Solute Transport in Heterogeneous Aquifers and Implications for Risk Assessment

Transcription

1 Solute Transport in Heterogeneous Aquifers and Implications for Risk Assessment University of Southern California Sonny Astani Department of Civil & Environmental Engineering Contact: CUAHSI Spring 2017 Cyber-seminar

2 Overview of Risks Associated with Subsurface Contamination Humans exposed through different pathways RISK MANAGERS ARE INTERESTED IN: Chemical concentration and/or human health risk (carcinogenic, non-carcinogenic). How long will humans be exposed to the contamination? What is the magnitude of exposure?

3 Challenges: A Hydrogeologist s Point of View Hydraulic properties display multi-scale variability (heterogeneity) Orders of magnitude Incomplete characterization m Use of stochastic methods to quantify flow & transport in natural geological media cm V S V S mm

4 Impact of Heterogeneity on Transport Dynamic evolution of length scales characterizing spreading and mixing Initial Time Early Time Late Time From Fiori & Jankovic, Math. Geosci. Vol. 44 (2), Plume is distorted (shearing & straining deformation) Irregular spreading rates (non-fickian) Existence of Solute Fingers Characterized by multiple scales Dentz & de Barros, J. Fluid Mech. Vol. 777, 2015.

5 Subsurface Heterogeneity and Uncertainty Equally probable aquifers with distinct solute plumes Goal is to statistically characterize transport - Plume deforms according to the velocity field (which also controls dilution rates!) - Specific kinematic features of the heterogeneous flow field have a clear role in dilution and UQ Numerical simulations taken from: Cirpka et al., Water Resour. Res., 47 (6) 2011 & Cirpka et al., Water Resour. Res., 47 (11) 2011.

6 Subsurface Heterogeneity and Mixing Topology Okubo-Weiss Parameter Θ Okubo-Weiss parameter (Eulerian measure): Maps regions of strain, vorticity and shear (Hot Spots of Mixing) Vorticity Dominated Θ < 0: E t ~t Θ x = 4Det ε x Shear Flow Strain Dominated Θ = 0: E t ~t 2 Θ > 0: E t ~e θt/2 with: ε ij = v i x j de Barros et al., Geophys. Res. Lett., 39, 2012 E(t): Dilution Index [see Kitanidis, Water Resour. Res., 30(7), 1994]

7 Subsurface Heterogeneity and Mixing Larger σ Y 2 implies larger heterogeneity Field example (Cape Cod) Results taken from: de Barros, Fiori, Boso & Bellin (2015), J. Cont. Hydrol., , pp

8 Challenges: From a Public Health Point of View Human metabolism & Exposure: Uncertain All substances are poison; there is none which is not poison. The right dose differentiates a poison and a remedy Dosis facit venenum Paracelsus

9 Risk Assessment: Multi-Component Stochastic System Extreme events (very important in risk analysis)

10 Goals Show how aquifer heterogeneity and engineering design affect risk and its stochastic characterization Heterogeneous structure of the aquifer Sampling device dimensions/ Source dimensions Control risk and its uncertainty Health parameters Identify locations of high risk (and temporal persistence) Illustrate how aquifer heterogeneity controls the spatiotemporal risk behavior

11 General Problem Statement Prob R < r crit x, t = f Structural Param., Sampling Vol., Source Dim. r x, t = a C x, t Linear dose-response relationship (e.g. EPA) a: Health-related parameter Prob R < r crit x, t = Prob C x, t < r crit a Risk CDF Probabilistic Mapping Concentration CDF More details: de Barros & Fiori (2014) Water Resour. Res. 50 (5) = F C r crit a Fundamental piece to risk analysis Concentration PDF/CDF: E.g., see works by - Dagan (1982) - Rubin et al. (1994) - Fiori (2001) - Dentz & Tartakovsky (2010) - Bellin & Tonina (2007) - Sanchez-Villa et al. (2009) - Bellin et al. (2011) - Cirpka et al. (2011) - Dentz (2012) - de Barros & Fiori (2014) - Boso et al. (2014) - Others

12 Physical Model Flow Local (Darcy) Scale Steady State, 3D, fully saturated conditions Boundary Condition: Constant Head Gradient J q = K x H q = 0 K x H = 0 Y = ln K is a stationary random function of univariate pdf f Y : Y ; Y = Y Y σ Y 2 ; C Y r = σ Y 2 ρ Y r ; I Y,i Transport Advection - (local) Dispersion Equation Inert Solute (Tracer) Instantaneous Release over a given injection zone C t + V x C = D o C Details on the solution technique (first-order analysis) and assumptions adopted can be found in de Barros & Fiori, (2014), Water Resour. Res. Vol. 50

13 Impact of the Sampling Volume on the Concentration CDF γ Sampling Device (#1) Sampling device impacts uncertainty estimates at high concentration values (tails) (#2) Increase of the sampler s volume leads to reduction of concentration variability (reduction of peak concentration) (see also discussions in Rubin et al. 1994; Fiori et al. 2002; Tonina & Bellin 2008) Results from the concentration CDF model in de Barros & Fiori (2014) Water Resour. Res. 50 (5)

14 Impact of the Source Dimensions on the Concentration CDF Larger plumes (e.g. larger ζ): Takes time to attenuate the concentration at the centroid Smaller plumes (e.g. smaller ζ): Diluted quickly Lower concentrations Pore-scale dispersion & diffusion In the plume s fringe (higher concentration gradients) Results from de Barros & Fiori (2014) Water Resour. Res. 50 (5)

15 Heterogeneity & Health Risk CDF Higher Heterogeneity Increased Plume Spreading Dilution Enhancement Higher Probability of Risk Being Less Than a Critical Value Increased Lifetime Cancer Risk CDF as a function of HETEROGENEITY Results from de Barros & Fiori (2014) Water Resour. Res. 50 (5)

16 Engineering Factors (Pumping Wells) and Risk Analysis Constant pumping rate (in time) Engineering control plays a fundamental role in controlling the probability of exceedance (risk) Variable pumping rate (in time) For the conditions explored, we observe: Multi-modality of the risk (pumping operation) Magnitude (heterogeneity) Results from Libera et al. (2017), J. of Hydrol., 546.

17 Application to Chemical Mixtures Chlorinated Solvents Reductive de-chlorination of Perchloroethylene (PCE) PCE TCE DCE VC Very toxic Carcinogenic REACTIVE TRANSPORT: ADE with first order decay in a 3D flow field (high resolution numerical simulations) Henri, Fernandez-Garcia & de Barros, (2015), Water Resour. Res., 51,

18 Spatiotemporal Persistence of High Risk Zones Low Heterogeneity High Heterogeneity ξ = Prob C i > MCL High risk (hot spots) Low risk ζ: Travel distance (source to control plane) τ: Time Temporal persistence of hot spots Higher vs. Lower Heterogeneity Increased spreading of the plume Enhanced dilution and reactive mixing of the plume Reflected in the spatiotemporal distribution of ξ Henri, Fernandez-Garcia & de Barros, (2015), Water Resour. Res. 51. KEY POINT: Structure of heterogeneity impacts the probability maps. Importance of site characterization in risk analysis.

19 Structure of the Flow Field & Uncertainty Models should assimilate data! x 2 + data! x 1 Certaintimeter! Most certain Most uncertain Stochastic hydrogeology broadens the scope of the deterministic approach to hydrogeology by considering the last as an end member to a wide spectrum of states of knowledge continuum of states representing varying degrees of uncertainty Taken from Chapter 1, Page 3, 2 nd Paragraph of Rubin s 2003 Applied Stochastic Hydrogeology book Model predictions should be conditional on available data

20 Importance of Source Zone Hydraulics Characterization 1 Less flow through source Mean[ C η < 1] Effectively narrow source Q Q sz sz Concentration peak LESS persistent with travel distance. Sources placed within low-volumetric flux zones will emit a smaller total flux and are shorter on average Concentration peak MORE persistent with travel distance. Sources placed within high-volumetric flux zones will emit a larger total contaminant flux and are longer on average Mean[ C η > 1] 1 More flow through source Nowak, de Barros & Rubin, (2010) Water Res. Resour. 46. de Barros & Nowak, (2010) J. Cont. Hydrol., 116. Effectively wide source

21 Back to Chemical Mixtures Conditional Simulations Low heterogeneity High heterogeneity η < 1: Less flow through the source Concentration peak LESS persistent with travel distance η > 1: More flow through the source Concentration peak MORE persistent with travel distance de Barros & Nowak, J. Cont. Hydrol. 116(1) (2010) ; Nowak et al., Water Resour. Res. 46, (2010) Increased Lifetime Cancer Risk Henri, Fernandez-Garcia & de Barros (2016), Adv. Water Resour. Vol. 88 Risk PDF (total chemical mixture) as a function of travel distance and heterogeneity (3D flow) Effect of source zone hydraulics maintained for long travel distances. Flow focusing (continuous line) in the source zone, lower risk for the total chemical mixture De-focusing (dashed line) on the source zone, higher risk for the total chemical mixture

22 Importance of Heterogeneity on Risk Important to characterize aquifer structure and propagate the geostatistical information to end-point predictions The propagation efficiency of hydrogeological information varies according to the risk metric and type of exposure (GOAL-ORIENTED SITE CHARACTERIZATION) o de Barros & Rubin (2008), Water Resour. Res., Vol. 44 o de Barros et al. (2009), Water Resour. Res., Vol. 45 o Nowak et al. (2010), Water Resour. Res. Vol. 46 o de Barros et al. (2012), Adv. Water Resour., Vol. 36 For an overview, see Fiori et al. Water Resour. Res. 51, (2015), 50 th Anniversary Special Issue Expected value of the increased lifetime cancer risk as a function of macro-dispersivity

23 Spatial Structure of Heterogeneity and Risk: Impact of Long-Range Correlations ANTI-PERSISTENT CORRELATION PERSISTENT CORRELATION K-fields displaying long correlation. Low values of H correspond to anti-persistent correlation High values of H correspond to persistent correlation Connected paths carry the bulk of the plume higher risk Moslehi and de Barros, J. Cont. Hydrol., 196, (2017)

24 Conclusions Heterogeneous structure of the subsurface has a clear impact on risk Aquifer heterogeneity controls hot spots (high risks) and its temporal persistence ( hot moments ). Importance of characterizing the geological formation (connectivity). Relevance of the interplay between spreading & mixing (non-reactive vs reactive). Engineering design (e.g. well operation, landfill) should be incorporated in risk analysis Impact on the tails of the CDF (e.g. extreme events) and temporal evolution of risk. Risk should be viewed as a multi-component stochastic system V S V S

25 THANK YOU!