Development of avapor intrusion model with variably saturated and non-isothermal unsaturated subsurface soils
Dawit N. Bekele A, B, Ravi NaiduA, B*, and Sreenivasulu Chadalavada C
Supplemental information: model development of indoorCARETM, model verification and validations data
Contents
A.List of symbols and abbreviations
B.Input parameters values Implemented in model comparison test
C.indoorCARETM model development for vapor intrusion into indoor air
Table B. 1 Input parameters for the model assessments
Table B. 2 Chemical specific properties adopted for the model assessments
Table D. 1Formulae for the indoorCARETM model development extensions to Johnson and Ettinger (1991) and BioVapor (2011)
A.List of symbols and abbreviations
VIM / Vapor intrusion modelVOC / Volatile organic compounds
PHC / Petroleum hydrocarbon compounds
CHC / Chlorinated hydrocarbon compounds
NA / Natural attenuation
VI / Vapor intrusion
CSM / Conceptual site model
r / Residual soil moisture content (-)
s / Saturated soil moisture (-)
w(z) / “Effective” degree of saturation (suction dependent) as function of depth (-)
a ,n / Air field pour space (-)
T / Soil total porosity (-)
Hz / Suction head (m)
α, n & m / Van-Genuchten parameters (-)
T(z,t) / Soil temperature at time t in days and depth z (oC)
Ta / Average daily soil temperature (oC)
A0
(oC) / Annual amplitude of annual temperature obtained from regression (maximum minus the minimum recorded temperature)
t0 / Time lag from an arbitrary date to the occurrence of the minimum temperature in a year (For this study the Australia weather condition is used and time lag is taken as June), (days)
Dg / the vapor diffusion coefficient in bulk air (cm2/ sec)
Dl / the vapor diffusion coefficientin water phase (cm2/ sec)
D / Damping depth is given by: D=2Dh/ , =2/365 day-1
Dh / Thermal diffusivity (m2/sec)
Cv / Soil thermal conductivity (W/m K)
? / Heat capacities (J/kg.oC)
Ji,T / Total mass flux (mg/cm2.sec)
JiV / Mass advection flux (mg/cm2.sec)
JiD / Bulk diffusive mass flux (mg/cm2.sec)
Ji, tz / Volumetric flux (m3/m2.sec)
g / Dynamic gas viscosity (g/cm.sec)
∇Pz / Pressure gradient (g/m.sec2)
g / Gravitation acceleration (m/sec2)
ρg / Density of vapor compound (g/cm3)
n / Number of moles of the vapor (mole)
M / Molar mass of the vapor (g/mole)
R / Ideal gas constant (m3 atm /K .mole)
T(z) / Vadose zone temperature at specific depth in the vadose zone soil (oC)
P (z) / Vadose zone pressure as function of depth and soil temperature (atm)
Po / Atmospheric pressure at Z=0 the ground surface, 1 atm
Mi / Molecular weight of chemical, i
krG(Z) / Relative gas permeability of vadose zone soil as a function of the gas saturation (SG) and depth (Z)
Kg (SG) / Permeability of the unsaturated medium at a particular gas saturation
kG / Gas permeability of vadose zone soil at 100% saturation (m2)
Se / Effective water saturation (-)
De (z,i) / Effective vapor diffusion of the chemical i, as a function of depth in the vadose zone soil (cm2/sec)
Dvi, Dwi / Chemical vapor air and water diffusivity coefficient (cm2/sec)
HR / Henry’s law constant at the reference temperature (atm-m3/mole)
HR (z,i) / Temperature adjusted Henry’s coefficient for the chemical i at the discrete layer Z (atm-m3/mole)
Hv,Tz (z,i) / Enthalpy of vaporization at the discrete layer Z (cal/mole)
R / Gas constant (8.205 E-05 atm-m3/mol-oK); RC Gas constant (1.9872 cal/mol-oK)
Hv,b / Enthalpy of vaporization at the normal boiling point (cal/mole)
TC / Critical temperature (oK)
TB / Normal boiling point (oK)
µg / First order volatile vapor natural attenuation in the gas phase (1/hr)
µw / First order volatile vapor natural attenuation in the water phase (1/hr)
Koc / Chemical organic partitioning coefficient (cm3/g)
foc / Soil organic contents (g/g)
φi / Chemical –specific mass ratio of oxygen to chemical consumption stoichiometric ratios ( mg-chemical/mg-oxygen)
Lt / Separation between building foundation and the source of contamination (cm)
La / Aerobic depth (separation between the building foundation and the reaction zone) (cm)
Lb / Anaerobic depth (separation between the reaction zone and source of contamination) (cm)
B.Input parameters values implemented in model comparison test
The Johnson and Ettinger(1991) model requires eight primary inputs for determining the attenuation coefficient (α). Primary inputs parameters ofindoorCARETM and BioVapor model (2009)for comparison test are not consistent with J&E model as a resultcareful selection of values is necessary to ensure results are comparable. Some primary input parameters of BioVapor and indoorCARETMmodel requires derivation from intermediate results of J&E model to match the comparison input parameters. For instance, foundation crack fractioninput parameters for J&E model is internal calculation however are primary inputs for indoorCARETM model. For this reason the J&E model run is used to calculate the inputs for the indoorCARETM.
Table B.1 and B.2 showsdetails on model inputs parameters used for the establishment of baseline conditions and justifications for recommended values or reasonable value ranges, and unknown parameters for which measurements are undertaken. Input parameters are classified as chemical, subsurface soil and building parameters.
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Table B. 1 Input parameters for the model assessments
Parameter / Symbol / UNIT / Recommended range / Model inputJ&E
(1991) / BioVapor
(2009) / indoorCARETM
(2012)
Soil parameters for the model assessments / Min. / Max.
Soil type / SCS / - / - / - / Sand / Sand / Sand
Soil bulk density (a) / ρs / g/cm / 1.25 / 1.75 / 1.7 / 1.7 / 1.7
Soil porosity (a) / n / - / 0.34 / 0.53 / 0.35 / 0.35 / 0.35
Soil moisture content (a) / θw / - / 0.039 / 0.17 / 0.05 / 0.05 / 0.05
Annual median soil temperature (a) / T / oC / - / - / 10 / 10 / 10
Organic fraction(a) / foc / - / NA / 0.005 / 0.005
Benzene source concentration / Csource / g/m3 / 0.01-100 / 0.01-100 / 0.01-100
Building parameters for the model assessments / Default
Foundation slab to soil gas Source Depth / L / cm / 300 / 300 / 300
Volume air exchanges (e) / ER / h-1 / 0.25 / 6 day-1 / 6 day-1
Room height to foundation slab (c) / Lmix / cm / 244 / 244 / 244
Foundations thickness (c) / Lcrack / cm / 15 / 15 / 15
Foundation area (c) / Ab / cm2 / 1060000 / 1060000 / 1060000
Convective flow rate from the soil into the
building (c) / Qs / cm3/s / 83 / 83 / 83
Advective air flow under the foundation (c) / Qf / cm3/s / NA / 83 / 83
Soil-building pressure difference (b) / ∇pwind / Pa / 40 / NA / NA
Soil permeability to vapor flow (b,d) / kv / cm2 / Min=1; max=10 / 5 / NA / NA
The average gas phase viscosity of the gas mixture / g / g/cm.s / 1.78E-04 / 1.78E-04 / 1.78E-04
Water content of the foundation cracks (c) / θfwcrack / - / NA / 0 / 0
Soil filed foundation cracks (c) / θfacrack / - / NA / 1 / 1
Floor- wall seam gap (f) / Xcrack / cm / Min=0.05, max=1.0 / 0.15 / NA / NA
Foundation crack fraction (b) / η / - / 3.69E-4† / 3.77E-04 / 3.77E-04
Minimum oxygen for bio-degradation (c) / O2- min / %v/v / Min=1; max=5 / NA / 1 / 1
Note : a U.S. EPA (U.S. EPA 1996b, 1996a)
b Johnson and Ettinger(1991)
c De Vault (2007)
dNazaroff et al.(1987)
e Koontz and Rector (1995)
f Loureiro et al. (1990); Eaton and Scott(1984)
†calculated
NA, not input value
‡ For indoorCARETM model for Site Conceptual model II soil moisture and temperature values are simulation value
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Table B. 2 Chemical specific properties adopted for the model assessments
Chemicals / MWg/g-mole / Dair
cm2/sec / Dw
cm2/sec / φ
mg-chem/mg-O2
Benzene†
Trichloroethylene‡
Oxygen† / 78.11
131.39
32.00 / 8.80E-02
7.90E-02
1.75E-01 / 9.80E-06
9.10E-06
1.70E-01 / 0.33
-
-
Chemicals / kw
1/hr / Koc,i
cm3/g / TB
oK / TC
oK / ΔHv,b
cal/mol
Benzene†
Trichloroethylene‡
Oxygen† / 0.79
-
- / 58.9
166
- / 353.24
360.36
- / 562.16
544.20
- / 7342
7505
-
† fromBioVapor chemical database
‡ from Johnson and Ettinger model chemical database
C.Model verifications
Vapor intrusion with underlying homogeneous subsurface (CSM–I)
Model simulations were executed using hypothetical homogeneous subsurface soil with a source located 300 cm beneath the foundation slab. Input values of uniform soil moisture content ranging from 0.05 to 0.3% v/v and uniform soil temperature input ranging from 8 to 25°C were considered in the first instance for model predictive output comparisons.
The unsaturated subsurface soil effective vapor diffusion coefficient and predicted values for alpha, calculated for CSM–I by the indoorCARETM model and the results obtained from J&E models are identical for the no-biodegradation case. The indoorCARETM model simulation results also align with the Bio model when biodegradation is included. The simulation results plotted in Figure 2a and 2b show that the codes for indoorCARETM model algorithms are accurately translated to Fortran 90 computer program from the original models used in the methodology. The alpha value shows significant difference with respect to the J&E model due to the contribution from biodegradation of benzene (Figure 2a). Similarly, an increase in uniform vadose zone soil temperature also increases soil vapor pressure, resulting in higher indoor concentrations (Figure 2b). The effect of spatial heterogeneity of subsurface soil moisture content and temperature are discussed the manuscript in sections 3.1.2 and 3.1.3.
Figure 1a
Figure 1b
Figure 1Model comparisons under homogeneous subsurface conditions where the moisture content and temperature are assumed to be constant from source zone to the surface or the slab: variable soil moisture content (2a) and non-isothermal/ variable soil temperature (2b)
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D.indoorCARETM model development algorithm
This section provides derivations of fate and transport equations used in the IndoorCARETM model development modified equation from Johnson and Ettingermodel, (1991) and BioVapor (2009) model. The modified model equations are illustrated in the table below.
Table D. 1Formulae for the indoorCARETM model development extensions to Johnson and Ettinger (1991) and BioVapor (2011)
Description / Formulae fate and transport of vapor with biodegradationA generalized mass balance equation at a steady state condition.
EQ 1
First order chemical degradation rate.
EQ 2
Effective vapor diffusion coefficient at mesh points(Millington and Quirk 1961; Hillel 1982; van Genuchten 1980).
where
, and
;
;EQ 3
Model simulation for no biodegrading compounds(Johnson and Ettinger 1991).
EQ 4
Zero-order baseline respiration.
;EQ 5
Oxygen flux at the foundation-soil interface with zero-order baseline respiration.
EQ 6
Oxygen flux at the aerobic-anaerobic interface with oxygen downward diffusion, soil resp., and thermal advections(Tillman and Smith 2005; Scanlon et al. 2002).
EQ 7
Change in oxygen flux across aerobic layer.
EQ 8
Chemical flux with no reaction in the anaerobic zone.
EQ 9
Oxygen flux at the reaction zone.
;EQ 10
Oxygen flux specified (oxygen flux is constraint condition). The quadratic solution for La/Lt, in the range of
0 < La/Lt <1
Substituting EQ 5 and 8 in to EQ 9
Substituting Jf,o2 from Equation 5, with Ct(i) = 0, and
Lt=La + Lb
; where
, and
CEQ 11
Oxygen concentration specified (oxygen concentration is constraint condition). The quadratic solution for La/Lt, in the range of
0 < La/Lt <1
Substituting EQ 5 and 8 in to EQ 9
;
Substituting with Ct(i) = 0 from Equation 5 and Lt=La + Lb
; where
;
; and
;EQ 12
Boundary condition with vapor concentration of chemical ‘i’ at near surface ‘Co’.
EQ 13
Dahmkoler number
; EQ 14
A steady state solution to EQ 2
;EQ 15
In the aerobic with degradation
;EQ 16
EQ 17
In the anaerobic with no degradation, flux is constant (Js=Jt). At the aerobic- anaerobic interface.
EQ 18
Attenuation factor with biodegradations
;EQ 19
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