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]))