Probabilistic risk assessment of contaminant transport in groundwater and vapour intrusion following remediation of a contaminant source

Transcription

1 Stoch Environ Res Risk Assess (216) 3: DOI 1.7/s ORIGINAL PAPER Probabilistic risk assessment of contaminant transport in groundwater and vapour intrusion following remediation of a contaminant source Kevin G. Mumford 1 Nizar Mustafa 2 Jason I. Gerhard 2 Published online: 21 September 215 Springer-Verlag Berlin Heidelberg 215 Abstract Community-scale simulations were performed to investigate the risk to groundwater and indoor air receptors downgradient of a contaminated site following the remediation of a long-term source. Six suites of Monte Carlo simulations were performed using a numerical model that accounted for groundwater flow, reactive solute transport, soil gas flow, and vapour intrusion in buildings. The model was applied to a three-dimensional, communityscale (25 m 9 m 9 14 m) domain containing heterogeneous, spatially correlated distributions of the hydraulic conductivity, fraction of organic carbon, and biodegradation rate constant, which were varied between realizations. Analysis considered results from both individual realizations as well as the suite of Monte Carlo simulations expressed through several novel, integrated parameters, such as the probability of exceeding a regulatory standard in either groundwater or indoor air. Results showed that exceedance probabilities varied considerably with the consideration of biodegradation in the saturated zone, and were less sensitive to changes in the variance of hydraulic conductivity or the incorporation of heterogeneous distributions of organic carbon at this spatial scale. A sharp gradient in exceedance probability existed at the lateral edges of the plumes due to variability in lateral dispersion, which defined a narrow region of exceedance uncertainty. Differences in exceedance probability between & Kevin G. Mumford kevin.mumford@civil.queensu.ca 1 2 Department of Civil Engineering, Queen s University, Kingston, ON K7L 3N6, Canada Department of Civil and Environmental Engineering, University of Western Ontario, London, ON N6A 5B9, Canada realizations (i.e., due to heterogeneity uncertainty) were similar to differences attributed to changes in the variance of hydraulic conductivity or fraction of organic carbon. Simulated clean-up times, defined by reaching an acceptable exceedance probability, were found to be on the order of decades to centuries in these community-scale domains. Results also showed that the choice of the acceptable exceedance probability level (e.g., 1 vs. 5 %) would likely affect clean up times on the order of decades. Moreover, in the scenarios examined here, the risk of exceeding indoor air standards was greater than that of exceeding groundwater standards at all times and places. Overall, simulations of coupled transport processes combined with novel spatial and temporal quantification metrics for Monte Carlo analyses, provide practical tools for assessing risk in wider communities when considering site remediation. Keywords Groundwater Reactive transport Remediation Vapor intrusion Monte Carlo Exceedance Probability Community-scale 1 Introduction Many former industrial properties have soil and groundwater that are contaminated by non-aqueous phase liquids (NAPLs) such as petroleum fuels and chlorinated solvents. These NAPL sources can persist under natural conditions, and are often only partially removed through the application of remediation technologies (e.g., Kueper et al. 214; NRC 24). The dissolution of these long-lived sources into groundwater can continue for decades, resulting in off-site plumes of dissolved volatile organic compounds (VOCs) that pose a risk to receptors in the communities that surround these contaminated sites. Example VOCs that are risk

2 118 Stoch Environ Res Risk Assess (216) 3: drivers include benzene, toluene, naphthalene, trichloroethene, and tetrachloroethene, many of which are known or suspected carcinogens. In the case of many community-scale VOC plumes there is a risk to groundwater receptors and also to indoor air receptors through vapour intrusion, because of the volatility of the VOCs. An example scenario is illustrated in Fig. 1, which shows VOC vapour and groundwater plumes produced by a NAPL source. The VOC vapour plume can arise from direct NAPL volatilization and also from VOC partitioning from groundwater adjacent to the vadose zone; in the case of community-wide impacts where distances to the source are significant, volatilization from groundwater dominates. The groundwater plume may contaminate drinking water wells in the community and the VOC plume may invade the indoor air of the overlying houses. Determining the risk to groundwater and indoor air receptors often involves the comparison of local concentrations at the receptor to regulatory standards. Local concentrations can be measured or be based on numerical simulation of contaminant transport. Simulations can be especially useful for larger plumes, where characterization of the entire plume may be cost prohibitive, and for predicting the extent of risk reduction following removal, or partial removal, of a source zone. A reduction in risk is a practical design objective for a remediation application, and can serve as a useful metric of remediation performance. However, risk reduction far from a source may not occur for years after remediation was applied. Simulation can provide a useful link between off-site risk reduction and remedial actions applied to source zones, allowing practitioners to establish design criteria and allowing regulators to set expectations for clean-up and monitoring. Any effort to model flow and reactive transport in the subsurface will be subject to uncertainty arising from data collection errors, estimated parameter values, and approximations made in model formulation (Tartakovsky 213; Mansour-Rezaei et al. 212). As such, predictions of risk from the transport of VOCs that rely on a single-value estimate, such as the expected value of the dissolved VOC concentration, may not be the most useful. Single-value estimates may over predict risk (Lahkim and Garcia 1999) or fail to consider lower-probability, but higher-consequence, outcomes (Lemke and Bahrou 1999). It is, therefore, important that uncertainty be considered when assessing risk using reactive transport simulations (Maxwell and Kastenberg 1999; Tartakovsky 213; Lahkim and Garcia 1999). Lemke and Bahrou (1999) highlighted that predictions of cancer risk due to exposure to VOCs may be most sensitive to uncertain hydrogeologic parameters used in contaminant transport simulations, and recommended that simulations more sophisticated than their one-dimensional, homogeneous simulations be conducted. A number of approaches have been considered to quantify the uncertainty associated with flow and reactive transport simulations; for example see recent reviews by Tartakovsky (213) and Zhang et al. (21). A popular approach is the Monte Carlo method, where parameter values are chosen randomly from probability density functions (PDF) specified for each input parameter, and results from multiple realizations are used to estimate the PDF of each output variable (e.g., Zhang et al. 21; Mohamed et al. 21; Lahkim and Garcia 1999; Lemke and Bahrou 1999). This is a flexible and straightforward approach that, in principle, allows the estimation of uncertainty using any contaminant transport model, including commonly-used numerical models based on the discretization of continuum-scale governing equations (i.e., finite difference and finite element schemes). A Monte Carlo approach, however, is limited by practical constraints on total simulation time, particularly when many physicochemical processes are simulated in larger domains. This Fig. 1 Conceptual model of the simulation domain, showing VOC vapour (red) and groundwater (blue) plumes in a three-dimensional heterogeneous subsurface. Houses are located along the plume centreline and 125 m laterally off-set from the centreline. The water table is indicated by the dashed line

3 Stoch Environ Res Risk Assess (216) 3: is the case when assessing the risk posed by a VOC plume in a community that surrounds a contaminated site. To asses this risk using numerical simulations, a numerical model needs to consider several processes, such as: (i) reactive transport between the source zone and the larger community domain, including advection, dispersion, sorption, and biodegradation in three dimensions; (ii) spatial heterogeneity of subsurface parameters, including hydraulic conductivity, sorption coefficients, and biodegradation rate constants; (iii) partitioning of VOC between the groundwater in the saturated zone and soil gas in the vadose zone; and (iv) the transport of soil gas into buildings (i.e., soil vapour intrusion). To address this need the model GW-VAP3D (Mustafa et al. 214) was developed to couple numerical models for groundwater flow, solute transport, and soil vapour intrusion and to consider this collection of relevant processes in a single simulation. The GW-VAP3D model can be applied to large three-dimensional domains to efficiently perform the multiple realizations of contaminant transport that are required for a Monte Carlo approach. An ability to simulate these coupled processes within larger domains is critical, because jurisdictions are increasingly moving to the management of contaminated sites by considering the larger surrounding community (Wycisk et al. 23; Malina et al. 26; Weiss et al. 26). This is particularly important when considering soil vapour intrusion, as most published studies of vapour intrusion are limited to a single contaminated site (Johnson and Ettinger 1991; Devaull et al. 22; Hers et al. 22; Abreu and Johnson 25; Bozkurt et al. 29; USEPA 212; Yao et al. 213; ITRC 214) or the immediately-surrounding area (i.e., within 2 m) (Wang et al. 212) despite the likelihood of VOC to be transported offsite in groundwater before being transported through the soil gas to surrounding buildings. This study investigated risk following removal of a long-term source, using numerical simulations conducted in three-dimensional, heterogeneous, community-scale (i.e., m) domains. Specifically, it examined the probability of exceeding regulatory standards in groundwater and indoor air as a function of time after remediation. Specific objectives were to: (i) predict the time required for the probability of exceeding a regulatory standard to drop below a threshold value; (ii) determine the sensitivity of this time to key site parameters such as the variance of hydraulic conductivity and the biological degradation rate; (iii) assess this sensitivity as a function of distance of the community receptor from the source; and (iv) identify the risk driver; specifically, compare the probability of exceeding a groundwater regulatory standard in a well to the probability of exceeding an indoor air regulatory standard in a basement at the same location. The investigation consisted of Monte Carlo suites of numerical simulations using conditions similar to those used to develop regulatory standards in Ontario, Canada (MOE 211). As such, the results of this study serve as examples and are not intended to be representative of any particular contaminated site. 2 Simulation approach 2.1 Model description Simulations were performed using the newly developed GW-VAP3D (Mustafa et al. 214), which is built on three well-accepted numerical models: MODFLOW (Harbaugh et al. 25) for groundwater flow, MT3DMS (Zhang et al. 21) for solute transport, and Abreu and Johnson (25) for soil vapour intrusion. The coupling of these models is described by Mustafa et al. (214), and the governing equations are summarized briefly here. Groundwater flow, in absence of sources, is based on (Rushton and Redshaw 1979): oh S s ¼r Krh ot ð Þ ð1þ where K is the hydraulic conductivity tensor (LT -1 ), h is the hydraulic head (L), S s is the specific storage (L -1 ), and t is time (T). Solute transport is based on (Zhang et al. 21): 1 þ q bk oc f oc h w ocw ot q w ¼ r C w h w kc w þr ðdrc w Þ ð2þ where C w is the concentration of chemical in the aqueous phase (ML -3 ), q b is the bulk density of the soil matrix (ML -3 ), K oc is the sorption coefficient of chemical to organic carbon (MM -1 oc L 3 M -1 ), f oc is the mass fraction of organic carbon in the soil (M oc M -1 soil ), q w is the groundwater specific discharge vector (LT -1 ), h w is the water-filled porosity (L 3 L -3 ), D is the dispersion tensor (L 2 T -1 ), and k is the first-order reaction rate constant in the saturated zone (T -1 ). Dissolution of a NAPL source was not simulated in this study, and the source was treated as a region of high aqueous concentration of VOCs. This study assumed that the only reaction in groundwater was due to biodegradation that could be described by a first-order rate expression, and that retardation was controlled by linear sorption to organic matter. The specific discharge is given by Darcy s law (q w ¼ Krh) based on the solution to Eq. 1 and the dispersion tensor is calculated in MT3DMS considering molecular diffusivity and dispersivity, including crossterms (Bear 1979). Gas flow, neglecting density-driven flow effects, is described by Massmann et al. (1991):

4 12 Stoch Environ Res Risk Assess (216) 3: op ot ¼ Patm h g l g r ðk g rpþ ð3þ where P is the absolute pressure (ML -1 T -2 ), P atm (ML -1 T -2 ) is the mean pressure approximated here by the atmospheric pressure, k g is the soil gas permeability tensor (L 2 ), h g is the gas-filled porosity (L 3 L -3 ), and l g is the soil gas dynamic viscosity (ML -1 T -1 ). Vapour transport in the gas phase, assuming no movement of water in the vadose zone, is described by Bear (1979): h g þ h w H þ q bk oc f oc H ocg ot ¼r D gw rc g h w k u C g H r qg C g ð4þ where H is the dimensionless Henry s law constant (ML -3 M -1 L 3 ), C g is the concentration of chemical in the gas phase (ML -3 ) assumed to be in equilibrium with the aqueous concentration according to Henry s law (C g ¼ HC w ), D gw is the overall diffusion coefficient (L 2 T -1 ) (e.g., Abreu and Johnson 25), q g is the soil gas specific discharge based on the solution of Eq. 3 and Darcy s law applied to the soil gas (LT -1 ), and k u is the first-order reaction rate constant in the unsaturated zone (T -1 ). As in the saturated zone (Eq. 2), this study assumed that the only reaction in the unsaturated zone was due to biodegradation that could be described by a first-order rate expression, and which occurs only in the soil moisture. Finally, the indoor air concentration, assuming the compound of interest enters the building only from the soil gas, is implicitly described by Mustafa et al. (214): 1 exp C ia ¼ Q ck V b A ex þ Q s ZLck exp Q ck W ck D ck d ck Q ck W ck D ck d ck C gck C ia 1 dl ck ð5þ where C ia is the indoor air concentration (ML -3 ), V b is the volume of the enclosed space within the building (L -3 ), A ex is the air exchange rate of the enclosed space (T -1 ), Q s is the soil gas flow to the enclosed space based on advection and diffusion through cracks in the foundation (Abreu and Johnson 25) (L 3 T -1 ), Q ck is the soil gas flow rate per unit length of crack (L 3 T -1 L -1 ), W ck is the crack width (L), d ck is the foundation thickness (L), D ck is the effective diffusion coefficient for transport through the crack (L 2 T -1 ), L ck is the total crack length (L), and C gck is the soil gas concentration at the soil-foundation crack interface (ML -3 ). Together, Eqs. 1 5 can simulate the concentrations of VOC in groundwater, soil gas, and indoor air over time at x, y, andz locations in a discretized domain. MT3DMS and MODFLOW use a split-operator approach (Barry et al. 22) to couple equations for groundwater flow (Eq. 1) and solute transport (Eq. 2) using a finite difference technique. GW-VAP3D implements the equations for soil vapour intrusion (Eqs. 3 5) within the split-operator approach by using groundwater concentrations at the water table to calculate vapour concentrations according to Henry s Law, which then serve as a boundary condition for vapour transport. Subsequently, groundwater concentrations are updated to conserve total VOC mass based on mass lost to the vapour phase. These calculations are conducted assuming a sharp interface between the saturated zone and the unsaturated zone, which is assumed to have constant moisture content. The capillary fringe was neglected in these simulations to reduce computational expense; this assumption provides conservative estimates of vapour intrusion risk, since vapour concentrations are expected to be increasingly reduced with increased thickness of the capillary fringe (Yu et al. 29). GW-VAP3D also allows heterogeneous distributions of (i) hydraulic conductivity in the saturated zone and soil gas permeability in the vadose zone, (ii) fraction of organic carbon, and (iii) biodegradation rate constants, which is not typical in applications of MODFLOW and MT3DMS. 2.2 Simulation approach A randomly-generated auto-correlated hydraulic conductivity field, K = K(x,y,z), was employed and Monte Carlo simulations used multiple realizations of this field. Some of the Monte Carlo simulations also included the biodegradation rate constant (k) and fraction of organic carbon (f oc )as random variables, each of which was also incorporated as a randomly-generated auto-correlated field k = k(x,y,z) and f oc = f oc (x,y,z). Heterogeneous distributions of K, f oc, and k were generated using the random field generator FGEN (Robin et al. 1993). The cases investigated using the Monte Carlo approach are described in Sect The K, k, and f oc fields were applied to a 25 m wide 9 m long 9 14 m deep domain (Fig. 1). The total depth of 14 m was divided into a 4 m deep vadose zone and a 1 m deep saturated zone, where the ground surface was assumed to be parallel to the slope of the water table to maintain a constant vadose zone depth. Constant head boundaries were applied to the left-hand and righthand edges of the domain to maintain a hydraulic gradient of.3, while no-flow was specified at all other boundaries except the free exit of soil gas was allowed at the right-hand boundary. A source zone of benzene at an aqueous concentration of 9 mg/l as a constant-concentration boundary condition, corresponding to half of its aqueous solubility, was placed in the lower left-hand corner

5 Stoch Environ Res Risk Assess (216) 3: of the domain. The source dimensions were 6.5 m wide 9 13 m long 9 2 m deep, where the top of the source was coincident with the water table (i.e., no vadose zone source). This source concentration is representative of a pure benzene NAPL source with an architecture that results in little mass transfer limitation during dissolution. Sources of mixed NAPL, such as petroleum fuels, or mass transfer-limited source zones would have lower concentrations. Additional parameters used in the simulations are presented in Table 1. The no-flow boundary assigned to the vertical face adjacent to the source represented a symmetry boundary along the average centreline of the plume downgradient of the source (Fig. 1). Many of the simulation conditions were chosen to be consistent with those used by the Ontario Ministry of the Environment (MOE) to establish regulatory standards for soil and groundwater that are protective of sites throughout Ontario (MOE 211). These conditions are expected to lead to higher groundwater and indoor air concentrations than those found at typical contaminated sites (i.e., conservative concentrations). Conditions leading to conservative concentrations include a shallow water table, no recharge, and a highconcentration source zone. Twelve houses were placed in the domain at varying distances from the source, to act as receptors for risk due to soil vapour intrusion (Fig. 1). The domain was discretized into grid blocks, each 1 m 9 1m9.5 m deep. Simulations were conducted until dissolved benzene concentrations did not change with time within the domain. In simulations that do not include biodegradation in the saturated zone this does not represent true steady-state conditions, as continued expansion of the plume would occur further downgradient. Once dissolved concentrations within the domain became steady in time the source was removed (i.e., benzene concentrations were set to a constant concentration of mg/l in the 6.5 m wide 9 13 m long 9 2 m deep source region) and simulations were continued for an additional 9 years to monitor changes to the risk to groundwater and indoor air following complete source removal. In each realization, i, concentrations of benzene in groundwater (w) were calculated at all grid block locations, C i w (x, y, z, t), and concentrations of benzene in indoor air (ia) were calculated at all house locations, C i ia (x h, y h, t) where x h and y h are the x and y locations of each house. Only the groundwater concentrations at the water table Table 1 Simulation parameters for all cases Parameter Value Parameter Value Flow and transport parameters Saturated zone thickness 1 m Mean horizontal hydraulic gradient a.3 Vadose zone thickness 4 m Water-filled porosity in vadose zone b.54 Porosity a.3 Longitudinal dispersivity 1 cm Dry bulk density a 1.81 g/cm 3 Transverse horizontal dispersivity 1 cm Recharge rate mm/year Transverse vertical dispersivity.1 cm Source zone thickness a 2 m Dynamic viscosity of air b.648 kg/(m h) Basement parameters Basement depth 2 m Perimeter crack width.1 m Foundation thickness.15 m Total crack length 39 m Enclosed space volume 244 m 3 Atmospheric concentration lg/m 3 Indoor air mixing height 2.44 m Building pressure 5 Pa below atmospheric Air exchange rate.5 h -1 Chemical parameters e Log K oc 1.56 Aqueous solubility at 15 C a 18 mg/l Groundwater standard a 5 lg/l Henry s coefficient at 15 C d.145 Indoor air standard f 3.1 lg/m 3 Diffusivity in air c cm 2 /s Diffusivity in water c cm 2 /s a MOE (211) b c d e f Abreu and Johnson (25) USEPA (23) USEPA (21) USEPA (1996) USEPA (1998)

6 122 Stoch Environ Res Risk Assess (216) 3: i (wt), C wt (x, y, t) = C i w (x, y, z = 4m,t), were considered in i i further probability calculations. The C wt and C ia values for all realizations were used to calculate cumulative probabilities of concentration at each location and at each time: F Cx;y;t ð Þ ðcþ ¼ 1 n X n i¼1 I i ðcþ ð6þ where F Cx;y;t ð Þ is the discrete cumulative probability, C refers to concentration and can represent groundwater at the water table (C wt ) or indoor air (C ia ), n is the total number of realizations, c is a particular value of C, and I i has a value of unity if C(x,y,t) B c and zero otherwise. These cumulative probabilities were fit using MATLAB to generate continuous cumulative density functions (CDF) based on the discrete probability values for groundwater and indoor air concentrations (F wt and F ia ). Each CDF was then used to determine the probability of exceeding the regulatory standards as: P j c [ C Std j ¼ 1 F j c ¼ C Std j ð7þ where C j Std is the regulatory standard, j refers to either groundwater at the water table (wt) or indoor air (ia), and P j (c [ C j Std ) is the probability of exceeding the regulatory standard for either groundwater or indoor air. In the following discussion, P j (c [ C j Std ) is referred to as an exceedance probability in either groundwater at the water table (EP wt ) or indoor air (EP ia ). A regulatory standard of 5 lg/l was used for benzene in groundwater (MOE 211) and a regulatory standard of 3.1 lg/m 3 was used for benzene in indoor air (USEPA 1998). Of interest in this study is the time required for the exceedance probability, as a measure of risk across a suite of Monte Carlo simulations, to decrease below a prescribed threshold following removal of a long-term source. This is analogous to the time required for groundwater or indoor air concentrations to decrease below a regularly standard if only a single simulation, rather than multiple realizations, is considered. Threshold exceedance probabilities of 1 and 5 % were considered, and the time to reach these threshold probabilities are referred to here as acceptance times (at.1 or at.5, respectively). The acceptance times are defined by: EP j ðx; y; t ¼ at a Þ ¼ TP ð8þ where TP is the threshold exceedance probability (e.g.,.1 or.5), and at a is the acceptance time. In this manner, results from each suite of Monte Carlo simulations (i.e., each case) could be combined and the overall probability of exceeding a threshold level of risk at any house in the community could be expressed quantitatively, particularly with respect to time after source cleanup. 2.3 Simulation cases A total of six simulation cases were used to investigate exceedance probabilities following removal of a benzene source and their sensitivity to hydraulic conductivity, biodegradation rate constant, and fraction of organic carbon (Table 2). Cases 1 3 were used to investigate the sensitivity of exceedance probability, EP j, and acceptance time, at a, to the variance of hydraulic conductivity. Cases 4 6 were used to investigate the sensitivity of EP j and at a to biodegradation and heterogeneous sorption. Each case represents a suite of 5 Monte Carlo realizations, with a total of 3 simulations being conducted in this study. 5 realizations was chosen based upon a preliminary study in which a suite of simulations using Case 1 conditions demonstrated convergence of dissolved benzene concentrations along the plume centreline and 5 m downgradient of the source after 5 realizations. In all cases, spatially distributed values of hydraulic conductivity were generated (Robin et al. 1993) based on a lognormal distribution with a mean(k) of 3.1 m/day, and assigned according to longitudinal, transverse, and vertical correlation lengths of 17.2, 7.4, and 1. m, respectively (Sudicky et al. 21), representative of naturally deposited, horizontally layered, near surface unconsolidated sediments. Table 2 Case descriptions and parameters varied between cases Case Case description Hydraulic conductivity (K) Biodegradation rate constant in the saturated zone (k) Fraction of organic carbon (f oc ) Mean (m/day) Variance a Mean (day -1 ) Variance Mean (g/g) Variance 1 Heterogeneous K (intermediate) Heterogeneous K (low) Heterogeneous K (high) Heterogeneous K and f oc Heterogeneous K and k Heterogeneous K, k and f oc a Variance for all parameters reported as the variance of the lognormal distribution, i.e., var(lnk), var(lnk) and var(lnf oc )

7 Stoch Environ Res Risk Assess (216) 3: For Cases 1 3, values of var(lnk) were chosen to include the minimum (.29), mean (1.79), and maximum (4.5) of five of the most well-characterized aquifers, including the Cape Cod, Borden, Oscoda, North Bay, and Columbus aquifers (Wolf 1988; Sudicky 1986; Woodbury and Sudicky 1991; Lemke et al. 24; Hess 1989; Sudicky et al. 21; Rehfeldt et al. 1992). Cases 1 3 considered sorption to homogeneously-distributed f oc equal to.3 and biodegradation in the vadose zone (k u =.83 day -1 ). This vadose zone biodegradation rate was used in all cases to simulate aerobic degradation as has been observed for the vapour intrusion of petroleum hydrocarbons in experiments (Baker et al. 1997; DeVaull et al. 22; Hohener et al. 23; Ostendorf et al. 2) and field settings (Laubacher 1997; Ostendorf and Kampbell 1991; Roggemans et al. 22). Biodegradation in the saturated zone was not considered (k = ) in Cases 1 3. Cases 4 and 6 considered sorption to heterogeneouslydistributed f oc based on a lognormal distribution with mean(f oc ) equal to.3, the single value used in Cases 1 3, var(lnf oc ) =.5, and correlation lengths equal to those used for hydraulic conductivity (e.g., Burr et al. 1994). The values of f oc were not correlated to values of K. Case 4 neglected biodegradation in the saturated zone. Cases 5 and 6 considered biodegradation in the saturated zone and the biodegradation rate constant was distributed randomly based on a lognormal distribution with mean(k) = day -1, var(lnk) =.5, and correlation lengths equal to those used for hydraulic conductivity (e.g., Miralles-Wilhelm et al. 1997). This mean(k) represents a lower estimate in the range of reported benzene degradation rate constants (Rifai and Newell 22), and was used here to represent conservative conditions as were used for the development of regulatory standards (MOE 211). 3 Results and discussion 3.1 Comparing concentrations and exceedance probabilities The results from simulations that do and do not include biodegradation in the saturated zone (i.e., Case 5 and Case 1, respectively) are shown in Figs. 2, 3, and 4 for a time immediately prior to removal of the source, when steady conditions had been achieved for the plume within the m long domain (left-hand column), and for 6 years following source removal (right-hand column). These results are for groundwater benzene concentrations at the water table (C wt ) and are shown in plan view on a plane coincident with the water table. Benzene concentrations in indoor air (C ia )are discussed later in Sect The three figures present the results in three different formats: (i) Fig. 2 shows maps of dissolved concentrations from a simulation conducted using a single realization of the hydraulic conductivity field, (ii) Fig. 3 shows collections of 5 lg/l isoconcentration lines from each of the 5 realizations in each case, and (iii) Fig. 4 shows maps of exceedance probabilities (EP wt ) based on the Groundwater concentration (mg/l) (a) (b) (c) (d) Fig. 2 Benzene concentrations in groundwater (plan view) for the first realization of Case 1 at a steady-state prior to source removal and b 6 years following source removal and of Case 5 at c steady-state prior to source removal and d 6 years following source removal

8 124 Stoch Environ Res Risk Assess (216) 3: Fig. 3 The mean (solid lines) and individual (dashed lines) 5 lg/l isoconcentration lines for benzene in groundwater (plan view) from the 5 realizations of Case 1 at a steady-state prior to source removal and b 6 years following source removal and of Case 5 at c steadystate prior to source removal and d 6 years following source removal Exceedance probability (%) (a) (b) (c) (d) Fig. 4 Exceedance probability maps for benzene in groundwater (plan view) for Case 1 at a steady-state prior to source removal and b 6 years following source removal and of Case 5 at c steady-state prior to source removal and d 6 years following source removal 5 realizations. Plume behaviour for a single realization (Fig. 2) is as expected, with concentrations being greater along the plume centreline and closer to the source prior to source removal, and biodegradation resulting in a shorter plume. Results for Case 1 were similar to those for Cases 2 4, and results for Case 5 were similar to those for Case 6. For example, in all of Cases 1 4 the region of the plume containing C wt C 5 lg/l extended to the downgradient boundary of the domain and differed in width from the centreline by only 3 m between cases. Similarly, in Cases 5 and 6, the region of the plume containing C wt C 5 lg/l did not reach the downgradient boundary and differed in length along the centreline by only 2 m. Comparisons between cases are discussed further in Sect The 5 lg/l groundwater isoconcentration line from any single realization divides the domain into areas that either exceed or do not exceed the regulatory standard for benzene in groundwater. The isoconcentration plots in Fig. 3 show that this division is subject to a region of uncertainty that is narrow (approximately 5 7 m) relative to the size of the community. This region of uncertainty is also observed in the 5 lg/l exceedance probability maps (Fig. 4), between EP wt = % and EP wt = %, which quantify the exceedance probabilities within this region.

9 Stoch Environ Res Risk Assess (216) 3: Figures 3 and 4 show that most of the community has an either or % exceedance probability under these conditions. The high fraction of the community with EP wt = % is due to the simulation of the high-concentration benzene source (i.e., five orders of magnitude above the regulatory standard). It is expected that a lowerconcentration source would show a smaller fraction of the community at EP wt = %, but that the region of uncertainty would be similarly narrow. The exceedance probability maps (Fig. 4) provide more information to decision makers than single- or multi-realization isoconcentration plots. If a single simulation is conducted as part of a site-specific risk assessment (Fig. 2), it will not be known if the predicted plume extent is representative of mean or extreme behaviour, due to uncertainty in the model parameters. If multiple realizations are conducted and the family of 5 lg/l isoconcentration lines are plotted (Fig. 3), the possibility of exceeding the standard at various locations can be identified but the probability of exceeding the standard would not be known. In the cases simulated in this study the region of uncertainty was narrow, but wider regions should be expected for greater variance in hydraulic conductivity, biodegradation, or sorption parameters, or the inclusion of receptor characteristics in the Monte Carlo simulations (Lemke and Bahrou 1999). For very wide regions of uncertainty, it may be impractical for decision makers to protect an entire community at a level of EP wt = %. In these cases, the exceedance probability maps provide valuable information. 3.2 Influence of stochastic variability and degree of heterogeneity The isoconcentration plots (Fig. 3) give an indication of the variation between realizations within each case. Each realization of each case accounts for heterogeneity, based on the spatial distribution of hydraulic conductivity, fraction of organic carbon, and/or biodegradation rate constant (Table 2). For the cases shown in Fig. 3, this variation is the result of heterogeneity in hydraulic conductivity (Case 1, Fig. 3a, b) or heterogeneity in hydraulic conductivity and the degradation rate constant (Case 5, Fig. 3c, d). Variation between realizations represents the uncertainty associated with K, f oc, and k fields that are not perfectly known (i.e., stochastic variability within the same degree of heterogeneity). The extents of the plumes, as defined by the 5 lg/l isoconcentration lines, are similar in each realization and vary by a maximum distance of approximately 5 7 m in the y-direction for Cases 1 and 5 prior to and 6 years following source removal. In contrast, results from a single realization of each of the six cases are shown in Fig. 5. Variation between cases represents different degrees of heterogeneity, either expressed through different var(lnk) (Cases 1 3) or the incorporation of additional heterogeneous parameters, f oc and/or k (Cases 1, 4 6). Identical K fields (i.e., identical realizations) were used in each of the Cases 1, 4 6 simulations, identical f oc fields were used in each of the Case 4 and 5 simulations, and identical k fields were used in each of the Cases 5 and 6 simulations shown in Fig. 5. A comparison of Figs. 3 and 5 shows that the uncertainty associated with different realizations of the same degree of heterogeneity in hydraulic conductivity (Fig. 3) is approximately the same as the uncertainty associated with different degrees of heterogeneity, expressed through the magnitude of var(lnk), or the incorporation of a heterogeneous f oc field (Fig. 5). All plume footprints were within approximately 5 7 m of each other. The relatively low sensitivity of the plume footprint to the magnitude of var(lnk) is unexpected considering the range of values employed in these simulations (Table 2), which includes values from well-characterized aquifers considered to have low to high heterogeneity. These results suggest that when assessing spatial uncertainty in plume footprint at this larger scale, the incorporation of different degrees of heterogeneity is as important as incorporating different realizations of a single degree of heterogeneity. An investigation of uncertainty in time showed different results, and is discussed in Sect Fig. 5 5 lg/l isoconcentration lines for the first realization of Cases 1 6 (plan view) at a steady-state prior to source removal and b 6 years following source removal

10 Stoch Environ Res Risk Assess (216) 3: Domain Width, y (m) 126 Domain length, x (m) Fig. 6 Exceedance probabilities ( % \ EPwt \ 5 %) for Cases 1 6 (plan view) at 6 years following source removal Unlike the investigation of different var(lnk) and the incorporation of a heterogeneous foc field, including biodegradation in the saturated zone (Cases 5 and 6) produced a significantly different plume footprint, and resulted in shorter plumes. As such, accounting for biodegradation is expected to be more important than accounting for different realizations of heterogeneity. Using exceedance probabilities, information related to both variation within a case (Fig. 3) and variation between cases (Fig. 5) can be displayed together. For example, Fig. 6 shows \ EPwt \ 5 % contours for each of the six cases 6 years following source removal. Two groupings are apparent, which correspond to the cases that do not include (Cases 1 4), and do include (Cases 5 and 6) biodegradation in the saturated zone. The width of each \ EPwt \ 5 % band is due to different realizations of 3.3 Time dependent change of exceedance probabilities following source removal An example of how exceedance probabilities in groundwater decrease following source removal is shown in Fig. 7 for locations 5 m downgradient of the source and either on the plume centreline or 125 m from the plume centreline. These locations correspond to two of the houses where indoor air concentrations were also simulated. As expected, the time dependent change of the exceedance probability is sensitive to the distance from the plume centreline. Exceedance probabilities were lower further away, in the transverse direction, from the plume centreline, which is consistent with dispersive mixing of the plume. (a) 8 Exceedance Probability (%) Exceedance Probability (%) heterogeneity (i.e., Monte Carlo simulations of a single case), and the different locations of the bands are due to changes in the mean parameters (i.e., different degrees of heterogeneity). However, while these cases are similar in space, their exceedance probabilities differ in time at a single location, as discussed in Sect Overall, these results show that the exceedance probability for the conditions simulated in this study is more sensitive to the decision to incorporate biodegradation than to modelling decisions involving the variance of hydraulic conductivity or fraction of organic carbon. 6 4 (b) Time a er source removal (years) Time a er source removal (years) Case 1 (centreline) Case 2 (centreline) Case 3 (centreline) Case 4 (centreline) Case 5 (centreline) Case 6 (centreline) Case 1 (125 m off-set) Case 2 (125 m off-set) Case 3 (125 m off-set) Case 4 (125 m off-set) Fig. 7 Exceedance probabilities for benzene in groundwater over time following source removal at a distance of 5 m downgradient of the source shown using a a linear axis and b a log axis to highlight the times at which the threshold probabilities of 1 and 5 % are met. Note that the steady-state plume did not reach a distance of 5 m downgradient of the source and 125 m off-set from the plume centreline in Cases 5 and 6 due to biodegradation in the saturated zone

11 Stoch Environ Res Risk Assess (216) 3: Unlike the relatively small differences in the plume footprint between cases discussed in Sect. 3.2, there are significant differences in the time dependent change of exceedance probabilities. At the same transverse location (i.e., plume centreline or 125 m from the plume centreline) a lower var(lnk) value (Case 2) resulted in exceedance probabilities that began to decline later but reached lower values (i.e., EP wt \ 3 %) sooner than similar simulations with a higher var(lnk) value (Case 3). Although these differences are less than those attributed to the transverse location, they affect the time required to achieve low exceedance probabilities by decades. For example, exceedance probability along the plume centreline and 5 m downgradient of the source decreased below the 5 % threshold (TP =.5) 165 years post-remediation in Case 2, but after 218 years in Case 3 (Fig. 7b). These differences are similar to those attributed to including bioremediation (Cases 5 and 6), which showed exceedance probabilities below 5 % after 164 and 168 years, respectively, compared to the base case without bioremediation (Case 1) of 187 years. These results show that the degree of heterogeneity, through the value of var(lnk), must be accounted (a) Acceptance me (years) (b) Acceptance me (years) Case number m (5%) 43 m (1%) 5 m (5%) 5 m (1%) m (5%) m (1%) Case number m (5%) 5 m (1%) m (5%) m (1%) Fig. 8 Acceptance times for benzene in groundwater using 1 and 5 % threshold exceedance probabilities at distances of 43, 5 and m downgradient of the source a along the plume centreline and b 125 m off-set from the plume centreline. Note that the steady-state plume did not reach a distance of m in Cases 5 and 6 due to biodegradation in the saturated zone and did not extend to 125 m offset from the source zone at a distance of 43 m in any case for to predict reductions in risk over time following source removal. The times required to achieve acceptance for exceedance probabilities of 1 and 5 % (i.e., at.1 and at.5 )in all cases at 43, 5, and m downgradient of the source are shown in Fig. 8. Acceptance times for a threshold exceedance probability of 1 % varied between 67 and 626 years post-remediation along the centreline and between 55 and 411 years post-remediation at 125 m offset from the centreline. Acceptance times for a threshold exceedance probability of 5 % varied between 55 and 538 years along the centreline and between 44 and 329 years 125 m off-set from the centreline. Note that the values in Fig. 8 for a distance of 5 m downgradient of the source correspond to the times at which the EP wt curves in Fig. 7 cross the threshold exceedance probabilities of 1 and 5 %. Within each case, acceptance times increased with a decreasing value of the threshold exceedance probability (i.e., 5 % compared to 1 %). If, for example, regulatory agencies were to choose a 5 % exceedance probability threshold over a 1 % exceedance probability threshold, acceptance times would be between approximately 1 and 88 years shorter across all the cases investigated here. Acceptance times also increased with increasing distance downgradient of the source (i.e., 43 m compared to 5 m and m), with the largest difference being 176 years, between Cases 2 and 4 along the plume centreline at a location m downgradient of the source using a 1 % exceedance probability. These results show that for receptors located further from a contaminated site within the surrounding community, failure to accurately incorporate the degree of heterogeneity could change predicted acceptance times by many decades. These results also illustrate, in general, the timescales associated with the clean-up of community-scale plumes. In all cases, acceptance times were measured in decades even at a distance of 43 m downgradient of the source. For scenarios without biodegradation and for receptors located on the plume centreline and m from the source, the acceptance times were greater than 4 years. 3.4 Comparison of exceedance probabilities in groundwater and indoor air The exceedance probabilities in groundwater (EP wt ) and in indoor air (EP ia ) were calculated at the location of each of the twelve houses throughout the domain, and are shown in Fig. 9 prior to and 6 years following source removal. At many locations and for many cases EP wt and EP ia were both equal to or %, and these are not shown on Figs. 9 and 1 for clarity. These results show that EP wt = EP ia only for exceedance probabilities of and

12 128 Stoch Environ Res Risk Assess (216) 3: (a) (a) Indoor Air Exceedance Probability (%) (b) m Case 1 5 m Case 2 75 m Case 3 2 m Case 4 Centreline Case m off-set Case Groundwater Exceedance Probability (%) Indoor Air Exceedance Probability (%) (b) m Case 1 5 m Case 2 75 m Case 3 2 m Case 4 Centreline Case m off-set Case Groundwater Exceedance Probability (%) Indoor Air Exceedance Probability (%) Indoor Air Exceedance Probability (%) Groundwater Exceedance Probability (%) Fig. 9 Exceedance probabilities for benzene in groundwater (EP wt ) and indoor air (EP ia )ata steady-state prior to source removal and b 6 years following source removal for a groundwater standard of 5 lg/l and an indoor air standard of 3.1 lg/m 3. Solid symbols represent houses on the plume centreline and open symbols represent houses located 125 m off of the centreline. The solid line represents equal exceedance probabilities (i.e., EP wt = EP ia ). For clarity, locations with EP wt and EP ia both equal to or % are not shown %. At locations where the exceedance probabilities are not equal, EP wt was less than EP ia. Therefore, at all locations and at all times following source removal, for the conditions simulated in this study, the indoor air standard is equally or more likely to be exceeded than the groundwater standard (i.e., EP wt B EP ia ). The results showing EP wt B EP ia in Fig. 9 indicate that, under the conditions investigated in this study, the indoor Groundwater Exceedance Probability (%) Fig. 1 Exceedance probabilities for benzene in groundwater (EP wt ) and indoor air (EP ia )ata steady-state prior to source removal and b 6 years following source removal for a groundwater standard of 5 lg/l and an indoor air standard of.31 lg/m 3. Solid symbols represent houses on the plume centreline and open symbols represent houses located 125 m off of the centreline. For clarity, locations with EP wt and EP ia both equal to or % are not shown air standard (3.1 lg/m 3 ) is more protective of indoor air receptors than the groundwater standard (5 lg/l) is of groundwater receptors. The more protective standard here is defined as that which has the lower exceedance probability, and assumes that each standard was developed in such a way that meeting the standard is equally protective of a receptor. Based on these results, if a remediation target were established using a non-zero exceedance probability for groundwater concentrations, that target would not be protective of indoor air at the same exceedance probability.

13 Stoch Environ Res Risk Assess (216) 3: The magnitude of this discrepancy depends strongly on the standards used to define exceedance. For example, Fig. 1 shows exceedance probabilities in groundwater and in indoor air calculated at the location of each of the twelve houses, as in Fig. 9, but with EP ia values calculated using an indoor air standard of.31 lg/m 3 rather than 3.1 lg/m 3. While Fig. 9 shows exceedance probabilities in indoor air that are approximately 5 % greater than those in groundwater, Fig. 1 shows exceedance probabilities that are substantially greater. When an indoor air standard of.31 lg/m 3 was considered, locations with EP wt \ 5 % approached % exceedance in indoor air 6 years following source removal (Fig. 1b). A comparison of exceedance probabilities in groundwater and indoor air is important, as both types of receptors are typically considered in risk assessments of VOC plumes. However, many jurisdictions and sites compare groundwater concentrations to groundwater standards as a screening-level measurement to protect indoor air receptors, rather than comparing indoor air concentrations to indoor air standards. These results show that the groundwater standards intended to be protective of indoor air receptors should be selected such that the exceedance probabilities in groundwater and indoor air are similar. Higher values of EP ia indicate that the groundwater standard is not sufficiently protective of indoor air, and lower values of EP ia could prompt greater-than-required remediation. These results highlight the importance of considering all receptors in setting risk-based remediation objectives, and the usefulness of conducting coupled groundwater-indoor air simulations for assessing risks to multiple receptor types within a larger community. 4 Summary and conclusions A series of Monte Carlo simulations were performed to simulate benzene transport in groundwater and soil gas in a heterogeneous, three-dimensional, community-scale domain. This is in contrast to typical approaches that simulate transport in groundwater separately from transport through soil gas leading to vapour intrusion, and that assess risk to indoor air receptors by considering only a single building or site. Predicted risk to groundwater and indoor air was quantified using exceedance probabilities, calculated from multiple realizations of cases with varying hydraulic conductivity, fraction of organic carbon, and biodegradation rate constant. Results showed that, for the conditions and domain sizes investigated in this study, the uncertainty associated with different realizations of the same degree of heterogeneity was similar to that associated with different variances in hydraulic conductivity or the incorporation of heterogeneous distributions of organic carbon. This despite simulations that used a wide range of variances in hydraulic conductivity from well-characterized aquifers. Only the incorporation of biodegradation in the saturated zone produced substantial differences in the footprint of the plume. The results also showed a sharp gradient in exceedance probability at the lateral edges of the plume, which defined a narrow region of exceedance uncertainty and much of the community as having either a near % or near % chance of exceeding regulatory standards. Simulated acceptance times, defined as the time required for exceedance probabilities to decrease to an acceptable level (1 or 5 %), were found to be on the order of decades to centuries in these community-scale domains, and that these acceptance times depend strongly on the acceptance level chosen. For example, in this study acceptance times were between 1 and 88 years shorter if a 5 % exceedance probability was considered acceptable rather than a 1 % exceedance probability, depending on the location at which the risk was evaluated. Results from coupled simulations of reactive solute transport and vapour intrusion were used to directly compare the probability of exceeding either a groundwater or an indoor air standard in the same simulation. This is a different approach than that used in many jurisdictions, where groundwater concentrations are compared to groundwater standards as a screening-level measurement to protect indoor air receptors. Results showed that for the compound (benzene) and standards considered in this study, the indoor air standard was more likely to be exceeded than the groundwater standard. As such, if a source remediation strategy resulted in changes to a plume that were protective of indoor air, they would also be protective of groundwater. It is acknowledged that the model employed and the scenario simulated uses numerous simplifying assumptions relative to real world scenarios. However, the scenarios were chosen to be conservative; as such, additional factors, such as recharge, biodegradation in the vadose zone, and source zone concentrations decreasing during the life of the source zone, might reduce the predicted risk relative to the results shown. The objective, however, was not to reproduce a specific real world scenario. Rather, this study demonstrates the benefit of simulating contaminant transport in both groundwater and soil gas when predicting risk to communities surrounding a contaminated site. Furthermore, it illustrates how exceedance probability maps, acceptance times, and other probabilistic variables that integrate the results of Monte Carlo simulations, can be used in a practical manner by stakeholders in considering risk prior to and following site remediation efforts. Acknowledgments Funding for this research was provided by the Ontario Ministry of the Environment, Best in Science-Research Grant Project The authors would like to thank the project steering committee. We acknowledge the contributions from SHARCNET, a consortium of Canadian academic institutions who share a network of high performance computers. We also thank Christopher Power for