WORKING FLUID FOR RANKINE CYCLE

Field of the invention

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

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.

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'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.

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.

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.

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.

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 Figure 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.

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 in most 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.

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.

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).

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.

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.

US 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.

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.

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

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.

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.

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 iow ODP and low or reasonable corrosion on copper (if this material is used for e.g. pipings and/or heat exchanger).

The working fluids according to the present invention comprise at least one compound having a structure according to Formula (I):

RNQ

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.

One embodiment of the present invention relates to an organic Rankine cycle working fluid comprising at least one compound having either the Formula (II):

R ¹ NHnF _2-n , wherein

R ¹ is fluorinated or non-fluorinated methyl, ethyl, vinyl or ethynyl, and n is 0 or 1 ; or

the Formula (III):

N

/ \

R ² C CR ³ wherein

R ² and R ³ are independently chosen from H ₂ , F ₂ and HF, and

p is 0 or 1, preferably 1.

Preferably, R ¹ in Formula (II) is a fluorinated or non-fluorinated methyl or ethyl group.

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 _2l CHF ₂ NF ₂ , CF ₃ NF ₂ , C ₂ H ₅ NHF, CH ₂ FCH ₂ NHF, CHF ₂ CH ₂ NHF, CHsCHFNHF, 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 .

R ² in Formula (III) contains preferably at least one fluorine. The compound according to Formula (III) is preferably tetrafluoroaziridine.

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:

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.

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.

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. Still another embodiment of the present invention relates to an organic Rankine cycle system comprising:

(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.

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.

In a further embodiment the expander is a turbine, screw expander, scroll expander, or piston expander.

Still one embodiment relates to use of a working fluid according to the present invention for transfer of heat.

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.

Another embodiment relates to a method for power generation comprising transfer of heat using a working fluid according to the present invention.

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.

Another embodiment relates to a compound having the Formula (IV):

H I

N

/ \

F ₂ C— CF ₂

Short summary of the drawings

Figure 1 shows a pressure-enthalpy graph.

Figure 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.

Figure 3 shows a schematic drawing of an organic Rankine Cycle system.

Detailed description of the invention

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.

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 Figure 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, 101.325KPa 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.

All the data of the working fluids to calculate the efficiencies η, 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.

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.

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.

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.

A working fluid according to the present invention comprises at least one compound having a structure according to Formula (I):

RNQ

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.

Preferably the working fluid according to the present invention comprises at least one compound having either the Formula (II): wherein

R ¹ is fluorinated or non-fluorinated methyl, ethyl, vinyl or ethynyl, and n is 0 or 1; or

the Formula (III):

HpFi. _p

I

N

/ \

R ² C— CR ³

wherein

R ² and R ³ are independently chosen from H ₂ , F ₂ and HF, and

p is 0 or 1.

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, CF3NHF, CH ₃ NF ₂ , CH2FNF2, CHF2NF2, CF ₃ NF2, C ₂ H ₅ NHF, CH ₂ FCH ₂ NHF, CHF2CH ₂ NHF, CH3CHFNHF,

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 CH3NHF, CH ₂ FNHF, CHF ₂ NHF, CF3NHF, CH3NF2, CH ₂ FNF ₂ , CHF ₂ NF ₂ , CF ₃ NF ₂ , C2H5NHF, CH2FCH ₂ NHF, CHF2CH2NHF, CH3CHFNHF, and CH ₂ FCHFNHF,

More preferably R ¹ is a fluorinated or non-fluorinated methyl group, and especially in combination with p being 0.

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.

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.

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.

One of the more preferred compounds having Formula (III) is tetrafluoroaziridine. The synthesis of the tetrafluoroaziridin may be done by the followin reaction steps:

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 tetrafluorovinyl- azide. 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

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

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

CF ₃ NF ₂ molecule weight: M=121.01

9 Calculating the normal boiling point T by Joback method

Group Number of ΔΤ_>Ι

groups

>c< 1 18.25

— N< 1 1 1.74

— F 5 -0.03x5

Total 29.84

T =198+∑ η,ΔΤω

=198+29.84

=227.84 K ® Calculating the latent heat A H _v at 60°C by CSGC-HW 1 method

Group Number of A T _S AP\

groups

>c<. 1 0.002200289 -0.003474154

~ N 1 -0.009525362 -0.07779588

— F 5 0.014653116x5 0.108614823x5

Total 0.065940508 0.46184082

T _c ^" =T _b /[A _T +B _T ∑ η,ΔΤ,+Οτ(Σ njATi) ² +Dr(∑ Π,ΔΤ,) ³ ]

=227.84/[0.5782359+1.064102x0.065940508 - 1.780121 ^χ

0.065940508 ² - 0.5002329 x0.065940508 ³ ]

=355.65 K

ηιΔΡι+0 _Ρ (∑ niAPi) ² +D _P (∑ η,ΔΡι) ³ ]

=1.01325ln227.84/[0.02912515+0.207087x0.46184082 - 0.04948187x0. 46184082 ² - 0.08637077 ^χ 0.46184082 ³ ]

=52.04 bar

T _br Tc =227.84/355.65=0.6405

AHvb=1.319767R To ^* T _br ^* [ln(P _c Vl .01325)- 1.140257]/(1.059397 -T _br ^* )

=1.319767x8.314x355.65x0.6405x[ln(52.04/1.01325)- 1.140257]/(1.0

59397-0,6405)

=18031 .90 J/mol

q=0.7815677 T _br ^' - 0.1072383

=0.7815677x0.6405-0.1072383

=0.3934

=18048.07x[(1 -0.9366)/(1 - 0.6405)] ^{0 3934}

=91 13.21 J/mol β Calculating saturated vapor pressure at 60°C by CSGC-PR method

Group Number of AT^O ⁴ ΔΡΙ*10 ³ groups

c< 1 27.54 -2.86

— N< 1 338.14 123.74

— F 5 35.32x5 12.25x5

Total 0.054228 0.18213 Tc ^" =T _b /[AT+B _T ∑ n,ATi+C _T (∑ niATi) ² +D _T (∑ ΓϋΔΤ ³ ]

=227.84/[0.5782585+1 .061273x0.054228- 1 .778714*0.054228 ² - 0.499

8375x0.054228 ³

=361.36 K

.01325lnT _b /[Ap+Bp∑ niAPi+C _P (∑ η _ί ΔΡι) ² +ϋ _Ρ (∑

=1.01325ln227.84/[0.04564342+0.3046466x0.18213-0.0652039x0.1 82 13 ² -0.04390779x0. 8213 ³ ]

=55.73 bar

TV =T _b / Tc =227.84/361.36=0.6305

φ _b =-35+36/ Tbr ^' +42ln T _br ^" -T _r " ⁶

= - 35+36/ 0.6305+42ln0.6305 - 0.6305 ⁶

=2.663

α ₀ =[0.315φ _b +ln(P _c 7l.01325)]/(0.0838(p _b Hn T _br ^' )

=[0.315x2.663+ In(55.73/1.01325)]/(0.0838x2.663 -ln 0.6305)

=7.081 1

Q=0.0838(3.758 -a ₀ )=0.0838x(3.758-7.081 )= -0.2785

A= - 35Q=- 35x ( - 0.2785)=9.747

B= -36Q= - 36x( - 0.2785)= 0.025

C=42Q+a _c =42x(-0.2785)+ 7.0811 =-4.615

D=-Q=0.2785

lnP _r =A-B/ Tr ^' +Cln T/+D T _r ^*6

=9.747- 10.025/0.9216 -4.850x|n0.9216+0.2683x0.9216 ⁶

= -0.5814

Because P _r '= Peo°d P _c ^"

we have P _60° r= P ₀ ^* P _r =55.73xexp( -0.5814)=31. 61 bar.

Through the similar procedure, we can obtain the saturated vapor pressure at 20°C:

P ₂₀ »c= 1 1.595 bar © Calculating the corresponding specific volume of the saturated vapor at 60°C

Firstly, the T _c and P _c were calculated using Joback method:

Group Number of Δ Τ _Α ; AP _C \

groups

c= 1 0.0067 -0.0168

— N 1 0.0169 0.0074

— F 5 0.01 11 x5 -0.0057x5

Total 0.0791 -0.0168

=227.84/[0.584+0.965x0.0791 -0.0791 ² ]

=348.3 K

Pc= (0.113+0.0032η _Α -∑ΠίΔΡ ^"2

=(0.113+0.0032x7 -0.0168) ^'2

=43.17 bar

Secondly, we calculate the saturated vapor pressure at T _r =0.7

(T=Tr*T _c =0.7x348.3=243.8 K) by the CSGC-PR method mentioned above, and the result is:

Ρ _ω =2.12 bar

w =-lgP _w - 1.0

= - |g(2.12/43.17) - 1.0

= 0.309

T _r =T/T _c = 333.15/348.3 = 0.9565

Pr= P ₆ o»c/Po=31 .161/43.17=0.7218

B ⁽⁰⁾ =0.083-0.422/T _r ^{1 6}

=0.0083 -0.422/0.9565 ^{1 6}

= -0.37012

B ⁽¹⁾ =0.139-0.172/T _r ²

=0.139 - 0.172/0.9565 ^{4 2}

=-0.0683

PV=ZRT

=[0.9565/0.7218 -0.37012+0.309x( -0.0683)]x8.3145x348.3/43.17/100 =0.62656 L/mol

Similarly, we can also figure out the specific volume of the vapor at 20°C: Vg ₂₀ °c=0.01438 m ³ /Kg

=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 Cm at 40°C

Group Number of a/

groups

— CF ₃ 1 15.423 -9.2464 2.8647 — F ₂ 1 6.1358 -0.17365 0.026272 Total 21.5588 -9.42005 2.890972

T=40+273.15=313.15 K

Cpi/R=∑n _i a _i +∑n _i bi(T/100)+∑n,C|(T/100) ²

C _p , =Rx{∑niai+∑nibi(T/100)+∑ηι¾(Τ/100) ² }

=8.3145*{21.5588+( -9.42005) ^χ (313. 5/100)+2.890972x(313. 5/100 ) ² }

=169.695J/moi-K

=1.402 Kj/Kg-K efficiency of the ORC 20-60 cycle:

=16.31 xln(31.161/1 1.595)/[75.31 +1.402x(60-20)]

=12.14%

Since the thermal efficiency correction scale factor is—0.652%

So the final result is η =12.14%-0.652% = 1 .49%

In conclusion:

At 60°C :

ΔΗ _ν = 9113.21 J/mol = 75.31 kJ/kg

P6o°c= 31.161 bar v _{g 6} o°c= 0.00518 m ³ /Kg

PV= 16.31 kJ/kg

At 20°C :

P ₂₀ =1 1.595 bar

v ₄ /v ₃ =2.69

At 40°C :

Cpi=1.402 Kj/Kg-K η = 1 .49%

The same types of calculations are made for all molecules according to the present invention.

Table : Results from rou contribution ca culations

Calculation of Thermal Efficiency

Equation of thermal efficiency

The Figure 1 shows the principle of the ORC cycle. The efficiency may be calculated using the equation: »7 = — (1 )

Λ ₃ - Λ,

Four basic equations of thermodynamics are:

dU = TdS - pdV (2a)

dH = TdS + Vdp (2b)

dA = -pdV -SdT (2c)

dG = Vdp - SdT (2d)

Also, for the ORC, the process from position 3 to position 4 is an isentropic process. Therefore,

The total heat absorption process should be from point 1 to point 3.

The total heat can be calculated as the efficiency η then can be written as, . ₍ 5)

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

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 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 p

PV \n '

]>

' ^? ™' ⁼ Δ// ₊ ,(7| - 7;) ^{' (2)} Comparing η ₃ and n,R _EFPRO p. and calculating the standard deviation σ=0.32%, one could see that the average correction to HREFPROP is about 0.32%. This average error comes from the formula which is a good approximation. Then, calculations were made of the efficiencies r\ _group contribution based on the same formula as equation (2) but using the thermodynamic data estimated by the group contribution method. Comparing η ₃ and r\ _g!0 up contribution and calculating the standard deviation σ=0.65%, one could see that the average correction to Hgroup 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 Figure 2. From Figure 2, one can see that ι¾ _ΓΟ υ _Ρ contribution is systematically higher than Ha, and that the average difference is just the standard deviation. Thus, by subtracting σ=0.65% from rjgroup contribution the efficiencies of the designed molecules of working fluids are obtained. Another issue to mention is: before correction of rigroup 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.

10.73%

10.47% 12.26% 10.91% 11.53% 11.37% 11.35% 11.21% 11.10% 10.75% 9.80% 11.53%

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

Molecules η GC η

P1 P2

MPa MPa

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 1 .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%

H N

HgC /V ^{1 1} CH2 0.1143 0.0237 12.57% 11.92% 0.3759 0.0968 12.11% 11.46%

H N

F ₂ C /\ CF ₂ 0.3968 0.1006 11.90% 11.25%

H

N.

/ \

F ₂ C CHF 0.3864 0.0986 12.01% 1.36%

H N

F ₂ C /\ CH2 0.3221 0.0796 12.26% 11.61% 0.3139 0.0783 12.29% 11.64%

F

N

/ \

HgC— " ""CHg 0.2195 0.0534 12.39% 11.74% F2C / \ CH2 0.2689 0.0667 12.07% 11.42%

0.2625 0.0657 12.17% 1 .52%

0.3139 0.0808 11.94% 1 1.29% 0.3219 0.0822 11.83% 1 1.18%

F N

F ₂ C / \ CF ₂ 0.3302 0.0837 11.72% 1 1.07%

Note:

qGC 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 flammabilitv of gases bv using the F-number analysis

F=1-(LJU)'

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+p9R US)x(1+p10RF+p1 1 RCI+p12RBr+p13ROH+p14RNO2+p15RNH2+p16RCN+ P17RCOOH) Table 4: Parameter values obtained by the analysis

No. Description Obtained value

p1 Main coefficient 0.581

p2 If one carbon -0.194

Ρ3 Ether 0.134

_P 4 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 CI -0.985

p12 Br -3.160

p13 OH 0.284

p14 N02 0.527

p15 NH2 -0.344

p16 CN -0.566

p17 COOH -0.850

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, CI, and so on, and COOH, respectively, divided by the total number of hydrogen atoms in the corresponding pure hydrocarbon molecule. Reference of Flammability:

R600 F = 0.581

R134a F = 0.4478 Application of group contribution method for predicting the toxicity of organic chemicals

Set C=-log(LC50)=∑Niai Equation: LC50=concentration casing 50% mortality in fathead minnow

Ni=number of group of type i

ai=contribution of group of type i

Currently, the C of common refrigerants is less than 2. Therefore, the working fluids with C values less than 2 are recommended.

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 CI 0.8712

7 Br 0.8515

8 O -0.4086

9 OH 0.3392

10 CO -0.2842

1 1 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 N02 0.7276 For example:

1 . Methyl benzene

C=5aArCH+aArC+aCH3

=5x0.4575+0.2913+0.6791 =3.26

FHC CHF

C=2aCH+2aF+aNH

=2x0.3305+2x0.4034+(-0.1 157) =1 .35

3. Butane

C=2aCH3+2aCH2

=2x0.6791 +2x0.2925

=1.94

. Methanol

C= aCH3+aOH

=0.6791 +0.3392

=1.02

5. Unconventional working fluids

CF3-CH2-NH2

C= aCH2+aC +aNH2+3aF

=0.2925+0.06214+0.1883+3x0.4034

=1 .75

Reference of Toxicity

R600 C = 1.9432

R134a C = 1.9682 Table 4. Flammability and toxicity calculations made by group contribution calculations. Results from molecules according to the present invention

Calculation of Ozone depletion potential

No bromine or chlorine in the molecules. Thus, ODP is 0.