def test_fuzz_dV_dP_and_d2V_dP2_derivatives():
from thermo import eos
eos_list = list(eos.__all__); eos_list.remove('GCEOS')
eos_list.remove('ALPHA_FUNCTIONS'); eos_list.remove('VDW')
phase_extensions = {True: '_l', False: '_g'}
derivative_bases_dV_dP = {0:'V', 1:'dV_dP', 2:'d2V_dP2'}
def dV_dP(P, T, eos, order=0, phase=True, Tc=507.6, Pc=3025000., omega=0.2975):
eos = globals()[eos_list[eos]](Tc=Tc, Pc=Pc, omega=omega, T=T, P=P)
phase_base = phase_extensions[phase]
attr = derivative_bases_dV_dP[order]+phase_base
return getattr(eos, attr)
x, y = [], []
for eos in range(len(eos_list)):
for T in np.linspace(.1, 1000, 50):
for P in np.logspace(np.log10(3E4), np.log10(1E6), 50):
T, P = float(T), float(P)
for phase in [True, False]:
for order in [1, 2]:
try:
# If dV_dx_phase doesn't exist, will simply abort and continue the loop
numer = derivative(dV_dP, P, dx=15., args=(T, eos, order-1, phase))
ana = dV_dP(T=T, P=P, eos=eos, order=order, phase=phase)
except:
continue
x.append(numer)
y.append(ana)
assert allclose_variable(x, y, limits=[.02, .04, .04, .05, .15, .45, .95],
rtols=[1E-2, 1E-3, 1E-4, 1E-5, 1E-6, 1E-7, 1E-9])
def test_fuzz_dPsat_dT():
from thermo import eos
eos_list = list(eos.__all__); eos_list.remove('GCEOS')
eos_list.remove('ALPHA_FUNCTIONS'); eos_list.remove('eos_list')
eos_list.remove('GCEOS_DUMMY')
Tc = 507.6
Pc = 3025000
omega = 0.2975
e = PR(T=400, P=1E5, Tc=507.6, Pc=3025000, omega=0.2975)
dPsats_dT_expect = [938.7777925283981, 10287.225576267781, 38814.74676693623]
assert_allclose([e.dPsat_dT(300), e.dPsat_dT(400), e.dPsat_dT(500)], dPsats_dT_expect)
# Hammer the derivatives for each EOS in a wide range; most are really
# accurate. There's an error around the transition between polynomials
# though - to be expected; the derivatives are discontinuous there.
dPsats_derivative = []
dPsats_analytical = []
for eos in range(len(eos_list)):
for T in np.linspace(0.2*Tc, Tc*.999, 50):
e = globals()[eos_list[eos]](Tc=Tc, Pc=Pc, omega=omega, T=T, P=1E5)
anal = e.dPsat_dT(T)
numer = derivative(e.Psat, T, order=9)
dPsats_analytical.append(anal)
dPsats_derivative.append(numer)
assert allclose_variable(dPsats_derivative, dPsats_analytical, limits=[.02, .06], rtols=[1E-5, 1E-7])
def test_SRK_Psat():
eos = SRK(Tc=507.6, Pc=3025000, omega=0.2975, T=299., P=1E6)
# ERROR actually for RK not SRK
Cs_SRK = [-3.0486334, -5.2157649E-2, 0.55002312, -0.44506984, 3.1735078E-2,
4.1819219E-2, -1.18709865E-2, 1.79267167E-3, -1.47491666E-4,
5.19352748E-6]
def Psat(T, Tc, Pc, omega):
Tr = T/Tc
e = SRK(Tc=Tc, Pc=Pc, omega=omega, T=T, P=1E5)
alpha = e.a_alpha/e.a
tot = 0
for k, Ck in enumerate(Cs_SRK[0:4]):
tot += Ck*(alpha/Tr-1)**((k+2)/2.)
for k, Ck in enumerate(Cs_SRK[4:]):
tot += Ck*(alpha/Tr-1)**(k+3)
P = exp(tot)*Tr*Pc
return P
Ts = np.linspace(160, 504, 100)
Psats_lit = [Psat(T, Tc=507.6, Pc=3025000, omega=0.2975) for T in Ts]
Psats_eos = [eos.Psat(T) for T in Ts]
assert_allclose(Psats_lit, Psats_eos, rtol=5E-2)
# Not sure why the fit was so poor for the original author
fugacity_ls, fugacity_gs = [], []
for T, P in zip(Ts, Psats_eos):
eos = SRK(Tc=507.6, Pc=3025000, omega=0.2975, T=T, P=P)
fugacity_ls.append(eos.fugacity_l)
fugacity_gs.append(eos.fugacity_g)
assert allclose_variable(fugacity_ls, fugacity_gs, limits=[0, .1, .5], rtols=[3E-2, 1E-3, 3E-4])
