Appendices © 2000 CRC Press LLC Appendix A. Sample Calculation for the Transport of PCE Vapor through Concrete Pavement A.1 INTRODUCTION 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 pave- ment. The diffusion equation in one dimension, therefore, reduces to (Crank, 1985): d 2 C/dx 2 = 0 (Eq. A.1) provided that the diffusion coefficient (D) is constant. On integrating with respect to x, the following expression arises: dC/dx = constant (Eq. A.2) and by introducing the conditions at x = 0 and x = l and integrating, then: [C – C 1 /C 2 – C 1 ] = x/l (Eq. A.3) The previous two expressions show that the concentration changes linearly from C 1 to C 2 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(C 1 – C 1 )/l (Eq. A.4) ©2000 CRC Press LLC If the thickness (l) and the surface concentrations (C 1 and C 2 ) 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 C 1 and at x = 1, then there is evaporation into an atmosphere for which the equilibrium concentration immediately within the paved surface is C 2 , so that: ∂C/∂x + h(C – C 2 ) = 0, x = l (Eq. A.5) then (C – C 1 )/(C 2 – C 1 ) = (hx)/(1 + hl) (Eq. A.6) and F = Dh(C 1 – C 2 )/(1 + hl) (Eq. A.7) If the surface conditions are ∂C/∂x + h 1 (C 1 – C) = 0, x = 0; and ∂C/∂x + h 2 (C – C 2 ) = 0, x = l (Eq. A.8) then C = [h 1 C 1 {1 + h 2 (l – x)} + h 2 C 2 (1 + h 1 x)]/ [h 1 + h 2 + h 1 h 2 l] (Eq. A.9) 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 m 3 /mol. • PCE is absent in the concrete and in the soil below it (C 2 = C o = 0). • The concentration of PCE in the vapor above the concrete is 1.272 ¥ 10 –4 g/cm 3 . ©2000 CRC Press LLC A graphical representation of this problem is shown in Figure A.1. In this case, the following governing equation becomes: QC Dt n Dnt t //–/–/ (– ) / exp(– / )ll l 1 222 1 2222 16 2 1= Â • pp (Eq. A.10) For a steady-state solution where time (t) goes to infinity, the flux rate is defined as Q t = DC 1 /l(t – l 2 /6D) (Eq. A.11) which has an intercept L on the t-axis described as: L = l 2 /6D (Eq. A.12) For a small period of time, then: Ft C D t m D M () (/ ) exp{–( ) /( )} / = Â + = • 2214 1 12 1 22 p l (Eq. A.13) For a small period of time, this series converges rapidly to: ln (t 1/2 F) = ln {2C 1 (D/p) 1/2 } – L 2 /4Dt (Eq. A.14) FIGURE A.1 Conceptual model of the transport of PCE vapor through concrete. ©2000 CRC Press LLC and t 1/2 F = exp [ln {2C 1 (D/p) 1/2 } – L 2 /4Dt] (Eq. A.15) and F = t –1/2 exp [ln {2C 1 (D/p) 1/2 } – L 2 /4Dt] (Eq. A.16) where D = the effective diffusion coefficient. The effective diffusion coefficient is defined as (Millington and Quirk, 1959): D e = D o (A 10/3 )/P T 2 (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 cm 2 / sec (for TCE ª 7100 cm 2 /day), then: D e = (0.0785 cm 2 /sec)((0.013 – 0.023) 3.33 /(0.06 – 0.14) 2 ) (Eq. A.18) = (0.078 cm 2 /sec)((2.67 ¥ 10 –5 ) – (9.73 ¥ 10 –4 )) (Eq. A.19) = (2.67 ¥ 10 –6 ) – (7.64 ¥ 10 –5 ) cm 2 /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) 10 0 10 2 0 10 3 0 10 4 (27 hr) 1.85 ¥ 10 –41 10 5 (1.16 days) 2.07 ¥ 10 –21 10 6 (11.6 days) 5.89 ¥ 10 –10 10 7 (116 days) 3.68 ¥ 10 –10 10 8 (1116 days) 1.25 ¥ 10 –10 Solving for the quantity of PCE vapor that has moved through the concrete (Q 1 ) yields: D t /L 2 = (7.64 ¥ 10 –5 cm 2 /sec)(t)/(15.2 cm) 2 (Eq. A.21) and Q 1 /LC 1 = 0.14 at 10 6 sec and 0.035 at 5 exp 5 sec (Eq. A.22) and ©2000 CRC Press LLC Q = (0.14)(15.2 sec)(1.274 ¥ 10 –4 g/cm 3 ) at 10 6 sec (Eq. A.23) so for a fast diffusion rate (F D1 ), Q = 2.71 ¥ 10 –4 , and 0.27% of the PCE vapor mass has diffused through the concrete in 10 6 sec (277 hours or 11.6 days); for a slow diffusion rate (F D2 ), Q = 1.15 ¥ 10 –4 , and about 0.19% of the PCE vapor mass has diffused through the concrete pavement in 3 ¥ 10 7 sec or 347 days, according to the following: F D1 = t –1/2 exp[–13.588 – 7.56 ¥ 10 5 /t (sec) ] (Eq. A.24) and F D2 = t –1/2 exp[–15.39 – 2.75 ¥ 10 7 /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 F D1 = 7.64 ¥ 10 –5 cm 2 /sec and F D2 = 2.10 ¥ 10 –6 cm 2 /sec is as follows: TTF D1 F a F D2 F (sec) (hr/days) (cm/sec) (g/day) (cm/sec) (g/day) 10 3 0.278 hr 0.00 0.00 0.00 0.00 10 4 2.78 1.85 ¥ 10 –41 2.97 ¥ 10 –34 0.00 0.00 2 ¥ 10 4 5.56 3.4 ¥ 10 –25 5.47 ¥ 10 –18 0.00 0.00 4 ¥ 10 4 11.1 3.89 ¥ 10 –17 6.25 ¥ 10 –10 0.00 0.00 10 5 27.8 2.07 ¥ 10 –12 3.32 ¥ 10 –5 0.00 0.00 1.5 ¥ 10 5 41 2.11 ¥ 10 –11 3.37 ¥ 10 –4 0.00 0.00 2 ¥ 10 5 2.3 days 6.41 ¥ 10 –11 1.03 ¥ 10 –3 8.92 ¥ 10 –70 1.43 ¥ 10 –62 4 ¥ 10 5 4.6 3.0 ¥ 10 –10 4.82 ¥ 10 –3 4.54 ¥ 10 –46 7.31 ¥ 10 –33 10 6 11.6 5.9 ¥ 10 –10 9.48 ¥ 10 –3 2.36 ¥ 10 –22 3.79 ¥ 10 –15 2 ¥ 10 6 23 6.1 ¥ 10 –10 9.78 ¥ 10 –3 1.56 ¥ 10 –16 2.51 ¥ 10 –9 10 7 115 — — 4.19 ¥ 10 –12 6.73 ¥ 10 –5 10 8 1157 — — 1.57 ¥ 10 –11 2.53 ¥ 10 –4 a F cm/cm ¥ 1.61 ¥ 10 7 = F g/day. In this sample problem, by day one about 3.3 ¥ 10 –5 g have diffused through the concrete. Steady-state conditions are reached in both instances between about 6 and 212 days. Approximately 1 to 23 days are required before any mass starts to emanate through the 15.2 cm of concrete. The diffusion of PCE through the concrete ranges from about 2.1 ¥ 10 –6 to 7.64 ¥ 10 –5 cm 2 /sec. This range is due to the variability of the concrete porosity and the values of air porosity selected for this example. REFERENCES Crank, J., 1985. The Mathematics of Diffusion, 2nd ed., Oxford University Press, New York, p. 345. Millington, J. and J. Quirk, 1959. Permeability of porous media, Nature (London), 183:387–388. ©2000 CRC Press LLC Appendix B. Sample Calculation for the Transport of PCE Liquid through Concrete via Diffusion B.1 INTRODUCTION Liquid diffusion of a chlorinated solvent through a paved surface is an extremely slow process. The transport of a chlorinated solvent through concrete via liquid diffusion assumes that the paved surface is saturated and that the effective porosity 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 cm 2 /sec (for TCE, the water diffusivity value ª 0.8304 cm 2 /day). • The diffusion of PCE (D L ) = D o q( 10/3 )/P T 2 . • Total concrete porosity is 0.06 to 0.14. • Volumetric content is equal to 0.02 to 0.04%. ©2000 CRC Press LLC Given these assumptions, D L , then: D L = 1.65 ¥ 10 –5 cm 2 /sec [(0.02 – 0.04 3.33 )/(0.06 – 0.14) 2 (Eq. B.1) = 1.68 ¥ 10 –8 to 1.6 ¥ 10 –9 cm 2 /sec (Eq. B.2) = 1.38 ¥ 10 –3 to 1.38 ¥ 10 –4 cm 2 /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 (2C 1 (D/p)) 1/2 ] – L 2 /4Dt (Eq. B.4) then the flux rates (F cm/day ) and mass (F g/cm ) for a diffusion rate of PCE in water of 1.65 ¥ 10 –5 cm 2 /sec are Time (days) F cm/day F g/cm 0.1 0.0 0.0 1.0 0.0 0.0 10 0.0 0.0 10 2 0.0 0.0 2 ¥ 10 2 2.61 ¥ 10 –92 6.21 ¥ 10 –86 300 4.53 ¥ 10 –62 1.08 ¥ 10 –56 400 5.73 ¥ 10 –47 1.36 ¥ 10 –41 1000 7.16 ¥ 10 –20 1.70 ¥ 10 –14 2000 6.35 ¥ 10 –11 1.51 ¥ 10 –5 2500 3.75 ¥ 10 –9 0.00089 2750 1.64 ¥ 10 –8 0.0039 3000 5.59 ¥ 10 –8 0.0133 4000 1.59 ¥ 10 –6 0.378 5000 1.16 ¥ 10 –5 2.75 6000 4.2 ¥ 10 –5 10.10 7000 1.07 ¥ 10 –4 25.50 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. ©2000 CRC Press LLC Appendix C. Properties of Alcohol Oxygenates and Ether Oxygenates Properties of Alcohol Oxygenates Property MeOH EtOH IPA BuOH GTBA Chemical name Methanol Ethanol Isopropyl alcohol n-Butanol Gasoline grade t-butanol Chemical formula CH 3 OH C 2 H 5 OH (CH 3 ) 2 CHOH C 4 H 9 OH (CH 3 ) 3 COH Flash point ∞F52555384 52 ∞C11131229 11 Heating value (Btu/gal) 56,800 76,000 87,400 96,800 94,100 Latent heat of vaporization 3340 2378 2100 1700 1700 (Btu/gal) Boiling point (∞F) 149 173 180 244 176–181 Composition (%wt) Carbon 37.49 52.14 59.96 64.82 65.0 Hydrogen 12.58 13.13 13.42 13.60 13.7 Oxygen 49.93 34.73 26.62 21.58 21.3 Molecular weight 32.04 46.07 60.09 74.12 73.5 Relative density (60∞F) 0.7963 0.7939 0.7899 0.8137 0.7810 Water solubility (70∞F) Fuel in water (%) 100 100 100 100 100 Water in fuel (%) 100 100 100 100 100 Viscosity (mm/sec) 68∞F 0.74 1.50 3.01 3.54 7.4 –4∞F 1.44 3.58 7.43 — Solid 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. ©2000 CRC Press LLC [...]... Crawhaspol; 1,1-Dichloro-2chloroethylene; Densinfluat; Dow-Tri, Dow-TriPhilex; Dukerson; Ethinyl Tri-Plus; Ethylene Trichloride; Ethinyl Trichloride; Fleck-Flip; Flock-Flip; Fluate; Germalgene; Hi-Tri; Lanadin; Lethurin; Narcogen; Narkosoid; Nialk; Neu-Tri; NCIC04546; Petzinol; Perm-a-chlor; Perm-a-clor; Petzinol; Philex; Trichloroethylene; 1,1,2-Trichloroethylene; Trichloroethene; Tri-Clene; Trielene;... beta-Dibromomethane; Bromofume; Celmide; 1,2-Dibromomethane; DBE; Dibrome, Dowfume; 40-Dowfume; Dowfume W-8; Dowfume W-90; Dibromoethane; EDB-85; Ethylene Bromide; Ethylene Bromide 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... Tap; Perm-Ethane; PCN UCD 5620; PCN-UCD 15620; Quik Shield; RCRA Waste Number U226; Solvent 111®; Solventclean SC-A Aerosol; Saf-Sol 20/20; TCA; SKC-NF/ZC-73; Tri-ethane; Turco Lock; UCD 784; VG; UN 2831; #10 Cleaner; #5141 Chlorinated Solvent Tetrachloroethylene (Cl2Cl4) Ankilostin; Antisol; Crack Check Cleaner C-NF; Didakene; Carbon Bichloirde; Carbon Dichloride; Dee-Sol; Didakene; Dow-Per; Dow-Clene... Water solubility (70∞F) Fuel in water (%) Water in fuel (%) Viscosity (mm/sec) 68∞F –4∞F MTBE Methyl-tertiarybutyl-ether (CH3)3COCH3 TAME THEME Tertiary-amylTertiary-hexylmethyl-ether methyl-ether (CH3)2(C2H5) COCH3 (CH3)2(C3H7) COCH3 ETBE TAEE DIPE Ethyl-tertiarybutyl-ether (CH3)3COC2H5 Tertiary-amylethyl-ether (CH3)2(C2H5)COC2H5 Diisopropyl ether (CH3)2CHOCH(CH3)2 –14 –26 93,500 863 11 –11 100,600 870... Alcohol 1,1,1-TCA (Cl3CCH3) a-T; a-Trichloroethane; Aerothene; Aerothene TT; Alpha1,1,1-trichloroethane; Alpha Trichloroethane; Amsco Solv 5620; Baltana; Blaco-Thane; Chloroethane NU; Chloroethene; Chlorten; Crack Check Cleaner C-NF; Genklene; DEV TAP; Devcon; Devon Metal Guard; FL-20 Flexane Primer Lube-Lok 4253; Locquic Primer T; Inhibisol; Methyltrichloromethane; Methyl Chloroform; M-60; NCI-C04626;... 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-1,2,2Trichloroethane; Trichlorotrifluoroethane; 1,1,2-Trichloro-1,2,2Trifluoroethane; 113; Ucon-113; Ucon Fluorocarbon; Ucon 113/Halocarbon 113 ©2000 CRC Press LLC Solvent and Chemical Formula Chemical and Commercial Synonyms Methylene chloride... NAPL-contaminated zone and upgradient and downgradient of the zone ©2000 CRC Press LLC REFERENCES Freeze, A and J Cherry, 1979 Appendix X, in Groundwater, Prentice-Hall, Englewood Cliffs, NJ, p 604 Hunkeler, D., Hoehn, E., Hohener, P., and J Zeyer, 1997 222Rn as a partitioning tracer to detect diesel fuel contamination in aquifers: laboratory study and field observations, Environmental Science and. .. Tetralex; Tetravec; Tetroguer; Tetropil 1,1,2-Trichloroethane (C2HCl3) Cement T-399; Ethane Trichloride; 1,2,2 Trichloroethane; d-T; b-trichloroethane; Vinyl Trichloride ©2000 CRC Press LLC Solvent and Chemical Formula Chemical and Commercial Synonyms Trichloroethene (C2HCl3) Acetylene Trichloride; Algylen; Anamenth; Anameneth; Benzinol; Blancosolv; Blacosolv; 1-Chloro-2,2dichloroethylene; Cecolene; Chlorylea;... 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;... Arctic R40; Freon-40; Methyl Chloride; Monochloromethane; UN 1063 1,1-Dichloroethane (C2H4Cl2) Chlorinated Hydrochloric Ether; Ethylidene Dinechloride; Ethyledene Dichloride; UN 2362 1,2-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; . DIPE Chemical name Methyl-tertiary- Tertiary-amyl- Tertiary-hexyl- Ethyl-tertiary- Tertiary-amyl- Diisopropyl butyl-ether methyl-ether methyl-ether butyl-ether ethyl-ether ether Chemical formula. Pestmaster; Pestmaster EDB-85; Soilbrome-40; Soilbrome-90; Soilbrom-90C; Soilbrom-100; Soilbrome-85; Unifume Freon-11 (CCl 3 F) Algonfrene Type 1; Arcton 9; Electro-CF 11; Eskimon 11; F11; FC. 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;