import numpy as np
from openpnm.models.phase import _phasedocs
__all__ = [
"liquid_mixture_tc",
"gas_mixture_ce",
"gas_mixture_fesg",
# "gas_mixture_wilke_fuller",
]
[docs]
@_phasedocs
def liquid_mixture_tc(
phase,
T='pore.temperature',
mu='pore.viscosity',
Vms_at_Tb='param.molar_volume_Tb.*',
sigmas_at_Tb='param.surface_tension_Tb.*',
):
r"""
Uses Tyn-Calus model to estimate diffusion coefficient in a dilute liquid
solution of A in B from first principles at conditions of interest
Parameters
----------
%(phase)s
%(T)s
%(mu)s
Vms_at_Tb : str or list of scalars
Molar volumes of each component at its boiling temperature (m3/mol).
Can either be a string to a parameter on each component of a list
of scalar values which are used directly
sigmas_at_Tb : float
Surface tension of component A at boiling temperature (N/m)
Returns
-------
"""
T = phase[T]
mu = phase[mu]
sigma_A, sigma_B = phase.get_comp_vals(sigmas_at_Tb).values()
VA, VB = phase.get_comp_vals(Vms_at_Tb).values()
A = 8.93e-8*(VB*1e6)**0.267/(VA*1e6)**0.433*T
B = (sigma_B/sigma_A)**0.15/(mu*1e3)
value = A*B*1e-4
return value
[docs]
@_phasedocs
def gas_mixture_ce(
phase,
T='pore.temperature',
P='pore.pressure',
Tcs='param.critical_temperature.*',
Pcs='param.critical_pressure.*',
omegas='param.acentric_factor.*',
MWs='param.molecular_weight.*',
epsilons='param.LJ_energy.*',
sigmas='param.LJ_diameter.*',
):
r"""
Calculate gas phase diffusion coefficient using Chapman-Enskog equation.
Parameters
----------
%(phase)s
%(T)s
%(P)s
%(Tcs)s
%(Pcs)s
%(omegas)s
%(MWs)s
%(epsilons)s
%(sigmas)s
Returns
-------
"""
# Fetch values from components
T = phase[T]
P = phase[P]
try:
MA, MB = phase.get_comp_vals(MWs).values()
except ValueError:
raise Exception('This function only works on binary mixtures')
MWAB = 2/(1/MA + 1/MB)
omega = phase.get_comp_vals(omegas).values()
Tc = phase.get_comp_vals(Tcs).values()
Pc = phase.get_comp_vals(Pcs).values()
k = 1.380649e-23 # Boltzmann constant
try:
eA, eB = phase.get_comp_vals(epsilons).values()
except Exception:
# Use correlation of Tee, Gotoh, & Stewart
eA, eB = (0.7915 + 0.1693*omega)*Tc*k
eAB = (eA*eB)**0.5
# Compute collision integral using Neufeld's correlation (RPP Eq.(11-3.6))
A, B, C, D, E, F, G, H = (1.06036, 0.15610, 0.19300, 0.47635, 1.03587,
1.52996, 1.76474, 3.89411)
Tstar = k*T/eAB
Omega = Omega = A/(Tstar**B) + C/np.exp(D*Tstar) + E/np.exp(F*Tstar) \
+ G/np.exp(H*Tstar)
# Now apply RPP Eq.(11-3.2)
try:
sA, sB = phase.get_comp_vals(sigmas).values()
except Exception:
# Use correlation of Tee, Gotoh, & Stewart
sA, sB = (2.3551 - 0.08847*omega)*(Tc/Pc)**(1/3)
sAB = (sA + sB)/2
DAB = 0.00266 * (T**1.5) / (P/101325 * MWAB**0.5 * sAB**2 * Omega) * 1e-4
return DAB
[docs]
@_phasedocs
def gas_mixture_fesg(
phase,
T='pore.temperature',
P='pore.pressure',
MWs='param.molecular_weight.*',
Vdms='param.molar_diffusion_volume.*',
):
r"""
Estimates the diffusion coefficient of both species in a binary gas
mixture using the Fuller et al correlation [1]_, [2]_, [3]_.
Parameters
----------
%(phase)s
%(T)s
%(P)s
%(MWs)s
%(Vdms)s
Returns
-------
Dij : dict[ndarray]
The dict contains one array for each component, containing the
diffusion coefficient of that component at each location.
References
----------
.. [1] Fuller, E. N., and J. C. Giddings: J. Gas Chromatogr., 3: 222 (1965).
.. [2] Fuller, E. N., P. D. Schettler, and J. C. Giddings: Ind. Eng. Chem.,
58(5): 18 (1966).
.. [3] Fuller, E. N., K. Ensley, and J. C. Giddings: J. Phys. Chem.,
73: 3679 (1969).
"""
T = phase[T]
P = phase[P]
# The following is to accomodate proper mixtures AND normal Phase objects
try:
MA, MB = phase.get_comp_vals(MWs).values()
except AttributeError:
MA, MB = phase[MWs]
try:
vA, vB = phase.get_comp_vals(Vdms).values()
except AttributeError:
vA, vB = phase[Vdms]
MAB = 2/(1/MA + 1/MB)
P = P/101325
DAB = 0.00143*T**1.75/(P*(MAB**0.5)*(vA**(1./3) + vB**(1./3))**2)*1e-4
return DAB
def gas_mixture_fw(
phase,
T='pore.temperature',
P='pore.pressure',
MWs='param.molecular_weight.*',
Vdms='pore.molar_diffusion_volume.*',
): # pragma: no cover
r"""
Estimates the diffusion coeffient of each species in a gas mixture
Uses the Fuller equation to estimate binary diffusivity between pairs,
then uses the correction of Fairbanks and Wilke [1]_ to account for the
composition of the gas mixture.
Parameters
----------
%(phase)s
%(T)s
%(P)s
%(MWs)s
%(Vdms)s
Returns
-------
Dij : dict[ndarray]
The dict contains one array for each component, containing the
diffusion coefficient of that component at each location.
References
----------
.. [1] Fairbanks DF and CR Wilke, Diffusion Coefficients in Multicomponent
Gas Mixtures. Industrial & Engineering Chemistry, 42(3), p471–475 (1950).
`DOI: 10.1021/ie50483a022 <http://doi.org/10.1021/ie50483a022>`_
"""
raise Exception('This function is not ready yet')
# comps = list(phase.components.values())
# values = {}
# for i in range(len(comps)):
# A = comps[i]
# denom = 0.0
# for j in range(len(comps)):
# if i != j:
# B = comps[j]
# D = gas_mixture_fesg(phase=phase,
# molecular_weight=MW_pair,
# molar_diffusion_volume=Vdm_pair,
# temperature=T,
# pressure=P)
# yB = phase['pore.mole_fraction.' + B.name]
# denom += yB/D
# yA = phase['pore.mole_fraction.' + A.name]
# values[A.name] = (1 - yA)/denom
# return values
