Erick Lavoie
email: erick.lavoie@mail.mcgill.cahendren@cs.mcgill.ca

Laurie Hendren

Frédéric Desprez
email: frederic.desprez@inria.fr

Pando: An Easy-to-Deploy P2P Volunteer Computing Platform for the Web

Clear Programming Model: Base the system on a programming model that is clear and guides a correct implementation;

Easy Deployment: Make the system easy to deploy, both for the project owner and the volunteers;

Usage of Existing Commodity Hardware: Use existing hardware including workstations, laptops, tablets and mobile phones that individuals, businesses, and universities already possess;

Scalability: Allow connecting at least a thousand volunteers;

Elasticity: Make the volunteer nodes available quickly;

Performance: Show a linear improvement in throughput compared to a single processor; On startup, pando provides a url at which volunteers can connect with a web browser;

3. Open the url in browser tabs on all compatible devices, one per core;

4. Share the url on social medias to invite friends to participate;

Components Computation Model

A web-based volunteer computing approach that is simple to deploy, does not require a dedicated server, and can leverage a wide variety of existing end-user devices because code is executed in browsers;

Open source implementations in JavaScript of stream abstractions, each individually available through the Node Package Manager (NPM) for reuse in other projects and that are easily composable with a growing list of community developed pull-stream modules;

An open-source command-line tool (pando), compatible with Unix pipelines that uses the stream abstractions as well as all scripts and procedures to replicate our performance experiments on the Grid'5000 testbed.

Squaring Number Test Collatz Conjecture

Linear speedup when increasing the number of volunteers!

Scales up to at least a thousand browser tabs! * Simulated computation time (computation delayed to take 1 second), with up to 13 browser tabs/core * Real computation time, 1 browser tab/core Current volunteer platforms in use today (ex: BOINC platform) require a significant amount of effort and money to deploy which limits the volunteer computing approach to a few high-profile projects. Moreover, the effort in installing a client a limits the number of participants.

The web platform now offers a combination of excellent execution performance, security sandboxing, and standard communication protocol including WebRTC (peer-to-peer browser communication), and portability across many devices and operating systems, and requires no installation of client software. Moreover, social medias enable the quick mobilization of millions of users.

Those capabilities now enable the construction of newer and simpler volunteer computing platforms that may tap into more devices than ever, reach significantly more participants, and make the deployment easy for smaller and even one-shot computation projects.

Three generations of projects, as surveyed by Fabisiak and Danilecki Presented Pando, a new volunteer computing platform designed to be easy to deploy and which does not require a dedicated server and can be scaled to a thousand browser tabs for computation. This makes it useful to leverage hardware investments already made in small-and medium-businesses and university departments.

We will perform an in-depth evaluation of the performance of Pando, support more applications, optimize the performance of single computation nodes, and explore various overlay topologies for applications with more complex communication patterns during computation.

Fault- tolerance :

 tolerance Tolerate individual nodes that suddenly disconnect or stop answering. Source Code Repository: https://github.com/elavoie/pando-computing Demo/Teaser: https://www.youtube.com/watch?v=29ABvs3wNNI Handbook: https://github.com/elavoie/pando-handbook Reproduction Steps for Performance Experiments: https://github.com/elavoie/pandohandbook#publication-specific-instructions-for-reproducing-experiments [1] Tomasz Fabisiak and Arkadiusz Danilecki. Browser-based harnessing of voluntary computational power. Foundations of Computing and Decision Sciences, 42(1):3-42, 2017. [2] David Dias. browserCloud.js -A federated community cloud served by a P2P overlay network on top of the web platform. Master's thesis, Tecnico Lisboa, 2015.Conclusion and Future Work Usage 1. Write or generate a JavaScript function for processing (ex: process.js) using the following conventions (supports NPM packages!): var module.exports['/pando/1.0.0'] = function (x, cb) { // perform computation if (error) return cb(error) return cb(null, result) } 2. Start Pando on a local laptop, desktop, or server: generate-inputs | pando process.js [options] | process-outputs

  [1] over more than 40 articles on browser-based voluntary computing published in over 20 years, to which we add a 4th generation: 1st Generation (90s and 2000s): Based on Java and Web Applet (requires installation of plugins) 2nd Generation (2007-2010): Based on JavaScript but really slow 3rd Generation (2010-2015): Based on JavaScript but now fast! (still require server) 4th Generation (2015-…): JavaScript + Peer-to-Peer communication (no server!), browserCloud.js [2], and Pando

Acknowledgements

Easy to Deploy

Usage of Existing Hardware Clear and Simple Programming Model

Quickly Scalable to a 1000

Browser Tabs

Automatic Recovery from Disconnecting Volunteers

Leverage all your (and your friend's!) devices to accelerate processing workflows with

Images from https://openclipart.com


Alexandre Dijoux
email: alexandre.dijoux@univ-reunion.fr

Frantz Sinama

Olivier Marc Marc

Bertrand Clauzade

Jean Castaing-Lasvignottes

Jean-Castaing Lasvignottes

Working fluid selection general method and sensitivity analysis of an Organic Rankine Cycle (ORC): application to Ocean Thermal Energy Conversion (OTEC)

Keywords: Ocean Thermal Energy Conversion (OTEC), Entropic Mean Temperature Difference (EMTD), Organic Rankine cycle (ORC), parametric sensitivity analysis

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Ocean Thermal Energy Conversion (OTEC) is a great opportunity in the tropical belt to produce non-fluctuant and environmentally friendly power [START_REF] Quinby-Hunt | Potential environmental impacts of closedcycle ocean thermal energy conversion[END_REF]. The temperature difference between hot surface and cold deep seawater is exploited through a power cycle in order to produce electricity [START_REF] Avery | Renewable energy from the ocean-A guide to OTEC[END_REF]. The temperature difference between hot and cold heat sources is very small compared to conventional Rankine cycles, or even compared with other applications working at low temperature, such as solar, geothermal or waste heat recovery [START_REF] Tchanche | Low-grade heat conversion into power using organic Rankine cycles -A review of various applications[END_REF].

Various approaches are used in order to increase the very low performance of an ORC (Organic Rankine Cycle):

 modifying the cycle structure,  optimizing the working conditions of the cycle,  choosing the most adapted working fluid for the application.

Considering the first point, Tchanche et al. have reviewed a lot of modified cycles (with a reheater for instance), or mixtures-adapted cycle like the Kalina cycle or Uehara cycle [START_REF] Tchanche | Heat resources and organic Rankine cycle machines[END_REF]. In parallel, Yoon et al. proposed an ammonia-based power cycle by using an expansion valve and a cooler [START_REF] Yoon | Performance characteristics of a high-efficiency R717 OTEC power cycle[END_REF] and Yuan et al. presented a water-ammonia based power absorption cycle with two ejectors [START_REF] Yuan | Performance analysis of an absorption power cycle for ocean thermal energy conversion[END_REF]. They both obtained better thermal efficiency than the conventional ORC, even if the Kalina and Uehara cycles also show good performances [START_REF] Zhang | A review of research on the Kalina cycle[END_REF]- [START_REF] Goto | Construction of simulation model for OTEC plant using Uehara cycle[END_REF]. Nonetheless, the basic ORC appears to be the simplest, and provides reliability, low investment costs, and easy maintenance [START_REF] Bao | A review of working fluid and expander selections for organic Rankine cycle[END_REF].

Considering the choice of the working fluid, various criteria and methods have been proposed to select the most suitable fluids. The main ones for a working fluid are good thermodynamic performances, non-toxicity, small environmental impact, low cost, availability, and compatibility with pipes and components materials. Unfortunately, it is difficult to find the perfect fluid that meets all of these qualities. Lee et al. [START_REF] Lee | Thermophysical capability of ozone-safe working fluids for an organic Rankine cycle system[END_REF] compared the performances of more than one hundred ozone-safe working fluids for an ORC applied to waste heat recovery. They found that thermodynamic performances of the fluids are correlated with their physical properties, such as normal boiling point, critical pressure and molecular weight. Stijepovic et al. [START_REF] Stijepovic | On the role of working fluid properties in Organic Rankine Cycle performance[END_REF] also carried out a theoretical study to evaluate the effect of physical properties of workings fluids on thermal and exergetic efficiency and the ratio of heat exchangers area and net power output. Saleh et al. [START_REF] Saleh | Working fluids for low-temperature organic Rankine cycles[END_REF] conducted simulations to compare the thermal efficiency and volume flow rates of various working fluids for different types of cycle. Wang et al. [START_REF] Wang | Cost-effectiveness performance analysis of organic Rankine cycle for low grade heat utilization coupling with operation condition[END_REF] provided a theoretical analysis of net power output and heat exchangers surface for a Waste Heat Recovery (WHR) system. They found that fluids with low Jacob number performed better. They also found in another study [START_REF] Wang | Efficiency and optimal performance evaluation of organic Rankine cycle for low grade waste heat power generation[END_REF] that the choice of the working fluid for WHR has a small impact on optimal performances of the cycle, and that the evaporator is the most important component in exergy losses. However, they only consider pure fluids. The use of mixtures as working fluid has also been discussed [START_REF] Radermacher | Thermodynamic and heat transfer implications of working fluid mixtures in Rankine cycles[END_REF], [START_REF] Zhao | Thermodynamic analysis of organic Rankine cycle using zeotropic mixtures[END_REF]. It is established that, in theory, the behavior of mixtures during phase change allows reducing the mean temperature difference between working fluid and source in heat exchangers, but the performance is not always better than pure fluids in practice. Some authors realized a complete cost study by using correlations for several components [START_REF] Wang | Efficiency and optimal performance evaluation of organic Rankine cycle for low grade waste heat power generation[END_REF], [START_REF] Yang | Thermo-economic optimization of an organic Rankine cycle system for large marine diesel engine waste heat recovery[END_REF]- [START_REF] El-Emam | Exergy and exergoeconomic analyses and optimization of geothermal organic Rankine cycle[END_REF]. This means that they should choose a precise technology of heat exchangers and expander. Zhang et al. [START_REF] Zhang | A new method used to evaluate organic working fluids[END_REF] proposed a method using the Hass Diagram Technique to compare working fluids with thermodynamic, security and environment considerations. However, no simulation was conducted to evaluate thermodynamic behavior of each fluid in a particular cycle.

The selection of the best fluids is also often related with the optimization of working conditions parameters of the cycle, like the evaporation and condensation temperature : each fluid is thus compared with his own optimized parameter [START_REF] Wang | Cost-effectiveness performance analysis of organic Rankine cycle for low grade heat utilization coupling with operation condition[END_REF], [START_REF] Yang | Analyzing the optimization of an organic Rankine cycle system for recovering waste heat from a large marine engine containing a cooling water system[END_REF], [START_REF] Roy | Parametric optimization and performance analysis of a waste heat recovery system using Organic Rankine Cycle[END_REF]. He et al. [START_REF] He | The optimal evaporation temperature and working fluids for subcritical organic Rankine cycle[END_REF] carried out an analytical study in order to evaluate the optimized evaporation temperature with net power output as the objective function and compared the optimal net power output for several fluids.

In that case, the objective function is decisive, as it influences the value of optimal parameters. Therefore, some efforts have been made to conduct multi-objective optimization [START_REF] Wang | Multi-objective optimization of an organic Rankine cycle (ORC) for low grade waste heat recovery using evolutionary algorithm[END_REF], [START_REF] Xiao | Multi-objective optimization of evaporation and condensation temperatures for subcritical organic Rankine cycle[END_REF].

Moreover, in the case of OTEC, which is very particular due to the weak temperature difference between heat sources, the literature about the choice of the working fluid is relatively poor. Sun et al. [START_REF] Sun | Optimization design and exergy analysis of organic rankine cycle in ocean thermal energy conversion[END_REF] provided an analytical method to optimize the performance of an OTEC power plant considering two working fluids, R134a and ammonia. Yang et al. [START_REF] Yang | Analysis of optimization in an OTEC plant using organic Rankine cycle[END_REF] conducted an optimization of evaporation and condensation temperature and a comparison of five pure working fluids considering an OTEC power plant with shell-and-tube heat exchangers. Yoon et al. [START_REF] Yoon | Efficiency comparison of subcritical OTEC power cycle using various working fluids[END_REF] compared the influence of various working fluids on the thermal efficiency of an OTEC power plant, but they didn't take into account net power output or volume flow rates.

Iqbal et al. [START_REF] Iqbal | Use Of Mixtures as Working Fluids in Ocean Thermal Energy Conversion Cycles[END_REF] analyzed the influence of mixtures on the performances of an OTEC system, but they compared only one of them with one pure fluid (propane). Hung et al. [START_REF] Hung | A study of organic working fluids on system efficiency of an ORC using low-grade energy sources[END_REF] carried out a comparison of eleven working fluids for solar and OTEC heat sources based on a study of physical properties of the fluids. They found that isentropic fluids performed generally better. Furthermore, some attention has been paid on increasing the temperature difference between the cold and the hot sources of an OTEC system by coupling it with solar energy [START_REF] Yamada | Thermal efficiency enhancement of ocean thermal energy conversion (OTEC) using solar thermal energy[END_REF], [START_REF] Straatman | A new hybrid ocean thermal energy conversion-Offshore solar pond (OTEC-OSP) design: A cost optimization approach[END_REF] or with the effluent of a nuclear power plant [START_REF] Kim | Using the condenser effluent from a nuclear power plant for Ocean Thermal Energy Conversion (OTEC)[END_REF]. The problem is that the power produced is no longer steady during all day and night, and nuclear power plant are often not available in tropical islands, where OTEC seems undoubtedly to be a good opportunity. In fact, little attention has been paid on comparing both pure and mixed working fluids for OTEC.

The previous short review shows that a lot of studies have been carried out for optimizing the performances of an ORC, from simple approaches using ideal cycles (preselecting the fluid before designing and sizing the components), to detailed energetic and economic studies and simulations (where design and size of the components are fixed). These last methods require a good knowledge about the technology of the system and its components, and are therefore not applicable in a preliminary design phase of the system. As the choice of the working fluid occurs early in the conception of an ORC, simple approaches are generally preferred. In this case, the comparison of very different fluids (in particular when comparing pure fluids and mixtures) remains tricky, especially when heat exchangers are not particularly described. To do so, some authors introduce the pinch point [START_REF] Wang | Efficiency and optimal performance evaluation of organic Rankine cycle for low grade waste heat power generation[END_REF], [START_REF] Roy | Parametric optimization and performance analysis of a waste heat recovery system using Organic Rankine Cycle[END_REF], defined by the minimal temperature difference between the working fluid and the heat transfer fluid in the HEX (Heat Exchanger). However, the location and the value of the pinch point depend on the fluid, the flow rates and the amount of heat exchanged and are sometimes difficult to determine and require a deep knowledge of the HEX structure and applied conditions. Other authors consider the temperature difference between the outlet of the working fluid and the inlet of the heat source [START_REF] Yoon | Performance characteristics of a high-efficiency R717 OTEC power cycle[END_REF], [START_REF] Yuan | Performance analysis of an absorption power cycle for ocean thermal energy conversion[END_REF], [START_REF] Borsukiewiczgozdur | Comparative analysis of natural and synthetic refrigerants in application to low temperature Clausius-Rankine cycle[END_REF]. This method is interesting when comparing pure fluids, because the phase change temperature is constant.

In the case of zeotropic mixtures, temperature is no longer constant during evaporation and condensation and this behavior allows to reduce the mean temperature difference between the working fluid and the heat source [START_REF] Radermacher | Thermodynamic and heat transfer implications of working fluid mixtures in Rankine cycles[END_REF]. However, the temperature variation of the mixture does not necessarily have the same profile as the heat source. Hence, one or more pinch points can be observed [START_REF] Kim | Assessment of pinch point characteristics in heat exchangers and condensers of ammonia-water based power cycles[END_REF]. So, when comparing zeotropic mixtures with pure fluids, this method becomes disadvantageous.

To overcome these drawbacks and provide a general method to compare working fluids in similar conditions with a reduce number of hypothesis, the entropic mean temperature difference is introduced in this study as a parameter for heat exchangers description. In the end, a general method for working fluid comparison is given, considering four criteria: technicity, thermodynamic performances, security and environment. This method is implemented for an OTEC application, for which input parameters are issued from an experimental land-based prototype in Reunion Island [START_REF] Journoud | Experimental Ocean Thermal Energy Conversion (OTEC) project on the Reunion Island[END_REF]. A parametric sensitivity analysis of the model is then carried out in order to explain the model operation, and to give the validity domain of previous results.

Cycle description 2.1. From the ideal Carnot cycle to the real ORC

The most efficient cycle for converting heat into work is the Carnot cycle (Figure 2.a). However, this ideal cycle is not found in practice and is replaced by the Rankine cycle (Figure 2.b). The latter is composed of four components: a pump (P), an evaporator (E), a turbine (T) and a condenser (C), as shown in Figure 1. A working fluid in the liquid state (point 1) is evaporated by using the heat from the hot source. The obtained vapour at high pressure (point 2) is expanded in the turbine producing mechanical work convertible in electricity. The vapour at low pressure (point 3) is then cooled and condensed by using the cold source (point 4). A pump brings back this liquid to the inlet of the evaporator (point 1). In the case of so called "wet fluids" (i.e. fluids with a negative slope of their vapour saturation curve (∂T/∂s)x=1 < 0), the fluid leaves the turbine in a two-phase flow, leading to droplets (Figure 2.c), whereas in the case of so called "dry" or "isentropic" fluids (i.e. fluids with a positive slope or with a vertical vapour saturation curve, respectively), the fluid at the output of the turbine is overheated (Figure 2.d and 2.e).  Due to heat exchangers, a temperature difference appears in the cycle between the working fluid and heat sources. Moreover, a little overheat or subcooling is often observed at the outlet (Figure 2.c, 2.d and 2.e).  The pump and the turbine are not perfect: the transformations occurring are in reality producing entropy, so the isentropic efficiency of these components has been considered.  In the particular case of low grade heat ORC, heat exchangers areas are very important, so as the pressure losses can be important, particularly for plate heat exchangers.

For an ORC applied to OTEC, the temperature difference between hot surface seawater (Thw = 25.5 °C) and cold deep seawater (Tcw = 5 °C) is very small, and the corresponding ideal thermal efficiency of the Carnot cycle (given by: hth = 1 -Tcw / Thw ) is only 6.9 %.

Figure 2. T-s diagram of thermodynamic cycles progressing from ideal to real

Cycle modeling

To avoid the drawbacks of the Pinch Point approach, it has been decided to introduce the Entropic Mean Temperature Difference (EMTD) concept. The latter is, by definition, the ratio of the enthalpy change to the entropy change, that is to say, the harmonic mean of temperature weighted by heat transfer, and is given by:

         q qh T q ss T (1)
This notion was used by Meunier et al. [START_REF] Meunier | Equivalent Carnot cycles for sorption refrigeration: Cycles de Carnot équivalents pour la production de froid par sorption[END_REF] for thermodynamic cycle analysis and by other authors [START_REF] Boisvert | Dispersion of alumina-coated TiO 2 particles by adsorption of sodium polyacrylate[END_REF]- [START_REF] Castaing-Lasvignottes | Equivalent Carnot cycle concept applied to a thermochemical solid/gas resorption system[END_REF]. The EMTD is then defined by the difference between entropic mean temperatures of both working and heat transfer fluids. This parameter is advantageous comparing to the most used temperature difference at the output Ts since it allows the comparison between pure fluids and mixtures. For the mixture, the mean temperature difference is greater than that of the pure fluid due to the temperature glide. When using EMTD, fluids can be compared in more similar operating conditions in terms of heat transfer, as shown in Figure 3. So as to compare different kind of working fluids, it can be supposed that the entropic mean temperature of the heat transfer fluid is the same for all the working fluids, taken equal to the input source temperature. EMTD in the evaporator and in the condenser are then given by:

𝑇 ̃evap = Thw -𝑇 ̃evap (2)
𝑇 ̃cond = 𝑇 ̃cond -Tcw (3)
Furthermore, considering the pump and the turbine, they are described by their respective isentropic efficiency:

pump = (h1 is -h4) / (h1 -h4) (4) turb = (h3 -h2) / (h3 is -h2) (5)
Energy balances for each component are given by: Evaporator:

qevap = h2 -h1 (6) Turbine: wturb = h2 -h1 (7) Condenser: qcond = h4 -h3 (8) Pump: wpump = h1 -h4 (9)
The performance of the cycle is then determined by two parameters: the widely used thermal efficiency and the net volumic work respectively determined by: th = wnet / qevap = (wturb + wpump) / qevap (10) wnet, vol = wnet / v3 = (wturb + wpump) / v3 [START_REF] Goto | Construction of simulation model for OTEC plant using Uehara cycle[END_REF] Where v3 is the maximum value of the specific volume of the working fluid at the turbine output.

In fact, as the work consumed by the pump is small compared to the work produced by the turbine, this parameter is approximately the inverse of the Size Parameter (SP) used by He et al. [START_REF] He | The optimal evaporation temperature and working fluids for subcritical organic Rankine cycle[END_REF], Macchi et al. [START_REF] Macchi | Efficiency prediction for axial-flow turbines operating with nonconventional fluids[END_REF], Lakew et al. [START_REF] Lakew | Working fluids for low-temperature heat source[END_REF] and Baik et al. [START_REF] Baik | Power-based performance comparison between carbon dioxide and R125 transcritical cycles for a low-grade heat source[END_REF] and allows having an idea of the turbine size.

Working fluid selection

A method for the comparison of working fluids based on the use of the precedent model has been developed and applied to OTEC. Fluids are compared according to 4 criteria: technicity, security, environmental impacts and thermodynamic performances. Methods and results are shown in this section.

Simulation hypothesis

The system is considered to be working under steady state conditions and heat losses are neglected. The properties of both pure working fluids and mixtures have been determined using the software Engineering Equation Solver (EES) [START_REF] Klein | Engineering Equation Solver EES Academic Commercial V7. 933[END_REF]. Input parameters have been obtained from an OTEC onshore prototype situated in Reunion Island [START_REF] Sinama | Etude expérimentale d'un prototype ETM à La Réunion[END_REF], [START_REF] Journoud | Experimental Ocean Thermal Energy Conversion (OTEC) project on the Reunion Island[END_REF] (an overseas French department located in Indian Ocean, close to Mauritius). Corresponding values are listed in Table 1. Otherwise, for an OTEC application, the low temperature difference between hot and cold heat sources involves very important heat exchange areas and volumes. So, pressure drop can be observed in the working fluid side, particularly for plate HEX and have been assumed to occur during the phase change of the fluid.

The results obtained for a list of selected working fluids is shown in Table 3.

Technicity

The first criterion used to compare working fluids in this study is the technicity represented by the working pressure range and the vapour quality at the turbine outlet. Extreme pressures of the cycle are calculated considering sources temperatures, while nominal pressures are determined by simulated working fluid temperatures. A pressure that ranges between 1 and 24 bar has been considered here and provides generally easier implementation and lower cost. Furthermore, the vapour quality is chosen greater than 97 % to reduce the risk of alteration of the turbine by any droplets. After a first selection between a list of 107 fluids according to these criteria, 26 fluids appears to be good candidates for an OTEC application. The list of selected working fluids is shown in Table 3, and their technicity indicators are illustrated in Figure 4. It is interesting to notice that the two criteria above are correlated. Fluids with the highest operating pressures are also those with the highest liquid quality at the turbine outlet. These fluids are the wet fluids. Most of dry fluids have low operating pressures, but they have a high overheating at the condenser inlet, which will affect cycle performances.

Security

The ASHRAE standard 34 reference [START_REF]Refrigerating and Air-Conditioning Engineers (ASHRAE[END_REF] has been chosen as the security indicator. This latter is composed of a letter that indicates the toxicity (from A for non-toxic to C for highly toxic) and a number that indicates flammability (from 1 for non-flammable to 3 for highly flammable). Among the candidates, 14 fluids have the best indicator A1, as shown in Table 3. NH3 is B2L, that is to say that it is toxic and slightly flammable, and R1234yf is A2L, so it is non-toxic and slightly flammable. Accordingly, R1234yf shows quite good properties for safety considerations, even if it isn't A1.The indicator was not given for H2S, but it is a toxic and flammable fluid.

Environmental considerations

A lot of working fluids have been forbidden in order to protect the ozone layer since the Montreal protocol in 1998. Furthermore, as OTEC claim to be an environment-friendly source of energy, it is important to consider the environmental impact of the working fluid. Three indicators have been chosen: the global warming potential (GWP), the ozone depletion potential (ODP), and the atmospheric lifetime (ALT). The GWP represents the impact on the global warming in terms of temperature variation, related to that of a similar mass of CO2. The ODP is the amount of destruction of the ozone layer, related to that of a similar mass of R11. The ALT is the time in years necessary for a substance to turn over the global atmospheric burden. Values of these three indicators are given in Figure 5. It appears that R1234yf, NH3, R600a, R600 and R290 have the lowest environmental impact.

Figure 5. Value of GWP, ALT and ODP for the fluids of the panel

Thermodynamic performances

According to results given in Table 3, the ranking of the different working fluids depends strongly on the selected criteria. Indeed, considering the specific work wnet, NH3 perform widely better than other fluids (41.98 kJ/kg for NH3 compared to 14.98 kJ/kg for H2S in second position). However, considering the thermal efficiency, the gap between different fluids is less important. R143m performs better, but NH3, R236ea and SO2 give very close values of thermal efficiency. Considering the net volumic work wnet, vol, H2S and R32 perform better.

Pure fluids Azeotropic Mixtures

Zeotropic Mixtures

x Not Available

To compare the results, thermal efficiency has been plotted versus volumic net work, as in Figure 6. A Pareto's frontier giving the best fluids is also represented in this figure. Working fluids on this curve are R143m, NH3, R507a and H2S. R143m is on the frontier because it has a better ηth than NH3. However, the difference in thermal efficiency between NH3 and R143m is very small (3.447 % for NH3 against 3.450 % for R143m), when the volumic work of NH3 is near twice than R143m. So, R143m do not provide great advantage over NH3. So, we will not consider R143m in the following of this study.

In conclusion, the best fluids according to the two selected thermodynamic criteria (ηth and wnet,vol) are in first position NH3, R507a and H2S. In second position, R134a, R1234yf, R22, R407c, R404a and R32 also show good performances. Figure 6. Thermal efficiency versus net volumic work for the selected fluids, and representation of the Pareto's frontier.

Comparison Synthesis

All fluids in the panel presented were suitable according to the technical criteria. Three working fluids have been chosen by the thermodynamic study, fourteen by the security study, and five by the environmental impact study, as shown in Table 2. As a result, no fluid meets the three criteria at the same time. However, NH3 is a very good candidate because it meets good thermodynamic performances and low environmental impact, even if it is toxic. R507a is also a good candidate because it presents good thermodynamic performances, non-toxicity and non-flammability, but its GWP and ALT are high. It is also interesting to notice that R1234yf seems also to be a good compromise because it is in second position for thermodynamic performances, it has very few environmental impacts and isn't toxic and just slightly flammable (A2L). So, in the end, three fluids appear to be the best candidates for OTEC: NH3, R507a and R1234yf. This selection was made assuming operating conditions and component properties to be constant. A parametric sensitivity analysis will be held in the next part to study the effect of their variations.

R1234yf

Parametric sensitivity analysis of the thermodynamic model 4.1 Method

The parametric sensitivity analysis sets out to determine the influence of the variance of each parameter of the model on the results. The most used method found in the literature is the "One Factor At Time" method. This later consists in varying one parameter and keeping the others constant to point out the local sensitivity of the model to this parameter. However, many authors, like Saltelli and Anonni [START_REF] Saltelli | How to avoid a perfunctory sensitivity analysis[END_REF] or Campolongo et al. [START_REF] Campolongo | An effective screening design for sensitivity analysis of large models[END_REF], consider that this method does not allow a complete comprehension of the model, because it uses many shortcomings and does not take into account the influence of combined effects. Thus, a global sensitivity analysis with the method named ANOVA (ANalysis Of VAriance), by using the Sobol sensitivity indices [START_REF] Archer | Sensitivity measures, ANOVA-like techniques and the use of bootstrap[END_REF] has been chosen. We consider that every input parameter Xi is a random variable, and the vector of all input parameters (X1, … , Xp) is described by its multidimensional probability distribution. The model then works out the output result Y=f(X1, … , Xp), also considered as a random variable whose distribution depends on that of the parameters Xi. The Sobol sensitivity indices are defined by:

    | ()  i X i X i i Var E Y X
Var Y S [START_REF] Bao | A review of working fluid and expander selections for organic Rankine cycle[END_REF] Where 𝑋 𝑖 is the i-th input parameter and 𝑋 ~𝑖 represents all parameters excepted 𝑋 𝑖 . This sensitivity index represents the reduction of the variance of the output 𝑌 if the parameter 𝑋 𝑖 is fixed, that is to say the percentage of the variance of 𝑌 due only to the parameter 𝑋 𝑖 . We can also define the total sensitivity index STi as the value of the remaining variance of 𝑌 if all parameters but 𝑋 𝑖 are fixed:

    | ()  i X X i i i E Var Y X Var S Y T ( 13
)
Thus, 𝑆𝑇 𝑖 represents the percentage of the variance of 𝑌 due to the parameter 𝑋 𝑖 including its interactions with other parameters. In the case of an additive model, 𝑆 𝑖 = 𝑆𝑇 𝑖 .

In this study, all input parameters are processed to match independent random variables uniformly distributed on the interval [-1,1]. Then, Polynomial Chaos Expansion, as described in the work of Sudret or Crestaux et al. [START_REF] Sudret | Global sensitivity analysis using polynomial chaos expansions[END_REF], [START_REF] Crestaux | Polynomial chaos expansion for sensitivity analysis[END_REF] is conducted. This method is efficient when the number of input parameters is lower than 20 and the function is relatively smooth. This conditions are verified for this study because only 10 parameters are used and the variation of outputs is continuous and regular with the variation of each parameter.

The model is approached by its decomposition in multidimensional polynomial series. To respect the conditions of ANOVA, an orthogonal basis of Legendre polynomials is used, under uniformly distributed variables in [-1,1]. The process followed is then:

 Generation of

Hypothesis

Input parameters of the ORC model are given in Table 4. They are processed with an affine transformation to become variables distributed in [-1,1]. Hot seawater temperatures in Reunion Island have been monitored during a ten year period by the ECOMAR Laboratory [START_REF] Conand | A ten-year period of daily sea surface temperature at a coastal station in Reunion Island, Indian Ocean[END_REF]. This temperature only presents a seasonal fluctuation between 23 °C in winter and 28 °C in summer. In regards to the cold deep seawater temperature, a local study realized by the ARER [START_REF] Hoarau | Note d'opportunités pour l'utilisation de l'Energie Thermique des Mers et la valorisation de l'eau froide profonde à Sainte Rose[END_REF] shows that very weak fluctuations are observed around 5 ° C to 1000 m depth. Other parameters are derived from the OTEC onshore prototype data. A maximal polynomial degree of 𝑛 = 6 and a size of the random sample of 𝑁 = 1000 were found to be sufficient to achieve the convergence of the calculation.

Results

The parametric sensitivity analysis has been conducted for NH3, R507a and R1234yf. Results are presented in Table 5 and Figure 7. 𝜂 𝑝𝑢𝑚𝑝 0.03% 0.03% 0.03% 0.03% 0.00% 0.00% 0.00% 0.00% 0.06% 0.07% 0.07% 0.07% 𝛥𝑃 𝑐𝑜𝑛𝑑 0.00% 0.00% 0.08% 0.09% 0.00% 0.00% 0.01% 0.01% 0.00% 0.00% 0.01% 0.01% 𝛥𝑃 𝑒𝑣𝑎𝑝 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Firstly, values of Sobol sensitivity index 𝑆 𝑖 are very close to those of total sensitivity index 𝑆𝑇 𝑖 . That means that, considering the domain of definition given for input variables (see Table 4), the model can be considered, in a good approximation as additive (it can be represented as a sum of univariate functions).

Secondly, there are four very influent parameters that stand out in the investigated case: 𝑇 ℎ𝑤 , Δ𝑇 ̃𝑐𝑜𝑛𝑑 , Δ𝑇 ̃𝑒𝑣𝑎𝑝 and 𝜂 𝑡𝑢𝑟𝑏 . Variations of cold seawater temperature are not very influent because, for an OTEC application, it is relatively constant and well known, so this interval of variation is very restricted. The pump has a low influence on the output of the simulations. This can be explained by the fact that the work used in the pump is very low compared to the work produced by the turbine. On the contrary, the influence of the isentropic efficiency of the turbine is very important, because it affects directly the work produced by the ORC. The most interesting results are for variables describing the transformations in HEX.

Indeed, variations of EMTD in both HEX has a strong influence on outputs (even if 𝑤 𝑛𝑒𝑡,𝑣𝑜𝑙 is a little more influenced by the evaporator than by the condenser), but the subcooling in the condenser, the overheating in the evaporator and pressure drops in both HEX have very low values of sensitivity index. That is to say that, when entropic mean temperature differences are fixed, adding an overheating in the evaporator, for example, doesn't change the values of the criteria used for the working fluid comparison, even if this parameters have an impact on the structure of the cycle itself. Therefore, the use of entropic mean temperatures allows to describe the behavior of HEX by just one parameter for fluid comparison, and thus, when this parameter is fixed for every fluid, we can compare fluids in similar conditions of work. This is the advantage of this model in order to carry out a preliminary comparison of working fluids without prejudging the technology of the components.

It is also interesting to notice that the sensitivity analysis gives similar results for the three chosen working fluids. Thus, in the range of variation of the selected parameters, relative performances of this three fluids do not change. Conclusions drawn previously for OTEC are thus valid in the whole domain of variation of the parameters.

Conclusion

A model of an Organic Rankine Cycle applied to OTEC is built by using simple parameters (Δ𝑇 ̃𝑒𝑣𝑎𝑝 , Δ𝑇 ̃𝑐𝑜𝑛𝑑 , 𝜂 𝑝𝑢𝑚𝑝 , 𝜂 𝑡𝑢𝑟𝑏 , …) for describing the different components, in order to be applicable to every kind of technology and to compare performances of different kinds of fluids in similar conditions. For this purpose, heat exchangers are described by the entropic mean temperature difference parameter. This model is used to establish the behavior of 26 fluids, using experimental measurements of an OTEC onshore prototype as input parameters. A comparison of these fluids is then carried out by considering various criteria. In particular, for thermodynamic performances, we use a plot with the representation of a Pareto's frontier on which the choice is based. A parametric sensitivity analysis was then carried out in order to understand the behavior of the model and the importance of each parameter. The main results of this study are:

-In order to compare pure fluids and mixtures, the entropic mean temperature difference in HEX allows to draw the cycle with a reduced number of hypothesis and is more representative of similar working conditions of the different fluids than traditional parameters such as the output temperature difference.

-There is no fluid that meets at the same time great thermodynamic performances, easy implementation, safety and low environmental impacts. However, NH3 and R507a seem to be good candidates because they both have good thermodynamic performance (thermal efficiency and volumic work). Moreover, NH3 has very low environmental impacts (GWP, ODP, ALT), but it is toxic and mildly flammable (B2L). R507a is neither toxic nor flammable, but it has high values of GWP and ALT. R1234yf is also a good candidate, even if it ranks second of the thermodynamic study, it is nontoxic unlike NH3, and it has very low environmental impacts.

-The parametric sensitivity analysis revealed that, in the chosen domain of input parameters, the model is approximatively additive and the most relevant parameters are 𝑇 ℎ𝑤 , Δ𝑇 ̃𝑒𝑣𝑎𝑝 , Δ𝑇 ̃𝑐𝑜𝑛𝑑 , and 𝜂 𝑡𝑢𝑟𝑏 for this application.

This study will be useful for helping in choosing the working fluid of an ORC in a preliminary study preceding the design of the components.

Figure 1 .

 1 Figure 1. Schematic of a basic ORC applied to OTEC (E: Evaporator, T: Turbine, C: Condenser, P: Pump)

  3.a. Case when Ts is fixed 3.b. Case when 𝑇 ̃ is fixed Figure 3. Typical temperature evolution profile in an evaporator throughout the heat transfer progress for a pure fluid and a mixture.

Figure 4 :

 4 Figure 4 : State of the fluid at the turbine outlet and working pressure range for the 26 fluids of the panel

  liquid at the turbine outlet 1-x (%) Overheating at the turbine outlet T-T sat (P) ( C)

  ], ALT [years], ODP[.]

  per unit volume flow rate wnet, vol [kJ/m3]

Figure 7 .

 7 Figure 7. Values of Sobol sensitivity index for the different input parameters for two output variables: the thermal efficiency and the net volumic work.

Table 1 :

 1 Input parameters used for simulations

	External conditions
	Hot seawater temperature (Thw)	25.5°C
	Cold seawater temperature (Tcw)	5°C
	Evaporator
	Overheating (Tover)	0.1°C
	Pressure losses (Pevap)	0.15 bar
	EMTD (𝑇 ̃evap)	4°C
	Condenser
	Subcooling (Tsub)	0.1°C
	Pressure losses (Pcond)	0.15 bar
	EMTD (𝑇 ̃cond)	4°C
	Pump and turbine characteristics
	Pump isentropic efficiency (pump)	0.8
	Turbine isentropic efficiency (turb) 0.8

Table 2 :

 2 Best fluids from thermodynamic, security and environment point of view

	Fluids with better thermodynamic performances	Fluids with better safety indicator	Fluids with low ALT, GWP and ODP
	NH3	R507a	R134a R1234yf
	R507a	R236fa R404a	NH3
	SO2	R218	R12	R600a
		R114	R410a	R600
		R500	RC318	R290
		R22	R125
		R502	R407c

Table 3 :

 3 Properties of selected working fluids and simulation results. The inputs for this simulation are given in Table1.

	Type of fluid	State at the turbine outlet [%]	ASHRAE	wnet [kJ/kg]	wnet, vol [kJ/m 3 ]	ηth
	PURE FLUIDS
	R1234yf	isen 1	Overheated: 2.57°C	A2L	5.57	129.4	3.364%
	R143m	isen 1	Overheated: 1.37°C	n.a. 2	6.76	113.2	3.390%
	SO2	wet 1	Diphasic: x=98.0%	B1	12.74	82.9	3.383%
	NH3	wet 1	Diphasic: x=97.4%	B2L	41.98	203.4	3.387%
	R142b	isen 1	Overheated: 1.12°C	A2	7.46	68.1	3.376%
	R600	dry 1	Overheated: 3.04°C	A3	13.37	49.6	3.384%
	R236ea	dry 1	Overheated: 4.40°C	n.a. 2	5.89	44.7	3.392%
	R152a	wet 1	Diphasic: x=99.3%	A2	10.27	117.1	3.365%
	R236fa	dry 1	Overheated: 4.17°C	A1	5.53	57.7	3.390%
	R600a	dry 1	Overheated: 3.07°C	A3	12.28	68.8	3.375%
	R114	dry 1	Overheated: 4.81°C	A1	4.79	44.1	3.359%
	H2S	wet 1	Diphasic: x=97.3%	n.a. 2	14.98	345.0	3.328%
	R22	wet 1	Diphasic: x=98.5%	A1	6.73	191.0	3.340%
	R134a	isen 1	Overheated: 0.34°C	A1	6.67	130.3	3.356%
	R12	wet 1	Overheated: 0.08°C	A1	4.97	117.9	3.271%
	R32	wet 1	Diphasic: x=96.6%	A2	9.99	302.8	3.323%
	R290	isen 1	Overheated: 0.31°C	A3	12.49	167.3	3.332%
	RC318	dry 1	Overheated: 6.38°C	A1	4.07	65.2	3.382%
	R125	isen 1	Overheated: 0.61°C	A1	4.29	239.1	3.285%
	R218	dry 1	Overheated: 4.98°C	A1	3.08	157.2	3.313%
	AZEOTROPIC MIXTURES
	R500	wet 1	Diphasic: x=99.7%	A1	5.95	138.6	3.257%
	R502	wet 1	Diphasic: x=99.9%	A1	4.55	193.5	3.153%
	R507a	wet 1	Diphasic: x=99.9%	A1	5.32	230.0	3.352%
	ZEOTROPIC MIXTURES
	R410a	wet 1	Diphasic: x=97.6%	A1	7.01	292.0	3.305%
	R404a	wet 1	Diphasic: x=99.9%	A1	5.42	222.1	3.326%
	R407c	wet 1	Diphasic: x=99.0%	A1	7.05	208.2	3.334%

  random sets of parameters with respect to the given distribution  Computation of the model results for each set of parameter  Determination of the coefficients 𝑎 𝑖 1 ,…,𝑖 𝑠 of the multidimensional Legendre polynomial (𝑃 𝑖𝑗 ) series that best fit the results (least square method) : Calculation of Sobol sensitivity indices: equations 12 and 13 are applied for the result given in equation 14 (for further details, see the work of Crestaux et al.[START_REF] Crestaux | Polynomial chaos expansion for sensitivity analysis[END_REF]).

	f		X	1	,...,	X	p				n ,..., ii s 1  i i i i ,..., ,..., 11   s ss a P		X	1 i	,...,	X	s i			1 1 a P	(	X	1	)		2 2 P X ( ) 2 a	12 12  1 2 ( , ) X a P X	.. .	(14)
			

Table 4 .

 4 Hypothesis of the parametric sensitivity analysis, each variable Xi is uniformly distributed in [-1,1].Two output variables are considered:-thermal efficiency 𝜂 𝑡ℎ = 𝑓(𝑋 1 , … , 𝑋 10 ) and -net volumic work 𝑤 𝑛𝑒𝑡,𝑣𝑜𝑙 = 𝑔(𝑋 1 , … , 𝑋 10 ).

	Variables Unit	Mean Value	Variation interval	Transformation
	𝑇 ℎ𝑤	°C	25.5	[ 23 ; 28 ]	𝑇 ℎ𝑤 = 25.5 + 2.5𝑋 1
	𝑇 𝑐𝑤	°C	5	[ 4.8 ; 5.2 ]	𝑇 𝑐𝑤 = 5 + 0.2𝑋 2
	𝛥𝑇 𝑜𝑣𝑒𝑟	°C	1	[ 0.5 ; 1.5 ]	𝛥𝑇 𝑜𝑣𝑒𝑟 = 1 + 0.5𝑋 3
	𝛥𝑇 𝑠𝑢𝑏	°C	1	[ 0.5 ; 1.5 ]	𝛥𝑇 𝑠𝑢𝑏 = 1 + 0.5𝑋 4
	𝛥𝑇 ̃𝑒𝑣𝑎𝑝	°C	4	[ 2 ; 6 ]	𝛥𝑇 ̃𝑒𝑣𝑎𝑝 = 4 + 2𝑋 5
	𝛥𝑇 ̃𝑐𝑜𝑛𝑑	°C	4	[ 2 ; 6 ]	𝛥𝑇 ̃𝑐𝑜𝑛𝑑 = 4 + 2𝑋 6
	𝜂 𝑡𝑢𝑟𝑏	%	0.8	[ 0.7 ; 0.9 ]	𝜂 𝑡𝑢𝑟𝑏 = 0.8 + 0.1𝑋 7
	𝜂 𝑝𝑢𝑚𝑝	%	0.8	[ 0.7 ; 0.9 ]	𝜂 𝑝𝑢𝑚𝑝 = 0.8 + 0.1𝑋 8
	𝛥𝑃 𝑐𝑜𝑛𝑑	bar	0.15	[ 0 ; 0.3 ]	𝛥𝑃 𝑐𝑜𝑛𝑑 = 0.15 + 0.15𝑋 9
	𝛥𝑃 𝑒𝑣𝑎𝑝	bar	0.15	[ 0 ; 0.3 ]	𝛥𝑃 𝑒𝑣𝑎𝑝 = 0.15 + 0.15𝑋 10

Table 5 .

 5 Results of the parametric sensitivity

analysis NH3 R1234yf R507a ηth wnet, vol ηth wnet, vol ηth wnet, vol

		Si	STi	Si	STi	Si	STi	Si	STi	Si	STi	Si	STi
	𝑇 ℎ𝑤 35.41% 35.61% 40.88% 41.18% 35.75% 35.95% 42.08% 42.39% 35.14% 35.37% 40.16% 40.49%
	𝑇 𝑐𝑤	0.25% 0.25% 0.14% 0.14% 0.25% 0.25% 0.12% 0.12% 0.24% 0.24% 0.13% 0.13%
	𝛥𝑇 𝑜𝑣𝑒𝑟 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
	𝛥𝑇 𝑠𝑢𝑏 0.00% 0.00% 0.01% 0.02% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01%
	𝛥𝑇 ̃𝑒𝑣𝑎𝑝 22.66% 22.78% 26.16% 26.35% 22.89% 23.01% 26.94% 27.13% 22.49% 22.63% 25.70% 25.91%
	𝛥𝑇 ̃𝑐𝑜𝑛𝑑 25.14% 25.27% 13.59% 13.73% 25.05% 25.19% 11.97% 12.11% 24.20% 24.36% 13.32% 13.48%
	𝜂 𝑡𝑢𝑟𝑏 16.06% 16.51% 18.53% 19.04% 15.60% 16.05% 18.31% 18.81% 17.32% 17.85% 19.95% 20.55%

isentropic, wet or dry: type of the fluid depending on the slope of the saturated vapor curve

n.a.: not available

Acknowledgements

The authors particularly acknowledge Jérôme Vigneron, technician in the laboratory of Physical and Mathematical Engineering for Energy and Environment, for his investment in the experimental work of the laboratory.

Funding

This work was supported by DCNS Energy, the territorial authority Region Reunion and the laboratory of Physical and Mathematical Engineering for Energy and Environment in Reunion Island.