In  this  work,  a  multi-physics  modelling  approach  has  been  developed  for  the  RED  process

Ciofalo, M

Cipollina, A

Gurreri, L

Micale, G

Santoro, F

Tamburini, A

GURRERI, Luigi

CIPOLLINA, Andrea

TAMBURINI, Alessandro

CIOFALO, Michele

MICALE, Giorgio Domenico Maria

Archivio istituzionale della ricerca - Università di Palermo

Tuning of two parameters characterizing membranes:• Ions diffusion coefficient, Di• Ions mass mobility, um,I (…by a b factor)A MULTI-PHYSICS MODELLING TOOLFOR REVERSE ELECTRODIALYSISL. Gurreri, F. Santoro, A. Cipollina*, A. Tamburini, M. Ciofalo, G. MicaleDipartimento di Ingegneria Chimica, Gestionale, Informatica, Meccanica, Università degli Studi di PalermoContact person:Andrea Cipollinaandrea.cipollina@unipa.itIntroductionReverse electrodialysis (RED) generateselectric power by direct conversion of thechemical potential difference of two salinesolutions (salinity gradient power). A REDstack is fed by the two solutions in alternatedchannels, separated by anion and cationexchange membranes. An electric potentialdifference, due to the chemical potentialdifference, is established over each membrane,along with an “oriented” flux of cations andanions from each concentrate channel towardsthe two adjoining dilute ones. Ionic flux isconverted into electric current by means ofreversible redox reactions at the electrodiccompartments (Figure 1).Various factors, identifying the stack configuration, affect in a complex way a number of phenomena that interact at various scales and affect the power output and the energy efficiency.PROCESS PERFORMANCETheoretical driving force Ohmic resistances Non-Ohmic resistances Pumping powerPHENOMENAFluid dynamics Ions transport Membrane/solution equilibria OhmicSTACK CONFIGURATIONMembranes Geometry Flow rate Feeding mode Feeds properties Temperature Electrodic systemAim of the workDeveloping a multi-physics modelling tool for the Reverse ElectroDialysis process, being able to describe the main phenomena involved and evaluate the process performance.ModellingFigure 2. Schematics of a cell pair domain, equations at the interfaces & boundary conditions.The system is completed by the algebraic equations for the cell pair potential, the average current densitymodule, the stack potential and the power density (Figure 3):Figure 3.  Equivalent electric circuit.Boundary conditionsThe boundary conditions are reported in Figure 2. Periodic conditions for concentrations and fluxes wereimposed at the terminal boundaries, while continuity of mass fluxes and electric current was imposed at eachsolution-membrane interface. Finally, the average computed current density was imposed at the terminalboundaries, assuming constant potential along them (this is supported by many other multi-cells simulations).Model calibration and validationComputational domainThe model was developed in COMSOLMultiphysics®.A single 2D cell pair is simulated as periodicunit of the stack (Figure 2). The discretisationwas done by multi-block quadrilateral gridswith finer discretisation near the walls. Apreliminary grid dependence analysis wasperformed and a 12,200 nodes-per-cell gridwas adopted in the end, corresponding to 37and 24 divisions for channels and membranesthickness, respectively.Assumptions and constant parameters• Pure NaCl solutions• Linear velocity = 1 cm/s• Temperature = 20 °C• Concentrate concentration = 4 M• Cfix,aem = 1.28 meq/gdry; Cfix,cem = 1.45 meq/gdry• Number of cell pairs = 10• Blank resistance = 0.94 WCases investigated• Diluate concentration: 0.5 M – 0.01 M• Channel filling (Figure 4): Empty channels Insulating squared cross-section filaments spacers Insulating round cross-section filaments spacers Profiled membranesResults and discussionPhenomenological description of the RED processThe governing phenomena were accurately predicted, as confirmed bythe fields of the main computed quantities. Some examples (computedwith the single-cell approach) are reported here, related to the case ofa 10-cells empty-channels stack, fed with 4M–0.5M NaCl solutions.Effect of spacers and dilute concentrationRED stacks equipped either with standard non-conductive spacers or with profiled membranes arecompared. In this part of the study, the channel length was reduced to 1.2 mm and the number of grid nodesincreased to about 30,000 per cell.This allowed to efficiently compare the four scenarios.Conclusions and future remarksA multi-physics model for the RED process was developed as a powerful tool for the thoroughcharacterisation of the complex process phenomenology and for the prediction of the stack performance.The behaviour of different spacers and profiled membranes was analysed and compared, highlightingadvantages and limitations of each case.Future developments: (i) 3D simulations for accurate predictions with complex spacers/channels geometry;(ii) structural mechanics analysis to simulate membranes bending and channel geometry deformation;(iii) implementation of an all-embracing model for the process design and optimisation.Equations system* solved in the fluid domains onlyMass balance 𝛻 ∙ 𝑁𝑖 = 0Current balance 𝛻 ∙  𝑗 = 0Electroneutrality  𝑖 𝑧𝑖𝐶𝑖 = 0Mass flux (Nerst-Planck eq.) 𝑁𝑖 = −𝒟𝑖𝛻𝐶𝑖 − 𝑧𝑖𝑢𝑚,𝑖𝐹𝐶𝑖𝛻𝜑 +  𝑣𝐶𝑖Electric current  𝑗 = 𝐹  𝑖 𝑧𝑖(−𝒟𝑖𝛻𝐶𝑖 − 𝑧𝑖𝑢𝑚,𝑖𝐹𝐶𝑖𝛻𝜑)Continuity* 𝜌𝛻 ∙  𝑣 = 0Momentum* 𝜌  𝑣 ∙ 𝛻  𝑣 = 𝛻 ∙ −𝑝 + 𝜇(𝛻  𝑣 + (𝛻  𝑣)𝑇)Cell pair potential 𝐸𝑐𝑝 = 𝜑1 − 𝜑0 with 𝜑0 ≠ 𝑓(𝑦) ≠ 𝜑1Avg. current density  𝑗𝑐𝑒𝑙𝑙 =  𝑁𝐸𝑐𝑝 𝐴(𝑅𝑏𝑙𝑎𝑛𝑘 + 𝑅𝑒𝑥𝑡)Stack potential 𝐸𝑠𝑡𝑎𝑐𝑘 = 𝑁𝐸𝑐𝑝 − 𝐴  𝑗𝑐𝑒𝑙𝑙𝑅𝑏𝑙𝑎𝑛𝑘Power density 𝑃𝑑 = 𝐸𝑠𝑡𝑎𝑐𝑘  𝑗𝑐𝑒𝑙𝑙/𝑁𝜑𝐷𝑜𝑛 = 𝜑𝑚 − 𝜑𝑠 ≅𝑅𝑇𝑧𝑖𝐹ln𝐶𝑖𝑠𝐶𝑖𝑚Interface sorption equilibriumPartition coefficients were adopted to relate themembrane-side co-ions concentration to thesolution-side one:𝐶𝑐𝑜𝑖𝑚𝐶𝑐𝑜𝑖𝑠 = 𝐾𝑒𝑞 =12 𝐶𝑓𝑖𝑥2 + 4𝐶𝑐𝑜𝑖𝐶𝑐𝑜𝑢 − 𝐶𝑓𝑖𝑥𝐶𝑐𝑜𝑖Donnan potential generationThe voltage generation at the membrane-solutioninterfaces was calculated by the Donnan exclusiontheory (assuming unitary activity coefficients):Figure 1. Reverse electrodialysis stack.AcknowledgementsThe financial support of EU within the REAPower project (contract no. 256736) and the RED Heat-to-Power project(contract no. 640667)0,01,02,03,04,05,00,0 0,1 0,2 0,3 0,4 0,5Pd,max[W/m2]Diluate inlet concentration [mol/l]beta = 0.2beta = 0.4beta = 0.6beta = 0.8beta = 1.0experimentalbest fittingExperimental data measurement:• Lab stack 10x10 cm2• Fujifilm membranes• Pure NaCl solutionsValidation exploring a wide range of dilute inlet concentrations and plotting electrical variables(e.g.  V-I and Pd-I diagrams)0,00,51,01,52,02,50,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8Estack[V]Iext [A]exp 0.01M model 0.01Mexp 0.02M model 0.02Mexp 0.05M model 0.05Mexp 0.08M model 0.08Mexp 0.1M model 0.1Mexp 0.3M model 0.3Mexp 0.5M model 0.5MComputed velocity fieldConcentration profiles, with polarisation phenomena in open circuit (O.C.) conditionsComputed Na+ fluxes (diffusive, migrative, convective and total) in O.C. conditionsComputed Na+ and Cl- total fluxes in O.C. conditionsComputed potential profiles in condition of open circuit, maximum Pd and shortcut (blank resistance neglected).Computed Na+ fluxes (diffusive, migrative, convective and total) in condition of maximum power density.Computed Na+ and Cl- total fluxes in condition of maximum power density.Computed pressure fieldCurrent density surface plots and streamlines(0.5M-4M, max Pd conditions)What happens when changing dilute concentration in profiled membranes?Concentrate Ch. CEMAEM AEMDiluate Ch. Concentrate Ch. CEMAEM AEMDiluate Ch. Concentrate Ch. CEMAEM AEMDiluate Ch.Concentrate Ch. CEMAEM AEMDiluate Ch. Concentrate Ch. CEMAEM AEMDiluate Ch. Concentrate Ch. CEMAEM AEMDiluate Ch.Empty channel.Current density results to be uniform and streamlines are mainly horizontal.jA/m2Concentrate Ch. CEMAEM AEMDiluate Ch.Insulating squared cross-section spacers. Current density is higher in the solutions and streamlines by-pass obstacles.jInsulating round cross-section spacers. Current density is higher in the solutions and streamlines by-pass obstacles.jA/m2Concentrate Ch. CEMAEM AEMDiluate Ch.Profiled conductive membranes (Cdil=0.5M).jA/m2Concentrate Ch. CEMAEM AEMDiluate Ch.Profiled conductive membranes (Cdil=0.1M).jA/m2Concentrate Ch. CEMAEM AEMDiluate Ch.Profiled conductive membranes (Cdil=0.01M).jA/m2Concentrate Ch. CEMAEM AEMDiluate Ch.Concentrate Ch. CEMAEM AEMDiluate Ch.A/m2Current density by-passes pins when leaving a concentrate channel… it converges towards pins when leaving a very dilute one.

A multi-physics modelling tool for Reverse Electrodialysis

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A multi-physics modelling tool for Reverse Electrodialysis

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