑢𝑟𝑏 Inlet turbine pressure ∆𝑇𝑎𝑝,𝑃𝐻𝐸 Approach temperature difference at PHE ∆𝑇𝑝𝑝,𝑃𝐻𝐸 Pinch point temperature difference at PHE ∆𝑇𝑎𝑝,𝑐𝑜𝑛𝑑 Approach temperature difference at condenser ∆𝑇𝑝𝑝,𝑐𝑜𝑛𝑑 ∗ Modified pinch point difference at condenser ∆𝑇𝑝𝑝,𝑟𝑒𝑐 Pinch point difference at recuperator 11 Development of a code for the design and optimization of Organic Rankine Cycles for power generation 2.3 Thermodinamic model In this section the thermodynamic model is presented. Once all the design parameters are fixed the thermodynamic properties at each point are computed with REFPROP® data base in a sequential-modular way by following the well-known laws of thermodynamics. Given the fact that the present work considers optimization of subcritical and transcritical configurations accounting on losses all along the cycle, the code computes a parallel algorithm to account on both scenarios. Fig 5. shows the different flow charts followed by the algorithm depending on the configuration. Appropriate attention is required for mixtures thermodynamic modeling. Particularly, behavior of mixtures, especially during non-isothermal phase transition, suggest promising results since the glide matching between temperature profiles in condenser and evaporator is remarkably higher. Herbele et al. [42] studied this phenomenon in the application of ORCs and proved that usage of binary zeotropic mixtures leads to higher efficiencies than pure fluids because of the reduction regarding irreversibility caused by the better temperature matching in heat exchanger equipment. Fig 5. Figure 5. T-s diagram differences between pure fluids and mixtures. Nonetheless, the aim of this work is to accomplish the optimization of binary mixtures composition in terms of molar fractions. For a given set of pure fluids the code returns the best binary combination among them as well as the corresponding optimal molar fractions with respect to the objective function, that can either be the net work output Eq. (1), plant efficiency Eq. (5) or second law efficiency Eq. (7) (accounting on reinjection limits if applied). 𝑊𝑛𝑒𝑡 󰇗 = 𝑚𝑊𝐹∗󰇗 (Δℎ𝑡𝑢𝑟𝑏−Δℎ𝑝𝑢𝑚𝑝) (1) 𝑄𝑖𝑛 󰇗= 𝑚𝐻𝑆∗󰇗 Δℎ𝑃𝐻𝐸 (2) 𝜂𝑐𝑦𝑐𝑙𝑒= 𝑊𝑛𝑒𝑡 󰇗 𝑄𝑖𝑛 󰇗 (3) System Modeling 12 𝜀𝑟𝑒𝑐= 𝑄𝑖𝑛 󰇗 𝑄𝑖𝑛,𝑚𝑎𝑥 󰇗 (4) 𝜂𝑝𝑙𝑎𝑛𝑡=𝜂𝑐𝑦𝑐𝑙𝑒 𝜂𝑟𝑒𝑐= 𝑊𝑛𝑒𝑡 󰇗 𝑄𝑖𝑛,𝑚𝑎𝑥 󰇗 (5) 𝜂𝐶𝐴𝑅𝑁𝑂𝑇=1 − 𝑇𝑎𝑚𝑏 𝑇𝐻𝑆,𝑖𝑛−𝑇𝐻𝑆,𝑜𝑢𝑡−𝑙𝑖𝑚 𝑙𝑛(𝑇𝐻𝑆,𝑖𝑛 𝑇𝐻𝑆,𝑜𝑢𝑡−𝑙𝑖𝑚 ) (6) 𝜂𝐼𝐼= 𝜂𝑝𝑙𝑎𝑛𝑡 𝜂𝐶𝐴𝑅𝑁𝑂𝑇 (7) In contrast to a vast majority of previous studies, the mass flow of the working fluid is not a required input, in fact the code produces the mass flow ratios of hot source to working fluid and cold sink to working fluid as outputs, thus none of the mass flows affect the optimization results (i.e. working fluid, heat source or cold sink mass flows). Whilst its obtainment is trivial for subcritical configurations (a simple energy balance in condenser and evaporator will lead to the respective mass flow ratios), if the optimal converges towards a transcritical cycle the calculation of the hot source to working fluid mass flow ratio (i.e. 𝑚𝐻𝑆−𝑊𝐹 󰇗) becomes non-trivial. Since in supercritical cycles the fluid’s heat absorption does not undergo phase change, the pinch point is not located in the saturated liquid curve at evaporating pressure as in subcriticals. In order to solve this problem, it is necessary to discretize the supercritical heat absorption in several steps and compute energy balance differentials to locate the pinch point (i.e. pinch point function). Additionally, the fact that mass flow ratios are output parameters that do not affect the optimal results brings the opportunity to achieve higher efficiencies in comparison to fixed flow analysis. Even if the potential heat source has a limited flow or the working fluid availability is low the present work converges to an optimal for such scenario. 13 Development of a code for the design and optimization of Organic Rankine Cycles for power generation Figure 6. Flow chart of thermodynamic algorithm. 𝑃 7 = 𝒇(∆𝑻 𝒂𝒑,𝑷𝑯𝑬 ,𝑷 𝒊𝒏,𝒕𝒖𝒓𝒃 ) 𝑃12 = 𝒇൫∆𝑻𝒂𝒑,𝒄𝒐𝒏𝒅,𝒍𝒊𝒒 𝒔𝒂𝒕൯ 𝑃 1 = 𝒇(∆𝑻 𝒂𝒑,𝒄𝒐𝒏𝒅 ,𝑻 𝒂𝒎𝒃 ,𝑷 𝟏𝟐 ) 𝑃11= 𝒇(𝑻𝟏𝟐, ∆𝑻𝒄𝒐𝒏𝒅,𝒗𝒂𝒑 𝒔𝒂𝒕) SUPERCRITICAL? 𝑃2 = 𝒇( 𝑷𝟕,∆𝑷𝒆𝒗𝒂𝒑, ∆𝑷𝒔𝒉, ∆𝑷𝒆𝒄𝒐,∆𝑷𝒓𝒆𝒈𝑪𝑺,𝑺𝟏, 𝜼𝒊𝒔𝒐,𝒑𝒖𝒎𝒑) 𝑃6 =𝒇(∆𝑷𝒔𝒉 , 𝑷𝟕, 𝒗𝒂𝒑 𝒔𝒂𝒕) 𝑃5 = 𝒇(∆𝑷𝒆𝒗𝒂𝒑,∆𝑷𝒔𝒉 , 𝑷𝟕) 𝑃4 = 𝒇(∆𝑷𝒆𝒗𝒂𝒑,∆𝑷𝒔𝒉 , 𝑷𝟕,𝑻𝟓) 𝑃 8 =𝒇(𝑷 𝟕 ,∆𝑷 𝒗𝒂𝒍𝒗 ,𝑺 𝟕 ) 𝑃9 =𝒇൫𝑷𝟏𝟏,∆𝑷𝒅𝒆𝒔,∆𝑷𝒓𝒆𝒈𝑯𝑺,𝜼𝒊𝒔𝒐,𝒕𝒖𝒓𝒃,𝑺𝟖൯ 𝑃10 =𝒇൫∆𝑻𝒑𝒑,𝒓𝒆𝒄,𝑻𝟐,𝑷𝟏𝟏, ∆𝑷𝒅𝒆𝒔൯ 𝑃3 =𝒇(𝑻𝟐,𝑻𝟑,𝑻𝟏𝟎,𝑷𝟕,∆𝑷𝒆𝒗𝒂𝒑,∆𝑷𝒔𝒉, ∆𝑷𝒆𝒄𝒐) 𝑃2 = 𝒇(𝑺𝟏, 𝜼𝒊𝒔𝒐,𝒑𝒖𝒎𝒑,𝑷𝟕, ∆𝑷𝑺𝑯𝑬, ∆𝑷𝒓𝒆𝒈𝑪𝑺) 𝑃 8 =𝒇(𝑷 𝟕 ,∆𝑷 𝒗𝒂𝒍𝒗 ,𝑺 𝟕 ) 𝑃9 =𝒇൫𝑷𝟏𝟏,∆𝑷𝒅𝒆𝒔,∆𝑷𝒓𝒆𝒈𝑯𝑺,𝜼𝒊𝒔𝒐,𝒕𝒖𝒓𝒃,𝑺𝟖൯ 𝑃10=𝒇൫∆𝑻𝒑𝒑,𝒓𝒆𝒄,𝑻𝟐,𝑷𝟏𝟏, ∆𝑷𝒅𝒆𝒔൯ 𝑃3 = 𝒇(𝑻𝟐,𝑻𝟑,𝑻𝟏𝟎,𝑷𝟕,∆𝑷𝒆𝒗𝒂𝒑 ∆𝑷𝒔𝒉, ∆𝑷𝒆𝒄𝒐) HOT SOURCE 𝑻𝑪=𝒇(∆𝑻𝒂𝒑,𝑷𝑯𝑬,𝑻𝟓) 𝒎󰇗𝒓𝒂𝒕𝒊𝒐,𝑯𝑺 𝑻𝑫,𝑻𝑩 = 𝒇(𝒎󰇗𝒓𝒂𝒕𝒊𝒐𝑯𝑺) HOT SOURCE 𝒎󰇗𝒓𝒂𝒕𝒊𝒐,𝑯𝑺 ,𝑻𝑫,𝑻𝑩, 𝑻𝑪, 𝑃4, 𝑃5, 𝑃6 = 𝒇 (Pinch point function) COLD SOURCE 𝑻𝒅= 𝒇൫∆𝑻𝒑𝒑,𝒄𝒐𝒏𝒅 ∗,𝑻𝟏𝟏൯ 𝒎󰇗𝒓𝒂𝒕𝒊𝒐,𝑪𝑺 𝑻𝒃,𝑻𝒄 = 𝒇(𝒎󰇗𝒓𝒂𝒕𝒊𝒐𝑪𝑺) COLD SOURCE 𝑻𝒅= 𝒇൫∆𝑻𝒑𝒑,𝒄𝒐𝒏𝒅 ∗,𝑻𝟏𝟏൯ 𝒎󰇗𝒓𝒂𝒕𝒊𝒐,𝑪𝑺 𝑻𝒃,𝑻𝒄 = = 𝒇(𝒎󰇗𝒓𝒂𝒕𝒊𝒐𝑪𝑺) YES NO System Modeling 14 2.4 Model OUTPUTS As a result of the optimization algorithm there are several outcomes produced by code to define the optimal solution and to facilitate the analisis of key points of the resulting optimal cycle. These Outputs are the following. 2.4.1 Optimal expansion pressure 𝑷𝒊𝒏,𝒕𝒖𝒓𝒃 and temperature difference between heat source and expansion temperature∆𝑻𝒂𝒑,𝑷𝑯𝑬 . According to several studiespublished in literature (Dai Y et al. [11] , Schuster A et al. [28]), these two parameters are proven to be among the most interesant and useful varaibles to optimize along literature due to the fact that they have a strong impact on the net work output obtained from the turbine, thus there is a revelevant interest in optimizing this for a given fluid. 2.4.2 Best performing fluid among the given selection. The code is fed up with a list of organic fluids the user is interested in analzing (input), then it executes the optimization for all of them and results in the best performing fluid among the inlet users list. Exhaustive criteria is strongly recommended inorder to decrease computational time, moreover similar complexity of fluids contributes to a potential mixture analysis resulting in a feasible fluid. 2.4.3 Best mixture between the given pure fluids and its optimal composition. If a mixture is taken into account as working fluid, the code looks for the best binary combination pairing the given list of pure fluids and result in the best binary mixture and it molar fractions in order to obtain the best suitable performance for the given parametrization. 2.4.4 Mass flow ratios of working fluid with respect to heat and cold sinks. As previously mentioned, the mass flow ratios are an output computed by the codedepending on the optimal result for the desired optimization function. Since there is no need to provide this as inputs to run the code the adaptability to the range of solutions is higher. 2.4.5 T-s diagram of entire cycle along with evolution of heat and cold temperature profiles. Fig 7 a) and b) show the output T-s diagram for both subcritical and supercritical configurations, along with the evolution of compressibility and saturation curve for optimal solution. Furthemore, for the case of supercritical configurations Fig 8. Shows a close up look to the pinch point as its location and calculation is not trivial. 2.4.6 Excel summary file with al data results. The Excel file contains the following sheets: • Cycle paramters (mass flow ratios, configuration of cycle, pressure ain condenser etc.) • Thermodynamic states of 12 points of model (Temperature, Pressure, Entropy, Enthalpy) • Hot source fluid and temperature evolution profile • Cold sink fluid and temperature evolution profile 15 Development of a code for the design and optimization of Organic Rankine Cycles for power generation • Turbine performance (model efficiencis and specific work output) • Pump performance (model efficiencis and specific work output) Figure 7 a). Temperature-Entropy diagram for a subcritical analysis of R245FA. System Modeling 16 Figure 7 b). Temperature-Entropy diagram for a supercritial analysis of MM. Figure 8. Close up view to pinch point location in supercritical cycle of MM. 17 Development of a code for the design and optimization of Organic Rankine Cycles for power generation 2.4.7 T – Q Diagram of hot source and cold sink. For a comprehensive description of solution, the code produces T-Q diagrams for both, heat source and cold sink, for a better analisys of heat transfer. Fig 9 a) , b) , c) and d) show this for any configuration. Figure 9 a). T-Q diagram for hot source under Subcritical conditions. Figure 9 b). T-Q diagram for hot source under Supercritical conditions. System Modeling 18 Figure 9 c). T-Q diagram for cold sink. 19 Development of a code for the design and optimization of Organic Rankine Cycles for power generation 2.4.8 T – Q Diagram of regenerator. Regeneration is an optional parameter, which has specialimpact for subcritical models. The code produces a T- Q diagram to analyze the effect of heat transfer and its effectivity in the cicle. Fig 10 shows an example, Figure 10. T-Q diagram for regenrator. Figure 11. Output Excel file with thermodynamic states of all cycle points. Optimization method 26 3.2.3 Working fluid optimization. The pure fluid optimization is performed by running the algorithm for every single fluid and choosing the one providing the best result towards termination criteria among all of them, however, this work aims to give further computational support to the theory of mixtures. For this purpose, the initial code for pure fluids optimization has been verified in first place (see verification section) to be later modified in order to include the optimization of binary mixtures also. This adds new problems with regards to the algorithm and thermodynamic state calculation, in one hand brings a new variable which is the molar concentrations of binary mixture and the other hand being the data base approach for thermodynamic states of mixture. The resolution of the first one is another reason to enhance the Genetic Algorithm as most suitable method given its multi objective nature, thus including a new variable will only increment the computational time but it won’t affect the capability of finding a global optimal. Meanwhile, REFPROP data base can calculate the mixtures properties by applying mixture rules to the pure-fluid Helmholtz energies. Thus, in analog way to how the pure fluids are optimized, the binary zeotropic mixtures run the identical model with the difference on the data base calculation, which in this case takes into consideration the molar fractions of each component to determine the properties of resulting mixture. Fig 12 shows output T-s diagram of mixture optimization with the optimal molar composition. Figure 15. T-s diagram for mixture RC318 and R142b optimization. 27 Development of a code for the design and optimization of Organic Rankine Cycles for power generation 28 4 VERIFICATION ith the purpose of proving evidences supporting the usefulness of the present work, it has been compared to previous studies. This screening comparison has been performed replicating faithfully the specific scenarios of those studies serving as references. 4.1 Reference studies. Given the fact that the present study is strongly based on Astolfi et al. [34], the first step to approach verification must be replicating Astolfis results as the modeling and parametrization matching between them is the highest in comparison to any other work. Thus, the error difference can not only be justified by comparison but also the potential improvements in model, algorithm and results. In this terms, exhaustive comparison is performed with respect to results fo Astolfi et al. [34], which is mainly focused on optimization for geothermal brines in the range of 120-180 ºC. Moreover, to present further verification and rely results on a more solid basis, this study’s parametrization has been adaptated to D. Maraver et al. [41]. Although presenting different modelation of cycle, it has a strong similarity of the consideration of several configuration scenarios (subcritical/supercritical, regeneration/nonregeneration). The choosen objective function for the mentioned study is the exergy efficiency which has been replicated in the present work as its flexibility allows multiobjective optimization. All in all, the criteria for each verification is to imitate configurations, paramters and sources to prove its generic capability: • Subcritical and supercritical solutions • Screening design parameters • Regenerative vs. non regenerative • Temperature profiles of heat source and sink • Objective functions • Working fluids It is crucial to mention that, for the verification purpose the working fluid is fixed whilst any other optimization variable remains un constrained, with the goal of comparing not only the optimal values of objective functions but the optimization variables as well, thus: • 𝑃𝑖𝑛,𝑡𝑢𝑟𝑏 • ∆𝑇𝑎𝑝,𝑃𝐻𝐸 W 29 Development of a code for the design and optimization of Organic Rankine Cycles for power generation 4.2 Verification with Astolfi’s study. As Astolf’s study focuses on the application of ORC to exploit geothermal brines the hot source fluid is water with inlet temperature and specific heat considered to be constant, whilst the sink fluid being air with constant heat capacity. Several of his analysis could be chosen, nevertheless, in order to aim for the most comprehensive verification each analysis is performed with respect to various fluids, in Astolfis case these will be: • RC 318 • C 4 F 10 • R227EA These will be tested under the same circumstances for different configurations. 4.2.1 Astolfi’s verification with reinjection limit. Being the scenario a 150ºC geothermal brine with a reinjection limit of 70ºC and ambient temperature of 25ºC the optimal solutions for the mentioned organic fluids provided by the present work are shown in Fig 16. Figure 16. Verification with Astolfis optimization work, reinjection limit applies. 10.97 10.83 10.42 10.75 10.58 10.37 RC318 E = 2 % C4F10 E = 2.3 % R227EA E = 0.5 % Plant efficiency (%) Optimal fluids Simulation results Astolfi's reference Verification 30 The optimal configurations for all fo the fluids converge to supercritical and regenerative. The objective function for the optimization is the cycle efficiency 𝜂𝑐𝑦𝑐𝑙𝑒 (Eq. 3). Being the standart deviation: 𝜎= √∑(𝑥𝑖−𝑥)2 𝑛 𝑖=1 𝑁 (16) Where: 𝑥𝑖= Deviation of fluid i 𝑥= arithmetic average of all deviations N = number of fluids The standard deviation for the current comparison is: 𝜎= 0.787 % 31 Development of a code for the design and optimization of Organic Rankine Cycles for power generation 4.2.2 Astolfi’s verification with NO reinjection limit. Scenario is a 150ºC geothermal brine with no reinjection limit and anambient temperature of 15ºC the optimal solutions for the mentioned organic fluids provided by the present work are shown in Fig 15. Figure 17. Verification with Astolfis optimization work, no reinjection limit. The optimal configurations for all fo the fluids converge to supercritical and regenerative, whilst the standart deviation for this analysis is: 𝜎= 0.315 % The efficiency improvement with respect to Astolfis results can be justified by the genetic algorithm, whose heuristic nature represent an improvement looking for a global optimal. 8.25 8.06 8.05 8.2 7.97 8.08 RC318 E = 0.6 % C4F10 E = 1.1 % R227EA E = 0.3 % Plant efficiency (%) Optimal fluids Simulation results Astolfi's reference Verification 32 4.3 Verification with Maraver’s study. In the other hand D. Maraver et al. [41] conducted quite a similar study to the intentions of the present one, focusing on the thermodynamic optimization of organic Rankine cycles (ORCs) forpower generation and CHP for a wide range of heat source profiles (waste heat recovery, thermaloil for cogeneration and geothermal). The general was providing guidelines for several operating conditions, including subcritical and transcritical, regenerative and non-regenerative cycles, thusit matches the goals of this work. Maraver also performed a parametrization of the equipment in the cycle (expander, heat exchangers and feed pump). An optimization model of the ORC. Nonetheless one of the main differences in the approach is that Maravers decided to optimize in terms of exergy efficiency, but as previously said this represents no obstacle. Finally, criterion to decide the fluids to be employed in the comparison was to run those considered the most commonly used in commercial ORC units (R134a, R245fa, Solkatherm, n-Pentane, Octamethyltrisiloxane and Toluene), Fig 16 shows verification for R134a, R245fa and n-Pentane. Figure 18. Verification with Maraver optimization work. 39.9 36.6 33.4 45.2 38.2 35.8 R134 E=4.3% R245FA E=1.6% N-PENTANE E=2.4% Second Law efficiency (%) Optimal fluids Simulation results Maraver's reference 33 Development of a code for the design and optimization of Organic Rankine Cycles for power generation In this case the analysis is performed for a 170 ºC geothermal source with a reinjection limit of 70 ºC and a cold sink of 10 ºC air. The configuration results are as follows: • For R134 it is a supercritical non-regenerative ORC • For R245FA it is a subcritical non-regenerative ORC • For N-PENTANE it is a subcritical non-regenerative ORC Overall standard deviation is: 𝜎= 1.385 % The deviation increases in comparison to Astolfis verification, this is due to the strong mirroring of this study with respect toAstolfis and the differences in modeling assumptions as losses coefficients, mass flow calculations and optimization algorithm, yet the standard deviation remains low enough to considere it quite a valid ans sucesfullverification. 4.4 Observations on verification process. Given the low deviation and screening configurations for comparison purposes, this matching optimization results are considered to represent valid verification for the present work, thus represents a trustful tool to perform further analysis with binary mixtures. Verification 34 35 5 RESULTS nce generic optimization has been verificated for pure fluids, the algorithm is adapted and run for the optimization of binary zeotropic mixtures. The thermodynamic state will be computed according to database applying mixture rules to the pure-fluid Helmholtz energies with relation to their molar fractions. The algorithm compares each binary combination of the provided input fluids and results in the best combination and molar fractions of optimal mixture. 5.1 Guidelines for mixture optimization. When optimizing pure fluids, it is relatively simple to choose a set of potential fluids once the heat source has been defined, it has been proven that fluids whose critical temperature is the closest (but not over) the heat source, provide the best efficiencies as the heat absorption results to be the most profitable. A good parameter for the analisis of this is the T𝑐𝑟𝑖𝑡 / Tℎ𝑜𝑡 𝑠𝑜𝑢𝑟𝑐𝑒 ratio, Astolfi et al. [34] found there is a convenient range between 0.88 and 0.92, this is easier for pure fluids than for mixture since the different components of mixtures and the influence of molar fraction compositions has a strong impact on the propiertes of the resulting mixture, for this reason a more accurreate screening criteria is needed when performing mixture analysis, other wise the computational time can be unfeasible or very tedious. Consencuenlty, fuids whose critical temperature is above the heat source are strongly recommended since the resulting mixture with other fluid with a critical temperature below the heat source can result in a mixture with a better T𝑐𝑟𝑖𝑡 / Tℎ𝑜𝑡 𝑠𝑜𝑢𝑟𝑐𝑒 ratio. 5.2 Mixture optimization reuslts. With the goal of finding fluids able to provide a better efficiency, thus give computational support to the theory of mixtures, the optimization of several scenarios has been performed. Fig 17 shows the results compared to a scenario from Astolfi et al. 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Towards optimal mixtures of working fluids: Integrated design of processes and mixtures for Organic Rankine Cycles 11