Duane equation

The relationship between the voltage of an X-ray tube (or other energy source), in volts, and the wavelength is given by the Duane-Hunt equation. ... 

Natural Gas. A search has also been made for data on alkane isomers from natural gas. So far the search has been very unsuccessful. Only one isomeric analysis has been found. This was provided by Duane Kniebes of the Institute of Gas Technology and is shown in Table IV. Comparison of natural gas data with those found in crude oil and in predictions of the Fischer-Tropsch equation is not very good, particularly in the Oz s. It is hoped that better data will be forthcoming both from natural gas and from coal. In the search for natural gas data, at least one company contacted has decided that its research department should obtain isomeric data on many natural gases. 

To estimate a gas hydrate solubility product requires knowing g, Pg, and aw (Eq. 3.36). The gas partial pressure, Pg, is experimentally measured. The activity of water, aw, is calculated by the FREZCHEM model (Eq. 2.37), as is the gas fugacity coefficient (g) using a model developed by Duan et al. (1992b). The equation used to calculate gas fugacity coefficients is given by... 

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.

Duan Z, M0ller N, Weare JH (1992b) An equation of state for the CH4-CO2-H2O I. Pure systems from 0 to 1000 °C and 0 to 8000 bar. Geochim Cosmochim Acta 56 2605-2617... 

Duan Z., Moller N., and Weare J. H. (1995) Equation of state for the NaCl-H20-C02 system prediction of phase equilibria and volumetric properties. Geochim. Cosmochim. Acta 59, 2869-2882. 

Figure 3A gives solubility curves and spinodals calculated by the PRSV equation of state at 323 K, 50°C in a pressure-mole fraction of CO2 diagram. For comparison, the solubility curve L(G) of CO2 in water, calculated by the more accurate model of Duan and Sun, is also drawn and shows that the PRSV equation of state imderestimates the CO2 solubility in water. The mechanical... 

Duan, Z., and Hu, J. (2004) A new cubic equation of state and its applications to the modeling of vapor-liquid equilibria and volumetric properties of natural fluids, Geochimica et Cosmochimica Acta 14, 2997-3009. 

There are other ways of accounting for the effect of water salinity. Ray F. Weiss proposed to use for the sea water directly the empiric equation (2.291), whose constants are presented in Table 2.30. And lastly, the Z. Duans group, combining the Pitzer equation (2.292) and equations of real gas solution state, calculated Bunsen coefficients for O, N, CH, H S and CO in conditions of temperature between 0 and 200-300 °C, pressure of 1 to 200-2,000 bar with NaCl content of 0 to 6 mole-kg" (Duan et at, 2006 Duan et al, 2007 Mao and Duan, 2006 Geng and Duan, 2010). However, their values are noticeably different from experimentally derived under high temperature. 

Duan et al. (1992a, b 1996a) developed an extension of the Lee-Kesler cubic equation of state for pure gases and mixtures in the systems CH4-CO2-H2O and H20-H2S-NaCl to quite high temperatures and pressures. The equation has 15 fit coefficients but is simple and easily programmed in a spreadsheet. The equation is... 

Duan et al. (1996b) later extended the application of this equation to include polar molecules such as H2O and mixtures of any of the components H2O, CO2, CH4, N2, CO, H2, O2, H2S, Ar, and fitted experimental data as well as... 

Duan ZH, Moller N, Weare JH (1995) Molecular dynamics equation of state for nonpolar geochemical fluids. Geochim Cosmochim Acta 59 1533-1538... 

Dr. Duan s research interests cover areas including inelastic behavior of reinforced concrete and steel structures, structural stability, seismic bridge analysis, and design. With more than 70 authored and coauthored papers, chapters, and reports, his research focuses on the development of unified interaction equations for steel beam-columns, flexural stiffness of reinforced concrete members, effective length factors of compression members, and design of bridge structures. 

The PLP is a well-known NHPP model used to study the reliability of the repairable systems. Duane (1964) was the first to report that the cumulative number of failures of such systems up to time t, N, often have a power-law growth pattern. Then, Crow (1974) formulated the corresponding model as a nonhomogeneous Poisson process model. The reliability function at time t are defined by the following equation ... 

S. Scheiner and X. Duan, Applicability of the Marcus equation to proton transfer in symmetric and unsymmetric systems, J. Mol. Struct. (Theochem), 285 (1993) 27. 

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