def test_solve(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().from_smiles("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().from_smiles("[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().from_smiles("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().from_smiles("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')))
core_species = [ch4, ch3, c2h6, c2h5]
edge_species = []
core_reactions = [rxn1]
edge_reactions = []
T = 1000
P = 1.0e5
rxn_system = SimpleReactor(T,
P,
initial_mole_fractions={
c2h5: 0.1,
ch3: 0.1,
ch4: 0.4,
c2h6: 0.4
},
n_sims=1,
termination=[])
rxn_system.initialize_model(core_species, core_reactions, edge_species,
edge_reactions)
tlist = np.array([10**(i / 10.0) for i in range(-130, -49)],
np.float64)
# Integrate to get the solution at each time point
t = []
y = []
reaction_rates = []
species_rates = []
for t1 in tlist:
rxn_system.advance(t1)
t.append(rxn_system.t)
# You must make a copy of y because it is overwritten by DASSL at
# each call to advance()
y.append(rxn_system.y.copy())
reaction_rates.append(rxn_system.core_reaction_rates.copy())
species_rates.append(rxn_system.core_species_rates.copy())
# Convert the solution vectors to np arrays
t = np.array(t, np.float64)
y = np.array(y, np.float64)
reaction_rates = np.array(reaction_rates, np.float64)
species_rates = np.array(species_rates, np.float64)
V = constants.R * rxn_system.T.value_si * np.sum(
y) / rxn_system.P.value_si
# Check that we're computing the species fluxes correctly
for i in range(t.shape[0]):
self.assertAlmostEqual(reaction_rates[i, 0],
species_rates[i, 0],
delta=1e-6 * reaction_rates[i, 0])
self.assertAlmostEqual(reaction_rates[i, 0],
-species_rates[i, 1],
delta=1e-6 * reaction_rates[i, 0])
self.assertAlmostEqual(reaction_rates[i, 0],
-species_rates[i, 2],
delta=1e-6 * reaction_rates[i, 0])
self.assertAlmostEqual(reaction_rates[i, 0],
species_rates[i, 3],
delta=1e-6 * reaction_rates[i, 0])
# Check that we've reached equilibrium
self.assertAlmostEqual(reaction_rates[-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().from_smiles("[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)")))
rxn_list = [
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'))),
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'))),
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'))),
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'))),
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'))),
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'))),
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'))),
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'))),
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'))),
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 rxn_list:
core_species = [ch4, ch3, c2h6, c2h5, h2]
edge_species = []
core_reactions = [rxn]
rxn_system0 = SimpleReactor(T,
P,
initial_mole_fractions={
ch4: 0.2,
ch3: 0.1,
c2h6: 0.35,
c2h5: 0.15,
h2: 0.2
},
n_sims=1,
termination=[])
rxn_system0.initialize_model(core_species, core_reactions,
edge_species, edge_reactions)
dydt0 = rxn_system0.residual(0.0, rxn_system0.y,
np.zeros(rxn_system0.y.shape))[0]
num_core_species = len(core_species)
dN = .000001 * sum(rxn_system0.y)
dN_array = dN * np.eye(num_core_species)
dydt = []
for i in range(num_core_species):
rxn_system0.y[i] += dN
dydt.append(
rxn_system0.residual(0.0, rxn_system0.y,
np.zeros(rxn_system0.y.shape))[0])
rxn_system0.y[i] -= dN # reset y to original y0
# Let the solver compute the jacobian
solver_jacobian = rxn_system0.jacobian(0.0, rxn_system0.y, dydt0,
0.0)
# Compute the jacobian using finite differences
jacobian = np.zeros((num_core_species, num_core_species))
for i in range(num_core_species):
for j in range(num_core_species):
jacobian[i, j] = (dydt[j][i] - dydt0[i]) / dN
self.assertAlmostEqual(jacobian[i, j],
solver_jacobian[i, j],
delta=abs(1e-4 * jacobian[i, j]))
# print 'Solver jacobian'
# print solver_jacobian
# print 'Numerical jacobian'
# print jacobian
# Unit test for the compute rate derivative
rxn_list = [
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'))),
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'))),
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')))
]
core_species = [ch4, ch3, c2h6, c2h5, h2]
edge_species = []
core_reactions = rxn_list
rxn_system0 = SimpleReactor(T,
P,
initial_mole_fractions={
ch4: 0.2,
ch3: 0.1,
c2h6: 0.35,
c2h5: 0.15,
h2: 0.2
},
n_sims=1,
termination=[])
rxn_system0.initialize_model(core_species, core_reactions,
edge_species, edge_reactions)
dfdt0 = rxn_system0.residual(0.0, rxn_system0.y,
np.zeros(rxn_system0.y.shape))[0]
solver_dfdk = rxn_system0.compute_rate_derivative()
# print 'Solver d(dy/dt)/dk'
# print solver_dfdk
integration_time = 1e-8
rxn_system0.termination.append(TerminationTime(
(integration_time, 's')))
model_settings = ModelSettings(tol_keep_in_edge=0,
tol_move_to_core=1,
tol_interrupt_simulation=0)
simulator_settings = SimulatorSettings()
rxn_system0.simulate(core_species,
core_reactions, [], [], [], [],
model_settings=model_settings,
simulator_settings=simulator_settings)
y0 = rxn_system0.y
dfdk = np.zeros((num_core_species, len(rxn_list))) # d(dy/dt)/dk
for i in range(len(rxn_list)):
k0 = rxn_list[i].get_rate_coefficient(T, P)
rxn_list[i].kinetics.A.value_si = rxn_list[
i].kinetics.A.value_si * (1 + 1e-3)
dk = rxn_list[i].get_rate_coefficient(T, P) - k0
rxn_system = SimpleReactor(T,
P,
initial_mole_fractions={
ch4: 0.2,
ch3: 0.1,
c2h6: 0.35,
c2h5: 0.15,
h2: 0.2
},
n_sims=1,
termination=[])
rxn_system.initialize_model(core_species, core_reactions,
edge_species, edge_reactions)
dfdt = rxn_system.residual(0.0, rxn_system.y,
np.zeros(rxn_system.y.shape))[0]
dfdk[:, i] = (dfdt - dfdt0) / dk
rxn_system.termination.append(
TerminationTime((integration_time, 's')))
model_settings = ModelSettings(tol_keep_in_edge=0,
tol_move_to_core=1,
tol_interrupt_simulation=0)
simulator_settings = SimulatorSettings()
rxn_system.simulate(core_species,
core_reactions, [], [], [], [],
model_settings=model_settings,
simulator_settings=simulator_settings)
rxn_list[i].kinetics.A.value_si = rxn_list[
i].kinetics.A.value_si / (1 + 1e-3) # reset A factor
for i in range(num_core_species):
for j in range(len(rxn_list)):
self.assertAlmostEqual(dfdk[i, j],
solver_dfdk[i, j],
delta=abs(1e-3 * dfdk[i, j]))
def test_specific_collider_model(self):
"""
Test the solver's ability to simulate a model with specific third body species collision efficiencies.
"""
chem_file = os.path.join(os.path.dirname(__file__), 'files',
'specific_collider_model', 'chem.inp')
dictionary_file = os.path.join(os.path.dirname(__file__), 'files',
'specific_collider_model',
'species_dictionary.txt')
species_list, reaction_list = load_chemkin_file(
chem_file, dictionary_file)
smiles_dict = {
'Ar': '[Ar]',
'N2(1)': 'N#N',
'O2': '[O][O]',
'H': '[H]',
'CH3': '[CH3]',
'CH4': 'C'
}
species_dict = {}
for name, smiles in smiles_dict.items():
mol = Molecule(smiles=smiles)
for species in species_list:
if species.is_isomorphic(mol):
species_dict[name] = species
break
T = 1000 # K
P = 10 # Pa
initial_mole_fractions = {
species_dict['Ar']: 2.0,
species_dict['N2(1)']: 1.0,
species_dict['O2']: 0.5,
species_dict['H']: 0.1,
species_dict['CH3']: 0.1,
species_dict['CH4']: 0.001
}
# Initialize the model
rxn_system = SimpleReactor(
T,
P,
initial_mole_fractions=initial_mole_fractions,
n_sims=1,
termination=None)
rxn_system.initialize_model(species_list, reaction_list, [], [])
# Advance to time = 0.1 s
rxn_system.advance(0.1)
# Compare simulated mole fractions with expected mole fractions from CHEMKIN
simulated_mole_fracs = rxn_system.y / np.sum(rxn_system.y)
expected_mole_fracs = np.array([
0.540394532, 0.270197216, 0.135098608, 0.027019722, 0.027019722,
0.000270202
])
# order: Ar, N2, O2, H, CH3, CH4
for i in range(len(simulated_mole_fracs)):
self.assertAlmostEqual(simulated_mole_fracs[i],
expected_mole_fracs[i], 6)
# Advance to time = 5 s
rxn_system.advance(5)
# Compare simulated mole fractions with expected mole fractions from CHEMKIN
expected_mole_fracs = np.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(simulated_mole_fracs)):
self.assertAlmostEqual(simulated_mole_fracs[i],
expected_mole_fracs[i], 6)
# Try a new set of conditions
T = 850 # K
P = 200 # Pa
initial_mole_fractions = {
species_dict['Ar']: 1.0,
species_dict['N2(1)']: 0.5,
species_dict['O2']: 0.5,
species_dict['H']: 0.001,
species_dict['CH3']: 0.01,
species_dict['CH4']: 0.5
}
# Initialize the model
rxn_system = SimpleReactor(
T,
P,
initial_mole_fractions=initial_mole_fractions,
n_sims=1,
termination=None)
rxn_system.initialize_model(species_list, reaction_list, [], [])
# Advance to time = 5 s
rxn_system.advance(5)
# Compare simulated mole fractions with expected mole fractions from CHEMKIN
simulated_mole_fracs = rxn_system.y / np.sum(rxn_system.y)
expected_mole_fracs = np.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(simulated_mole_fracs)):
self.assertAlmostEqual(simulated_mole_fracs[i],
expected_mole_fracs[i], 6)
def test_collider_model(self):
"""
Test the solver's ability to simulate a model with collision efficiencies.
"""
chem_file = os.path.join(os.path.dirname(__file__), 'files',
'collider_model', 'chem.inp')
dictionary_file = os.path.join(os.path.dirname(__file__), 'files',
'collider_model',
'species_dictionary.txt')
species_list, reaction_list = load_chemkin_file(
chem_file, dictionary_file)
smiles_dict = {
'H': '[H]',
'HO2': '[O]O',
'O2': '[O][O]',
'Ar': '[Ar]',
'N2': 'N#N',
'CO2': 'O=C=O',
'CH3': '[CH3]',
'CH4': 'C'
}
species_dict = {}
for name, smiles in smiles_dict.items():
mol = Molecule(smiles=smiles)
for species in species_list:
if species.is_isomorphic(mol):
species_dict[name] = species
break
T = 1000 # K
P = 10 # Pa
initial_mole_fractions = {
species_dict['O2']: 0.5,
species_dict['H']: 0.5,
species_dict['CO2']: 1.0,
species_dict['Ar']: 4.0
}
# Initialize the model
rxn_system = SimpleReactor(
T,
P,
initial_mole_fractions=initial_mole_fractions,
n_sims=1,
termination=None)
rxn_system.initialize_model(species_list, reaction_list, [], [])
# Advance to time = 0.1 s
rxn_system.advance(0.1)
# Compare simulated mole fractions with expected mole fractions from CHEMKIN
simulated_mole_fracs = rxn_system.y / np.sum(rxn_system.y)
expected_mole_fracs = np.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(simulated_mole_fracs)):
self.assertAlmostEqual(simulated_mole_fracs[i],
expected_mole_fracs[i])
# Advance to time = 5 s
rxn_system.advance(5)
# Compare simulated mole fractions with expected mole fractions from CHEMKIN
expected_mole_fracs = np.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(simulated_mole_fracs)):
self.assertAlmostEqual(simulated_mole_fracs[i],
expected_mole_fracs[i])
# Try a new set of conditions
T = 850 # K
P = 200 # Pa
initial_mole_fractions = {
species_dict['O2']: 0.5,
species_dict['H']: 1,
species_dict['CO2']: 1,
species_dict['N2']: 4,
species_dict['CH3']: 1
}
# Initialize the model
rxn_system = SimpleReactor(
T,
P,
initial_mole_fractions=initial_mole_fractions,
n_sims=1,
termination=None)
rxn_system.initialize_model(species_list, reaction_list, [], [])
# Advance to time = 5 s
rxn_system.advance(5)
# Compare simulated mole fractions with expected mole fractions from CHEMKIN
simulated_mole_fracs = rxn_system.y / np.sum(rxn_system.y)
expected_mole_fracs = np.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(simulated_mole_fracs)):
self.assertAlmostEqual(simulated_mole_fracs[i],
expected_mole_fracs[i])