MODELING A METAL HYDRIDE HYDROGEN STORAGE SYSTEM. Apurba Sakti EGEE 520, Mathematical Modeling of EGEE systems Spring 2007

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1 MODELING A METAL HYDRIDE HYDROGEN STORAGE SYSTEM Apurba Sakti EGEE 520, Mathematical Modelin of EGEE systems Sprin 2007

2 Table of Contents Abstract Introduction Governin Equations Enery balance Momentum balance Hydroen mass balance Reaction kinetics Boundary Conditions Formulation and Solution usin FEMLAB Validation/Parametric Study Conclusion References Appendix A

3 Abstract Metal hydrides have the potential for reversible on-board hydroen storae and release at low temperatures and pressures. Hence they offer much promise towards an effective hydroen economy. The followin is a study on the theory, modelin, and simulation of the physics and chemistry of hydroen interactions in a metal hydride bed. The objective was to model the formation of hydride in a metal hydride reactor in 2D. The model considers heat and mass transfer occurrin durin the hydridin process alon with the flow of a coolin fluid. The findins of this study suest slihtly hiher hydride formation near the cooler reions as the reaction proresses. This areed to data available from literature. Overall this paper presents a ood test case on hydroen storae modelin usin FEMLAB and lays the round for further improvements in the model.

4 Introduction Hydroen storae is a key enablin technoloy for the advancement of hydroen and fuel cell power technoloies. The ability to carry enouh hydroen on-board a vehicle to enable a drivin rane of reater than 300 miles, within packain and cost constraints, is the focus of the Department of Enery s hydroen storae activities [1]. Its taret for 2010 for a hydroen storae system is 6 wt % of the entire system [2]. Storae in the form of hydrides is one of the options bein considered. Metal hydrides have the potential for reversible on-board hydroen storae and release at low temperatures and pressures [3, 4]. Theory, modelin, and simulation will enable the understandin of the physics and chemistry of hydroen interactions at the appropriate size scale. It will also further the ability to simulate, predict, and desin materials to enhance their performance [5]. Hydroen storae in a hydride bed is a complex process includin heat and mass transfer, fluid flow and chemical reactions which include the hydridin and dehydridin kinetics. Fiure 1 is a schematic of a kind of metal hydride hydroen storae Fiure 1 Schematic of the Savannah River National Laboratory metal hydride hydroen storae vessel vessel which in this case contains Aluminum as well [3]. Literature [3, 4, 6-22] provides evidence that mathematical modelin of hydroen storae in metal hydride beds have received considerable attention over the past 10 years. Jemni and Nasrallah presented a theoretical study of the mass and heat transfer dynamics in a metal hydride reactor [10]. In subsequent papers they validated their assumptions as well as presented experimental approaches to determine the reaction kinetics, equilibrium condition and transport properties in a LaNi 5 -H 2 system [11, 19]. Nakaawa et. al. presented a 2-D model for the transient heat and mass transfer within a metal hydride bed [18]. Matt et. al and Aldas et. al besides work on lanthanum beds also presented an interated model of heat and mass transfer, reaction kinetics and fluid dynamics in a hydride bed [6, 16, 17, 21]. Kaplan and

5 Vezirolu investiated numerically the hydroen storae process in a 2-D metal hydride bed includin the full momentum balance equation [22]. Kikkinedes et. al presented a detailed mathematical model which included both the axial and radial dimensions of the storae bed [14]. Apart from the heat and mass transfer effects, a coolin medium for the system was modeled and optimized by them. The objective of this modelin study is to understand the process by first reproducin some of the results throuh a 2-D model. Governin Equations A two dimensional metal hydride reactor is considered as shown in Fiure2. The system mirrors the experimental confiuration of Jemni et al. [10-12] and that of Kaplan Fiure 2 Schematic sketch of the reactor considered bed: Enery equation T 1 T T ( ρ C p ) e = ( rλe ) + ( λe ) ρc t r r r z z ρ C et al. [22]. The reactor has a 50 mm inner diameter and 100 mm heiht and filled with crushed LaNi 5 alloy. A coolin fluid is used to remove the enery released durin the hydridin process and the heat transfer coefficient h w between the bed wall and the coolin fluid is assumed to be constant. The followin are the equations overnin the heat and mass transfer and chemical reaction within the hydroen storae p p T v r T o w m& [ H T ( C p C ps )] z The aforesaid continuum equation was obtained assumin thermal equilibrium between the storae bed and hydroen. Here ρ, C p and λ e are the effective density,

6 specific heat and thermal conductivity respectively. Additional nomenclature can be found in Appendix A. (ρc ) is calculated as ( ρ C ) = ρ C + (1 ) ρ C p e p where, is the porosity. The effective thermal conductivity is expressed as λ = λ + ( 1 ) λ e s p s e ps where, λ and λs are the thermal effective conductivities of the as and solid phases, respectively. Momentum equation The as velocity can be expressed by Darcy s law: r V k = µ r rad ( P ) Hydroen mass balance (ρ ) + div (ρ V ) = m& t Hydroen is assumed to obey the perfect as law equation P = ρ T R / M where R is the universal as constant and M is the molecular weiht of hydroen. Reaction kinetic The amount of hydroen absorbed is iven by m& = C a Ea exp( RT s P ) ln( P eq )( ρ ss ρ ) s where C a is a material dependent constant, ρss is the density of the solid phase at saturation and P eq is the equilibrium pressure calculated usin the Van t Hoff relationship: ln P eq = A B T where A and B are material constants obtained from literature [12]

7 Initial and boundary conditions The hydride bed is initially assumed to have constant temperature and pressure and hydroen is assumed to be at rest. Mathematically, At t = 0 P = P o T = T o v = w = 0 The boundary walls are assumed to be impermeable and no slip conditions are valid at the boundary walls. The reaction heat is removed from the boundary walls with a coolin fluid whose temperature is T f. Hydroen is chared at z = 0 with constant pressure, P o and constant temperature T o. The boundary conditions can be expressed as T at r = 0, ( z,0, t) = 0 r T at z = 0, λ ( 0, r, t) = h1 ( T0 T ) z T at r = Γ 0, λ ( z, Γ0, t) = h2 ( T T f ) z T at z = H, λ ( H, r, t) = h2 ( T T f ) z where h 1 and h 2 are the heat transfer coefficients between hydride bed and hydroen as and between the boundary walls and the coolin fluid respectively. Problem formulation and solution usin FEMLAB The problem was formulated in a FEMLAB model incorporatin Darcy s Law, Convection & Conduction and Convection & Diffusion modes. A 2D axis-symmetric model was considered. A rectanle representin half of the mid-section of the reactor was enerated (1m by 0.5m). The momentum equations and mass balance equations were coupled throuh the Darcy s law mode to et a sinle 2 dp d p equation of the form = A 2. Subsequently the enery balance and the mass of the dx dx hydride formed was modeled usin the convection & conduction and convection & diffusion modes by incorporatin the necessary terms to represent the overnin

8 equations. Where necessary the parameters have been calculated usin established correlations. The solution was obtained by solvin the three systems of equations. Initially, a coarse mesh was selected which was subsequently refined (8032 elements) till the computer ran out of available memory. The eventual result yielded estimates of the temperature and pressure variation and the concentration of the metal hydride. Fiure 3 Pressure, temperature and concentration variation in the metal hydride reactor.

9 Fiure 3 shows the results obtained from the FEMLAB solution. After 600 seconds, it is seen that the pressure and the temperature become uniform for most part of the reactor. The concentration of hydride formed is also shown. It is relatively hiher towards the cooled boundaries in comparison with the central part. This is in areement with the data present in literature [22]. Fiure 4 shows the variation of the concentration showin reater formation of hydrides closer to the cooled boundaries. The cell peclet number which is the ratio of advective terms to diffusive terms should nominally be less than 10. It was within this rane for this model. Fiure 4 Concentration of hydride formed alon the axial direction. Cooled walls have relatively hiher concentrations. Validation/Parametric Study Validation is an important part of a model. This model was compared to similar work done in the literature. Thouh not entirely in areement, the temperature profile was similar to what was reported in a 3D model in literature as shown in Fiure 5.

10 (a) (b) Fiure 5 Similar temperature profiles of the model (a) and as found in literature (b)[22] (c) shows the hydride formation in the bed. The hydride formation profile observed (Fiure 4) in the model is similar to what has been reported in the literature (Fiure 5c) For the parametric study, the temperature of the hydride bed was varied. Two cases were considered. Fiures 5 and 6 illustrate the variation in the concentration of hydride formed. It is proportional to the amount of heat in the bed and this arees with literature data, thereby addin in to validate the model. (c)

11 Fiure 6 Concentration of hydride formed in the reactor when the temperature is decreased by a factor of 10. Hydride formation decreases. Fiure 7 Concentration of hydride formed in the reactor when the temperature is increased by a factor of 10. Hydride formation increases.

12 Conclusion In this study the roundwork for modelin hydroen storae in metal hydrides was investiated. The effect of a coolin fluid too was incorporated. However the model is still at a preliminary stae and needs to be built upon. The effect of temperature on hydride formation was shown to aree with literature and hence the importance of the coolin fluid was demonstrated. The model also successfully presents hydridin behavior similar to that available from literature data.

13 References Saran, A.G., D.E. Armin, and A.R. James, Two Dimensional Model for the Desin of Metal Hydride Hydroen Storae Systems. Adsorption, V11(0): p Das, L.M., On-board hydroen storae systems for automotive application. International Journal of Hydroen Enery, (9): p Aldas, K., M.D. Mat, and Y. Kaplan, A three-dimensional mathematical model for absorption in a metal hydride bed. International Journal of Hydroen Enery, (10): p Gadre, S.A., et al., Practical Modelin of Metal Hydride Hydroen Storae Systems. Ind. En. Chem. Res., (8): p Inomata, A., H. Aoki, and T. Miura, Measurement and modellin of hydridin and dehydridin kinetics. Journal of Alloys and Compounds, (1-2): p Isselhorst, A., Heat and mass transfer in coupled hydride reaction beds. Journal of Alloys and Compounds, (1-2): p Jemni, A. and S.B. Nasrallah, Study of two-dimensional heat and mass transfer durin absorption in a metal-hydroen reactor. International Journal of Hydroen Enery, (1): p Jemni, A. and S.B. Nasrallah, Study of two-dimensional heat and mass transfer durin desorption in a metal-hydroen reactor. International Journal of Hydroen Enery, (11): p Jemni, A., S.B. Nasrallah, and J. Lamloumi, Experimental and theoretical study of ametal-hydroen reactor. International Journal of Hydroen Enery, (7): p Jian, Z., et al., Simulation of a thermally coupled metal-hydride hydroen storae and fuel cell system. Journal of Power Sources, (1-2): p Kikkinides, E.S., M.C. Georiadis, and A.K. Stubos, Dynamic modellin and optimization of hydroen storae in metal hydride beds. Enery, (13): p MacDonald, B.D. and A.M. Rowe, Impacts of external heat transfer enhancements on metal hydride storae tanks. International Journal of Hydroen Enery, (12): p Mahmut D. Mat, Y.K.K.A., Investiation of three-dimensional heat and mass transfer in a metal hydride reactor. International Journal of Enery Research, (11): p Mat, M.D. and Y. Kaplan, Numerical study of hydroen absorption in an Lm-Ni5 hydride reactor. International Journal of Hydroen Enery, (9): p Nakaawa, T., et al., Numerical analysis of heat and mass transfer characteristics in the metal hydride bed. International Journal of Hydroen Enery, (4): p

14 19. Nasrallah, S.B. and A. Jemni, Heat and mass transfer models in metal-hydroen reactor. International Journal of Hydroen Enery, (1): p Pons, M. and P. Dantzer, Determination of thermal conductivity and wall heat transfer coefficient of hydroen storae materials. International Journal of Hydroen Enery, (7): p Y. Kaplan, M.I.M.D.M.M.D.T.N.V., Investiation of thermal aspects of hydroen storae in a LaNi5-H2 reactor. International Journal of Enery Research, (6): p Yuksel Kaplan, T.N.V., Mathematical modellin of hydroen storae in a LaNi5 hydride bed. International Journal of Enery Research, (11): p

15 Appendix A Nomenclature A = material constant B = material constant C a = material constant C p = specific heat E a = activation enery h = heat transfer coefficient H = reactor heiht k = permeability m& = hydroen mass absorbed M = molecular weiht P = pressure r = radial co-ordinate R = universal as constant t = time T = temperature v = velocity component in radial direction w = velocity component in axial direction z = axial co-ordinate 0 H = reaction heat of formation = porosity λ = thermal conductivity µ = dynamic viscosity ρ = density φ = eneric variable that representin the variable solved (i.e. u,v,t) Γ = exchane coefficient Γ = radius of hydride bed 0 Subscripts e = effective eq = equilibrium f = coolin fluid = as 0 = initial s = solid ss = saturated