Self‐diffusion measurements in methane by pulsed nuclear magnetic resonance

Abstract

The self-diffusion coefficient of methane has been measured from 150" to 350°K. and from 200 to 5,000 tb./sq. in. abs. A t constant temperature, the density-diffusivity product is constant up to neighborhood of critical density and decreases sharply above that density. The temperature dependence of tke low density data agrees with Chapman-Enskog theory. The LennardJones (6-12) parameters determined from the low density data ( e / k = 130"K., u = 3.85A.) are in good agreement with those determined by other methods. A correlation for the sewdiffusion coefficient for methane has been developed which may provide predictions of other spherical nonpolar gores.The coefficient of self-diffusion was considered (9) to be the limiting case of the binary diffusion coefficient until Carr and Purcell (2) developed the pulsed (or spin echo) nuclear magnetic resonance (NMR) technique to measure self-diffusion. Directly, the study of this significant transport property, self-diffusion, has led to interesting results.The self-diff usion coefficient has considerable theoretical interest. I t is the transport coefficient most easily calculated by kinetic theory, and it provides a good check for the vnrious theories of the dense gas state. The possibility exists ( I ) that binary (mutual) diffusion coefficients may be calculated from the self-diffusion coefficients of the two pure components. The measurement of the self-diffusion coefficient of methane in the dilute and dense gas regions is reported here. T H E O R Y Theory o f Self-DiffusionThe molecules in a fluid are continuously in motion. In a uniform homogeneous fluid, this motion is random and represents the thermal energy present in all fluids. This random motion causes any particular molecule of the fluid to move from place to place in the fluid; this movement is called setf-digusion.The coefficient of self-diffusion is defined aswhere <rz> is the mean square net distance a molecule moves in time t. This definition is consistent with the Ficks law definition of a binary diffusion coefficient, 0 1 2 :On this basis D is defined as the limit of D12 as the molecules of 1 and 2 become identical.In the past, the closest approach to the limit of identical molecules was obtained by observing diffusion of isotopes.For example, C14 methane may be observed diffusing in C12 methane (20). The radioactivity of the former and the nuclear stability of the latter serves to distinguish the two and allows the motion of particular methane molecules to be observed. The change in the diffusion coefficient, caused by the difference in molecular weight of the two species, is small but not negligible. Spin echo NMR fol- Rapier Dawson is with Esso Production Research Company, Houston, Texas.lows the molecules by observing their nuclear spin states; this is a much more subtle "tag." Spin Echo N M RThe basic method of generating nuclear spin echos was discovered by Hahn ( 7 ) , who also suggested their use for measuring self-diffusion coefficients. His suggestions were clarified and the experimental me...

Diffusion of benzene, toluene, naphthalene, and phenanthrene in supercritical dense 2,3‐dimethylbutane

“…As the solvent molar volume decreases, both collision transfer (as opposed to molecular transfer) and collective molecular motion become more important, which leads to a sharper decline in the molecular diffusivity. This qualitative behavior is also exhibited by the self-diffusion in methane at a comparable TR (Dawson et al, 1970) across a wider range of VR, as plotted in Figure 3. Figure 4 is intended to reveal the inconsistency and probable lack of accuracy of the tracer diffusion data in supercritical dense carbon dioxide reported in the past (Tsekhanskaya, 1971;Swaid and Schneider, 1979;Feist and Schneider, 1982).…”

Transport properties of mixtures of rarefied gases. Hydrogen–methane system

“…Now these data are mainly of historical interest, if we take into account accuracy of new viscosity measurements. In addition to the data on the viscosity of methane, we have included, in the processing, the results of measurements of the self-diffusion coefficient of a rarefied gas D 11 (T), referred to a pressure of 1 atm; they include the experimental data of [37] (195-353 K, four points, δ D 11 = 5%, the data of [38] (298, 353, and 382 K, these points, δ D 11 = 3%), the data of [39] (154-354 K, nine points, δ D 11 = 3%), and the data of [40] (273-382 K, four points, δ D 11 = 2%). A priori generalizations of the parameters of the L-J cross potential U 12 (R, a 12 ) have also been included in the procedure of joint data processing.…”

The self-diffusion coefficient of liquid methane

“…Such extensive results do not exist for any simple fluid other than methane [3]. Methane self-diffusion data have been reported by several authors [18][19][20][21][22] [19] and of Oosting and Trappeniers [19]. Their data cover the experimental range of interest and are mutually consistent to within 10 per cent, which is a conservative estimate of their accuracy.…”

“…Downloaded by [University of Waterloo] at 07:55 01 April 2015 the dilute gas diffusion coefficient. Accordingly, the dilute gas property (pD)o, where p is the mass density, was calculated from kinetic theory [24]]-using the potential parameters of equation (2) and compared with experimental measurements extracted from references [18] and [19]. The deviation curve is given as figure 4 and is seen that the agreement between theory and experiment is excellent.…”

“…(2). Data from references [18] and [19]. Downloaded by [University of Waterloo] at 07:55 01 April 2015 the dilute gas diffusion coefficient.…”