Carbon dioxide diffusion coefficients

Kholyavenko and Rubanik (143) investigated the effect of internal diffusion on the ethylene oxidation rate, using the diaphragm method, and calculated the effective diffusion coefficients for ethylene and carbon dioxide diffusing through a silver diaphragm. 

The crystallization of the PLA matrix induces a decrease in the carbon dioxide permeability coefficient [123, 132]. According to Sawada et al, [128] the effect of crystallinity on CO permeability is similar to the one on oxygen, that is to say there is a slight increase in the diffusion coefficient at low crystallinity followed by a decrease of 40%, whereas solubility decreases slowly in relation with the crystallinity degree. 

Carbon dioxide diffuses through a high-den-sity polyethylene (HDPE) sheet 50 mm thick at a rate of 2.2 X 10 (cm STP)/cm -s at 325 K. The pressures of carbon dioxide at the two faces are 4000 kPa and 2500 kPa, which are maintained constant. Assuming conditions of steady state, what is the permeability coefficient at 325 K ... 

The diffusion and solubihty coefficients for oxygen and carbon dioxide in selected polymers have been collected in Table 5. Determination of these coefficients is neither common, nor difficult. Methods are discussed later. The values of S for a permeant gas do not vary much from polymer to polymer. The large differences that are found for permeabihty are due almost entirely to differences in D. 

Table 5. Diffusion and Solubility Coefficients for Oxygen and Carbon Dioxide in Selected Polymers at 23°C, Dry ...

Reasonable prediction can be made of the permeabiUties of low molecular weight gases such as oxygen, nitrogen, and carbon dioxide in many polymers. The diffusion coefficients are not compHcated by the shape of the permeant, and the solubiUty coefficients of each of these molecules do not vary much from polymer to polymer. Hence, all that is required is some correlation of the permeant size and the size of holes in the polymer matrix. Reasonable predictions of the permeabiUties of larger molecules such as flavors, aromas, and solvents are not easily made. The diffusion coefficients are complicated by the shape of the permeant, and the solubiUty coefficients for a specific permeant can vary widely from polymer to polymer. 

Carbon Dioxide Transport. Measuring the permeation of carbon dioxide occurs far less often than measuring the permeation of oxygen or water. A variety of methods ate used however, the simplest method uses the Permatran-C instmment (Modem Controls, Inc.). In this method, air is circulated past a test film in a loop that includes an infrared detector. Carbon dioxide is appHed to the other side of the film. AH the carbon dioxide that permeates through the film is captured in the loop. As the experiment progresses, the carbon dioxide concentration increases. First, there is a transient period before the steady-state rate is achieved. The steady-state rate is achieved when the concentration of carbon dioxide increases at a constant rate. This rate is used to calculate the permeabiUty. Figure 18 shows how the diffusion coefficient can be deterrnined in this type of experiment. The time lag is substituted into equation 21. The solubiUty coefficient can be calculated with equation 2. 

Fig. 18. Diffusion coefficient D12 for hydrogen+carbon dioxide. measure-...

Fig. 20. Diffusion coefficient JDia for nitrogen4-carbon dioxide. A, measurement of Boardman and Wild A > Waldmann V, Boyd, et al. O, Schafer, Corte, and Moesta , Andrew.

The formation of carbon dioxide depends on both the isocyanate and water concentrations in the paint film. The carbon dioxide concentration in the paint film depends on the diffusion coefficient, the film thickness and the difference in carbon dioxide concentration between paint film and gas phase ... 

Diffusion coefficients can be estimated with the aid of the mathematical description of the diffusion of carbon dioxide from the paint film (Scheme II). Film thickness, saturation concentration and carbon dioxide equilibrium concentration are known. The emission curves of carbon dioxide calculated by the model have been fitted with the actual emission curves in Figure 7. In this case carbon dioxide is not formed chemically. 

Figures 9 and 10 give the calculated carbon dioxide concentration in the paint film, using different values for the diffusion coefficient and reaction rate constants.

A supercritical fluid exhibits physical-chemical properties intermediate between those of liquids and gases. Mass transfer is rapid with supercritical fluids. Their dynamic viscosities are nearer to those in normal gaseous states. In the vicinity of the critical point the diffusion coefficient is more than 10 times that of a liquid. Carbon dioxide can be compressed readily to form a liquid. Under typical borehole conditions, carbon dioxide is a supercritical fluid. 

Supercritical fluid extraction (SFE) is a technique in which a supercritical fluid [formed when the critical temperature Tf) and critical pressure Pf) for the fluid are exceeded simultaneously] is used as an extraction solvent instead of an organic solvent. By far the most common choice of a supercritical fluid is carbon dioxide (CO2) because CO2 has a low critical temperature (re = 31.1 °C), is inexpensive, and is safe." SFE has the advantage of lower viscosity and improved diffusion coefficients relative to traditional organic solvents. Also, if supercritical CO2 is used as the extraction solvent, the solvent (CO2) can easily be removed by bringing the extract to atmospheric pressure. Supercritical CO2 itself is a very nonpolar solvent that may not have broad applicability as an extraction solvent. To overcome this problem, modifiers such as methanol can be used to increase the polarity of the SFE extraction solvent. Another problem associated with SFE using CO2 is the co-extraction of lipids and other nonpolar interferents. To overcome this problem, a combination of SFE with SPE can be used. Stolker et al." provided a review of several SFE/SPE methods described in the literature. 

Sassiat, P.R., Mourier, P., Caude, M.H. and Rosset, R.H. (1987) Measurement of diffusion coefficients in supercritical carbon dioxide and correlation with the equation of Wilke and Chang. Analytical Chemistry, 59 (8), 1164-1170. 

Carbon dioxide supply, for the molten carbonate fuel cell, 72 220 Carbon dioxide ternary systems, phase behavior of, 24 4—5 Carbon diselenide, 22 75t Carbon disulfide, 4 822-842 23 567, 568, 621. See also CS2 in cellulose xanthation, 77 254 chemical reactions, 4 824—828 diffusion coefficient in air at 0° C, 7 70t economic aspects, 4 834-835 electrostatic properties of, 7 621t handling, shipment, and storage, 4 833-834... 

PEN has lower gas permeation coefficients than PET for carbon dioxide, oxygen and moisture for both film types. Although the gas-barrier properties of PEN are similar to those of poly(vinyl dichloride), it is not affected by moisture in the environment. Both oriented and unoriented PEN films restrict gas diffusion more... 

The first use of supercritical fluid extraction (SFE) as an extraction technique was reported by Zosel [379]. Since then there have been many reports on the use of SFE to extract PCBs, phenols, PAHs, and other organic compounds from particulate matter, soils and sediments [362, 363, 380-389]. The attraction of SFE as an extraction technique is directly related to the unique properties of the supercritical fluid [390]. Supercritical fluids, which have been used, have low viscosities, high diffusion coefficients, and low flammabilities, which are all clearly superior to the organic solvents normally used. Carbon dioxide (C02, [362,363]) is the most common supercritical fluid used for SFE, since it is inexpensive and has a low critical temperature (31.3 °C) and pressure (72.2 bar). Other less commonly used fluids include nitrous oxide (N20), ammonia, fluoro-form, methane, pentane, methanol, ethanol, sulfur hexafluoride (SF6), and dichlorofluoromethane [362, 363, 391]. Most of these fluids are clearly less attractive as solvents in terms of toxicity or as environmentally benign chemicals. Commercial SFE systems are available, but some workers have also made inexpensive modular systems [390]. 

Tamimi K., Rinker E.B., and Sandall O.C. (1994) Diffusion coefficients for hydrogen sulfide, carbon dioxide, and nitrous oxide in water over the temperature range of 293-368 K. /. Chem. Eng. Data 39, 330-332. 

The concept of permeability. Pm, described first in Section 4.3.2.2 also applies to membranes. Equation (4.77) relates the permeability to the diffusion coefficient and solubility. Some representative values of permeabilities for common gases in common polymer films are given in Table 4.17. The units of permeability in Table 4.17 are obtained when diffusivity is in units of m /s, and gas solubility is in units of m gas m /(m soUd-N). Note that carbon dioxide permeabilities are generally 3-4 times... 

Fig. 16. Variation of effective diffusion coefficient of carbon dioxide through carbon monoxide at N.T.P. with porosity of spectroscopic carlion rods. Porosity developed by reaction with carbon dioxide at 950°.

Supercritical fluid chromatography provides increased speed and resolution, relative to liquid chromatography, because of increased diffusion coefficients of solutes in supercritical fluids. (However, speed and resolution are slower than those of gas chromatography.) Unlike gases, supercritical fluids can dissolve nonvolatile solutes. When the pressure on the supercritical solution is released, the solvent turns to gas. leaving the solute in the gas phase for easy detection. Carbon dioxide is the supercritical fluid of choice for chromatography because it is compatible with flame ionization and ultraviolet detectors, it has a low critical temperature. and it is nontoxic. 

The only published work on the diffusion of gas in coals of different rank appears to be that of Bolt and Innes (2) who studied the diffusion of carbon dioxide from eleven samples of coal at 38°C. They found the diffusion coefficient to range from 3.5 to 9.2 x 10 8 sq. cm./sec., with no apparent correlation with coal rank. Diffusion data on coals of different rank at temperatures higher than 38°C. have only been reported by the present authors (6). It has been shown (7) that the diffusion of inert or noble gases from coal above room temperatures can be rigorously analyzed by using simple diffusion theory, and that true diffusion parameters of the micropore systems can be obtained. In this paper our measurements on the unsteady state release of argon from coals of various rank, over a temperature range, are reported. 

The diffusion coefficient as defined by Fick s law, Eqn. (3.4-3), is a molecular parameter and is usually reported as an infinite-dilution, binary-diffusion coefficient. In mass-transfer work, it appears in the Schmidt- and in the Sherwood numbers. These two quantities, Sc and Sh, are strongly affected by pressure and whether the conditions are near the critical state of the solvent or not. As we saw before, the Schmidt and Prandtl numbers theoretically take large values as the critical point of the solvent is approached. Mass-transfer in high-pressure operations is done by extraction or leaching with a dense gas, neat or modified with an entrainer. In dense-gas extraction, the fluid of choice is carbon dioxide, hence many diffusional data relate to carbon dioxide at conditions above its critical point (73.8 bar, 31°C) In general, the order of magnitude of the diffusivity depends on the type of solvent in which diffusion occurs. Middleman [18] reports some of the following data for diffusion. 

Knaff and Schlunder [9] studied the evaporation of naphthalene and caffeine from a cylindrical surface (a sintered metallic rod impregnated with the solute) to high-pressure carbon dioxide flowing over an annular space around the rod. They studied the diffusion flux within the bar and in the boundary layer. The mass-transfer coefficient owing to forced convection from cylinder to the gas flowing in the annular duct was correlated, using the standard correlation due to Stephan [7]. For caffeine, it does not require a free-convection correction, as the Reynolds dependence is that expected by a transfer by forced convection. This is... 

In the cases above, a two-parameter model well represents the data. A model with more parameters would be more flexible, but by using a partition constant, K, or a desorption rate constant ka and k, , for the mass-transfer coefficients, the data are well described (see Figs. 3.4-15 and 3.4-13). While K would be a value experimentally determined, kp can be estimated from eqn. (3.4-97) with the external mass-transfer coefficient, km, estimated from the correlation of Stiiber et al. [25] or from that of Tan et al. [27], and the effective diffusivity from the Wakao Smith model [36], Typical values of kp obtained by fitting the data of Tan and Liou are shown in Fig. 3.4-16. As expected, they are below the usual mass-transfer correlations, because internal resistance diminishes the global mass transfer coefficient. These data correspond to the regeneration of spent activated carbon loaded with ethyl acetate, using high-pressure carbon dioxide, published by Tan and Liou [45]. 

The diffusion and solubility coefficients for oxygen and carbon dioxide in selected polymers have been collected in Table 2. 

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