def testSolve(self):
"""
Test the simple batch reactor with a simple kinetic model. Here we
choose a kinetic model consisting of the hydrogen abstraction reaction
CH4 + C2H5 <=> CH3 + C2H6.
"""
CH4 = Species(
molecule=[Molecule().fromSMILES("C")],
thermo=ThermoData(
Tdata=([300, 400, 500, 600, 800, 1000, 1500], "K"),
Cpdata=([8.615, 9.687, 10.963, 12.301, 14.841, 16.976,
20.528], "cal/(mol*K)"),
H298=(-17.714, "kcal/mol"),
S298=(44.472, "cal/(mol*K)")))
CH3 = Species(molecule=[Molecule().fromSMILES("[CH3]")],
thermo=ThermoData(
Tdata=([300, 400, 500, 600, 800, 1000, 1500], "K"),
Cpdata=([
9.397, 10.123, 10.856, 11.571, 12.899, 14.055,
16.195
], "cal/(mol*K)"),
H298=(9.357, "kcal/mol"),
S298=(45.174, "cal/(mol*K)")))
C2H6 = Species(molecule=[Molecule().fromSMILES("CC")],
thermo=ThermoData(
Tdata=([300, 400, 500, 600, 800, 1000, 1500], "K"),
Cpdata=([
12.684, 15.506, 18.326, 20.971, 25.500, 29.016,
34.595
], "cal/(mol*K)"),
H298=(-19.521, "kcal/mol"),
S298=(54.799, "cal/(mol*K)")))
C2H5 = Species(molecule=[Molecule().fromSMILES("C[CH2]")],
thermo=ThermoData(
Tdata=([300, 400, 500, 600, 800, 1000, 1500], "K"),
Cpdata=([
11.635, 13.744, 16.085, 18.246, 21.885, 24.676,
29.107
], "cal/(mol*K)"),
H298=(29.496, "kcal/mol"),
S298=(56.687, "cal/(mol*K)")))
rxn1 = Reaction(reactants=[C2H6, CH3],
products=[C2H5, CH4],
kinetics=Arrhenius(A=(686.375 * 6, 'm^3/(mol*s)'),
n=4.40721,
Ea=(7.82799, 'kcal/mol'),
T0=(298.15, 'K')))
coreSpecies = [CH4, CH3, C2H6, C2H5]
edgeSpecies = []
coreReactions = [rxn1]
edgeReactions = []
T = 1000
P = 1.0e5
rxnSystem = SimpleReactor(T,
P,
initialMoleFractions={
C2H5: 0.1,
CH3: 0.1,
CH4: 0.4,
C2H6: 0.4
},
termination=[])
rxnSystem.initializeModel(coreSpecies, coreReactions, edgeSpecies,
edgeReactions)
tlist = numpy.array([10**(i / 10.0) for i in range(-130, -49)],
numpy.float64)
# Integrate to get the solution at each time point
t = []
y = []
reactionRates = []
speciesRates = []
for t1 in tlist:
rxnSystem.advance(t1)
t.append(rxnSystem.t)
# You must make a copy of y because it is overwritten by DASSL at
# each call to advance()
y.append(rxnSystem.y.copy())
reactionRates.append(rxnSystem.coreReactionRates.copy())
speciesRates.append(rxnSystem.coreSpeciesRates.copy())
# Convert the solution vectors to numpy arrays
t = numpy.array(t, numpy.float64)
y = numpy.array(y, numpy.float64)
reactionRates = numpy.array(reactionRates, numpy.float64)
speciesRates = numpy.array(speciesRates, numpy.float64)
V = constants.R * rxnSystem.T.value_si * numpy.sum(
y) / rxnSystem.P.value_si
# Check that we're computing the species fluxes correctly
for i in range(t.shape[0]):
self.assertAlmostEqual(reactionRates[i, 0],
speciesRates[i, 0],
delta=1e-6 * reactionRates[i, 0])
self.assertAlmostEqual(reactionRates[i, 0],
-speciesRates[i, 1],
delta=1e-6 * reactionRates[i, 0])
self.assertAlmostEqual(reactionRates[i, 0],
-speciesRates[i, 2],
delta=1e-6 * reactionRates[i, 0])
self.assertAlmostEqual(reactionRates[i, 0],
speciesRates[i, 3],
delta=1e-6 * reactionRates[i, 0])
# Check that we've reached equilibrium
self.assertAlmostEqual(reactionRates[-1, 0], 0.0, delta=1e-2)
#######
# Unit test for the jacobian function:
# Solve a reaction system and check if the analytical jacobian matches the finite difference jacobian
H2 = Species(molecule=[Molecule().fromSMILES("[H][H]")],
thermo=ThermoData(
Tdata=([300, 400, 500, 600, 800, 1000, 1500], "K"),
Cpdata=([6.89, 6.97, 6.99, 7.01, 7.08, 7.22,
7.72], "cal/(mol*K)"),
H298=(0, "kcal/mol"),
S298=(31.23, "cal/(mol*K)")))
rxnList = []
rxnList.append(
Reaction(reactants=[C2H6],
products=[CH3, CH3],
kinetics=Arrhenius(A=(686.375 * 6, '1/s'),
n=4.40721,
Ea=(7.82799, 'kcal/mol'),
T0=(298.15, 'K'))))
rxnList.append(
Reaction(reactants=[CH3, CH3],
products=[C2H6],
kinetics=Arrhenius(A=(686.375 * 6, 'm^3/(mol*s)'),
n=4.40721,
Ea=(7.82799, 'kcal/mol'),
T0=(298.15, 'K'))))
rxnList.append(
Reaction(reactants=[C2H6, CH3],
products=[C2H5, CH4],
kinetics=Arrhenius(A=(46.375 * 6, 'm^3/(mol*s)'),
n=3.40721,
Ea=(6.82799, 'kcal/mol'),
T0=(298.15, 'K'))))
rxnList.append(
Reaction(reactants=[C2H5, CH4],
products=[C2H6, CH3],
kinetics=Arrhenius(A=(46.375 * 6, 'm^3/(mol*s)'),
n=3.40721,
Ea=(6.82799, 'kcal/mol'),
T0=(298.15, 'K'))))
rxnList.append(
Reaction(reactants=[C2H5, CH4],
products=[CH3, CH3, CH3],
kinetics=Arrhenius(A=(246.375 * 6, 'm^3/(mol*s)'),
n=1.40721,
Ea=(3.82799, 'kcal/mol'),
T0=(298.15, 'K'))))
rxnList.append(
Reaction(reactants=[CH3, CH3, CH3],
products=[C2H5, CH4],
kinetics=Arrhenius(A=(246.375 * 6, 'm^6/(mol^2*s)'),
n=1.40721,
Ea=(3.82799, 'kcal/mol'),
T0=(298.15, 'K')))) #
rxnList.append(
Reaction(reactants=[C2H6, CH3, CH3],
products=[C2H5, C2H5, H2],
kinetics=Arrhenius(A=(146.375 * 6, 'm^6/(mol^2*s)'),
n=2.40721,
Ea=(8.82799, 'kcal/mol'),
T0=(298.15, 'K'))))
rxnList.append(
Reaction(reactants=[C2H5, C2H5, H2],
products=[C2H6, CH3, CH3],
kinetics=Arrhenius(A=(146.375 * 6, 'm^6/(mol^2*s)'),
n=2.40721,
Ea=(8.82799, 'kcal/mol'),
T0=(298.15, 'K'))))
rxnList.append(
Reaction(reactants=[C2H6, C2H6],
products=[CH3, CH4, C2H5],
kinetics=Arrhenius(A=(1246.375 * 6, 'm^3/(mol*s)'),
n=0.40721,
Ea=(8.82799, 'kcal/mol'),
T0=(298.15, 'K'))))
rxnList.append(
Reaction(reactants=[CH3, CH4, C2H5],
products=[C2H6, C2H6],
kinetics=Arrhenius(A=(46.375 * 6, 'm^6/(mol^2*s)'),
n=0.10721,
Ea=(8.82799, 'kcal/mol'),
T0=(298.15, 'K'))))
for rxn in rxnList:
coreSpecies = [CH4, CH3, C2H6, C2H5, H2]
edgeSpecies = []
coreReactions = [rxn]
rxnSystem0 = SimpleReactor(T,
P,
initialMoleFractions={
CH4: 0.2,
CH3: 0.1,
C2H6: 0.35,
C2H5: 0.15,
H2: 0.2
},
termination=[])
rxnSystem0.initializeModel(coreSpecies, coreReactions, edgeSpecies,
edgeReactions)
dydt0 = rxnSystem0.residual(0.0, rxnSystem0.y,
numpy.zeros(rxnSystem0.y.shape))[0]
numCoreSpecies = len(coreSpecies)
dN = .000001 * sum(rxnSystem0.y)
dN_array = dN * numpy.eye(numCoreSpecies)
dydt = []
for i in range(numCoreSpecies):
rxnSystem0.y[i] += dN
dydt.append(
rxnSystem0.residual(0.0, rxnSystem0.y,
numpy.zeros(rxnSystem0.y.shape))[0])
rxnSystem0.y[i] -= dN # reset y to original y0
# Let the solver compute the jacobian
solverJacobian = rxnSystem0.jacobian(0.0, rxnSystem0.y, dydt0, 0.0)
# Compute the jacobian using finite differences
jacobian = numpy.zeros((numCoreSpecies, numCoreSpecies))
for i in range(numCoreSpecies):
for j in range(numCoreSpecies):
jacobian[i, j] = (dydt[j][i] - dydt0[i]) / dN
self.assertAlmostEqual(jacobian[i, j],
solverJacobian[i, j],
delta=abs(1e-4 * jacobian[i, j]))
#print 'Solver jacobian'
#print solverJacobian
#print 'Numerical jacobian'
#print jacobian
###
# Unit test for the compute rate derivative
rxnList = []
rxnList.append(
Reaction(reactants=[C2H6],
products=[CH3, CH3],
kinetics=Arrhenius(A=(686.375e6, '1/s'),
n=4.40721,
Ea=(7.82799, 'kcal/mol'),
T0=(298.15, 'K'))))
rxnList.append(
Reaction(reactants=[C2H6, CH3],
products=[C2H5, CH4],
kinetics=Arrhenius(A=(46.375 * 6, 'm^3/(mol*s)'),
n=3.40721,
Ea=(6.82799, 'kcal/mol'),
T0=(298.15, 'K'))))
rxnList.append(
Reaction(reactants=[C2H6, CH3, CH3],
products=[C2H5, C2H5, H2],
kinetics=Arrhenius(A=(146.375 * 6, 'm^6/(mol^2*s)'),
n=2.40721,
Ea=(8.82799, 'kcal/mol'),
T0=(298.15, 'K'))))
coreSpecies = [CH4, CH3, C2H6, C2H5, H2]
edgeSpecies = []
coreReactions = rxnList
rxnSystem0 = SimpleReactor(T,
P,
initialMoleFractions={
CH4: 0.2,
CH3: 0.1,
C2H6: 0.35,
C2H5: 0.15,
H2: 0.2
},
termination=[])
rxnSystem0.initializeModel(coreSpecies, coreReactions, edgeSpecies,
edgeReactions)
dfdt0 = rxnSystem0.residual(0.0, rxnSystem0.y,
numpy.zeros(rxnSystem0.y.shape))[0]
solver_dfdk = rxnSystem0.computeRateDerivative()
#print 'Solver d(dy/dt)/dk'
#print solver_dfdk
integrationTime = 1e-8
rxnSystem0.termination.append(TerminationTime((integrationTime, 's')))
rxnSystem0.simulate(coreSpecies, coreReactions, [], [], 0, 1, 0)
y0 = rxnSystem0.y
dfdk = numpy.zeros((numCoreSpecies, len(rxnList))) # d(dy/dt)/dk
for i in range(len(rxnList)):
k0 = rxnList[i].getRateCoefficient(T, P)
rxnList[i].kinetics.A.value_si = rxnList[i].kinetics.A.value_si * (
1 + 1e-3)
dk = rxnList[i].getRateCoefficient(T, P) - k0
rxnSystem = SimpleReactor(T,
P,
initialMoleFractions={
CH4: 0.2,
CH3: 0.1,
C2H6: 0.35,
C2H5: 0.15,
H2: 0.2
},
termination=[])
rxnSystem.initializeModel(coreSpecies, coreReactions, edgeSpecies,
edgeReactions)
dfdt = rxnSystem.residual(0.0, rxnSystem.y,
numpy.zeros(rxnSystem.y.shape))[0]
dfdk[:, i] = (dfdt - dfdt0) / dk
rxnSystem.termination.append(
TerminationTime((integrationTime, 's')))
rxnSystem.simulate(coreSpecies, coreReactions, [], [], 0, 1, 0)
rxnList[i].kinetics.A.value_si = rxnList[i].kinetics.A.value_si / (
1 + 1e-3) # reset A factor
for i in range(numCoreSpecies):
for j in range(len(rxnList)):
self.assertAlmostEqual(dfdk[i, j],
solver_dfdk[i, j],
delta=abs(1e-3 * dfdk[i, j]))
def testColliderModel(self):
"""
Test the solver's ability to simulate a model with collision efficiencies.
"""
chemFile = os.path.join(os.path.dirname(__file__), 'files',
'collider_model', 'chem.inp')
dictionaryFile = os.path.join(os.path.dirname(__file__), 'files',
'collider_model',
'species_dictionary.txt')
speciesList, reactionList = loadChemkinFile(chemFile, dictionaryFile)
smilesDict = {
'H': '[H]',
'HO2': '[O]O',
'O2': '[O][O]',
'Ar': '[Ar]',
'N2': 'N#N',
'CO2': 'O=C=O',
'CH3': '[CH3]',
'CH4': 'C'
}
speciesDict = {}
for name, smiles in smilesDict.iteritems():
mol = Molecule(SMILES=smiles)
for species in speciesList:
if species.isIsomorphic(mol):
speciesDict[name] = species
break
T = 1000 # K
P = 10 # Pa
initialMoleFractions = {
speciesDict['O2']: 0.5,
speciesDict['H']: 0.5,
speciesDict['CO2']: 1.0,
speciesDict['Ar']: 4.0
}
# Initialize the model
rxnSystem = SimpleReactor(T,
P,
initialMoleFractions=initialMoleFractions,
termination=None)
rxnSystem.initializeModel(speciesList, reactionList, [], [])
# Advance to time = 0.1 s
rxnSystem.advance(0.1)
# Compare simulated mole fractions with expected mole fractions from CHEMKIN
simulatedMoleFracs = rxnSystem.y / numpy.sum(rxnSystem.y)
expectedMoleFracs = numpy.array([
0.6666667, 0, 0, 0, 0.1666667, 0, 0.08333333, 0.08333333,
2.466066000000000E-10, 0, 0, 0, 0, 0
])
for i in range(len(simulatedMoleFracs)):
self.assertAlmostEqual(simulatedMoleFracs[i], expectedMoleFracs[i])
# Advance to time = 5 s
rxnSystem.advance(5)
# Compare simulated mole fractions with expected mole fractions from CHEMKIN
simulatedMoleFracs = rxnSystem.y / numpy.sum(rxnSystem.y)
expectedMoleFracs = numpy.array([
0.6666667, 0, 0, 0, 0.1666667, 0, 0.08333332, 0.08333332,
1.233033000000000E-08, 0, 0, 0, 0, 0
])
for i in range(len(simulatedMoleFracs)):
self.assertAlmostEqual(simulatedMoleFracs[i], expectedMoleFracs[i])
# Try a new set of conditions
T = 850 # K
P = 200 # Pa
initialMoleFractions = {
speciesDict['O2']: 0.5,
speciesDict['H']: 1,
speciesDict['CO2']: 1,
speciesDict['N2']: 4,
speciesDict['CH3']: 1
}
# Initialize the model
rxnSystem = SimpleReactor(T,
P,
initialMoleFractions=initialMoleFractions,
termination=None)
rxnSystem.initializeModel(speciesList, reactionList, [], [])
# Advance to time = 5 s
rxnSystem.advance(5)
# Compare simulated mole fractions with expected mole fractions from CHEMKIN
simulatedMoleFracs = rxnSystem.y / numpy.sum(rxnSystem.y)
expectedMoleFracs = numpy.array([
0, 0, 0, 0.5487241, 0.137181, 0, 0.1083234, 0.0685777,
1.280687000000000E-05, 0, 0, 0, 0.1083362, 0.02884481
])
for i in range(len(simulatedMoleFracs)):
self.assertAlmostEqual(simulatedMoleFracs[i], expectedMoleFracs[i])
def testSolve(self):
"""
Test the simple batch reactor with a simple kinetic model. Here we
choose a kinetic model consisting of the hydrogen abstraction reaction
CH4 + C2H5 <=> CH3 + C2H6.
"""
CH4 = Species(
molecule=[Molecule().fromSMILES("C")],
thermo=ThermoData(Tdata=([300,400,500,600,800,1000,1500],"K"), Cpdata=([ 8.615, 9.687,10.963,12.301,14.841,16.976,20.528],"cal/(mol*K)"), H298=(-17.714,"kcal/mol"), S298=(44.472,"cal/(mol*K)"))
)
CH3 = Species(
molecule=[Molecule().fromSMILES("[CH3]")],
thermo=ThermoData(Tdata=([300,400,500,600,800,1000,1500],"K"), Cpdata=([ 9.397,10.123,10.856,11.571,12.899,14.055,16.195],"cal/(mol*K)"), H298=( 9.357,"kcal/mol"), S298=(45.174,"cal/(mol*K)"))
)
C2H6 = Species(
molecule=[Molecule().fromSMILES("CC")],
thermo=ThermoData(Tdata=([300,400,500,600,800,1000,1500],"K"), Cpdata=([12.684,15.506,18.326,20.971,25.500,29.016,34.595],"cal/(mol*K)"), H298=(-19.521,"kcal/mol"), S298=(54.799,"cal/(mol*K)"))
)
C2H5 = Species(
molecule=[Molecule().fromSMILES("C[CH2]")],
thermo=ThermoData(Tdata=([300,400,500,600,800,1000,1500],"K"), Cpdata=([11.635,13.744,16.085,18.246,21.885,24.676,29.107],"cal/(mol*K)"), H298=( 29.496,"kcal/mol"), S298=(56.687,"cal/(mol*K)"))
)
rxn1 = Reaction(reactants=[C2H6,CH3], products=[C2H5,CH4], kinetics=Arrhenius(A=(686.375*6,'m^3/(mol*s)'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K')))
coreSpecies = [CH4,CH3,C2H6,C2H5]
edgeSpecies = []
coreReactions = [rxn1]
edgeReactions = []
T = 1000; P = 1.0e5
rxnSystem = SimpleReactor(T, P, initialMoleFractions={C2H5: 0.1, CH3: 0.1, CH4: 0.4, C2H6: 0.4}, termination=[])
rxnSystem.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions)
tlist = numpy.array([10**(i/10.0) for i in range(-130, -49)], numpy.float64)
# Integrate to get the solution at each time point
t = []; y = []; reactionRates = []; speciesRates = []
for t1 in tlist:
rxnSystem.advance(t1)
t.append(rxnSystem.t)
# You must make a copy of y because it is overwritten by DASSL at
# each call to advance()
y.append(rxnSystem.y.copy())
reactionRates.append(rxnSystem.coreReactionRates.copy())
speciesRates.append(rxnSystem.coreSpeciesRates.copy())
# Convert the solution vectors to numpy arrays
t = numpy.array(t, numpy.float64)
y = numpy.array(y, numpy.float64)
reactionRates = numpy.array(reactionRates, numpy.float64)
speciesRates = numpy.array(speciesRates, numpy.float64)
V = constants.R * rxnSystem.T.value_si * numpy.sum(y) / rxnSystem.P.value_si
# Check that we're computing the species fluxes correctly
for i in range(t.shape[0]):
self.assertAlmostEqual(reactionRates[i,0], speciesRates[i,0], delta=1e-6*reactionRates[i,0])
self.assertAlmostEqual(reactionRates[i,0], -speciesRates[i,1], delta=1e-6*reactionRates[i,0])
self.assertAlmostEqual(reactionRates[i,0], -speciesRates[i,2], delta=1e-6*reactionRates[i,0])
self.assertAlmostEqual(reactionRates[i,0], speciesRates[i,3], delta=1e-6*reactionRates[i,0])
# Check that we've reached equilibrium
self.assertAlmostEqual(reactionRates[-1,0], 0.0, delta=1e-2)
#######
# Unit test for the jacobian function:
# Solve a reaction system and check if the analytical jacobian matches the finite difference jacobian
H2 = Species(
molecule=[Molecule().fromSMILES("[H][H]")],
thermo=ThermoData(Tdata=([300,400,500,600,800,1000,1500],"K"), Cpdata=([6.89,6.97,6.99,7.01,7.08,7.22,7.72],"cal/(mol*K)"), H298=( 0,"kcal/mol"), S298=(31.23,"cal/(mol*K)"))
)
rxnList = []
rxnList.append(Reaction(reactants=[C2H6], products=[CH3,CH3], kinetics=Arrhenius(A=(686.375*6,'1/s'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[CH3,CH3], products=[C2H6], kinetics=Arrhenius(A=(686.375*6,'m^3/(mol*s)'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[C2H6,CH3], products=[C2H5,CH4], kinetics=Arrhenius(A=(46.375*6,'m^3/(mol*s)'), n=3.40721, Ea=(6.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[C2H5,CH4], products=[C2H6,CH3], kinetics=Arrhenius(A=(46.375*6,'m^3/(mol*s)'), n=3.40721, Ea=(6.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[C2H5,CH4], products=[CH3,CH3,CH3], kinetics=Arrhenius(A=(246.375*6,'m^3/(mol*s)'), n=1.40721, Ea=(3.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[CH3,CH3,CH3], products=[C2H5,CH4], kinetics=Arrhenius(A=(246.375*6,'m^6/(mol^2*s)'), n=1.40721, Ea=(3.82799,'kcal/mol'), T0=(298.15,'K'))))#
rxnList.append(Reaction(reactants=[C2H6,CH3,CH3], products=[C2H5,C2H5,H2], kinetics=Arrhenius(A=(146.375*6,'m^6/(mol^2*s)'), n=2.40721, Ea=(8.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[C2H5,C2H5,H2], products=[C2H6,CH3,CH3], kinetics=Arrhenius(A=(146.375*6,'m^6/(mol^2*s)'), n=2.40721, Ea=(8.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[C2H6,C2H6], products=[CH3,CH4,C2H5], kinetics=Arrhenius(A=(1246.375*6,'m^3/(mol*s)'), n=0.40721, Ea=(8.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[CH3,CH4,C2H5], products=[C2H6,C2H6], kinetics=Arrhenius(A=(46.375*6,'m^6/(mol^2*s)'), n=0.10721, Ea=(8.82799,'kcal/mol'), T0=(298.15,'K'))))
for rxn in rxnList:
coreSpecies = [CH4,CH3,C2H6,C2H5,H2]
edgeSpecies = []
coreReactions = [rxn]
rxnSystem0 = SimpleReactor(T,P,initialMoleFractions={CH4:0.2,CH3:0.1,C2H6:0.35,C2H5:0.15, H2:0.2},termination=[])
rxnSystem0.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions)
dydt0 = rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0]
numCoreSpecies = len(coreSpecies)
dN = .000001*sum(rxnSystem0.y)
dN_array = dN*numpy.eye(numCoreSpecies)
dydt = []
for i in range(numCoreSpecies):
rxnSystem0.y[i] += dN
dydt.append(rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0])
rxnSystem0.y[i] -= dN # reset y to original y0
# Let the solver compute the jacobian
solverJacobian = rxnSystem0.jacobian(0.0, rxnSystem0.y, dydt0, 0.0)
# Compute the jacobian using finite differences
jacobian = numpy.zeros((numCoreSpecies, numCoreSpecies))
for i in range(numCoreSpecies):
for j in range(numCoreSpecies):
jacobian[i,j] = (dydt[j][i]-dydt0[i])/dN
self.assertAlmostEqual(jacobian[i,j], solverJacobian[i,j], delta=abs(1e-4*jacobian[i,j]))
#print 'Solver jacobian'
#print solverJacobian
#print 'Numerical jacobian'
#print jacobian
###
# Unit test for the compute rate derivative
rxnList = []
rxnList.append(Reaction(reactants=[C2H6], products=[CH3,CH3], kinetics=Arrhenius(A=(686.375e6,'1/s'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[C2H6,CH3], products=[C2H5,CH4], kinetics=Arrhenius(A=(46.375*6,'m^3/(mol*s)'), n=3.40721, Ea=(6.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[C2H6,CH3,CH3], products=[C2H5,C2H5,H2], kinetics=Arrhenius(A=(146.375*6,'m^6/(mol^2*s)'), n=2.40721, Ea=(8.82799,'kcal/mol'), T0=(298.15,'K'))))
coreSpecies = [CH4,CH3,C2H6,C2H5,H2]
edgeSpecies = []
coreReactions = rxnList
rxnSystem0 = SimpleReactor(T,P,initialMoleFractions={CH4:0.2,CH3:0.1,C2H6:0.35,C2H5:0.15, H2:0.2},termination=[])
rxnSystem0.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions)
dfdt0 = rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0]
solver_dfdk = rxnSystem0.computeRateDerivative()
#print 'Solver d(dy/dt)/dk'
#print solver_dfdk
integrationTime = 1e-8
rxnSystem0.termination.append(TerminationTime((integrationTime,'s')))
modelSettings = ModelSettings(toleranceKeepInEdge = 0,toleranceMoveToCore=1,toleranceInterruptSimulation=0)
simulatorSettings = SimulatorSettings()
rxnSystem0.simulate(coreSpecies, coreReactions, [], [], [],[], modelSettings = modelSettings, simulatorSettings=simulatorSettings)
y0 = rxnSystem0.y
dfdk = numpy.zeros((numCoreSpecies,len(rxnList))) # d(dy/dt)/dk
for i in range(len(rxnList)):
k0 = rxnList[i].getRateCoefficient(T,P)
rxnList[i].kinetics.A.value_si = rxnList[i].kinetics.A.value_si*(1+1e-3)
dk = rxnList[i].getRateCoefficient(T,P) - k0
rxnSystem = SimpleReactor(T,P,initialMoleFractions={CH4:0.2,CH3:0.1,C2H6:0.35,C2H5:0.15, H2:0.2},termination=[])
rxnSystem.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions)
dfdt = rxnSystem.residual(0.0, rxnSystem.y, numpy.zeros(rxnSystem.y.shape))[0]
dfdk[:,i]=(dfdt-dfdt0)/dk
rxnSystem.termination.append(TerminationTime((integrationTime,'s')))
modelSettings = ModelSettings(toleranceKeepInEdge=0,toleranceMoveToCore=1,toleranceInterruptSimulation=0)
simulatorSettings = SimulatorSettings()
rxnSystem.simulate(coreSpecies, coreReactions, [], [], [], [], modelSettings=modelSettings, simulatorSettings=simulatorSettings)
rxnList[i].kinetics.A.value_si = rxnList[i].kinetics.A.value_si/(1+1e-3) # reset A factor
for i in range(numCoreSpecies):
for j in range(len(rxnList)):
self.assertAlmostEqual(dfdk[i,j], solver_dfdk[i,j], delta=abs(1e-3*dfdk[i,j]))
def testSpecificColliderModel(self):
"""
Test the solver's ability to simulate a model with specific third body species collision efficiencies.
"""
chemFile = os.path.join(os.path.dirname(__file__),'files','specific_collider_model','chem.inp')
dictionaryFile = os.path.join(os.path.dirname(__file__),'files','specific_collider_model','species_dictionary.txt')
speciesList, reactionList = loadChemkinFile(chemFile, dictionaryFile)
smilesDict = {'Ar':'[Ar]','N2(1)':'N#N','O2':'[O][O]','H':'[H]','CH3':'[CH3]','CH4':'C'}
speciesDict = {}
for name, smiles in smilesDict.iteritems():
mol = Molecule(SMILES=smiles)
for species in speciesList:
if species.isIsomorphic(mol):
speciesDict[name] = species
break
T = 1000 # K
P = 10 # Pa
initialMoleFractions = {speciesDict['Ar']:2.0,
speciesDict['N2(1)']:1.0,
speciesDict['O2']:0.5,
speciesDict['H']:0.1,
speciesDict['CH3']:0.1,
speciesDict['CH4']:0.001}
# Initialize the model
rxnSystem = SimpleReactor(T,P,initialMoleFractions=initialMoleFractions,termination=None)
rxnSystem.initializeModel(speciesList, reactionList, [], [])
# Advance to time = 0.1 s
rxnSystem.advance(0.1)
# Compare simulated mole fractions with expected mole fractions from CHEMKIN
simulatedMoleFracs = rxnSystem.y/numpy.sum(rxnSystem.y)
expectedMoleFracs = numpy.array([0.540394532, 0.270197216, 0.135098608, 0.027019722, 0.027019722, 0.000270202]) # order: Ar, N2, O2, H, CH3, CH4
for i in xrange(len(simulatedMoleFracs)):
self.assertAlmostEqual(simulatedMoleFracs[i],expectedMoleFracs[i],6)
# Advance to time = 5 s
rxnSystem.advance(5)
# Compare simulated mole fractions with expected mole fractions from CHEMKIN
expectedMoleFracs = numpy.array([0.540394573, 0.270197287, 0.135098693, 0.027019519, 0.027019519, 0.00027041]) # order: Ar, N2, O2, H, CH3, CH4
for i in range(len(simulatedMoleFracs)):
self.assertAlmostEqual(simulatedMoleFracs[i],expectedMoleFracs[i],6)
# Try a new set of conditions
T = 850 # K
P = 200 # Pa
initialMoleFractions = {speciesDict['Ar']:1.0,
speciesDict['N2(1)']:0.5,
speciesDict['O2']:0.5,
speciesDict['H']:0.001,
speciesDict['CH3']:0.01,
speciesDict['CH4']:0.5}
# Initialize the model
rxnSystem = SimpleReactor(T,P,initialMoleFractions=initialMoleFractions,termination=None)
rxnSystem.initializeModel(speciesList, reactionList, [], [])
# Advance to time = 5 s
rxnSystem.advance(5)
# Compare simulated mole fractions with expected mole fractions from CHEMKIN
simulatedMoleFracs = rxnSystem.y/numpy.sum(rxnSystem.y)
expectedMoleFracs = numpy.array([0.398247713, 0.199123907, 0.199123907, 0.000398169, 0.003982398, 0.199123907]) # order: Ar, N2, O2, H, CH3, CH4
for i in range(len(simulatedMoleFracs)):
self.assertAlmostEqual(simulatedMoleFracs[i],expectedMoleFracs[i],6)
def testColliderModel(self):
"""
Test the solver's ability to simulate a model with collision efficiencies.
"""
chemFile = os.path.join(os.path.dirname(__file__),'files','collider_model','chem.inp')
dictionaryFile = os.path.join(os.path.dirname(__file__),'files','collider_model','species_dictionary.txt')
speciesList, reactionList = loadChemkinFile(chemFile, dictionaryFile)
smilesDict = {'H':'[H]','HO2':'[O]O','O2':'[O][O]','Ar':'[Ar]','N2':'N#N','CO2':'O=C=O','CH3':'[CH3]','CH4':'C'}
speciesDict = {}
for name, smiles in smilesDict.iteritems():
mol = Molecule(SMILES=smiles)
for species in speciesList:
if species.isIsomorphic(mol):
speciesDict[name] = species
break
T = 1000 # K
P = 10 # Pa
initialMoleFractions = {speciesDict['O2']:0.5,
speciesDict['H']:0.5,
speciesDict['CO2']:1.0,
speciesDict['Ar']:4.0}
# Initialize the model
rxnSystem = SimpleReactor(T,P,initialMoleFractions=initialMoleFractions,termination=None)
rxnSystem.initializeModel(speciesList, reactionList, [], [])
# Advance to time = 0.1 s
rxnSystem.advance(0.1)
# Compare simulated mole fractions with expected mole fractions from CHEMKIN
simulatedMoleFracs = rxnSystem.y/numpy.sum(rxnSystem.y)
expectedMoleFracs = numpy.array([0.6666667,0,0,0,0.1666667,0, 0.08333333,0.08333333,2.466066000000000E-10,0,0,0,0,0])
for i in range(len(simulatedMoleFracs)):
self.assertAlmostEqual(simulatedMoleFracs[i],expectedMoleFracs[i])
# Advance to time = 5 s
rxnSystem.advance(5)
# Compare simulated mole fractions with expected mole fractions from CHEMKIN
expectedMoleFracs = numpy.array([0.6666667,0,0,0, 0.1666667,0,0.08333332,0.08333332,1.233033000000000E-08,0,0,0,0,0])
for i in range(len(simulatedMoleFracs)):
self.assertAlmostEqual(simulatedMoleFracs[i],expectedMoleFracs[i])
# Try a new set of conditions
T = 850 # K
P = 200 # Pa
initialMoleFractions = {speciesDict['O2']:0.5,
speciesDict['H']:1,
speciesDict['CO2']:1,
speciesDict['N2']:4,
speciesDict['CH3']:1}
# Initialize the model
rxnSystem = SimpleReactor(T,P,initialMoleFractions=initialMoleFractions,termination=None)
rxnSystem.initializeModel(speciesList, reactionList, [], [])
# Advance to time = 5 s
rxnSystem.advance(5)
# Compare simulated mole fractions with expected mole fractions from CHEMKIN
simulatedMoleFracs = rxnSystem.y/numpy.sum(rxnSystem.y)
expectedMoleFracs = numpy.array([0,0,0,0.5487241, 0.137181,0, 0.1083234, 0.0685777, 1.280687000000000E-05, 0,0,0, 0.1083362, 0.02884481])
for i in range(len(simulatedMoleFracs)):
self.assertAlmostEqual(simulatedMoleFracs[i],expectedMoleFracs[i])
def testSolve(self):
"""
Test the simple batch reactor with a simple kinetic model. Here we
choose a kinetic model consisting of the hydrogen abstraction reaction
CH4 + C2H5 <=> CH3 + C2H6.
"""
CH4 = Species(
molecule=[Molecule().fromSMILES("C")],
thermo=ThermoData(Tdata=([300,400,500,600,800,1000,1500],"K"), Cpdata=([ 8.615, 9.687,10.963,12.301,14.841,16.976,20.528],"cal/(mol*K)"), H298=(-17.714,"kcal/mol"), S298=(44.472,"cal/(mol*K)"))
)
CH3 = Species(
molecule=[Molecule().fromSMILES("[CH3]")],
thermo=ThermoData(Tdata=([300,400,500,600,800,1000,1500],"K"), Cpdata=([ 9.397,10.123,10.856,11.571,12.899,14.055,16.195],"cal/(mol*K)"), H298=( 9.357,"kcal/mol"), S298=(45.174,"cal/(mol*K)"))
)
C2H6 = Species(
molecule=[Molecule().fromSMILES("CC")],
thermo=ThermoData(Tdata=([300,400,500,600,800,1000,1500],"K"), Cpdata=([12.684,15.506,18.326,20.971,25.500,29.016,34.595],"cal/(mol*K)"), H298=(-19.521,"kcal/mol"), S298=(54.799,"cal/(mol*K)"))
)
C2H5 = Species(
molecule=[Molecule().fromSMILES("C[CH2]")],
thermo=ThermoData(Tdata=([300,400,500,600,800,1000,1500],"K"), Cpdata=([11.635,13.744,16.085,18.246,21.885,24.676,29.107],"cal/(mol*K)"), H298=( 29.496,"kcal/mol"), S298=(56.687,"cal/(mol*K)"))
)
rxn1 = Reaction(reactants=[C2H6,CH3], products=[C2H5,CH4], kinetics=Arrhenius(A=(686.375*6,'m^3/(mol*s)'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K')))
coreSpecies = [CH4,CH3,C2H6,C2H5]
edgeSpecies = []
coreReactions = [rxn1]
edgeReactions = []
T = 1000; P = 1.0e5
rxnSystem = SimpleReactor(T, P, initialMoleFractions={C2H5: 0.1, CH3: 0.1, CH4: 0.4, C2H6: 0.4}, termination=[])
rxnSystem.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions)
tlist = numpy.array([10**(i/10.0) for i in range(-130, -49)], numpy.float64)
# Integrate to get the solution at each time point
t = []; y = []; reactionRates = []; speciesRates = []
for t1 in tlist:
rxnSystem.advance(t1)
t.append(rxnSystem.t)
# You must make a copy of y because it is overwritten by DASSL at
# each call to advance()
y.append(rxnSystem.y.copy())
reactionRates.append(rxnSystem.coreReactionRates.copy())
speciesRates.append(rxnSystem.coreSpeciesRates.copy())
# Convert the solution vectors to numpy arrays
t = numpy.array(t, numpy.float64)
y = numpy.array(y, numpy.float64)
reactionRates = numpy.array(reactionRates, numpy.float64)
speciesRates = numpy.array(speciesRates, numpy.float64)
# Check that we're computing the species fluxes correctly
for i in range(t.shape[0]):
self.assertAlmostEqual(reactionRates[i,0], speciesRates[i,0], delta=1e-6*reactionRates[i,0])
self.assertAlmostEqual(reactionRates[i,0], -speciesRates[i,1], delta=1e-6*reactionRates[i,0])
self.assertAlmostEqual(reactionRates[i,0], -speciesRates[i,2], delta=1e-6*reactionRates[i,0])
self.assertAlmostEqual(reactionRates[i,0], speciesRates[i,3], delta=1e-6*reactionRates[i,0])
# Check that we've reached equilibrium
self.assertAlmostEqual(reactionRates[-1,0], 0.0, delta=1e-2)
def testSolve(self):
"""
Test the simple batch reactor with a simple kinetic model. Here we
choose a kinetic model consisting of the hydrogen abstraction reaction
CH4 + C2H5 <=> CH3 + C2H6.
"""
CH4 = Species(
molecule=[Molecule().fromSMILES("C")],
thermo=ThermoData(Tdata=([300,400,500,600,800,1000,1500],"K"), Cpdata=([ 8.615, 9.687,10.963,12.301,14.841,16.976,20.528],"cal/mol*K"), H298=(-17.714,"kcal/mol"), S298=(44.472,"cal/mol*K"))
)
CH3 = Species(
molecule=[Molecule().fromSMILES("[CH3]")],
thermo=ThermoData(Tdata=([300,400,500,600,800,1000,1500],"K"), Cpdata=([ 9.397,10.123,10.856,11.571,12.899,14.055,16.195],"cal/mol*K"), H298=( 9.357,"kcal/mol"), S298=(45.174,"cal/mol*K"))
)
C2H6 = Species(
molecule=[Molecule().fromSMILES("CC")],
thermo=ThermoData(Tdata=([300,400,500,600,800,1000,1500],"K"), Cpdata=([12.684,15.506,18.326,20.971,25.500,29.016,34.595],"cal/mol*K"), H298=(-19.521,"kcal/mol"), S298=(54.799,"cal/mol*K"))
)
C2H5 = Species(
molecule=[Molecule().fromSMILES("C[CH2]")],
thermo=ThermoData(Tdata=([300,400,500,600,800,1000,1500],"K"), Cpdata=([11.635,13.744,16.085,18.246,21.885,24.676,29.107],"cal/mol*K"), H298=( 29.496,"kcal/mol"), S298=(56.687,"cal/mol*K"))
)
rxn1 = Reaction(reactants=[C2H6,CH3], products=[C2H5,CH4], kinetics=Arrhenius(A=686.375*6, n=4.40721, Ea=7.82799*4184., T0=298.15))
coreSpecies = [CH4,CH3,C2H6,C2H5]
edgeSpecies = []
coreReactions = [rxn1]
edgeReactions = []
T = 1000; P = 1.0e5
rxnSystem = SimpleReactor(T, P, initialMoleFractions={C2H5: 0.1, CH3: 0.1, CH4: 0.4, C2H6: 0.4})
rxnSystem.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions)
tlist = numpy.array([10**(i/10.0) for i in range(-130, -49)], numpy.float64)
# Integrate to get the solution at each time point
t = []; y = []; reactionRates = []; speciesRates = []
for t1 in tlist:
rxnSystem.advance(t1)
t.append(rxnSystem.t)
# You must make a copy of y because it is overwritten by DASSL at
# each call to advance()
y.append(rxnSystem.y.copy())
reactionRates.append(rxnSystem.coreReactionRates.copy())
speciesRates.append(rxnSystem.coreSpeciesRates.copy())
# Convert the solution vectors to numpy arrays
t = numpy.array(t, numpy.float64)
y = numpy.array(y, numpy.float64)
reactionRates = numpy.array(reactionRates, numpy.float64)
speciesRates = numpy.array(speciesRates, numpy.float64)
import pylab
fig = pylab.figure(figsize=(6,6))
pylab.subplot(2,1,1)
pylab.semilogx(t, y)
pylab.ylabel('Concentration (mol/m$^\\mathdefault{3}$)')
pylab.legend(['CH4', 'CH3', 'C2H6', 'C2H5'], loc=4)
pylab.subplot(2,1,2)
pylab.semilogx(t, speciesRates)
pylab.legend(['CH4', 'CH3', 'C2H6', 'C2H5'], loc=4)
pylab.xlabel('Time (s)')
pylab.ylabel('Rate (mol/m$^\\mathdefault{3}$*s)')
fig.subplots_adjust(left=0.12, bottom=0.10, right=0.95, top=0.95, wspace=0.20, hspace=0.35)
pylab.show()
