Concentration polarization in hydrogen permeation through self-supported Pdbased

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1 Material Science Session 7 O_1 Concentration polarization in hydrogen permeation through self-supported dbased membranes Giuseppe Barbieri 1, Alessio Caravella 1, and Enrico Drioli 1, 1 National Research Council - Institute on Membrane Technology (ITM-CNR) Via ietro BUCCI, c/o The University of Calabria, Cubo 17C, 87036, Rende CS, Italy g.barbieri@itm.cnr.it Fax: The University of Calabria - Department of Chemical and Materials Engineering, Via ietro BUCCI, Cubo 44A, 87036, Rende CS, Italy Concentration polarization present in any membrane separation affects the system performance depending on the membrane permeance, i.e., a higher permeance leads to a higher polarization. ydrogen transport in d-based supported membranes was described by means of a model [1] considering several elementary steps of the permeation process, improving what done by Ward and Dao for self-supported membranes. The model includes the external mass transfer in the multicomponent gaseous phases on both membrane sides, described by the Stefan-Maxwell equations. The transport of the multicomponent mixture in the multilayered porous support was also considered and described by means of the Dusty Gas Model, which takes into account Knudsen, oiseuille and ordinary diffusion. The diffusion in the d-alloy layer is modeled by taking the hydrogen chemical potential as the driving force of the diffusion in the metallic bulk. The interfacial phenomena (adsorption, desorption, transition from d-based surface to d-based bulk and vice-versa) were described by the same expressions used by Ward and Dao. The model separates the permeation steps and consequently their influence, quantifying the relative resistances offered by each of them. Comparison with some experimental literature data shows a good agreement. The developed tool is able to describe hydrogen transport through a supported d-based membrane, recognizing the rate determining steps (e.g., diffusion in the metallic bulk or in the porous support) involved in the permeation. The concentration polarization coefficient was evaluated by an opportune coefficient[] expressed as a function of the ratio of the flux calculated by means of this new validated complex model and the one obtained by the Sieverts' law utilizing the bulk driving force and hydrogen permeance. It was evaluated as a function of several operating conditions: upstream hydrogen molar fraction ([0...1]), total pressure of upstream ([00,...,1000] ka), total pressure of down-stream ([100,...,800] ka), temperature ([300,...,500] C), membrane thickness ([1,...,150] μm), permeance ([0.1,...,0] mmol m - s -1 a -0.5 ) and upstream fluiddynamic conditions (Reynolds' number). The analysis shows that the polarization effect can be relevant not only when using very thin membranes (1-5 μm ca.), but also when thicker ones (100 μm ca.) are operated in specific conditions. The so-called "polarization maps", on which the influence of concentration polarization can be evaluated quantitatively in different conditions, provide concentration polarization coefficient in several operating conditions. 1) Caravella A., Barbieri G. and Drioli E., 008. Modelling and Simulation of ydrogen ermeation through Supported d-based Membranes with a Multicomponent Approach. Chemical Engineering Science, 63 (8), ) Caravella A., Barbieri G. and Drioli E., 009. Concentration polarization analysis in selfsupported d-based membranes. Separation and urification Technology, 66: ICCF-15 55

2 ICCF-15 Conference 009 Concentration olarization in hydrogen permeation through self-supported d-based membranes Giuseppe BARBIERI 1, Alessio CARAVELLA 1 and Enrico DRIOLI 1, 1 National Research Council - Institute on Membrane Technology, ITM-CNR, c/o The University of Calabria, Via. Bucci - Cubo 17C, Rende (CS), Italy. The University of Calabria - Dept. of Chemical and Materials Engineering, Via. Bucci - Cubo 44A, Rende (CS), Italy.

3 resentation Topics Motivation of the analysis Elementary step-based permeation model Description and details Results and comments Concentration polarization analysis Definition of the concentration polarization coefficient CC Results and comments Overall conclusions

4 Motivation of the analysis The d-based membranes present an infinite selectivity towards hydrogen with respect to all the other chemical species. ence, their integration in production and purification process could lead up to significant advantages with respect to traditional equipments. Many empirical models have been already developed in literature to interpret and investigate the d-based membrane behaviour. owever, the possibility to use massively these membranes is related to a deep knowledge of their behaviour in different conditions. Nevertheless, systematic approaches to model the complex transport and kinetic phenomena regarding these membranes, evaluating also the concentration polarization influence, are still missing or inadequate.

5 Description of the permeation model Model based on a multicomponent approach hysical system M e m b r a n e l a y e r s orous support d-b based layer h a n i s m s M a s s t r a n s f e r m e c h Mathematical description

6 Mathematical details of the model Feed Side Adsorption Surface-to-bulk Bulk Film { } Film F,..., F,..., F θ F j n F j = artial pressure of the j th species Feed side θ = Surface degree covered by atomic, mol mol -1 d Diffusion ξ F ξ = Atomic concentration inside the d-based lattice Bulk-to-surface ξ Desorption Layer 1 Layer n ermeate Side Film Bulk θ {,...,,..., } j m {,...,,..., } Layer1 { } LayerN,...,,..., j m { } Film,...,,..., j j m m Layer Each step is modelled by its own equations, which provide the value of the overall permeating flux as well as the profile through the membrane

7 Mathematical details of the model ermeation Step Adsorption Desorption Diffusion Surface-to-Bulk J SB J J J Diff S F ( θ ) Flux Equation E Ads 0 F 0 F exp θ = Des N S kdes FG π M RT RT = N k E exp θ G ( θ ) ( θ ) ( θ ) Des 0 Des 0 S Des RT π M RT N EDiff exp RT S F 1 b ( ξ F ξ ) + + ( ξ F ξ ) = b 0 D Mem δ T ( θ ) ( ) F θ F E BS ξ F exp Fθ F 0.5 N = S λ j0 T E G ( ) SB 1 ξ F exp 6 c RT RT 1 F Bulk-to-Surface J N λ ξ E exp BS RT E exp SB RT ( θ ) ( ) θ θ 0.5 BS S j0 = ( 1 ξ ) 6 c F 1 T G Mass transfer in film on Feed and ermeate side (Multicomponent film theory) r N = 1 RT r r Bulk Surface Total Surface { Kc} { Z} ( ) + N Total r Mass transfer in each layer of the porous support (Dusty Gas Model) x N x N Ni D xivi B0 = xi xi RT η D n j i i j + MaxwellStefan Knudsen Knudsen j= 1 CTotal Dij, effective CTotal i, effective i, effective

8 Model validation with data from literature ting Flux, mmol m - s -1 ermeat Dittmeyer et al. [1] resent model 355 ka 55 ka Feed = 155 ka Liang and ughes [] resent model Temperature, C N Sweep Rate, mmol s -1 A good accordance between model and experimental data is found for two supported membranes in several conditions. [1] Dittmeyer et al., 001. J. Mol. Cat. A: Chem., 173: [] Liang and ughes, 005. Chem. Eng. J., 11:

9 Operating conditions ressure, ka Side Reynolds number, - C 4 CO O CO N Total Retentate * ** ermeate * ** Temperatures = [ ]ºC *Laminar flow conditions. **Turbulent flow conditions. Multicomponent mixtures have been considered in both retentate and permeate side to reproduce a more real situation of separation process.

10 Transmembrane profiles Laminar flow ressure, ka artial ntate Re Reten Retentate Side Bulk Film Adsorption Surface to Bulk Supported Membrane T, C 1 µm Bulk to Surface Flux Desorption Layer 1 Layer 5 ermeate Side T, C d-alloy Bulk orous Support Film Bulk ate Re ermea The model solution provides the flux value and the transmembrane partial pressure profiles as functions of the operating conditions.

11 Transmembrane profiles Turbulent flow ressure, ka artial tate Re Retent Retentate Side Bulk Film Adsorption Surface to Bulk Supported Membrane 1 µm T, C Bulk to Surface Flux Desorption Layer 1 Layer 5 ermeate Side d-alloy Bulk orous Support Film Bulk eate Re erme The variables θ and ξ on the membrane surface and inside the lattice, respectively, are expressed in form of equivalent partial pressures.

12 Step resistances to flux Laminar flow 100 Relative Resistances, % δ Membrane = 1 µm Re Retentate Re ermeate Adsorption Diffusion Desorption orous Support Film - Retentate Film - ermeate R. R. Step Tot j Temperature, C In laminar conditions, the influence of the external mass transfer can be relevant.

13 Step resistances to flux Turbulent flow 100 Relative Resistances, % δ Membrane = 1 µm Re Retentate Re ermeate Adsorption Desorption Diffusion orous Support R. R. Step Tot j Temperature, C In turbulent conditions, only four steps influences the overall permeation process.

14 Flux vs. T Laminar and Turbulent flow x, mmol m - s -1 ermeating Flux Temperature, C Limited by Mass Transfer in Retentate Limited by Mass Transport in Support Diffusion Limited Limited by Mass Transfer in Retentate Adsorptio Adsorptio tion tion Limited Limited Desorption Desorption Limited Limited Resulting Flux Resulting Flux The overall flux can be seen as the results of a complex combination of all the limiting fluxes related to the elementary steps considered. Depending on the operating conditions, the flux tends to follow the behaviour of the 1000/T, K -1 most influencing step.

15 Evaluation of the Concentration olarization Flux Bulk Bulk Membrane Bulk ( ElementarySteps) = π DF = ( 1 CC) π DF, O O, CO N, C 4 DF DF CC = 1 Flux π ( Elementary Steps) Membrane DF Bulk Upstream Downstream ( ) DF Sieverts DF = = The quantities π Mem and DF Bulk are directly evaluable from pure test and from the external operating conditions, respectively. DF CC = 1 DF CC = 1 Mem Bulk π = 1 π Flux π Bulk Mem ( Elementary Steps) Membrane Bulk 0, No olarization 1, Maximum olarization

16 Concentration polarization analysis ermeating Flux, mol m - s Data from eters et al. [3] Data used in the model rediction of the model ure Test artial ressure in Feed, bar ermeating Flux, mol m - s Data from eters et al. [3] Model prediction Mixture :N Test Total Feed ressure, bar olarization in the system of eters et al. [3] predicted by the model CC, Test type ure in both membrane sides Concentration olarization Case (Feed: Binary mixture :N at 50:50) ermeate: Sweep of pure N Conditions δ Membrane =. µm T = 400 C Feed = [3,..., 6] bar ermeate = 1.01 bar [3] eters T.A. et al., 008. J. Mem. Sci., 316:

17 olarization analysis - Operating conditions Molar fraction, - Side Total pressure, ka Reynolds number, - C 4 CO O O N Mixture {0... 1} { } for each species { } ure 1 Absent { } Not influent Temperatures = [ ]ºC

18 Flux and permeance vs. x Mixture = 1000 ka, ure = 00 ka, T = 500 C, 500 Flux, mmol m - s -1 10,000 1, Zero-flux line Back-flux Forward-flux 1 µm 5 µm 15 µm 50 µm 150 µm Membrane Bulk Zero flux Back-flux Gap Forward-flux 1 µm 5 µm 15 µm 50 µm 150 µm ermeance, mmo ol m - s -1 a molar fraction in the mixture side, -

19 olarization maps CC vs. x Concentration olariz zation Coefficient, Mixture = 1000 ka, ure = 00 ka Zero-Flux Line 300 C 500 C 350 C 1 µm 5 µm 50 µm Mixture = 1000 ka, T = 500 C Zero-Flux Line ure 800 ka 100 ka 1 µm 5 µm 50 µm ure = 00 ka, T = 500 C Zero-Flux Line Mixture 400 ka 1000 ka 5 µm 50 µm 1 µm molar fraction in mixture, -

20 olarization maps CC vs. x Concentration olarization Coefficient, Zero-Flux Line δ Membrane = 5 µm Re Zero-Flux Line Re δ Membrane = 15 µm δ Membrane = 50 µm δ Membrane = 100 µm Zero-Flux Line molar fraction in the mixture side, - Re Zero-Flux Line Re The influence of the concentration polarization significantly decreases as high membrane thicknesses are considered, because the diffusion in the d-based bulk progressively tends to become the only rate-determining step.

21 Overall Conclusions A new model for permeation through supported d-based membranes was developed, accounting for several elementary steps. The model predictions were compared with some experimental data, showing a good agreement with them. The rate determining steps were identified as functions of temperature, membrane thickness and fluid-dynamic conditions. The overall permeating flux has been evaluated as a function of the limiting fluxes of all the elementary steps considered. A systematic analysis was provided for the concentration polarization in self-supported d-based membranes by modifying the original Sieverts' law. The effect of the concentration polarization has been evaluated by means of an appropriately defined Concentration olarization Coefficient CC. CC has been calculated as a function of several conditions (temperature, membrane thickness, feed and permeate pressure, and Reynolds' number) in order to better predict the hydrogen flux.

22 ICCF-15 Conference 009 Thanks for Your Kind Attention

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