RADIAN '3RPQRA71QN 84-222-078-17-07 PROTOCOLS FOR CALCULATING VOC EMISSIONS FROM LAND APPLICATIONS USING EMISSION MODELS TECHNICAL NOTE EPA Contract No. 68-02-3850 Work Assignment 17 Prepared for: Mr. Clyde E. Riley Task Manager U.S. Environmental Protection Agency Research Triangle Park, NC 27711 Prepared by: G. B. DeWolf R. G. Wetherold Radian Corporation P.O. Box 9948 Austin, Texas 78766 17 December 1984 8501 Mo-Pac Blvd./P.O. Box 9948 / Austin, Texas 78766 / (512)45^7C>7 ------- radian CORPOMTIOfl SECTION 1 INTRODUCTION A number of emission models have been proposed for estimating volatile organics emissions from landfills and landfarming sites. This technical note discusses these models in detail and presents a protocol for their use. Equations for the models are presented, required input variables defined, sources of information for these variables suggested, and approximate preci- sion levels for the variables presented. Physical property inputs are discussed and methods for their estimation are provided, as are selected values for some materials. Models are presented for covered landfills and for landtreatment (landfarming). For landfills, the recommended model is that of Farmer, as modified by Shen and Hwang, and for landtreatment, the Thibodeaux-Hwang model is recommended (1). 1 ------- COffPOHOTKM SECTION 2 LANDTREATMENT EMISSIONS Two models which have been proposed for predicting emissions of vola- tile compounds from landtreatment operations are the Hartley and the Thibodeaux-Hwang models. These two models were presented and briefly dis- cussed in an earlier report(l). Since the Hartley model is inadequate for describing evaporation of volatile waste material which has permeated below the soil surface, it is not recommended for consideration in the kinds of applications addressed by this protocol. Therefore, the Thibodeaux-Hwang model must be used. This model is presented in Table 2-1. In the development of this model, the emission rate of a volatile chemical compound was assumed to be a funct ion of: • the evaporation rate of the compound from the inter- stitial soil surfaces, and • the diffusion rate of the chemical compound through the air-filled pore spaces of the soil. The emission rate is assumed to be controlled by the diffusion rate in the air pore pace when the oil loading and soil particles are both small. At soil loadings substantially greater than typical1waste loadings, the mathematical description of the emission process is extremely complex. Thibodeaux and Hwang made a significant number of simplifying assumptions to develop a usable mathematical expression. The resulting model is a highly idealized and simplified description of a very complex process. 2 ------- RADIAN TABLE 2-1. THIBODEAUX-HWANG MODEL FOR VOLATILE ORGANIC EMISSIONS FROM LANDTREATMENT OPERATIONS Basis: Emission rate is controlled by diffusion rate of vapor through the air-filled pores of the landtreated soil. Form: E. = i D C ei ig "a '2 D t A (h -h )C ei p s ig M 10 1/2 H C. c io ig 1 + H D . Z c ei o D . A f(y) wi s and Symbo1 f(y) = (hp + ys - 2hs)/6 Symbol/Parameter Definition Typical Source of Precision Input Parameter surface area over which waste is applied, _+ 2% cm' measured interfacial area per unit volume of soil interracial area per unit v for the oily waste, cm^/cm calculated effective wet zone pore space concentration of component i, g/cm Cio Dg^ ^effective diffusivity of component i in the +_ 25% air-filled soil pore spaces, cm^ls calculated concentration of component i in oil, g/cm +_ 25% calculated published data; esti- mat ion soil clump diameter, cm average cal- culated from measurement s or estimated (Continued) 3 ------- coCTooojmoM TABLE 2-1. THIBODEAUX-HWANG MODEL FOR VOLATILE ORGANIC EMISSINS FROM LANDTREATMENT OPERATIONS (Continued) Dwi effective diffusivity of compound i in the oil, cm^/s + 52 published data; esti- mat ion Ei flux of component i from the soil surface, g/cm^-sec - calculated f (y) (h^ + hphg-2hg)/6 accounts for the lengthing dry zone - calculated Hc Henry's Law constant in concentration form, cm^ oil/cm air + 15% publ ished data or measurement hP depth of soil contaminated or wetted with landtreated waste, cm + 10% measured Mio initial mass of component i incorporated into the zone (h -h ), g r b + 5% measured t time after application, sec measured y height of wetted soil remaining after partial drying, cm - measured wf weight fraction oil in film form in soil - calculated Zo oil layer diffusion length, cm calculated or esti- mated f fraction of oil in film form - estimated PP soil clump density, g/cm + 10% measured or estimated j?aste-oil density, g/cm + 10% measured or estimated 4 ------- RADIAN coffPOiumoN Much of the material that is typically landtreated consists of oily sludges. These sludges are usually mixtures of solids, water, and a complex solution of a very large number of organic compounds. The sludges may consist of two- or three-phase solutions or even emulsions. They are applied to the landtreatment area at high soil loadings. At this time, the Thibodeaux-Hwang model has not been validated and/or calibrated under ex- perimental and field conditions in the range of typical landtreatment opera- ting conditions. Without such validation, no estimate of the accuracy of the model predicted emission rates can be determined. There is very little available data which can be used to validate this model under any conditions. Thibodeaux and Hwang (2) used two sets of data to compare measured emission rates with rates predicted by the model. The initial results of a joint API/EPA study were used as one data set. Partial agreement of the data with predicted results was obtained. However, the conditions during the short period (<30 minutes after sludge application) of time in which data were reported deviated substantially from those described by the model. Much of the applied sludge was still in the process of soaking into the soil, and substantial amounts were still present as liquid pools on the soil surface. Thibodeaux and Hwang also used experimentally determined emission rates of Spencer and Cliath (3) and Farmer and Letey (4) to compare with emission rates predicted with the model. There appears to be good agreement between the predicted and measured emission rates of the pesticide dieldrin. How- ever, the dieldrin soil loadings were two orders of magnitude lower than those typically encountered in landtreatment operations. Dieldrin is also a solid iri*the normal ambient temperature range.Therefore, the experimental conditions are very different from those encountered during typical land- treatment operations, and this comparison is not a verification of the model under typical landtreatment conditions. The computational procedure for using the Thibodeaux-Hwang model is: 5 ------- u^mim cogpomnow 1. Calculate ZQ. If oil is in film form ZQ = dpPpf/6Pw if oil is in lump form ZQ = dp/2 2. Calculate As, the interfacial area per unit volume of soil, If oil is in film form A = 6/d s p If oil is in lump form Ag = 2.70/dp 3. Calculate f(y) = (hp+hphs~2hg)/6. 4. Calculate wet zone pore space concentration. H C. c io C- = L8 / H D .Z / c ei o 1 + D„iAsf(y> ) 5. Calculate emission rate for component i, Ei = D C ei lg 2D t A (h -h )C \ 1/2 2 I ei p s lg n _ + ' 3 ^ Mio 6. Calculate total emission rate of all components, N Et = E Ei i=l In practice, it is often not practical to calculate individual compo- nent emissions in order to estimate total emissions. In such cases, an estimate of total emissions may be made by summing the emissions estimated for several classes of compounds using a representative individual component for each class. 6 ------- GSMSQZsXKl cofltPOSunoN The selection of a representative individual component is somewhat - arbitrary. Some compounds are more likely to be encountered than others, and compounds in the mid-molecular weight ranges (4-8 carbons) are likely to dominate in frequency of occurrence. Therefore, at this time, the following classes and compounds have been selected as representative for making emis- sions estimates: Clas s Compound Paraffins Olef ins Aromatics Halogenated hydrocarbons Oxygenated hydrocarbons Toluene Acetone Hexane Butene Methylene chloride Key properties of some compounds are found in Table 5-1 of Section 5. 7 ------- COffPORJtTKM SECTION 3 LANDFILL EMISSIONS The most generally accepted model for the prediction of emission rates from covered landfills is the mathematical expression proposed by Farmer, et. al. (5). In this model, shown in Table 3-1, the emission rate from a covered landfill is assumed to be controlled by the diffusion rate of pollu- tant gases through the soil cover. Two forms of the model were developed; a rigorous form and a simplified form. The model in its rigorous form was validated by Farmer using laboratory simulation data for hexachlorobenzene. The model was simplified by Farmer for use in the predictive mode, and modified slightly by Shen (6). A multiplicative factor of 6.0 was added to account for convective effects due to gases generated by the codisposal of biologically degradable wastes (7). The limited validation performed by Farmer supports the basic technical integrity of the rigorous model. It should not be considered as verifica- tion of the simplified model with the added codisposal factor. Furthermore, the validity of the model for predicting emissions from complex, multicom- ponent waste mixtures has not been tested. The computational procedure for the Farmer model is as follows: 1. From field measurements or a given value, calculate A, the land- fill surface area. 2. Calculate the saturation vapor concentration. cs = P1m/rt 8 ------- cottpomwoii TABLE 3-1. FARMER MODEL FOR VOLATILE ORGANIC EMISSIONS FROM COVERED LANDFILLS Bas is: Emission rate is assumed to be mass transfer controlled by diffusion of gases through the air-filled soil pores. Form: E. = K D. C A i D i s (P ) a 10/3 (ptr 1 \/Wi 2 \ L A W P M i i RT P = 1 C P, P, = P„ a c Symbol/Parameter Definition Symbol A Surface area of the landfill (cn^) Precision Input Parameter +0.1% File data or direct measure- ment Soil bulk density (g/cnio) Cg Saturation vapor concentration (g/m^) _+8% Varies from 1 to 2 g/cc. Need direct measure- ment for accuracy. .05% Calculated from gas law and species vapor pressure. (Continued) 9 ------- radian COOPOMTKM TABLE 3-1. FARMER MODEL FOR VOLATILE ORGANIC EMISSIONS FROM COVERED LANDFILLS (Continued) D- Diffusion coefficient of the species of +5% i.air . 2/ \ ~ interest in air (cm /sec) Mi Mass emission rate (g/sec) Codisposal factor. Use 1.0 for isolated +_10% toxic waste disposal and 6.0 for toxic -21 waste codisposed with biologically de- gradable wastes. Depth of soil cover (cm) _^17% Molecular weight of the species (g/mole) Air-filled porosity (dimensionless) +30% Vapor pressure of the species in interest 5% (mm Hg) Soil particle density (g/cm ) Soil porosity (dimensionless) Density of water (g/cm ) + 8% + 13% + 2% Calculated value from literature or ratio to a compound with a known D by molecular weight. Literature Gas constant 62,300 mm Hg - cm' °K - mole File data or measurement Literature Calculated Literature or direct measure- ment . Recommends 2.65 g/cm3 for most mineral material. Can be estimated based on soil bulk density and soil particle density. L iterature Given (Cont inued) 10 ------- RADIAN C04HHJWJIIIOW TABLE 3-1. FARMER MODEL FOR VOLATILE ORGANIC EMISSIONS FROM COVERED LANDFILLS (Continued) WL/y Weight fraction of the species of +20% Direct measure- interest in the disposed waste (gig) ment. W ,/W Weight fraction of water in the soil cover +5% Direct measure- w ~~ ment. T Temperature (°K) +_1°K Direct measure- ment . 9 Volume fraction of water in the soil +_17% Direct measure- cover (g/g) ment. 11 ------- izadian 3. Calculate soil porosity. Pt = 1 - B/Ps 4. Calculate volume fraction water in soil. e = (ww/w)(b/pw) 5. Calculate mass emission rate of component i, (Pa)10/3 / 1 \ / W- E- = Kn D C„ A —1- 1 ° s (Pt)2 \LA«. 6. Calculate total emissions. N Et = Z Ei i=l In practice, it is often not practical to calculate individual compo- nent emissions in order to estimate total emissions. In such cases, an estimate of total emissions may be made by summing the emissions estimated for several classes of compounds using a representative individual component for each class. .... « The selection of a representative individual component is somewhat arbitrary. Some compounds are more likely to be encountered than others, and compounds in the mid-molecular weight ranges (4-8 carbons) are likely to dominate in frequency of occurrence. Therefore, at this time, the following classes find compounds have been selected as representative for making emis- sions estimates: 12 ------- RADBAN cogpoajmow Class Compound Paraffins Hexane Olefins Butene Aromatics Toluene Halogenated hydrocarbons Methylene chloride Oxygenated hydrocarbons Acetone Key properties of some compounds are found in Table 5-1 of Section 5. 13 ------- COOPOQATtOM SECTION 4 SOURCES OF PHYSICAL PROPERTY DATA Physical property data for air, water, and some chemical species are available in various literature sources. Where data are not available, it is possible to use methods to estimate the properties. Properties required for the models discussed in this report are listed in Table 4-1. 4.1 GASEOUS DIFFUSION COEFFICIENTS A recommended equation for estimating the diffusivity of a nonpolar specie"i" in air is the method of Fuller, Schettler, and Giddings (8): -3 1-75 r, w ,1/2 10 T »V"ai.r»MiMai.r' "i.air " P[(Ev)l'3 «¦ (Zv)1'3] 2 air where, P = pressure, (atm) T = temperature, (°K) = molecular weight of "i" Ma^r = molecular weight of air v = diffusion volume increments for components of species "i1 molecular structure tabulated in Table 4-2. 20-1 Errors are in the range of 5 to 10%. For a polar specie, the method of Brokaw is recommended (6): -3 3/2 l("irtlair'/MiMairl1/2 D. . = 1.858x10 T o i.air P a: . fL i,air D 14 ------- RJ&DBAN cospewmoN TABLE 4-1. PHYSICAL PROPERTIES REQUIRED FOR EMISSIONS ESTIMATE MODELS a£r Diffusivity of compound i in air (cm /sec) 2, D- Diffusivity of compound i in water (cm /sec) 1 • W y Viscosity of air (cp) O 1^ Viscosity of water (cp) Pg Density of air (g/cm ) pw Density of water (g/cm ) 15 ------- TABLE 4-2. ATOMIC DIFFUSION VOLUMES FOR NON-POLAR DIFFUSIVITY ESTIMATES Structural Increment Diffusion Volume Increment, v C 16.5 H 1.98 0 5.48 N 5.69 CI 19.5 S 17.0 Aromatic ring -20.2 Heterocyclic ring -20.2 Source: Adapted from Reference 8, 16 ------- RADflAN where, P = pressure (atm) T = temperature (°K) 0- • = characteristic length (A°) 1 I a ir ^ = dimensionless collision integral and ^ are calculated from additional equations as follows: D = + c + T* expDT* expFT* expHT* where, T* = kT/ i>air k = Boltzman's constant T = temperature, °K ,1/2 + (0.19)6 . i ,air T* = (£ • E • ) 'i,air v i' air' + 6- = 1.94 x 103 Vi ,-/VKl-T = 1.18k (1 + 1.36?)Tbi l rpi' bi bi Vi • = dipole moment, debyes P >1 n Vbi = liquid molar volume at boiling point, cm /g-mol Tbi = normal boiling point, °K 1.585V . \ 1/3 a, = I b>1 1+1.36^ l.air A * B C D (0i °air> 1.06036 0.15610 0.19300 0.47635 1/2 E F G H 1.03587 1.52996 1.76474 3.89411 17 ------- coBPomwoM A discussion of these equations and terms and sources of values for various terms for some compounds are given in Reference 8. 4.2 LIQUID DIFFUSION COEFFICIENTS The diffusion coeffient in water at infinite dilution can be estimated from the Wilke-Chang method (8) which when expressed specifically for a specie O —g Q £ D. = 50.6xl0~ TU\i V * ) iw w i where, D = diffusion coefficient of i in water at infinite dilution, L'w ( 2/ ^ (cm /sec) = viscosity of water at temperature of interest, (cp) V. = mol^l volume of solute at its normal boiling point, (cm /g-mole) T = temperature (°K) Diffusion in multicomponent mixtures can be approximated by taking the molal average value of the diffusion coefficient of i in each of the possible binary combinations in the system (9). The molal volume of a solute can be estimated from the following equation (8): V^ = 0.285 Vc ^'04-8 where = the critical volume of specie "i" (cm /g-mol). Values of Vc are available in various literature sources. Values of aqueous phase diffusion coefficients for various compounds are given in Section 5. 18 ------- cocrPoumoM 4.3 VISCOSITY Viscosities of air and water are readily available from handbooks (10). In Section 5, Table 5-2 presents the viscosity of air and Table 5-4 the viscosity of water as functions of temperature. 4.4 DENSITY Densities of air and water are readily available from handbooks (10). In Section 5, Table 5-3 presents the density of air and Table 5-5 the density of water as functions of temperature. 4.5 HENRY'S LAW CONSTANT Henry's law constant is central to expressing the vapor-liquid equilibrium relationship between the liquid and gaseous phases. This relationship is: Pi = Hi Ci wherej = partial pressure of specie "i" in the air C^ = concentration of specie "i" in the water = Henry's law constant Compilations of Henry's law constant for various materials are avail- able in literature sources. Values for selected compounds are given in Table 5-1 of Section 5 along with other properties. In the absence of experimentally determined values, methods exist for estimating Henry's law constants by calculation (9). The calculational method is based on the foregoing equation written as: H (m^-atm/g-mole) = 18x10"^ Y Pv 19 ------- RADIAN COffPOMTNM where, Y = the liquid phase activity coefficient, and is the pure component vapor pressure. Y can be estimated as a function of molecular properties as discussed in Reference 9. Another method of estimating is : "i ' Pi/Si,sat whe re Si sat = max solubility in water at system temperature. 20 ------- RABBJ&S* coffPowmoN SECTION 5 TABULATIONS OF DATA FOR USE IN EMISSION'S MODEL CALCULATIONS This section presents constants, conversion factors, and property data to be used in the emission models. The following tables are included: • Table 5-1 Property Data for Use in Emissions Estimates of Selected Organic Compounds • Table 5-2 Viscosity of Air at Various Temperatures • Table 5-3 Density of Air at Various Temperatures • Table 5-4 Viscosity of Water at Various Temperatures • Table 5-5 Density of Water at Various Temperatures • Table 5-6 Units Conversion Factors 21 ------- TABLE 5-1. PROPERTY DATA FOR USE LN EMISSIONS ESTIMATES OF SELECTED ORGANIC COMPOUNDS3 Compound Solub i1j t y Molecular Normal Vapor Henry1* Law in IUO CAS Weight Boiling Pt . Pressure @ 25*C Conalant 0 @ 25"C Number (HW^ (Tfa i)f *C (P^, D>m II g Liquid Ho 1 a 1 Volume a t No rma1 B.P. Diffuaivity Diffuaivity in Air 0 2 5 *C in WaIe r 0 25*C - , - -- - , - ------- TAliM:) 5-l • (Continued) Compound Mo 1 ecu 1 a r Norma I Vapor SolubiI it y llenry'a Law in ll70 CAS Humbe r Weight Boiling PL. Prefigure (? 25*C Constant $ 25#C 0 2?C (HW-) (T^ •), *C Hlin •tm-m /do 1 (mg/t) Oiffuaivity Diffueivity (V Llqu id Ho 1 a I Vo 1 time at No rma 1 B . P . b,i>' cm it- in Air g 25'C (D J I in Uaier £ 25*C l,alr> -tDi}w) '/eec 10 cm/se NJ UJ Epichlorohydrin 106-89-8 92.5 116.5 Ethy1 benzene 100-41-4 106.2 136,2 Methyl acetate 79-20-9 74.08 57 Methyl chloride 74-87-3 50 -24,2 (Chlo rome th ane) Naphthalene 91-20-3 81 218 n-Propyl benzene 103-65-1 120 159.2 Propylene oxide 75-56-9 58.08 34.3 Styreiiu 100-42-5 104. 16 145.2 1,1,2,2-Tetrachloroethane 79-34-5 168 146.2 Tet rach loroethy 1 ene 1 27-18 — 4 166 12] Toluene 108-88-3 92 110.6 1,1,1-Trichloroethane 71-55-6 133 74.1 Trichloroethylene 79-01-6 131 87 Vinyl chloride 75-01-4 62.5 -13.4 Vinylidene chloride 75-35-4 97 37 (1,1-Dichloroethylene) o-Xylene 95-47-6 J06 137-140 ta-Xylene 108-38-3 106 139 £-Xylene 106-42-3 106 138 18.8 1 .27 5(20) 6.7(30) 3.8 x 10 4.2 26.8 1 17** 71.6 344(20*) 630. 1 2.77 3.20 3.15 4.8 x 10 2.8 X 10 -2 6.64 i 10 4.92 x 10** 5.92 x 10" -3 1.5 x 10 5.27 x 10 2.55 x 10 2.51 x 10 60,000 4,000 30 3,000 100 515 9 50 1 ,100 1 75 141.6 84.3 50. 6 156.0 166.0 68. 1 108. 5 118.7 95.2 61.6 89.0 J 39. 7 142.4 143.6 0.086 0.075 0. 1 26 0.0622 0.079 0.0794 0.0875 0.090 0.0628 0.98 0.76 0.65 0.893 0.60 0.79 0.877 0.88 0 .9 '< 5 1.04 Blanka indicate that data were not found In readily available sourcoa. ------- RADIAN TABLE 5-2. VISCOSITY OF AIR AT VARIOUS TEMPERATURES AT PRESSURE = 1 ATM Temperature, °C Viscosity, cp 38 0.0185 27 0.0181 16 0.0178 4 0.0170 Source: Reference 10. TABLE 5-3. DENSITY OF AIR AT VARIOUS TEMPERATURES AT PRESSURE - 1 ATM Temperature, °C Density3 g/L 40 1.1034 30 1.1507 20 1.1981 10 1.2454 0 1.2928 aFarm Reference 10 at 0°C. Other values calculated from ideal gas law absolute temperature ratio dependence. 24 ------- TABLE 5-4. VISCOSITY OF WATER AT VARIOUS TEMPERATURES AT PRESSURE = 1 ATM Temperature, °C Viscosity, cp 38 0.73 32 0.82 27 0.90 21 1.02 16 1.13 10 1.27 4 1.40 Source: Reference 10 TABLE 5-5. DENSITY OF WATER AT VARIOUS TEMPERATURES AT PRESSURE - 1 ATM O Temperature, °C Density g/cm 40 0.9922 35 0.9941 30 0.9957 25 0.9971 20 0.9982 15 0.9991 10 0.9997 Source: Reference 10 25 ------- radian coiiPOtumoN TABLE 5-6. UNITS CONVERSION FACTORS To Convert From: To: Multiply By: liter (L) meter (m ) grams (g) pounds (lb) foot (ft) meter (m) foot (ft) centimeter ( cm) foot3 (ft3) centimeter ( cm) lb/ft3 g/cm3 Btu/hour horsepower* f t-lb/sec horsepower* Ergs/sec horsepower* Kilowatts horsepower* watts horsepower* lb/ft-sec cent ipo ises (cp) g/cm-sec (poise) centipoises (cp) lb/ft2-hr g/cm^-s mm Hg atmospheres (atm) 1 x 10"3 2.2046 x 10 -1 -3 3.048 x 30.48 2.832 x 10 10 1.6017 x 10 -2 3.933 1.818 1.341 1.341 1.341 1.488 1 x 10 1.3566 1.3158 10" 10 10 -3 -10 x 10 -3 10- 10 10 -4 -3 Temperature Conversion °C = 5/9 (°F - 32) °K = 273.15 + °C Constants acceleration of gravity (g) 32.17 ft/sec^ 9.807 x 10^ cm/sec^ *Mechanical horsepower, equal to 550 ft-lb/sec 26 ------- imOIAN CO0POMTMM SECTION 6 REFERENCES 1. Wetherold, R.G. and D.A. DuBose. A Review of Selected Theoretical Models for Estimating and Describing Atmospheric Emissions from Waste Disposal Operations, Draft Interim Report, EPA Contract No. 68-03-3038, Work Assignment 63, Prepared for Paul dePercin, IERL, Office of Re- search and Development, U.S. Environmental Protection Agency, Cincin- nati, Ohio, June 24, 1982. 2. Thibodeaux, L.J. and S.T. Hwang. "Landfarming of Petroleum Wastes - Modeling the Air Emission Problem," Environmental Progress, 1_ (1). 42- 46, February 1982. 3. Spencer, W.F. and M.M. Cliath, "Pesticide Volatilization as Related to Water Loss from Soil," J. Environ. Quality. 2_, 284, 1973 . 4. Farmer, W.J. and J. Letey. Volatilization Losses of Pesticides from Soils, EPA-660/2-74-054, U.S. Environmental Protection Agency, Office of Research and Development, Washington, D.C., August 1974. 5. Farmer, W.J., M.S. Yang, and J. Letey. Land Disposal of Hexachloroben- zene Wastes - Controlling Vapor Movement in Soil, EPA-600/2-80-119, Municipal Environmental Research Laboratory, Cincinnati, Ohio, August 1980. 6. Shen, T.T. , "Estimating Hazardous Air Emissions from Disposal Sites," Pollution Engineering, August 1981. 27 ------- radian COflPOOATMN 7. U.S. Environmental Protection Agency. Guidance Document for Subpart F. Air Emission Monitoring. Land Disposal Toxic Air Emissions Evaluation Guideline. December 1980. 8. Reid, R.C., J.M. Prausnitz, and T.K. Sherwood, The Properties of Gases and Liquids, Third Edition, McGraw-Hill Book Company, New York, NY, 1977. 9. Reid, R.C., and T.K. Sherwood, The Properties of Gases and Liquids, Second Edition, McGraw-Hill Book Company, New York, NY, 1966. 10. Perry, R.H. and C.H. Chilton, Chemical Engineer's Handbook, Fifth Edition, McGraw-Hill Book Company, New York, NY, 1973. 28 ------- |