Add MATLAB example files for BinarySolutionTabulatedThermo class
This commit is contained in:
Manik Mayur
Ray Speth
parent
a7449c6cc8
commit
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2 changed files with 313 additions and 0 deletions
214
data/inputs/lithium_ion_battery.cti
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data/inputs/lithium_ion_battery.cti
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#=====================================================================================
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# Cantera input file for an LCO/graphite lithium-ion battery
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# Reference:
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# M. Mayur, S. DeCaluwe, B. L. Kee, W. G. Bessler, "Modeling
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# thermodynamics and kinetics of intercalation phases for lithium-ion
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# batteries in Cantera", Computer Physics Communications
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#=====================================================================================
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#=====================================================================================
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# Bulk phases
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#=====================================================================================
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#------------------------------------------------------------------
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# Graphite (anode)
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# Thermodynamic data based on half-cell measurements by K. Kumaresan et al., J. Electrochem. Soc. 155, A164-A171 (2008)
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# Density: 5031.67 kg/m3 - used to calculate species molar volume as molecular weight (MW)/density
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#------------------------------------------------------------------
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BinarySolutionTabulatedThermo(
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name = "anode",
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elements = "Li C",
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species = "Li[anode] V[anode]",
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standard_concentration = "unity",
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tabulated_species = "Li[anode]",
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tabulated_thermo = table(
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moleFraction = ([5.75000E-03, 1.77591E-02, 2.97682E-02, 4.17773E-02, 5.37864E-02, 6.57954E-02, 7.78045E-02, 8.98136E-02, 1.01823E-01, 1.13832E-01,
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1.25841E-01, 1.37850E-01, 1.49859E-01, 1.61868E-01, 1.73877E-01, 1.85886E-01, 1.97896E-01, 2.09904E-01, 2.21914E-01, 2.33923E-01,
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2.45932E-01, 2.57941E-01, 2.69950E-01, 2.81959E-01, 2.93968E-01, 3.05977E-01, 3.17986E-01, 3.29995E-01, 3.42004E-01, 3.54014E-01,
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3.66023E-01, 3.78032E-01, 3.90041E-01, 4.02050E-01, 4.14059E-01, 4.26068E-01, 4.38077E-01, 4.50086E-01, 4.62095E-01, 4.74104E-01,
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4.86114E-01, 4.98123E-01, 5.10132E-01, 5.22141E-01, 5.34150E-01, 5.46159E-01, 5.58168E-01, 5.70177E-01, 5.82186E-01, 5.94195E-01,
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6.06205E-01, 6.18214E-01, 6.30223E-01, 6.42232E-01, 6.54241E-01, 6.66250E-01, 6.78259E-01, 6.90268E-01, 7.02277E-01, 7.14286E-01,
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7.26295E-01, 7.38305E-01, 7.50314E-01, 7.62323E-01, 7.74332E-01, 7.86341E-01, 7.98350E-01],
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"1"),
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enthalpy = ([-6.40692E+04, -3.78794E+04, -1.99748E+04, -1.10478E+04, -7.04973E+03, -7.13749E+03, -8.79728E+03, -9.93655E+03, -1.03060E+04, -1.00679E+04,
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-9.69664E+03, -9.31556E+03, -8.90503E+03, -8.57057E+03, -8.38117E+03, -8.31928E+03, -8.31453E+03, -8.32977E+03, -8.33292E+03, -8.32931E+03,
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-8.31339E+03, -8.21331E+03, -8.08920E+03, -8.00131E+03, -7.92294E+03, -7.81543E+03, -7.77498E+03, -7.79440E+03, -7.78804E+03, -7.73218E+03,
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-7.69063E+03, -7.69630E+03, -7.63241E+03, -7.41910E+03, -7.06828E+03, -6.64544E+03, -6.17193E+03, -5.67055E+03, -5.14299E+03, -4.55704E+03,
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-3.94568E+03, -3.35408E+03, -2.87825E+03, -2.57690E+03, -2.43468E+03, -2.33952E+03, -2.23218E+03, -2.11482E+03, -2.03976E+03, -2.01990E+03,
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-2.01329E+03, -1.97991E+03, -1.92686E+03, -1.86602E+03, -1.81419E+03, -1.77693E+03, -1.74908E+03, -1.71494E+03, -1.67287E+03, -1.63685E+03,
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-1.59649E+03, -1.52295E+03, -1.39033E+03, -1.11524E+03, -5.34643E+02, 3.73854E+02, 1.60442E+03],
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"J/mol"),
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entropy = ([3.05724E+01, 4.04307E+01, 4.75718E+01, 5.25690E+01, 5.10953E+01, 4.43414E+01, 3.71575E+01, 3.23216E+01, 2.91586E+01, 2.70081E+01,
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2.53501E+01, 2.40845E+01, 2.30042E+01, 2.19373E+01, 2.07212E+01, 1.93057E+01, 1.77319E+01, 1.61153E+01, 1.46399E+01, 1.34767E+01,
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1.27000E+01, 1.23377E+01, 1.22815E+01, 1.23700E+01, 1.24863E+01, 1.26368E+01, 1.26925E+01, 1.26250E+01, 1.24861E+01, 1.23294E+01,
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1.21865E+01, 1.20723E+01, 1.21228E+01, 1.24383E+01, 1.30288E+01, 1.37342E+01, 1.44460E+01, 1.50813E+01, 1.56180E+01, 1.62213E+01,
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1.70474E+01, 1.80584E+01, 1.88377E+01, 1.92094E+01, 1.92957E+01, 1.93172E+01, 1.93033E+01, 1.92971E+01, 1.92977E+01, 1.92978E+01,
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1.92980E+01, 1.92978E+01, 1.92945E+01, 1.92899E+01, 1.92877E+01, 1.92882E+01, 1.92882E+01, 1.92882E+01, 1.92882E+01, 1.92882E+01,
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1.92885E+01, 1.92876E+01, 1.92837E+01, 1.92769E+01, 1.92850E+01, 1.93100E+01, 1.93514E+01],
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"J/mol/K")))
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# Lithium intercalated in graphite, MW: 79.0070 g/mol
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species(
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name = "Li[anode]",
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atoms = "Li:1 C:6",
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thermo = const_cp(h0 = (0, 'kJ/mol'), s0 = (0.0, 'J/mol/K')), # these are dummy entries because the values are taken from the table
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standardState = constantIncompressible(molarVolume = (79.0070/5.0317, 'cm3/gmol')))
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# Vacancy in graphite, MW: 72.0660 g/mol. Note this species includes the carbon host matrix.
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species(
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name = "V[anode]",
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atoms = "C:6",
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thermo = const_cp(h0 = (0.0, 'kJ/mol'), s0 = (0.0, 'J/mol/K')), # values are set to 0 because this is the reference species for this phase
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standardState = constantIncompressible(molarVolume = (72.0660/5.0317, 'cm3/gmol')))
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#------------------------------------------------------------------
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# Lithium cobalt oxide (cathode)
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# Thermodynamic data based on half-cell measurements by K. Kumaresan et al., J. Electrochem. Soc. 155, A164-A171 (2008)
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# Density: 2292 kg/m3 - used to calculate species molar volume as molecular weight (MW)/density
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#------------------------------------------------------------------
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BinarySolutionTabulatedThermo(
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name = "cathode",
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elements = "Li Co O",
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species = "Li[cathode] V[cathode]",
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standard_concentration = "unity",
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tabulated_species = "Li[cathode]",
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tabulated_thermo = table(
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moleFraction = ([4.59630E-01, 4.67368E-01, 4.75105E-01, 4.82843E-01, 4.90581E-01, 4.98318E-01, 5.06056E-01, 5.13794E-01, 5.21531E-01, 5.29269E-01,
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5.37007E-01, 5.44744E-01, 5.52482E-01, 5.60219E-01, 5.67957E-01, 5.75695E-01, 5.83432E-01, 5.91170E-01, 5.98908E-01, 6.06645E-01,
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6.14383E-01, 6.22121E-01, 6.29858E-01, 6.37596E-01, 6.45334E-01, 6.53071E-01, 6.60809E-01, 6.68547E-01, 6.76284E-01, 6.84022E-01,
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6.91759E-01, 6.99497E-01, 7.07235E-01, 7.14972E-01, 7.22710E-01, 7.30448E-01, 7.38185E-01, 7.45923E-01, 7.53661E-01, 7.61398E-01,
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7.69136E-01, 7.76873E-01, 7.84611E-01, 7.92349E-01, 8.00087E-01, 8.07824E-01, 8.15562E-01, 8.23299E-01, 8.31037E-01, 8.38775E-01,
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8.46512E-01, 8.54250E-01, 8.61988E-01, 8.69725E-01, 8.77463E-01, 8.85201E-01, 8.92938E-01, 9.00676E-01, 9.08413E-01, 9.16151E-01,
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9.23889E-01, 9.31627E-01, 9.39364E-01, 9.47102E-01, 9.54839E-01, 9.62577E-01, 9.70315E-01, 9.78052E-01, 9.85790E-01],
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"1"),
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enthalpy = ([-4.16188E+05, -4.14839E+05, -4.12629E+05, -4.09620E+05, -4.05334E+05, -3.99420E+05, -3.92499E+05, -3.85940E+05, -3.81474E+05, -3.80290E+05,
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-3.81445E+05, -3.83295E+05, -3.85062E+05, -3.86633E+05, -3.87928E+05, -3.88837E+05, -3.89240E+05, -3.89238E+05, -3.89157E+05, -3.89174E+05,
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-3.89168E+05, -3.88988E+05, -3.88675E+05, -3.88478E+05, -3.88443E+05, -3.88346E+05, -3.88083E+05, -3.87768E+05, -3.87531E+05, -3.87356E+05,
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-3.87205E+05, -3.87052E+05, -3.86960E+05, -3.86957E+05, -3.86918E+05, -3.86814E+05, -3.86785E+05, -3.86957E+05, -3.87146E+05, -3.87188E+05,
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-3.87239E+05, -3.87507E+05, -3.87902E+05, -3.88142E+05, -3.88316E+05, -3.88464E+05, -3.88563E+05, -3.88687E+05, -3.89000E+05, -3.89414E+05,
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-3.89735E+05, -3.90005E+05, -3.90317E+05, -3.90632E+05, -3.90865E+05, -3.91100E+05, -3.91453E+05, -3.91742E+05, -3.91833E+05, -3.91858E+05,
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-3.91910E+05, -3.91798E+05, -3.91470E+05, -3.91005E+05, -3.90261E+05, -3.89181E+05, -3.85506E+05, -3.73450E+05, -3.53926E+05],
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"J/mol"),
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entropy = ([-2.52348E+01, -2.54629E+01, -2.26068E+01, -1.68899E+01, -6.74549E+00, 9.76522E+00, 3.08711E+01, 4.98756E+01, 5.85766E+01, 5.46784E+01,
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4.40727E+01, 3.30834E+01, 2.37109E+01, 1.61658E+01, 1.02408E+01, 5.75684E+00, 2.19969E+00, -6.93265E-01, -3.40166E+00, -6.03548E+00,
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-8.45666E+00, -1.03459E+01, -1.18860E+01, -1.35610E+01, -1.53331E+01, -1.68255E+01, -1.81219E+01, -1.95052E+01, -2.07093E+01, -2.16274E+01,
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-2.25743E+01, -2.38272E+01, -2.52029E+01, -2.65835E+01, -2.77164E+01, -2.86064E+01, -2.96044E+01, -3.09551E+01, -3.21990E+01, -3.31284E+01,
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-3.40633E+01, -3.53177E+01, -3.66599E+01, -3.76439E+01, -3.85616E+01, -3.96433E+01, -4.06506E+01, -4.15566E+01, -4.27485E+01, -4.41419E+01,
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-4.52082E+01, -4.61154E+01, -4.71614E+01, -4.82305E+01, -4.89739E+01, -4.96529E+01, -5.06905E+01, -5.18080E+01, -5.26580E+01, -5.32766E+01,
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-5.39817E+01, -5.45468E+01, -5.48125E+01, -5.51520E+01, -5.54526E+01, -5.52961E+01, -5.50219E+01, -5.46653E+01, -5.42305E+01],
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"J/mol/K")))
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# Lithium cobalt oxide, MW: 97.8730 g/mol
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species(
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name = "Li[cathode]",
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atoms = "Li:1 Co:1 O:2",
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thermo = const_cp(h0 = (0.0, 'kJ/mol'), s0 = (0.0, 'J/mol/K')), # these are dummy entries because the values are taken from the table
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standardState = constantIncompressible(molarVolume = (97.8730/2.292, 'cm3/gmol')))
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# Vacancy in the cobalt oxide, MW: 90.9320 g/mol. Note this species includes the host matrix.
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species(
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name = "V[cathode]",
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atoms = "Co:1 O:2",
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thermo = const_cp(h0 = (0.0, 'kJ/mol'), s0 = (0.0, 'J/mol/K')), # values are set to 0 because this is the reference species for this phase
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standardState = constantIncompressible(molarVolume = (90.9320/2.292, 'cm3/gmol')))
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#------------------------------------------------------------------
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# Electron conductor
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#------------------------------------------------------------------
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metal(
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name = "electron",
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elements = "E",
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species = "electron",
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density = (1.0, 'kg/m3'), # dummy entry
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initial_state = state( mole_fractions = "electron:1.0"))
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# Electron, MW: 0.000545 g/mol
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species(
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name = "electron",
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atoms = "E:1",
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thermo = const_cp(h0 = (0.0, 'kJ/mol'), s0 = (0.0, 'J/mol/K'))) # dummy entries because chemical potential is set to zero for a "metal" phase
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#--------------------------------------------------------------------
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# Carbonate based electrolyte
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# Solvent: Ethylene carbonate:Propylene carbonate (1:1 v/v)
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# Salt: 1M LiPF6
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# Density: 1260.0 kg/m3 - used to calculate species molar volume as molecular weight (MW)/density
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#--------------------------------------------------------------------
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IdealSolidSolution(
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name = "electrolyte",
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elements = "Li P F C H O E",
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species = "C3H4O3[elyt] C4H6O3[elyt] Li+[elyt] PF6-[elyt]",
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initial_state = state(pressure = OneAtm, mole_fractions = 'C3H4O3[elyt]:0.47901 C4H6O3[elyt]:0.37563 Li+[elyt]:0.07268 PF6-[elyt]:0.07268'),
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standard_concentration = "unity")
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# Ethylene carbonate, MW: 88.0630 g/mol
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species(
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name = "C3H4O3[elyt]",
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atoms = "C:3 H:4 O:3",
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thermo = const_cp(h0 =(0.0, 'J/mol'), s0 = (0.0, 'J/mol/K')), # Dummy entries as this species does not participate in chemical reactions
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standardState = constantIncompressible(molarVolume = (88.0630/1.260, 'cm3/gmol')))
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# Propylene carbonate, MW: 102.0898 g/mol
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species(
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name = "C4H6O3[elyt]",
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atoms = "C:4 H:6 O:3",
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thermo = const_cp(h0 =(0.0, 'J/mol'), s0 = (0.0, 'J/mol/K')), # Dummy entries as this species does not participate in chemical reactions
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standardState = constantIncompressible(molarVolume = (102.0898/1.260, 'cm3/gmol')))
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# Lithium ion, MW: 6.940455 g/mol
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species(
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name = "Li+[elyt]",
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atoms = "Li:1 E:-1",
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thermo = const_cp(h0 = (-278.49, 'kJ/mol'), s0 = (13.4, 'J/mol/K')), # Li+(aq) from P. Atkins "Physical Chemistry", Wiley-VCH (2006)
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standardState = constantIncompressible(molarVolume = (6.940455/1.260, 'cm3/gmol')))
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# Hexafluorophosphate ion, MW: 144.964745 g/mol
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species(
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name = "PF6-[elyt]",
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atoms = "P:1 F:6 E:1",
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thermo = const_cp(h0 = (0.0, 'J/mol'), s0 = (0.0, 'J/mol/K')), # Dummy entries as this species does not participate in chemical reactions
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standardState = constantIncompressible(molarVolume = (144.964745/1.260, 'cm3/gmol')))
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#=====================================================================================
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# Interfaces for electrochemical reactions
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#=====================================================================================
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#--------------------------------------------------------------------
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# Anode reaction
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#--------------------------------------------------------------------
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ideal_interface(
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name = "edge_anode_electrolyte",
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phases = "anode electron electrolyte",
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reactions = "anode_*",
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elements = "Li E C",
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species = "(dummy)", # dummy entry for global kinetics
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site_density = (1.0e-2, 'mol/cm2')) # dummy entry for global kinetics
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edge_reaction("Li[anode] <=> Li+[elyt] + V[anode] + electron", [4, 0.0, (0, 'kJ/mol')], rateCoeff = "exchangecurrentdensity", beta = 0.5,id="anode_reaction")
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#--------------------------------------------------------------------
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# Cathode reaction
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#--------------------------------------------------------------------
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ideal_interface(
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name = "edge_cathode_electrolyte",
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phases = "cathode electron electrolyte",
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reactions = "cathode_*",
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elements = "Li E Co O",
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species = "(dummy)", # dummy entry for global kinetics
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site_density = (1.0e-2, 'mol/cm2')) # dummy entry for global kinetics
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edge_reaction("Li+[elyt] + V[cathode] + electron <=> Li[cathode]", [100, 0.0, (0, 'kJ/mol')], rateCoeff = "exchangecurrentdensity", beta = 0.5,id="cathode_reaction")
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# Dummy species
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species(
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name = "(dummy)",
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atoms = "",
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thermo = const_cp(h0 = (0.0, 'kJ/mol'), s0 = (0.0, 'J/mol/K')))
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99
samples/matlab/lithium_ion_battery.m
Normal file
99
samples/matlab/lithium_ion_battery.m
Normal file
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@ -0,0 +1,99 @@
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function E_cell = lithium_ion_battery(X_Li_ca, X_Li_an, T, P, I_app, R_elyt)
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% Returns the cell voltage (in Volt) of a lithium-ion cell for a given cell
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% current and active material lithium stoichiometries.
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%
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% Input:
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% - stoichiometries X_Li_ca and X_Li_an [-] (can be vectors)
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% - temperature T [K]
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% - pressure P [Pa]
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% - externally-applied current I_app [A]
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% - electrolyte resistance R_elyt [Ohm]
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%
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% Reference:
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% M. Mayur, S. DeCaluwe, B. L. Kee, W. G. Bessler, "Modeling
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% thermodynamics and kinetics of intercalation phases for lithium-ion
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% batteries in Cantera", Computer Physics Communications
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% Parameteres
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inputCTI = 'lithium_ion_battery.cti'; % cantera input file name
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F = 96485; % Faraday's constant [C/mol]
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S_ca = 1.1167; % [m^2] Cathode total active material surface area
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S_an = 0.7824; % [m^2] Anode total active material surface area
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% Import all Cantera phases
|
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anode = importThermoPhase(inputCTI, 'anode');
|
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cathode = importThermoPhase(inputCTI,'cathode');
|
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elde = importThermoPhase(inputCTI,'electron');
|
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elyt = importThermoPhase(inputCTI,'electrolyte');
|
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anode_interface = importEdge(inputCTI, 'edge_anode_electrolyte', anode, elde, elyt);
|
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cathode_interface = importEdge(inputCTI, 'edge_cathode_electrolyte', cathode, elde, elyt);
|
||||
|
||||
% Set the temperatures and pressures of all phases
|
||||
phases = [anode elde elyt cathode];
|
||||
for ph = phases
|
||||
set(ph,'T',T,'P',P);
|
||||
end
|
||||
|
||||
% Calculate cell voltage, separately for each entry of the input vectors
|
||||
E_cell = zeros(length(X_Li_ca),1);
|
||||
for i = 1:length(X_Li_ca)
|
||||
% Set anode electrode potential to 0
|
||||
phi_s_an = 0;
|
||||
|
||||
% Calculate anode electrolyte potential
|
||||
phi_l_an = fzero(@(E) anode_curr(phi_s_an,E,X_Li_an(i))+I_app, 0);
|
||||
|
||||
% Calculate cathode electrolyte potential
|
||||
phi_l_ca = phi_l_an + I_app*R_elyt;
|
||||
|
||||
% Calculate cathode electrode potential
|
||||
phi_s_ca = fzero(@(E) cathode_curr(E,phi_l_ca,X_Li_ca(i))+I_app, 0);
|
||||
|
||||
% Calculate cell voltage
|
||||
E_cell(i) = phi_s_ca - phi_s_an;
|
||||
end
|
||||
|
||||
|
||||
%--------------------------------------------------------------------------
|
||||
% Sub-functions
|
||||
|
||||
% This function returns the ThermoPhase class instance from CTI file
|
||||
function phase = importThermoPhase(inputCTI, name)
|
||||
doc = XML_Node('doc', inputCTI);
|
||||
node = findByID(doc, name);
|
||||
phase = ThermoPhase(node);
|
||||
end
|
||||
|
||||
% This function returns the Cantera calculated anode current (in A)
|
||||
function anCurr = anode_curr(phi_s,phi_l,X_Li_an)
|
||||
% Set the active material mole fraction
|
||||
set(anode,'X',['Li[anode]:' num2str(X_Li_an) ', V[anode]:' num2str(1-X_Li_an)]);
|
||||
|
||||
% Set the electrode and electrolyte potential
|
||||
setElectricPotential(elde,phi_s);
|
||||
setElectricPotential(elyt,phi_l);
|
||||
|
||||
% Get the net reaction rate at the cathode-side interface
|
||||
r = rop_net(anode_interface).*1e3; % [mol/m2/s]
|
||||
|
||||
% Calculate the current
|
||||
anCurr = r*F*S_an*1;
|
||||
end
|
||||
|
||||
% This function returns the Cantera calculated cathode current (in A)
|
||||
function caCurr = cathode_curr(phi_s,phi_l,X_Li_ca)
|
||||
% Set the active material mole fractions
|
||||
set(cathode,'X',['Li[cathode]:' num2str(X_Li_ca) ', V[cathode]:' num2str(1-X_Li_ca)]);
|
||||
|
||||
% Set the electrode and electrolyte potential
|
||||
setElectricPotential(elde,phi_s);
|
||||
setElectricPotential(elyt,phi_l);
|
||||
|
||||
% Get the net reaction rate at the cathode-side interface
|
||||
r = rop_net(cathode_interface).*1e3; % [mol/m2/s]
|
||||
|
||||
% Calculate the current
|
||||
caCurr = r*F*S_ca*(-1);
|
||||
end
|
||||
end
|
||||
Loading…
Add table
Reference in a new issue