def test_TWUSRK_quick():
# Test solution for molar volumes
eos = TWUSRK(Tc=507.6, Pc=3025000, omega=0.2975, T=299., P=1E6)
Vs_fast = eos.volume_solutions(299, 1E6, eos.b, eos.delta, eos.epsilon, eos.a_alpha)
Vs_slow = eos.volume_solutions(299, 1E6, eos.b, eos.delta, eos.epsilon, eos.a_alpha, quick=False)
Vs_expected = [(0.00014689217317770398+0j), (0.001169565653511148+0.0013011778220658073j), (0.001169565653511148-0.0013011778220658073j)]
assert_allclose(Vs_fast, Vs_expected)
assert_allclose(Vs_slow, Vs_expected)
# Test of a_alphas
a_alphas = [3.71966709357206, -0.007269721309490377, 2.305588658885629e-05]
a_alphas_fast = eos.a_alpha_and_derivatives(299)
assert_allclose(a_alphas, a_alphas_fast)
a_alphas_slow = eos.a_alpha_and_derivatives(299, quick=False)
assert_allclose(a_alphas, a_alphas_slow)
# back calculation for T
eos = TWUSRK(Tc=507.6, Pc=3025000, omega=0.2975, V=0.00014689217317770398, P=1E6)
assert_allclose(eos.T, 299)
T_slow = eos.solve_T(P=1E6, V=0.00014689217317770398, quick=False)
assert_allclose(T_slow, 299)
eos = TWUSRK(Tc=507.6, Pc=3025000, omega=0.2975, T=299., P=1E6)
# Derivatives
diffs_1 = [504446.40946384566, -2676841551251.3125, 1.8844836341846153e-07, -3.735745956022468e-13, 5306493.417400694, 1.982371132471449e-06]
diffs_2 = [-586.164516927993, 2.6624358487625542e+17, 1.308861795972448e-09, 1.3880693263695398e-20, -195576504984.95178, 4.566404923205853e-15]
diffs_mixed = [-5.015403880635795e-15, -14235388178.812284, 0.06816570409464781]
departures = [-31612.591872087483, -74.02294100343829, 34.24266185576879]
known_derivs_deps = [diffs_1, diffs_2, diffs_mixed, departures]
for f in [True, False]:
main_calcs = eos.derivatives_and_departures(eos.T, eos.P, eos.V_l, eos.b, eos.delta, eos.epsilon, eos.a_alpha, eos.da_alpha_dT, eos.d2a_alpha_dT2, quick=f)
for i, j in zip(known_derivs_deps, main_calcs):
assert_allclose(i, j)
# Test Cp_Dep, Cv_dep
assert_allclose(eos.Cv_dep_l, 34.24266185576879)
assert_allclose(eos.Cp_dep_l, 54.35177004420726)
# Integration tests
eos = TWUSRK(Tc=507.6, Pc=3025000, omega=0.2975, T=299.,V=0.00013)
fast_vars = vars(eos)
eos.set_properties_from_solution(eos.T, eos.P, eos.V, eos.b, eos.delta, eos.epsilon, eos.a_alpha, eos.da_alpha_dT, eos.d2a_alpha_dT2, quick=False)
slow_vars = vars(eos)
[assert_allclose(slow_vars[i], j) for (i, j) in fast_vars.items() if isinstance(j, float)]
# Error checking
with pytest.raises(Exception):
TWUSRK(Tc=507.6, Pc=3025000, omega=0.2975, T=299.)
from thermo.eos import TWU_a_alpha_common
with pytest.raises(Exception):
TWU_a_alpha_common(299.0, 507.6, 0.2975, 2.5171086468571824, method='FAIL')
# Superctitical test
eos = TWUSRK(Tc=507.6, Pc=3025000, omega=0.2975, T=900., P=1E6)
eos = TWUSRK(Tc=507.6, Pc=3025000, omega=0.2975, V=0.007422210444471012, P=1E6)
assert_allclose(eos.T, 900)
def test_APISRK_quick():
# Test solution for molar volumes
eos = APISRK(Tc=507.6, Pc=3025000, omega=0.2975, T=299., P=1E6)
Vs_fast = eos.volume_solutions(299, 1E6, eos.b, eos.delta, eos.epsilon, eos.a_alpha)
Vs_slow = eos.volume_solutions(299, 1E6, eos.b, eos.delta, eos.epsilon, eos.a_alpha, quick=False)
Vs_expected = [(0.00014681823858766455+0j), (0.0011696026208061676+0.001304203394096485j), (0.0011696026208061676-0.001304203394096485j)]
assert_allclose(Vs_fast, Vs_expected)
assert_allclose(Vs_slow, Vs_expected)
# Test of a_alphas
a_alphas = [3.727474247064678, -0.0073349099227097685, 1.9482539852821945e-05]
a_alphas_fast = eos.a_alpha_and_derivatives(299)
assert_allclose(a_alphas, a_alphas_fast)
a_alphas_slow = eos.a_alpha_and_derivatives(299, quick=False)
assert_allclose(a_alphas, a_alphas_slow)
# SRK back calculation for T
eos = APISRK(Tc=507.6, Pc=3025000, omega=0.2975, V=0.00014681823858766455, P=1E6)
assert_allclose(eos.T, 299)
T_slow = eos.solve_T(P=1E6, V=0.00014681823858766455, quick=False)
assert_allclose(T_slow, 299)
# with a S1 set
eos = APISRK(Tc=514.0, Pc=6137000.0, S1=1.678665, S2=-0.216396, P=1E6, V=7.045692682173252e-05)
assert_allclose(eos.T, 299)
eos = APISRK(Tc=514.0, Pc=6137000.0, omega=0.635, S2=-0.216396, P=1E6, V=7.184691383223729e-05)
assert_allclose(eos.T, 299)
T_slow = eos.solve_T(P=1E6, V=7.184691383223729e-05, quick=False)
assert_allclose(T_slow, 299)
eos = APISRK(Tc=507.6, Pc=3025000, omega=0.2975, T=299., P=1E6)
# Derivatives
diffs_1 = [507160.19725861016, -2694519535687.8096, 1.8821915764257067e-07, -3.7112367780430196e-13, 5312955.453232907, 1.9717635678142185e-06]
diffs_2 = [-495.7033432051597, 2.686049371238787e+17, 1.3462136329121424e-09, 1.3729982416974442e-20, -201893579486.30624, 3.80002419401769e-15]
diffs_mixed = [-4.990227751881803e-15, -14325368140.50364, 0.06593414440492529]
departures = [-31759.397282361704, -74.38420560550391, 28.946472091343608]
known_derivs_deps = [diffs_1, diffs_2, diffs_mixed, departures]
for f in [True, False]:
main_calcs = eos.derivatives_and_departures(eos.T, eos.P, eos.V_l, eos.b, eos.delta, eos.epsilon, eos.a_alpha, eos.da_alpha_dT, eos.d2a_alpha_dT2, quick=f)
for i, j in zip(known_derivs_deps, main_calcs):
assert_allclose(i, j)
# Test Cp_Dep, Cv_dep
assert_allclose(eos.Cv_dep_l, 28.946472091343608)
assert_allclose(eos.Cp_dep_l, 49.17373456158243)
# Integration tests
eos = APISRK(Tc=507.6, Pc=3025000, omega=0.2975, T=299.,V=0.00013)
fast_vars = vars(eos)
eos.set_properties_from_solution(eos.T, eos.P, eos.V, eos.b, eos.delta, eos.epsilon, eos.a_alpha, eos.da_alpha_dT, eos.d2a_alpha_dT2, quick=False)
slow_vars = vars(eos)
[assert_allclose(slow_vars[i], j) for (i, j) in fast_vars.items() if isinstance(j, float)]
# Error checking
with pytest.raises(Exception):
APISRK(Tc=507.6, Pc=3025000, omega=0.2975, T=299.)
with pytest.raises(Exception):
APISRK(Tc=507.6, Pc=3025000, P=1E6, T=299.)
def test_TWUPR_quick():
# Test solution for molar volumes
eos = TWUPR(Tc=507.6, Pc=3025000, omega=0.2975, T=299., P=1E6)
Vs_fast = eos.volume_solutions(299, 1E6, eos.b, eos.delta, eos.epsilon, eos.a_alpha)
Vs_slow = eos.volume_solutions(299, 1E6, eos.b, eos.delta, eos.epsilon, eos.a_alpha, quick=False)
Vs_expected = [(0.0001301754975832377+0j), (0.0011236542243270918+0.0012949257976571766j), (0.0011236542243270918-0.0012949257976571766j)]
assert_allclose(Vs_fast, Vs_expected)
assert_allclose(Vs_slow, Vs_expected)
# Test of a_alphas
a_alphas = [3.806982284033079, -0.006971709974815854, 2.3667018824561144e-05]
a_alphas_fast = eos.a_alpha_and_derivatives(299)
assert_allclose(a_alphas, a_alphas_fast)
a_alphas_slow = eos.a_alpha_and_derivatives(299, quick=False)
assert_allclose(a_alphas, a_alphas_slow)
# back calculation for T
eos = TWUPR(Tc=507.6, Pc=3025000, omega=0.2975, V=0.0001301754975832377, P=1E6)
assert_allclose(eos.T, 299)
T_slow = eos.solve_T(P=1E6, V=0.0001301754975832377, quick=False)
assert_allclose(T_slow, 299)
eos = TWUPR(Tc=507.6, Pc=3025000, omega=0.2975, T=299., P=1E6)
# Derivatives
diffs_1 = [592877.7698667891, -3683686154532.3066, 1.6094687359218388e-07, -2.7146720921640605e-13, 6213230.351611896, 1.6866883037707508e-06]
diffs_2 = [-708.101408196832, 4.512488462413035e+17, 1.168546207434993e-09, 9.027515426758444e-21, -280283966933.572, 3.397816790678971e-15]
diffs_mixed = [-3.82370615408822e-15, -20741143317.758797, 0.07152333089484428]
departures = [-31652.726391608117, -74.1128253091799, 35.189125483239366]
known_derivs_deps = [diffs_1, diffs_2, diffs_mixed, departures]
for f in [True, False]:
main_calcs = eos.derivatives_and_departures(eos.T, eos.P, eos.V_l, eos.b, eos.delta, eos.epsilon, eos.a_alpha, eos.da_alpha_dT, eos.d2a_alpha_dT2, quick=f)
for i, j in zip(known_derivs_deps, main_calcs):
assert_allclose(i, j)
# Test Cp_Dep, Cv_dep
assert_allclose(eos.Cv_dep_l, 35.189125483239366)
assert_allclose(eos.Cp_dep_l, 55.40579090446679)
# Integration tests
eos = TWUPR(Tc=507.6, Pc=3025000, omega=0.2975, T=299.,V=0.00013)
fast_vars = vars(eos)
eos.set_properties_from_solution(eos.T, eos.P, eos.V, eos.b, eos.delta, eos.epsilon, eos.a_alpha, eos.da_alpha_dT, eos.d2a_alpha_dT2, quick=False)
slow_vars = vars(eos)
[assert_allclose(slow_vars[i], j) for (i, j) in fast_vars.items() if isinstance(j, float)]
# Error checking
with pytest.raises(Exception):
TWUPR(Tc=507.6, Pc=3025000, omega=0.2975, T=299.)
# Superctitical test
eos = TWUPR(Tc=507.6, Pc=3025000, omega=0.2975, T=900., P=1E6)
eos = TWUPR(Tc=507.6, Pc=3025000, omega=0.2975, V=0.0073716980824289815, P=1E6)
assert_allclose(eos.T, 900)
def test_SRK_quick():
# Test solution for molar volumes
eos = SRK(Tc=507.6, Pc=3025000, omega=0.2975, T=299., P=1E6)
Vs_fast = eos.volume_solutions(299, 1E6, eos.b, eos.delta, eos.epsilon, eos.a_alpha)
Vs_slow = eos.volume_solutions(299, 1E6, eos.b, eos.delta, eos.epsilon, eos.a_alpha, quick=False)
Vs_expected = [(0.00014682102759032+0j), (0.00116960122630484+0.0013040890734249049j), (0.00116960122630484-0.0013040890734249049j)]
assert_allclose(Vs_fast, Vs_expected)
assert_allclose(Vs_slow, Vs_expected)
# Test of a_alphas
a_alphas = [3.7271789178606376, -0.007332989159328508, 1.947612023379061e-05]
a_alphas_fast = eos.a_alpha_and_derivatives(299)
assert_allclose(a_alphas, a_alphas_fast)
# PR back calculation for T
eos = SRK(Tc=507.6, Pc=3025000, omega=0.2975, V=0.00014682102759032, P=1E6)
assert_allclose(eos.T, 299)
T_slow = eos.solve_T(P=1E6, V=0.00014682102759032, quick=False)
assert_allclose(T_slow, 299)
# Derivatives
diffs_1 = [507071.37815795804, -2693849768980.0884, 1.8823298314439377e-07, -3.7121594957338967e-13, 5312565.222604471, 1.9721089437796854e-06]
diffs_2 = [-495.525429968177, 2.685153659083702e+17, 1.3462639881888625e-09, 1.3735644012106488e-20, -201856646370.53476, 3.800656805086382e-15]
diffs_mixed = [-4.991347301209541e-15, -14322106590.423191, 0.06594013142212454]
departures = [-31754.65309653571, -74.3732468359525, 28.936520816725874]
known_derivs_deps = [diffs_1, diffs_2, diffs_mixed, departures]
for f in [True, False]:
main_calcs = eos.derivatives_and_departures(eos.T, eos.P, eos.V_l, eos.b, eos.delta, eos.epsilon, eos.a_alpha, eos.da_alpha_dT, eos.d2a_alpha_dT2, quick=f)
for i, j in zip(known_derivs_deps, main_calcs):
assert_allclose(i, j)
# Integration tests
eos = SRK(Tc=507.6, Pc=3025000, omega=0.2975, T=299.,V=0.00013)
fast_vars = vars(eos)
eos.set_properties_from_solution(eos.T, eos.P, eos.V, eos.b, eos.delta, eos.epsilon, eos.a_alpha, eos.da_alpha_dT, eos.d2a_alpha_dT2, quick=False)
slow_vars = vars(eos)
[assert_allclose(slow_vars[i], j) for (i, j) in fast_vars.items() if isinstance(j, float)]
# Compare against some known in Walas [2] functions
eos = SRK(Tc=507.6, Pc=3025000, omega=0.2975, T=299., P=1E6)
V = eos.V_l
Z = eos.P*V/(R*eos.T)
D = -eos.T*eos.da_alpha_dT
S_dep_walas = R*(-log(Z*(1-eos.b/V)) + D/(eos.b*R*eos.T)*log(1 + eos.b/V))
S_dep_expect = -74.3732468359525
assert_allclose(-S_dep_walas, S_dep_expect)
assert_allclose(S_dep_expect, eos.S_dep_l)
H_dep_walas = eos.T*R*(1 - Z + 1/(eos.b*R*eos.T)*(eos.a_alpha+D)*log(1 + eos.b/V))
H_dep_expect = -31754.65309653571
assert_allclose(-H_dep_walas, H_dep_expect)
assert_allclose(H_dep_expect, eos.H_dep_l)
phi_walas = exp(Z - 1 - log(Z*(1 - eos.b/V)) - eos.a_alpha/(eos.b*R*eos.T)*log(1 + eos.b/V))
phi_l_expect = 0.02174822767621331
assert_allclose(phi_l_expect, eos.phi_l)
assert_allclose(phi_walas, eos.phi_l)
def test_RK_quick():
# Test solution for molar volumes
eos = RK(Tc=507.6, Pc=3025000, T=299., P=1E6)
Vs_fast = eos.volume_solutions(299, 1E6, eos.b, eos.delta, eos.epsilon, eos.a_alpha)
Vs_slow = eos.volume_solutions(299, 1E6, eos.b, eos.delta, eos.epsilon, eos.a_alpha, quick=False)
Vs_expected = [(0.00015189341729751865+0j), (0.0011670650314512406+0.0011171160630875456j), (0.0011670650314512406-0.0011171160630875456j)]
assert_allclose(Vs_fast, Vs_expected)
assert_allclose(Vs_slow, Vs_expected)
# Test of a_alphas
a_alphas = [3.279647547742308, -0.005484360447729613, 2.75135139518208e-05]
a_alphas_fast = eos.a_alpha_and_derivatives(299)
assert_allclose(a_alphas, a_alphas_fast)
# PR back calculation for T
eos = RK(Tc=507.6, Pc=3025000, V=0.00015189341729751865, P=1E6)
assert_allclose(eos.T, 299)
T_slow = eos.solve_T(P=1E6, V=0.00015189341729751865, quick=False)
assert_allclose(T_slow, 299)
diffs_1 = [400451.9103658808, -1773163557098.2456, 2.258403680601321e-07, -5.63963767469079e-13, 4427906.350797926, 2.49717874759626e-06]
diffs_2 = [-664.0592454189432, 1.5385265309755005e+17, 1.5035170900333218e-09, 2.759679192734741e-20, -130527989946.59952, 1.0340837610012813e-14]
diffs_mixed = [-7.870472890849004e-15, -10000515150.46239, 0.08069822580205277]
departures = [-26160.833620674082, -63.01311649400543, 39.8439858825612]
known_derivs_deps = [diffs_1, diffs_2, diffs_mixed, departures]
for f in [True, False]:
main_calcs = eos.derivatives_and_departures(eos.T, eos.P, eos.V_l, eos.b, eos.delta, eos.epsilon, eos.a_alpha, eos.da_alpha_dT, eos.d2a_alpha_dT2, quick=f)
for i, j in zip(known_derivs_deps, main_calcs):
assert_allclose(i, j)
# Test Cp_Dep, Cv_dep
assert_allclose(eos.Cv_dep_l, 39.8439858825612)
assert_allclose(eos.Cp_dep_l, 58.57054992395785)
# Integration tests
eos = RK(Tc=507.6, Pc=3025000, T=299.,V=0.00013)
fast_vars = vars(eos)
eos.set_properties_from_solution(eos.T, eos.P, eos.V, eos.b, eos.delta, eos.epsilon, eos.a_alpha, eos.da_alpha_dT, eos.d2a_alpha_dT2, quick=False)
slow_vars = vars(eos)
[assert_allclose(slow_vars[i], j) for (i, j) in fast_vars.items() if isinstance(j, float)]
# One gas phase property
assert 'g' == RK(Tc=507.6, Pc=3025000, T=499.,P=1E5).phase
# Compare against some known in Walas [2] functions
eos = RK(Tc=507.6, Pc=3025000, T=299., P=1E6)
V = eos.V_l
Z = eos.P*V/(R*eos.T)
phi_walas = exp(Z - 1 - log(Z*(1 - eos.b/V)) - eos.a/(eos.b*R*eos.T**1.5)*log(1 + eos.b/V))
phi_l_expect = 0.052632270169019224
assert_allclose(phi_l_expect, eos.phi_l)
assert_allclose(phi_walas, eos.phi_l)
S_dep_walas = -R*(log(Z*(1 - eos.b/V)) - eos.a/(2*eos.b*R*eos.T**1.5)*log(1 + eos.b/V))
S_dep_expect = -63.01311649400542
assert_allclose(-S_dep_walas, S_dep_expect)
assert_allclose(S_dep_expect, eos.S_dep_l)
H_dep_walas = R*eos.T*(1 - Z + 1.5*eos.a/(eos.b*R*eos.T**1.5)*log(1 + eos.b/V))
H_dep_expect = -26160.833620674082
assert_allclose(-H_dep_walas, H_dep_expect)
assert_allclose(H_dep_expect, eos.H_dep_l)
def test_PR_quick():
# Test solution for molar volumes
eos = PR(Tc=507.6, Pc=3025000, omega=0.2975, T=299., P=1E6)
Vs_fast = eos.volume_solutions(299, 1E6, eos.b, eos.delta, eos.epsilon, eos.a_alpha)
Vs_slow = eos.volume_solutions(299, 1E6, eos.b, eos.delta, eos.epsilon, eos.a_alpha, quick=False)
Vs_expected = [(0.00013022208100139953-0j), (0.001123630932618011+0.0012926962852843173j), (0.001123630932618011-0.0012926962852843173j)]
assert_allclose(Vs_fast, Vs_expected)
assert_allclose(Vs_slow, Vs_expected)
# Test of a_alphas
a_alphas = [3.801259426590328, -0.006647926028616357, 1.6930127618563258e-05]
a_alphas_fast = eos.a_alpha_and_derivatives(299, quick=True)
assert_allclose(a_alphas, a_alphas_fast)
a_alphas_slow = eos.a_alpha_and_derivatives(299, quick=False)
assert_allclose(a_alphas, a_alphas_slow)
# PR back calculation for T
eos = PR(Tc=507.6, Pc=3025000, omega=0.2975, V=0.00013022208100139953, P=1E6)
assert_allclose(eos.T, 299)
T_slow = eos.solve_T(P=1E6, V=0.00013022208100139953, quick=False)
assert_allclose(T_slow, 299)
diffs_1 = [582232.4757941157, -3665180614672.2373, 1.588550570914177e-07, -2.7283785033590384e-13, 6295046.681608136, 1.717527004374129e-06]
diffs_2 = [-506.2012523140166, 4.482165856521269e+17, 1.1688513685432287e-09, 9.103361314057314e-21, -291578941282.6521, 2.564684443970742e-15]
diffs_mixed = [-3.772507759880179e-15, -20523303691.115646, 0.06994170496262654]
departures = [-31134.740290463407, -72.47559475426019, 25.165377505266793]
known_derivs_deps = [diffs_1, diffs_2, diffs_mixed, departures]
for f in [True, False]:
main_calcs = eos.derivatives_and_departures(eos.T, eos.P, eos.V_l, eos.b, eos.delta, eos.epsilon, eos.a_alpha, eos.da_alpha_dT, eos.d2a_alpha_dT2, quick=f)
for i, j in zip(known_derivs_deps, main_calcs):
assert_allclose(i, j)
# Test Cp_Dep, Cv_dep
assert_allclose(eos.Cv_dep_l, 25.165377505266747)
assert_allclose(eos.Cp_dep_l, 44.50559908690951)
# Exception tests
a = GCEOS()
with pytest.raises(Exception):
a.a_alpha_and_derivatives(T=300)
with pytest.raises(Exception):
PR(Tc=507.6, Pc=3025000, omega=0.2975, T=299)
# Integration tests
eos = PR(Tc=507.6, Pc=3025000, omega=0.2975, T=299.,V=0.00013)
fast_vars = vars(eos)
eos.set_properties_from_solution(eos.T, eos.P, eos.V, eos.b, eos.delta, eos.epsilon, eos.a_alpha, eos.da_alpha_dT, eos.d2a_alpha_dT2, quick=False)
slow_vars = vars(eos)
[assert_allclose(slow_vars[i], j) for (i, j) in fast_vars.items() if isinstance(j, float)]
# One gas phase property
assert 'g' == PR(Tc=507.6, Pc=3025000, omega=0.2975, T=499.,P=1E5).phase
eos = PR(Tc=507.6, Pc=3025000, omega=0.2975, T=299., P=1E6)
B = eos.b*eos.P/R/eos.T
A = eos.a_alpha*eos.P/(R*eos.T)**2
D = -eos.T*eos.da_alpha_dT
V = eos.V_l
Z = eos.P*V/(R*eos.T)
# Compare against some known in Walas [2] functions
phi_walas = exp(Z - 1 - log(Z - B) - A/(2*2**0.5*B)*log((Z+(sqrt(2)+1)*B)/(Z-(sqrt(2)-1)*B)))
phi_l_expect = 0.022212524527244357
assert_allclose(phi_l_expect, eos.phi_l)
assert_allclose(phi_walas, eos.phi_l)
# The formula given in [2]_ must be incorrect!
# S_dep_walas = R*(-log(Z - B) + B*D/(2*2**0.5*A*eos.a_alpha)*log((Z+(sqrt(2)+1)*B)/(Z-(sqrt(2)-1)*B)))
# S_dep_expect = -72.47559475426013
# assert_allclose(-S_dep_walas, S_dep_expect)
# assert_allclose(S_dep_expect, eos.S_dep_l)
H_dep_walas = R*eos.T*(1 - Z + A/(2*2**0.5*B)*(1 + D/eos.a_alpha)*log((Z+(sqrt(2)+1)*B)/(Z-(sqrt(2)-1)*B)))
H_dep_expect = -31134.740290463407
assert_allclose(-H_dep_walas, H_dep_expect)
assert_allclose(H_dep_expect, eos.H_dep_l)
# Author's original H_dep, in [1]
H_dep_orig = R*eos.T*(Z-1) + (eos.T*eos.da_alpha_dT-eos.a_alpha)/(2*2**0.5*eos.b)*log((Z+2.44*B)/(Z-0.414*B))
assert_allclose(H_dep_orig, H_dep_expect, rtol=5E-3)
# Author's correlation, with the correct constants this time
H_dep_orig = R*eos.T*(Z-1) + (eos.T*eos.da_alpha_dT-eos.a_alpha)/(2*2**0.5*eos.b)*log((Z+(sqrt(2)+1)*B)/(Z-(sqrt(2)-1)*B))
assert_allclose(H_dep_orig, H_dep_expect)
