High-Throughput Screening of Working Fluids for the Organic Rankine

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High-Throughput-Screening of Working Fluids for the Organic Rankine Cycle (ORC) based on COSMO-RS and Thermodynamic Process Simulations Johannes A. H. Schwöbel, Markus Preißinger, Dieter Brüggemann, and Andreas Klamt Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b03857 • Publication Date (Web): 22 Dec 2016 Downloaded from http://pubs.acs.org on December 27, 2016

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Industrial & Engineering Chemistry Research

High-Throughput-Screening of Working Fluids for the Organic Rankine Cycle (ORC) based on COSMO-RS and Thermodynamic Process Simulations Johannes A. H. Schwöbel1,*,‡, Markus Preißinger2,‡, Dieter Brüggemann2, Andreas Klamt1,3

1

COSMOlogic GmbH & Co. KG, Imbacher Weg 46, 51379 Leverkusen, Germany

2

Center of Energy Technology (ZET), Chair of Engineering Thermodynamics and Transport

Processes (LTTT), University of Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany 3

Institute of Physical and Theoretical Chemistry, University of Regensburg, Universitätsstraße

31, 93053 Regensburg, Germany

KEYWORDS Organic Rankine Cycle; ORC; COSMO-RS; Cubic Equations of State; Patel-Teja EoS; Process Simulation; Vapor Pressure; Critical Point; Critical Temperature; Critical Volume; Critical Pressure; High-Throughput Screening; HTS; Vapor-Liquid Equilibrium; VLE; Fluid Selection

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ABSTRACT

Waste heat recovery by a thermodynamic Organic Rankine Cycle (ORC) is an auspicious technique to increase the efficiency of motor vehicles and, therefore, reduce fuel consumption and carbon dioxide emission. Instead of relying on a limited number of currently known ORC fluids, a high-throughput screening (HTS) was performed in the search for the optimal fluid. This screening covered almost the complete known chemical space based on the structures provided by the PubChem database with more than 72 million entries. After application of structural and thermodynamic filter criteria based on quantum chemical calculations for more than 2 million structures, a set of 3,147 potential working fluids was considered for a ranking by thermodynamic performance. A combination of computational chemistry methods to predict all physico-chemical properties of interest by the COSMOtherm software (e.g., vapor pressures, critical points) and thermodynamic process simulation (e.g., net power output) by the fast simulation tool DetailSimORC was applied. The COSMO-RS theory was combined with a generalized Patel-Teja equation of state to extend the applicability range of the thermodynamic calculations up to the critical point. The screening turned out to be successful and revealed that only twelve compounds in the TOP 100 list (ranked by thermodynamic performance) have been considered before as ORC working fluids.


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INTRODUCTION To meet future regulatory targets on fuel savings in heavy duty trucks and passenger cars, the usage of waste heat from the exhaust gas based on the Organic Rankine Cycles (ORC) has gained increased interest in the last years.1 However, the performance of the thermodynamic cycle strongly depends on the working fluid, its pressure levels and the efficiency and kind of expander. The Organic Rankine Cycle (ORC) differs from the conventional Rankine Cycle (RC) through the usage of an organic working fluid instead of water. The technology is almost state of the art for biomass-fired power plants as well as for geothermal applications,2–4 where siloxanes or alkylbenzenes are used in high temperature,5,6 alkanes and refrigerants in low temperature applications.7–9 One advantage of the ORC compared to the RC is the huge number of available working fluids, each having different thermodynamic properties (e.g., critical temperature and pressure). According to the heat source temperature, a thermodynamic optimal working fluid (in terms of evaporation temperature, slope of the temperature/entropy-diagram etc.) can be selected for specific applications in the automotive sector, such as heavy trucks or passenger cars. Linke et al. have published an excellent review on systematic methods for working fluid selection on ORC. They showed that until about 2010 working fluid selection was based on limited databases just including several hundred working fluids.10 Instead of relying on a limited number of currently known ORC fluid systems, different approaches have been reported in literature. Several research groups use Computer-Aided Molecular Design (CAMD),11–17 which results in virtual fluids and requires post-processing to evaluate their synthetic accessibility. Another approach is to focus on already synthesized chemical substances from the very beginning. Kazakov et al. demonstrated the strenght of this approach in the context of refrigerants.18–20 However, no study on ORC working fluid selection 3 ACS Paragon Plus Environment


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based on this approach have been found in the literature. Therefore, a High-ThroughputScreening (HTS) is performed in the search for the optimal ORC working fluid, covering the complete known chemical space up to 108 structures. For this reason, the German Research Association for Combustion Engines (FVV) initiated a project to find an optimal fluid for the exhaust gas usage in mobile applications by screening the complete chemical space defined by the PubChem database that covers around 72 million entries at the moment. Possible advantages of such a fluid could be: 1. higher net power output and, therefore, higher fuel savings and CO2 reduction; 2. lower costs and reduced weight and size of the Rankine-system (e.g. through different pressure levels); 3. lower additional costs for condensation/cooling of the working fluid (e.g. through improved thermodynamic behaviour). Furthermore, by finding an optimal fluid that all OEMs and supplier accept as the standard fluid, reduced manufacturing costs, reduced research and development costs for components and the overall system and reduced effort for certification and market entry may be achieved. To find the optimal fluid, a simulation tool in Matlab is programmed and combined with thermodynamic properties from the COSMOtherm software to ensure that the complete known chemical space can be investigated and simulation results can be gained in less than five seconds per working fluid. Such screening requires the knowledge of a set of basic thermodynamic data for each of the compounds, or at least good etimates of them. These were generated by the Conductor-like Screening Model for Realistic Solvation (COSMO-RS) methodology, which is based on quantum chemical calculations and, therefore, suitable in the full organic chemistry space and not biased towards specific compound classes.21 To extend the applicability domain of COSMO-RS (which is designed to handle liquids as incompressible fluids) up to the critical point of vapor-liquid equilibria (VLE), the methodology is combined with cubic equations of state. This was investigated before for the Peng-Robinson 4 ACS Paragon Plus Environment

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equation of state by the workgroup of Leonhard.22 However, we decided to use the more general Patel-Teja equation of state23 together with a general COSMO-RS based functionality of the temperature dependent interaction parameters (electrostatic interactions, hydrogen bonds, van der Waals etc.), as well as a prediction of the critical point. This new approach assures a general applicability of the equation of state, independent of the particular compound class of investigation, ranging from non-polar alkenes, aromatic compounds, refrigerants up to polar alcohols and siloxanes at the same time. To summarize, this study aims to find the highest performing ORC working fluid for waste heat recovery in mobile applications in terms of net power output and, therefore, to meet future regulatory targets for overall fuel consumption and CO2 emission.



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MATERIALS AND METHODS COSMO-RS. The quantum chemically based Conductor-like Screening Model for Realistic Solvation (COSMO-RS) is a rather general method for predicting the chemical potentials of almost arbitrary molecules in almost any dense pure or mixed liquid. This chemical potential difference can be transformed into properties such as vapor pressures, activities or solubilities. In general, COSMO-RS is composed of two fundamental steps: At first, quantum chemical calculations have to be performed for all compounds of interest. In these calculations a virtual conductor embedding the molecule is taken into account by the continuum solvation model COSMO.24 The molecule induces a polarization charge density σ on the interface to the conductor, and these charges interact with the molecule, generating a more polarized electron density than in vacuum. Simultaneously solving the quantum chemical equations and the conductor boundary condition, the solute molecule is optimized with respect to electron density and geometry to its energetically optimal state in a conductor, and the energies, geometries and polarization charge densities on the surface segments get stored in a COSMO file. In the second step of COSMO-RS, the statistical thermodynamics of the molecular interactions, this polarization charge density is used for the quantification of the interaction energy of pairs of surface segments. As most important molecular interaction modes, electrostatics and hydrogen bonding are taken into account in this way. The less specific dispersive interactions are described to first order based on element specific surface energies. The electrostatic energy deviations to the conductor reference state are taken into account as misfit energies 6 ACS Paragon Plus Environment

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1 Emisfit (σ , σ ' )= aeff α misfit (σ+σ ' )2 2

(1)

and the additional hydrogen bond interaction energy is quantified approximately as 2

Ehb (σ ,σ ' )=a eff c hb( T ) min ( 0 , σ σ '−σ hb )

(2)

where σ and σ‘ are the polarization charge densities of the two interacting surface segments and aeff is the effective size of a thermodynamically independent contact. αmisfit is the misfit energy coefficient, taking into account the average electronic polarizability of the neighboring molecules. The hydrogen bond coefficient chb has a temperature dependence which expresses the entropy loss going along with hydrogen bond formation, and σmin is a kind of minimum polarity for hydrogen bond formation. The quantum chemical information about the polarization charge densities σ plays the key role for the evaluation of the molecular interactions in the liquid phase. As a preparation for an efficient statistical thermodynamics treatment, the 3D distribution of the polarization charge densities σ on the surface of each molecule is converted into a surface composition function pX(σ), commonly called σ-profile. It describes the amount of molecular surface with polarity σ on the surface of a particular molecule. σ-profiles provide detailed information about the molecular polarity distribution.21,25,26 For the purpose of the calculation of vapor-liquid equilibria, separate gas phase quantum chemical calculations are performed for each molecule and its relevant conformations. The σ-profiles of typical working fluids are shown in Figure 1. Based on the surface pair interaction model introduced above, the statistical thermodynamics itself is done using a coupled set of non-linear equations for the activity coefficients of the surface segments.27 This results in a solvent specific free energy response function μ S(σ), called σ-potential, which gives the chemical potential of a surface segment of polarity σ in a particular solvent.



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μ S (σ)=−kT ln

(

(

E (σ , σ ')−μ S (σ ')

∫ p s (σ ') exp −kTint

) ) d σ'

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(3)

Finally, the chemical potentials of the compounds in a pure or mixed solvent are calculated by summation of the σ-potentials of the surface segments of a compound and slightly corrected by an empirical combinatorial term which takes into account surface areas and volumes of solutes and solvents resulting from the COSMO cavities. The chemical potential μ forms the basis for the prediction of thermodynamic vapor-liquid equilibria, e.g., vapor pressures:

(

pivap (T ) μ i (T )−μ iliq (T ) =exp − gas pref RT

)

(4)

The relationship to a series of thermodynamic equilibrium properties is presented in the literature.21 Equation of State Model. The classic COSMO-RS theory is based on the assumption of incompressible liquids and ideal gases. The ORC process, however, uses temperatures and pressures up to the critical point. In this range of application, the treatment of both liquid phase compressibility and real gas behaviour is essential. In order to extend the applicability range of COSMO-RS, the theory is combined with cubic equations of state. The latter are routinely used in engineering applications, while being more empirical in nature. There have been different approaches to combine these two levels of theory, especially with regard to the Peng-Robinson equation of state.22,28,29 In the ORC fluid screening an equation of state with a general applicability to all compound classes of investigation is required, including non-polar and polar compounds, with and without hydrogen bonding potential or dispersive interactions. Dispersive interactions are especially important with regard to typically halogenated refrigerants. For this reason, an internally modified version of the PatelTeja equation of state is chosen:23 8 ACS Paragon Plus Environment

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p(V , T )=

a α (T ) RT − V −b V (V + b)+ c(V −b)

(5)

Of the cubic equations of state, the Patel-Teja equation shows the best general performance in predicting specific enthalpies, specific entropies and liquid phase densities.30 The initial step of each equation of state is the knowledge about the pure compound critical point. As will be shown below, the critical temperature can be correlated to the boiling point, predicted by the application of COSMO-RS. The critical volume is well-correlated to the COSMO volume in a non-linear fashion. And the critical pressure of organic molecules can be predicted by an evaluation of a logarithmic function of the critical volume and critical temperature ratio. The Patel-Teja parameters a, b, c can be calculated based on critical point data, and the temperature dependence α(T) based on COSMO-RS derived vapor-liquid equilibria (details shown in the supporting information). Now the cubic equation for the compressibility calculation can be solved by standard root-finding algorithms for each temperature and pressure point. The liquid and vapor phase density is directly correlated to the particular compressibility. At the same time, the liquid or vapor phase compressibility is the basis for the fugacity, specific enthalpy and specific entropy calculations, which are requested as input parameters for ORC simulations. Specific enthalpies and entropies are calculated from the Patel-Teja equation of state as described in the literature.31,32 Database. The ORC fluid screening requires a preferably diverse chemical structure dataset, if possible containing the complete known chemical space. For this purpuse, the PubChem33 database containing about seventy million unique entries was chosen for several reasons: it is the largest inventory publically available, so the coverage of the complete known chemical space is very likely. And the database is accessible in an automatized manner via its power user gateway. 9 ACS Paragon Plus Environment


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Workflow and Software Packages. A scheme of the calculation workflow is presented in Figure 2. To initiate the automatized workflow, the particular molecular structures are required. The molecular structures are extracted from the PubChem database. While the investigation covers ‒ in principle ‒ the complete known chemical space, a range of thermodynamic criteria should be fulfilled for a successful operation of an ORC thermodynamic cycle. All of these thermodynamic criteria are applied to the full PubChem database, resulting in a screening of the dataset. The initial analysis of the molecular formula is very fast, applying the basic filter criterion of the maximum atom count, not counting hydrogen or fluorine atoms. As an initial guess, compounds having more than 15 atoms ‒ not counting hydrogen or fluorine ‒ would have too low vapor pressures and are excluded, therefore. A more detailed analysis searches for potential reactive substructures as part of the molecular structure, also called chemotypes, 34 and excludes compounds containing at least one adverse substructure match. Based on organic chemical knowledge, reactive substructures are excluded, which would in the extreme case initiate bursting or explosions while operating under high temperature and pressure ORC conditions. For example, such substructures are peroxides, nitro groups or alkynes (e.g., acetylene). At the same time, ionic compounds, isotopes, metal or metalloid containing compounds are removed from the screening datasets. The exception are silicone containing compounds, as siloxanes are used as high-temperature working fluids on a regular basis.5,6 These reactive substructures are defined by so-called SMARTS patterns (“SMiles ARbitrary Target Specification”) based on common organic chemical knowledge.18 For all compounds passing the initial structure-based filter criteria, computationally demanding quantum chemical calculations are started for the generation of COSMO surfaces. These calculations are performed by the TURBOMOLE software.35 Individual conformers (i.e., different possible molecular 3D structures of a particular compound) have not been generated for 10 ACS Paragon Plus Environment

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initial screening calculations at the SVP level, but for the accurate TZVPD-FINE level (see next section) by the COSMOconf software.36 Having the COSMO surfaces at hand, subsequent COSMO-RS calculations are run by the COSMOtherm software package for the prediction of thermodynamic filter criteria, vapor pressure curves and all parameters required by equation of state calculations. 37 Additionally, melting points are predicted by the COSMOquick software, which also provides the SMARTS pattern analysis functionality described above.38,39 At this stage, the next set of compounds can be excluded not passing the thermodynamic criteria. The minimum pressure of condensation is set to 75 kPa at 100 °C (i.e., the operational point with the largest condensation temperature). And the full ORC process should be driven in a subcritical way. Therefore, the critical temperature is set as last filter criterion, which should be larger than 70 °C. Specific enthalpies and entropies require information about pressure and temperature dependent heat capacities. These are obtained by analysis of the vibrational, translational and rotational degrees of freedom, as available from the MOPAC software 40 at the most recent PM7 parameterization,41,42 or alternatively from TURBOMOLE calculations at the TZVP level. The vibrational analysis is also required for IR spectra as essential part for the prediction of the global warming potential (GWP), which will be presented in an upcoming publication. The final step in the workflow for a particular compound is the calculation of ORC simulation specific input parameters: liquid and vapor phase densities, enthalpies and entropies in a temperature range between 0 °C and 300 °C and a pressure range between 75 kPa and the critical pressure. These ORC specific thermodynamic properties are passed to the DetailSimORC simulation software via look-up-tables. DetailSimORC is a MATLAB® source code developed at the Center



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of Energy Technology (ZET) of the University of Bayreuth, and firstly published in this publication. The individual steps were assembled to the full workflow by a Python interface to the software packages described above, called COSMOpy.43 Quantum Chemical Level. Quantum chemical calculations can be performed at different levels of theory and accuracy. The screening of a large number of compounds typically requires a good compromise between computational demands of quantum chemistry and quality of the thermodynamic predictions. This includes the optimization of molecular geometry on a computationally cheap semi-empirical level with a subsequent calculation of the COSMO surface by the density functional theory functional B88-VWN-P86 using the small def-SVP basis set (in short: “SVP” level). On avarage, for small- to medium-sized compounds the computational time is about twenty seconds per molecule. The fast screening level is optimal for the purpose of filtering out thermodynamically unsuitable fluids from the simulation dataset. However, a higher thermodynamic prediction quality is recommended for the final engineering applications. The currently best performance is achieved with a full optimization of the molecular geometry using the larger def-TZVP basis set and COSMO calculations using the def2-TZVPD basis set with additional diffuse basis functions and a novel fine grid cavity (in short: “TZVPD-FINE” level). However, the computation time is significantly larger than for the screening level, on average about ten to thirty minutes per conformer. Thus, this level cannot be applied to the original PubChem set of millions of compounds, but certainly to a pre-filtered set of thousands of potential ORC fluids. ORC

Simulations.

Thermodynamic

process

simulation

are

carried

out

in

DetailSimORC. It is a steady state simulation model for ORCs in mobile application which is based on energy balances and thermodynamic fluid properties. A simplified flow chart is given in Figure 3. Starting from a given condensation temperature and subcooling temperature 12 ACS Paragon Plus Environment

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difference, the condensation pressure is calculated. Subsequently, a polytropic pressure increase and an isobaric heat input takes place. After the polytropic expansion and condensation of the working fluid, state point 1 is reached again. In a first step, net power output is taken as evaluation criterion. Net power output can steadily increase as well as decrease with working pressure or a bell-shaped behavior is observed.3 To reproduce this dependency, DetailSimORC is based on a polynomial simulation approach. First, the highest possible working pressure according to the given boundary conditions is simulated, followed by four additional simulations at 25 %, 50 %, 75 % and 95 % of the maximum pressure. If a bell-shaped behavior is observed, the optimum working pressure is deduced from the polynomial dependency and taken for further calculations. Within DetailSimORC it is possible to distinguish between two different ORC configurations displayed in Figure 4. The first configuration is applied for passenger cars without exhaust gas recirculation. However, for waste heat recovery from heavy duty trucks the exhaust gas energy from aftertreatment as well as energy from exhaust gas recirculation are taken into account based on a configuration with mass flow splitting after the pump. In case of mass flow splitting, both streams have to be fully evaporated. Further boundary conditions are summarized in Table 1. Calculation Time. One important aspect of a high-throughput screening is the calculation time, in other words, the computational resources required for the achievement of the project goals. The overall calculation time per fluid (and single CPU core on a contemporary Linux cluster computer) in the full workflow can be divided into the following parts: the DetailSimORC simulations are very fast, about 2 seconds per simulation run. The simulations are based on general look-up tables, which can be used multiple times for each operational point and each of the evaporation temperatures. The COSMO-RS calculations and generation of look-up tables last for around 1 ‒ 2 minutes per fluid, including typically 18,000 temperature/pressure points and 80,000 thermodynamic values per fluid. The most time-consuming part are the 13 ACS Paragon Plus Environment


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quantum chemical COSMO calculations: around twenty seconds per fluid at the screening level (SVP) and around fifteen minutes up to a few hours per fluid at the accurate level (TZVPDFINE), including the generation of multiple conformers. The quantum chemical calculations are required only once per fluid, afterwards any subsequent thermodynamic prediction can be performed relatively fast.

RESULTS AND DISCUSSION Prediction of the Critical Point. Vapor-liquid critical points are one prerequisite for the application of equation of state models. The experimental critical point data are collected from the literature.44–48 In order to keep the critical temperature Tcrit prediction as general as possible, a polynomic relationship to the experimental boiling point Tboil at standard pressure is applied, irrespective of the actual compound class. Indeed, this provides a reliable relationship for organic compounds in general: Tcrit = 1.68 Tboil − 4.68 10-4 Tboil2

(6)

n = 335; R2 = 0.976; AAE = 3.8 %; SE = 23 K. Here, n is the number of compounds, R2 the squared Pearson correlation coefficient; AAE the average absolute percentage error and SE the standard error. The experimental boiling points Tboil and critical temperatures Tcrit values (both in K) used for this correlation are listed in the supporting information. A closer inspection reveales (see Figure 5) that there is a deviation in the prediction for linear alkanes in the high temperature range (boiling points Tboil > 500 K), starting with tetradecane up to tetracosane. The deviation is probably caused by larger entropic contributions (because of the larger flexibility in the conformational space) and vibrational


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contributions (because of the higher boiling point temperature), as compared to alkanes with shorter chain lengths. The regression, now applied to linear or branched − but not to cyclic − alkanes in the dataset leads to the following excellent relationship: Tcrit (alkanes) = 1.80 Tboil − 9.11 10-4 Tboil2

(7)

n = 70; R2 = 0.999; AAE = 1.0 %; SE = 5.5 K However, the ORC process relies on volatile compounds, therefore high molecular weight alkanes such as tetradecane (or higher) are not of interest in this study. As a consequence, we stick to the general relationship above for all compound classes (eq. 6). Next, inorganic compounds (e.g., hydrazine, bromine, iodine, tri-/tetra-/pentasulfane) are clearly out of domain of the organic chemistry space, so these compounds are left out in the relationship above. Experimental boiling points are mostly not available in the screening of the known chemical space. So in the following, the boiling point Tboil is systematically predicted by the COSMO-RS methodology. On the TZVPD-FINE level, the correlation between predicted and experimental Tcrit values is as follows, using calculated boiling points: Tcrit,exp. = 0.993 Tcrit,calc.

(8)

n = 370; R2 = 0.868; AAE = 4.3 %; SE = 33 K Without making any adjustments, the slope is very close to one, and the errors are in a similar range as in the direct relationship with experimental boiling points (4.3 % versus 3.8 %). The critical volume Vcrit (in m3/mol) has a clear polynomic relationship to the COSMO volume (in Å3, at TZVPD-FINE level, see Figure 6): Vcrit = 1.467 10-9 VCOSMO2 + 2.130 10-6 VCOSMO

(9)

n = 248; R2 = 0.986; AAE = 5.3 %; SE = 0.285 10-4 m3/mol



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The relationship between experimental critical pressures pcrit (in kPa) and the other critical parameters is logarithmic in nature (Tcrit in K; Vcrit in m3/mol; R is the ideal gas constant: 8.314 10-3 kJ/mol/K, see Figure 7): log10(pcrit) = 0.938 log10(R Tcrit / Vcrit) − 0.330

(10)

n = 465; R2 = 0.945; AAE = 0.85 %; SE = 0.051 log10(kPa) units This critical pressure pcrit prediction method is independent of the actual compound class, in the following using predicted Tcrit and Vcrit values instead of experimental ones. Combined COSMO-RS and Equation of State Model. Having all the critical parameters at hand, the compound specific Patel-Teja parameters a (attractive interactions), b (repulsion) and c (compressibility related factor) can be calculated from mathematical side conditions at the critical point, more specific, for the occurence of an inflection point on an isotherm in the p/V plane, eventually resulting in the following relationships for the Patel-Teja equation:46–48 a=Ωa

(RT crit )2 ; with: Ω a=3 ζ 2crit +3(1−2 ζcrit )Ωb +Ω2b +1−3 ζcrit p crit

(11)

b=Ωb

(RT crit ) ; with: Ω3b +( 2−3 ζ crit) Ω2b +3 ζ crit 2Ω b−3 ζ 3crit=0 p crit

(12)

c=Ω c

(RT crit) ; with: Ωc =1−3 ζcrit p crit

(13)

As shown in the equations (11 ‒ 13), the Patel-Teja equation uses the critical compressibility related parameter ξcrit as additional degree of freedom (in contrast to the Peng-Robinson equation, which assumes a constant critical compressibility for all liquids). The next step is the calculation of the temperature dependent interaction parameter α(T) of the Patel-Teja equation. Classical cubic equations of state lack the correct treatment of molecular interaction terms in a predictive manner,49 e.g. hydrogen bonds. Therefore, it was decided not rely on empirical relationships (e.g. based on acentric factors), but on the explicit temperature 16 ACS Paragon Plus Environment

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dependent COSMO-RS calculation of these interaction parameters, as included for example in the vaporization enthalpy. The COSMO-RS vaporization enthalpy is weighted by an exponential factor to the correct vaporization enthalpy up to the critical temperature, where it should become zero by definition. The parameters of the exponential factor are calibrated in order to reproduce experimental vaporization enthalpy curves best in a wide temperature range. Based on these corrected COSMO-RS vaporization enthalpies, the interaction parameter α(T) can now be calculated systematically for all compound classes and the full temperature range up to the critical temperature. The calculation method for the compound specific Patel-Teja parameters a, b, c and α(T) is presented in the supporting information. A temperature dependent state point interpolation is applied for the pure compound liquid compressibility (linear interpolation) and vapor compressibility (quadratic polynomial interpolation) at a particular pressure in order to speed up the calculations by about a factor of 12. Comparison of COSMOtherm and RefProp Data. For validation purposes, the COSMOtherm predictions are compared to the NIST RefProp database as benchmark in engineering applications.50 Overall, the COSMOtherm predictions are in a good agreement with RefProp data for a diverse set of small molecules, as shown below for the nonpolar compound nhexane (see Figure 8), the refrigerant R-245fa and the polar compound ethanol on the accurate level for engineering applications (TZVPD-FINE). The vapor pressures in a range between 0 °C and the critical temperature are correlated in an excellent way on a decadic logarithmic scale: hexane (correlation coefficient r2 = 99.86 %; standard error se = 0.030); R-245fa (r2 = 99.99 %; se = 0.003); ethanol (r2 = 99.88 %; se = 0.038). The specific enthalpies along the vapor pressure curve in the same temperature range as above are also well-correlated: hexane (r2 = 99.67 %; average relative error = 3.0% for the liquid phase 17 ACS Paragon Plus Environment


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and 1.2% for the vapor phase); R-245fa (r2 = 99.49 %; average relative error = 3.8 % liq.; 2.8 % vap.); ethanol (r2 = 98.64 %; average relative error = 5.8 % liq.; 4.5 % vap.). The same holds for the specific entropies along the vapor pressure curve: hexane (r2 = 99.04 %; average relative error = 4.7 % for the liquid phase and 1.3 % for the vapor phase); R-245fa (r2 = 99.53 %; average relative error = 5.4 % liq.; 1.7 % vap.); ethanol (r2 = 99.30 %; average relative error = 5.1 % liq.; 5.2 % vap.). It is worthwhile mentioning that all COSMOtherm predictions shown here are entirely ab initio based without a single experimental data point (e.g., critical point data) being used. The accuracy can be improved further by including available experimental data (e.g., from the database COSMObase51). This is not shown here, as the purpose is the systematic prediction of thermodynamic data especially for the complete known chemical space, where experimental data are mostly unavailable. For a primary analysis about the predictivity of the equation of state based simulations, about twenty potential ORC working fluids were selected from RefProp. DetailSimORC simulation results based on RefProp data were compared to equivalent simulation results based on entirely predicted thermodynamic values. It turned out that the deviation in thermal efficiency of the ORC simulations was less than 2.4 % on average and generally less than 6 % for the investigated working fluids, even at the initial screening level (SVP), as shown in Figure 9. Application of Filter Criteria. Suitable working fluids are extracted from the full PubChem database. For this reason, thermodynamic filter criteria are applied, as described in the methods section. The performance of the individual filter criteria is as follows: The initial screening dataset starts with 72,725,677 PubChem entries. The molecular formula is checked first and apparently unsuitable entries, are excluded, for example, too large compounds, multi-compound structures, ionic structures, or metal or isotope containing compounds. This way, the dataset is reduced by 96 % to 2,849,780 structures. The stability filter excluding 18 ACS Paragon Plus Environment

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compounds with reactive substructures reduces the dataset further by 5 % to 2,697,529 structures. Still, around three million structures have to be evaluated by thermodynamic COSMOtherm calculations. The most efficient filter is the vapor pressure criterion, reducing the dataset further by 99.75 % to “only” 6,782 structures. And finally, the minimum critical temperature criterion keeps 6,384 structures in the ORC simulation screening dataset, thus removing 6 % of the remaining structures. The initial DetailSimORC simulations of those 6,384 structures are based on the ‒ faster, but less accurate ‒ SVP screening level. The best performing TOP 100 ORC fluids are selected for further evaluation at the more accurate TZVPD-FINE level. To include existing knowledge about working fluids, this TOP 100 dataset is combined with a set of known working fluids. This set contains 274 organic compounds used as working fluids in thermodynamic cycles, or which have been investigated before in the context of the ORC process according to a literature research and experiments performed at the Center of Energy Technology (ZET), Bayreuth. Next, a list of typical chemical refrigerants with R numbers designated from the society of the American Society of Heating, Refrigerating and AirConditioning Engineers (ASHRAE) are included in the dataset of known working fluids. Now, more restrictive filter rules are applied to the remaining and filtered PubChem dataset (but not to the TOP 100 or known working fluids): compounds with double bonds or containing sulfur are excluded for stability or olfactory reasons. Finally, duplicates, stereo-isomers (better to say, enantiomers; as R- and S-isomers provide the same thermodynamic efficiency), and flawed structures (according to a COSMOquick based integrity check) are removed. The refined set for further evaluation at the TZVPD-FINE level contains 3,174 fluids. Subsequently, these are evaluated by accurate DetailSimORC simulations. 19 ACS Paragon Plus Environment


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Simulation of Thermodynamic Performance. Thermodynamic process simulation is carried out for two different applications, namely waste heat recovery for heavy duty trucks and for internal combustion engines of passenger cars. First, the influence of the screening levels SVP and TZVPD-FINE is analyzed for about 450 working fluids (see Figure 10). It is obvious that the general trend of net power output for the application passenger car is similar for both screening levels. However, the scattering is significant. Therefore, TZVPD-FINE level is applied for the filtered set of 3,174 fluids as stated above. Ranking by Thermodynamic Net Power Output. Based on the mentioned two applications and three condensation temperatures, net power output of six operational points is evaluated for 3,174 working fluids. Three operational points are taken from the engine map of a heavy duty truck, the other three from a passenger car. All operational points represent typical engine operational points in the driving cycle. A fully dynamic simulation including for example the New European Driving Cycle (or similar reference driving cycles) is not feasible for a large scale screening. Subsequently, a ranking for each operational point as well as an overall ranking is deduced. As evaluation criterion the efficiency index EIi is defined as the relative difference between the net power output of a specific working fluid i with the maximum net power output in each of the NOP = 6 operational points j: 1 EI i= N OP

N OP

P

(14)

∑ Pi , j j=1

max , j

Note that the net power output is taken as objective function as for a fixed value of available exergy (heat flux from EGR and EGA), maximum net power output leads directly to maximum fuel saving. Another possible objective function are minimum specific system costs (€/kW), however, for such a huge number of working fluids a cost analysis is not possible and has to be carried out subsequently with the most promising candidates. Figure 11 gives the EIi for the final set of working fluids. It is obvious that after a steep decrease the curve flattens and the difference 20 ACS Paragon Plus Environment

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between the working fluids become less pronounced. Having a closer look on the TOP 100 working fluids it can be seen that one working fluid behaves remarkably better than the others reaching an EIi of 95 %. It is ranked no. 15, no. 2 and no. 1 for 40 °C, 75 °C and 100 °C condensation temperature in heavy duty trucks. For passenger cars it is ranked no. 3, no. 4 and no. 2 for the different condensation temperatures. The working fluid is related to the PubchemID 177 and is acetaldehyde. Interestingly, acetaldehyde has also been found by means of CAMD in a slightly different context.52 So actually two different approaches lead to similar results, which confirms the validity of the approach presented herein. Hence, an ideal working fluid which covers both applications and all condensation temperatures can be found by the proposed screening approach of the Pubchem database. As a further six working fluids gain an EIi above 90 %, a further 33 above 80 %, it can be concluded that a diverse set of working fluids reach high efficiencies in a broad range of applications and condensation temperatures. A list of best performing working fluids from a thermodynamic point of view is provided in Table 2. A remarkable result of the screening is found by investigating the rankings of known working fluids (commonly known and investigated working fluids from industry and literature). Within the TOP 10 working fluids, only two and within the TOP 100 working fluids only twelve from this dataset of known working fluids can be found. Thus the screening approach proposed in this work is able to find between 80 and 90 top performing working fluids which have not been discussed in the literature so far. Security aspects of acetaldehyde. Although acetaldehyde is an ideal working fluid from a thermodynamic point of view, it is hardly possible to use it in series vehicles due to major security concerns. Acetaldehyde is extremely flammable, its vapor phase leads to highly explosive vapour-air-mixture, in combination with air, highly explosive peroxides occur and the auto ignition temperature is just about 155 °C. This shows that the thermodynamic performance



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has to be coupled with security and regulatory aspects as well as with constructional parameters to allow for a holistic evaluation of the screened working fluids.

SUMMARY AND CONCLUSIONS New potential ORC working fluids are identified in a high-throughput screening for different operational points (car and truck, each at three different condensation temperatures) by process simulation. The thermodynamic data are predicted successfully up to the critical point by an extension of the COSMO-RS methodology to compressible fluids at high pressures. This quantum chemistry based COSMO-RS methodology is neither dependent on specific group contributions nor limited to specific compound classes; in other words, it is able to handle even a large scale screening of millions of compounds in the complete known chemical space in a fully predictive manner. The fluid screening provided several outstanding working fluids with very high thermodynamic performance in all investigated applications and operational points, with acetaldehyde clearly being top ranked from a thermodynamic point of view. Unfortunately, acetaldehyde is extremely flammable and combustible, therefore its use as ORC working fluid is not conceivable in the automotive area of application. Obviously, entirely thermodynamic criteria for the selection of an ORC fluid are not sufficient; safety, regulatory and constructional aspects should play definitely an important role. In an upcoming publication, a more holistic evaluation based on thermodynamic performance, security aspects (e.g. flammability, thermal stability), regulatory criteria (e.g. GWP, ODP) and constructional parameters (e.g. pressure ratio, maximum temperature) will be presented.


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FIGURES Figure 1. σ-profiles of selected ORC fluids n-hexane (dashed), R-245fa (dotted), ethanol (solid), and the connection between the COSMO surface of ethanol and its σ-profile.



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Figure 2. Schema of the PubChem database screening by COSMOtherm calculations and DetailSimORC simulations.


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Figure 3. Simplified flowchart of DetailSimORC; nomenclature: cond: condensation, SC: subcooling, sat: saturation, max: maximum, HS: heat source.



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Figure 4. ORC configuration for application passenger car without mass flow splitting (solid line) and for heavy duty truck with mass flow splitting (including dashed lines); EGA: exhaust gas aftertreatment, EGR: exhaust gas recirculation.


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Figure 5. Experimental boiling points Tboil and critical temperatures Tcrit; squares: all compound classes, diamonds: alkanes (linear or branched, not cyclic), triangles: inorganic compounds.



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Figure 6. Critical volume (Vcrit) in relationship to the COSMO volume (Vcosmo).


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Figure 7. Relationship between experimental critical pressures pcrit and the other critical parameters Tcrit and Vcrit.



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Figure 8. Comparison between RefProp and COSMO-RS + EoS based enthalpies for selected points in ORC process simulations for n-hexane.


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Figure 9. Comparison between RefProp (squares) and COSMO-RS + EoS (diamonds) based thermal efficiencies ηth = |(h2−h1)+(h4−h3)|/(h3−h2) for a series of potential ORC fluids in process simulations (see Figure 3) at the initial screening level (SVP). The error bars show two times the standard deviation. 25 20

Thermal efficiency [%]

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15 10 5 0

9 e 3 e a 4 a e e b 3 e e e e ol fa 3I fc fa ol er er 7e 36 -64 -11 CF 5m tan 45c pan 45 eth -12 tan 141 -11 eth xan an tan ton xan tan an 2 2 2 h h c u l l n u n e R R -b R y 2 Re e R he et et 36 -b R-2 pro R- thy ve h ac loh ope Rn nm n-p o R- iso e et c No cl cl y di m y y i c c c d RefProp

COSMOtherm



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Figure 10. Comparison of calculation level SVP and TZVPD-FINE for the passenger car application.


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Figure 11. Efficiency index for final set of 3,174 working fluids; see equation (14).



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TABLES. Table 1. Boundary Conditions for ORC Simulation Parameter

Value

Unit

Maximum working pressure

40

bar

Maximum volume flow ratio

100

−

Minimum condensation pressure (at corresponding condensation temperature)

75

kPa

Isentropic efficiency of expander

70

%

Isentropic efficiency of pump

80

%

Mechanical efficiency expander

95

%

Mechanical efficiency pump

70

%

Condensing temperature

40/75/100 °C

Temperature difference subcooling

8.75

K

Pinch point temperature difference condenser

10

K

Pinch point temperature difference (other heat exchangers)

20

K


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Table 2. Best performing working fluids (TOP 3), ranked by the thermodynamic efficiency index, and − for comparison − the performance of the best known working fluids (in the TOP 100 list). Rank Working fluid

PubChem CID

EIi

1

Acetaldehyde

177

95 %

2

1,2-Difluoroethane (R-152)

12 223

91 %

3

Methyl formate (R-611)

7 865

91 %

15

Dichloromethane (R-30)

6 344

84 %

16

Ethanol

702

83 %

21

Sulfur dioxide (R-764)

1 119

82 %

27

cis-1,2-Dichloroethene (R-1130)

643 833

82 %

42

Methanol

887

78 %

49

1,1-Dichloroethane (R-150a)

6 365

77 %

56

1,2-Dichloroethane (R-150)

11

77 %

63

1-Chloro-1,2-difluoroethane (R-142)

164 579

77 %

81

Acetone

180

75 %

87

Trichloroethylene (R-1120)

6 575

75 %



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SUPPORTING INFORMATION Compound specific Patel-Teja parameters; calculation of the temperature dependent Patel-Teja interaction parameter α(T); experimental critical point data. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author * Johannes Schwöbel, COSMOlogic GmbH & Co.KG, Imbacher Weg 46, 51379 Leverkusen, Germany. E-mail: [email protected]

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ‡These authors contributed equally.

Notes The authors declare the following competing financial interest(s): Andreas Klamt is chief executive officer and Johannes Schwöbel is an employee of COSMOlogic. COSMOlogic commercially distributes the COSMOtherm, COSMOquick and TURBOMOLE software packages used in this paper. Markus Preißinger and Dieter Brüggemann declare no competing financial interest.


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ACKNOWLEDGMENT The project was funded by the FVV (German Research Association for Combustion Engines e.V. / Project 1155 / PG 1).

ABBREVIATIONS AAE, Average Absolute Percentage Error COSMO-RS, Conductor-like Screening Model for Realistic Solvation DFT, Density Functional Theory EI, Thermodynamic Efficiency Index (eq. 14) EGA, Exhaust Gas Aftertreatment EGR, Exhaust Gas Recirculation EoS, Equation of State FINE, Fine Grid Marching Tetrahedron Cavity for the COSMO Molecular Surface HTS, High-Throughput Screening IR, Internal Recuperator ORC, Organic Rankine Cycle R2, Squared Pearson Correlation Coefficient SE, Standard Error SMARTS, SMiles ARbitrary Target Specification SVP, Screening COSMO-RS Level (Split-Valence Basis Set with Polarization) TZVPD-FINE, Accurate COSMO-RS Level (Triple-Zeta Valence Basis Set with Polarization and Diffusion) VLE, Vapor-Liquid Equilibrium 37 ACS Paragon Plus Environment


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High-Throughput Screening of Working Fluids for the Organic Rankine

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