PATENT DOCUMENT

Abstract:
An organic Rankine cycle working fluid comprising at least one compound having formula (I): RNQ, wherein R is fluorinated or non-fluorinated methyl, ethyl, vinyl or ethynyl, N is element nitrogen, the connection of R—N is a ring structure or a straight chain structure, and Q is a hydrogen and/or at least one fluorine atom. A process for converting thermal energy into mechanical energy, a method for power generation, an organic Rankine cycle system, and the use of the working fluid for heat transfer or in a mechanical power generation device are also provided. The organic Rankine cycle working fluid has a high energy conversion efficiency, low flammability, low toxicity and low corrosion on copper.

Full Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates to a working fluid for the organic Rankine cycle, having improved energy conversion efficiency, heat exchange characteristics and thermal stability. The present invention also relates to a process for converting thermal energy to mechanical energy, method for power generation, an organic Rankine cycle system and use of a working fluid for transfer of heat or in a mechanical power generation device. 
       TECHNICAL BACKGROUND 
       [0002]    As energy is becoming an increasingly expensive resource, efforts are made to look for new technologies to generate electricity or useful work from heat sources such as e.g. waste heat from industrial processes and combustion engines, or geothermal heat sources. One way to convert heat energy to mechanical work, useful work, such as electricity is the organic Rankine cycle. 
         [0003]    The organic Rankine cycle (ORC) involves an organic fluid with a liquid-vapor phase change occurring at a lower temperature than the water-steam phase change. Due to the organic fluid&#39;s low phase change temperature heat recovery from low temperature sources such as industrial waste heat, geothermal heat and solar ponds, is made possible and economical. The low-temperature heat is converted into useful work that can itself be converted into electricity. 
         [0004]    In the organic Rankine cycle the working fluid is fed or pumped into a heat exchange relationship with a heat source, e.g. a boiler, where the working fluid is evaporated, thereafter passed through a turbine of some sort and then finally re-condensed. 
         [0005]    The ORC could be used for waste heat recovery in e.g. industrial and farming processes, hot exhausts from ovens or furnaces, flue gas condensation, and exhaust gases from vehicles. 
         [0006]    The selection of the working fluid is of key importance in low temperature ORCs. Due to the low temperature, heat transfer inefficiencies are highly prejudicial. These inefficiencies depend very strongly on the thermodynamic characteristics of the fluid and on the operating conditions. In order to recover low-grade heat, the fluid generally has a lower boiling temperature than water. Refrigerants and hydrocarbons are the two commonly used components. Most researchers choose existing refrigerants, such as R152a or R134a, as working fluids of the ORC. 
         [0007]    A general disadvantage of most working fluids made commercial for organic Rankine cycles are the fact that they have been designed specifically for the refrigeration cycle commonly used in air condition systems and heat pump systems. However, the refrigeration cycle is the anti-cycle of the Carnot cycle to generate power. Thus, working fluids for the purpose to generate power from low-grade heat should have distinct features from refrigerants. A pressure-enthalpy graph is shown in  FIG. 1 . The energy conversion process is from point H3 to point H4. For refrigeration applications, the working fluid should influence to decrease the enthalpy difference between H3 and H4 in order to reduce the compressor power. For the ORC, the working fluid should influence to increase the enthalpy difference between H3 and H4 in order to convert more power from heat. 
         [0008]    Some refrigerants like e.g. R600a, are also used as working fluids in the ORC to convert heat to electrical power but the flammability of the R600a is a big problem inmost industrial or commercial environments. Isobutane used as a refrigerant in domestic refrigerators may upon leakage into the refrigerator cabinet be ignited by sparks from the electrical system. The use of a flammable gas as a refrigerant is quite dangerous and encompasses a great deal of risk. The normal risks that chlorofluorocarbon compounds (CFC) or other potentially toxic refrigerants would have upon escape, are mainly related to depletion of breathable air and frosting at the point of escape. 
         [0009]    The ozone depletion potential (ODP) of a chemical compound is the relative amount of degradation of the ozone layer it may cause. ODP of a specific substance is defined as the ratio of global loss of ozone due to given substance over the global loss of ozone due the same mass of trichlorofluoro-methane (R-11 or CFC-11) having a fixed ODP of 1.0. R11 has the maximum potential amongst all chlorocarbons due to the presence of three chlorine atoms in the molecule. Chlorodifluoromethane (R-22) has an ODP of 0.05. Thus, the ODP can be estimated from the structure of a given substance. Chlorofluorocarbons have ODPs in the vicinity of 1 and hydrochlorofluoro-carbons (HCFC) have ODPs often in the range of 0.005 to 0.2, since the presence of hydrogen causes the compounds to react readily in the troposphere, therefore reducing their chance to reach the stratosphere. Hydrofluorocarbons (HFC) have no chlorine content, so their ODPs are essentially zero. Some used refrigerants such as CFCs, HCFCs and HFCs, e.g. R11 and R22, show relatively good performance on heat efficiency in the ORC but due to stricter environmental legislations such refrigerants, due to their halogen content, already have been or in the near future probably will be phased out from the market. 
         [0010]    Other features affecting the choice of a chemical in an ORC may be the resistance to corrosion on copper and the global warming potential (GWP). 
         [0011]    US 2010/139274 discloses chloro- and bromo-fluoro-olefins useful as organic Rankine cycle working fluids for efficiently converting waste heat generated from industrial processes, such as electric power generation from fuel cells, into mechanical energy or further to electric power. 
         [0012]    WO 2006/014609 discloses a process for recovering heat and a working fluid for an organic Rankine cycle system comprising one or more compounds of Formula (I) (I) CR′y, wherein y is 3 or 4 and each R′ is independently H, F, I, Br, substituted or unsubstituted C3-C9 alkyl, substituted or unsubstituted C2-C9 alkoxy, substituted or unsubstituted fluoropolyether, substituted or unsubstituted C2-C9 alkenyl, substituted or unsubstituted aryl, substituted or unsubstituted C6-C9 alkylaryl, or substituted or unsubstituted C6-C9 alkenyaryl, provided said compound includes at least two carbon atoms, at least one fluorine atom, and no chloride atoms, and further provided that any OH substituted alkyl preferably has at least three carbon atoms. 
         [0013]    U.S. Pat. No. 4,541,943 discloses a working fluid to be used in a mechanical vapor recompression heat pump system. The working fluid can be either a saturated hydrocarbon or a fluorohydrocarbon ether or a fluorinated amine. Also, the heat pumps may operate on reverse Rankine cycle. 
         [0014]    US 2010/0095703 discloses a working medium for refrigeration processes comprising at least one sorbent material and at least one refrigerant. The sorbent material contains at least one nonvolatile organic salt. A list of suitable anions to be included in the salt is presented. The list of anions includes bis(perfluoroalkylsulfonyl)amides. Suitable ionic liquids are 1-methyl-3-octylimidazolium tetrafluoroborate and butylmethylpyrrolidinium bis(trifluoromethylsulfonyl)-imide. 
         [0015]    As disclosed above legislations are pushing towards more reuse of heat thus making an incentive to reuse low grade heat not normally considered economical to do. In the future a choice between high fines for releasing waste heat into the environment and reusing the generated waste heat to a large extent is probable. In view of this the choice of working media becomes crucial. There exists a need to find new working fluids for use in an ORC to achieve a high output of work from the retrieved heat in a resource effective and thus economically favourable way. 
       SUMMARY OF THE INVENTION 
       [0016]    It is an object of this invention to provide working fluids for an organic Rankine cycle which fluids can increase the efficiency of conversion of thermal energy to mechanical energy. 
         [0017]    It is another object of this invention to provide working fluids for a organic Rankine cycle which fluids are stable and can be used safely. 
         [0018]    The characteristics for the working fluid according to the present invention is a high thermal efficiency, low or reasonable flammability, low or reasonable toxicity (i.e. low degree of poisoning during operation, no or low ODP and low or reasonable corrosion on copper (if this material is used for e.g. pipings and/or heat exchanger). 
         [0019]    The working fluids according to the present invention comprise at least one compound having a structure according to Formula (I): 
         [0000]      RNQ 
         [0000]    wherein
 
R is fluorinated or non-fluorinated methyl, ethyl, vinyl, or ethynyl,
 
N is the element nitrogen,
 
the connection of R—N is a ring structure (i.e. a heterogeneous ring) or a straight chain structure, and
 
Q is chosen from a hydrogen atom and/or at least one fluorine atom.
 
         [0020]    One embodiment of the present invention relates to an organic Rankine cycle working fluid comprising at least one compound having either the Formula (II): 
         [0000]      R 1 NH n F 2-n , 
         [0000]    wherein
 
R 1  is fluorinated or non-fluorinated methyl, ethyl, vinyl or ethynyl, and
 
n is 0 or 1;
 
or
 
       the Formula (III): 
       [0021]    
       
                 
         
             
             
         
       
     
         [0000]    wherein
 
R 2  and R 3  are independently chosen from H 2 , F 2  and HF, and
 
p is 0 or 1, preferably 1.
 
         [0022]    Preferably, R 1  in Formula (II) is a fluorinated or non-fluorinated methyl or ethyl group. 
         [0023]    Preferably, said compound according to Formula (II) is chosen from the group consisting of CH 3 NHF, CH 2 FNHF, CHF 2 NHF, CF 3 NHF, CH 3 NF 2 , CH 2 FNF 2 , CHF 2 NF 2 , CF 3 NF 2 , C 2 H 5 NHF, CH 2 FCH 2 NHF, CHF 2 CH 2 NHF, CH 3 CHFNHF, CH 2 FCHFNHF, C 2 H 5 NF 2 , CH 2 FCH 2 NF 2 , CH 3 CHFNF 2 , and CHF 2 CF 2 NF 2 ; preferably CH 3 NF 2 , CH 2 FNF 2 , CHF 2 NF 2 , and CF 3 NF 2 . 
         [0024]    R 2  in Formula (III) contains preferably at least one fluorine. The compound according to Formula (III) is preferably tetrafluoroaziridine. 
         [0025]    In another embodiment of the present invention relates to a process for converting thermal energy to mechanical energy in an organic Rankine cycle comprising the steps of: 
         [0000]    a) vaporizing a liquid working fluid according to the present invention, by bringing it in contact with a heat source;
 
b) expanding the vaporized working fluid, wherein said heat is converted into mechanical work; and
 
c) cooling the expanded vaporized working fluid with a cooling source to condense the vapor to liquid phase.
 
         [0026]    In an embodiment the temperature of the working fluid after being brought in contact with a heat source in a) is at most 100° C., preferably said temperature is 25 to 90° C. 
         [0027]    Another embodiment of the present invention relates to an organic Rankine cycle system using the working fluid according to the present invention for a heat cycle. 
         [0028]    Still another embodiment of the present invention relates to an organic Rankine cycle system comprising: 
         [0000]    (a) a working fluid according to the present invention; (b) a heat exchanging device containing said working fluid, connected to a heat source, for vaporizing the working fluid; (c) an expansion device responsive to said vaporized working fluid for expanding said working fluid vapor resulting in heat depleted working fluid; (d) an electric generator driven by said expansion device for producing electrical power; (e) a condenser for condensing the heat depleted working fluid and producing condensate; and (f) means for effecting the return of said condensate to said heat exchanging device. 
         [0029]    In one embodiment of the present invention the heat source is heat from a boiler or a fuel cell, waste heat from an industrial or farming process, geothermal heat, waste heat from a combustion engine or power plant, or solar heat. 
         [0030]    In a further embodiment the expander is a turbine, screw expander, scroll expander, or piston expander. 
         [0031]    Still one embodiment relates to use of a working fluid according to the present invention for transfer of heat. 
         [0032]    Yet another embodiment relates to use of a working fluid according the present invention in a mechanical power generation device adapted to use an organic Rankine cycle or a modification thereof. 
         [0033]    Another embodiment relates to a method for power generation comprising transfer of heat using a working fluid according to the present invention. 
         [0034]    One embodiment relates to a method for power generation according to the present invention, using a Rankine cycle or a modification thereof to generate work from heat. 
         [0035]    Another embodiment relates to a compound having the Formula (IV): 
         [0000]    
       
                 
         
             
             
         
       
     
     
    
     
       SHORT SUMMARY OF THE DRAWINGS 
         [0036]      FIG. 1  shows a pressure-enthalpy graph. 
           [0037]      FIG. 2  shows a graph of the entropy and efficiency for known existing working fluids of the ORC for a temperature shift between 20 to 60° C. in the system. This temperature cycle in the ORC, i.e. 60° C. is the evaporating temperature for the working fluid and 20° C. is the condensing temperature, is in the following referred to as an ORC 20-60 cycle. 
           [0038]      FIG. 3  shows a schematic drawing of an organic Rankine Cycle system. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0039]    Conversion of low grade heat into work and thereafter to electricity using the highest efficiency is in many cases obtained by using an ORC. A heat source supplies heat to an ORC with the aid of a heat exchanging device. The temperature of the working fluid in the ORC in this heat exchanging section can be below 90° C. Thus, heat sources suitable for use in the ORC include industrial waste heat or geothermal waste heat. One advantage of the working fluid according to the present invention is that it increases the thermal efficiency in the conversion of heat into work. The heat source is able to give the working fluid in the ORC system a temperature of at most 100° C., preferably at most 90° C., preferably at most 80° C., and at least a temperature of 25° C., preferably 30-75° C., e.g. 40-70° C., 40-65° C., or 50-70° C., in the heat retrieving section (the evaporation section) of the ORC. 
         [0040]    By investigating the relation between the entropy and efficiency of ORC for corresponding working fluids, it has been found that, generally speaking, working fluids with low absolute entropy (i.e. the entropy at OK, (−273° C.)) will have higher efficiencies. This result is shown in  FIG. 2  in which the ORC at 20° C.-60° C. is taken as an example. The third law of thermodynamics relates itself to the entropy of a system. It states that the entropy of a pure substance approaches zero as the temperature approaches absolute zero. This law provides a reference point in the calculation of the entropy, where the entropy calculated relative to this point is considered the absolute entropy. Here, the thermodynamic property (absolute entropy) in the gaseous state at the 293.15K, 101.325 KPa is calculated for all the molecules using density functional theory (DFT) with Gaussian 09 program. Absolute entropy means the increment of entropy when the temperature is increased from OK to 293.15K. All calculations for the molecules were carried out with B3LYP/6-31 G(d) Opt Freq. The calculation results of absolute entropy are in good agreement with experimental data, although only a few such data are available. On the calculation results of absolute entropy, the calculation results obtained by B3LYP/6-31G(d) seem to be accurate, since Gaussian employ the mature theoretical methods and statistical thermodynamics to compute this thermodynamic properties, and this computational level is moderate. 
         [0041]    All the data of the working fluids to calculate the efficiencies n, are taken from the software Refprop8.0. The values of entropy are calculated from software Gaussian 03 by the HF/3-21 G method. Presenting a working fluid having molecules with low entropies has been found of interest according to the present invention. 
         [0042]    Thus, it has been found that the working fluids according to the present invention are to be selected from molecule structures which might contribute to less entropy, such as cyclic structures, double bonds, triple bonds, and/or molecules with a low total number of atoms but with proper boiling point. Also, atoms making up the working fluid according to the present invention are four atoms, i.e. C, N, F and H. 
         [0043]    Workings fluids used in an ORC preferably present characteristics like:
       a) an isentropic saturation vapor curve, and preferably displaying a small superheating at the exhaust of the evaporator;   b) a low freezing point and high stability temperature, wherein the freezing point should be lower than the lowest temperature in the cycle and maximum temperature of the heat source is limited by the chemical stability of the working fluid;   c) a high heat of vaporization and density, since a fluid with a high latent heat and density will absorb more energy from the heat source in the evaporator;   d) a low environmental impact, wherein the ozone depletion potential (ODP) and the global warming potential (GWP) are examples of such parameters; and   e) low flammability, and low or no toxicity.       
 
         [0049]    It has been found that the working fluids according to the present invention present a high efficiency in an ORC compared to conventional working fluids. 
         [0050]    A working fluid according to the present invention comprises at least one compound having a structure according to Formula (I): 
         [0000]      RNQ 
         [0000]    wherein
 
R is fluorinated or non-fluorinated methyl, ethyl, vinyl, or ethynyl,
 
N is the element nitrogen,
 
the connection of R—N is a ring structure (i.e. a heterogeneous ring) or a straight chain structure, and
 
Q is chosen from a hydrogen atom and/or at least one fluorine atom.
 
         [0051]    Preferably the working fluid according to the present invention comprises at least one compound having either the Formula (II): 
         [0000]      R 1 NH n F 2-n , 
         [0000]    wherein
 
R 1  is fluorinated or non-fluorinated methyl, ethyl, vinyl or ethynyl, and
 
n is 0 or 1;
 
or
 
       the Formula (III): 
       [0052]    
       
                 
         
             
             
         
       
     
         [0000]    wherein
 
R 2  and R 3  are independently chosen from H 2 , F 2  and HF, and
 
p is 0 or 1.
 
         [0053]    If the working fluid comprises a compound having a structure according to Formula (II) R 1  may be non-fluorinated, or fully or partially fluorinated. In one preferred embodiment R 1  is a fluorinated or non-fluorinated methyl or ethyl group. Preferred compounds according to Formula (II) are chosen from CH 3 NHF, CH 2 FNHF, CHF 2 NHF, CF 3 NHF, CH 3 NF 2 , CH 2 FNF 2 , CHF 2 NF 2 , CF 3 NF 2 , C 2 H 5 NHF, CH 2 FCH 2 NHF, CHF 2 CH 2 NHF, CH 3 CHFNHF, CH 2 FCHFNHF, C 2 H 5 NF 2 , CH 2 FCH 2 NF 2 , CH 3 CHFNF 2 , CHF 2 CF 2 NF 2 , in particular CH 3 NHF, CH 2 FNHF, CHF 2 NHF, CF 3 NHF, CH 3 NF 2 , CH 2 FNF 2 , CHF 2 NF 2 , CF 3 NF 2 , C 2 H 5 NHF, CH 2 FCH 2 NHF, CHF 2 CH 2 NHF, CH 3 CHFNHF, and CH 2 FCHFNHF. 
         [0054]    More preferably R 1  is a fluorinated or non-fluorinated methyl group, and especially in combination with p being 0. 
         [0055]    If the working fluid comprises a compound having a structure according to Formula (III) it is preferred that p is 1. Regarding R 2  and R 3 , the more fluorine that is present in Formula (III) the better the compound seems to perform in an ORC. Thus, fluorinated aziridines are preferred. 
         [0056]    When comparing which compounds of the Formula (I) are preferred according to the present invention, it has been found that compounds having either Formula (II) or Formula (III) are preferable. However, comparing the compounds having either Formula (II) or Formula (III), compounds according to Formula (II) are considered preferable. In turn, of the compounds according to Formula (II) the ones having only one carbon atom are preferred according to the present invention. 
         [0057]    The compound according to Formula (I), such as e.g. Formula (II) and/or (III), preferably constitutes the main part of the working fluid. Preferably the compound according to Formula (I), such as e.g. Formula (II) and/or (III), constitutes 60-100%, by weight of the working fluid, preferably 80-100%, more preferably 90-100%, most preferably 95-100%, by weight. 
         [0058]    One of the more preferred compounds having Formula (III) is tetrafluoroaziridine. The synthesis of the tetrafluoroaziridin may be done by the following reaction steps: 
         [0000]    
       
                 
         
             
             
         
       
     
         [0059]    Tetrafluoroethene and triethylammoniumazide react in sym-tetrachloro-ethane at −5° C. to generate intermediates with one negative charge. The unstable intermediates decompose immediately to produce tetrafluorovinylazide. The tetrafluorovinylazide decomposes at a convenient rate at a temperature of 25 to 40° C. and lose nitrogen to form 2,3,3-trifluoro-2H-aziridine. 2,3,3-trifluoro-2H-aziridine reacts with hydrogen fluoride at a temperature of 25° C. to produce tetrafluoroaziridine. 
       Calculations 
       [0060]    Disclosed below are the calculations which have been used as basis for determining which molecule structures have an increased efficiency in the ORC. The compounds for use in a working fluid according to the present invention were chosen on the basis of these calculations. By using a working fluid with an increased efficiency in the ORC more of the transferred heat may be made into work. Also, by using a working fluid having an increased efficiency heating sources of lower temperatures can become economical to recover heat from and make into work. 
       Group Contribution Method 
       [0061]    The performed calculations for efficiency have been compensated in view of the contribution that different chemical groups make. The group contribution method has been made to get a more accurate value in practice. Disclosed below is a calculation on one example to show how to calculate the data based on the chemical structure. All compounds according to the present invention with the disclosed specific molecule structures have been calculated with this method by computer. 
       Sample Molecule 
       [0062]    CF 3 NF 2  molecule weight: M=121.01
       Calculating the normal boiling point T b  by Joback method       
 
         [0000]    
       
         
               
               
               
               
             
           
               
                   
               
               
                   
                   
                 Number of 
                   
               
               
                   
                 Group 
                 groups 
                 ΔT bi   
               
               
                   
               
             
             
               
                   
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 1 
                 18.25 
               
               
                   
               
               
                   
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 1 
                 11.74 
               
               
                   
               
               
                   
                 —F 
                 5 
                      −0.03 × 5 
               
               
                   
                 Total 
                   
                 29.84 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                     b 
                   
                   = 
                     
                    
                   
                     198 
                     + 
                     
                       Σ 
                        
                       
                           
                       
                        
                       
                         n 
                         i 
                       
                        
                       Δ 
                        
                       
                           
                       
                        
                       
                         T 
                         bi 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     198 
                     + 
                     29.84 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     227.84 
                      
                     
                         
                     
                      
                     K 
                   
                 
               
             
           
         
       
       
         
           
             Calculating the latent heat ΔH v  at 60° C. by CSGC-HW1 method 
           
         
       
     
         [0000]    
       
         
               
               
               
               
             
           
               
                   
               
               
                   
                 Number of 
                   
                   
               
               
                 Group 
                 groups 
                 ΔT i   
                 ΔP i   
               
               
                   
               
             
             
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 1 
                 0.002200289 
                 −0.003474154 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 1 
                 −0.009525362   
                 −0.07779588   
               
               
                   
               
               
                 —F 
                 5 
                       0.014653116 × 5 
                        0.108614823 × 5 
               
               
                 Total 
                   
                 0.065940508 
                 0.46184082 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                     c 
                     * 
                   
                   = 
                     
                    
                   
                     
                       T 
                       b 
                     
                     / 
                     
                       [ 
                       
                         
                           A 
                           T 
                         
                         + 
                         
                           
                             B 
                             T 
                           
                            
                           Σ 
                            
                           
                               
                           
                            
                           
                             n 
                             i 
                           
                            
                           Δ 
                            
                           
                               
                           
                            
                           
                             T 
                             i 
                           
                         
                         + 
                         
                           
                             
                               C 
                               T 
                             
                              
                             
                               ( 
                               
                                 Σ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   n 
                                   i 
                                 
                                  
                                 Δ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   T 
                                   i 
                                 
                               
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                           2 
                         
                         + 
                         
                           
                             
                               D 
                               T 
                             
                              
                             
                               ( 
                               
                                 Σ 
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                                   n 
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                               ) 
                             
                           
                           3 
                         
                       
                       ] 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     227.84 
                     / 
                     
                       [ 
                       
                         0.5782359 
                         + 
                         
                           1.064102 
                           × 
                           0.065940508 
                         
                         - 
                         
                           1.780121 
                           × 
                         
                       
                     
                   
                 
               
             
             
               
                 
                     
                    
                   
                     
                       0.065940508 
                       2 
                     
                     - 
                     
                       0.5002329 
                       × 
                       
                         0.065940508 
                         3 
                       
                     
                   
                   ] 
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     355.65 
                      
                     
                         
                     
                      
                     K 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     c 
                     * 
                   
                   = 
                     
                    
                   
                     1.01325 
                      
                     
                         
                     
                      
                     ln 
                      
                     
                         
                     
                      
                     
                       
                         T 
                         b 
                       
                       / 
                       
                         [ 
                         
                           
                             A 
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                              
                             Σ 
                              
                             
                                 
                             
                              
                             
                               n 
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                              
                             
                                 
                             
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                                 C 
                                 P 
                               
                                
                               
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                                     n 
                                     i 
                                   
                                    
                                   Δ 
                                    
                                   
                                       
                                   
                                    
                                   
                                     P 
                                     i 
                                   
                                 
                                 ) 
                               
                             
                             2 
                           
                           + 
                           
                             
                               
                                 D 
                                 P 
                               
                                
                               
                                 ( 
                                 
                                   Σ 
                                    
                                   
                                       
                                   
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                                     n 
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                             3 
                           
                         
                         ] 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     1.01325 
                      
                     
                         
                     
                      
                     ln 
                      
                     
                         
                     
                      
                     
                       227.84 
                       / 
                       
                         [ 
                         
                           0.029125 
                           + 
                           
                             0.207087 
                             × 
                             0.46184082 
                           
                           - 
                         
                       
                     
                   
                 
               
             
             
               
                 
                     
                    
                   
                     
                       0.04948187 
                       × 
                       
                         0.46184082 
                         2 
                       
                     
                     - 
                     
                       0.08637077 
                       × 
                       
                         0.46184082 
                         3 
                       
                     
                   
                   ] 
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     52.04 
                      
                     
                         
                     
                      
                     bar 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       T 
                       br 
                       * 
                     
                     = 
                       
                      
                     
                       
                         T 
                         b 
                       
                       / 
                       
                         T 
                         c 
                         * 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     227.84 
                     / 
                     355.65 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   0.6405 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       H 
                       vb 
                     
                   
                   = 
                     
                    
                   
                     1.319767 
                      
                     
                         
                     
                      
                     R 
                      
                     
                         
                     
                      
                     
                       T 
                       c 
                       * 
                     
                      
                     
                       
                         
                           T 
                           br 
                           * 
                         
                          
                         
                           [ 
                           
                             
                               ln 
                                
                               
                                 ( 
                                 
                                   
                                     P 
                                     c 
                                     * 
                                   
                                   / 
                                   1.01325 
                                 
                                 ) 
                               
                             
                             - 
                             1.140257 
                           
                           ] 
                         
                       
                       / 
                       
                         ( 
                         
                           1.059397 
                           - 
                           
                             T 
                             br 
                             * 
                           
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     1.319767 
                     × 
                     8.314 
                     × 
                     355.65 
                     × 
                     0.6405 
                     × 
                     
                       [ 
                       
                         
                           ln 
                            
                           
                             ( 
                             
                               52.04 
                               / 
                               1.01325 
                             
                             ) 
                           
                         
                         - 
                       
                     
                   
                 
               
             
             
               
                 
                   
                       
                      
                     1.140257 
                     ] 
                   
                   / 
                   
                     ( 
                     
                       1.059397 
                       - 
                       0.6405 
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     18031.90 
                      
                     
                         
                     
                      
                     J 
                      
                     
                       / 
                     
                      
                     mol 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     q 
                     = 
                       
                      
                     
                       
                         0.7815677 
                          
                         
                             
                         
                          
                         
                           T 
                           br 
                           * 
                         
                       
                       - 
                       0.1072383 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       0.7815677 
                       × 
                       0.6405 
                     
                     - 
                     0.1072383 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   0.3934 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 
                   
                     
                       T 
                       r 
                       * 
                     
                     = 
                       
                      
                     
                       T 
                       / 
                       
                         T 
                         c 
                         * 
                       
                     
                   
                 
               
               
                 
                   
                     = 
                       
                      
                     
                       
                         ( 
                         
                           60 
                           + 
                           273.15 
                         
                         ) 
                       
                       / 
                       355.65 
                     
                   
                 
               
               
                 
                   
                     = 
                       
                      
                     0.9366 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         H 
                         v 
                       
                     
                     = 
                       
                      
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         
                           
                             H 
                             vb 
                           
                            
                           
                             [ 
                             
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     T 
                                     r 
                                     * 
                                   
                                 
                                 ) 
                               
                               / 
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     T 
                                     br 
                                     * 
                                   
                                 
                                 ) 
                               
                             
                             ] 
                           
                         
                         q 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     18048.07 
                     × 
                     
                       
                         [ 
                         
                           
                             ( 
                             
                               1 
                               - 
                               0.9366 
                             
                             ) 
                           
                           / 
                           
                             ( 
                             
                               1 
                               - 
                               0.6405 
                             
                             ) 
                           
                         
                         ] 
                       
                       0.3934 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     9113.21 
                      
                     
                         
                     
                      
                     J 
                      
                     
                       / 
                     
                      
                     mol 
                   
                 
               
             
           
         
       
       
         
           
             Calculating saturated vapor pressure at 60° C. by CSGC-PR method 
           
         
       
     
         [0000]    
       
         
               
               
               
               
               
             
           
               
                   
               
               
                   
                   
                 Number of 
                   
                   
               
               
                   
                 Group 
                 groups 
                 ΔT i  × 10 4   
                 ΔP i  × 10 3   
               
               
                   
               
             
             
               
                   
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 1 
                  27.54 
                     −2.68 
               
               
                   
               
               
                   
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 1 
                 338.14 
                 123.74 
               
               
                   
               
               
                   
                 —F 
                 5 
                  35.32 × 5 
                  12.25 × 5 
               
               
                   
                 Total 
                   
                  0.054228 
                  0.18213 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                     c 
                     * 
                   
                   = 
                     
                    
                   
                     
                       T 
                       b 
                     
                     / 
                     
                       [ 
                       
                         
                           A 
                           T 
                         
                         + 
                         
                           
                             B 
                             T 
                           
                            
                           Σ 
                            
                           
                               
                           
                            
                           
                             n 
                             i 
                           
                            
                           Δ 
                            
                           
                               
                           
                            
                           
                             T 
                             i 
                           
                         
                         + 
                         
                           
                             
                               C 
                               T 
                             
                              
                             
                               ( 
                               
                                 Σ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   n 
                                   i 
                                 
                                  
                                 Δ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   T 
                                   i 
                                 
                               
                               ) 
                             
                           
                           2 
                         
                         + 
                         
                           
                             
                               D 
                               T 
                             
                              
                             
                               ( 
                               
                                 Σ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   n 
                                   i 
                                 
                                  
                                 Δ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   T 
                                   i 
                                 
                               
                               ) 
                             
                           
                           3 
                         
                       
                       ] 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     227.84 
                     / 
                     
                       [ 
                       
                         0.5782585 
                         + 
                         
                           1.061273 
                           × 
                           0.054228 
                         
                         - 
                         
                           1.778714 
                           × 
                         
                       
                     
                   
                 
               
             
             
               
                 
                     
                    
                   
                     
                       0.054228 
                       2 
                     
                     - 
                     
                       0.4998375 
                       × 
                       
                         0.054228 
                         3 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     361.36 
                      
                     
                         
                     
                      
                     K 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     c 
                     * 
                   
                   = 
                     
                    
                   
                     1.01325 
                      
                     
                         
                     
                      
                     ln 
                      
                     
                         
                     
                      
                     
                       
                         T 
                         b 
                       
                       / 
                       
                         [ 
                         
                           
                             A 
                             P 
                           
                           + 
                           
                             
                               B 
                               P 
                             
                              
                             Σ 
                              
                             
                                 
                             
                              
                             
                               n 
                               i 
                             
                              
                             Δ 
                              
                             
                                 
                             
                              
                             
                               P 
                               i 
                             
                           
                           + 
                           
                             
                               
                                 C 
                                 P 
                               
                                
                               
                                 ( 
                                 
                                   Σ 
                                    
                                   
                                       
                                   
                                    
                                   
                                     n 
                                     i 
                                   
                                    
                                   Δ 
                                    
                                   
                                       
                                   
                                    
                                   
                                     P 
                                     i 
                                   
                                 
                                 ) 
                               
                             
                             2 
                           
                           + 
                           
                             
                               
                                 D 
                                 P 
                               
                                
                               
                                 ( 
                                 
                                   Σ 
                                    
                                   
                                       
                                   
                                    
                                   
                                     n 
                                     i 
                                   
                                    
                                   Δ 
                                    
                                   
                                       
                                   
                                    
                                   
                                     P 
                                     i 
                                   
                                 
                                 ) 
                               
                             
                             3 
                           
                         
                         ] 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     1.01325 
                      
                     
                         
                     
                      
                     ln 
                      
                     
                         
                     
                      
                     
                       227.84 
                       / 
                       
                         [ 
                         
                           0.04564342 
                           + 
                           
                             0.3046466 
                             × 
                             0.18213 
                           
                           - 
                         
                       
                     
                   
                 
               
             
             
               
                 
                     
                    
                   
                     
                       0.0652039 
                       × 
                       
                         0.18213 
                         2 
                       
                     
                     - 
                     
                       0.04390779 
                       × 
                       
                         0.18213 
                         3 
                       
                     
                   
                   ] 
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     55.73 
                      
                     
                         
                     
                      
                     bar 
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 
                   
                     
                       T 
                       r 
                       * 
                     
                     = 
                       
                      
                     
                       T 
                       / 
                       
                         T 
                         c 
                         * 
                       
                     
                   
                 
               
               
                 
                   
                     = 
                       
                      
                     
                       
                         ( 
                         
                           60 
                           + 
                           273.125 
                         
                         ) 
                       
                       / 
                       361.36 
                     
                   
                 
               
               
                 
                   
                     = 
                       
                      
                     0.9216 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       T 
                       br 
                       * 
                     
                     = 
                       
                      
                     
                       
                         T 
                         b 
                       
                       / 
                       
                         T 
                         c 
                         * 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     227.84 
                     / 
                     361.36 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   0.6305 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       ϕ 
                       b 
                     
                     = 
                       
                      
                     
                       
                         - 
                         35 
                       
                       + 
                       
                         36 
                         / 
                         
                           T 
                           br 
                           * 
                         
                       
                       + 
                       
                         42 
                          
                         
                             
                         
                          
                         ln 
                          
                         
                             
                         
                          
                         
                           T 
                           br 
                           * 
                         
                       
                       - 
                       
                         T 
                         br 
                         
                           * 
                           6 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       - 
                       35 
                     
                     + 
                     
                       36 
                       / 
                       0.6305 
                     
                     + 
                     
                       42 
                        
                       
                           
                       
                        
                       ln 
                        
                       
                           
                       
                        
                       0.6305 
                     
                     - 
                     
                       0.6305 
                       6 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   2.663 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     α 
                     c 
                   
                   = 
                     
                    
                   
                     
                       [ 
                       
                         
                           0.315 
                            
                           
                             ϕ 
                             b 
                           
                         
                         + 
                         
                           ln 
                            
                           
                             ( 
                             
                               
                                 P 
                                 c 
                                 * 
                               
                               / 
                               1.01325 
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     / 
                     
                       ( 
                       
                         
                           0.0838 
                            
                           
                             ϕ 
                             b 
                           
                         
                         - 
                         
                           ln 
                            
                           
                               
                           
                            
                           
                             T 
                             br 
                             * 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       [ 
                       
                         
                           0.315 
                           × 
                           2.663 
                         
                         + 
                         
                             
                         
                          
                         
                           ln 
                            
                           
                             ( 
                             
                               55.73 
                               / 
                               1.01325 
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     / 
                     
                       ( 
                       
                         
                           0.0838 
                           × 
                           2.663 
                         
                         - 
                         
                           ln 
                            
                           
                               
                           
                            
                           0.6305 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   7.0811 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 
                   
                     Q 
                     = 
                       
                      
                     
                       0.0838 
                        
                       
                         ( 
                         
                           3.758 
                           - 
                           
                             α 
                             c 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   
                     = 
                       
                      
                     
                       0.0838 
                       × 
                       
                         ( 
                         
                           3.758 
                           - 
                           7.0811 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   
                     = 
                       
                      
                     
                       - 
                       0.2785 
                     
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 
                   
                     A 
                     = 
                       
                      
                     
                       
                         - 
                         35 
                       
                        
                       
                           
                       
                        
                       Q 
                     
                   
                 
               
               
                 
                   
                     = 
                       
                      
                     
                       
                         - 
                         35 
                       
                       × 
                       
                         ( 
                         
                           - 
                           0.2785 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   
                     = 
                       
                      
                     9.747 
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 
                   
                     B 
                     = 
                       
                      
                     
                       
                         - 
                         36 
                       
                        
                       
                           
                       
                        
                       Q 
                     
                   
                 
               
               
                 
                   
                     = 
                       
                      
                     
                       
                         - 
                         36 
                       
                       × 
                       
                         ( 
                         
                           - 
                           0.2785 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   
                     = 
                       
                      
                     10.025 
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 
                   
                     C 
                     = 
                       
                      
                     
                       
                         
                           - 
                           42 
                         
                          
                         
                             
                         
                          
                         Q 
                       
                       + 
                       
                         α 
                         c 
                       
                     
                   
                 
               
               
                 
                   
                     = 
                       
                      
                     
                       
                         42 
                         × 
                         
                           ( 
                           
                             - 
                             0.2785 
                           
                           ) 
                         
                       
                       + 
                       7.0811 
                     
                   
                 
               
               
                 
                   
                     = 
                       
                      
                     
                       - 
                       4.615 
                     
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 
                   
                     D 
                     = 
                       
                      
                     
                       - 
                       Q 
                     
                   
                 
               
               
                 
                   
                     = 
                       
                      
                     0.2785 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     ln 
                      
                     
                         
                     
                      
                     
                       P 
                       r 
                       * 
                     
                   
                   = 
                     
                    
                   
                     A 
                     - 
                     
                       B 
                       / 
                       
                         T 
                         r 
                         * 
                       
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       ln 
                        
                       
                           
                       
                        
                       
                         T 
                         r 
                         * 
                       
                     
                     + 
                     
                       D 
                        
                       
                           
                       
                        
                       
                         T 
                         r 
                         
                           * 
                           6 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     9.747 
                     - 
                     
                       10.025 
                       / 
                       0.9216 
                     
                     - 
                     
                       4.850 
                       × 
                       ln 
                        
                       
                           
                       
                        
                       0.9216 
                     
                     + 
                     
                       0.2683 
                       × 
                       
                         0.9216 
                         6 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     - 
                     0.5814 
                   
                 
               
             
           
         
       
     
       Because P r *=P 60° C. /P c * 
       [0066]    we have P 60° C. =P c *P r *=55.73×exp(−0.5814)=31.161 bar.
 
Through the similar procedure, we can obtain the saturated vapor pressure at 20° C.:
 
       P 20° C. =11.595 bar 
       [0000]    
       
         
           
             Calculating the corresponding specific volume of the saturated vapor at 60° C.
 
First, the T 0  and P c  were calculated using Joback method:
 
           
         
       
     
         [0000]    
       
         
               
               
               
               
               
             
           
               
                   
               
               
                   
                   
                 Number of 
                   
                   
               
               
                   
                 Group 
                 groups 
                 ΔT ci   
                 ΔP ci   
               
               
                   
               
             
             
               
                   
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 1 
                 0.067 
                 −0.0168 
               
               
                   
               
               
                   
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 1 
                 0.0169 
                   0.0074 
               
               
                   
               
               
                   
                 —F 
                 5 
                 0.0111 × 5 
                 −0.0057 × 5 
               
               
                   
                 Total 
                   
                 0.0791 
                 −0.0168 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                     c 
                   
                   = 
                     
                    
                   
                     
                       T 
                       b 
                     
                     / 
                     
                       [ 
                       
                         0.584 
                         + 
                         
                           0.965 
                            
                           Σ 
                            
                           
                               
                           
                            
                           
                             n 
                             i 
                           
                            
                           Δ 
                            
                           
                               
                           
                            
                           T 
                         
                         - 
                         
                           
                             ( 
                             
                               Σ 
                                
                               
                                   
                               
                                
                               
                                 n 
                                 i 
                               
                                
                               Δ 
                                
                               
                                   
                               
                                
                               
                                 T 
                                 i 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       ] 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     227.84 
                     / 
                     
                       [ 
                       
                         0.584 
                         + 
                         
                           0.965 
                           × 
                           0.0791 
                         
                         - 
                         
                           0.0791 
                           2 
                         
                       
                       ] 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     348.3 
                      
                     
                         
                     
                      
                     K 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     c 
                   
                   = 
                     
                    
                   
                     
                       ( 
                       
                         0.113 
                         + 
                         
                           0.0032 
                            
                           
                               
                           
                            
                           
                             n 
                             A 
                           
                         
                         - 
                         
                           Σ 
                            
                           
                               
                           
                            
                           
                             n 
                             i 
                           
                            
                           Δ 
                            
                           
                               
                           
                            
                           
                             P 
                             i 
                           
                         
                       
                       ) 
                     
                     
                       - 
                       2 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       ( 
                       
                         0.113 
                         + 
                         
                           0.0032 
                           × 
                           7 
                         
                         - 
                         0.0168 
                       
                       ) 
                     
                     
                       - 
                       2 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     43.17 
                      
                     
                         
                     
                      
                     bar 
                   
                 
               
             
           
         
       
     
         [0000]    Secondly, we calculate the saturated vapor pressure at T r =0.7
 
(T=T r *T c =0.7×348.3=243.8 K) by the CSGC-PR method mentioned above, and the result is:
 
         [0000]    
       
         
           
             
               P 
               ω 
             
             = 
             
               2.12 
                
               
                   
               
                
               bar 
             
           
         
       
       
         
           
             
               
                 
                   ω 
                   = 
                     
                    
                   
                     
                       - 
                       
                         lgP 
                         
                           ω 
                            
                           
                               
                           
                            
                           r 
                         
                       
                     
                     - 
                     1.0 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       lg 
                        
                       
                         ( 
                         
                           
                             P 
                             ω 
                           
                           / 
                           
                             P 
                             c 
                           
                         
                         ) 
                       
                     
                     - 
                     1.0 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       - 
                       
                         lg 
                          
                         
                           ( 
                           
                             2.12 
                             / 
                             43.17 
                           
                           ) 
                         
                       
                     
                     - 
                     1.0 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   0.309 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     T 
                     r 
                   
                   = 
                     
                    
                   
                     T 
                     / 
                     
                       T 
                       c 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     333.15 
                     / 
                     348.3 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   0.9565 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     r 
                   
                   = 
                     
                    
                   
                     
                       P 
                       
                         60 
                          
                         ° 
                          
                         
                             
                         
                          
                         
                           C 
                           . 
                         
                       
                     
                     / 
                     
                       P 
                       c 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     31.161 
                     / 
                     43.17 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   0.7218 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     B 
                     
                       ( 
                       0 
                       ) 
                     
                   
                   = 
                     
                    
                   
                     0.083 
                     - 
                     
                       0.422 
                       / 
                       
                         T 
                         r 
                         1.6 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     0.0083 
                     - 
                     
                       0.4220 
                       / 
                       
                         0.9565 
                         1.6 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     - 
                     0.37012 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     B 
                     
                       ( 
                       1 
                       ) 
                     
                   
                   = 
                     
                    
                   
                     0.139 
                     - 
                     
                       0.172 
                       / 
                       
                         T 
                         r 
                         4.2 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     0.139 
                     - 
                     
                       0.172 
                       / 
                       
                         0.9565 
                         4.2 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     - 
                     0.0683 
                   
                 
               
             
           
         
       
       
         
           
             PV 
             = 
             ZRT 
           
         
       
       
         
           
             PV 
             = 
             
               
                 [ 
                 
                   1 
                   + 
                   
                     
                       ( 
                       
                         
                           B 
                           
                             ( 
                             0 
                             ) 
                           
                         
                         + 
                         
                           ω 
                            
                           
                               
                           
                            
                           
                             B 
                             
                               ( 
                               1 
                               ) 
                             
                           
                         
                       
                       ) 
                     
                      
                     
                       
                         T 
                         r 
                       
                       / 
                       
                         P 
                         r 
                       
                     
                   
                 
                 ] 
               
                
               RT 
             
           
         
       
       
         
           
             
               
                 
                   V 
                   = 
                     
                    
                   
                     
                       ( 
                       
                         
                           
                             T 
                             r 
                           
                           / 
                           
                             P 
                             r 
                           
                         
                         + 
                         
                           B 
                           
                             ( 
                             0 
                             ) 
                           
                         
                         + 
                         
                           ω 
                            
                           
                               
                           
                            
                           
                             B 
                             
                               ( 
                               1 
                               ) 
                             
                           
                         
                       
                       ) 
                     
                      
                     
                       
                         RT 
                         c 
                       
                       / 
                       
                         P 
                         c 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       [ 
                       
                         
                           0.9565 
                           / 
                           0.7218 
                         
                         - 
                         0.37012 
                         + 
                         
                           0.309 
                           × 
                           
                             ( 
                             
                               - 
                               0.0683 
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     × 
                   
                 
               
             
             
               
                 
                     
                    
                   
                     8.3145 
                     × 
                     
                       
                         348.3 
                         / 
                         43.17 
                       
                       / 
                       100 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     0.62656 
                      
                     
                         
                     
                      
                     L 
                      
                     
                       / 
                     
                      
                     mol 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     V 
                     
                       g 
                        
                       
                           
                       
                        
                       60 
                        
                       ° 
                        
                       
                           
                       
                        
                       
                         C 
                         . 
                       
                     
                   
                   = 
                     
                    
                   
                     V 
                     / 
                     M 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     0.62656 
                     / 
                     121.01 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     0.00518 
                      
                     
                         
                     
                      
                     
                       m 
                       3 
                     
                      
                     
                       / 
                     
                      
                     Kg 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   PV 
                   = 
                     
                    
                   
                     P 
                     
                       60 
                        
                       ° 
                        
                       
                           
                       
                        
                       
                         C 
                         . 
                         
                           V 
                           
                             g 
                              
                             
                                 
                             
                              
                             60 
                              
                             ° 
                              
                             
                                 
                             
                              
                             C 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     31.161 
                     × 
                     0.00518 
                     × 
                     1000 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     16.31 
                      
                     
                         
                     
                      
                     Kj 
                      
                     
                       / 
                     
                      
                     Kg 
                   
                 
               
             
           
         
       
     
         [0000]    Similarly, we can also figure out the specific volume of the vapor at 20° C.: 
         [0000]    
       
         
           
             
               V 
               
                 g 
                  
                 
                     
                 
                  
                 20 
                  
                 ° 
                  
                 
                     
                 
                  
                 
                   C 
                   . 
                 
               
             
             = 
             
               0.01438 
                
               
                   
               
                
               
                 m 
                 3 
               
                
               
                 / 
               
                
               Kg 
             
           
         
       
       
         
           
             
               
                 
                   
                     
                       V 
                       4 
                     
                     / 
                     
                       V 
                       3 
                     
                   
                   = 
                     
                    
                   
                     
                       V 
                       
                         g 
                          
                         
                             
                         
                          
                         20 
                          
                         ° 
                          
                         
                             
                         
                          
                         
                           C 
                           . 
                         
                       
                     
                     / 
                     
                       V 
                       
                         g 
                          
                         
                             
                         
                          
                         60 
                          
                         ° 
                          
                         
                             
                         
                          
                         
                           C 
                           . 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     0.01438 
                     / 
                     0.00518 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   2.69 
                 
               
             
           
         
       
       
         
           
             Calculating the corresponding specific heat of the saturated liquid at 40° C. The Rozicka-Domalski method was used to calculate the C pl  at 40° C. 
           
         
       
     
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                   
                 Number of 
                   
                   
                   
               
               
                   
                 Group 
                 groups 
                 a i   
                 B i   
                 c i   
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 —CF 3   
                 1 
                 15.423 
                 −9.2464 
                 2.8647 
               
               
                   
                 —NF 2   
                 1 
                 6.1358 
                 −0.17365 
                 0.026272 
               
               
                   
                 Total 
                   
                 21.5588 
                 −9.42005 
                 2.890972 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
           
             
               
                 
                   T 
                   = 
                     
                    
                   
                     40 
                     + 
                     273.15 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     313.15 
                      
                     
                         
                     
                      
                     K 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 C 
                 pl 
               
               / 
               R 
             
             = 
             
               
                 Σ 
                  
                 
                     
                 
                  
                 
                   n 
                   i 
                 
                  
                 
                   a 
                   i 
                 
               
               + 
               
                 Σ 
                  
                 
                     
                 
                  
                 
                   n 
                   i 
                 
                  
                 
                   
                     b 
                     i 
                   
                    
                   
                     ( 
                     
                       T 
                       / 
                       100 
                     
                     ) 
                   
                 
               
               + 
               
                 Σ 
                  
                 
                     
                 
                  
                 
                   n 
                   i 
                 
                  
                 
                   
                     
                       c 
                       i 
                     
                      
                     
                       ( 
                       
                         T 
                         / 
                         100 
                       
                       ) 
                     
                   
                   2 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     C 
                     pl 
                   
                   = 
                     
                    
                   
                     R 
                     × 
                     
                       { 
                       
                         
                           Σ 
                            
                           
                               
                           
                            
                           
                             n 
                             i 
                           
                            
                           
                             a 
                             i 
                           
                         
                         + 
                         
                           Σ 
                            
                           
                               
                           
                            
                           
                             n 
                             i 
                           
                            
                           
                             
                               b 
                               i 
                             
                              
                             
                               ( 
                               
                                 T 
                                 / 
                                 100 
                               
                               ) 
                             
                           
                         
                         + 
                         
                           Σ 
                            
                           
                               
                           
                            
                           
                             n 
                             i 
                           
                            
                           
                             
                               
                                 c 
                                 i 
                               
                                
                               
                                 ( 
                                 
                                   T 
                                   / 
                                   100 
                                 
                                 ) 
                               
                             
                             2 
                           
                         
                       
                       } 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     8.3145 
                     × 
                     
                       { 
                       
                         21.5588 
                         + 
                         
                           
                             ( 
                             
                               - 
                               9.42005 
                             
                             ) 
                           
                           × 
                           
                             ( 
                             
                               313.15 
                               / 
                               100 
                             
                             ) 
                           
                         
                         + 
                       
                     
                   
                 
               
             
             
               
                 
                     
                    
                   
                     2.890972 
                     × 
                     
                       
                         ( 
                         
                           313.15 
                           / 
                           100 
                         
                         ) 
                       
                       2 
                     
                   
                   } 
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     169.695 
                      
                     
                         
                     
                      
                     J 
                      
                     
                       / 
                     
                      
                     
                       mol 
                       · 
                       K 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     1.402 
                      
                     
                         
                     
                      
                     Kj 
                      
                     
                       / 
                     
                      
                     
                       Kg 
                       · 
                       K 
                     
                   
                 
               
             
           
         
       
       
         
           
             Calculating the thermal efficiency of the ORC 20-60 cycle: 
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     η 
                     GC 
                   
                   = 
                     
                    
                   
                     
                       
                         P 
                         1 
                       
                        
                       V 
                        
                       
                           
                       
                        
                       ln 
                        
                       
                           
                       
                        
                       
                         
                           P 
                           1 
                         
                         
                           P 
                           2 
                         
                       
                     
                     
                       
                         VH 
                         v 
                       
                       + 
                       
                         
                           C 
                           
                             p 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                          
                         
                           ( 
                           
                             
                               T 
                               1 
                             
                             - 
                             
                               T 
                               2 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     16.31 
                     × 
                     
                       
                         ln 
                          
                         
                           ( 
                           
                             31.161 
                             / 
                             11.595 
                           
                           ) 
                         
                       
                       / 
                       
                         [ 
                         
                           75.31 
                           + 
                           
                             1.402 
                             × 
                             
                               ( 
                               
                                 60 
                                 - 
                                 20 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     12.14 
                      
                     % 
                   
                 
               
             
           
         
       
     
         [0000]    Since the thermal efficiency correction scale factor is −0.652%
 
So the final result is η=12.14%-0.652%=11.49%
 
In conclusion:
 
       At 60° C.: 
       [0070]    ΔH v =9113.21 J/mol=75.31 kJ/kg 
       P 60° C. =31.161 bar 
       [0071]    v g 60° C. =0.00518 m 3 /Kg
 
PV=16.31 kJ/kg
 
       At 20° C.: 
     P 20° C. =11.595 bar 
       [0072]    v g 20° C. =0.01438 m 3 /Kg
 
v 4 /v 3 =2.69
 
       At 40° C.: 
     C pl =1.402 Kj/Kg·K 
       [0073]    η=11.49%
 
The same types of calculations are made for all molecules according to the present invention.
 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Results from group contribution calculations 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Latent 
                   
                   
               
               
                   
                 Critical 
                   
                   
                   
                   
                   
                   
                   
                 heat 
                 Specific 
                   
               
               
                   
                 points 
                 P1 
                 P2 
                 v g3   
                 v 4   
                 v g4   
                 Density 4l   
                 v l   
                 ΔH v   
                 heat C p   
                 PV 
               
               
                 Molecules 
                 (K) 
                 MPa 
                 MPa 
                 m 3 /Kg 
                 m 3 /Kg 
                 m 3 /Kg 
                 Kg/m 3   
                 m 3 /Kg 
                 (kJ/kg) 
                 (kJ/kg•K) 
                 kJ/kg 
               
               
                   
               
             
          
           
               
                 CH3—NHF 
                 428.8 
                 0.7866 
                 0.2323 
                 0.0633 
                 0.2143 
                 0.2023 
                 693.552 
                 0.00144 
                 411.46 
                 2.208 
                 49.78 
               
               
                 CH2F—NHF 
                 418.8 
                 0.8415 
                 0.2437 
                 0.0428 
                 0.14778 
                 0.1404 
                 772.906 
                 0.00129 
                 299.72 
                 1.827 
                 36.01 
               
               
                 CHF2—NHF 
                 412.4 
                 0.8863 
                 0.2567 
                 0.0317 
                 0.10958 
                 0.1047 
                 854.775 
                 0.00117 
                 232.59 
                 1.571 
                 28.13 
               
               
                 CF3—NHF 
                 406.3 
                 0.9737 
                 0.2914 
                 0.0235 
                 0.07857 
                 0.0755 
                 1,025.16 
                 0.00098 
                 182.95 
                 1.38 
                 22.9 
               
               
                 CH3—NF2 
                 406.6 
                 1.1723 
                 0.3875 
                 0.0297 
                 0.08977 
                 0.0863 
                 923.882 
                 0.00108 
                 255.15 
                 1.721 
                 34.79 
               
               
                 CH2F—NF2 
                 360 
                 2.698 
                 0.9858 
                 0.0089 
                 0.02445 
                 0.0248 
                 1,028.57 
                 0.00097 
                 134.02 
                 1.664 
                 24.1 
               
               
                 CHF2—NF2 
                 354.4 
                 2.859 
                 1.0426 
                 0.0068 
                 0.01868 
                 0.0191 
                 1,108.33 
                 0.0009 
                 102.21 
                 1.513 
                 19.47 
               
               
                 CF3—NF2 
                 348.4 
                 3.1125 
                 1.1585 
                 0.0052 
                 0.01393 
                 0.0144 
                 1,271.63 
                 0.00079 
                 75.27 
                 1.402 
                 16.13 
               
               
                 CH3—CH2—NHF 
                 453.5 
                 0.3772 
                 0.0957 
                 0.1069 
                 0.4215 
                 0.3906 
                 672.635 
                 0.00149 
                 378.33 
                 2.154 
                 40.34 
               
               
                 CH2F—CH2—NHF 
                 443.7 
                 0.398 
                 0.0984 
                 0.0783 
                 0.37989 
                 0.295 
                 669.078 
                 0.00149 
                 295.97 
                 1.849 
                 37.38 
               
               
                 CHF2—CH2—NHF 
                 437.5 
                 0.418 
                 0.1032 
                 0.0607 
                 0.28125 
                 0.2296 
                 704.21 
                 0.00142 
                 240.21 
                 1.622 
                 29.02 
               
               
                 CF3—CH2—NHF 
                 431.6 
                 0.4641 
                 0.119 
                 0.0458 
                 0.19913 
                 0.1676 
                 833.068 
                 0.0012 
                 195.41 
                 1.442 
                 23.7 
               
               
                 CH3—CHF—NHF 
                 446.9 
                 0.396 
                 0.1002 
                 0.0788 
                 0.19909 
                 0.2896 
                 760.097 
                 0.00132 
                 292.16 
                 1.808 
                 19.95 
               
               
                 CH2F—CHF—NHF 
                 437.5 
                 0.418 
                 0.1032 
                 0.0607 
                 0.28116 
                 0.2296 
                 704.21 
                 0.00142 
                 240.21 
                 1.622 
                 29.02 
               
               
                 CHF2—CHF—NHF 
                 431.5 
                 0.4393 
                 0.1083 
                 0.0485 
                 0.21881 
                 0.1847 
                 714.374 
                 0.0014 
                 201.48 
                 1.466 
                 23.7 
               
               
                 CF3—CHF—NHF 
                 425.6 
                 0.4879 
                 0.1249 
                 0.0375 
                 0.16016 
                 0.1381 
                 826.802 
                 0.00121 
                 167.69 
                 1.33 
                 20 
               
               
                 CH3—CF2—NHF 
                 440.8 
                 0.4388 
                 0.1152 
                 0.0576 
                 0.14968  
                 0.2051 
                 922.119 
                 0.00108 
                 230.17 
                 1.561 
                 17.24 
               
               
                 CH2F—CF2—NHF 
                 431.6 
                 0.4641 
                 0.119 
                 0.0458 
                 0.19857 
                 0.1676 
                 833.068 
                 0.0012 
                 195.41 
                 1.442 
                 23.63 
               
               
                 CHF2—CF2—NHF 
                 425.6 
                 0.4879 
                 0.1249 
                 0.0375 
                 0.15972 
                 0.1381 
                 826.791 
                 0.00121 
                 167.7 
                 1.33 
                 19.95 
               
               
                 CF3—CF2—NHF 
                 419.8 
                 0.5407 
                 0.1435 
                 0.0295 
                 0.52019 
                 0.1054 
                 939.588 
                 0.00106 
                 141.91 
                 1.228 
                 74.65 
               
               
                 CH3—CH2—NF2 
                 395 
                 1.2373 
                 0.4077 
                 0.0228 
                 0.06906 
                 0.0671 
                 921.083 
                 0.00109 
                 203.1 
                 1.79 
                 28.16 
               
               
                 CH2F—CH2—NF2 
                 386.3 
                 1.3348 
                 0.4322 
                 0.017 
                 0.06328  
                 0.0514 
                 903.794 
                 0.00111 
                 162.58 
                 1.616 
                 27.35 
               
               
                 CHF2—CH2—NF2 
                 380.6 
                 1.411 
                 0.4565 
                 0.0134 
                 0.04867 
                 0.0409 
                 927.941 
                 0.00108 
                 133.52 
                 1.469 
                 22.22 
               
               
                 CF3—CH2—NF2 
                 374.8 
                 1.5417 
                 0.5128 
                 0.0104 
                 0.03641 
                 0.0312 
                 1,064.63 
                 0.00094 
                 108.11 
                 1.345 
                 18.67 
               
               
                 CH3—CHF—NF2 
                 389.1 
                 1.3039 
                 0.4297 
                 0.0174 
                 0.03721 
                 0.0518 
                 1,012.68 
                 0.00099 
                 161.79 
                 1.579 
                 15.99 
               
               
                 CH2F—CHF—NF2 
                 380.6 
                 1.411 
                 0.4565 
                 0.0134 
                 0.04872 
                 0.0409 
                 927.941 
                 0.00108 
                 133.52 
                 1.469 
                 22.24 
               
               
                 CHF2—CHF—NF2 
                 375.3 
                 1.4895 
                 0.4817 
                 0.0108 
                 0.03876 
                 0.0334 
                 929.472 
                 0.00108 
                 111.69 
                 1.362 
                 18.67 
               
               
                 CF3—CHF—NF2 
                 369.4 
                 1.6326 
                 0.542 
                 0.0085 
                 0.02964 
                 0.0258 
                 1,042.93 
                 0.00096 
                 91.63 
                 1.269 
                 16.07 
               
               
                 CH3—CF2—NF2 
                 383.1 
                 1.4215 
                 0.4817 
                 0.0133 
                 0.02906 
                 0.0386 
                 1,177.56 
                 0.00085 
                 128.9 
                 1.416 
                 14 
               
               
                 CH2F—CF2—NF2 
                 374.8 
                 1.5417 
                 0.5128 
                 0.0104 
                 0.0363 
                 0.0312 
                 1,064.63 
                 0.00094 
                 108.11 
                 1.345 
                 18.61 
               
               
                 CHF2—CF2—NF2 
                 369.4 
                 1.6326 
                 0.542 
                 0.0085 
                 0.0295 
                 0.0258 
                 1,042.93 
                 0.00096 
                 91.63 
                 1.269 
                 15.99 
               
               
                 CF3—CF2—NF2 
                 363.6 
                 1.7839 
                 0.6076 
                 0.0068 
                 0.02009 
                 0.0203 
                 1,161.13 
                 0.00086 
                 75.33 
                 1.198 
                 12.21 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 536.2 
                 0.1143 
                 0.0237 
                 0.546 
                 2.63334 
                 2.3648 
                 679.138 
                 0.00147 
                 684.94 
                 2.183 
                 62.41 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 461.4 
                 0.3759 
                 0.0968 
                 0.0861 
                 0.33416 
                 0.3086 
                 1,007.23 
                 0.00099 
                 301.37 
                 1.524 
                 32.35 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 456.1 
                 0.3968 
                 0.1006 
                 0.0559 
                 0.22034 
                 0.2039 
                 1,374.11 
                 0.00073 
                 208.23 
                 1.184 
                 22.17 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 458.7 
                 0.3864 
                 0.0986 
                 0.0681 
                 0.26685 
                 0.2467 
                 1,202.83 
                 0.00083 
                 246.29 
                 1.323 
                 26.31 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 475.5 
                 0.3221 
                 0.0796 
                 0.1018 
                 0.4118 
                 0.3777 
                 1,146.78 
                 0.00087 
                 315.71 
                 1.454 
                 32.78 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 478.3 
                 0.3139 
                 0.0783 
                 0.1353 
                 0.54259 
                 0.4972 
                 901.88 
                 0.00111 
                 407.39 
                 1.819 
                 42.48 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 499.2 
                 0.2195 
                 0.0534 
                 0.1961 
                 0.80611 
                 0.7331 
                 873.019 
                 0.00115 
                 423.06 
                 1.703 
                 43.05 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 478.7 
                 0.2689 
                 0.0667 
                 0.0995 
                 0.40101 
                 0.3674 
                 1,239.43 
                 0.00081 
                 257.47 
                 1.29 
                 26.75 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 481.5 
                 0.2625 
                 0.0657 
                 0.1252 
                 0.50028 
                 0.458 
                 1,021.68 
                 0.00098 
                 314.83 
                 1.484 
                 32.87 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 464.6 
                 0.3139 
                 0.0808 
                 0.0842 
                 0.32692 
                 0.3015 
                 1,106.62 
                 0.0009 
                 246.43 
                 1.348 
                 26.42 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 462 
                 0.3219 
                 0.0822 
                 0.0691 
                 0.27075 
                 0.2499 
                 1,277.47 
                 0.00078 
                 208.55 
                 1.205 
                 22.26 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 459.4 
                 0.3302 
                 0.0837 
                 0.0582 
                 0.22964 
                 0.2122 
                 1,428.48 
                 0.0007 
                 180.91 
                 1.102 
                 19.22 
               
               
                   
               
             
          
         
       
     
       Calculation of Thermal Efficiency 
     Equation of Thermal Efficiency 
       [0074]    The  FIG. 1  shows the principle of the ORC cycle. The efficiency may be calculated using the equation: 
         [0000]    
       
         
           
             
               
                 
                   η 
                   = 
                   
                     
                       
                         h 
                         3 
                       
                       - 
                       
                         h 
                         4 
                       
                     
                     
                       
                         h 
                         3 
                       
                       - 
                       
                         h 
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Four basic equations of thermodynamics are: 
         [0000]        dU=TdS−pdV   (2a)
 
         [0000]        dH=TdS+Vdp   (2b)
 
         [0000]        dA=−pdV−SdT   (2c)
 
         [0000]        dG=Vpd−SdT   (2d)
 
         [0000]    Also, for the ORC, the process from position 3 to position 4 is an isentropic process. Therefore, 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       h 
                       3 
                     
                     - 
                     
                       h 
                       4 
                     
                   
                   = 
                   
                     PV 
                      
                     
                         
                     
                      
                     ln 
                      
                     
                       
                         
                           P 
                           1 
                         
                         
                           P 
                           2 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The total heat absorption process should be from point 1 to point 3.
 
The total heat can be calculated as
 
         [0000]        h   3   −h   1   =ΔH   v   +C   y ( T   1   −T   2 ) 
         [0000]    the efficiency η then can be written as, 
         [0000]    
       
         
           
             
               
                 
                   η 
                   = 
                   
                     
                       
                         
                           h 
                           3 
                         
                         - 
                         
                           h 
                           4 
                         
                       
                       
                         
                           h 
                           3 
                         
                         - 
                         
                           h 
                           1 
                         
                       
                     
                     = 
                     
                       
                         
                           PV 
                            
                           
                               
                           
                            
                           ln 
                            
                           
                             
                               P 
                               1 
                             
                             
                               P 
                               2 
                             
                           
                         
                         
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               H 
                               v 
                             
                           
                           + 
                           
                             
                               C 
                               p 
                             
                              
                             
                               ( 
                               
                                 
                                   T 
                                   1 
                                 
                                 + 
                                 
                                   T 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The efficiency of new molecules can be estimated by the equation (5), and the useful parameters in the new molecules are calculated by the Group Contribution Method. 
       Systematic Error of Efficiency 
       [0075]    A standard deviation method was used to correct the systematic error of the efficiencies calculation of the candidate molecules and give the thermal efficiency.
 
At first, usage was made of the efficiencies
 
         [0000]    
       
         
           
             
               
                 
                   
                     η 
                     a 
                   
                   = 
                   
                     
                       
                         h 
                         3 
                       
                       - 
                       
                         h 
                         4 
                       
                     
                     
                       
                         h 
                         3 
                       
                       - 
                       
                         h 
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    calculated by using the enthalpy of the working fluids in software Refprop as the accurate results. Then, calculating the same efficiencies by another formula developed by using the thermodynamic data in software Refprop 
         [0000]    
       
         
           
             
               
                 
                   
                     η 
                     REFPROP 
                   
                   = 
                   
                     
                       
                         PV 
                          
                         
                             
                         
                          
                         ln 
                          
                         
                           
                             P 
                             1 
                           
                           
                             P 
                             2 
                           
                         
                       
                       
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             H 
                             v 
                           
                         
                         + 
                         
                           
                             C 
                             p 
                           
                            
                           
                             ( 
                             
                               
                                 T 
                                 1 
                               
                               + 
                               
                                 T 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Comparing η a  and η REFPROP , and calculating the standard deviation σ=0.32%, one could see that the average correction to η REFPROP  is about 0.32%. This average error comes from the formula which is a good approximation. Then, calculations were made of the efficiencies η group contribution  based on the same formula as equation (2) but using the thermodynamic data estimated by the group contribution method. Comparing η a  and η group contribution  and calculating the standard deviation σ=0.65%, one could see that the average correction to η group contribution  is about 0.65%. The average deviation comes from both the approximate formula and the group contribution method. The results from the above mentioned calculations are listed in the following Table 2 and  FIG. 2 . From  FIG. 2 , one can see that η group contribution  is systematically higher than η a , and that the average difference is just the standard deviation. Thus, by subtracting σ=0.65% from η group contribution  the efficiencies of the designed molecules of working fluids are obtained. Another issue to mention is: before correction of η group contribution  by subtracting 0.65%, some efficiencies of the candidate working fluids are larger than 12% which are beyond the limit of the ideal Carnot cycle, which is 40/333.15=12%. Thus, after the correction, all the efficiencies are less than 12%, which is reasonable. Although the standard deviation 0.65% is calculated from the existing molecules, it is also applicable for the designed molecules. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Efficiency calculations with and without group contribution. Results from known existing molecules 
               
             
          
           
               
                   
                   
                   
                   
                   
                 η Group   
                 σ Group   
               
               
                 Substances 
                 Molecules 
                 η a   
                 η REFPROP   
                 σ REFPROP   
                 Contribution 
                 Contribution 
               
               
                   
               
             
          
           
               
                 R21 
                 CHCl 2 F 
                 11.14% 
                 11.71% 
                 0.32% 
                 12.04% 
                 0.65% 
               
               
                 R22 
                 CHClF 2   
                 11.11% 
                 11.03% 
                   
                 12.28% 
               
               
                 R11 
                 CCl 3 F 
                 11.07% 
                 11.55% 
                   
                 11.92% 
               
               
                 trifluoroiodomethane 
                 CF 3 I 
                 11.05% 
                 11.15% 
                   
                 11.69% 
               
               
                 R12 
                 CCl 2 F 2   
                 10.97% 
                 10.85% 
                   
                 11.70% 
               
               
                 dimethylether 
                 CH 3 OCH 3   
                 11.02% 
                 11.13% 
                   
                 11.78% 
               
               
                 R141b 
                 FCCl 2 —CH 3   
                 11.01% 
                 11.47% 
                   
                 11.79% 
               
               
                 R152a 
                 CH 3 CHF 2   
                 10.97% 
                 10.96% 
                   
                 11.75% 
               
               
                 R123* 
                 CHCl 2 CF 3   
                 10.87% 
                 11.13% 
                   
                 11.50% 
               
               
                 R113* 
                 CCl 2 FCClF 2   
                 10.79% 
                 11.10% 
                   
                 11.50% 
               
               
                 R134a 
                 CH 2 FCF 3   
                 10.78% 
                 10.43% 
                   
                 11.40% 
               
               
                 R124* 
                 Cl—CHF—CF 3   
                 10.73% 
                 10.51% 
                   
                 11.15% 
               
               
                 R142b 
                 ClCF 2 CH 3   
                 10.89% 
                 10.94% 
                   
                 11.22% 
               
               
                 R114 
                 CClF 2 CClF 2   
                 10.58% 
                 10.48% 
                   
                 11.04% 
               
               
                 propyne 
                 CH≡CCH 3   
                 11.21% 
                 11.45% 
                   
                 11.89% 
               
               
                 propylene 
                 CH 2 ═CHCH 3   
                 11.08% 
                 10.71% 
                   
                 12.24% 
               
               
                 propane 
                 CH 3 CH 2 CH 3   
                 10.97% 
                 10.57% 
                   
                 11.80% 
               
               
                 R245ca* 
                 CHF 2 CF 2 CH 2 F 
                 10.73% 
                 10.85% 
                   
                 11.24% 
               
               
                 R245fa* 
                 CF 3 CH 2 CHF 2   
                 10.70% 
                 10.77% 
                   
                 11.11% 
               
               
                 R236fa* 
                 CF 3 CH 2 CF 3   
                 10.48% 
                 10.14% 
                   
                 10.73% 
               
               
                 R227ea* 
                 CF 3 —CHF—CF 3   
                 10.28% 
                 9.57% 
                   
                 10.47% 
               
               
                 Acetone 
                 CH 3 COCH 3   
                 11.17% 
                 11.90% 
                   
                 12.26% 
               
               
                 R236ea* 
                 CF 3 —CHF—CHF 2   
                 10.52% 
                 10.37% 
                   
                 10.91% 
               
               
                 trans-butene* 
                 CH 3 CH═CHCH 3   
                 10.91% 
                 11.04% 
                   
                 11.53% 
               
               
                 1-butene* 
                 CH 2 ═CHCH 2 CH 3   
                 10.90% 
                 10.95% 
                   
                 11.37% 
               
               
                 isobutene* 
                 CH 2 ═C(CH 3 )CH 3   
                 10.86% 
                 10.87% 
                   
                 11.35% 
               
               
                 butane* 
                 CH 3 CH 2 CH 2 CH 3   
                 10.80% 
                 10.80% 
                   
                 11.21% 
               
               
                 isobutane* 
                 CH(CH 3 ) 3   
                 10.76% 
                 10.60% 
                   
                 11.10% 
               
               
                 R365mfc* 
                 CF 3 —CF 2 —CH 2 —CF 3   
                 10.58% 
                 10.71% 
                   
                 10.75% 
               
               
                 perfluorobutane* 
                 CF 3 —CF 2 —CF 2 —CF 3   
                 9.67% 
                 9.02% 
                   
                 9.80% 
               
               
                 cis-butene 
                 CH 3 CH═CHCH 3   
                 10.96% 
                 11.20% 
                   
                 11.53% 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Results from efficiency calculations using group contribution method 
               
               
                 and final efficiency after calculations using enthalpies, software Refprop 
               
               
                 and group contribution method. Results from molecules according to the 
               
               
                 present invention 
               
             
          
           
               
                   
                 P1 
                 P2 
                   
                   
               
               
                 Molecules 
                 MPa 
                 MPa 
                 η  GC   
                 η 
               
               
                   
               
             
          
           
               
                 CH3—NHF 
                 0.7866 
                 0.2323 
                 12.15% 
                 11.50% 
               
               
                 CH2F—NHF 
                 0.8415 
                 0.2437 
                 11.97% 
                 11.32% 
               
               
                 CHF2—NHF 
                 0.8863 
                 0.2567 
                 11.80% 
                 11.15% 
               
               
                 CF3—NHF 
                 0.9737 
                 0.2914 
                 11.60% 
                 10.95% 
               
               
                 CH3—NF2 
                 1.1723 
                 0.3875 
                 11.89% 
                 11.23% 
               
               
                 CH2F—NF2 
                 2.698 
                 0.9858 
                 12.10% 
                 11.45% 
               
               
                 CHF2—NF2 
                 2.859 
                 1.0426 
                 12.07% 
                 11.42% 
               
               
                 CF3—NF2 
                 3.1125 
                 1.1585 
                 12.14% 
                 11.49% 
               
               
                 CH3—CH2—NHF 
                 0.3772 
                 0.0957 
                 11.91% 
                 11.26% 
               
               
                 CH2F—CH2—NHF 
                 0.398 
                 0.0984 
                 11.78% 
                 11.12% 
               
               
                 CHF2—CH2—NHF 
                 0.418 
                 0.1032 
                 11.63% 
                 10.98% 
               
               
                 CF3—CH2—NHF 
                 0.4641 
                 0.119 
                 11.42% 
                 10.77% 
               
               
                 CH3—CHF—NHF 
                 0.396 
                 0.1002 
                 11.76% 
                 11.11% 
               
               
                 CH2F—CHF—NHF 
                 0.418 
                 0.1032 
                 11.63% 
                 10.98% 
               
               
                 CHF2—CHF—NHF 
                 0.4393 
                 0.1083 
                 11.48% 
                 10.83% 
               
               
                 CF3—CHF—NHF 
                 0.4879 
                 0.1249 
                 11.28% 
                 10.63% 
               
               
                 CH3—CF2—NHF 
                 0.4388 
                 0.1152 
                 11.56% 
                 10.91% 
               
               
                 CH2F—CF2—NHF 
                 0.4641 
                 0.119 
                 11.42% 
                 10.77% 
               
               
                 CHF2—CF2—NHF 
                 0.4879 
                 0.1249 
                 11.28% 
                 10.63% 
               
               
                 CF3—CF2—NHF 
                 0.5407 
                 0.1435 
                 11.08% 
                 10.43% 
               
               
                 CH3—CH2—NF2 
                 1.2373 
                 0.4077 
                 11.38% 
                 10.73% 
               
               
                 CH2F—CH2—NF2 
                 1.3348 
                 0.4322 
                 11.24% 
                 10.59% 
               
               
                 CHF2—CH2—NF2 
                 1.411 
                 0.4565 
                 11.09% 
                 10.44% 
               
               
                 CF3—CH2—NF2 
                 1.5417 
                 0.5128 
                 10.92% 
                 10.27% 
               
               
                 CH3—CHF—NF2 
                 1.3039 
                 0.4297 
                 11.23% 
                 10.57% 
               
               
                 CH2F—CHF—NF2 
                 1.411 
                 0.4565 
                 11.09% 
                 10.44% 
               
               
                 CHF2—CHF—NF2 
                 1.4895 
                 0.4817 
                 10.96% 
                 10.31% 
               
               
                 CF3—CHF—NF2 
                 1.6326 
                 0.542 
                 10.80% 
                 10.15% 
               
               
                 CH3—CF2—NF2 
                 1.4215 
                 0.4817 
                 11.03% 
                 10.38% 
               
               
                 CH2F—CF2—NF2 
                 1.5417 
                 0.5128 
                 10.92% 
                 10.27% 
               
               
                 CHF2—CF2—NF2 
                 1.6326 
                 0.542 
                 10.80% 
                 10.15% 
               
               
                 CF3—CF2—NF2 
                 1.7839 
                 0.6076 
                 10.67% 
                 10.02% 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.1143 
                 0.0237 
                 12.57% 
                 11.92% 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.3759 
                 0.0968 
                 12.11% 
                 11.46% 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.3968 
                 0.1006 
                 11.90% 
                 11.25% 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.3864 
                 0.0986 
                 12.01% 
                 11.36% 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.3221 
                 0.0796 
                 12.26% 
                 11.61% 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.3139 
                 0.0783 
                 12.29% 
                 11.64% 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.2195 
                 0.0534 
                 12.39% 
                 11.74% 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.2689 
                 0.0667 
                 12.07% 
                 11.42% 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.2625 
                 0.0657 
                 12.17% 
                 11.52% 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.3139 
                 0.0808 
                 11.94% 
                 11.29% 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.3219 
                 0.0822 
                 11.83% 
                 11.18% 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.3302 
                 0.0837 
                 11.72% 
                 11.07% 
               
               
                   
               
               
                 Note: 
               
               
                 ηGC is calculated by the Group Contribution Method 
               
               
                 η is the final estimated efficiency 
               
               
                 η is equal to: (η  GC ) − (systematic error) 
               
               
                 The systematic error is shown above and is the standard deviation σ = 0.65% 
               
             
          
         
       
     
       Calculation of Flammability and Toxicity 
     Prediction of Flammability of Gases by Using the F-Number Analysis 
       [0076]        F= 1−( L/U ) 0.5  
 
         [0000]    L is the lower flammability limit
 
U is the upper flammability limit
 
F=0.0-0.2 vaguely flammable
 
F=0.2-0.4 weakly flammable
 
F=0.4-0.6 normally flammable
 
F=0.6-0.8 strongly flammable
 
F=0.8-1.0 super flammable
 
F=p1(1+p2C1+p3ROE+p4RCO+p5RCOO+p6RNH+p7RRNG+p8RARM+p9RUS)×(1+p10RF+p11RCI+p12RBr+p13ROH+p14RNO2+p15RNH2+p16RCN+P17RCOOH)
 
         [0000]    
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Parameter values obtained by the analysis 
               
             
          
           
               
                   
                 No. 
                 Description 
                 Obtained value 
               
               
                   
                   
               
             
          
           
               
                   
                 p1 
                 Main coefficient 
                 0.581 
               
               
                   
                 p2 
                 If one carbon 
                 −0.194 
               
               
                   
                 p3 
                 Ether 
                 0.134 
               
               
                   
                 p4 
                 Carbonyl 
                 0.028 
               
               
                   
                 p5 
                 Ester 
                 −0.097 
               
               
                   
                 p6 
                 NH 
                 −0.014 
               
               
                   
                 p7 
                 Aliphatic ring 
                 0.299 
               
               
                   
                 p8 
                 Aromatic ring 
                 −0.125 
               
               
                   
                 p9 
                 Unsaturation 
                 0.290 
               
               
                   
                 p10 
                 F 
                 −0.344 
               
               
                   
                 p11 
                 Cl 
                 −0.985 
               
               
                   
                 p12 
                 Br 
                 −3.160 
               
               
                   
                 p13 
                 OH 
                 0.284 
               
               
                   
                 p14 
                 NO2 
                 0.527 
               
               
                   
                 p15 
                 NH2 
                 −0.344 
               
               
                   
                 p16 
                 CN 
                 −0.566 
               
               
                   
                 p17 
                 COOH 
                 −0.850 
               
               
                   
                   
               
             
          
         
       
     
         [0077]    C1 takes the value of 1 or 0 according to whether the molecule is a compound of mono-carbon skeleton or not. However, the methane derivatives that contain CO, COO, CN, or COOH group are treated exceptionally; C1 takes the value of 0 for these compounds. ROE, RCO, RCOO, and RNH denote numbers of ether, carbonyl, ester, and imine groups, respectively, divided by the total number of skeletal carbons. RRNG and RARM denote numbers of aliphatic and aromatic rings, respectively, divided by the total number of skeletal carbons. RUS denotes the total number of unsaturation in the carbon skeleton including aliphatic and aromatic rings divided by the total number of skeletal carbons. RF, RCI, and so on, and RCOOH denote numbers of F, Cl, and so on, and COOH, respectively, divided by the total number of hydrogen atoms in the corresponding pure hydrocarbon molecule. 
         [0078]    Reference of Flammability: 
       R600 F=0.581 
     R134a F=0.4478 
     Application of Group Contribution Method for Predicting the Toxicity of Organic Chemicals 
       [0079]      Set  C=− log( LC 50)=Σ Niai  
 
         [0000]    Equation: LC50=concentration casing 50% mortality in fathead minnow 
         [0080]    Ni=number of group of type i 
         [0081]    ai=contribution of group of type i 
         [0082]    Currently, the C of common refrigerants is less than 2. Therefore, the working fluids with C values less than 2 are recommended. 
         [0000]                                                TABLE 5                   Toxicity contribution for substituent groups in       the data-set chemicals for fathead minnow toxicity            No.   Group Name   Contribution values                    1   CH3   0.6791       2   CH2   0.2925       3   CH   0.3305       4   C   0.06214       5   F   0.4034       6   Cl   0.8712       7   Br   0.8515       8   O   −0.4086       9   OH   0.3392       10   CO   −0.2842       11   CHO   1.331       12   ArCH   0.4575       13   ArC   0.2913       14   CN   0.6333       15   N   −0.7043       16   NH   −0.1157       17   NH2   0.1883       18   NO2   0.7276                    
For example:
 
         [0000]    
       
                 
         
             
             
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Flammability and toxicity calculations made by group contribution 
               
               
                 calculations. Results from molecules according to the present invention 
               
             
          
           
               
                   
                 Flammability 
                 Toxicity 
               
               
                 Molecules 
                 (F) 
                 C 
               
               
                   
               
             
          
           
               
                 CH3—NHF 
                 0.420579 
                 0.9668 
               
               
                 CH2F—NHF 
                 0.381006 
                 0.9836 
               
               
                 CHF2—NHF 
                 0.341433 
                 1.425 
               
               
                 CF3—NHF 
                 0.30186 
                 1.56004 
               
               
                 CH3—NF2 
                 0.387741 
                 0.7816 
               
               
                 CH2F—NF2 
                 0.347468 
                 0.7984 
               
               
                 CHF2—NF2 
                 0.307196 
                 1.2398 
               
               
                 CF3—NF2 
                 0.266923 
                 1.37484 
               
               
                 CH3—CH2—NHF 
                 0.543856 
                 1.2593 
               
               
                 CH2F—CH2—NHF 
                 0.510778 
                 1.2761 
               
               
                 CHF2—CH2—NHF 
                 0.477701 
                 1.7175 
               
               
                 CF3—CH2—NHF 
                 0.444623 
                 1.2593 
               
               
                 CH3—CHF—NHF 
                 0.510778 
                 1.7007 
               
               
                 CH2F—CHF—NHF 
                 0.477701 
                 1.7175 
               
               
                 CHF2—CHF—NHF 
                 0.444623 
                 2.1589 
               
               
                 CF3—CHF—NHF 
                 0.411546 
                 2.29394 
               
               
                 CH3—CF2—NHF 
                 0.477701 
                 1.83574 
               
               
                 CH2F—CF2—NHF 
                 0.444623 
                 1.85254 
               
               
                 CHF2—CF2—NHF 
                 0.411546 
                 2.29394 
               
               
                 CF3—CF2—NHF 
                 0.378468 
                 2.42898 
               
               
                 CH3—CH2—NF2 
                 0.514379 
                 1.0741 
               
               
                 CH2F—CH2—NF2 
                 0.481068 
                 1.0909 
               
               
                 CHF2—CH2—NF2 
                 0.447757 
                 1.5323 
               
               
                 CF3—CH2—NF2 
                 0.414447 
                 1.66734 
               
               
                 CH3—CHF—NF2 
                 0.481068 
                 1.5155 
               
               
                 CH2F—CHF—NF2 
                 0.447757 
                 1.5323 
               
               
                 CHF2—CHF—NF2 
                 0.414447 
                 1.9737 
               
               
                 CF3—CHF—NF2 
                 0.381136 
                 2.10874 
               
               
                 CH3—CF2—NF2 
                 0.447757 
                 1.65054 
               
               
                 CH2F—CF2—NF2 
                 0.414447 
                 1.66734 
               
               
                 CHF2—CF2—NF2 
                 0.381136 
                 2.10874 
               
               
                 CF3—CF2—NF2 
                 0.347825 
                 2.24378 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.748038 
                 0.4693 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.619375 
                 1.3521 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.490713 
                 1.62218 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.555044 
                 1.48714 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.619375 
                 1.04574 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.683706 
                 0.9107 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.687424 
                 0.2841 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.558062 
                 0.86054 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.622743 
                 0.7255 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.558062 
                 1.1669 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.493381 
                 1.30194 
               
               
                   
               
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
                 0.4287 
                 1.43698 
               
               
                   
               
             
          
         
       
     
       Calculation of Ozone Depletion Potential 
       [0083]    No bromine or chlorine in the molecules. Thus, ODP is 0.