def create_eos(kind, pc, tc, **kwargs):
"""
Create an EoS object.
Parameters
----------
kind : string
Type of EoS: VDW, SRK, or PR
pc : float
Critical pressure
tc : float
Critical temperature
omega : float
Acentric factor. Required for SDK and PR.
Returns
-------
VanDerWaalsEos, SoaveRedlichKwongEos, or PengRobinsonEos
"""
if kind == 'VDW':
return VanDerWaalsEos(pc, tc)
elif kind == 'SRK':
if 'omega' not in kwargs:
raise KeyError("Key 'omega' is not found!")
omega = kwargs['omega']
return SoaveRedlichKwongEos(pc, tc, omega)
elif kind == 'PR':
if 'omega' not in kwargs:
raise KeyError("Key 'omega' is not found!")
omega = kwargs['omega']
return PengRobinsonEos(pc, tc, omega)
else:
raise ValueError('kind must be VDW, SRK, or PR.')
def test_near_critical_point():
# PENG-ROBINSON
props = input_properties_case_dissertation_PR()
(_, _, global_molar_fractions,
critical_pressure, critical_temperature, acentric_factor,
molar_mass, omega_a, omega_b, binary_interaction) = props
eos_pr = PengRobinsonEos(critical_pressure, critical_temperature, acentric_factor,
omega_a, omega_b, binary_interaction)
# temperature = 366.5 # [K] Easy ss flash converges
temperature = 408.0 # [K] Hard, number of iter reached!
pressure = np.linspace(30.0, 80.0, num=200) * 1.0e5 # [Pa]
result_pr = calculate_molar_fraction_curve(
eos_pr, pressure,
temperature, global_molar_fractions, print_statistics=False
)
pressure_bar = pressure / 1.0e5
plt.plot(pressure_bar, result_pr, label='Peng-Robinson')
plt.xlabel('Pressure [bar]')
plt.ylabel('Vapor molar fraction [mol/mol]')
plt.legend(loc='upper center')
plt.axis([np.min(pressure_bar), np.max(pressure_bar), 0.0, 1.0])
plt.show()
def test_retrograde_condensation():
# PENG-ROBINSON
props = input_properties_case_7_psudocomponents()
(_, _, global_molar_fractions,
critical_pressure, critical_temperature, acentric_factor,
molar_mass, omega_a, omega_b, binary_interaction) = props
eos_pr = PengRobinsonEos(critical_pressure, critical_temperature, acentric_factor,
omega_a, omega_b, binary_interaction)
temperature = 350.0 # [K]
pressure = np.linspace(1.0, 250.0, num=200) * 1.0e5 # [Pa]
result_pr = calculate_molar_fraction_curve(eos_pr, pressure, temperature, global_molar_fractions)
pressure_bar = pressure / 1.0e5
plt.plot(pressure_bar, result_pr, label='Peng-Robinson')
plt.xlabel('Pressure [bar]')
plt.ylabel('Vapor molar fraction [mol/mol]')
plt.legend(loc='upper center')
plt.axis([np.min(pressure_bar), np.max(pressure_bar), 0.0, 1.0])
plt.show()
def test_different_eos():
# PENG-ROBINSON
props = input_properties_case_whitson_problem_18_PR()
(_, _, global_molar_fractions,
critical_pressure, critical_temperature, acentric_factor,
molar_mass, omega_a, omega_b, binary_interaction) = props
eos_pr = PengRobinsonEos(critical_pressure, critical_temperature, acentric_factor,
omega_a, omega_b, binary_interaction)
# SOAVE-REDLICH-KWONG
props = input_properties_case_whitson_problem_18_SRK()
(_, _, global_molar_fractions,
critical_pressure, critical_temperature, acentric_factor,
molar_mass, omega_a, omega_b, binary_interaction) = props
eos_srk = SoaveRedlichKwongEos(critical_pressure, critical_temperature, acentric_factor,
omega_a, omega_b, binary_interaction)
# VAN DER WAALS
props = input_properties_case_whitson_problem_18_VDW()
(_, _, global_molar_fractions,
critical_pressure, critical_temperature, acentric_factor,
molar_mass, omega_a, omega_b, binary_interaction) = props
eos_vdw = VanDerWaalsEos(critical_pressure, critical_temperature, acentric_factor,
omega_a, omega_b, binary_interaction)
temperature = 350.0 # [K]
pressure = np.linspace(1, 135.0, num=200) * 1.0e5 # [Pa]
result_pr = calculate_molar_fraction_curve(eos_pr, pressure, temperature, global_molar_fractions)
result_srk = calculate_molar_fraction_curve(eos_srk, pressure, temperature, global_molar_fractions)
result_vdw = calculate_molar_fraction_curve(eos_vdw, pressure, temperature, global_molar_fractions)
pressure_bar = pressure / 1.0e5
plt.plot(pressure_bar, result_pr, label='Peng-Robinson')
plt.plot(pressure_bar, result_srk, label='Soave-Redlich-Kwong')
plt.plot(pressure_bar, result_vdw, label='Van der Waals')
plt.xlabel('Pressure [bar]')
plt.ylabel('Vapor molar fraction [mol/mol]')
plt.legend(loc='upper center')
plt.axis([np.min(pressure_bar), np.max(pressure_bar), 0.0, 1.0])
plt.show()
def test_vapor_liquid_curves():
temperature = 350.0 # [K]
pressure = np.linspace(2.5, 150.0, num=200) * 1.0e5 # [Pa]
# Create EoS object and set properties
props = input_properties_case_whitson_problem_18_PR()
(_, _, global_molar_fractions,
critical_pressure, critical_temperature, acentric_factor,
molar_mass, omega_a, omega_b, binary_interaction) = props
eos = PengRobinsonEos(critical_pressure, critical_temperature, acentric_factor,
omega_a, omega_b, binary_interaction)
result = calculate_molar_fraction_curve(eos, pressure, temperature, global_molar_fractions)
pressure_bar = pressure / 1.0e5
plt.plot(pressure_bar, result, label='Vapor molar fraction')
plt.plot(pressure_bar, 1.0-result, label='Liquid molar fraction')
plt.xlabel('Pressure [bar]')
plt.ylabel('Phase molar fraction [mol/mol]')
plt.legend(loc='upper center')
plt.axis([np.min(pressure_bar), np.max(pressure_bar), 0.0, 1.0])
plt.show()
def test_phase_equilibria():
# Get input properties
#props = input_properties_case_7_psudocomponents()
props = input_properties_case_whitson_problem_18_PR()
#props = input_properties_case_whitson_problem_18_SRK()
#props = input_properties_case_whitson_problem_18_VDW()
(pressure, temperature, global_molar_fractions, critical_pressure,
critical_temperature, acentric_factor, molar_mass, omega_a, omega_b,
binary_interaction) = props
#temperature = 350.0 # [K]
#pressure = 50.0 * 1e5 # [Pa]
# Estimate initial K-values
initial_K_values = calculate_K_values_wilson(pressure, temperature,
critical_pressure,
critical_temperature,
acentric_factor)
# Create EoS object and set properties
#eos = VanDerWaalsEos, PengRobinsonEos, SoaveRedlichKwongEos
eos = PengRobinsonEos(critical_pressure, critical_temperature,
acentric_factor, omega_a, omega_b,
binary_interaction)
is_stable, K_values_est = calculate_stability_test(eos, pressure,
temperature,
global_molar_fractions,
initial_K_values)
print('System is stable?', is_stable)
print('K_values estimates:', K_values_est)
K_values_from_ss_flash, F_V, f_L = ss_flash(eos,
pressure,
temperature,
global_molar_fractions,
K_values_est,
tolerance=1.0e-1)
fugacity_expected = np.array([294.397, 148.342, 3.02385]) * 6894.75729
K_values_expected = np.array([6.65071, 0.890061, 0.03624])
x_expected = np.array([0.08588, 0.46349, 0.45064])
y_expected = np.array([0.57114, 0.41253, 0.01633])
print('K_values Successive Subst:', K_values_from_ss_flash)
print('Vapor molar fraction:', F_V)
print('\n-----\nFugacities obtained:', f_L)
print('Fugacities expected:', fugacity_expected)
# Use estimates from Wilson's Equation!!!
#x0 = np.append(initial_K_values, F_V) # It does not work!
# Use estimates from stability test!!!
#x0 = np.append(K_values_est, F_V) # It does not work!
# Use estimates from successive substitutions!!!
x0 = np.append(K_values_from_ss_flash, F_V) # Good estimate!
result = fsolve(
func=flash_residual_function,
x0=x0,
args=(temperature, pressure, eos, global_molar_fractions),
)
size = result.shape[0]
K_values_newton = result[0:size - 1]
F_V = result[size - 1]
print('K_values newton:', K_values_newton)
print('K_values expected:', K_values_expected)
print('Norm difference:',
np.linalg.norm(K_values_expected - K_values_newton))
print('Vapor molar fraction:', F_V)
assert np.allclose(K_values_newton, K_values_expected, rtol=0.01)
assert np.allclose(fugacity_expected, f_L, rtol=0.1)
def test_multiphase_flash_residual_function():
# Get input properties
temperature = 278.0 # [K]
pressure = 0.5 * 1e5 # [Pa]
props = input_properties_case_Ghafri(temperature)
(_, _, global_molar_fractions, critical_pressure, critical_temperature,
acentric_factor, molar_mass, omega_a, omega_b, binary_interaction) = props
# Estimate initial K-values
initial_K_values = calculate_K_values_wilson(pressure, temperature,
critical_pressure,
critical_temperature,
acentric_factor)
# Create EoS object and set properties
eos = PengRobinsonEos(critical_pressure, critical_temperature,
acentric_factor, omega_a, omega_b,
binary_interaction)
P, T = pressure, temperature
z = global_molar_fractions
K_values_est = initial_K_values
x0 = np.r_[K_values_est, K_values_est, 0.1, 0.2]
n_extra_phases = 2
result, infodict, ier, mesg = fsolve(
func=multiphase_flash_residual_function,
x0=x0,
args=(T, P, eos, z, n_extra_phases),
full_output=1)
print(mesg)
shape = (n_extra_phases, z.size)
# Get values from unknown vector
K_values = result[:-n_extra_phases].reshape(shape)
β = result[-n_extra_phases:]
print('K_values:\n', K_values)
print('Molar phase fractions:', β)
assert ier == 1
Mi = molar_mass
K = K_values
denominator = 1 + (β[:, np.newaxis] * (K - 1)).sum(axis=0)
y_iF = z / denominator
y_i = K * y_iF
print('Molar component phase fractions:\n', y_i)
# Reference phase density
ρ_F = calculate_density(y_iF, P, T, Mi, eos)
ρ = []
for j in range(n_extra_phases):
ρ_j = calculate_density(y_i[j], P, T, Mi, eos)
ρ = np.r_[ρ, ρ_j]
ρ = np.r_[ρ, ρ_F]
print('Obtained Densities:', ρ)
def test_phase_equilibria_CO2():
# Get input properties
temperature = 290.0 # [K]
pressure = 1.0 * 1e5 # [Pa]
props = input_properties_case_Ghafri(temperature)
(_, _, global_molar_fractions, critical_pressure, critical_temperature,
acentric_factor, molar_mass, omega_a, omega_b, binary_interaction) = props
# Estimate initial K-values
initial_K_values = calculate_K_values_wilson(pressure, temperature,
critical_pressure,
critical_temperature,
acentric_factor)
# Create EoS object and set properties
#eos = VanDerWaalsEos, PengRobinsonEos, SoaveRedlichKwongEos
eos = PengRobinsonEos(critical_pressure, critical_temperature,
acentric_factor, omega_a, omega_b,
binary_interaction)
is_stable, K_values_est = calculate_stability_test(eos, pressure,
temperature,
global_molar_fractions,
initial_K_values)
print('System is stable?', is_stable)
#print ('K_values estimates:', K_values_est)
K_values_from_ss_flash, F_V, f_L = ss_flash(eos,
pressure,
temperature,
global_molar_fractions,
K_values_est,
tolerance=1.0e-1,
print_statistics=True)
print('K_values Successive Subst:', K_values_from_ss_flash)
print('Vapor molar fraction:', F_V)
print('\n-----\nFugacities obtained:', f_L)
# Use estimates from Wilson's Equation!!!
#x0 = np.append(initial_K_values, F_V) # It does not work!
K_values_est = np.array([
2.71350413e+01, 9.23075054e+01, 1.17478417e+01, 2.84833217e+00,
8.98083183e-02, 1.48315222e-02, 2.65989146e-03, 7.30566453e-04,
7.76675634e-04, 1.00536144e-04, 4.54130173e-05, 3.11385702e-05,
1.71481448e-06, 2.66939726e-06, 1.64767536e-07, 2.36654995e-08,
1.10913280e-08, 1.60469889e-09, 8.82593963e-11, 1.10828717e-13,
5.96510411e-03
])
# Use estimates from stability test!!!
x0 = np.append(K_values_est, 0.749313901696) # It does not work!
# Use estimates from successive substitutions!!!
#x0 = np.append(K_values_from_ss_flash, F_V) # Good estimate!
result = fsolve(func=flash_residual_function,
x0=x0,
args=(temperature, pressure, eos, global_molar_fractions),
full_output=1)
converged = result[2]
msg = result[3]
print(msg)
X = result[0]
size = X.shape[0]
K_values_newton = X[0:size - 1]
F_V = X[size - 1]
print('K_values newton:', K_values_newton)
print('Vapor molar fraction:', F_V)
assert converged == 1
Mi = molar_mass
P, T = pressure, temperature
z = global_molar_fractions
K = K_values_newton
x_L = z / (F_V * (K - 1) + 1)
x_V = K * x_L
ρ_V = calculate_density(x_V, P, T, Mi, eos)
ρ_L = calculate_density(x_L, P, T, Mi, eos)
print('Vapor density:', ρ_V)
print('Liquid density:', ρ_L)