Preliminary Review of Radon in Linde Tunnels 1 SC&A – October 13, 2010 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

However, this report is pre-decisional and has not been reviewed by the Advisory Board on Radiation and Worker 

Health for factual accuracy or applicability within the requirements of 42 CFR 82. 

TO: Advisory Board on Radiation and Worker Health Work Group on Linde Ceramics Plant 

FROM: Robert Anigstein, SC&A 

SUBJECT: Preliminary Review of NIOSH White Paper on Radon in Utility Tunnels at Linde 

DATE: October 13, 2010 

Preliminary Review of “Evaluation of Radon Concentrations in the Utility Tunnels at 

Linde Ceramics” 

In a NIOSH White Paper, Allen (2010) developed models to estimate the plausible upper bound 

of 222Rn concentrations in utility tunnels at Linde Ceramics. The Advisory Board's Work Group 

on the Linde Ceramics Plant tasked SC&A with reviewing NIOSH's revised approach to the 

issue of 222Rn in the utility tunnels. We have accordingly reviewed the White Paper and have a 

number of comments, observations, and findings. 

1. Sequential Review 

We first present a sequential review of the White Paper, discussing the development and 

application of the models in the same sequence as presented by Allen (2010). According to 

Allen, there are two separate sources of radon in the tunnels: 226Ra contamination on the inner 

surfaces of the tunnels and elevated levels of 226Ra in the soil surrounding the tunnel. In the 

remainder of this review, “radon” is understood to mean 222Rn and “radium” means 226Ra. For 

the purpose of the present review, we will treat the methods of calculating the contributions of 

these two sources as separate models, since each method is specific to the source term 

considered. 

1.1 Part 1 – Radon Present from Radium Contamination Inside the Tunnels 

In Part 1, Allen (2010) calculates the contribution of the radium contamination inside the tunnels 

to the radon concentration, equating the buildup of the daughter product from the decay of the 

parent to the rate of removal by radioactive decay of the daughter plus the air exchange rate in 

the tunnel. Site-specific parameters include the surficial concentration of radium, the surface 

area per linear cm (equal to the perimeter of the cross-section in cm), the volume per linear cm 

(equal to the area of the cross-section in cm2

), and the air exchange rate. The radium 

concentration is based on the 95th percentile contamination levels measured by IT (2002); the air 

exchange rate of 0.1 h-1 is taken from the same document. The tunnel in Allen's model has a 

square cross-section, 2 m high by 2 m wide. The surface area is equal to the lower end of the 

range of cross-sections presented by IT. This is a claimant-favorable assumption, since the radon 

concentration due to the surficial contamination by radium is proportional to the ratio, where 

A is the interior surface area and V is the volume. IT states that the cross-section of the tunnel is 

cylindrical in some places. The square shape used in the model yields a higher ratio, and is 

again claimant favorable. We find that the model for estimating the contribution of the radium 

contamination inside the tunnel to the radon concentration is scientifically correct; the assumed 

parameters are plausible and claimant favorable. 
1.2 Part 2 – Radon Infiltration into the Tunnels 

In Part 2, Allen (2010) presents an elegant derivation of the differential equations which he uses 

to model the infiltration of radon into the tunnel from the surrounding soil. We have verified the 

derivation up through his Equation 8, which we reproduce in slightly different form: 

cs = radon concentration in pore space in soil 

 = radon decay constant 

= 2.0979 × 10-6 s-1

D = diffusion coefficient (cm2/s) 

S = rate of ingrowth of radon from radium in soil (pCi cm-3 s-1) 

= 

Preliminary Review of Radon in Linde Tunnels 2 SC&A – October 13, 2010 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

However, this report is pre-decisional and has not been reviewed by the Advisory Board on Radiation and Worker 

Health for factual accuracy or applicability within the requirements of 42 CFR 82.

) 

 

 cp = radium concentration in soil (pCi/g

 ε = radon emanation coefficient 

 n = porosity of soil 

Allen (2010) then presents his Equation 9 as the general solution to his Equation 8: 

r = 

K1 and K2 are constants that determine the particular solutions for a given set of boundary 

conditions. 

Allen (2010) then discusses three sets of boundary conditions for each of which he evaluates K1

and K2 to derive a solution to Equation (2).1

 We have confirmed the derivation of the particular 

solution for Allen's symmetrical source boundary conditions, presented by Allen (2010, 

Attachment A). This solution is mathematically valid for the values of K1 and K2 derived by 

Allen. We will confine the remainder of this review to a discussion of the results for the 

symmetrical source boundary conditions. 

1

 We enclose equation numbers in this review in parentheses to distinguish them from those of Allen (2010). 
2. Findings and Observations

Preliminary Review of Radon in Linde Tunnels 3 SC&A – October 13, 2010 

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However, this report is pre-decisional and has not been reviewed by the Advisory Board on Radiation and Worker 

Health for factual accuracy or applicability within the requirements of 42 CFR 82.

all 

, 

ent to the contaminated zone. 

The model geometry described by Allen 

(2010) is shown in Figure 1. The 

contaminated zone is assumed to be 100 cm 

deep. The calculation of the area of the w

subject to infiltration implies that the radium 

contamination is present on only one side of 

the tunnel. The tunnel is lined with concrete

which Allen implies is impervious to 

infiltration by radon. However, he assumes 

that the concrete has cracks that constitute 10% of the area adjac

Figure 1. Geometry of Radon Infiltration 

Model as Described by Allen (2010)

We have several conceptual problems with this model. Allen (2010) likens the cracked concrete 

to a picket fence, the cracks being the openings in the fence. Let us assign the x direction to the 

lateral movement of radon illustrated in Figure 1, and assume that the cracks, according to the 

“picket fence” analogy, run in the z direction. Since the radon, according to the model, cannot 

flow through the solid concrete, the x component of the concentration gradient at the location of 

a crack will be different than at the location of the solid concrete. The gradient will therefore 

also have a y component. Furthermore, the stratification of the radium contamination shown in 

Figure 1 will also create a gradient in the z direction. Thus, the 1-dimensional model is not 

applicable to this situation. 

Another issue is the omission of infiltration through the left side of the tunnel, as illustrated in 

Figure 1. Also, since the tunnel runs underground, there is likely to be contaminated soil above 

the tunnel. Furthermore, the radon generated by the decay of naturally-occurring radium in the 

soil outside the contaminated zone also needs to be accounted for in dose reconstruction under 

EEOICPA. Radon would thus infiltrate the tunnel through the sides, top, and bottom, again 

causing a problem for the 1-dimensional model. In addition, the assumption that concrete is 

impervious to infiltration except in the area of the crack is questionable. According to Yu et al. 

(1993, table 7.1), the radon diffusion coefficient in concrete has been reported to be as high as 

4 × 10-7 m

2

/s (4 × 10-3 cm

2

/s). Given that 90% of the concrete is not cracked, and given the 

relatively thin layer of concrete compared to the thick soil layer, the infiltration through concrete 

needs to be accounted for in what is intended to be a bounding assessment. 

We have further questions regarding the values of the parameters used in the model. The value 

of the soil diffusion coefficient, D = 0.02 cm2

/s, is not claimant favorable. Yu et al. (1993, 

table 7.1) list values of (3.2 ± 1.5) × 10-6 m

2

/s, which means that D could be as high as 

4.7 × 10-6 m

2

/s (0.47 cm2/s)—more than twice the value used by Allen (2010). Since the purpose 

of Allen's analysis is to produce a bounding assessment, it should use the highest plausible value. 

The assumption that cracks comprise 10% of the area of the concrete needs to be documented or 

justified; it appears to be an arbitrary choice. 

We also question the assumed radium concentration in the contaminated zone, as well as the 

depth of the zone. Allen derived the 95th percentile by calculating the median and geometric 

standard deviation of 711 soil samples. This method is a mix of the rank-order method, by 

which the middle member of the ranked values (in this case, the 356th value) denotes the median, 

and an analytical method in which the geometric standard deviation is calculated from the 
Preliminary Review of Radon in Linde Tunnels 4 SC&A – October 13, 2010 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

However, this report is pre-decisional and has not been reviewed by the Advisory Board on Radiation and Worker 

Health for factual accuracy or applicability within the requirements of 42 CFR 82.

standard deviation of the logarithms of all the values. Such a method is valid where the 

underlying distribution is known to be lognormal. 

We have estimated the 95th percentile radium concentration using a subset of the samples used 

by Allen (2010). Bechtel (1993, Table 4-6) lists the radium concentrations in 46 soil samples 

collected in Area 4. According to Davidson (2009, Figure 2-1), Building 30 was located in 

Area 4. According to an annotated map of the utility tunnels furnished to SC&A during an 

interview with a Linde site expert, the utility tunnels pass near Building 30, so that some portion 

of the tunnels is in Area 4 (SC&A 2010, Attachment 1). We calculated the geometric mean and 

g.s.d. of these data, using all 46 values, and derived a 95th percentile concentration (assuming 

that the underlying distribution is lognormal) equal to 24.1 pCi/g. The 95th percentile derived 

using the rank-order method, which makes no assumption about the form of the underlying 

distribution, is 28 pCi/g. Using Allen's method on this subset of soil samples, we obtain a value 

of 16.6 pCi/g. 

Our analysis demonstrates that Area 4, which lies close to at least a portion of the tunnels, has 

higher radium levels than the areas covered by the 711 samples analyzed by Allen (2010). 

Furthermore, the distribution is not lognormal but highly skewed, since the true 95th percentile 

value obtained by the rank-order method is almost twice the value obtained by taking the median 

and the g.s.d., while the value obtained by what we shall call a purely analytical method lies in 

between. We believe that the value used by Allen is not a claimant-favorable representation of 

the 95th percentile radium concentration in the vicinity of the tunnels. 

In another observation, we note that the maximum depth of radioactive contamination in Area 4 

is 2.7 m in borehole B29R36 beneath Building 30 (Bechtel 1993). Therefore, the assumption 

made by Allen (2010) that the contamination is limited to a depth of 100 cm is neither correct 

nor claimant favorable. 

3. Summary and Conclusions 

We have confirmed the model presented by Allen (2010) to model the buildup of radon in the 

tunnel from the decay of radium contamination on the inner surfaces of the tunnel, as well as the 

parameters used with that model to calculate the radon concentrations generated by that source. 

We have also confirmed his derivation of the differential equation used to model the 

1-dimensional diffusion of radon into the tunnel from the radium-contaminated soil outside the 

tunnel. We have further confirmed his derivation of a general solution to this equation and of the 

particular solution of the symmetrical source boundary conditions. We have closely matched the 

maximum radon concentrations based on this particular solution and the parameters listed in 

Attachment B to the report. 

We do not agree that the 1-dimensional model adequately describes the actual 3-dimensional 

geometry that governs the diffusion of radon from the soil into the tunnels, nor that the results 

produced by the model necessarily produce bounding radon concentrations in the tunnels. Using 

this model, Allen (2010) would need to justify his assumption that cracks constitute 10% of the 

area of the concrete encasing the tunnel. He also would need to demonstrate that the diffusion of 

radon through the 90% of the concrete that is intact can be ignored. We do not find that the 

value of the diffusion coefficient used with the model is bounding or claimant favorable. 

Similarly, the values assigned to the average radium concentration in the soil and the depth of the 

contaminated zone used in the analysis are neither bounding nor claimant favorable. 
Preliminary Review of Radon in Linde Tunnels 5 SC&A – October 13, 2010 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

However, this report is pre-decisional and has not been reviewed by the Advisory Board on Radiation and Worker 

Health for factual accuracy or applicability within the requirements of 42 CFR 82.

This preliminary review is limited to an analysis of the models and the resulting calculations 

presented by Allen (2010). It does not address other issues, such as the buildup of radon in the 

tunnels due to advective transport of radon from the soil, which has been shown to be a 

significant contributor to indoor radon concentrations. 
Preliminary Review of Radon in Linde Tunnels 6 SC&A – October 13, 2010 

This report has been reviewed for Privacy Act information and has been cleared for distribution. 

However, this report is pre-decisional and has not been reviewed by the Advisory Board on Radiation and Worker 

Health for factual accuracy or applicability within the requirements of 42 CFR 82.

NOTICE: 

SC&A. 2010. “Linde Worker Interview Notes Niagara Falls, New York, May 19-21, 2010.” 

SC&A, Inc., Vienna, Virginia, and Saliant, Inc., Jefferson, Maryland. 

References

Allen, D. (NIOSH/DCAS). 2010. “Evaluation of Radon Concentrations in the Utility Tunnels at 

Linde Ceramics.” 

Bechtel National, Inc. 1993. “Remedial Investigation Report For The Tonawanda Site 

Tonawanda, New York,” DOE/OR/21949-300, Vol. 1. Oak Ridge, Tennessee: United States 

Department of Energy, Oak Ridge Operations Office. [SRDB Ref ID 9026: Section 4.0: “Nature 

and Extent of Contamination.”] 

Davidson, G. R. 2009. “An Exposure Matrix for Linde Ceramics Plant (Including Tonawanda 

Laboratory),” ORAUT-TKBS-0025, Revision: 01 PC-1. ORAU Team Dose Reconstruction 

Project for NIOSH. 

IT Corporation (IT). 2002. “Dose Assessment for the Existing Contamination Levels within the 

Linde Site Tunnel Complex: FUSRAP Linde Remedial Action, Tonawanda, New York,” [SRDB 

Ref ID 49892]. 

Yu, C., et al. 1993. “Data Collection Handbook to Support Modeling of Impacts of Radioactive 

Material in Soil,” ANL/EAIS-8. Argonne, IL: Argonne National Laboratory.