Binary gas mixtures

Fuller s equation, applied for the estimation of the coefficient of diffusion of a binary gas mixture, at a pressure greater than 10 bar, predicts values that are too high. As a first approximation, the value of the coefficient of diffusion can be corrected by multiplying it by the compressibility of the gas /... 

This process has been used for various situations (1—14). Eor the condensation of a single component from a binary gas mixture, the gas-stream sensible heat and mass-transfer equations for a differential condenser section take the following forms ... 

Thermal-Conductivity Analyzer. The thermal-conductivity analy2er operates on the principle that the loss of heat from a hot wire by gaseous conduction to a surface at a lower temperature varies with the thermal conductivity of the gas, and is virtually independent of pressure between 1.3 kPa (10 mm Hg) and 101 kPa (1 atm). This technique is frequently used in continuous monitors for tritium in binary gas mixtures for immediate detection of process change. 

H2—HD and Ar— Ar binary gas mixtures have been measured (34,35). A vortex tube has been used for isotope separation (36), and for the separation of gases in nuclear rocket or ramjet engines. 

Equation 65 gives the pressure at any point within the centrifuge, (r), as a function of the coordinate r, the pressure at the axis (0), the angular velocity of the centrifuge, and the temperature and mol wt of the gas. Should the centrifuge contain not a single pure gas, but a gas mixture, equations of the above forms could be written for each species present. In particular for the case of a binary gas mixture, consisting of species M and B. 

Mass Transport. An expression for the diffusive transport of the light component of a binary gas mixture in the radial direction in the gas centrifuge can be obtained directly from the general diffusion equation and an expression for the radial pressure gradient in the centrifuge. For diffusion in a binary system in the absence of temperature gradients and external forces, the general diffusion equation retains only the pressure diffusion and ordinary diffusion effects and takes the form... 

An alternate method for gas diffiisivity of binary gas mixtures at low pressures is the method of Hirschfelder et al. The method requires several molecular parameters and, when evaluated, gives an average absolute error of about 10 percent. The method is discussed in detail in the Data Vrediction Manual. 

In a binary gas mixture, the diffusion coefficient of the species i at a mole fraction jc, widr respect to tlrat of the species j is given after evaluating the constants by tire equation... 

Table 10.5. Values of thermal diffusion factor (a) for binary gas mixtures (A is the heavier component, which moves towards the cooler end)...

Diffusivity Estimation Method for Binary Gas Mixtures from Treybal, Mass-Transfer Operations, 3rd Edition... 

The theory which forms the basis for discussions of the transport phenomena in dense gases is Enskog s kinetic theory for a pure gas made up of rigid spheres (E3, C3, Chapter 16 Hll, 9.3). To date, this theory in one of several modifications is the best theory available for calculating the temperature and density dependence of the transport coefficients. Recently Enskog s theory has been extended to a pure gas made up of nonrigid molecules by Curtiss and Snider (CIO, C14). Enskog s theory has also been extended to binary gas mixtures by Thorne (C3, p. 292). 

At moderate pressures the diffusion coefficient of a binary gas mixture of molecules i and j is well described by the Chapman-Enskog theory, discussed in Section 12.4 ... 

The sorption and diffusion behaviour of gas mixtures is of particular interest from the point of view of membrane gas separation, which is steadily gaining in importance by virtue of its low energy requirements. On the basis of the dual mode sorption model, one may reasonably expect that sorption of a binary gas mixture A, B in the polymer matrix will exhibit little gas-gas interaction and hence will tend to occur essentially additively. In the Langmuir-like mode of sorption, on the other hand, there will be competition between A and B for the limited number of available sites. These considerations led 67) to the following reformulation of Eqs. (8) and (9)... 

Bulk diffusion coefficients in binary gas mixture are almost independent of the ratio of components of the mixture. Therefore, it was supposed that if diffusion in the measurements described above is of the bulk type, i.e., the free path of molecules is much lesser than the diameter of pores, then the first gas diffuses into the second gas at the same rate as the second gas diffuses into the first. 

The explanation of Graham s law given by Hoogschagen is not complete, as subsequent authors (17,18) stated. However, the attempts of these authors to give a more complete explanation for the law are not convincing. It is known that at conventional measurements of diffusion coefficients in binary gas mixtures using wide capillaries, equal velocities of counterdiffusion of the components are observed. From the considerations developed... 

To evaluate the phase equilibria of binary gas mixtures in contact with water, consider phase diagrams showing pressure versus pseudo-binary hydrocarbon composition. Water is present in excess throughout the phase diagrams and so the compositions of each phase is relative only to the hydrocarbon content. This type of analysis is particularly useful for hydrate phase equilibria since the distribution of the guests is of most importance. This section will discuss one diagram of each binary hydrate mixture of methane, ethane, and propane at a temperature of 277.6 K. 

The chemical potential of species B in a binary gas mixture above the solution is... 

It can be shown that the composition of the permeate gas, P 11, for permeation of a binary gas mixture is given by the following quadratic equation ... 

The separation efficiency for a given membrane with a particular binary gas mixture will be dependent mainly upon three factors gas composition, the pressure ratio between feed and permeate gas, and the sepration factor for the two components. A higher separation factor gives a more selective membrane, resulting in a greater separation efficiency. This parameter is a function of the membrane material and is determined by the individual gas permeation rates. 

P 21] The mixing of gaseous methanol and oxygen was simulated. The equations applied for the calculation were based on the Navier-Stokes (pressure and velocity) and the species convection-diffusion equation [57]. As the diffusivity value for the binary gas mixture 2.8 x 10 m2 s 1 was taken. The flow was laminar in all cases adiabatic conditions were applied at the domain boundaries. Compressibility and slip effects were taken into account The inlet temperature was set to 400 K. The total number of cells was —17 000 in all cases. 

The above-mentioned inverse selectivity/permeability relationship of polymers has been summarized by Robeson by means of log-log plots of the overall selectivity versus the permeability coefficient, where A is considered to be the more rapidly permeating gas. These plots were made for a variety of binary gas mixtures from the list He, H2, O2, N2, C02, and CH4, and for a large number of rubbery and glassy polymer membranes. Such representations, shown in Fig. 8 and Fig. 9 are often referred to as upper bound plots (Robeson, 1991). The upper bound lines clearly show the inverse selectivity/permeability relationship of polymer membranes. While these plots were prepared in 1991, only small advances have been made to push the upper bound higher since that time. 

The rationalizations of signs for HE of binary liquid mixtures presented in Sec. 16.7 apply approximately to the signs of S 2 for binary gas mixtures. Thus, positive Su is the norm for NP/NP, NA/NP, and AS/NP mixtures, whereas is usually negative for NA/NA mixtures comprising solvating species. One expects < 12 to be essentially zero for ideal solutions of real gases, e.g., for binary gas mixtures of the isomeric xylenes. 

Equation (2.71) can be compared with Eq. (2.46) for the thermal conductivity of gases, and with Eq. (2.19) for the viscosity. For binary gas mixtures at low pressure, is inversely proportional to the pressure, increases with increasing temperature, and is almost independent of the composition for a given gas pair. For an ideal gas law P = cRT, and the Chapman-Enskog kinetic theory yields the binary diffusivity for systems at low density... 

Similar equations can be written for components J2 and J3. The coefficients Dx x and D22 are the main coefficients they are not self-diffusion coefficients. Du and D2l are the cross-coefficients and assumed to be equal to each other for binary gas mixtures. 

Several experimental techniques have been developed for the investigation of the mass transport in porous catalysts. Most of them have been employed to determine the effective diffusivities in binary gas mixtures and at isothermal conditions. In some investigations, the experimental data are treated with the more refined dusty gas model (DGM) and its modifications. The diffusion cell and gas chromatographic methods are the most widely used when investigating mass transport in porous catalysts and for the measurement of the effective diffusivities. These methods, with examples of their application in simple situations, are briefly outlined in the following discussion. A review on the methods for experimental evaluation of the effective diffusivity by Haynes [1] and a comprehensive description of the diffusion cell method by Park and Do [2] contain many useful details and additional information. 

---