Transport modeling in performance assessments for the Yucca Mountain disposal system for spent nuclear fuel and high-level radioactive waste

Reliability Engineering and System Safety 122 (2014) 189–206

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Transport modeling in performance assessments for the Yucca Mountain disposal system for spent nuclear fuel and high-level radioactive waste Rob P. Rechard a,n, Bill W. Arnold b, Bruce A. Robinson c, James E. Houseworth d a

Nuclear Waste Disposal Research & Analysis, P.O. Box 5800, Sandia National Laboratories, Albuquerque, NM 87185-0747, USA Applied Systems Analysis & Research, Sandia National Laboratories, Albuquerque, NM 87185-0747, USA c Environmental Management and Nuclear Waste Programs, P.O. Box 1663, Los Alamos National Laboratory, MS A127, Los Alamos, NM 87545, USA d Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA b

art ic l e i nf o

a b s t r a c t

Available online 4 July 2013

This paper summarizes modeling of radionuclide transport in the unsaturated and saturated zone conducted between 1984 and 2008 to evaluate feasibility, viability, and assess compliance of a repository for spent nuclear fuel and high-level radioactive waste at Yucca Mountain, Nevada. One dimensional (1-D) transport for a single porosity media without lateral dispersion was solved in both the saturated zone (SZ) and unsaturated zone (UZ) for the first assessment in 1984 but progressed to a dual-porosity formulation for the UZ in the second assessment in 1991. By the time of the viability assessment, a dualpermeability transport formulation was used in the UZ. With the planned switch to a dose performance measure, individual dose from a drinking water pathway was evaluated for the third assessment in 1993 and from numerous pathways for the viability assessment in 1998 and thereafter. Stream tubes for transport in the SZ were initially developed manually but progressed to particle tracking in 1991. For the viability assessment, particle tracking was used to solve the transport equations in the 3-D UZ and SZ flow fields. To facilitate calculations, the convolution method was also used in the SZ for the viability assessment. For the site recommendation in 2001 and licensing compliance analysis in 2008, the 3-D transport results of the SZ were combined with 1-D transport results, which evaluated decay of radionuclides, in order to evaluate compliance with groundwater protection requirements. Uncertainty in flow within the unsaturated and saturated zone was generally important to explaining the spread in the individual dose performance measure. & 2013 Elsevier Ltd. All rights reserved.

Keywords: Radionuclide transport High-level radioactive waste Spent nuclear fuel Radioactive waste disposal Performance assessment Yucca Mountain

1. Introduction This paper presents the evolution of transport modeling of radioactive waste to provide a helpful perspective on the performance assessment (PA) for the license application (PA-LA) for a repository at Yucca Mountain (YM) (Fig. 1). PA-LA underlies the Safety Analysis Report (SAR/LA) submitted by the United States (US) Department of Energy (DOE) [1,2], which is summarized in this special issue of Reliability Engineering and System Safety. Companion papers provide a historical summary of (a) site selection and regulatory development by the US Environmental Protection Agency (EPA) and US Nuclear Regulatory Commission (NRC) [3]; (b) hazards and scenarios identified [4]; and (c) site characterization and repository design [5,6].

n

Corresponding author. Tel.: +1 505 844 1761; fax: +1 505 844 2348. E-mail address: [email protected] (R.P. Rechard).

0951-8320/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ress.2013.06.031

The general progression of analysis of the YM repository has been summarized by noting the changes in linkages of the modules within the exposure pathway/consequence model [7]. However, presenting some of the simplifications within the unsaturated zone (UZ) transport module (M UZtrans) and the saturated zone (SZ) module (M SZ), as discussed here, is necessary to understand the information flowing through the linkages, along with the modeling evolution of other pertinent phenomena [8– 10]. These details help the reader get a glimpse of the complexity and the challenge of using numerous model simplifications in a PA simulation for the Yucca Mountain Project (YMP). In addition, results of sensitivity analysis have been summarized elsewhere [11]; but, a brief summary of the equations underlying the models, as included here, is necessary to define the parameters that were identified as important in explaining the variance in performance measures (expected cumulative release R prior to 1998 and expected individual dose DðtÞ], thereafter [3]. As understanding of the disposal system increased, M UZtrans for the UZ (Fig. 2) and M SZ have evolved from solution of one-dimensional

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Fig. 1. Location of repository, controlled area, and pertinent wells at Yucca Mountain, Nevada.

(1-D) transport along manually developed stream tubes in 1984 to particle tracking in 3-D flow fields to solve the transport equations in 2008. Seven iterations of the PAs conducted to evaluate the YM disposal system provide historical markers for the evolution of M UZtrans and M SZ. In PA–EA, the PA for the initial environmental assessment, the performance was evaluated deterministically [12,13]. PA-91, the first stochastic PA to evaluate site feasibility, serves as the second marker [14]. PA-91 was followed by two assessments in 1993, one conducted by the recently awarded management and operating (M&O) contractor, TRW (PA-M&O93) [15]; and one conducted by Sandia National Laboratories (SNL) (PA-93) [16]. Only the latter is discussed herein [16, Fig. 1-1]. The next analysis discussed, PA-95, was conducted by the M&O contractor [17]. PA-93 and PA-95 provided preliminary guidance on the repository design options. These four early PAs were followed by three PAs to support major decisions. In 1997, the

US Congress asked for a viability assessment, which was completed the following year (PA–VA) and serves as the fifth marker [18]. An analysis completed in 2000 for recommending the site— PA-SR—serves as the sixth marker [19]. The licensing case (PA-LA) serves as the final marker.

2. Transport modeling for PA–EA PA–EA was conducted to support the environmental assessment (EA) to screen sites for further characterization [3]. In the analysis, commercial spent nuclear fuel (CSNF) contained in 33,000 small, thin-walled stainless steel packages was emplaced either vertically in the floor or horizontally in pillars of rooms blasted out of the volcanic tuff. Cumulative, normalized release 4 e (R84 U ðe Þ) over 10 yr to the accessible environment boundary

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191

Fig. 3. For PA–EA, discrete matrix and fracture pathways through the nonwelded vitric and zeolitic tuff under the repository were modeled [12, Fig. 25].

value specified in 40 CFR 191 for radionuclide r; ee is an ordered nE-tuplet of epistemic model parameters, e¼ {φ1,.., φn,.., φnE}, which for PA–EA were deterministically varied; and R U,gw,r(  ) is the exposure consequence model for AU that calculates the flux across a boundary. The R U;gw;r ð  Þ consisted of two model components in a single code [7, Fig. 1]: (1) transport in fractures and matrix of the UZ (M UZtrans), and (2) transport in the matrix of the SZ (M SZ). 2.1. UZ transport in PA–EA PA–EA solved 1-D ordinary differential equations (ODEs) for transport below the repository in the UZ and SZ, based on a basic code, SAMPLE. For downward vertical flow in the UZ, two pathways were considered to the water table: (1) for 40% of the groundwater percolation flux (qperc ), a short segment through the repository host rock, Topopah Spring welded tuff hydrologic unit (TSw), followed by a 250-m segment through the vitric Calico Hills nonwelded tuff unit (CHnv); and (2) for 60% of qperc, a 50-m segment of the TSw followed by a 100-m segment through the zeolitic Calico Hill unit (CHnz) (Fig. 3). In the first pathway, flow was predominately in the matrix regardless of the percolation flux. In the second pathway, flow was predominately in the matrix when qperc o1 mm/yr (current arid conditions) and predominately in fractures when qperc 41 mm/yr (pluvial conditions), as suggested by the equivalent continuum model (ECM), that was being used for process modeling and more fully explained elsewhere [8]. For PA–EA, the transport formulation considered advective transport with radioactive decay and in-growth from radioisotope parents but with no hydrodynamic dispersion or diffusion and no explicit coupling between fractures and the matrix. The 1-D transport equation for matrix dominated flow was (without the complication of the in-growth from radioisotope parents) [12, Eq. 22] d dθm C m;r _ CSNF;r ðqm C m;r Þ ¼ Rrtrd m m;r dx dt rtrd þ λr Rrtrd m;r θ m C m;r λr1 Rm;r1 θ m C m;r1

Fig. 2. General stratigraphy of Yucca Mountain at SD-6 borehole [2, Fig. 6.3.1–8; 16, Fig. 6–7].

10 km from the repository (xae), the performance measure proposed in the draft EPA radiation protection standards 40 CFR 191, was evaluated for the undisturbed scenario class (AU) along a groundwater pathway as [3,7,20] e R84 U;gw ðe Þ ¼

nrU ¼ 17

1

r¼1

Lr f mass

∑

Z 0

104 yr

where x represents the direction of flow (vertical in the UZ and horizontal in the SZ). In PA–EA through PA-LA, transport of adsorbing radioisotopes in both the UZ and SZ was modeled using a linear Freundlich sorption model; hence, the Rrtrd m;r is the chemical retardation in the matrix for radioisotope r as defined by [12, Eq. 19; 21, Eq. 9.14] Rrtrd m;r ¼ 1 þ

ρbulk m θtotal m

tuf f

R U;gw;r ðt; ee Þjxae ¼ 10 km dt

ð1Þ

where fmass is the mass fraction of metric tons of heavy metal (MTHM) in the repository (MTHM/103 MT); Lr is the limiting

ð2Þ

tuf f

Kdm;e

ð3Þ

where Kdm;e is matrix sorption coefficient in either the UZ or SZ tuff for elements e and the same value for all radioisotopes for PA–EA (but later differed and important for Np in PA-93 and PA95 [11, Table 2]); ρbulk is the bulk density, and θm is moisture content of m the matrix and set to the product of saturation and total matrix

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porosity ϕtotal (i.e., θtotal ¼ ssat ϕtotal m m m ) where the saturation is 1 for the SZ. For the cases with fracture dominated flow, the transport equation was dθf C f ;r d _ CSNF;r m ðqf C f ;r Þ ¼ Rrtrd f ;r dxf dt rtrd þ λr Rrtrd f ;r θ f C f ;r λr1 Rf ;r1 θ f C f ;r1

ð4Þ

Rrtrd f ;r

is the chemical retardation in fractures for radioThe isotope r. In early PAs, Rrtrd was defined directly to implicitly f ;r include substantial diffusion into the matrix or related to the small fracture sorption coefficient for radioelements e using the fracture aperture (bf) [12, 21; Eq. 21, Eq. 9.18] Rrtrd f ;r ¼ 1 þ

2 Kaf ;e bf

ð5Þ

In Eqs. (2) and (4) C f ;r and C m;r are the concentration for radionuclide r for the fracture and matrix, respectively; θf and θm, are the moisture content in the fracture or matrix, respectively, and set to the product of saturation and effective fracture and matrix f f sat ef f porosity ϕef and ϕef m (e.g., θ m ¼ s ϕm ); qf and qm are the Darcy f discharge and equal to the product of the moisture content and the pore velocity in respectively the fracture and matrix (e.g., θm vm); _ p;r is the sourceλr is the decay constant for radionuclide r, and m term—either from various waste types p as calculated by the M Waste module (p CSNF for PA–EA) [10] or from M UZtrans for the SZ. Provided flow was in the tuff matrix in either pathway (Fig. 3), the vertical flow velocity and, thus, travel times in the UZ to the water table were long for current arid conditions (minimum of 2  104 yr). The slow travel time (τ) in the zeolitic pathway permitted substantial sorption of radionuclides (i.e., τ¼d/vUZ where dUZ ¼ 100 m, vUZ ¼qperc/ f f ssat θUZef where ssat θUZef was set at an effective composite moisture m m content of 0.1 and qperc 0.1 or 0.5 mm/yr). The UZ retardation (RUZrtrd ) was an important parameter in the zeolitic pathway in m;r PA–EA [11, Table 2].1 2.2. SZ flow and transport in PA–EA In the SZ, transport of 17 radionuclides (nrU ) from the repository to an accessible boundary 10 km away (xae ¼ 10 km) was envisioned to occur in fractures near the top 100 m of a mostly confined tuff aquifer composed of the nonwelded Prow Pass (PPn) tuff in PA–EA. Transport in the confined carbonate aquifer far below the repository was not thought possible since the one UE25p#1 well to that aquifer at the time of PA–EA had a higher head than the overlying, tuff aquifer (Fig. 4). However, by PA-LA the regional flow model suggested that the carbonate aquifer was connected to the overlying volcanic aquifer far to the south at the Nevada-California border [22, p. 3–46]. The horizontal flow velocity vf was high; thus, the travel time in the SZ to the 10-km boundary was short: either 200 or 2000 yr based on a fracture hydraulic conductivity (Kf) for the PPn unit of either 30 or 300 m/yr, measured hydraulic gradient (dh/dl) from available wells of f 3.4  10  4, and effective porosity ϕSZef of 0.002 (i.e., τSZ ¼ dSZ/vSZ f f SZef f SZ SZ SZ SZ where d ¼10 km, vf ¼ qf =φf and qf ¼ K SZ f dh=dl) [12, Section 4.1]. Furthermore, only small changes in flow direction and groundwater flux because of climatic change were anticipated, based on modeling by the US Geological Survey (USGS) where infiltration had been doubled and had caused only a factor of 2 to 4 increase in flux (similar to the situation for PA–VA and thereafter) [24,25]. Flow 1

By PA–VA, analysts concluded that the CHnz permeability was low such that a substantial amount of flow was diverted down dip to faults; hence, much less flow occurred in the second pathway through the adsorptive, zeolitic layers using a 3-D model.

Fig. 4. Formal stratigraphy and common modeling layers in SZ [23, Fig. A6-21; 58, Fig. 3].

properties in the regional-scale, 2-D, 1984 USGS model of flow, which extended 70 km to Death Valley, were calibrated to  90 hydraulic head measurements in wells around Yucca Mountain, Amargosa Valley, and in Death Valley [6; 24, Fig. 3].

3. Transport modeling for PA-91 PA-91 was conducted to demonstrate the ability to conduct stochastic calculations and assess site feasibility [26]. CSNF was placed in a container and repository of similar design to PA–EA, but as specified in the 1988 Site Characterization Plan (SCP) [5]. In addition to evaluating release of 14C gas at the surface, the expected cumulative, 91 normalized release via a groundwater pathway (Rj;gw;acm ) over 104 yr was evaluated at a 5-km boundary (xae) for 3 scenario classes [3; 4, Table 1]: undisturbed—AU, human intrusion—AH, and volcanic eruption—AVE, (i.e., j U,H,VE), but only AU is discussed herein. The 91 complementary cumulative distribution function (CCDF) of RU;gw;acm from the releases in the UZ and SZ for the transport of 9 radionuclides (nrU ¼ 9) was evaluated using Latin Hypercube Sampling (LHS—a form of Monte Carlo integration to determine the expectation) with either 300 or 1000 samples (nLHS U ) [7] ℘fR91 U;gw;acm 4 Rg ¼

1

nLHS U

∑ H

nLHS U ℓ¼1

(

nrU ¼ 9

1

r¼1

Lr f mass

∑

Z 0

104 yr

) R U;gw;r;acm ðt; eeℓ Þjxae ¼ 5 km dtR

ð6Þ where H {x}¼ 0 if x≤0; H {x}¼1 if x40 and the derivation explained elsewhere [7, App. B]. The two alternative conceptualizations of UZ

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193

Table 1 Progression of conceptual models for flow and transport modeling in the saturated and unsaturated of the Yucca Mountain disposal system. PA

Unsaturated zone Flow

Saturated zone Transport

Flow (site scale)

Transport

EA

1-D

1-D Single porosity (matrix or fracture) Advection only Radionuclides with decay

1-D

1-D Single porosity (matrix or fracture) Advection only Radionuclides with decay

91

TOSPAC-STEADY ECM 1-D, 6 columns

TOSPAC-TRANS 1-D Dual porosity Advection/Dispersion Radionuclides with decay

STAFF2D Single porosity 2 Velocity PDFs developed from particle tracking

TOSPAC-TRANS 1-D Single porosity Advection/Dispersion Radionuclides with decay

WEEPTSA 1-D

UZ bypassed

Same

Same

TOSPAC-STEADY ECM 1-D, 8 columns

TOSPAC-TRANS 1-D Dual porosity Advection/Dispersion Radionuclides with decay

STAFF3D Single porosity 2 Velocity PDFs developed from particle tracking

TOSPAC-TRANS 1-D Single porosity Advection/Dispersion Radionuclides with decay 8 stream tubes

WEEPTSA 1-D

UZ bypassed

Same

Same but 1 stream tube

95

TOUGH2 1-D ECM (column 153 in 3-D model)

RIP 1-D Markovian algorithm for Matrix/fracture flow

PA-91 results used Velocity PDF developed

RIP 1-D Single porosity Advection/Dispersion Radionuclides with no decay

VA

TOUGH2 3-D Dual-permeability 9 flow fields (3 climate states and 3 uncertain fields)

FEHM 3-D Dual-permeability Advection/Dispersion RTTF particle tracking Radionuclides/colloids with decay

FEHM 3-D Single porosity

FEHM 1-D and SZ CONVOLUTE Single porosity Fixed pore velocity in 6 flow paths Advection: RTTF tracking Dispersion: Random walk Radionuclides/colloids, no decay

SR

Same

Same

FEHM 3-D Single porosity 6 uncertain flow fields (3 fluxes at upper model boundary and 2 anisotropy fields)

FEHM 3-D and SZ-CONVOLUTE for dose Dual porosity Advection: RTTF tracking Dispersion: Random walk Radionuclides/colloids, no decay

93

GOLDSIM 1-D for GW protection Dual porosity Radionuclides/colloids with decay LA

TOUGH2 3-D Dual-permeability 16 flow fields (4 Climate states and 4 uncertain fields)

Same

FEHM 3-D Single porosity 200 uncertain flow fields (from samples of boundary flux and anisotrophy)

flow (i.e., acm) and the conceptualization of UZ and SZ transport for R U;gw;r;acm ðt; ee Þ in PA-91 are as follows. 3.1. UZ transport model in PA-91 Two flow conceptualizations were modeled in the UZ flow module M UZflow described elsewhere (Table 1) [8]: (1) the equivalent-continuum model (ECM), incorporated into TOSPAC [27], that partitioned flow primarily in the matrix until the matrix was almost saturated, and (2) a weeps model, WEEPTSA, which placed flow solely in the fractures (i.e., R U;gw;r;acm ðt; ee Þ where acm  ECM, Weep). Although both a groundwater and a gaseous pathway in the UZ were evaluated for the undisturbed scenario, we only discuss the groundwater pathway. Groundwater transport in the UZ was assumed instantaneous and radionuclides injected directly into the SZ for the weeps conceptual model. Groundwater transport of radionuclides in the UZ (M UZtrans) for the ECM conceptual formulation was based on the TRANS transport subroutine of TOSPAC, under development since 1985.

Same

For PA-91 and PA-93, the transport model used a dual-porosity formulation that included radioactive decay with 1-D diffusive and advective flow down the fracture and 1-D diffusive flow into the matrix (where the later phenomenon had only been implicitly included through a large Rrtrd m;r in PA–EA) [14, Eq. 4.55; 27, Eq. 3.1–10]   ∂C f ;r ∂ f ∂C f ;r Γ p;r Ψ r ¼ θf Rrtrd θf Ddif q C f ;r f f ;r f ;r ∂x ∂xf ∂t f rtrd þ λr θf Rrtrd f ;r C f ;r λr1 θ f Rf ;r C f ;r1

ð7Þ

  ∂ ∂C m;r f ∂C m;r θm Ddif ¼ θm Rrtrd m;r m;r ′ ′ ∂zm ∂zm ∂t rtrd þ λr Rrtrd m;r θ m C m;r λr1 Rm;r1 θ m C m;r1

ð8Þ

where xf is the direction of 1-D fluid flow in the fracture (vertical in UZ and horizontal in SZ), and zm ′ is the direction of diffusion into the matrix perpendicular to fluid flow. Ψr is a matrix-fracture transfer term, which enters into Eq. (8) through a boundary

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Fig. 5. For PA-91, radionuclide release from the UZ was the source for a general welded tuff pathway in the SZ [14, Figs. 4-18 and 4-30].

f f condition; Ddif and Ddif m;r are the diffusive parameters for radiof ;r nuclide r for respectively the fracture and matrix, which includes a contribution from the both hydrodynamic dispersion and molecular diffusion that had been omitted in PA–EA. These compof n L nents are defined as Ddif Ω;r ¼ Dr þ αΩ vΩ where Ω  f,m [27, Eq. 3.1L 16]; αΩ is dispersivity in longitudinal direction to flow for 1-D flow (and later an important parameter in PA-93 [11, Table 2]); o tort Dnr ¼ τtort is tortuosity, Dor is molecular diffusion. Other Ω Dr , τΩ terms are as previously defined. The hydrologic parameters for the UZ UZ—Darcy discharge (qUZ f ðtÞ and qm ðtÞ) and moisture content UZ (θUZ ðtÞ and θ ðtÞ)—were supplied by the STEADY flow module of m f TOSPAC [7, Fig. 2; 8]. Six transport 1-D columns were modeled along a cross-section between H-5, G-4, and UE25a#1 from 10-m above the repository to the water table  240 m below the repository [14, Table 4-3, Fig. 4-17] (Fig. 5). Up to 5 layers were modeled in each layer: TSw, Topopah Spring vitrophyre (TSv), a Calico Hills nonwelded vitric tuff (CHnv), a composite nonwelded zeolitic tuff aquifer, and possibly a composite welded tuff.

3.2. SZ flow model in PA-91 In PA-91, the SZ module M SZ evaluated the Darcy velocity field within the fractured SZ (qSZ f (x, t)) based on regional-scale, 2-D, finite-element computational code STAFF2D v3.1 [7, Fig. 2; 28]. As in PA–EA, flow was envisioned to occur mostly in the saturated fractures, thus, a composite-porosity model with parameters based on a composite of matrix and fracture properties was used (e.g., the permeability tensor was the composite of matrix and fracture permeability kECM ). The 1991 2-D flow model to calculate the fracture Darcy velocity field qSZ f (x, t) used identical fracture flow parameters and roughly the same 80 km by 60 km irregular area of the earlier regional 2-D 1984 USGS model of flow [24, Fig. 3]. 3.3. SZ transport model in PA-91 Rather than use the transport capability in STAFF2D and, thereby, introduce excessive numerical dispersion, the evaluation of the transport of radionuclides in the SZ to the 5-km accessible environment boundary was via a 1-D tube, based on the TRANS transport module of TOSPAC (Table 1). However, only a single porosity formulation was used (only Eq. (7) [14, p. 4-72]). The 1-D tube model extended 100 m up-gradient and 5 km down-gradient from a 25 m region representing the repository [26, Fig. 4-29] (Fig. 5). The 1-D path and the probability distribution function (PDF) of SZ fracture velocity for use in TRANS was calculated from the distribution of travel times of 500 particles released at the repository into the fracture velocity field qSZ f (x, t). The mean pore SZef f velocity of 4.1 m/yr and range of 3.2–5.9 m/yr (qSZ f =ϕECM where the SZef f effective composite porosity ϕECM is 0.175) resulted in an average travel time of 1200 yr and a range of 850 to 1560 yr for unretarded

Fig. 6. For PA-93, radionuclide release from the UZ was the source for two possible pathways in the SZ [16, Figs. 7-1 and 11-1].

radionuclides, which was a smaller range than considered in PA– EA [26, Table 4-6].

4. Transport modeling for PA-93 YMP conducted PA-93 to provide guidance on (a) characterizing the site; (b) two options for heat loading (14 and 28 W/m2); and (c) two options of package placement in the repository (vertical and in-drift) [5,16]. CSNF was placed either vertically in boreholes in the floor in thin-walled containers of nickel Alloy 825 or horizontally in the repository drift in thick, double-layered containers of Alloy 825 and carbon steel. Two performance measures were evaluated at a 5-km boundary in PA-93 [3, Table 4]: (1) the CCDF of cumulative, 93 normalized release at 104 yr (e.g., RU;gw;acm from Eq. (6)); and (2) dose from drinking contaminated water over 106 yr. The cumulative 93 normalized release (Rj;gw;acm ) was evaluated for 3 scenarios classes [4]: AU+EF, AH, and igneous activity AV where (a) the undisturbed scenario included early failure of the container vessel of the waste package and (b) the igneous scenario included the igneous intrusion subclass AVI and volcanic eruption AVE from PA-91 (i.e., j U+EF,H,V). As in PA-91, cumulative normalized release for both a groundwater and gaseous pathway in the UZ were evaluated, but only the ground93 water pathway is discussed (RUþEF;gw;acm ). Dose was also evaluated (new for PA-93) but only for AU+EF along the groundwater pathway (i. max 93 e., D93 DUþEF;gw;acm in UþEF;gw;acm ). The CCDF of the maximum doses the groundwater pathway from 7 transported radionuclides (nrU ) was calculated at the 5-km boundary of accessible environment (xae) for to106 yr as [7,11, Fig. 3] ℘fmax D93 UþEF;gw;acm 4 Dg ( r ) nU ¼ 7 BDCF f U;r e R ðt; e Þj  D ¼H for ℓ ¼ 1; :::; nLHS ∑ ae UþEF;gw;r;acm ℓ x ¼ 5 km U indv r ¼ 1 Q 93;ℓ ð9Þ BDCF f U;r ,

Q indv 93;ℓ ,

where the biological dose conversion factor, and the dilution in the SZ, are described in a later section. The model for undisturbed transport along the groundwater pathway (R UþEF;gw;r;acm ðt; ee Þ) again used an ECM or weeps model alternative conceptualization (i.e., acm ECM,Weeps) as follows. 4.1. UZ transport in PA-93 For the weeps formulation, transport was again instantaneous in the UZ in PA-93 (M UZtrans). For the ECM formulation, transport was again modeled with TOSPAC TRANS subroutine using up to 8 columns (with 5 columns west for the hot 28 W/m2 repository option and an additional 3 columns east of the Ghost Dance Fault for the cool 14 W/m2 repository option) (Fig. 5) [16, Fig. 14-5; 27]. Each column started 12 m (rather than 10 m as in PA-91) above the repository and extended to the water table. As with PA-91, up to

R.P. Rechard et al. / Reliability Engineering and System Safety 122 (2014) 189–206

5 layers were modeled but the composition of the bottom 2 layers differed [16, Table 7-23 Fig. 14-5] (Fig. 6): Topopah Spring welded tuff (TSw), Topopah Spring vitrophyre (TSv), a combined Calico Hills (CHnv), Calico Hills nonwelded zeolitic/Prow Pass welded tuff (CHnz/PPw), and Bull Frog welded tuff (BFw).2

4.2. SZ flow and transport models in PA-93 Use of dose as a health indicator increased the importance of dilution (Q indv 93;ℓ ) provided by the SZ and so PA-93 improved the underlying SZ process model to determine the flow velocities transporting radionuclides. An 8 km by 8 km by 200 m deep 3-D site-scale model consisting of four layers (TSw, CHn, PPw, and BFw —Fig. 4) was created using the finite-element code STAFF3D v2.5 [30]. Two alternative conceptual models of flow in the SZ were investigated in order to explain the 300 m change in water table elevation north and west of the repository [6]. Travel times and, thereby, pore velocities were determined by calculating transport of a conservative tracer injected into one of three layers directly below the repository to a location 5 km down-gradient from the repository. For the tracer transport, longitudinal dispersivity (αSZ m) was assumed to be uniformly distributed between 100 and 500 m (0.1 of travel distance). Based on the travel times for a conservative tracer, the 6 results (3 sources and 2 conceptual models) were abstracted as two uniform PDF for 2 pathways in the volcanic tuff aquifer (rather than one in PA–EA and PA-91) (Fig. 6). Only 2 pathways were necessary rather than 3 since two of the velocities were similar. For the early PAs, climate change was assumed to not influence water movement in the SZ. Hence, the pore velocity for transport SZef f through the Bullfrog hydrologic layer (qSZ where f ;BFw =ϕECM SZef f ϕECM ¼0.2 [16, Section 11.6.3]) was uniformly sampled between 8.5 and 12.5 m/yr. The pore velocity for transport through the SZef f combined CHnz/PPw hydrologic layer (qSZ f ;PPn =ϕECM ) was uniformly sampled between 5.5 and 11 m/yr [16, Table 11-7]. The mean transport time of 600 yr for the BFw and 800 yr for the combined CHnz/PPw layer calculated in PA-93 [16, Fig. 11-26] were faster than the mean 1200 yr travel time observed in PA-91 but travel times in both PAs were rapid relative to the potential delay in the UZ and relative to the anticipated regulatory time period of 106 yr. Based on uranium-isotopic dating of ancient spring deposits, future climate change was approximated by a uniformly distributed water-table rise between 50 and 120 m [16, Sections 8.8 and 14.5.1]. The water table could also rise under current arid conditions and was approximated by a uniform distribution between 0 and 10 m. Water table rise was decoupled from velocity and transport parameters in the SZ in PA-93. Transport of decaying radioisotopes in the SZ was again modeled using TOSPAC TRANS. For the weep formulation, one 1D homogeneous, composite-porosity flow tube was used; however, for the ECM formulation, a 1-D flow tube was used for each UZ column [16, Section 11] (Fig. 6). Each transport pathway represented a composite of several rock types, but to be conservative and consistent with PA-91, a single porosity was used and the sorption coefficients in the flow tubes were for the SZdevit devitrified tuff rock type (Kdm;e in Eq. (5)) rather than use sorption coefficients for one of the other two rock types present in the UZ (i.e., not vitric tuff nor zeolitic tuff) [6]. 2 Up until PA-95, SNL conducted a series of groundwater travel time calculations in parallel with transport calculations for the PAs to compare current understanding of the YM disposal system with the 1000 yr groundwater travel time criterion in 10 CFR 60 (e.g., [29]). Discussion of this work is beyond the scope of this paper.

195

4.3. Biosphere modeling in PA-93 For PA-93, the dose calculation only considered an ingestion pathway because of the small difference between a subsistence farmer and resident using drinking water in a previous analysis BDCF [31]. Fixed drinking water dose conversion factors f U;r , as recommended by DOE and based on consumption of 2 L/d (0.73 m3/yr), were used [16, Tables 14-1]. For PA-93, the mass release from the transport calculations R U+EF,gw,r(t;e) was mixed with the dilution volume of the SZ to calculate the mass concentration. The dilution volume was estimated as the product of the maximum velocity range defined above SZef f SZef f (5.5oqSZ f ;path;ℓ =ϕECM o12.5 m/yr), SZ porosity (ϕECM ¼0.2), and cross-sectional area of a contaminate plume after traveling 5 km [16, Tables 11-7 and 14-11]. The cross-sectional area (hSZ wre), which was an important parameter in PA-93 [11, Table 2], was assumed to range loguniformly between 2  104 and 2  106 m2 based on an estimated plume width (3400 to 4400 m increase from 3000 m repository width) and depth (50 to 500 m) [16, 4 Section 11.6.2]. Hence, Q indv 93 in Eq. (9) ranged between 2  10 and SZ rep SZ 5  106 m3/yr for PA-93 (i.e., Q indv ¼q ðh w Þ ). Although ℓ 93;ℓ f ;path;ℓ percolation flux increased and water table rose with changes in climate percolation flux, velocity through the SZ did not and so while the amount of radionuclides released increased with a climate change, the dilution in the SZ did not in PA-93.

5. Transport modeling for PA-95 YMP conducted PA-95 to provide guidance on characterizing the site and two options for the heat load with and without backfill. For PA-95, the package was a large, thick-walled, 2–layer container placed inside a disposal drift. Based on previous PAs, only groundwater releases over 104 yr and dose over 104, 105, and 106 yr for AU were evaluated. A gaseous pathway for 14C was not included because of the anticipated change to a dose standard at an accessible boundary at least 5 km from the repository such that gaseous doses would be inconsequential [3, Table 4]. PA-95 used the Repository Integration Program (RIP) stochastic simulator with 95 100 LHS samples (nLHS cumulative release (RU ) U ) to evaluate 95 at 104 yr and individual dose (DU ðtÞ) over 104, 105, and 106 yr at a 5-km accessible boundary (xae) for 39 radionuclides (nrU ) [7,17,32] 95

DU ðtÞ ¼

1 nLHS U

nLHS ¼ 100 nrU ¼ 39 BDCF U f U;r;ℓ ∑ ∑ indv ℓ¼1 r ¼ 1 Q 95;ℓ

R U;r ðt; eeℓ Þjxae ¼ 5 km

ð10Þ

5.1. UZ transport in PA-95 The matrix flow velocities of percolation and the fraction of fracture flow in the UZ, estimated by the ECM formulation using the TOUGH2 code in M UZflow [8], were used in a 1-D, finitedifference formulation available in RIP to calculate radionuclide transport that included sorption but not radioactive decay. For the hot repository option, 6 columns (or zones z) west of the Ghost Dance fault were used. Each column was composed of 5 layers as in PA-93 but with a slightly different designation of the bottom layer: TSw, TSv, CHnv, CHnz, and PPn. For the cool repository option, 4 addition columns east of the Ghost Dance fault were used (Fig. 7). A dual-porosity or dual-permeability transport formulation was not formally used. Rather, interaction between the fracture flow and matrix flow pathways was approximated using two schemes: (1) a Markovian process that randomly moved particles

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Fig. 7. For PA-95, one pathway through the SZ was evaluated [17, Fig. 3.8-4].

between pathways within layers and (2) an interaction fraction parameter where higher interaction resulted in more fracture flow being diverted into the matrix at the interface between layers [17, Section 7.4] (Table 1) . The fraction of fracture flow in the TSw unit TSw hosting the repository (f f ) and in the thin, underlying vitrophyre TSv layer (f f ) were important parameters in PA-95 [11, Table 2].

information as interpreted by expert panels [18]. The emphasis was on dose from the undisturbed scenario class solely via a groundwater pathway. However, an early waste container failure scenario was included with the undisturbed scenario (AU+EF), similar to PA-93. PA–VA used [7, Fig. 5] (1) a new UZ transport model based on the LANL finite element heat and mass (FEHM) transport code [34] M UZtrans FEMH ; (2) a new SZ flow and transport model based on FEHM and a transport simplification based on convolution that included colloid transport M SZ CONVOLUTE;FEMH ; and (3) a new biosphere transport model, based on GENII-S, that developed uncertain biological dose conversion factors (fBDCF) specific to potential water use at Amargosa Valley near Yucca Mountain M Bio GENIIS . YMP simulated the concentration (i.e., dilution provided by the disposal system) for PA–VA and evaluated the expected undisturbed total dose (including early container failure) DUþEF ðtÞ for 9 radioisotopes and 100 LHS samples for to106 yr as [7, Eq. 16] 1

VA

DUþEF ðtÞ ¼

nLHS U

nLHS ¼ 100 nrU ¼ 9 U

∑

ℓ¼1

BDCF

e ∑ f U;r;ℓ ðwðtÞÞR SZ UþEF;r;ℓ ðt; eℓ Þjxae ¼ 20 km

r¼1

ð11Þ

5.2. SZ flow and transport in PA-95 No new process flow modeling of the SZ was conducted for PA95. Also, PA-95 reverted to the flow modeling done for PA-91. However, the full range of nodal velocities in the process model underlying PA-91 were used and resulted in a similar pore velocity SZ SZadv as in PA-93 (qSZ f ¼2 m/yr and qf =ϕECM ¼ 10 m/yr). The sampled SZ qf , which was an important parameter in PA-95 [11, Table 2], was used in a homogeneous, 1-D advective/dispersive model with sorption but no radioactive decay, based on finite-difference numerical formulation available in RIP. The model was still of a single composite media and did not include diffusion into the matrix (i.e., only Eq. (7) without radioactive decay) [17, Section 7.6]. The SZ pathway was set entirely in upper Prow Pass welded tuff unit of the volcanic aquifer (with a mixing depth of 50 m) and SZdevit mostly used devitrified tuff sorption coefficients (Kde ) developed for PA-93 [15, Appendix H; 16, Section 9.3]. Modifications were made to sorption coefficients for Np, U, Pu, and Se based on recent experiments at Los Alamos National Laboratory (LANL) [17, Section 7.4.6, Table 7.4-3]. Furthermore, sorption coefficients in the SZ were modified from those used in the UZ because of potential UZdevit SZdevit differences in ionic strength (I ), (i.e., in general, Kde ≠Kde in PA-95) [17, Table 7.4-2]. The SZ did not provide much of a time delay and so the mass injected from the UZ generally equaled the SZdevit _ UZ _ SZ mass release at 5 km (i.e., m was r ðtÞ≈mr ðtÞ); yet, KdNp important for PA-95 [11, Table 2]. 5.3. Biosphere model in PA-95 Similar to PA-93, the only human exposure pathway evaluated was ingestion through drinking water. Fixed dose conversion BDCF factors f N;r for drinking water ingestion as recommended by EPA were used (rather than as tabulated by DOE and used in PA93) [17, Table 7.6-1; 33, Tables 2-2]. As in PA-93, the dose concentration was the mass injection rate into the SZ mixed with the volume of the SZ. The mixing volume was evaluated as before SZ SZ rep (i.e., Q indv ); however, the uncertainty in Q indv 95;ℓ ¼qf ;ℓ h w 95 derived SZ solely from the uncertainty in qSZ was fixed at a mixing f ;ℓ since h height of 50 m and wrep was fixed at the 4000-m width of the indv repository for PA-95; hence, for the mean Q 95 ¼ 4  105 m3/yr. 6. Transport modeling for PA–VA PA–VA was conducted to demonstrate the viability of the YM disposal system to Congress. YMP used the most current

where the concentrations at the 20-km boundary, as calculated e UZtrans and by R SZ UþEF;r;ℓ ðt; eℓ Þjxae ¼ 20 km , was evaluated by M FEMH BDCF

M SZ CONVOLUTE;FEMH , and the biological dose conversion factor (f U;r;ℓ ) as a function of climate state (w(t)) was evaluated by M Bio GENIIS as follows. 6.1. UZ transport model in PA–VA In the UZ transport module M UZtrans , the mass from several regions of the UZ was transported in both the fractures and matrix (i.e., dual-permeability transport) based on FEHM v2.0 [34,35]: ∇ðθf Ddisp ∇C f ;r qf C f ;r Þ f ;r ¼ θf Rrtrd f ;r

∂C f ;r rtrd rtrd _ UZ m z;r Ψ r þ λr Rf ;r θ f C f ;r λr1 Rf ;r θ f C f ;r1 ∂t

ð12Þ

f disp ∇ðθef m Dm;r ∇C m;r qm C m;r Þ

¼ θm Rrtrd m;r Ddisp m;r

∂C m;r rtrd rtrd _ UZ m z;r Ψ r þ λr Rm;r θ m C m;r λr1 Rm;r θ m C m;r1 ∂t Ddisp f f ;r

ð13Þ

and are respectively the dispersive tensor for where radionuclide r for the matrix and fracture (with tensor components a function of the effective molecular diffusion for radionuclide r—Dnr —and the longitudinal, transverse horizontal, and transverse vertical dispersivities—αL, αTH , and αTV , respectively _ UZ [36]); m z;r ðtÞ is the radionuclide source to the UZ regions z calculated by the EBS transport module M EBStrans module described elsewhere [10] (6 percolation zones z in PA–VA, 4 percolation bins in PA-SR, and 4 percolation zones z in PA-LA). The advective and diffusive transport Eqs. (12) and (13) were solved using a new, computationally efficient residence time/ transfer function (RTTF) particle tracking method (Lagrangian solution method) [37, Section 7.4.2; 38; 39]. Two steps were used in the RTTF approach (1) statistically determine the time a particle spends in a given cell, and (2) statistically determine which cell the particles travels to next. In the first step, a cumulative distribution function of the residence time, as determined from solution of Eqs. (12) and (13) for a cell, was randomly sampled. In the second step, the probability of moving to an adjacent cell was determined by the relative mass flux to that cell versus other cells. The actual cell choice for a particular particle was sampled randomly. Hence, the method only tracked movement into and out of cell rather than interpolate a velocity field within each cell

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[37, Section 7.4.1.2; 40; 41]. During a simulation, millions of particles (i.e., 105 particles in each of the numerous grid cells of the repository area) were tracked in the 3-D flow field generated by M UZflow, as described elsewhere [8], based on time (i.e., climate state w(t)) and probability of the occurrence of calibrated infiltration-hydrologic property set h [37, Section 7.5.3.1]. The RTTF could accurately transport both decay and ingrowth of radionuclides in a dual permeability system with a wide disparity of velocities between the matrix and fractures. The only limitation of RTTF was that flow had to be advection dominated with a Peclet number 41. Similar to other particle tracking schemes, the RTTF particle tracking method greatly diminished artificial numerical dispersion that occurred in earlier PAs (using the Eulerain method). An instantaneous water table rise of 80 m occurred from a dry, current climate to a long-term average climate, and an instantaneous rise of another 40 m (120 m total) occurred from a longterm average to a super pluvial climate for PA–VA [18, vol. 3, Table 3-4]. The water table would fall 120 m at the return to a dry, current climate [8, Fig. 5]. For water table rise, radionuclides in transit between the past water table position and new higher water table position were instantaneously injected into SZ. When the water table fell, the transport distance increased, and a time gap occurred in radionuclides reaching the SZ. The radionuclide mass in the 6 SZ input regions u (unrelated to the 6 UZ input percolation zones z) from both the fractures and matrix was _ SZ _ UZ _ UZ summed for input into M SZ (i.e., m u;r ðtÞ ¼ mf ;u;r ðtÞ þ mm;u;r ðtÞ) for u ¼1,..,6.

6.2. SZ flow model in PA–VA A 3-D, single fracture porosity, site-scale flow model, based on the FEHM v2.0 code, was used to determine the flow path to the accessible environment 20 km from the repository in M SZ [34; 42, Section 8.3.2; 43]: 0 ¼ ∇

ρw kECM _ ∇ðP m þ ρw gzÞ þ m μw

ð14Þ

Applying Darcy's law with a flowing fracture Darcy velocity of qSZ f ¼ ðρw =μw ÞkECM ∇ðP m þ ρw gzÞ, results in the familiar expression _ 0 ¼ ∇qSZ f þm

ð15Þ

The SZ flow model used the same hydrologic strata of the USGS 1997 site-scale model [18,44]. The model domain was a 20 km by 36 km area to a depth of 950 m that included 16 homogeneous, isotropic units with uniform elements 500 m by 500 m by 50 m. By limiting the depth to 950 m, not all of the deep carbonate aquifer could be included in the northern and western portions of the model (Fig. 4). The permeability for each of the 16 equivalentcontinuum, homogeneous, hydrologic units modeled were set at the median value specified in distributions provided by the Saturated Zone Expert Elicitation (SZEE) panel. The permeability was approximately equal to the fracture permeability (kx,ECM≈kx,f) [18, vol. 3, Section 3.7.1.4]. The SZEE panel was formed for PA–VA to evaluate the current status of models and to aggregate disparate data available in the literature in order to provide information necessary for M SZ prior to completion of site characterization. For 5 units not defined by the SZEE panel, the permeability values for 3 of the 5 units were set by the USGS site-scale model and the permeability for the remaining 2 units was adjusted via calibration [6]. Also, permeability for faults and the alluvium were adjusted via calibration [42, Section 8.4.2]. The layers were assumed isotropic in PA–VA (kx ¼ ky ¼ kz), but anisotropy would be considered in PA-SR and PA-LA. As in earlier PAs, the SZ flow model assumed 2 low permeability barriers to the north and west

197

(Solitario Canyon Fault) of the repository to better match well heads; however, many of the SZEE panel favored the explanation that the high water levels measured north of Yucca Mountain was perched water unconnected to the water table [18, vol. 3, p. 3-138; 45, p. 3-5]. 6.3. SZ transport model in PA–VA The transport portion of M SZ was also based on FEHM v2.0. Although M UZtrans modeled advective and diffusive transport in the fracture and matrix (dual-permeability formulation) in a 3-D UZ flow-field, M SZ modeled only 1-D transport using composite parameter values (i.e., Eq. (12) without the radioactive decay terms and matrix-fracture transfer term3) (Table 1). Similar to UZ transport, the solution of the advective portion of Eq. (12) was through the RTTF particle tracking algorithm. The solution of the dispersive portion of Eq. (12) was by a random-walk algorithm in PA–VA, PA-SR, and PA-LA [40]. In 1997, LLNL and LANL scientists had discovered the migration of Pu via colloids 1.6 km from the Benham bomb test detonated in 1968 below the water table at NTS [6, App. A; 46]; hence, FEHM was modified to include colloid-facilitated transport of radionuclides for PA–VA [47]. Specifically, an expression for fracture retardation (Rrtrd f ;r ) was developed for reversible colloidal and solute transport of 239Pu and 240Pu [42, Section 8.4.2; 48] ( allv 1þρbulk Kde =ϕtotal þKce Rf ilter in alluvium 1þKce ¼ ð16Þ Rrtrd f ;r 1 in volcanic units where Rf ilter was retardation from reversible colloidal filtration (and set to 1 for PA–VA), and Kce was the colloidal partition coefficient (ratio of mass in colloidal and aqueous form) and assigned directly between 10  5 and 10 in PA–VA for the alluvium (PA-SR and PA-LA would estimate Kce by linking it to C coll gw [10]). However, Pu was also transported irreversibly attached to colloids (239Puirr, 242Puirr). and retardation in the fracture tuff and alluvium was assigned directly 8 < Rcoll allv retardation in alluvium of colloids rtrd Rf ;r ¼ ð17Þ : Rcoll tuf f retardation in volcanic units of colloids

Seven non-colloidal radionuclides were also transported in PA– VA in the tuff matrix in Eq. (7) (nrU  14C, 79Se, 99Tc, 129I, 231Pa, 234U, 237 Np). Hence, Eq. (12) was solved for 9 solute transported radionuclides r and the 2 irreversible Pu colloids for a total of 11 times. For the 7 non-colloidal radionuclides, the matrix retardation Rrtrd m;r was related to sorption coefficients such as Kdm;e (Eq. (3)), but a total total porosity (ϕ ) was used to estimate the total surface area that was accessible to the solute in Eq. (3) rather than the somewhat smaller effective composite porosity (ϕeff) used in the Darcy flow calculations [48, Section 6.5.1] ( bulk allv 1 þ ϕρtotal Kde in alluvium ð18Þ ¼ Rrtrd m;r 1 in volcanic units To represent the transport path through the SZ, six 20-km long 1-D stream tubes consisting of 3 volcanic tuff segments and an alluvium segment were defined manually in PA–VA based on particle paths in the 3-D flow model [18, vol. 3, Section 4.1.12]. Because the accessible environment had been extended to 3 Radioactive decay was not included for SZ transport, even though it was an option with FEHM and used for UZ transport in M UZtrans; rather for SZ transport of radionuclides with ingrowth, the initial mass was increased to the maximum potential mass in order to use the convolution technique. For PA-SR and PA-LA, 1-D transport with decay was also evaluated for several radionuclides (Table 1).

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between 18 and 20 km, the SZ model included volcanic strata of the aquifer fingering into a single porosity alluvium 10 to 15 km from the site. Each flow path had an average 1-D, single-porosity, flowingfracture Darcy velocity qSZ of 0.6 m/yr for the current climate f based on a transport analysis interpreted by the SZEE panel (i.e., the SZ flow simulations were not used directly in PA–VA, but interpreted by the SZEE panel) [18, vol. 3, Section 4.1.12; 45]. The cross-sectional area of each tube was adjusted such that the volumetric flow rate through a stream tube was equal to the volumetric flow rate to the water table in a SZ region as evaluated by M UZflow [8]. The influence of climate change, was modeled by increasing the flowing-fracture Darcy velocity proportional to that observed in the USGS regional-scale SZ flow model [49] (i.e., 2.3 m/yr for long-term, semi-arid climate; 3.7 m/yr for short-term, superpluvial climate) [18, vol. 3, Table 3-4]. Also, the length of the alluvium segment was uncertain for each of the six stream tubes because of the limited well data between 10 and 15 km from the repository in PA–VA. The analysis generated concentration breakthrough curves for a _ step H ðtÞ) for the 11 transported unit step input at time zero (m species through each of 6 flow paths [18, vol. 3, Section 3.7.2.1; 42, Section 8.3.3]. Seventeen parameter characteristics of the 6 flow paths were sampled 101 times (100 LHS and one expected-value case) to produce 6666 breakthrough curves for the 11 transported species (6  101  11) [18, vol. 3, Table 3-20]. For each PA–VA simulation within RIP, a breakthrough curve was selected for use in the convolution method using SZCONVOLUTE v1.0 developed for YMP [7, Fig. 5; 50, Table 11-2], to determine the concentration for radionuclide r at the end of the stream tube s (C SZ r;s ðt; x ¼ 20 kmÞ) [18, vol. 3, Section 3.7.2.3; 42; 48],4 that is C SZ r;s ðt; x ¼ 20 kmÞ ¼ f

dilute

Z

t

0

SZ

_ UZ m r;s ðtτÞ

dC^ r;s ðτ; x ¼ 20 kmÞ _ step dt m

dτ

ð19Þ

where the two primary inputs for the convolution method are (1) _ UZ m dependent mass flux entering the SZ r;s ðtÞ, which is the time SZ from M UZtrans, and (2) C^ r;s ðt; x ¼ 20 kmÞ, which is the concentration for radionuclide r at the end of the stream tube s from a unit step _ step . mass flux m YMP adjusted the concentration in the SZ by an estimate of lateral dispersion in the SZ [18, vol. 3 3.7.2.3, Section 5.7.3, Figs. 411 and 4-19] using the following algorithm. The total concentration at the accessible environment (xae ¼20 km) at each time step was (a) the sum of the concentrations in each stream tube when the sampled transverse dilution factor (fdilute), which had been defined to approximate transverse dispersion for the 1-D formulation, was large or (b) the maximum in any stream tube when fdilute was small, that is

C SZ r ðt; x ¼ 20 kmÞ ¼

8 6 > max < ∑ C SZ C SZ;r;t ðt; xÞ=f dilute r;t ðt; xÞ if greater than t¼1

> : max C

SZ;r;t ðt; xÞ

otherwise ð20Þ

6.4. Biosphere model in PA–VA For the first time, uncertainty was incorporated into the BDCF biological dose conversion factor f U;r;ℓ for PA–VA and became an important parameter [11, Table 2]. For the receptor, PA–VA used an Amargosa Valley resident whose lifestyle and dietary habits in consuming locally grown foods matched the average of the survey data for the area completed in June 1997 [18, vol. 3, Section 3.8.1; 52]; however, the dietary habits of a hypothetical resident farmer and subsistence farmer were considered in a sensitivity analysis, similar to the analysis in 1991 by Pacific Northwest National Laboratory (PNNL) [31]. BDCF The f U;r;ℓ included three major pathways to the resident: (1) inhalation of contaminated soil; (2) external exposure from (a) contaminated soil on the ground, (b) submersion in suspended dust while outdoors, and (c) immersion in contaminated water; and (3) ingestion of (a) contaminated drinking water, (b) contaminated soil on garden crops, and several products grown with contaminated water: (c) leafy vegetables grown, (d) other types of garden crops, (e) meat from livestock only fed local crops (mostly alfalfa), (f) poultry meat, and (g) dairy products from BDCF livestock. Ingestion of drinking water contributed most to f U;r;ℓ but ingestion of leafy vegetables was also important. BDCF The f U;r;ℓ depends somewhat on the climate in that irrigation needs are reduced in wetter climates, different food crops can be grown, and drinking water consumption is less. Although time was not available to incorporate changes in crop consumption, the reduction in irrigation needs was included. Yet, the influence was minor because (1) drinking water consumption was fixed by the EPA and NRC regulations at 2 L/d (0.73 m3/yr) [3], and (2) the increase in precipitation was primarily in the winter [18, vol. 3, Fig. 3-80]. Hence, only the arid climate values were used in PA–VA. BDCF Variation of f U;r;ℓ ðwðtÞÞ with climate was not considered for PA-SR but was reintroduced for PA-LA. PA–VA used GENII-S [18,53], a modification of GENII develBDCF oped by PNNL, to determine f U;r;ℓ ðwðtÞÞ. The WIPP Project had also used GENII-S for dose calculations reported in the WIPP environmental impact statement (EIS) [51]. Conceptually, M Bio could have been used directly within the RIP stochastic simulation. However, for PA–VA and thereafter, a distribution BDCF gðf U;r;ℓ ðwðtÞÞ) was developed using a separate stochastic evaluation of M Bio (130 LHS samples DVi ðtÞ were used for PA–VA and by BDCF PA–LA, 1000 samples) since the influence of f U;r;ℓ ðwðtÞÞ on dose BDCF was linear (e.g., Eq. (10)). The probabilistic output of f U;r;ℓ ðwðtÞÞ for the 9 radionuclides r transported for the undisturbed and early container failure scenario (AU+EF) was fit to 9 lognormal distributions. During the simulations for PA–VA within RIP, the distributions were perfectly correlated so that all radioisotopes BDCF had high (or low) values of f U;r;ℓ ðwðtÞÞ. In Eq. (11), the concentration was calculated directly for PA–VA. However for comparison with other PAs, the maximum range for Q indv was between 2.7  104 and 4  107 m3/yr assuming VA indv Q V A ðwÞ≈fdilute Q rep ðwÞ where the dilution factor (fdilute) varied between 1 and 100, as noted earlier for M SZ, and Q rep ðwÞ varied between the discharge through the repository for arid and superpluvial climate conditions (i.e., Q rep ðaridÞ¼ 2.7  104 and Q rep ðSPÞ ¼4  105 m3/yr [18, vol. 3, Table 3-21]).

dilute

where max C SZ;r;t ðt; xÞ=f is the maximum undiluted concentration in any stream tube t. The fdilute ranged between 1 and 100 [18, vol. 3, Table 3-20], as specified by the SZEE, and was an important parameter for PA–VA [11, Table 2]. 4 The PA for the Waste Isolation Pilot Plant (WIPP) had adopted the convolution method for evaluating transport of radionuclides in the overlying Culebra somewhat earlier in 1996 for the compliance analysis [51, Fig. 15].

7. Transport modeling for PA-SR In late 2000, YMP completed PA-SR to inform the decision of the Secretary of Energy and President concerning the YM site for a repository [3, Table 2; 19]. A more concerted effort was made to describe the underlying models of the PA. The expected total dose SR D ðtÞ included the contribution of the undisturbed scenario class

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with seismic failure of cladding (AU+SGclad), and, for the first time since PA-93, igneous dike intrusive releases (AVE, and AVI). Per the new EPA radiation protection standards, 40 CFR 197, the consequence of the human intrusion scenario was evaluated but its probability was not, and, thus, the expected dose was not calculated SR nor added to D ðtÞ. The dose expectation DUþSGclad ðtÞ for to106 yr at a 20-km boundary from 23 radioisotopes r from 300 samples ℓ of the numerous epistemic parameters eeℓ was calculated as [7, Eq. 20] SR

DUþSGclad ðtÞ ¼

nLHS ¼ 300 nrU ¼ 23 BDCF U f U;r;ℓ ∑ ∑ indv nLHS ℓ¼1 r ¼ 1 Q SR;ℓ U

1

R UþSGclad;r;ℓ ðt; eeℓ Þjxae

SR

¼ 20 km

ð21Þ

199

the prevailing faulting. For propagating uncertainty, the 2 alternative models of anisotropy were assumed to be equally probable. The 3 values of groundwater flow were (a) the original calibrated flow field for current arid conditions, and (b) 2 additional flow fields determined by simultaneously decreasing or increasing all strata permeability and boundary conditions fluxes (from the regional SZ model) by a factor of 10 [57, Section 3.8.1.3]. This approach maintained the calibration since it is the relative values of permeability that are calibrated not the absolute values for steady-state flow. For propagating uncertainty, the assigned probability of the groundwater flow for SZ current arid conditions was 0.52 for qSZ arid (x), 0.24 for 0.1qarid (x), and SZ 10qarid (x), as determined from the distribution provided by the SZEE panel for PA–VA.

7.1. UZ transport model in PA-SR

7.3. SZ transport model in PA-SR

For PA-SR, 19 dissolved radionuclides (with 4 more radionuclides evaluated by secular equilibrium) and 6 irreversible colloidal species were transported in 9 UZ flow fields from M UZflow. Besides the added radionuclides, several small changes were made in the transport calculations. Four output regions at the UZ-SZ interface were defined for PA-SR and PA-LA (versus the 6 in PA– _ waste VA), but rather than evenly distributing m ðtÞ over an entire z;r output region, a release point in each region u was randomly assigned, which required two coordinates for a total of 8 parameters. Using one release point eliminated the initial dilution that had occurred in PA–VA when spreading the mass from the UZ over the 6 large areas. Also, a fluctuating water table rise was not modeled but instead set at 850 m above sea level under the repository (120 m above the current water elevation of 730 m at the repository) for the monsoon and glacial transition climate periods for PA-SR (and PA-LA). In addition, not all colloids were excluded from the matrix in the UZ as in PA–VA; rather, a size distribution was sampled, which permitted partial transport in the UZ through the matrix in PA-SR. However colloid transport was still excluded in the dual porosity formulation for the SZ. Furthermore, the radionuclides irreversibly attached to colloids could not diffuse into the SZ matrix and, thus, be delayed beyond that caused by retardation (i.e., Eq. (17)) [54, Table 6-28].

For SZ transport in PA-SR, a 3-D dual-porosity model without radionuclide decay was used (along with a 1-D dual-porosity model) (Table 1) [58]:

7.2. SZ flow model in PA-SR Several improvements were made to the 3-D, single-porosity model based on FEHM v2.0 used in PA-SR to calibrate one steadystate SZ flow field. First, the modeled area increased to 30 by 45 km (versus 20 by 36 km in PA–VA) and the depth increased to 3950 m ( 2750 to 1200 m above sea level) to match the depth of the USGS regional flow model, and included 19 homogeneous hydrologic units [55, Table 5; 56]. The number of grid layers increased to 38 with vertical spacing varying between 10 and 550 m. A 500 by 500 m square grid was used for the 30 by 45 km area for a total of  143,000 grid blocks. Because of the increased modeled depth, the increase of water temperature with depth was estimated to include changes in viscosity and density in PA-SR (and PA–LA); however, the analysis remained isothermal. The SZ flow model was calibrated using 115 well head measurements [6; 55, Section 6.4, Fig. 6, Table 7]. To include flow uncertainty in PA-SR, 6 flow fields for the current climate were developed based on 2 conceptual models of anisotropic hydraulic conductivity and 3 values of groundwater flow. The 2 models of anisotropy were (1) the anisotropy of the calibrated model, which is horizontally isotropic but vertically anisotropic (i.e., kxyiso ¼kx ¼ky ¼ 10kz, where x is west to east and y is south to north), and (2) a fully anisotropic model (i.e., kx ¼kxyiso/ 2.24 and ky ¼2.24kxyiso, which results in horizontal anisotropy) for y:x of 5:1 as NRC estimated from C-well tests [6; 57, Section 3.8.11]. The higher permeability in the north–south (y) direction matched

f disp f rtrd ∇ðϕef Df f ;r ∇C f f ;r qf f C f f ;r Þ ¼ ϕef Rf f ;r ff ff

  ∂ f disp ∂C m;r f rtrd ∂C m;r ¼ ϕef ϕef m Dm;r m Rm;r ′ ′ ∂zm ∂zm ∂t

∂C f f ;r _ UZ m r Ψ r ∂t

ð22Þ ð23Þ

where Ψr ¼

SZef f ϕtotal m ϕf SZ bf f

Ddisp m;r

∂C m;r at zm ¼ BSZ ff ∂zm

ð24Þ

and where BSZ f f is the half block width between flowing fractures, SZ _ UZ 2bf f is the flowing fracture aperture, and m is the radionuclide r source to the SZ regions u calculated by the M UZtrans module (4 regions u in PA-SR and PA-LA versus 6 in PA–VA). An important distinction was made in the SZ between the general fracture network with a small fracture spacing and the flowing fractures with a much larger fracture spacing 2BSZ f f þ 2bf f as measured in wells with a flow meter [6,59] and later an important parameter in PA-LA [11, Table 2]. The M SZ generated breakthrough curves at 20 km for 8 groups of radionuclides: (1-5) one group each for 5 radioelements 14C, 99 Tc, 129I, 237Np, U (238U, 236U, 234U); (6) a group for radionuclides that are irreversibly sorbed on colloids (i.e., 241Amirr, 243Amirr, 238 Puirr, 239Puirr, 240Puirr, 242Puirr); (7) a group for radionuclides that are strongly sorbed reversibly (241Am, 243Am, 238Pu, 239Pu, 240 Pu, 242Pu); and (8) a group for the igneous intrusion scenario that included radionuclides moderately sorbed reversibly (90Sr, 137 Cs, 231Pa). The 3200 breakthrough curves for the 8 radionuclide groups, 4 source regions at the interface between the UZ and SZ, and 100 PA-SR simulations were evaluated using the streamline particle tracking feature of FEHM v2.1 by counting the arrival of 1000 particles at the 20-km boundary. The streamline particle tracking algorithm for the SZ included 3-D hydrodynamic dispersion [36] and was linked to an analytical solution for matrix diffusion in fractured volcanic rock units, which provided a more realistic conceptualization for transport than previous models [60,61]. For the monsoon and glacial transition climates in the first 104 yr in the 3-D model, the breakthrough curves were scaled by a factor of 2.7 and 3.9, respectively (equivalent to increasing the flow velocity at all points by the scale factors such that flow paths were not altered) [57, Table 3.8-1]. The factor of 2.7 derives from the ratio of mean UZ infiltration in the monsoon climate to the mean infiltration in the current climate, averaged over the entire UZ flow domain, but is approximately the ratio of the mean infiltration averaged over the repository area. The factor of 3.9 derives from the observed increase in flow when modeling fully glacial conditions some 250,000 yr in

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the future by the USGS for the PA–VA, but is also approximately the ratio of the means over the repository domain [6; 8, Fig. 5]. The same approach was used for PA-LA but the monsoon climate factor was reduced to 1.9 [2, Table 6.3.10-3]. Besides the new hydrogeologic data used for calibrating the fluid flow, simulation of SZ transport was improved by using [62] (a) geostatistical and heterogeneity analysis to scale up from laboratory to model values for sorption coefficients (KdSZ) for some radionuclides, and (b) field and laboratory experiments to derive parameters for aqueous and colloid-facilitated transport. For example, some sorption of 99Tc and 129I was assumed to occur SZ SZ on the alluvium (KdTc;allv ; KdI;allv ) based on experiments, which was new in PA-SR [57, Table 3.8.3]. Also, a colloidal partition coefficient (Kc), as used in Eq. (16), was evaluated in PA-SR and PA-LA rather than assigned directly as in PA–VA [47]: coll

Kce ¼ Kde C coll gw

ð25Þ

coll

where Kde was the sorption coefficient on the colloidal particle and C coll gw was the colloidal concentration in the groundwater and also used in the waste form module (M Waste). The C coll gw was fixed at 0.02 kg/L for PA-SR, but it was uncertain, evaluated in M Waste [10], and an important parameter in PA-LA [11, Table 2]. Because of the importance of the influence of alluvium sorption and because of the limited well data between 10 and 20 km from the repository, the location of the contact between volcanic units and the alluvium was uncertain in PASR and PA-LA. An east–west and north–south coordinate was sampled in each realization for the SZ site-scale flow in PA-SR and PA-LA. A 1-D, dual-porosity transport model was also constructed using a Laplace transform analytic solution for advection dominated mass transport that had been implemented in the stochastic simulator Goldsims adopted for PA-SR, which had evolved from RIP (Table 1). The purpose of the analytic model was to determine the concentration of 10 radionuclides, which primarily resulted from decay during transport, for use in evaluating the groundwater protection requirements in 40 CFR 197 [3]. Although not included in the 3-D SZ transport model, radioactive ingrowth was included in the EBS, UZ, and in the 1-D SZ transport models. Four decay chains consisting of 19 transported radionuclides were represented for the calculations carried out to 106 yr as follows: Neptunium series: 241Am-237Np233 243 U-229Th; Actinium series Am-239Pu-235U-231Pa-227Ac where 227Ac was not transported but its concentration established by assuming secular equilibrium with 231Pa; Thorium series: 240Pu-236U-232Th-228Ra where 228Ra was not transported but its concentration evaluated by secular equilibrium; and Uranium series: 242

Pu-238 U 238

Pu

) 234

U-

230

Th-226 Ra-

210

7.4. Biosphere model in PA-SR A biosphere model, again based on GENII-S, was used to BCDF evaluate distributions of f U;r;ℓ in PA-SR. The primary changes from PA–VA were (1) consideration of buildup of radionuclides in the soil from 6 irrigation periods prior to exposure and wind erosion of the soil, (2) addition of more radionuclides for AU+SGclad (23 radionuclides for the 106 yr simulations versus 9 in PA–VA), and (3) ingestion of fish from a fish farm using contaminated water. Again drinking water consumption and consumption of leafy BCDF vegetables contributed most to f U;r;ℓ for most actinides but consumption of fish was important for more mobile 14C activation product and 137Cs fission product [57, Section 3.9; 63, Table 4]. Based on EPA and NRC guidance in 40 CFR 197 and 10 CFR 63, PA-SR and PA-LA assumed the entire contaminant plume was captured by a well. For PA-SR, the influence of the withdrawal well on the biosphere was defined by NRC in the draft 10 CFR 63 [64, Section 63.115]. In the draft, NRC specified constraints on the withdrawal of contaminated water from the aquifer (i.e., farming community of  100 individuals on 15 to 25 farms  20 km from the repository in an arid or future semiarid climate) but left details to be provided by YMP (e.g., average consumptive use in a semiarid climate). YMP specified that the 15 to 25 farms (nfarm uniformly distributed) consumed between 7.3  104 and 1.7  105 m3/yr of groundwater per farm (Qfarm uniformly distributed) [54, Section 6.3.8.2]; thus, the maximum range for the indv 6 6 3 dilution factor Q indv SR;ℓ was 1.1  10 oQ SR;ℓ o 4.2  10 m /yr where f arm f arm indv Q SR;ℓ ¼ nℓ Q ℓ . The uncertainty in Qfarm was an important parameter for PA-SR [11, Table 2].

8. Transport modeling for PA-LA A compliance analysis, seeking an NRC license to construct the repository, was started after Congressional authorization in July 2002 [3]. Two interim PAs were completed in 2004 and 2005. PALA was completed by March for the June 2008 SAR/LA. For PA-LA, the major emphasis was on a more thorough examination of potential doses from seismic ground motion, fault displacement, early drip shield failure, and early container failure. The consequence of seismic ground motion is closely dependent upon the state of the repository at the time of the seismic event and so it was not possible to separate the undisturbed scenario class from the seismic ground motion (except for the first 104 yr when containers were mostly intact). The expected total dose for the undisturbed scenario class (including seismic ground motion) DUþSG ðtÞ was calculated for 104 o to106 yr as [7, Eq. 25] LA

DUþSG ðtÞ ¼

1 nLHS U

nLHS ¼ 300 nrU ¼ 32 BDCF U f U;r;ℓ ðwðtÞÞ SZ R UþSG;r;ℓ ðt; eeℓ Þjxae ¼ 18 km ∑ ∑ LA Q indv ℓ¼1 r¼1 LA;ℓ

ð26Þ

Pb

where both 226Ra and 210Pb concentrations were evaluated by secular equilibrium. The 3 other radionuclides (out of 19) transported were 14C, 99Tc, and 129I in PA-SR [54, Table 6-28]. The SZ 1-D transport model had 5 pipe segments, but only the first 3 segments were necessary to reach the 20-km accessible boundary (i.e., 0 to 5 km, 5 km to uncertain alluvium boundary, and alluvium boundary to accessible boundary). Similar to PA–VA, the 1-D pathway was determined from particle traces in the 3-D flow model. The transport pathway in the alluvium in the 1-D simulation was sampled from a uniform distribution between 1 and 8 km (values that approximated the range in the 3-D simulation).

8.1. UZ transport model in PA-LA For PA-LA, transport of radionuclide mass in 5 percolation zones was modeled in 16 UZ flow fields (qperc ðt; xÞ) produced by M UZflow. In M UZtrans (based on FEHM v2.24-01 [65]), the RTTF method was modified to better represent the exchange of radionuclide mass between the factures and matrix, which had the effect of improving the numerical representation and removing some conservatism introduced in the previous version [39,66,67]. Furthermore, the number of containers that had breached was tracked and used to assign releases at nodes within each

R.P. Rechard et al. / Reliability Engineering and System Safety 122 (2014) 189–206

percolation zone z to more accurately simulate the release distribution as containers failed. If one container had failed in a percolation zone z at time t the mass release was randomly placed in one node within z. If two containers had failed at t, the mass release was spread between two randomly selected nodes within z. At t+Δt, the number of failed containers was used to define the release at other randomly selected nodes (chosen without replacement), and so on until all the nodes were used, after which the mass release was spread over all nodes [2, Section 6.3.9.3]. Among the transport characteristics varied in PA-LA were (1) fracture porosity and fracture frequency to calculate aperUZ ture (2bf ;tuf f ) for 9 categories of tuff (e.g.,CHn1 to CHn6 of Fig. 2 [2, Tables 6.3.9-6 and 6.3.9-7]); and (2) fracture-matrix coupling UZ m 5 m exponent γ ftuf . The uncertainty of 2bf ;tuf f and γ ftuf had a minor f f influence on dose uncertainty in PA-LA, as shown in other papers of this special issue. The UZ transport parameters had not been important since early PAs (i.e., retardation in UZ, RUZrtrd , for PA–EA when substantial sorption on zeolitics below f ;e the repository was thought possible; retardation of gaseous 14C when using a cumulative release performance measure for PA91; and dispersivity, αUZ m , for PA-93) [11, Table 2]. The reason for the lack of sensitivity of dose to uncertainties in UZ transport parameters is because strongly sorbing radionuclides are effectively retarded in the UZ and weakly or non-sorbing radionuclides reach the water table relatively quickly, regardless of the assigned uncertainty [41]. 8.2. SZ flow and transport models in PA-LA PA-LA used the same basic modeling framework as PA-SR to calculate the release at a ~18 km boundary for the combined undisturbed and seismic ground motion scenario class e (R SZ ¼ 18 km ). This framework consisted of (1) a 3-D UþSG;r;ℓ ðt; eℓ Þjxae LA single-porosity flow model to calibrate one flow field, (2) a 3-D dual-porosity transport model to develop breakthrough curves for the convolution method (both based on FEHM v2.24-01) [68], and (3) a 1-D dual-porosity transport model to evaluate concentrations of daughter products from radioactive decay (available in GoldSim) (Table 1). For the 3-D flow model, the number of hydrologic units increased from 19 to 23 and areal grid spacing was reduced to 250 m by 250 m from 500 m by 500 m [48, Table 6-9[a]; 69]. Also, the SZ flow model was recalibrated from 161 potentiometric data that included the water levels from 115 wells used in PA-SR and potentiometric data from wells drilled for the Nye County Early Warning Drilling Program (NC-EWDP) [6] (Fig. 1). Based on the data, the calibrated permeability of the Bullfrog hydrologic unit (BFw of Fig. 2 or unit 15 of Fig. 3) was reduced from 1.5  10  11 m2 in PA-SR to 5.2  10  14 m2 in PA-LA. The transport paths dipped into possibly lower oxygenated layers in the first 5 km, of the Tram and Prow Pass units (Fig. 8, Table 2). The uncertainty in anisotropy of horizontal permeability and groundwater flow was sampled directly for PA-LA for the uncertain transport parameters rather than develop 6 separate flow models as in PA-SR. The horizontal anisotropy of permeability for the ratio of ky:kx (where x is west to east and y is south to north) varied between 0.05 and 20 but with 50% of the distribution between 1 and 5; thus, the sampled values were similar to the discrete values of 1 and 5 used for PA-SR. On average, the Darcy velocity (qSZ f ) from the repository to the 5-km and 18-km accessible boundary was 0.36 m/yr and 0.55 m/yr, respectively and less than the 0.6 m/yr constraint by the SZEE Panel [6, Section 2.6.6]. UZ

m 5 Although 2bf ;tuf f was fixed and γ ftuf ðxÞ calibrated for M UZflow, M UZtrans sampled f both values to better incorporate uncertainty. A major inconsistency does not occur m with M UZflow, however, since the 16 UZ flow fields are less sensitive to γ ftuf ðxÞ and f UZ not sensitive to 2bf ;tuf f [2, p. 6.3.9-8 and Section 6.3.9.4.1].

201

The average flow distance to the ~18-km accessible boundary was 23 km (Fig. 9) [23, p. 8-6]. The uncertainty in groundwater flow was expressed by a distribution that varied between 0.11qSZ f ;arid (x) and 8.9qSZ f ;arid (x), a range that was slightly reduced from the discrete values of 0.1 and 10 used for PA-SR. Besides qSZ f :arid [11, Table 2], two other parameters moderately important for SZ transport were colloidal groundwater concentration (C coll gw ) and SZ flowing fracture spacing (2BSZ þ 2b ) where the parameter disff ff SZ tribution for 2BSZ f f þ 2bf f developed for PA-SR was used again for PA-LA [48,59]. The 12 radionuclide groups of breakthrough curves produced at the  18 km boundary (rather than 8 as in PA-SR) [2, Table 6.3.7-6] were (1) a group for 5 nonsorbing radionuclides (14 C, 99 Tc, 129 I, 36 Cl—added for PA-LA); (2-6) one group each for 5 other radioelements 79 Se (added), 90 Sr (added), 226 Ra (added), 237 Np, U (238 U, 236 U, 234 U); (7-10) 4 groups for radionuclides that are reversibly sorbed 126 Sn (added), (135 Cs,137 Cs) (added), (241Am, 243 Am, 232 Th, 231Pa), (238 Pu, 239 Pu, 240 Pu, 242 Pu); (11) a group for Am and Pu isotopes that are irreversibly sorbed on colloids (i.e., 241Amirr, 243 Amirr , 238 Pu irr, 239 Pu irr, 240 Pu irr, 242Pu irr ); and (12) an added group for Pu and Am isotopes that are irreversibly sorbed on colloids but not retarded (i.e., a fast fraction). For PA–LA, colloids with irreversibly engulfed radionuclides could attach and detach from tuff and alluvium, based on a kinetic model. A total of 9600 breakthrough curves were produced, based on 12 radionuclide groups, 4 source regions at the UZ-SZ interface, and 200 samples of 44 uncertain flow and transport parameters (e.g., parameters for anisotropy and flow at the upper boundary of the SZ site-scale model) [2, p. 6.3.10-5]. The median transport times in SZ along 23-km pathway for nonsorbing radionuclides (group 1) was 620 yr; for 90Sr and 226 Ra (group 3 and 4) 4 105 yr; for 237Np (group 5), 17100 yr; for U (group 6), 23300 yr; for reversibly sorbed Cs, Am, Th, Pa, and Pu isotopes (groups 7-10) 4 105 yr; for irreversibly sorbed Am and Pu isotopes (group 11), 19400 yr; and for the irreversibly but not sorbed (group 12 fast fraction), 310 yr [48, Table 6-16]. Recall that the transport time for a nonsorbing tracer in SZ was between 200 and 2000 yr to 10 km boundary in PA–EA; mean of 1200 yr in PA-91 to 5-km boundary; and mean of 600 yr in BFw layer in PA-93 to 5-km boundary.

8.3. Biosphere model in PA-LA For PA-LA, the receptor was a reasonably maximally exposed individual (REMI), as defined by NRC in the 2005 draft of 10 CFR 63 [70], that (a) Lives in the accessible environment above the highest concentration of radionuclides in the plume of contamination; (b) Has a diet and living style representative of the people who now reside in the Town of Amargosa Valley, Nevada. DOE must use projections based upon surveys of the people residing in the Town of Amargosa Valley, Nevada, to determine their current diets and living styles and use the mean values of these factors in the assessments conducted for Sections 63.311 and 63.321; (c) Uses well water with average concentrations of radionuclides based on an annual water demand of 3000 acre-feet; (d) Drinks 2 liters of water per day from wells drilled into the ground water at the location specified in paragraph (a) of this section; and (e) Is an adult with metabolic and physiological considerations consistent with present knowledge of adults. Hence, several different types of hypothetical residents were no longer considered as in PA–VA. Furthermore, Q indv was fixed at

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Fig. 8. Cross-sections of stratigraphy along flow path for PA-LA with units identified in Table 2 [23, Figs. 6-8 and 6-9]: (a) north–south cross-section at UTM 552500; and (b) east–west cross-section at UTM 407600.

3.7  106 m3/yr (3000 acre-ft/yr or 40% greater than PA-SR mean) rather than varied. EPA based the volume on the estimated water demands of two alfalfa farms, some industrial water use, and some municipal water wells near Amargosa Valley [71, p. 32113]. A new biosphere model, the Environmental Radiation Model for Yucca Mountain, Nevada (ERMYN), was constructed for PA-LA BCDF to calculate f j;r;ℓ ðwðtÞÞ [72]. ERMYN was based on GoldSim, the stochastic simulator adopted earlier for PA-SR. NRC, through acceptance criteria in their YM Review Plan, and the International Atomic Energy Agency (IAEA) team reviewing the biosphere model in PA-SR [73], recommended changes, which YMP thought best implemented in a new model rather than modifying GENII-S. The vast majority of equations used to model transport between the numerous compartments of the biosphere were based on GENII-S. The primary additions were [72, Table 6.7-2] (1) implementation of long-term irrigation directly rather than using multiple irrigation periods as in PA-SR; (2) consideration of overhead irrigation, irrigation frequency, and crop type rather than using a single factor for all crop types and irrigation methods; (3) directly incorporating radionuclide removal from soil through leaching and soil erosion (such as volcanic ash) rather than using an external calculation as in PA-SR; (4) averaging human activity

based on time spent active outdoors, inactive outdoors, active indoors, asleep indoors, and time away from the contaminated area; (5) adding an exposure pathway from use of evaporative coolers; (6) considering contamination of animal products by soil ingestion (not just water and feed); (7) adding pathways for 14C exposure that included direct external exposure, inhalation, and soil ingestion, and indirect exposure through use by plants during photosynthesis rather than just root uptake as in GENII-S; (8) adding radon exposure and using various levels of human activity to calculate inhalation and external exposure and indoor radon exposure; (9) updating dose conversion factors for inhalation and ingestion, consistent with International Commission on Radioactive Protection (ICRP) Publications 60 and 72 and Federal Guidance Report 13, as required by the 2005 draft 40 CFR 197 [74, Appendix A]; (10) considering volcanic ash deposition on uncultivated land, which could be resuspended; and (11) automatically combining 3 pathway/time periods for exposure from volcanic ash (external and ingestion, long-term inhalation, and short-term inhalation) rather than conducting separate calculations of the pathway as in PA-SR. BDCF BDCF The uncertainty in f U;Tc99 ðaridÞ and f U;Np237 ðaridÞ for the current modern interglacial climate (w  arid) was important in

R.P. Rechard et al. / Reliability Engineering and System Safety 122 (2014) 189–206

203

Table 2 Units and calibrated permeability in site-scale SZ flow model for PA-SR and PA-LA [23, Tables 6-2 and 6-9]. ID Geologic/hydrologic unit in PA-LA

Permeability (m2)a

Description

PA-LA 2 3 4

Intrusive confiningb Crystalline confining (granites) Lower clastic confining (same)

5 6

Lower carbonate aquifer (same) Upper clastic confining (same)

7

Upper carbonate aquifer (same)

8

Lower clastic confining thrust

9

Lower carbonate aquifer thrust (same)

11 Lower Volcanic/sedimentary (undifferentiated valley fill) 12 Older Volcanic (Lower Volcanic confining) 14 Crater flat tram aquifer (same) 15 Crater Flat bullfrog confining (same) 16 Crater flat prow pass aquifer (same) 17 Wahmonie volcanic 18 Calico hills volcanic (upper volcanic confining) 19 Paintbrush volcanic aquifer (upper volcanic aquifer) 20 Timber Mountain volcanic aquifer 21 Upper volcanic/sedimentary (valley  fill aquifer) 23 Lava flow (same) 24 Limestone aquifer (Cenozoic limestone) 26 Older alluvial aquifer (valley-fill aquifer) 27 Young alluvial confining (valley-fill confining) 28 Young alluvial aquifer (valley-fill aquifer) a b

All intrusive rocks, regardless of age Middle Proterozoic metamorphic and igneous rocks Late proterozoic through Lower Cambrian primarily siliciclastic rocks including the Pahrump group and noonday dolomite, Cambrian through Devonian predominantly carbonate rocks Upper Devonian to Mississippian Eleana Formation (upper 2/3rds argillite, lower 1/3 quartzite) and Chainman shale Paleozoic carbonate rocks (unit only used where Upper Clastic Confining unit exists otherwise lumped with lower carbonate aquifer) Late Proterozoic through Lower Cambrian primarily siliciclastic rocks including the Pahrump Group and Noonday dolomite Cambrian through Devonian carbonate rocks (separate group necessary for modeling thrusted strata) Cenozoic volcanic and sedimentary rocks, where named Cenozoic Volcanic rocks exist, this unit underlies them Oligocene to Miocene Miocene Miocene Miocene Miocene Miocene

Crater Flat Group, Tram Tuff Crater Flat Group, Bullfrog Tuff Crater Flat Group, Prow Pass Tuff Wahomonie and Salyer Formations Calico Hills Formation

PA-SR

9.9  10  17 1.0  10  16 2.0  10  16 9.7  10  17 1.0  10  16 9.7  10  15 1.0  10  14 9.8  10  16 1.0  10  16 1.1  10  12 4.1  10  14 5.6  10  12 5.6  10  12 1.0  10  14 1.1  10  11 5.0  10  15 9.8  10  16 2.0  10  15 9.4  10  13 5.2  10  14 3.1  10  12 9.8  10  14 2.4  10  13

2.4  10  13 1.5  10  11 8.0  10  12 5.0  10  14

Miocene Paintbrush Group

6.5  10  14 8.0  10  14

Miocene Thirsty Canyon and Timber Mountain Groups Cenozoic volcanic and sedimentary rocks

9.5  10  14 8.7  10  13

Cenozoic basalt cones and flows and surface outcrops of rhyolite-lava flow Cenozoic limestone Pliocene to Holocene coarse-grained basin-fill deposits Pliocene to Holocene playa and fine-grained basin-fill deposits

8.9  10  14 1.0  10  12 9.8  10  14 1.0  10  12 1.5  10  13 5.0  10  12 9.9  10  15

Pliocene to Holocene coarse-grained basin-fill deposits

9.8  10  13

Permeability under and south of the repository, not permeability in the thermally altered zone north of the repository. The terms confining and aquifer in unit names are used relative to nearby strata.

PA-LA for the combined scenario classes including seismic and BDCF igneous disruptive events [11, Table 2]. For f U;Tc99 ðaridÞ, water consumption accounted for nearly half of the value, and the remainder of the value was from consumption of locally produced food (milk, leafy vegetables and eggs), similar to PA–VA and PA-SR. Because water consumption was fixed by the EPA radiation protection standards at 2 L/d [3,74], the uncertainty in BDCF f U;Tc99 ðaridÞ was due to the uncertainty in radionuclide concentration on locally produced food. Similarly, water consumption BDCF accounted for nearly half of the value for f U;Np237 ðaridÞ. Unlike previous PAs, however, inhalation was the second most important exposure pathway and caused from re-suspended soil while active outdoors, a pathway improved for PA-LA, and evaporative coolers, a pathway added for PA-LA [75, Fig. 6.2-7, Tables 6.2.1 and 6.2.3].

9. Summary One dimensional UZ and SZ transport without lateral dispersion was solved for PA–EA but progressed to a dual-porosity transport formulation for the UZ and a 2-D flow model for the SZ in PA-91 (Table 1). In response to the proposed use of a dose health indicator, PA-93 improved SZ flow modeling by progressing to a 3-D flow model. By PA–VA and thereafter, an important advancement in particle tracking (i.e., RTTF) was used to solve the transport equations in the 3-D flow fields of

the UZ. In the SZ, particle tracking was used to develop breakthrough curves for a unit step function for several groups of radionuclide. The convolution method, a flexible technique that was also applied at WIPP [51, Fig. 15], was then used to transport time varying concentrations of radionuclides injected from the UZ. Furthermore, the extent of the SZ was greatly expanded from 5 km to 20 km in the Amargosa valley for the dose calculations in PA–VA, in anticipation of the new site-specific EPA radiation protection standards. By PA-LA, characterization of the SZ from additional wells allowed a detailed description of the flow path in the SZ (Fig. 8) in comparison to the simplistic flow paths used in early PAs (Figs. 5–7). Also, a biosphere model was developed to determine individual dose at a ~18 km boundary from several exposure pathways in addition to consumption of drinking water. For PA-SR and PA-LA, a 1-D transport model with decay was used to determine concentrations of daughter products to compare with groundwater protection requirements specified by EPA in 40 CFR 197 [3]. For PA-LA, the calculation of the biological dose conversion factors was determined using a new code to conform to the revised method of evaluating dose, as specified by EPA and NRC. Uncertainties in SZ and UZ flow (e.g., qSZ f ) were important for most PAs. Furthermore, uncertainties in two additional parameters were moderately important for UZ groundwater transport in early PAs: general radionuclide retardation (RUZrtrd ) for f ;e PA–EA, and dispersivity (αUZ m ) for PA-93. Uncertainties in three

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Fig. 9. Potential radionuclide pathway from YM repository [1, Fig. 2.3.9-14]. Although sufficient to carry some radionuclides [8, Fig. 5], the small volume of percolation at Yucca Mountain caused little noticeable recharge to the SZ flow system on a site-scale, with boundary conditions set by the USGS regional flow model.

parameters were important in SZ transport: U and Np retardaSZ SZ tion (KdU and KdNp ) for PA-93, and groundwater colloidal coll concentration (C gw ) and the spacing of flowing fractures SZ (2BSZ f f þ 2bf f ) for PA-LA. For dose calculations, uncertainty in dilution in the SZ was important: hSZwrep for PA-93, fdilute for PA– VA, and Qfarm for PA-SR. Also, uncertainties in dose conversion BDCF factors were important in later PAs (f r for PA–VA, and BDCF BDCF f Np237 ðaridÞ and f Tc99 ðaridÞ for PA-LA).

Acknowledgments Sandia National Laboratories (SNL) is a multi-program laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the DOE National Nuclear Security Administration under contract DE-AC04-94AL85000. The authors wish to thank L.A. Connolly, SNL, for help with references, and S.K. Best, Raytheon, for illustration support. The

historical perspective and opinions presented are those of the authors and are not necessarily those held by reviewers, SNL, or DOE. As a historical perspective, the authors are reporting on the work of others; however, any interpretative errors of documentation are those of the authors alone. Each performance assessment discussed in this paper required numerous participants with expertise in many areas of science and technology. The most complete listing of these participants is made by examining the extensive reference list. However, many of the references are corporate documents without authors. Furthermore, the extensive time some scientists and engineers devoted to the analysis of fluid flow and transport in YMP and the handoff between persons as YMP transitioned through four study phases (site identification, feasibility analysis, suitability analysis, and compliance analysis [6, Table 1]) is more evident if acknowledge here in somewhat chronological order. These persons include G.E. Barr, SNL (SZ flow for PA-91 and PA-93); B.W. Arnold, SNL (groundwater travel time prior to 1995 [29], SZ flow and transport for

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PA–VA [42], PA-SR [40], and PA-LA [69,76]); B.A. Robinson, LANL (process modeling of UZ and SZ transport for PA–VA [38], PA-SR [41], and PA-LA [39]); J.E. Houseworth, LBNL (abstraction for UZ transport in PA–VA, PA-SR, and PA-LA); G.A. Zyvoloski, LANL (development of FEHM for use in PA–VA [35] and thereafter [65] and site-scale flow model for PA-SR [56]); S.P. Kuzio, SNL (SZ flow and transport PA–VA, PA-SR [40], and PA-LA [59]); S. James, SNL (SZ flow for PA-LA [23]), A. Meijer (PA–VA, PA-SR [58], and PA-LA [62]); S. Kelkar, LANL (PA-SR and PA-LA [62]); P.W. Reimus, LANL (PA-SR [58] and PA-LA); A.A. Eddebbarh, LANL (PA-SR [58] and PA-LA [68]); B. Lester (abstraction for PA-LA); A.J. Smith, Duke/Areva (biosphere transport module for PA–VA, PA-SR, and PA-LA [72]); D.W. Wu (development of ERMYN for PA-LA [72]); and M.A. Olszewska-Wasiolek, Areva (biosphere transport module for PA-LA [75]). Contributors to the experimental evaluation of transport are acknowledged in a companion paper on characterization of the natural barrier [6]. Because so many scientists and engineers were involved in evaluating radionuclide transport at YMP, the authors recognize that this list is unavoidably incomplete, and we apologize for omissions and oversights.

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