def test_compute_flux(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')))
core_species = [self.CH4, self.CH3, self.C2H6, self.C2H5]
edge_species = []
core_reactions = [rxn1]
edge_reactions = []
c0 = {self.C2H5: 0.1, self.CH3: 0.1, self.CH4: 0.4, self.C2H6: 0.4}
rxn_system = LiquidReactor(self.T, c0, 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)
reaction_rates = np.array(reaction_rates, np.float64)
species_rates = np.array(species_rates, np.float64)
# 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)
def test_corespecies_rate(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')))
core_species = [self.CH4, self.CH3, self.C2H6, self.C2H5]
edge_species = []
core_reactions = [rxn1]
edge_reactions = []
sensitivity = []
termination_conversion = []
sensitivity_threshold = 0.001
const_species = ["CH4"]
sens_conds = {
self.C2H5: 0.1,
self.CH3: 0.1,
self.CH4: 0.4,
self.C2H6: 0.4,
'T': self.T
}
rxn_system = LiquidReactor(self.T,
c0,
1,
termination_conversion,
sensitivity,
sensitivity_threshold,
const_spc_names=const_species,
sens_conditions=sens_conds)
# The test regarding the writing of constantSPCindices from input file is check with the previous test.
rxn_system.const_spc_indices = [0]
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)
self.assertEqual(
rxn_system.core_species_rates[0], 0,
"Core species rate has to be equal to 0 for species hold constant. "
"Here it is equal to {0}".format(
rxn_system.core_species_rates[0]))
def test_compute_derivative(self):
rxn_list = [
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'))),
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'))),
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'))),
]
core_species = [self.CH4, self.CH3, self.C2H6, self.C2H5, self.H2]
edge_species = []
core_reactions = rxn_list
edge_reactions = []
num_core_species = len(core_species)
c0 = {
self.CH4: 0.2,
self.CH3: 0.1,
self.C2H6: 0.35,
self.C2H5: 0.15,
self.H2: 0.2
}
rxn_system0 = LiquidReactor(self.T, c0, 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
model_settings = ModelSettings(tol_keep_in_edge=0,
tol_move_to_core=1,
tol_interrupt_simulation=0)
simulator_settings = SimulatorSettings()
rxn_system0.termination.append(TerminationTime(
(integration_time, 's')))
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
c0 = {
self.CH4: 0.2,
self.CH3: 0.1,
self.C2H6: 0.35,
self.C2H5: 0.15,
self.H2: 0.2
}
for i in range(len(rxn_list)):
k0 = rxn_list[i].get_rate_coefficient(self.T)
rxn_list[i].kinetics.A.value_si = rxn_list[
i].kinetics.A.value_si * (1 + 1e-3)
dk = rxn_list[i].get_rate_coefficient(self.T) - k0
rxn_system = LiquidReactor(self.T, c0, 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_jacobian(self):
"""
Unit test for the jacobian function:
Solve a reaction system and check if the analytical jacobian matches
the finite difference jacobian.
"""
core_species = [self.CH4, self.CH3, self.C2H6, self.C2H5, self.H2]
edge_species = []
num_core_species = len(core_species)
c0 = {
self.CH4: 0.2,
self.CH3: 0.1,
self.C2H6: 0.35,
self.C2H5: 0.15,
self.H2: 0.2
}
edge_reactions = []
rxn_list = [
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'))),
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'))),
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'))),
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'))),
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'))),
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'))),
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'))),
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'))),
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'))),
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]]
jaco = np.zeros((5, 5))
jaco[1, 1] = -4 * kf * c1 * c2
jaco[1, 2] = -2 * kf * c1 * c1
jaco[1, 3] = 4 * kr * c3 * c4
jaco[1, 4] = 2 * kr * c3 * c3
jaco[2, 1:] = 0.5 * jaco[1, 1:]
jaco[3, 1:] = -jaco[1, 1:]
jaco[4, 1:] = -0.5 * jaco[1, 1:]
return jaco
# 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]]
jaco = np.zeros((5, 5))
jaco[1, 1] = -4 * kr * c1 * c2
jaco[1, 2] = -2 * kr * c1 * c1
jaco[1, 3] = 4 * kf * c3 * c4
jaco[1, 4] = 2 * kf * c3 * c3
jaco[2, 1:] = 0.5 * jaco[1, 1:]
jaco[3, 1:] = -jaco[1, 1:]
jaco[4, 1:] = -0.5 * jaco[1, 1:]
return jaco
for rxn_num, rxn in enumerate(rxn_list):
core_reactions = [rxn]
rxn_system0 = LiquidReactor(self.T, c0, 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]
dN = .000001 * sum(rxn_system0.y)
# Let the solver compute the jacobian
solver_jacobian = rxn_system0.jacobian(0.0, rxn_system0.y, dydt0,
0.0)
if rxn_num not in (6, 7):
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
# 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]))
# The forward finite difference is very unstable for reactions
# 6 and 7. Use Jacobians calculated by hand instead.
elif rxn_num == 6:
kforward = rxn.get_rate_coefficient(self.T)
kreverse = kforward / rxn.get_equilibrium_constant(self.T)
jacobian = jacobian_rxn6(c0, kforward, kreverse, core_species)
for i in range(num_core_species):
for j in range(num_core_species):
self.assertAlmostEqual(jacobian[i, j],
solver_jacobian[i, j],
delta=abs(1e-4 *
jacobian[i, j]))
elif rxn_num == 7:
kforward = rxn.get_rate_coefficient(self.T)
kreverse = kforward / rxn.get_equilibrium_constant(self.T)
jacobian = jacobian_rxn7(c0, kforward, kreverse, core_species)
for i in range(num_core_species):
for j in range(num_core_species):
self.assertAlmostEqual(jacobian[i, j],
solver_jacobian[i, j],
delta=abs(1e-4 *
jacobian[i, j]))
