1 SOIL GAS MODELLING SENSITIVITY ANALYSIS USING DIMENSIONLESS PARAMETERS FOR J&E EQUATION Introduction Chris Bailey, Tonkin & Taylor Ltd, PO Box 5271, Wellesley Street, Auckland 1036 Phone (64-9)355-6005 Fax (64-9)355-6066 cbailey@tonkin.co.nz Site investigations at two Auckland sites indicated chlorinated organic contaminants in near surface soil and shallow groundwater beneath existing and/or proposed buildings. Vapour intrusion modelling was carried out as part of an environmental assessment to establish whether the levels of contaminants at each site posed health risks to building occupants. In accordance with established practice in New Zealand, the Johnson and Ettinger heuristic model 1 was used to conduct this modelling. Sensitivity analysis was carried out with the model to determine how conclusions would vary if data or assessment assumptions changed. This was accomplished using the conventional method of varying input parameter values over potential ranges and also by using a method presented by Johnson, one of the authors of the J&E model. The Johnson method 2 consists of determining the value of three dimensionless parameters from eight primary inputs to define what model outputs are sensitive to. The method also determines the dominant vapour transport mechanism, i.e. whether transport is chiefly advection or diffusion and whether it is through the soil or foundation. Johnson and Ettinger heuristic model The J&E model is widely used to estimate the concentrations of volatile contaminants migrating into indoor air from impacted soil and/or groundwater. It is a screening level model used to support risk-based decisions at contaminated sites. The United States Environmental Protection Agency (USEPA) J&E model users guide 3 describes the model as a one-dimensional analytical solution to convective and diffusive vapour transport into indoor spaces.provides an estimated attenuation coefficient that relates the vapour concentration in the indoor space to the vapour concentration at the source of contamination.inputs to the model include chemical properties of the contaminant, saturated and unsaturated zone soil properties, and structural properties of the building. Output is provided as an attenuation factor, alpha: C α = vapourindoorair Where C vapourindoorair is the concentration of vapour in indoor air (mg/m 3 ) and C soilgas is the concentration of vapour in the soil at the source (mg/m 3 ). The J&E equation determines α as: C soilgas 1 Johnson, P. C, and R. A. Ettinger. 1991. Heuristic model for predicting the intrusion rate of contaminant vapors in buildings. Environ. Sci. Technol. 25: 1445-1452. 2 Johnson, P. C, May 2002. Identification of critical parameters for the Johnson and Ettinger (1991) vapor intrusion model, API soil and groundwater technical task force paper no. 17. 3 United States Environmental Protection Agency, Office of Emergency and Remedial Response, 1997, Users Guide for the Johnson and Ettinger (1991) Model for Subsurface Vapor Intrusion into Buildings
2 Where α Q soil L crack exp + D crack η A B D T A B Q B L T D T A B Q B L T Q soil L crack exp D crack η A B D T A B Q soil L crack + exp 1 Q soil L T D crack η A B A B is the surface area of the enclosed space in contact with soil (m 2 ) D crack is the effective overall vapour-phase diffusion coefficient through the walls and foundation cracks (m 2 /day) L crack is the enclosed space foundation thickness (m) L T is the depth to the vapour source (m) Q B is the enclosed space volumetric flow rate of fresh air (m 3 /day) usually estimated to be the product of the enclosed space volume indoor air exchange rate with outdoor air Q soil is the pressure-driven soil-gas flow rate from the subsurface into the enclosed space (m 3 /day) equal to the product of the exchange rate and building volume η is the fraction of enclosed space surface area open for vapour intrusion (m 2 /m 2 ) referred to as the crack fraction as shown in Figure 1 below. The following assumptions were made in the derivation of the J&E equation: Vapours enter structures through cracks and other openings in the foundations and walls Convective transport is most significant very close to the foundations and vapour velocities decrease rapidly with increasing distance from the structure Vapour diffusion is the dominant mechanism for transporting vapours from sources away from the structure Vapours originating from directly below the foundation will enter the structure Figure 1 Johnson and Ettinger conceptual model with primary inputs (courtesy American Petroleum Institute) Determining critical inputs using dimensionless approach J&E model outputs are dependent upon on three dimensionless parameters. When determined, they establish the dominant transport mechanism across the foundation and the
3 overall rate limiting process for vapour intrusion. The three dimensionless parameters are determined from the eight primary inputs listed above. Site characteristics Modelling was conducted using site-specific data (where available) and literature data for input values. Both sites reviewed were contaminated with chlorinated organic compounds, namely trichloroethylene (), tetrachloroethylene (), chloroform and vinyl chloride. At both sites, the contamination is located about 1m depth in soil and groundwater. Soil gas measurements were available at Site A and these were used as source concentrations. At Site B, no soil gas measurements had been collected and so source concentrations were determined from groundwater data assuming equilibrium partitioning. Site A is underlain by a moist silty sand material (hydraulic conductivity estimated at about 10-6 m/s). Site B has a top layer of soil consisting of about 0.3m of relatively dry permeable material (hydraulic conductivity conservatively estimated at about 10-4 m/s). This is underlain of about 0.7m of moist, lower permeability material. Building characteristics Building area, foundation thickness and crack fraction were similar between the two sites. Differences between sites existed for the indoor air/subsurface pressure differential and indoor air exchange rates. The air conditioning systems proposed for Site A were considered to preclude a negative pressure differential between indoor air and the subsurface. Whereas Site B was considered to have the potential for a negative pressure differential. The Ministry for the Environment guidelines 4 value for pressure differential was used for Site B ( P = 3.5 Pa). Review of building information allowed site specific data to be used for the Site A indoor air exchange rate (ER). The value of ER for Site A was about ¼ of that used for Site B. Results of modelling factors averaged 8 x 10-4 for Site A and 3 x 10-4 for Site B. The modelling predicted that at Site A, and would be above acceptable levels for commercial land use. The modelling results predicted that at Site B, would be above acceptable levels for commercial land use. The alpha factors determined using the J&E equation for Site A and B are within observed alpha factor ranges 5and6. Conditions were such that no calibration data were available to compare the model results against for these sites. Sensitivity analysis As discussed above, sensitivity testing was accomplished using Johnson s dimensionless method and the conventional approach of varying input parameter values over potential ranges. 4 Ministry for the Environment, 1999, Guidelines for Assessing and Managing Contamination at Petroleum Hydrocarbon Sites 5 Hers et al, March 2006, AEHS Workshop, Vapour Intrusion, Status of Generic Screening levels Update on Empirical Vapour Attenuation Factor Analysis 6 Johnson, PC et al, Migration of Soil Gas Vapors to Indoor Air: Determining Vapor Attenuation Factors Using a Screening Level Model and Field Data From the CDOT-MTL Denver, Colorado Site, API Technical Paper 16 American Petroleum Institute, April 2002.
4 The dimensionless parameter method identified following: Significant differences in model inputs Dominant transport mechanism across foundation Site A Moist silty sand material (K h 10-6 m/s). P = 0 Pa Diffusion Site B 0.3m of dry permeable material (K h 10-4 m/s) underlain of about 0.7m of moist, lower permeability material. P = 3.5 Pa Advection Overall rate limiting process Diffusion through soil Not defined Critical parameters note critical does not imply there are large changes. Building height, depth to contamination, diffusion through soil and exchange rate. Building height, depth to contamination, diffusion through the soil, exchange rate and the ratio of the pressure driven advective flow from under the slab to the air flow through the building To enhance understanding of the results of the dimensionless analysis and to conduct conventional sensitivity testing, the attenuation factor, α, was charted against a suitable range of values for each of the primary input parameters. The critical parameters identified from the dimensionless analysis for both sites have been plotted first, i.e. building height, depth to contamination, diffusion through soil and exchange rate. Note that Site A charts are plotted for a different range of alpha factors than Site B and that an increase in α represents an increase in predicted indoor air concentration.
5 Parameters identified through dimensionless analysis as critical for both sites: Site A: vs building height (Lb) Site B: vs building height (Lb) 1 2 3 4 5 1 2 3 4 5 Building height (m) Building height (m) Site A: vs vapour contamination depth (Lt) Site B: vs vapour contamination depth (Lt) 0 0 1 2 3 4 5 Depth to vapour contamination (m) 0 1 2 3 4 5 Depth to vapour contamination (m) Site A: vs Diffusion coefficent (Dt) Site B: vs Diffusion coefficent (Dt) 0 10 7 10 7 10 7 10 7 10 6 Diffusion coefficient (m2/s) 0 10 7 10 7 10 7 10 7 10 6 Diffusion coefficient (m2/s) Site A: vs exchange rate (ER) Site B: vs exchange rate (ER) 0 1 2 3 4 Exchange rate (per hour) 0 1 2 3 4 Exchange rate (per hour)
6 Parameters identified through dimensionless analysis as critical for site B only: Note that because the subsurface/indoor air pressure differential at Site A was assigned a value of 0Pa, the value for Q soil (convective flow into the building) was also zero. Site B: vs Qsoil/Qb 0 Parameters identified through dimensionless analysis as non-critical for either site: Qsoil/Qb Site A: vs foundation thickness (Lcrack) Site B: vs foundation thickness (Lcrack) 0 0.1 0.2 0 0.1 0.2 Foundation thickness (m) Foundation thickness (m) Site A: vs crack fraction Site B: vs crack fraction 0 0.01 Crack fraction 0 0.01 Crack fraction Site A: vs crack fraction Site B: vs crack diffusion coefficent (Dcrack) 10 7 10 7 10 7 10 7 10 6 Crack diffusion coefficient (m2/s) 10 7 10 7 10 7 10 7 10 6 Crack diffusion coefficient (m2/s)
7 Discussion In general, sensitivity analysis is carried out to determine how conclusions would vary if data or assessment assumptions changed. Sensitivity analysis is also used to ensure that where there was less certainty in the value selected for a parameter, that conservative values are selected. This is accomplished by varying the value of a specific input so that an understanding of the effects on the result can be gained. This can be used to guide the modeller to ensure that the inputs err on the cautionary side, lessening the potential for under-prediction. Vapour intrusion assessments are usually conducted with sparse data. Uncertainty exists in the conceptualisation of the model problem and in the selection of values for the model parameters. Uncertainty arises in the use of information which is not site-specific, where spatial variability is not accounted for and where model results are not compared against field measurements. Any modelling faces significant challenges to address these uncertainties. For the J&E model uncertainties, it is generally considered that precision no greater than one order of magnitude 7. For the analysis presented in this paper, the charts show that the model is sensitive to the parameters identified as critical by the dimensionless method. These critical parameters produce obvious sensitivities while non-critical parameters produce little change in the predicted attenuation factor. The charts give a good understanding of the model s sensitivity with changes in the critical parameters. Where model results indicate unacceptable risks (as determined at both of these sites), it is useful to have an understanding of the output sensitivity to changes in the input values. This focuses further investigation (if undertaken) which can be used to verify the parameters which cause the largest changes to the output. Some parameters are clearly not subject to any further assessment, e.g. building height. Others, such as diffusion coefficients, can benefit from further investigation. For Site A, collection of additional diffusion coefficient inputs (soil moisture and porosity) would provide confidence in model predictions (see discussion below). With Site A having no pressure differential and therefore no advection across the foundation, the J&E equation simplifies considerably to: α DTA Q L B B T The result is that foundation parameters (L crack, D crack etc) have no influence on model predictions for Site A (the Site A charts for the foundation parameters were presented for completeness). This is inline with the derivation assumption that vapours originating from directly below the foundation will enter the structure regardless of foundation characteristics (unless it is vapour impervious). Diffusion coefficients are the only chemical dependent primary parameter used in the J&E equation. So when alpha is plotted against diffusion coefficient as show above, there is only one line represents each of the contaminants. The simplified equation for alpha determined without any pressure differential means that alpha is plotted as a straight line against diffusion coefficient in this case. Diffusion coefficients are determined using the Millington-Quirk equation which uses the chemical specific diffusion coefficients for air and water, soil porosity and moisture content data. The calculation of the coefficient is sensitive to secondary parameters such as porosity and moisture content and so for cases such as Site A where the dominant transport mechanism is diffusion, collection of this relatively inexpensive data is important. While Johnson indicates that varying the critical parameters does not force large output changes, there are exceptions to this. For example, small changes to air exchange rates produce large changes in alpha, especially for Site A. Air exchange rates this low are not typical however. 7 Weaver, James W. and Fred D. Tillman, 2005. Uncertainty and the Johnson-Ettinger Model for Vapor Intrusion Calculations. EPA Office of Research and Development, National Exposure Research Laboratory, EPA/600/R-05/110.
The EPA run an online sensitivity analysis tool 8 for the J&E model based on a paper by EPA researchers 9. This allows uncertainty to be assessed for changes to multiple parameters simultaneously for which larger alpha changes are noted. The choice of whether multi-parameter anlsysis should be carried out is up to individual assessors and reviewers. Johnson s dimensionless method could be used to identify which parameters to vary in a multi-parameter analysis. Conclusions Johnson s dimensionless method was used to identify the critical parameters for vapour intrusion modelling for 2 sites in Auckland. At Site A, diffusion was identified as the dominant mechanism for vapour movement through the floor slab and diffusion through soil was the overall rate limiting mechanism. The critical parameters were building height, depth to contamination, diffusion through soil and exchange rate. At Site B, an overall rate limiting mechanism was not identified but advection was found to be the dominant mechanism for vapour movement through the floor slab. The critical parameters were building height, depth to contamination, diffusion through the soil, exchange rate and the ratio of the pressure driven advective flow from under the slab to the air flow through the building. Review of the sensitivity of model outputs to changes in the remaining parameters (non-critical) corroborated the results of the dimensionless analysis. The review was accomplished by charting changes to all of the primary inputs against alpha, the attenuation factor. These charts also provided useful information about how sensitive model changes were to changes in the parameters identified as critical through the dimensionless method. In conclusion, it is advantageous to determine the critical parameters using the dimensionless method and then the sensitivity of outputs to these parameters can be determined. The remaining non-critical parameters would not require further attention. However it is noted that because vapour intrusion modelling only gives an order of magnitude accuracy, the results of sensitivity analyses, however they are conducted, should be considered in the context of uncertainties that are not identified with the method e.g. sensitivity to secondary inputs, conceptualisation of the model problem, heterogeneities and model calibration. The options for further assessment should also be considered alongside remedial measures where this might also be appropriate. 8 8 http://www.epa.gov/athens/learn2model/part-two/onsite/uncertainty-vi.htm 9 F.D Tillman and J.W. Weaver, 2006, Uncertainty from synergistic effects of multiple parameters in the Johnson and Ettinger (1991) vapor intrusion model, Atmospheric Environment, 40(22), 4098-4112.