Marohomogenou Li-Ion-Battery Modeling - Strength and Limitation Marku Lindner Chritian Wieer Adam Opel AG
Sope Purpoe of the reearh: undertand and quantify impat of implifiation in marohomogeneou model by omparion to truture-reolving miroheterogeneou model Content introdution to marohomogeneou and miroheterogeneou approahe ode to ode omparion ytemati and reult key meage and outlook
Marohomogenou peudo 2D approah (BDS) 1D olid (pherial): r ~ 5µm r r diambiguation: propertie of material ompoite (olid + pore/eletrolyte) are homogenized ( effetive propertie ) domain (eletrode, eparator) ubdivided (diretized) into ontrol volume with effetive, maroopi ompoite propertie n = 5 n = 5 1D eletrolyte: x ~ 130µm
Miroheterogenou 3D approah (OpelLib) diambiguation: truture (olid and pore morphology) patially reolved in 3D omputational domain tranport equation olved eparately in olid (ative material) and pore (eletrolyte) phae (interfae oupling by Butler-Volmer) bulk propertie intead of effetive propertie ued (exeption: eparator) poitive eletrode truture negative eletrode truture homogenized eparator tranport in olid (ative partile): D t 0 tranport in pore (eletrolyte): f F T t j F t D t e e e e e e log log log 1 1 0 oupling at olid/eletrolyte interfae (Butler-Volmer): a a a T F T F e e e k i,max iothermal battery model; referene: A. Latz, J. Zauh, Thermodynami onitent tranport theory of Li-ion batterie, J. Power Soure 196 (2011) 3296-3302 eletrode truture obtained by tomographial imaging oure: GM
Parameter Set ued for ode to ode omparion domain parameter value referene poitive eletrode Range of Stoihiometry 0.405 ~1 repreentative value for tehnial appliation OCP relation f (SOC) Fuller et al., Simulation and Optimization of Dual Li Ion Inertion Cell, J. Eletrohem. So. 141 (1994) Li diffuion oeffiient 110-9 m²/ Jeong et al., J. Power Soure 102 (2001) eletron ondutivity 0.038 S/m Doyle et al., J. Eletrohem. So. 143 (1996) reation rate ontant 0.2 (A/m²)/(mol/m³)^1.5 repreentative value for tehnial appliation negative eletrode Range of Stoihiometry ~0 0.64 repreentative value for tehnial appliation OCP relation f (SOC) Fuller et al., Simulation and Optimization of Dual Li Ion Inertion Cell, J. Eletrohem. So. 141 (1994) Li diffuion oeffiient 3.910-10 m²/ Wen et al., J. Eletrohem. So. 126 (1979) eletron ondutivity 1 S/m Doyle et al., J. Eletrohem. So. 143 (1996) reation rate ontant 0.2 (A/m²)/(mol/m³)^1.5 repreentative value for tehnial appliation eletrolyte initial alt onentration 100010-6 mol/m³ repreentative value for tehnial appliation ativity term 1 Simplifiation for model omparion ion ondutivity f ( ) Albertu et al., J. Eletrohem. So. 156 (2009) Li diffuion oeffiient 7.510-6 m²/ repreentative value for tehnial appliation tranferene number 0.363 Doyle et al., J. Eletrohem. So. 143 (1996) eparator MaMullin number 4.4432 (1/(poroity) 1.5 ) marohomogenuou model require truture related geometrial data: diffuion length olid / urfae area olid / poroity / tortuoity
Sytemati of marohomogeneou v. miroheterogeneou ode to ode omparion tarting point: peudo 2D approah utilize porou media theory whih aume that partile are mall relative to material thikne (homogeneity aumption): d partile << l eletrode approah: ompare reult from marohomogeneou and miroheterogeneou imulation for onitent ae et-up ytemati: inreae eletrode truture omplexity from imple generi (pearl neklae arrangement of pherial ative partile refleting peudo 2D approah) to omplex realiti (random arrangement of non-pherial primary partile) ae 0 (referene): pearl neklae of 5 pherial partile reflet peudo 2D approah for 5 ontrol volume ae 1: rod ompried of 10 pherial partile having 50% overlap ae 2: pearl neklae of 10 pherial partile of different diameter fore 2 partile into one ontrol volume ae 3: random omplex truture baed on pherial bae partile ( high poroity) ae 4: random omplex truture with non-pherial bae partile (low poroity)
Miroheterogenou 3D-model baed on marohomogenou Peudo-2D approah geometrial parameter (ae 0) footprint: 10 x 10 µm² radiu partile: 5 µm thikne ative material: 50 µm for n = 5 one partile / ontrol volume homogenized propertie: poroity = 1 volume phere / ontrol volume urfae ative material = urfae phere tortuoity = 1 / poroity 0.5 (Bruggeman) reenhot OpelLib one eletrode 0.25µm voxel reolution no homogenized propertie tortuoity i a reult
Miroheterogenou 3D-model baed on marohomogenou Peudo-2D approah reult (ae 0) for 1C: abolute value differene in voltage between model - the reult of OpelLib and BDS are in good agreement - the different reolution of OpelLib (800.000 ontrol volume) and BDS (1D eletrolyte: 15 node, 1D olid: 5 node) orrepond with the omputational effort (hour v. eond)
Influene of Diretization on marohomogenou Peudo-2D approah expetation: diretization affet reult reult (ae 0) for 1C: abolute value 1D eletrolyte: volume fitted to phere 6 node 6 node 1D Solid 11 node 11 node 1D eletrolyte: volume to mall for phere obervation -numerially: a refinement of the grid doe not influene the reult with the given parameter et -phyial: no parameter adjutment neeary to aount for the too mall volume
Miroheterogenou 3D-model baed on marohomogenou Peudo-2D approah ae 1 ae 2 eletrode 10 partile with r = 5µm 5 partile with r = 3.5µm 5 partile with r = 1.5µm abolute value reult for 1C differene in voltage between model
Marohomogenou Peudo-2D Model baed on miroheterogenou 3D approah ae 3 OpelLib truture: non-overlapping pherial partile 4 µm diameter random arrangement ae 0 to 3: good agreement between OpelLib and BDS abolute value 1C derived from truture: - poroity (59.1%) - peifi urfae area ued a input for BDS 10C bet math for ae 1 (overlapping phere), with lowet fration of mirotrutural heterogeneity differene in voltage
Marohomogenou Peudo-2D Model baed on miroheterogenou 3D approah ae 4 OpelLib truture: overlapping planar pentahedral partile 2 µm thik, 5µm radiu random arrangement mot realiti ae in term of morphology and poroity yield wort agreement between OpelLib and BDS abolute value differene in voltage 1C derived from truture: - poroity (30.3%) - peifi urfae area - partile ize ditribution ued a input for BDS 10C
Calibration of marohomogeneou model to miroheterogeneou reult hypothei: omplex pore/partile truture not well repreented in marohomogeneou model alibrate marohomogeneou model with truture parameter a) 1C 10C BDS ref alibration a) peifi urfae OpelLib 0.22 * OpelLib b) diffuion length OpelLib (PSD) 9.8 * OpelLib ) tortuoity = 1/poroity n n = 0.5 n = 2.1 b) obervation: omparable improvement an be ahieved by either alibrating diffuion length (1D olid) or tortuoity (1D eletrolyte) ambiguity undeired for preditive imulation )
Parameterization of marohomogeneou model with miroheterogeneou reult tortuoity of pore truture an be derived a input for BDS diagram how the reult when applying the equivalent exponent (n=1.9) in BDS. abolute value 1C 10C Hypothei: differene Effetive lithium ion in voltage tranport reitane depend on rate and SOC (loal and global). Thi annot be aptured by a rigid parameterization of a implified truture model (e.g. phere).
Next tep next tep: DoE of tranport parameter and analyi of loal ondition needed to quantify truture ontribution to maro/miro direpany experimental validation of model ( omparion i not verifiation i not validation ) preliminary reult of miroheterogeneou imulation ugget tranport limitation at high harge/diharge rate may aue early performane drop
Key Meage imple model truture and low harge/diharge rate marohomogeneou and miroheterogeneou approahe math well omplex model truture and high harge/diharge rate direpany of marohomogeneou and miroheterogeneou approahe alibration w/ marohomogeneou model parameter ambiguou miroheterogeneou imulation reult may provide ophitiated parameterization of marohomogeneou model and maintain overall preditive apability hallenge: appropriately derive marohomogeneou parameter (e.g. peifi urfae, diffuion length) from µ-imulation reult (e.g. PSD) outlook: onitently preditive proe hain utilizing CPU-onuming miroheterogeneou imulation to parameterize fat marohomogeneou model for produtive imulation run