Environmental Forensics: Principles and Applications - Appendices docx

To examine this question using the diffusion mathematics outlined in Crank 1985, a one-dimensional plane diffusion gas or liquid through a porous plate is assumed.. SampleCalculation for

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The basic approach is to consider the diffusion of a liquid through a medium bounded

by two parallel plates with the planes at z = 0 and x = 1 After a time, a steady-state

is reached in which the concentration remains constant at all locations in the ment The diffusion equation in one dimension, therefore, reduces to (Crank, 1985):

provided that the diffusion coefficient (D) is constant On integrating with respect to

x, the following expression arises:

and by introducing the conditions at x = 0 and x = l and integrating, then:

[C – C1/C2 – C1] = x/l (Eq A.3) The previous two expressions show that the concentration changes linearly from C1

to C2 through the pavement The transfer rate of the diffusing substance is the same across all sections of the membrane, as described by the following expression:

F = –DdC/dx = D(C1 – C1)/l (Eq A.4)

If the thickness (l) and the surface concentrations (C1 and C2) are known, then D can

be deduced from an observed value of F using this equation.

If the surface x = 0 is maintained at a constant concentration C1 and at x = 1, then there is evaporation into an atmosphere for which the equilibrium concentration immediately within the paved surface is C2, so that:

∂C/∂x + h(C – C2) = 0, x = l (Eq A.5) then

(C – C1)/(C2 – C1) = (hx)/(1 + hl) (Eq A.6) and

A.2 SAMPLE CALCULATION

Given these relationships, the one-dimensional gas diffusion rate through a paved surface can be approximated using variations of the previous equations In this example, it is assumed that a vapor cloud of PCE has accumulated within the concrete catch basin housing a vapor degreaser The concrete is not cracked, nor are there expansion joints (i.e., it was poured in placed) The vapor cloud has been allowed to accumulate and collect within the concrete catch basin over a holiday during which the forced air system in the building is not operating The question

therefore, is can the PCE vapor move through the concrete over the 5-day holiday

period and, if so, at what rate?

To examine this question using the diffusion mathematics outlined in Crank (1985), a one-dimensional plane diffusion (gas or liquid) through a porous plate is assumed The following parameters and values are assumed in this example:

• Henry’s Law constant for PCE is 2.82 ¥ 10–2 atm m3/mol

• PCE is absent in the concrete and in the soil below it (C2 = Co = 0)

• The concentration of PCE in the vapor above the concrete is 1.272 ¥ 10–4 g/cm3

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A graphical representation of this problem is shown in Figure A.1 In this case, the following governing equation becomes:

For a small period of time, then:

M( ) = Â ( / ) / exp{–( + ) /( )}

=

•

1 2 1

De = Do(A10/3)/PT2 (Eq A.17) Assuming that the volumetric air content of the concrete is 0.013 – 0.023, the total porosity is between 0.06 and 0.14, and the gas diffusion rate for PCE is 0.0785 cm2/ sec (for TCE ª 7100 cm2/day), then:

De = (0.0785 cm2/sec)((0.013 – 0.023)3.33/(0.06 – 0.14)2) (Eq A.18) = (0.078 cm2/sec)((2.67 ¥ 10–5) – (9.73 ¥ 10–4)) (Eq A.19) = (2.67 ¥ 10–6) – (7.64 ¥ 10–5) cm2/sec (Eq A.20) Using this range of values, the flux rate through the concrete per unit area of surface areas at x = L is

Time Flux Rate (F) (sec) (cm/sec)

Q = (0.14)(15.2 sec)(1.274 ¥ 10–4 g/cm3) at 106 sec (Eq A.23)

so for a fast diffusion rate (FD1), Q = 2.71 ¥ 10–4, and 0.27% of the PCE vapor mass has diffused through the concrete in 106 sec (277 hours or 11.6 days); for a slow diffusion rate (FD2), Q = 1.15 ¥ 10–4, and about 0.19% of the PCE vapor mass has diffused through the concrete pavement in 3 ¥ 107 sec or 347 days, according to the following:

FD1 = t–1/2 exp[–13.588 – 7.56 ¥ 105/t(sec)] (Eq A.24) and

FD2 = t–1/2 exp[–15.39 – 2.75 ¥ 107/t(sec)] (Eq A.25) Using the expression in Equation A.13 (Crank 1985), the numerical approximation

of the time-dependent flux of PCE vapor through the 15.2 cm of concrete pavement where FD1 = 7.64 ¥ 10–5 cm2/sec and FD2 = 2.10 ¥ 10–6 cm2/sec is as follows:

Appendix B Sample

Calculation for the

Transport of PCE Liquid

of the pavement provides a continuous pathway for the solvent dissolution These calculations assume an absence of cracks and expansion joints in the pavement that could provide a preferential pathway for liquid migration into the underlying soil.

B.2 SAMPLE CALCULATION

An estimation of perchloroethylene (PCE) transport through a porous media such as concrete via liquid diffusion can be developed based on the mathematics provided in

The Mathematics of Diffusion (Crank, 1985) The reader is encouraged to examine

this treatise when developing a liquid diffusion model, as numerous mathematical constructs are available for various problem assumptions.

In this example, the following conditions are assumed:

• Length of the concrete is 15.2 cm

• The diffusion rate of PCE in water = 1.5 ¥ 10–5 cm2/sec (for TCE, the waterdiffusivity value ª 0.8304 cm2/day)

• The diffusion of PCE (DL) = Doq(10/3)/PT2

• Total concrete porosity is 0.06 to 0.14

• Volumetric content is equal to 0.02 to 0.04%

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Given these assumptions, DL, then:

DL = 1.65 ¥ 10–5 cm2/sec [(0.02 – 0.043.33)/(0.06 – 0.14)2 (Eq B.1)

= 1.68 ¥ 10–8 to 1.6 ¥ 10–9cm2/sec (Eq B.2)

= 1.38 ¥ 10–3 to 1.38 ¥ 10–4 cm2/sec (Eq B.3) Given that the flux rate (F) is defined as (see Appendix A for a more thorough derivation):

F = t–1/2 exp[ln (2C1(D/ p ))1/2] – L2/4Dt (Eq B.4) then the flux rates (Fcm/day) and mass (Fg/cm) for a diffusion rate of PCE in water of 1.65 ¥ 10–5 cm2/sec are

Time (days) F cm/day F g/cm

In excess of about 2000 days or 5.4 years are required before any appreciable (1.51

¥ 10–5 g/cm) quantity of perchloroethylene diffuses through the concrete For a brief, transient spill of PCE on concrete, therefore, PCE transport via liquid diffusion through 15.2 cm of concrete is insignificant, especially when mechanisms such as evaporation are considered.

REFERENCES

Crank, J., 1985 The Mathematics of Diffusion, 2nd ed., Oxford University Press, New York,

p 345

Appendix C Properties

of Alcohol Oxygenates and Ether Oxygenates

Properties of Alcohol Oxygenates

Flash point

From Gibbs, L., in Proc of the Southwest Focused Ground Water Conference: Discussing the Issue of MTBE and Perchlorate in Ground Water

(suppl.), National Ground Water Association, Dublin, OH, 1998 With permission.

Properties of Ether Oxygenates

Chemical formula (CH3)3COCH3 (CH3)2(C2H5) COCH3 (CH3)2(C3H7) COCH3 (CH3)3COC2H5 (CH3)2(C2H5)COC2H5 (CH3)2CHOCH(CH3)2Flash point

From Gibbs, L., in Proc of the Southwest Focused Ground Water Conference: Discussing the Issue of MTBE and Perchlorate in Ground Water (suppl.), National Ground

Water Association, Dublin, OH, 1998 With permission

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Environmental Science and Technology It is recommended that the reader interested

in this method examine this source paper in addition to references used to solve the various solutions of Darcy’s Law (Freeze and Cherry, 1979; Wang and Anderson, 1982) The derivation of Darcy’s Law for advective transport with dispersion is presented here, along with the partitioning derivation reported by Hunkeler et al for

222Rn While this approach is specific to radon, it provides interesting possibilities for other types of contaminants.

qx, qy, qz = specific discharge vectors (Eq D.4)

x, y, z = Cartesian coordinate system (Eq D.5)

k = saturated hydraulic conductivity (Eq D.6) The specific discharge vector with components qx, qy, qz can be expressed as qi, with the notation (i) representing x, y, or z, and the partial derivatives ∂f/∂x, ∂f/∂y, and

∂f/∂z representing the three components of the hydraulic gradient The hydraulic

gradient can then be written as:

∂if = [∂f/∂x), (∂f/∂y), (∂f/∂z)] (Eq D.7) which can be compressed in tensor notation as:

by substituting the derivative (–k ∂if) for qi in the continuity equation, which yields:

∂/∂x [k∂f/∂x] + ∂/∂y [k∂f/∂y] + ∂/∂z [k∂f/∂z] = 0 (Eq D.10)

If the saturated hydraulic conductivity (k) is treated as a constant, then Equation D.10

is reduced to (Laplace’s equation in three dimensions):

[ ∂2f/∂x2] + [ ∂2f/∂y2] + [ ∂2f/∂z2] = 0 (Eq D.11) The technique, described by Hunkeler et al (1997), included the use of Darcy’s equation in one dimension for solving for 222Rn in a non-aqueous phase liquid (NAPL)-contaminated aquifer Assumptions included:

• The average distribution of 226Ra, the parent nuclide of 222Rn, in the solid phase ishomogeneous at a macroscopic scale

• Aquifer porosity is constant

•222Rn loss from the saturated to the unsaturated zone is neglected

• Partitioning of 222Rn between the NAPL and water phase is in equilibrium

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• The partition coefficient is independent of the NAPL saturation.

• The NAPL is immobile

• Sorption of 222Rn to the soil is neglected

The one-dimensional advective and dispersive equation for 222Rn transport, 222Rn release from mineral surfaces, and the 222Rn decay and partitioning of 222Rn between the NAPL and water phase are described as:

∂/∂t [(1 – S)qA + qSANAPL] = – ∂/∂x [qA – (1 – S)qD ∂A/∂x] +

(1 – q)rPl – [(1 – S)qA + qSANAPL] l (Eq D.12)

A = the 222Rn activity in the water phase at location (x) at time (t)

ANAPL= the 222Rn activity in the NAPL at location (x) at time (t)

x = flow distance in meters

q = the groundwater discharge

D = dispersion coefficient of 222Rn in groundwater (m sec–1)

r = density of the soil (kg m–3)

P = the emanation of 222Rn decay from mineral surfaces per mass of dry aquifer

material (kBq kg–1)

l = radioactive decay constant of 222Rn (sec–1)

The partitioning of 222Rn between the water phase and NAPL phase at equilibrium

Environmental Science and Technology, 31:3180–3187.

Wang, H and M Anderson, 1982 Introduction to Groundwater Modeling: Finite Difference

and Finite Element Methods, W.H Freeman, San Francisco, CA, p 235.

©2000 CRC Press LLC

Appendix E Chemical

and Commercial

Synonyms for Selected

Chlorinated Solvents and

Aromatic Hydrocarbons

Solvent and Chemical Formula Chemical and Commercial Synonyms

Benzene (C6H6) Annulene; Benzeen (Dutch); Benzen (Polish); Benzin; Benzine;

Benzol; Benzole; Benzolene; Benzolo (Italian); Bicarburet ofHydrogen; Carbon Oil; Coal Naphtha; Cyclohexatriene; Fenzen(Czech.); Mineral Naphtha; Motor Benzol; Nitration Benzene;Phene; Phenyl Hydride; Phrobenzol; Pyrobenzole

Bromoform (CHBr3) Bromoforme (French); Bromoformio (Italian); Methenyl

Tribromide; Tribrommethaan (Dutch); Tribrommethan(German); Tribromometan (Italian); TribromomethaneCarbon tetrachloride (CCl4) Carbon Bisulfide; Carbon Bisulphide; Carbon Chloride; Carbon

Disulphide; Carbon Sulfide; Carbon Sulphide; DithiocarbonicAnhydride; NCI-C04591; Sulphocarbonic Anhydride; UN 1131;Weeviltox; Benzinoform; Carbona; Carbon Chloride; CarbonTet; ENT 4705; Fasciolin; Flukoids; Freon-10; Halon-104;Methane Tetrachloride; Necatorina; Necatorine;

Perchloromethane; R 10; RCRA Waste Number U211;Tetrachloormetaan; Tetrachlorocarbon;

Tetrachloromethane; Tetrafinol; Tetraform; Tetrasol;

UN 1846; Univerm; Vermoestricid

Chloroform (CHCl3) Chloroforme (French); Choroformio (Italian); Freon-20;

R 20; R 20 refrigerant; Formyl Trichloride; Methenyl Chloride;Methyl Trichloride; Trichloroform; Trichloromethane;Methan Trichloride: Methenyl Trichloride; Methyltrichloride;Trichloromethane; Trichloormethaan (Dutch); Trichlormethan(Czech.); Trichloroform; Trichlorometano (Italian); UN 1888Chloromethane (CH3Cl) Arctic R40; Freon-40; Methyl Chloride; Monochloromethane;

UN 10631,1-Dichloroethane (C2H4Cl2) Chlorinated Hydrochloric Ether; Ethylidene Dinechloride;

Ethyledene Dichloride; UN 23621,2-Dichloroethane (C2H4Cl2) 1,2-Bichloroethane; Borer Sol; Brocide; 1,2-DCA; Destruxol

Borer-Sol; Dichloremulsion; Dichlormulsion; Dichloroethylene;Dutch Liquid; Dutch Oil; Ethylene Dichloride; Freon-150;EDC; ENT 1656; Glycol Dichloride; NCI-C00511; UN 11841,1-Dichloroethylene (C2H2Cl2) Chlorure de Vinylidene (French); 1,1-DCE; 1,1-Dichloroethene;

Sconatex; VDC; Vinylidene Chloride II; Vinylidene Chloride;Vinylidene Dichloride; Vinylidine chloride

Dichloromethane (CH2Cl2) Aerothene; DCM; Freon-30; MM; Methylene Bichloride;

Methylene Chloride; Methylene Dichloride; Narcotil; C50102; Solaesthin; Solmethine; UN1593

NCI-Ethylene dibromide (C2H4Br2) Alphat; beta-Dibromomethane; Bromofume; Celmide;

1,2-Dibromomethane; DBE; Dibrome, Dowfume;

40-Dowfume; Dowfume W-8; Dowfume W-90;

Dibromoethane; EDB-85; Ethylene Bromide; EthyleneBromide Glycol Dibromide, Fumo-Gas; Glycol Bromide;Glycol Dibromide; Iscobrome D; Kopfume; Nephis;

Soilfume; Pestmaster; Pestmaster EDB-85; Soilbrome-40;Soilbrome-90; Soilbrom-90C; Soilbrom-100; Soilbrome-85;Unifume

Freon-11 (CCl3F) Algonfrene Type 1; Arcton 9; Electro-CF 11; Eskimon 11; F11;

FC 11; Fluorocarbon 11; Fluorotrichloromethane; Freon-11A;Freon-11B; Freon HE; Freon MF; Frigen 11; Genetron 11;Halocarbon 11; Isceon 11; Isotron 11; Ledon 11;

Monofluorotrichloromethane; Refrigerant 11;

Trichlorofluoromethane; Ucon 11; Ucon Fluorocarbon; UconRefrigerant 11

Freon-113 (FCl2CCF2Cl) Arcton 63; Arklone P; Daiflon S3; Fluorocarbon 113; F-113;

FC-113; Freon® 113; Frigen 113a; TR-T; Genetron 113;Halocarbon 113; Isceon 113; Khladeon; Kaiser Chemicals 11;R-113; R113; Refrigerant 113; TTE; 1,1,2-Trifluoro-1,2,2-Trichloroethane; Trichlorotrifluoroethane; 1,1,2-Trichloro-1,2,2-Trifluoroethane; 113; Ucon-113; Ucon Fluorocarbon; Ucon113/Halocarbon 113

Solvent and Chemical Formula Chemical and Commercial Synonyms

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Methylene chloride (CH2Cl2) Dichloromethane; DCM; Methylene Dichloride; Methylene

Bichloride; Aerothene MM; Freon-30; Narcotil; NCI-C50102;RCRA Waste Number 84.16; RTECS; GY 4640000; Turco5873; #5141 Chlorinated Solvent

Phenol (C6H60) Acide Carbolique (French); Baker’s P and S Liquid and

Ointment; Benzenol; Carbolic Acid; Carboilsaure (German);Fenol (Dutch, Polish); Fenolo (Italian); Hydroxybenzene;Monohydroxybenzene; Monophenol; Oxybenzene; Phenic Acid;Phenol Alcohol; Phenol Molten; Phenole (German);

Phenylhydrate; Phenyl Hydroxide: Phenylic Acid; PhenylicAlcohol

1,1,1-TCA (Cl3CCH3) a-T; a-Trichloroethane; Aerothene; Aerothene TT;

Alpha-1,1,1-trichloroethane; Alpha Trichloroethane; Amsco Solv5620; Baltana; Blaco-Thane; Chloroethane NU; Chloroethene;Chlorten; Crack Check Cleaner C-NF; Genklene; DEV TAP;Devcon; Devon Metal Guard; FL-20 Flexane Primer Lube-Lok4253; Locquic Primer T; Inhibisol; Methyltrichloromethane;Methyl Chloroform; M-60; NCI-C04626; NU; Rapid Tap;Perm-Ethane; PCN UCD 5620; PCN-UCD 15620; Quik Shield;RCRA Waste Number U226; Solvent 111®; Solventclean SC-AAerosol; Saf-Sol 20/20; TCA; SKC-NF/ZC-73; Tri-ethane;Turco Lock; UCD 784; VG; UN 2831; #10 Cleaner; #5141Chlorinated Solvent

Tetrachloroethylene (Cl2Cl4) Ankilostin; Antisol; Crack Check Cleaner C-NF; Didakene;

Carbon Bichloirde; Carbon Dichloride; Dee-Sol; Didakene;Dow-Per; Dow-Clene ECENT 1860; Ethylene Tetrachloride;Fedal-UN; NCI-C04580; Nema; PCE; PER; PERC; Percelene;Perawin; Perchlor; Perchlorethylene; Perchloroethylene;Perclene; Percosolv; Perk; Persec; PerSec 1; Tetlen; Tetrophil;Tetracap; Tetrachloroethylene; Tetrachloroethene; 1,1,2,2-Tetrachloroethylene; Tetropil; Tetracap; Tetraleno; Tetravec;Tetroguer; Tetropil; UN 1897; #5141 Chlorinated Solvent1,1,2,2-Tetrachloroethylene (C2Cl4) Ankilostin; Antisol 1; Carbon Bichloride; Carbon Dichloride;

Czterochloroetylen (Poland); Didakene; Dow-Per; Ent 1.860;Ethylene Tetrachloride; Fedal-UN; Nema; Perawin;

Perchloorethyleen Per (Dutch); Perchlor; Perchloraethylen, Per(German); Perchlorethylene; nPerchlorethylene, Per (French);Perclene; Perchloroetilene (Italian); Percosolve; Perkcosolve;Perk; Perklone; Persec; Tetlen; Tetracap; Tetrachlooretheen(Dutch); Tetrachloraethen (German); Tetrachloroethene;Tetrachloroetene (Italian); Tetraleno; Tetralex; Tetravec;Tetroguer; Tetropil

1,1,2-Trichloroethane (C2HCl3) Cement T-399; Ethane Trichloride; 1,2,2 Trichloroethane; d-T;

b-trichloroethane; Vinyl Trichloride

Solvent and Chemical Formula Chemical and Commercial Synonyms