Kinetic Transport Models and Minimum Detection Limits of Atmospheric Particulate Resuspension Shaun Marshall 1, Charles Potter 2, David Medich 1 1 Worcester Polytechnic Institute, Worcester, MA 01609 2 Sandia National Laboratories, Albuquerque, NM 87185 NECHPS Annual Symposium Westford Regency Inn and Conference Center Westford, MA Wednesday, June 6, 2018 Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy s National Nuclear Security Administration under contract DE-NA-0003525. haun Marshall 1, Charles Potter 2, David Medich 1 ( 1 Worcester Polytechnic Kinetic Transport Institute, Models Worcester, and Minimum MA 01609 Detection 2 SandiaLimits National of Atmospheric Laboratories Particulate, Albuquerque, Resuspension NMWednesday, 87185 NECHPS June 6, Annual 2018 Symposium 1 / 16
Overview Inhalation dosimetry, resuspension factor observations and reassessment Particulate transport mechanisms, kinetic models, and rates of transfer Neutron activation analysis, detection limits, and experimental results Shaun Marshall 1, Charles Potter 2, David Medich 1 ( 1 Worcester Polytechnic Kinetic Transport Institute, Models Worcester, and Minimum MA 01609 Detection 2 SandiaLimits National of Atmospheric Laboratories Particulate, Albuquerque, Resuspension NMWednesday, 87185 NECHPS June 6, Annual 2018 Symposium 2 / 16
Inhalation dosimetry resuspension Many environmental pathways are available to radioactive particulates in accidental or continuous releases. Inhalation of resuspended radionuclides from contamination delivers a dose of radiation. Figure 1: Potential exposure pathways in a radionuclide release (NRC, 2016) Prediction of internal dose depends upon site-specific parameters and exposure time period. Shaun Marshall 1, Charles Potter 2, David Medich 1 ( 1 Worcester Polytechnic Kinetic Transport Institute, Models Worcester, and Minimum MA 01609 Detection 2 SandiaLimits National of Atmospheric Laboratories Particulate, Albuquerque, Resuspension NMWednesday, 87185 NECHPS June 6, Annual 2018 Symposium 3 / 16
Inhalation dosimetry - Resuspension factor Dose due to inhalation of some resuspended radionuclide : D inh = C D,inh f B KP, (1) C D,inh is the inhalation committed dose coefficient (Sv Bq 1 ), f B is the activity-averaged human breathing rate ( 0.92 m 3 h 1 ), KP is the resuspension parameter (Bq s m 3 ), which considers airborne concentration during time phase TP following deposition: KP = Dp e λt S f (t) dt, (2) TP Dp is the initial areal deposition (Bq m 2 ) λ is the radionuclide decay constant (s 1 ) S f (t) is the empirical resuspension factor (m 1 ) (FRMAC, 2015); simplified Shaun Marshall 1, Charles Potter 2, David Medich 1 ( 1 Worcester Polytechnic Kinetic Transport Institute, Models Worcester, and Minimum MA 01609 Detection 2 SandiaLimits National of Atmospheric Laboratories Particulate, Albuquerque, Resuspension NMWednesday, 87185 NECHPS June 6, Annual 2018 Symposium 4 / 16
Resuspension factor observations Airborne activity concentration measurements are taken periodically following known surface dispersal events: S f (t) = 1 t+ts t s t 1 A C air (x, y, z; r, t) dt A C surface(x, y, d; r, t) da [ Bq m 3 = m 1 Bq m 2 S f (t) is dependent upon particle radius r (generally taken as 1 µm). ] (3) Latest evaluation of historic dataset of observations produced exponential regression fit: S f (t) = (1.93 10 6 )e (4.514 10 7 )t +(1.71 10 8 )e (2.894 10 8 )t +10 9 (4) (Maxwell and Anspaugh, 2011) haun Marshall 1, Charles Potter 2, David Medich 1 ( 1 Worcester Polytechnic Kinetic Transport Institute, Models Worcester, and Minimum MA 01609 Detection 2 SandiaLimits National of Atmospheric Laboratories Particulate, Albuquerque, Resuspension NMWednesday, 87185 NECHPS June 6, Annual 2018 Symposium 5 / 16
Resuspension factor model reassessment Figure 2: Averaged resuspension factor observations, overlaid with recent resuspension factor models including author s previous work as indicated. (Marshall et al, 2018) haun Marshall 1, Charles Potter 2, David Medich 1 ( 1 Worcester Polytechnic Kinetic Transport Institute, Models Worcester, and Minimum MA 01609 Detection 2 SandiaLimits National of Atmospheric Laboratories Particulate, Albuquerque, Resuspension NMWednesday, 87185 NECHPS June 6, Annual 2018 Symposium 6 / 16
Particulate transport mechanisms Transfer between air (A), surface layer (S) and underground (G): k A k A S A k A S S k S G G k G (5) k S G Table 1: Kinetic rate constants for transport mechanisms (s 1, depends on particle size) Term k A k A S k A S k S G k S G k G Description Weathering rate; local removal via dispersion and sampling Settling rate v terminal enhanced by wet deposition Resuspension rate; upward drift by wind and other forces Infiltration rate; based on ground porosity and colloidal properties Bioturbation rate; mixing by decontamination or biota activity Migration rate; local removal via infiltration enhanced by wet deposition Shaun Marshall 1, Charles Potter 2, David Medich 1 ( 1 Worcester Polytechnic Kinetic Transport Institute, Models Worcester, and Minimum MA 01609 Detection 2 SandiaLimits National of Atmospheric Laboratories Particulate, Albuquerque, Resuspension NMWednesday, 87185 NECHPS June 6, Annual 2018 Symposium 7 / 16
Particulate transport kinetic models (Air sampling) Indoor resuspension catenary model: ( ) ka A k A S S (6) k A S (Wet) Outdoor resuspension catenary model: A k A S k A S S k S G k S G G ( ) kg (7) (Wet) Outdoor resuspension catenary model with weathering: k A k A S A k A S S k S G k S G G ( ) kg (8) Shaun Marshall 1, Charles Potter 2, David Medich 1 ( 1 Worcester Polytechnic Kinetic Transport Institute, Models Worcester, and Minimum MA 01609 Detection 2 SandiaLimits National of Atmospheric Laboratories Particulate, Albuquerque, Resuspension NMWednesday, 87185 NECHPS June 6, Annual 2018 Symposium 8 / 16
Particulate transport rates of transfer Average air sampling rate constant proportional to sampling flow rate : dm A dt = f ɛ f C air (t) = k A M air (t), k A f (9) t Gravitational settling proportional to terminal velocity: dm A S dt = v t AC air (t) = k A S M air (t), k A S v t (10) t Resuspension proportional to average upward velocity from forces dm A S dt = v u AC surface (t) = k A S M surface (t), k A S v u (11) t (NRC, 2012) haun Marshall 1, Charles Potter 2, David Medich 1 ( 1 Worcester Polytechnic Kinetic Transport Institute, Models Worcester, and Minimum MA 01609 Detection 2 SandiaLimits National of Atmospheric Laboratories Particulate, Albuquerque, Resuspension NMWednesday, 87185 NECHPS June 6, Annual 2018 Symposium 9 / 16
Particulate transport compartment equations In general for early timeframes post deposition, dx surface dt Closed two-compartment model: 0 so S f (t) = X A (t) Open two-compartment model: X A (t) = X 0 + X 1e ω1t (12) X A (t) = X 0e ω 0t + X 1e ω 1t (13) Closed three-compartment model: X A (t) = X 0 + X 1e ω1t + X 2e ω2t (14) Open two-compartment model: X A (t) = X 0e ω0t + X 1e ω1t + X 2e ω2t (15) Shaun Marshall 1, Charles Potter 2, David Medich 1 ( 1 Worcester Polytechnic Kinetic Transport Institute, Models Worcester, and Minimum MA 01609 Detection 2 SandiaLimits National of Atmospheric Laboratories Particulate, Albuquerque, Resuspension NM Wednesday, 87185 NECHPS June 6, 2018 Annual Symposium 10 / 16
Neutron activation analysis (NAA) Air sampling took place over hourly, daily, and weekly time intervals. Used filters were activated with neutrons for mass analysis. I Samples are barricaded with solid water to increase scatter and incident flux. sampler head 47mm glass fiber filter target chamber beam portal polypropylene magnetron solid water acrylic chamber aluminum shielding Figure 3: Resuspension chamber with vacuum pump head. Figure 4: DD110M neutron generator beam-line at WPI. 1 2 1 1 2, Albuquerque, Shaun Marshall, Charles Potter, David Medich ( Worcester Polytechnic Kinetic Transport Institute, Models Worcester, and Minimum MA 01609 Detection Sandia Limits National of Atmospheric Laboratories Particulate Resuspension NM Wednesday, 87185 NECHPS June 6, 2018 Annual Symposium 11 / 16
Neutron activation detection limits Minimum detectable activity (MDA) from gamma spectroscopic analysis: MDA = L D ɛ t = k2 + 2k 2µb ɛ t (16) Detector efficiency ɛ and background rate µb Minimum detectable mass (MDM) from neutron activation analysis MDM = L D ɛyp(σ)s(λ, τ)t (λ, t d, t) P(σ) = Nσφ m, S(λ, τ) = 1 e λτ, T (λ, t d, t) = where (17) ( e λt d ) (1 e λ t ) λ Decay gamma yield Y, neutron flux φ, absorbtion cross-section σ, and irradiation and delay times τ, t d (Currie, 1968) Shaun Marshall 1, Charles Potter 2, David Medich 1 ( 1 Worcester Polytechnic Kinetic Transport Institute, Models Worcester, and Minimum MA 01609 Detection 2 SandiaLimits National of Atmospheric Laboratories Particulate, Albuquerque, Resuspension NM Wednesday, 87185 NECHPS June 6, 2018 Annual Symposium 12 / 16
Neutron activation detection limits (continued) Minimum detectable resuspension factor (MDS f ) from neutron activation mass analysis of air sampled filters: MDS f = C air (volume) C surface (area) MDM ɛ f V m0χ A = MDM A ɛ f m 0 χft s (18) Mass fraction of radionuclide of interest relative to sample material χ Sf obtained by replacing MDM with m Specifically, replacing detection limit L D with count C Error propagation of S f σ Sf in first order: σc 2 = S f C 2 + σ2 m 0 m0 2 + σ2 t s ts 2 + λ 2 σt 2 d + λσ2 τ e λτ 1 + λσ2 t e λ t 1 (19) Shaun Marshall 1, Charles Potter 2, David Medich 1 ( 1 Worcester Polytechnic Kinetic Transport Institute, Models Worcester, and Minimum MA 01609 Detection 2 SandiaLimits National of Atmospheric Laboratories Particulate, Albuquerque, Resuspension NM Wednesday, 87185 NECHPS June 6, 2018 Annual Symposium 13 / 16
Neutron activation experimental results Figure 5: Preliminary resuspension factor (S f ) results from NAA of resuspension chamber filters, including null data minimum detectable resuspension factor (MDS f ). Shaun Marshall 1, Charles Potter 2, David Medich 1 ( 1 Worcester Polytechnic Kinetic Transport Institute, Models Worcester, and Minimum MA 01609 Detection 2 SandiaLimits National of Atmospheric Laboratories Particulate, Albuquerque, Resuspension NM Wednesday, 87185 NECHPS June 6, 2018 Annual Symposium 14 / 16
Model kinetic parameters results Table 2: Best-fit linear regression parameters in log-space of averaged experimental observations. Term Value X 0 9.844 10 9 X 1 5.096 10 11 ω 1 67.11 ω 2 0.00433 Table 3: Initial fractional quantities and kinetic rate constants for open two-compartment catenary model as determined by experimental observations. Fractional quantity X A (0) 9.895 10 9 X S (0) 1 X S (0) Rate constants (d 1 ) k A 66.77 k S S 0.3456 k A S 3.463 10 9 haun Marshall 1, Charles Potter 2, David Medich 1 ( 1 Worcester Polytechnic Kinetic Transport Institute, Models Worcester, and Minimum MA 01609 Detection 2 SandiaLimits National of Atmospheric Laboratories Particulate, Albuquerque, Resuspension NM Wednesday, 87185 NECHPS June 6, 2018 Annual Symposium 15 / 16
Conclusions / Future work Compartmental kinetic models reproduce widely used multi-exponential functional form of resuspension factor. Constant term not appropriate without accounting for weathering removal. Models predict wide initial variance depending on compartment initializatons. Background resuspension behavior observed under calm, indoor lab conditions after two weeks of sampling from ideal surface release. Additional data needed to verify steady increase from zero air concentration. Thank you! Shaun Marshall 1, Charles Potter 2, David Medich 1 ( 1 Worcester Polytechnic Kinetic Transport Institute, Models Worcester, and Minimum MA 01609 Detection 2 SandiaLimits National of Atmospheric Laboratories Particulate, Albuquerque, Resuspension NM Wednesday, 87185 NECHPS June 6, 2018 Annual Symposium 16 / 16