reverse electrodialysis Gurreri L. * , Tamburini A., Cipollina A., - PowerPoint PPT Presentation

Second International Conference on Salinity Gradient Energy September 10 th -12 th , 2014, Leeuwarden, The Netherlands Scuola Politecnica Dipartimento di Ingegneria Chimica, Gestionale, Informatica e Meccanica (DICGIM), viale delle Scienze (Ed.6), 90128 Palermo, Italy CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis Gurreri L. * , Tamburini A., Cipollina A., Micale G., Ciofalo M. * e-mail address: luigi.gurreri @unipa.it 1

Objectives and background RED CHANNELS Channel Fluid Dynamics Performance geometry • Hydraulic friction • Concentration Polarization Net spacers for membranes separation  Mixing promotion X Higher friction factor Two layers Woven filaments (overlapped) filaments Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands 2 CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Objectives and background OBJECTIVES, TOOLS AND ACTIVITIES Objective: prediction of fluid flow and mass transfer in spacer-filled channels for RED applications Process optimization Tools: 3D-Computational Fluid Dynamics (CFD) modelling Activities: parametric analysis - Wires shape: woven and non woven spacers - Pitch to height ratio ( l/h ) - Channel orientation (fluid flow direction) - Reynolds numbers typical of RED applications Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands 3 CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

NUMERICAL METHODOLOGIES Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands 4 CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies CASES INVESTIGATED Diamond spacers Overlapped Woven α 0 l α 0 l α 45 α 45 Size Filaments shape  Pitch to height ratio l/h = 2, 3, 4 Overlapped (o)  (h = 0.3 mm) Woven (w) Reynolds number Re Fluid flow direction α  0 ° 1, 4, 16, 64  45 ° Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands 5 CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies CFD MODELING The finite volumes code Ansys-CFX 14 was employed to discretize and solve the governing equations (Newtonian and incompressible fluid). Steady regime at all flow rates investigated   u 0  u           2 u u p u P  Body force → fluid motion t in a periodic domain     b        Cu D C ku       s    b a M C ks   e NaCl solution Molarity Density Viscosity Diffusivity at T = 25 °C [mol/l] [kg/m 3 ] [Pa s] [m 2 /s] Seawater 0.5 1017.2 9.31e-04 1.47e-09 For details see L. Gurreri, A. Tamburini, A. Cipollina, G. Micale, M. Ciofalo, CFD prediction of concentration polarization phenomena in spacer-filled channels for reverse electrodialysis, J. Membr. Sci., 468 (2014) 133-148. Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands 6 CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies BASIC EQUATIONS * Transport equation for a binary electrolyte Multicomponent diffusion equation (Stefan-Maxwell) Electroneutrality condition binary electrolyte     C C         i j C K u u RT u u   i i ij j i j i C D z C z C j j     T ij salt diffusivity solvent concentration solvent velocity ≈ u transport number         0 d ln C i t C       0 i   Cu  D 1 C  0       t d ln C z F i i Accumulation Convection Diffusion Migration * J.S. Newman, Electrochemical Systems, Second Edition, 2nd edition, Prentice Hall, Englewood Cliffs, NJ (1991) K. Kontturi, L Murtomäki, J.A. Manzanares, Ionic Transport Processes In Electrochemistry and Membrane Science, Oxford University Press (2008) Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands 7 CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies CFD MODELLING DEVELOPMENT Implementation of transport equations Assuming density as a linear function of C   aC  b 1.20 1.15 Density [kg/l] 1.10 Diffusive term 1.05  d   C    1.00 d ln C b dC     0 1   C     0.95 d ln C C M b a M 0 1 2 3 4 5 6 0 0 C Molarity [mol/l] Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands 8 CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies CFD MODELLING DEVELOPMENT Implementation of transport equations Migrative term       0 i t C b        i Cu D C   0       t b a M C z F   C i i • Current density • Equations system not closed • Above transport equation can be solved • when coupled with other equations → entire stack as domain • or when current density distribution is known (spacer-less channel) Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands 9 CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies CFD MODELLING DEVELOPMENT Implementation of transport equations Simulations of an empty channel • Concentration profiles were unaffected by the migrative term • Migrative term is negligible compared to the diffusive one • → Migrative flux is quite uniform most unfavourable case (low concentration and high current density) 1.5 28 21 26 Diffusive and Migrative terms 20 1.0 24 20 22 C [mol/m 3 ] 0.5 19 [mol/m 3 s] 20 19 0.0 18 18 0.14 0.15 0.16 0.17 0.18 0.19 0.0 0.2 0.4 0.6 0.8 1.0 16 -0.5 14 Diffusive term Without migrative term -1.0 12 Migrative term x 100 With migrative term 10 -1.5 0.0 0.2 0.4 0.6 0.8 1.0 y/H [-] y/H [-]       0 Migrative term i t C b        i Cu D C   0     neglected   t b a M C z F   C i i Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands 10 CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies MODELLING APPROACH Transport equation implemented for Unit Cell Fully developed flow → Linear variation of concentration along the flow direction (s) Periodic boundary conditions despite the change of the bulk concentration Conc. gradient    C C x y z t ( , , , ) k s Fluid flow direction Periodic concentration Transport equation for the electrolyte in unit cell      C b        Cu D C ku           s t b a M C ks   e Q     Q J ( A A ) TOT k TOT CEM AEM  V u s ave , Ingoing flux throug membrane Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands 11 CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies MODELLING APPROACH Computational domain Sea One channel water Brine Brine No double layer Woven - + - Overlapped + Unit Cell 0.3 mm 0.3 mm Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands 12 CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies MODELLING APPROACH Wall boundary at membrane-solution interface CEM NaCl 0 t  m i J i i i z F i d J        tot d m 1 J 0 J J , CEM    , CEM , CEM , CEM m 0 J  t      d m J J i , CEM   , CEM , CEM z F  d J  , CEM d 0 J t 0.5       , CEM d J i i   m CEM J  z F F    , CEM Uniform flux at the membrane-solution interfaces Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands 13 CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies MODELLING APPROACH Mesh and grid dependence analysis Grid dependence by varying the size Size = 0.006 mm • results independent of the discretization degree 420,000 - 5,760,000 vol. • accuracy • computational savings Woven Overlapped Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands 14 CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

RESULTS Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands 15 CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis