def test_corespeciesRate(self):
"""
Test if a specific core species rate is equal to 0 over time.
"""
c0 = {self.C2H5: 0.1, self.CH3: 0.1, self.CH4: 0.4, self.C2H6: 0.4}
rxn1 = Reaction(
reactants=[self.C2H6, self.CH3],
products=[self.C2H5, self.CH4],
kinetics=Arrhenius(A=(686.375*6, 'm^3/(mol*s)'), n=4.40721, Ea=(7.82799, 'kcal/mol'), T0=(298.15, 'K'))
)
coreSpecies = [self.CH4, self.CH3, self.C2H6, self.C2H5]
edgeSpecies = []
coreReactions = [rxn1]
edgeReactions = []
sensitivity = []
terminationConversion = []
sensitivityThreshold = 0.001
ConstSpecies = ["CH4"]
rxnSystem = LiquidReactor(self.T, c0, terminationConversion, sensitivity, sensitivityThreshold, ConstSpecies)
# The test regarding the writing of constantSPCindices from input file is check with the previous test.
rxnSystem.constSPCIndices = [0]
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)
self.assertEqual(rxnSystem.coreSpeciesRates[0], 0, "Core species rate has to be equal to 0 for species hold constant. Here it is equal to {0}".format(rxnSystem.coreSpeciesRates[0]))
def testComputeFlux(self):
"""
Test the liquid batch reactor with a simple kinetic model.
"""
rxn1 = Reaction(reactants=[self.C2H6, self.CH3],
products=[self.C2H5, self.CH4],
kinetics=Arrhenius(A=(686.375 * 6, 'm^3/(mol*s)'),
n=4.40721,
Ea=(7.82799, 'kcal/mol'),
T0=(298.15, 'K')))
coreSpecies = [self.CH4, self.CH3, self.C2H6, self.C2H5]
edgeSpecies = []
coreReactions = [rxn1]
edgeReactions = []
c0 = {self.C2H5: 0.1, self.CH3: 0.1, self.CH4: 0.4, self.C2H6: 0.4}
rxnSystem = LiquidReactor(self.T, c0, termination=[])
rxnSystem.initializeModel(coreSpecies, coreReactions, edgeSpecies,
edgeReactions)
tlist = numpy.array([10**(i / 10.0) for i in xrange(-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)
reactionRates = numpy.array(reactionRates, numpy.float64)
speciesRates = numpy.array(speciesRates, numpy.float64)
# Check that we're computing the species fluxes correctly
for i in xrange(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 test_corespeciesRate(self):
"Test if a specific core species rate is equal to 0 over time"
c0={self.C2H5: 0.1, self.CH3: 0.1, self.CH4: 0.4, self.C2H6: 0.4}
rxn1 = Reaction(reactants=[self.C2H6,self.CH3], products=[self.C2H5,self.CH4], kinetics=Arrhenius(A=(686.375*6,'m^3/(mol*s)'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K')))
coreSpecies = [self.CH4,self.CH3,self.C2H6,self.C2H5]
edgeSpecies = []
coreReactions = [rxn1]
edgeReactions = []
sensitivity=[]
terminationConversion = []
sensitivityThreshold=0.001
ConstSpecies = ["CH4"]
rxnSystem = LiquidReactor(self.T, c0, terminationConversion, sensitivity,sensitivityThreshold,ConstSpecies)
##The test regarding the writting of constantSPCindices from input file is check with the previous test.
rxnSystem.constSPCIndices=[0]
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)
self.assertEqual(rxnSystem.coreSpeciesRates[0], 0,"Core species rate has to be equal to 0 for species hold constant. Here it is equal to {0}".format(rxnSystem.coreSpeciesRates[0]))
def test_compute_derivative(self):
rxnList = []
rxnList.append(Reaction(reactants=[self.C2H6], products=[self.CH3,self.CH3], kinetics=Arrhenius(A=(686.375e6,'1/s'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[self.C2H6,self.CH3], products=[self.C2H5,self.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=[self.C2H6,self.CH3,self.CH3], products=[self.C2H5,self.C2H5,self.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 = [self.CH4,self.CH3,self.C2H6,self.C2H5, self.H2]
edgeSpecies = []
coreReactions = rxnList
edgeReactions = []
numCoreSpecies = len(coreSpecies)
c0={self.CH4:0.2,self.CH3:0.1,self.C2H6:0.35,self.C2H5:0.15, self.H2:0.2}
rxnSystem0 = LiquidReactor(self.T, c0,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
modelSettings = ModelSettings(toleranceKeepInEdge = 0,toleranceMoveToCore=1,toleranceInterruptSimulation=0)
simulatorSettings = SimulatorSettings()
rxnSystem0.termination.append(TerminationTime((integrationTime,'s')))
rxnSystem0.simulate(coreSpecies, coreReactions, [], [], [],[], modelSettings=modelSettings,simulatorSettings=simulatorSettings)
y0 = rxnSystem0.y
dfdk = numpy.zeros((numCoreSpecies,len(rxnList))) # d(dy/dt)/dk
c0={self.CH4:0.2,self.CH3:0.1,self.C2H6:0.35,self.C2H5:0.15, self.H2:0.2}
for i in xrange(len(rxnList)):
k0 = rxnList[i].getRateCoefficient(self.T)
rxnList[i].kinetics.A.value_si = rxnList[i].kinetics.A.value_si*(1+1e-3)
dk = rxnList[i].getRateCoefficient(self.T) - k0
rxnSystem = LiquidReactor(self.T, c0,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 xrange(numCoreSpecies):
for j in xrange(len(rxnList)):
self.assertAlmostEqual(dfdk[i,j], solver_dfdk[i,j], delta=abs(1e-3*dfdk[i,j]))
def test_jacobian(self):
"""
Unit test for the jacobian function:
Solve a reaction system and check if the analytical jacobian matches the finite difference jacobian
"""
coreSpecies = [self.CH4,self.CH3,self.C2H6,self.C2H5]
edgeSpecies = []
rxn1 = Reaction(reactants=[self.C2H6,self.CH3], products=[self.C2H5,self.CH4], kinetics=Arrhenius(A=(686.375*6,'m^3/(mol*s)'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K')))
coreReactions = [rxn1]
edgeReactions = []
numCoreSpecies = len(coreSpecies)
rxnList = []
rxnList.append(Reaction(reactants=[self.C2H6], products=[self.CH3,self.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=[self.CH3,self.CH3], products=[self.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=[self.C2H6,self.CH3], products=[self.C2H5,self.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=[self.C2H5,self.CH4], products=[self.C2H6,self.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=[self.C2H5,self.CH4], products=[self.CH3,self.CH3,self.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=[self.CH3,self.CH3,self.CH3], products=[self.C2H5,self.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=[self.C2H6,self.CH3,self.CH3], products=[self.C2H5,self.C2H5,self.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=[self.C2H5,self.C2H5,self.H2], products=[self.C2H6,self.CH3,self.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=[self.C2H6,self.C2H6], products=[self.CH3,self.CH4,self.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=[self.CH3,self.CH4,self.C2H5], products=[self.C2H6,self.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 = [self.CH4,self.CH3,self.C2H6,self.C2H5,self.H2]
edgeSpecies = []
coreReactions = [rxn]
c0={self.CH4:0.2,self.CH3:0.1,self.C2H6:0.35,self.C2H5:0.15, self.H2:0.2}
rxnSystem0 = LiquidReactor(self.T, c0,termination=[])
rxnSystem0.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions)
dydt0 = rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0]
dN = .000001*sum(rxnSystem0.y)
dN_array = dN*numpy.eye(numCoreSpecies)
dydt = []
for i in xrange(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 xrange(numCoreSpecies):
for j in xrange(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]))
def test_compute_derivative(self):
rxnList = []
rxnList.append(Reaction(reactants=[self.C2H6], products=[self.CH3,self.CH3], kinetics=Arrhenius(A=(686.375e6,'1/s'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[self.C2H6,self.CH3], products=[self.C2H5,self.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=[self.C2H6,self.CH3,self.CH3], products=[self.C2H5,self.C2H5,self.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 = [self.CH4,self.CH3,self.C2H6,self.C2H5, self.H2]
edgeSpecies = []
coreReactions = rxnList
edgeReactions = []
numCoreSpecies = len(coreSpecies)
c0={self.CH4:0.2,self.CH3:0.1,self.C2H6:0.35,self.C2H5:0.15, self.H2:0.2}
rxnSystem0 = LiquidReactor(self.T, c0,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
c0={self.CH4:0.2,self.CH3:0.1,self.C2H6:0.35,self.C2H5:0.15, self.H2:0.2}
for i in xrange(len(rxnList)):
k0 = rxnList[i].getRateCoefficient(self.T)
rxnList[i].kinetics.A.value_si = rxnList[i].kinetics.A.value_si*(1+1e-3)
dk = rxnList[i].getRateCoefficient(self.T) - k0
rxnSystem = LiquidReactor(self.T, c0,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 xrange(numCoreSpecies):
for j in xrange(len(rxnList)):
self.assertAlmostEqual(dfdk[i,j], solver_dfdk[i,j], delta=abs(1e-3*dfdk[i,j]))
def testComputeFlux(self):
"""
Test the liquid batch reactor with a simple kinetic model.
"""
rxn1 = Reaction(
reactants=[self.C2H6, self.CH3],
products=[self.C2H5, self.CH4],
kinetics=Arrhenius(A=(686.375*6, 'm^3/(mol*s)'), n=4.40721, Ea=(7.82799, 'kcal/mol'), T0=(298.15, 'K'))
)
coreSpecies = [self.CH4, self.CH3, self.C2H6, self.C2H5]
edgeSpecies = []
coreReactions = [rxn1]
edgeReactions = []
c0 = {self.C2H5: 0.1, self.CH3: 0.1, self.CH4: 0.4, self.C2H6: 0.4}
rxnSystem = LiquidReactor(self.T, c0, 1, termination=[])
rxnSystem.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions)
tlist = numpy.array([10**(i/10.0) for i in xrange(-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)
reactionRates = numpy.array(reactionRates, numpy.float64)
speciesRates = numpy.array(speciesRates, numpy.float64)
# Check that we're computing the species fluxes correctly
for i in xrange(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 test_jacobian(self):
"""
Unit test for the jacobian function:
Solve a reaction system and check if the analytical jacobian matches
the finite difference jacobian.
"""
coreSpecies = [self.CH4, self.CH3, self.C2H6, self.C2H5, self.H2]
edgeSpecies = []
numCoreSpecies = len(coreSpecies)
c0 = {self.CH4: 0.2, self.CH3: 0.1, self.C2H6: 0.35, self.C2H5: 0.15, self.H2: 0.2}
edgeReactions = []
rxnList = []
rxnList.append(Reaction(
reactants=[self.C2H6],
products=[self.CH3, self.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=[self.CH3, self.CH3],
products=[self.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=[self.C2H6, self.CH3],
products=[self.C2H5, self.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=[self.C2H5, self.CH4],
products=[self.C2H6, self.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=[self.C2H5, self.CH4],
products=[self.CH3, self.CH3, self.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=[self.CH3, self.CH3, self.CH3],
products=[self.C2H5, self.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=[self.C2H6, self.CH3, self.CH3],
products=[self.C2H5, self.C2H5, self.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=[self.C2H5, self.C2H5, self.H2],
products=[self.C2H6, self.CH3, self.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=[self.C2H6, self.C2H6],
products=[self.CH3, self.CH4, self.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=[self.CH3, self.CH4, self.C2H5],
products=[self.C2H6, self.C2H6],
kinetics=Arrhenius(A=(46.375*6, 'm^6/(mol^2*s)'), n=0.10721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K'))
))
# Analytical Jacobian for reaction 6
def jacobian_rxn6(c, kf, kr, s):
c1, c2, c3, c4 = c[s[1]], c[s[2]], c[s[3]], c[s[4]]
J = numpy.zeros((5, 5))
J[1, 1] = -4 * kf * c1 * c2
J[1, 2] = -2 * kf * c1 * c1
J[1, 3] = 4 * kr * c3 * c4
J[1, 4] = 2 * kr * c3 * c3
J[2, 1:] = 0.5 * J[1, 1:]
J[3, 1:] = -J[1, 1:]
J[4, 1:] = -0.5 * J[1, 1:]
return J
# Analytical Jacobian for reaction 7
def jacobian_rxn7(c, kf, kr, s):
c1, c2, c3, c4 = c[s[1]], c[s[2]], c[s[3]], c[s[4]]
J = numpy.zeros((5, 5))
J[1, 1] = -4 * kr * c1 * c2
J[1, 2] = -2 * kr * c1 * c1
J[1, 3] = 4 * kf * c3 * c4
J[1, 4] = 2 * kf * c3 * c3
J[2, 1:] = 0.5 * J[1, 1:]
J[3, 1:] = -J[1, 1:]
J[4, 1:] = -0.5 * J[1, 1:]
return J
for rxn_num, rxn in enumerate(rxnList):
coreReactions = [rxn]
rxnSystem0 = LiquidReactor(self.T, c0, 1, termination=[])
rxnSystem0.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions)
dydt0 = rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0]
dN = .000001*sum(rxnSystem0.y)
# Let the solver compute the jacobian
solverJacobian = rxnSystem0.jacobian(0.0, rxnSystem0.y, dydt0, 0.0)
if rxn_num not in (6, 7):
dydt = []
for i in xrange(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
# Compute the jacobian using finite differences
jacobian = numpy.zeros((numCoreSpecies, numCoreSpecies))
for i in xrange(numCoreSpecies):
for j in xrange(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]))
# The forward finite difference is very unstable for reactions
# 6 and 7. Use Jacobians calculated by hand instead.
elif rxn_num == 6:
kforward = rxn.getRateCoefficient(self.T)
kreverse = kforward / rxn.getEquilibriumConstant(self.T)
jacobian = jacobian_rxn6(c0, kforward, kreverse, coreSpecies)
for i in xrange(numCoreSpecies):
for j in xrange(numCoreSpecies):
self.assertAlmostEqual(jacobian[i, j], solverJacobian[i, j], delta=abs(1e-4*jacobian[i, j]))
elif rxn_num == 7:
kforward = rxn.getRateCoefficient(self.T)
kreverse = kforward / rxn.getEquilibriumConstant(self.T)
jacobian = jacobian_rxn7(c0, kforward, kreverse, coreSpecies)
for i in xrange(numCoreSpecies):
for j in xrange(numCoreSpecies):
self.assertAlmostEqual(jacobian[i, j], solverJacobian[i, j], delta=abs(1e-4*jacobian[i, j]))
def test_jacobian(self):
"""
Unit test for the jacobian function:
Solve a reaction system and check if the analytical jacobian matches
the finite difference jacobian.
"""
coreSpecies = [self.CH4, self.CH3, self.C2H6, self.C2H5, self.H2]
edgeSpecies = []
numCoreSpecies = len(coreSpecies)
c0 = {self.CH4: 0.2, self.CH3: 0.1, self.C2H6: 0.35, self.C2H5: 0.15, self.H2: 0.2}
edgeReactions = []
rxnList = []
rxnList.append(Reaction(
reactants=[self.C2H6],
products=[self.CH3, self.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=[self.CH3, self.CH3],
products=[self.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=[self.C2H6, self.CH3],
products=[self.C2H5, self.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=[self.C2H5, self.CH4],
products=[self.C2H6, self.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=[self.C2H5, self.CH4],
products=[self.CH3, self.CH3, self.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=[self.CH3, self.CH3, self.CH3],
products=[self.C2H5, self.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=[self.C2H6, self.CH3, self.CH3],
products=[self.C2H5, self.C2H5, self.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=[self.C2H5, self.C2H5, self.H2],
products=[self.C2H6, self.CH3, self.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=[self.C2H6, self.C2H6],
products=[self.CH3, self.CH4, self.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=[self.CH3, self.CH4, self.C2H5],
products=[self.C2H6, self.C2H6],
kinetics=Arrhenius(A=(46.375*6, 'm^6/(mol^2*s)'), n=0.10721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K'))
))
# Analytical Jacobian for reaction 6
def jacobian_rxn6(c, kf, kr, s):
c1, c2, c3, c4 = c[s[1]], c[s[2]], c[s[3]], c[s[4]]
J = numpy.zeros((5, 5))
J[1, 1] = -4 * kf * c1 * c2
J[1, 2] = -2 * kf * c1 * c1
J[1, 3] = 4 * kr * c3 * c4
J[1, 4] = 2 * kr * c3 * c3
J[2, 1:] = 0.5 * J[1, 1:]
J[3, 1:] = -J[1, 1:]
J[4, 1:] = -0.5 * J[1, 1:]
return J
# Analytical Jacobian for reaction 7
def jacobian_rxn7(c, kf, kr, s):
c1, c2, c3, c4 = c[s[1]], c[s[2]], c[s[3]], c[s[4]]
J = numpy.zeros((5, 5))
J[1, 1] = -4 * kr * c1 * c2
J[1, 2] = -2 * kr * c1 * c1
J[1, 3] = 4 * kf * c3 * c4
J[1, 4] = 2 * kf * c3 * c3
J[2, 1:] = 0.5 * J[1, 1:]
J[3, 1:] = -J[1, 1:]
J[4, 1:] = -0.5 * J[1, 1:]
return J
for rxn_num, rxn in enumerate(rxnList):
coreReactions = [rxn]
rxnSystem0 = LiquidReactor(self.T, c0, 1, termination=[])
rxnSystem0.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions)
dydt0 = rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0]
dN = .000001*sum(rxnSystem0.y)
# Let the solver compute the jacobian
solverJacobian = rxnSystem0.jacobian(0.0, rxnSystem0.y, dydt0, 0.0)
if rxn_num not in (6, 7):
dydt = []
for i in xrange(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
# Compute the jacobian using finite differences
jacobian = numpy.zeros((numCoreSpecies, numCoreSpecies))
for i in xrange(numCoreSpecies):
for j in xrange(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]))
# The forward finite difference is very unstable for reactions
# 6 and 7. Use Jacobians calculated by hand instead.
elif rxn_num == 6:
kforward = rxn.getRateCoefficient(self.T)
kreverse = kforward / rxn.getEquilibriumConstant(self.T)
jacobian = jacobian_rxn6(c0, kforward, kreverse, coreSpecies)
for i in xrange(numCoreSpecies):
for j in xrange(numCoreSpecies):
self.assertAlmostEqual(jacobian[i, j], solverJacobian[i, j], delta=abs(1e-4*jacobian[i, j]))
elif rxn_num == 7:
kforward = rxn.getRateCoefficient(self.T)
kreverse = kforward / rxn.getEquilibriumConstant(self.T)
jacobian = jacobian_rxn7(c0, kforward, kreverse, coreSpecies)
for i in xrange(numCoreSpecies):
for j in xrange(numCoreSpecies):
self.assertAlmostEqual(jacobian[i, j], solverJacobian[i, j], delta=abs(1e-4*jacobian[i, j]))
