| import numpy as _np |
| import scipy.constants as _const |
| from openpnm.models import _doctxt |
| from openpnm.models.physics._utils import _poisson_conductance |
|
|
|
|
| __all__ = [ |
| "generic_diffusive", |
| "ordinary_diffusion", |
| "mixed_diffusion", |
| "taylor_aris_diffusion", |
| ] |
|
|
|
|
| @_doctxt |
| def generic_diffusive(phase, |
| pore_diffusivity="pore.diffusivity", |
| throat_diffusivity="throat.diffusivity", |
| size_factors="throat.diffusive_size_factors"): |
| r""" |
| Calculates the diffusive conductance of conduits in network. |
| |
| Parameters |
| ---------- |
| %(phase)s |
| pore_diffusivity : str |
| %(dict_blurb)s pore diffusivity |
| throat_diffusivity : str |
| %(dict_blurb)s throat diffusivity |
| size_factors : str |
| %(dict_blurb)s conduit diffusive size factors |
| |
| Returns |
| ------- |
| %(return_arr)s diffusive conductance |
| |
| """ |
| return _poisson_conductance(phase=phase, |
| pore_conductivity=pore_diffusivity, |
| throat_conductivity=throat_diffusivity, |
| size_factors=size_factors) |
|
|
|
|
| @_doctxt |
| def ordinary_diffusion(phase, |
| pore_diffusivity="pore.diffusivity", |
| throat_diffusivity="throat.diffusivity", |
| size_factors="throat.diffusive_size_factors"): |
| r""" |
| Calculates the diffusive conductance of conduits in network. |
| |
| Parameters |
| ---------- |
| %(phase)s |
| pore_diffusivity : str |
| %(dict_blurb)s pore diffusivity |
| throat_diffusivity : str |
| %(dict_blurb)s throat diffusivity |
| size_factors: str |
| %(dict_blurb)s conduit diffusive size factors |
| |
| Returns |
| ------- |
| %(return_arr)s diffusive conductance |
| |
| """ |
| return _poisson_conductance(phase=phase, |
| pore_conductivity=pore_diffusivity, |
| throat_conductivity=throat_diffusivity, |
| size_factors=size_factors) |
|
|
|
|
| @_doctxt |
| def mixed_diffusion(phase, |
| pore_diameter="pore.diameter", |
| throat_diameter="throat.diameter", |
| pore_diffusivity="pore.diffusivity", |
| throat_diffusivity="throat.diffusivity", |
| pore_temperature="pore.temperature", |
| throat_temperature="throat.temperature", |
| molecular_weight="pore.molecular_weight", |
| size_factors="throat.diffusive_size_factors"): |
| r""" |
| Calculates the diffusive conductance of conduits in network with |
| Knudsen correction. |
| |
| Parameters |
| ---------- |
| %(phase)s |
| pore_diameter : str |
| %(dict_blurb)s pore diameter |
| throat_diameter : str |
| %(dict_blurb)s throat diameter |
| pore_diffusivity : str |
| %(dict_blurb)s pore diffusivity |
| throat_diffusivity : str |
| %(dict_blurb)s pore diffusivity |
| pore_temperature : str |
| %(dict_blurb)s pore temperature |
| molecular_weigth : str |
| %(dict_blurb)s pore molecular weight |
| size_factors : str |
| %(dict_blurb)s size factor |
| |
| Returns |
| ------- |
| %(return_arr)s diffusive conductance |
| |
| """ |
| |
| Dp = phase[pore_diffusivity] |
| Dt = phase[throat_diffusivity] |
| dp = phase.network[pore_diameter] |
| dt = phase.network[throat_diameter] |
| MWp = phase[molecular_weight] |
| MWt = phase.interpolate_data(propname='throat.'+molecular_weight.split('.', 1)[-1]) |
| Tp = phase[pore_temperature] |
| Tt = phase[throat_temperature] |
|
|
| |
| DKp = dp/3 * (8*_const.R*Tp / (_const.pi*MWp)) ** 0.5 |
| DKt = dt/3 * (8*_const.R*Tt / (_const.pi*MWt)) ** 0.5 |
|
|
| |
| Dp_eff = (1/DKp + 1/Dp) ** -1 |
| Dt_eff = (1/DKt + 1/Dt) ** -1 |
|
|
| return _poisson_conductance(phase=phase, |
| pore_conductivity=Dp_eff, |
| throat_conductivity=Dt_eff, |
| size_factors=size_factors) |
|
|
|
|
| @_doctxt |
| def taylor_aris_diffusion(phase, |
| pore_area="pore.area", |
| throat_area="throat.cross_sectional_area", |
| pore_diffusivity="pore.diffusivity", |
| throat_diffusivity="throat.diffusivity", |
| pore_pressure="pore.pressure", |
| throat_hydraulic_conductance="throat.hydraulic_conductance", |
| size_factors="throat.diffusive_size_factors"): |
| r""" |
| Calculates the diffusive conductance of conduits in network |
| considering the Taylor-Aris effect (effect of flow on diffusion). |
| |
| Parameters |
| ---------- |
| %(phase)s |
| pore_area : str |
| %(dict_blurb)s pore cross-sectional area |
| throat_area : str |
| %(dict_blurb)s throat cross-sectional area |
| pore_diffusivity : str |
| %(dict_blurb)s pore diffusivity |
| throat_diffusivity : str |
| %(dict_blurb)s pore diffusivity |
| pore_pressure : str |
| %(dict_blurb)s pore pressure |
| throat_hydraulic_conductance : str |
| %(dict_blurb)s throat hydraulic conductance |
| size_factors : str |
| %(dict_blurb)s conduit size factors |
| |
| Returns |
| ------- |
| %(return_arr)s diffusive conductance |
| |
| """ |
| network = phase.network |
| cn = network['throat.conns'] |
| F = network[size_factors] |
|
|
| |
| A1, A2 = network[pore_area][cn].T |
| At = network[throat_area] |
| D1, D2 = phase[pore_diffusivity][cn].T |
| Dt = phase[throat_diffusivity] |
| P = phase[pore_pressure] |
| gh = phase[throat_hydraulic_conductance] |
|
|
| |
| Qt = -gh * _np.diff(P[cn], axis=1).squeeze() |
| u1, ut, u2 = [Qt/Ai for Ai in [A1, At, A2]] |
| Pe1 = u1 * ((4 * A1 / _np.pi) ** 0.5) / D1 |
| Pe2 = u2 * ((4 * A2 / _np.pi) ** 0.5) / D2 |
| Pet = ut * ((4 * At / _np.pi) ** 0.5) / Dt |
|
|
| if F.ndim > 1: |
| g1 = D1 * (1 + Pe1**2 / 192) * F[:, 0] |
| gt = Dt * (1 + Pet**2 / 192) * F[:, 1] |
| g2 = D2 * (1 + Pe2**2 / 192) * F[:, 2] |
| gtot = 1 / (1/g1 + 1/gt + 1/g2) |
| else: |
| gtot = Dt * (1 + Pet**2 / 192) * F |
| return gtot |
|
|
