import matplotlib.pyplot as plt
import numpy as np
from chempy import ReactionSystem
from chempy.units import to_unitless, SI_base_registry as si, default_units as u, default_constants as const
from chempy.kinetics.ode import get_odesys
%matplotlib inline
R = 8.314472
T_K = 300
dH=80e3
dS=10
rsys1b = ReactionSystem.from_string("""
NO + Br -> NOBr; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
""".format(dH=dH, dS=dS))
c0 = 1 # mol/dm3 === 1000 mol/m3
kbref = 20836643994.118652*T_K*np.exp(-(dH - T_K*dS)/(R*T_K))/c0
kbref
NO0_M = 1.5
Br0_M = 0.7
init_cond = dict(
NOBr=0*u.M,
NO=NO0_M*u.M,
Br=Br0_M*u.M
)
t = 5*u.second
params = dict(
temperature=T_K*u.K
)
def analytic_b(t):
U, V = NO0_M, Br0_M
d = U - V
return (U*(1 - np.exp(-kbref*t*d)))/(U/V - np.exp(-kbref*t*d))
def integrate_and_plot(rsys):
odesys, extra = get_odesys(rsys, unit_registry=si, constants=const)
fig, axes = plt.subplots(1, 4, figsize=(14, 6))
res = odesys.integrate(t, init_cond, params, integrator='cvode')
t_sec = to_unitless(res.xout, u.second)
NOBr_ref = analytic_b(t_sec)
cmp = to_unitless(res.yout, u.M)
ref = np.empty_like(cmp)
ref[:, odesys.names.index('NOBr')] = NOBr_ref
ref[:, odesys.names.index('Br')] = Br0_M - NOBr_ref
ref[:, odesys.names.index('NO')] = NO0_M - NOBr_ref
axes[0].plot(t_sec, cmp)
axes[1].plot(t_sec, ref)
axes[2].plot(t_sec, cmp - ref)
res.plot_invariant_violations(ax=axes[3])
assert np.allclose(cmp, ref)
print({k: v for k, v in res.info.items() if not k.startswith('internal')})
integrate_and_plot(rsys1b)
rsys2b = ReactionSystem.from_string("""
NO + Br -> NOBr; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
""".format(dH=dH, dS=dS))
integrate_and_plot(rsys2b)