U.S. Department of Energy Offie of Civilian Radioative Waste Management Mehanisti Model for Reative Transport of Radionulides on Iron-(Oxy)Hydroxide Colloids at the Yua Mountain Repository Presented to: 2 nd Annual GoldSim User Conferene Seattle, WA Presented by: S. David Sevougian, Ph.D. Manager, TSPA Model Design/Analysis Performane Assessment Strategy and Sope Sandia National Laboratories June 19, 2003
Aknowledgements Mihael Lord, Sandia National Laboratories Sunil Mehta, Framatome ANP Patrik Brady, Sandia National Laboratories Stephen Alorn, ISSI Ian Miller, Golder Assoiates Sevougian_GoldSim_User_Conf_06/19/03.ppt 2
Outline Coneptual model Chemial reations and assoiated state variables Constitutive equations Experimental evidene Balane equations Numerial solution Asymptoti solution Type urve or response surfae Sevougian_GoldSim_User_Conf_06/19/03.ppt 3
Coneptual Model Transport of atinides (Pu & Am) on iron-oxy(hydr)oxide pseudoolloids in the Engineered Barrier System (EBS): pseudoolloid FeOOH pseudoolloid R n+ real olloid O O O-Pu-O-Pu-O O O O-Pu-O-Pu-O O O waste-form olloid R n+ alteration phases waste form Physial-hemial proesses: Dissolution/repreipitation of UO x fuel rods and glass logs Advetion of the fluid phase and its suspended olloidal partiles Diffusion of both solute partiles and olloids within the fluid phase Reversible and irreversible sorption of atinides onto FeOOH olloids and FeOOH stationary phase (orrosion produts inside the waste pakage) Sevougian_GoldSim_User_Conf_06/19/03.ppt 4
Coneptual Model (ontinued) upstream domain downstream domain u Pu ( aq ) sol FeO olloids Pu (r) Pu (i) Pu ( aq ) Fuel rods Pu (s) Corrosion Produts Pu (r) Pu (i) Fundamental spatial disretization: Fuel rods are spatially separated from orrosion produts Treat fuel rods and orrosion produts as permeable media Liquid flows from fuel rods to orrosion produts Dissolved onentration of atinides in upstream fuel rod domain will generally be at a solubility limit, ontrolled by a dissolving or repreipitating mineral phase. No sorption reations our in this domain. Consider only Pu for this presentation Downstream orrosion produt domain is where all the ation is Sevougian_GoldSim_User_Conf_06/19/03.ppt 5
Chemial Reations and Assoiated State Variables Chemial reations: irrev R 1 : Pu(aq) Pu(FeO ) irreversible Pu sorption onto olloids olloids irrev R 2 : Pu(aq) Pu(FeO ) irreversible Pu sorption onto orrosion produts orrosion_produts rev R 3 : Pu(aq) Pu(FeO ) reversible Pu sorption onto olloids olloids rev R 4 : Pu(aq) Pu(FeO ) reversible Pu sorption onto orrosion produts State variables: orrosion_produts Denote the onentrations for the Pu in the five possible states as [Pu-mass/pore volume]: _ = onentration of dissolved Pu mass in the aqueous phase Pu Pu aq _ = onentration of Pu mass in the olloidal phase from reversible sorption _ = onentration of Pu mass in the stationary FeOOH phase from reversible sorption Pu Irrv _ Pu _ = onentration of Pu mass in the olloidal phase from irreversible sorption Irrv _ Pu _ = onentration of Pu mass in the stationary FeOOH phase from irreversible sorption The onentrations of the FeOOH in the two states are [FeOOH-mass/pore-volume]: _ = onentration of FeO-mass in the olloid state FeO _ = onentration of FeO-mass in the orrosion produt state. FeO Sevougian_GoldSim_User_Conf_06/19/03.ppt 6
Constitutive equations Rate equations for the two kinetially limited irreversible sorption reations (on a saturated pore volume basis): R φ R φ = S ˆ k = R FeO _ FeO _ FeO _ FeO _ = S ˆ k = R Mass ation equations for the two reversible equilibrium sorption reations: Pu _ = FeO _ KdPu _ aq = K d Pu _ = FeO _ Kd Pu _ aq = K d Sevougian_GoldSim_User_Conf_06/19/03.ppt 7
Experimental and Laboratory Evidene It is observed (e.g., the Benham weapon shot at the Nevada Test Site ) that most transport of atinides is by the movement of olloids and that most of the mass in the aqueous phase is mass assoiated with olloidal partiles This model of transport on FeOOH olloids will attempt to reprodue the following experimental observation: Irrv _ Pu _ + + Irrv _ Pu _ Pu _ + Pu _ 0.9 In order to reprodue this mass flux ratio, the forward rate onstant, k, for the irreversible sorption of Pu onto olloids and orrosion produt surfaes, is onsider a free parameter in the problem, and will be derived from a response surfae. Sevougian_GoldSim_User_Conf_06/19/03.ppt 8
1-D Balane Equations Conservation equation for Pu dissolved, Pu reversibly sorbed onto olloids, and Pu reversibly sorbed onto stationary orrosion produts inluding irreversible reation and radioative deay: (1 + K d + K d ) t + u (1 + K d ) x 2 Pu ( Daq + Dolloid Kd ) 2 x = ( R + R ) λ + _ aq (1 + Kd Kd ) Conservation equations for Pu irreversibly sorbed onto olloids and Pu irreversibly sorbed onto stationary orrosion produts: Irrv _ Pu _ t + u Irrv _ Pu _ x D olloid 2 Irrv _ pu _ 2 x = R λ Irrv _ Pu _ Irrv _ Pu _ t = R λ Irrv _ Pu _ Sevougian_GoldSim_User_Conf_06/19/03.ppt 9
Numerial Solution Goal was to implement this model in GoldSim (the TSPA model software), whih has a ell model that an be used to approximate transport in a finite differene type of representation: Convert aqueous Pu into another speies alled irreversibly sorbed Pu and then give this speies an infinite K d onto FeOOH General Goldsim solver is impliit in time, but did not have the option to onsider kineti reations An expliit-in-time option was used as a first approximation ( disrete mass hange objet used to injet appropriate amount of kinetially reated mass at eah time step), but resulted in inaurate results due to the high Courant number The first-order nature of the kineti reations auses them to be similar to the radioative deay term, whih allowed us to modify the deay feature in GoldSim to solve the equations impliitly Closed-form solutions of the differene equations were also possible and were implemented in Exel Goldsim and Exel solutions were verified against eah other Asymptoti solution was also possible at large time (but not very large with respet to 10,000 years) Sevougian_GoldSim_User_Conf_06/19/03.ppt 10
Asymptoti Solution Limiting flux out ratio (at large time): where R Ω = lim n = Sˆ k is the reative rate onstant for sorption onto FeO _ n FeO _ + n Irrv _ Pu _ n Pu _ + n Irrv _ Pu _ olloids and p 1 and p 2 are terms aounting for advetion, diffusion, reversible sorption of Pu onto olloids, and radioative deay. W has a value between zero and one. Qualitatively, if the advetive-diffusive-deay rates dominate the reative rate onstant, R, then the flux ratio W is small, i.e., there is little transport of Pu on olloids ompared to dissolved Pu transport. However, if R dominates, then the flux ratio W is lose to one, i.e., most aqueous transport is by olloids. The latter is the expeted qualitative behavior of the system, i.e., W 0.9. = p p 1 2 + + R R Sevougian_GoldSim_User_Conf_06/19/03.ppt 11
Response Surfae or Type Curve Invert the previous equation for W to solve for the forward rate onstant, k: p2ω p1 k = ( 1 Ω) Sˆ FeO 1.E+00 _ FeO _ k vs. W response surfae for typial values of the system parameters k: irreversible reation rate onstant [m/yr] 1.E-01 1.E-02 1.E-03 irreversible rate fitting urve Omega = 0.95 1.E-04 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Omega: olloid flux to total flux ratio Variability of various system parameters, suh as mass of orrosion produts, Dary flux, and solubility may neessitate a multidimensional response surfae Sevougian_GoldSim_User_Conf_06/19/03.ppt 12
Summary of New Colloid Model Model reprodues the observed ratio of Pu transported on olloids to Pu transported in solution, with reasonable values of the system parameters For typial input parameters, the ratio of Pu mass flux exiting the orrosion produt domain to the Pu mass flux entering the domain is on the order of 10-4, whih demonstrates that most of the Pu mass is sorbed reversibly and irreversibly onto the stationary orrosion produts Sevougian_GoldSim_User_Conf_06/19/03.ppt 13
Summary (ontinued) There are two primary ompeting effets that will have the most influene on the final fate of Pu: A signifiant amount of Pu is sorbed onto the stationary orrosion produt phase, whih redues Pu releases from the EBS A fration of the Pu from CSNF waste is now transported irreversibly on olloids, whih are only slightly retarded by interation with the rok in the unsaturated and saturated zones (previously, irreversible sorption of Pu was only onsidered for the HLW glass waste form) Sevougian_GoldSim_User_Conf_06/19/03.ppt 14