Bruno Bastos Sales, Joost Helsen and Arne Verliefde
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1 FEM modeling of capacitive deionization for complex streams Dennis Cardoen Bruno Bastos Sales, Joost Helsen and Arne Verliefde International Conference on Numerical and Mathematical ing of Flow and Transport in Porous Media Dubrovnik, Croatia, 29 September - 3 October, 2014
2 Outline»»»»»»»» duction Literature models 2
3 Purification Regeneration Electro-sorption of counter ions on porous electrodes Voltage reversal for desorption of ions from electrodes 3
4 Advantages Disadvantages Low energy usage High recovery No regeneration chemicals Reversible (long lifetime)/ Low fouling Only for low salt concentration streams? CAPEX (20-30% > RO) Scaling, oxidation of electrode surface Current sweet spot Established models Low TDS applications (cooling tower water, water softening, groundwater Low concentrations, equilibrium decontamination, ) Complex streams streams, for which (vs eg RO) a relatively low desal rate is acceptable, but a high recovery is desired Mostly binary electrolytes Optimization challenges ing challenges Improving desal rate Dynamic models Selective removal of components from complex streams Multi-ionic models 4
5 Porada et al. Prog Mater Sci 2013;58 5
6 FEM model Operational & design optimization» momentum and mass transport in spacer channel» mass transport through membrane» mass transport in porous medium» ion storage in EDL» chemical equilibria» faradaic reactions»»»» Stack level (cm) operational modes operational parameters electrode and membrane materials stack and cell geometries Cell level (µm) Pore level (nm) 6
7 Porada et al. Prog Mater Sci 2013;58 7
8 » Momentum transport in spacer channel» Mass transport (diffusion and electro-migration) in» Spacer channel» Charged porous medium Porada et al. Prog Mater Sci 2013;58 8
9 » Multi-scale» Activated carbon powder electrodes Macro scale Interparticle scale Intraparticle scale Porada et al. Prog Mater Sci 2013;58 9
10 » Non-linearity» Electric double layer capacitance (steric effects): Linear regime» Weakly non-linear regime» Highly non-linear regime Capacitance of diffuse layer vs Kilic et al. Phys Rev E 2007;75 10
11 » Time-dependent Desalination capacity Desalination rate (equilibrium) (dynamic) 11
12 » Electrode-electrolyte interface level models multiscale» Yang et al: 1-D Poisson Boltzmann eq. with cut-off pore width Yang et al. Langmuir 2001;17(6)» Jeon & Cheon: 2-D Poisson-Nernst-Planck eq. with Stern layer Jeon & Cheon Des. and water tr. 2013;51 Based on dilute solutions theory. Not coupled to macroscale mass transport through porous electrode 12
13 » Linear circuit models Non-linearity» Andelman et al, Jande & Kim: Lumped Andelmann Sep Pur Tech 2011; 80 Jande & Kim Sep Pur Tech 2013; 115» Suss et al : Suss et al. J Power Sources 2013; 241 Interparticle pore Intraparticle pore Quasi-thermal equilibrium: Equilibration time of double layer is assumed fast compared the time scales of transport in the bulk electrolyte. Thin double layer limit. Empirical fitting of 4 parameters: inter- and intraparticle pore resistances and capacitances. 13
14 » Highly overlapping double layer model Time-dependance (non-equilibrium)» Biesheuvel et al: Modified Donnan model Boltzmann equilibrium between inter- and intraparticle pores Excess chemical potential Doesn t account for contributions from non-overlapping EDLs. Equilibrium model. Biesheuvel et al. J Solid St Electrochem 2014;18:
15 » Bimodal pore distribution: o Macro-scale mass transport through interparticle pores Electroneutrality in macropores o Ion storage in EDL in interparticle and (mainly) in intraparticle pores EDL in quasi-equilibrium with bulk electrolyte Non-overlapping EDLs» No advective transport in porous electrodes» One-way coupling between fluid flow and mass transport» 2D 15
16 Stack level (cm) Cell level (µm) Pore level (nm)» Cell level: FEM geometry» Interparticle: effective medium approximation» Intraparticle: capacitance source term 16
17 » Dependent variables: (Electroneutrality in interparticle pores)» Solvent flow o Open feed channel Incompressible NS: 17
18 » Mass transport o Feed channel Nernst-Planck & Einstein: Poisson: Electroneutrality: Inward flux: Danckwert BC o Porous electrodes Simple mass transport model: Bruggeman equations Bimodal pore hierarchy: electroneutrality in interparticle pores 18
19 » Electron transport o Current conduction through porous electrode o BC: time-dependent current or voltage 19
20 » Current source term: surface area» C : Electrical double layer differential capacitance: Poisson-Boltzmann» Thin double layer approximation: quasi-thermal equilibrium. 20
21 » Solved using COMSOL Multiphysics 4.4» Solver: MUMPS» Time-stepping method: BDF (max order 2)» Mesh:» quadrilateral» refined near spacer-electrode interface and electrode-current collector interface 21
22 Constant voltage, reverse voltage desorption, PB Vmax= 0.1 V vavg= 1 cm/s c = 5 mm εma = 0.5 Convergence limited to low voltages. Kilic et al. Phys Rev E 2007;75 PB approach not valid at CDI voltages. 22
23 » Current source term: surface area» C : Electrical double layer differential capacitance: Poisson-Boltzmann Modified Poisson-Boltzmann : Effective ion size» Thin double layer approximation: quasi-thermal equilibrium. Kilic et al. Phys Rev E 2007;75 23
24 Constant voltage, reverse voltage desorption, MPB Vmax= 0.1 V vavg= 1 cm/s c = 5 mm l = 4.5 nm εma =
25 Constant voltage, reverse voltage desorption, MPB Vmax= 0.1 V vavg= 1 cm/s c = 5 mm l = 0.45 nm εma =
26 Constant voltage, reverse voltage desorption, MPB Vmax= 0.1 V vavg= 1 cm/s c = 5 mm l = 0.45 nm εma =
27 Constant voltage, reverse voltage desorption, MPB Speed up mass εma transport Increase sterical l hindrance effects Increase driving force V cell Increase concentration c At CDI conditions, hypothesis: Mismatch in time scales of relaxation of C-element (too slow) and macroscale mass transport. Macrotransport too fast close to voltage switching points (strong driving force). Quasi thermal equilibrium description of C unsatisfactory. 27
28 Warning: strong transients» CDI Optimization potential:» Narrowing and deepening the peak (faster desalination rate): material optimization» Switching voltages at the optimal moment: operational optimization» Importance for selective removal from complex streams 28
29 Time-dependent ion selectivity for capacitive deionization of complex streams Cation storage vs cell voltage Cation storage vs time» Equilibrium modified Donnan model not useful (extremely long equilibration).» Non-equilibrium effects stronger for complex streams. Zhao et al. J Colloid & Interf. Sc. 2012;384 29
30 » Multiscale model, non-equilibrium description of EDL + Intraparticle pore ½ width (macro) interparticle (micro) intraparticle» Solve (M)PNP equations at microscale level» Boundary coupling between macro-scale and micro-scale:» Boltzmann equilibrium:» Non-equilibrium: overpotential formulation 30
31 Thank you for your attention Thanks to: Bruno Bastos Sales Joost Helsen Arne Verliefde 31
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