Estimation—Gases

Whenever measured values of diffusivities are available, they should be used. Typically, measurement errors are less than those associated with predictions by empirical or even semitheoretical equations. A few general sources of data are Sec. 2 of this handbook e.g., experimental values for gas mixtures are listed in Table 2-371. Estimation methods for some gaseous applications appear in Eqs. (2-150) through (2-154). Other pertinent references are Schwartzberg and Chao Poling et al. Gammon et al. and Daubert and Danner. Many other more restricted sources are listed under specific topics later in this subsection. 

Before using diffusivities from either data or correlations, it is a good idea to check their reasonableness with respect to values that have been commonly observed in similar situations. Table 5-9 is a compilation of several rules of thumb. These values are not authoritative they simply represent guidelines based on experience. 

Diffusivity correlations for gases are outlined in Table 5-10. Specific parameters for individual equations are defined in the specific text regarding each equation. References are given at the beginning of the Mass Transfer subsection. The errors reported for Eqs. (5-202) through (5-205) were compiled by Poling et al., who compared the predictions with 68 experimental values of D. Errors cited for Eqs. (5-206) to (5-212) were reported by the authors. 

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Dilling, W.L., Gonsior, S.J., Boggs, G.U., Mendoza, C.G. (1988) Organic photochemistry. 20. A method for estimating gas-phase rate for reactions of hydroxyl radicals with organic compounds from their relative rates of reaction with hydrogen peroxide under photolysis in 1,1,2-trichlorotrifluoroethane solution. Environ. Sci. Technol. 22, 1447-1453. 

The key to establishing gas hydrates as a significant energy resource is whether the methane gas will ever be economically and safely producible. The current state of knowledge is still too limited to allow reliable estimates on the start of an economic gas hydrate production. The BGR (2003) estimates gas hydrate resources at 500 Tm3. 

The transport of disulfoton from water to air can occur due to volatilization. Compounds with a Henry s law constant (H) of <10 atm-m /mol volatilize slowly from water (Thomas 1990). Therefore, disulfoton, with an H value of 2.17x10" atm-m /mol (Domine et al. 1992), will volatilize slowly from water. The rate of volatilization increases as the water temperature and ambient air flow rate increases and decreases as the rate of adsorption on sediment and suspended solids increases (Dragan and Carpov 1987). The estimated gas- exchange half-life for disulfoton volatilization from the Rhine River at an average depth of 5 meters at 11 °C was 900 days (Wanner et al. ] 989). The estimated volatilization half-life of an aqueous suspension of microcapsules containing disulfoton at 20 °C with still air was >90 days (Dragan and Carpov 1987). 

Kleinberg et al. (2005) and Takayama et al. (2005) show that NMR-log measurement of sediment porosity, combined with density-log measurement of porosity, is the simplest and possibly the most reliable means of obtaining accurate gas hydrate saturations. Because of the short NMR relaxation times of the water molecules in gas hydrate, they are not discriminated by the NMR logging tool, and the in situ gas hydrates would be assumed to be part of the solid matrix. Thus the NMR-calculated porosity in a gas-hydrate-bearing sediment is apparently lower than the actual porosity. With an independent source of accurate in situ porosities, such as the density-log measurements, it is possible to accurately estimate gas hydrates saturations by comparing the apparent NMR-derived porosities with the actual reservoir porosities. Collett and Lee (2005) conclude that at relatively low gas... 

Gas exchange studies of total toxaphene in Lakes Superior, Michigan and Ontario were conducted between 1996-2000 [46,50,67] using concurrently measured water and air concentrations. The air and water data from these studies are discussed in Sects. 2.2, 3.1.1 and 3.1.2, and are summarized in Tables 3, 5, and 6. An earlier mass budget for toxaphene [65] estimated gas exchange from measured water concentrations and historical air data from Hoff et al. [64], All studies based their fugacity and flux calculations on the temperature-dependent Henry s law constant for technical toxaphene [15]. 

Table B.l lists all the chemical reactions and their temperature dependence. Table B.2 lists the Debye-Hiickel constants A,p and Av) as a function of temperature and pressure. Table B.3 lists the numerical arrays used for calculating unsymmetrical interactions (Equations 2.62 and 2.66). Table B.4 lists binary Pitzer-equation parameters for cations and anions as a function of temperature. Table B.5 lists ternary Pitzer-equation parameters for cations and anions as a function of temperature. Table B.6 lists binary and ternary Pitzer-equation parameters for soluble gases as a function of temperature. Table B.7 lists equations used to estimate the molar volume of liquid water and water ice as a function of temperature at 1.01 bar pressure and their compressibilities. Table B.8 lists equations for the molar volume and the compressibilities of soluble ions and gases as a function of temperature. Table B.9 lists the molar volumes of solid phases. Table B.10 lists volumetric Pitzer-equation parameters for ion interactions as a function of temperature. Table B.ll lists pressure-dependent coefficients for volumetric Pitzer-equation parameters. Table B.12 lists parameters used to estimate gas fugacities using the Duan et al. (1992b) model.

Perhaps the best source of information on estimating gas solubility is the book by Reid et al. (1987), which not only lists the various solubility models but also compares them with a database of experimental measurements. 

A great number of studies related to thermochemical properties of QDO and PDO derivatives have been recently described by Ribeiro da Silva et al. [98-103]. These studies, which have involved experimental and theoretical determinations, have reported standard molar enthalpies of formation in the gaseous state, enthalpies of combustion of the crystalline solids, enthalpies of sublimation, and molar (N - O) bond dissociation enthalpies. Table 5 shows the most relevant determined parameters. These researchers have employed, with excellent results, calculations based in density functional theory in order to estimate gas-phase enthalpies of formation and first and second N - O dissociation enthalpies [103]. 

The liquid-phase mixing in a multistage mechanically agitated reactor is best correlated by Eq. (2.31) in the absence of gas flow and by Eq. (2.32) in the presence of gas flow. The mixing time can be estimated from the study of Paca et al. (1976). Experimental work is needed to estimate gas-phase back-mixing. The use of Eq. (2.36) for the calculation of the gas-liquid volumetric mass transfer coefficient in a multistage mechanically agitated column is recommended. 

The average absolute relative error for estimated gas holdup is 7.8 percent when using Equation (7). 

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