| r""" |
| Details about the continum and numerical model equations can be found on: |
| Agnaou, M., Sadeghi, M. A., Tranter, T. G., & Gostick, J. (2020). |
| |
| Modeling transport of charged species in pore networks: solution of the |
| Nernst-Planck equations coupled with fluid flow and charge conservation |
| equations. Computers & Geosciences, 104505. |
| |
| """ |
| import openpnm as op |
| from openpnm.phase import mixtures |
| import numpy as np |
|
|
|
|
| ws = op.Workspace() |
| proj = ws.new_project() |
| export = False |
|
|
| |
| np.random.seed(0) |
|
|
| net = op.network.Cubic(shape=[8, 8, 1], spacing=9e-4, project=proj) |
| Ps = (net['pore.back'] * net['pore.right'] |
| + net['pore.back'] * net['pore.left'] |
| + net['pore.front'] * net['pore.right'] |
| + net['pore.front'] * net['pore.left']) |
| Ts = net['throat.surface'] |
| op.topotools.trim(network=net, pores=net.Ps[Ps], throats=net.Ts[Ts]) |
|
|
| geo = op.geometry.SpheresAndCylinders(network=net, pores=net.Ps, throats=net.Ts) |
| pore_d = op.models.misc.constant |
| throat_d = op.models.misc.constant |
| geo.add_model(propname='pore.diameter', model=pore_d, value=1.5e-4) |
| geo.add_model(propname='throat.diameter', model=throat_d, value=1e-4) |
| geo.regenerate_models() |
|
|
| sw = mixtures.SalineWater(network=net) |
| |
| Na = sw.components['Na_' + sw.name] |
| Cl = sw.components['Cl_' + sw.name] |
| H2O = sw.components['H2O_' + sw.name] |
|
|
| |
| phys = op.physics.GenericPhysics(network=net, phase=sw, geometry=geo) |
|
|
| flow = op.models.physics.hydraulic_conductance.hagen_poiseuille |
| phys.add_model(propname='throat.hydraulic_conductance', |
| pore_viscosity='pore.viscosity', |
| throat_viscosity='throat.viscosity', |
| model=flow, regen_mode='normal') |
|
|
| current = op.models.physics.ionic_conductance.electroneutrality |
| phys.add_model(propname='throat.ionic_conductance', ions=[Na.name, Cl.name], |
| model=current, regen_mode='normal') |
|
|
| eA_dif = op.models.physics.diffusive_conductance.ordinary_diffusion |
| phys.add_model(propname='throat.diffusive_conductance.' + Na.name, |
| pore_diffusivity='pore.diffusivity.' + Na.name, |
| throat_diffusivity='throat.diffusivity.' + Na.name, |
| model=eA_dif, regen_mode='normal') |
|
|
| eB_dif = op.models.physics.diffusive_conductance.ordinary_diffusion |
| phys.add_model(propname='throat.diffusive_conductance.' + Cl.name, |
| pore_diffusivity='pore.diffusivity.' + Cl.name, |
| throat_diffusivity='throat.diffusivity.' + Cl.name, |
| model=eB_dif, regen_mode='normal') |
|
|
| s_scheme = 'powerlaw' |
| ad_dif_mig_Na = op.models.physics.ad_dif_mig_conductance.ad_dif_mig |
| phys.add_model(propname='throat.ad_dif_mig_conductance.' + Na.name, |
| pore_pressure='pore.pressure', model=ad_dif_mig_Na, |
| ion=Na.name, s_scheme=s_scheme) |
|
|
| ad_dif_mig_Cl = op.models.physics.ad_dif_mig_conductance.ad_dif_mig |
| phys.add_model(propname='throat.ad_dif_mig_conductance.' + Cl.name, |
| pore_pressure='pore.pressure', model=ad_dif_mig_Cl, |
| ion=Cl.name, s_scheme=s_scheme) |
|
|
| |
| setts1 = {'solver_max_iter': 5, 'solver_tol': 1e-08, 'solver_rtol': 1e-08, |
| 'nlin_max_iter': 10, 'cache': False} |
| setts2 = {'g_tol': 1e-4, 'g_max_iter': 4, 't_output': 5000, 't_step': 500, |
| 't_final': 20000, 't_scheme': 'implicit'} |
|
|
| |
| sf = op.algorithms.StokesFlow(network=net, phase=sw, settings=setts1) |
| sf.set_value_BC(pores=net.pores('back'), values=0.01) |
| sf.set_value_BC(pores=net.pores('front'), values=0.00) |
| sf.run() |
| sw.update(sf.results()) |
|
|
| p = op.algorithms.TransientIonicConduction(network=net, phase=sw, |
| settings=setts1) |
| p.set_value_BC(pores=net.pores('left'), values=0.1) |
| p.set_value_BC(pores=net.pores('right'), values=0.00) |
| p.settings['charge_conservation'] = 'electroneutrality' |
|
|
| eA = op.algorithms.TransientNernstPlanck(network=net, phase=sw, ion=Na.name, |
| settings=setts1) |
| eA.set_value_BC(pores=net.pores('back'), values=100) |
| eA.set_value_BC(pores=net.pores('front'), values=90) |
|
|
| eB = op.algorithms.TransientNernstPlanck(network=net, phase=sw, ion=Cl.name, |
| settings=setts1) |
| eB.set_value_BC(pores=net.pores('back'), values=100) |
| eB.set_value_BC(pores=net.pores('front'), values=90) |
|
|
| it = op.algorithms.TransientNernstPlanckMultiphysicsSolver(network=net, |
| phase=sw, |
| settings=setts2) |
| it.settings["potential_field"] = p.name |
| it.settings["ions"] = [eA.name, eB.name] |
| it.run() |
|
|
| sw.update(sf.results()) |
| sw.update(p.results()) |
| sw.update(eA.results()) |
| sw.update(eB.results()) |
|
|
| |
| if export: |
| proj.export_data(phases=[sw], filename='out', filetype='xdmf') |
|
|
