Hydrocarbon diffusivity equation

The diffusion-enhanced olefin readsorption model described in Section III,C was used to predict the effect of carbon number on chain growth probability and paraffin selectivity. The model requires only one adjustable parameter the exponent c in a hydrocarbon diffusivity equation that depends on molecular size ( ), but that is identical for paraffins and olefins of equal size ... 

With the advent of picosecond-pulse radiolysis and laser technologies, it has been possible to study geminate-ion recombination (Jonah et al, 1979 Sauer and Jonah, 1980 Tagawa et al 1982a, b) and subsequently electron-ion recombination (Katsumura et al, 1982 Tagawa et al, 1983 Jonah, 1983) in hydrocarbon liquids. Using cyclohexane solutions of 9,10-diphenylanthracene (DPA) and p-terphenyl (PT), Jonah et al. (1979) observed light emission from the first excited state of the solutes, interpreted in terms of solute cation-anion recombination. In the early work of Sauer and Jonah (1980), the kinetics of solute excited state formation was studied in cyclohexane solutions of DPA and PT, and some inconsistency with respect to the solution of the diffusion equation was noted.1... 

Mass transfer One more difficulty arises from the fact that there are two phases in the reactor (i) hydrocarbon and (ii) acid. The reaction occurs in the acid phase while reactants are feed in hydrocarbon phase. This implies that, in order to reaction occurs, there is mass transfer from hydrocarbon to acid phase. The mass transfer is a very complex phenomenon which can involve the reaction-diffusion equation. However, such a phenomenon is beyond of the goal of this chapter. Both isobutane and propilene are feed in hydrocarbon phase. Solubility of propylene in acid phase is very... 

Returning to the survival probability, in Fig. 57, the kinetic theory and diffusion equation [cf. eqn. (132)] predictions are compared. Three values of the activation rate coefficient are used, being 0.5, 1.0 and 2.0 times the Smoluehowski rate coefficient for a purely diffusion-limited homogeneous reaction, 4ttoabD. With a diffusion coefficient of 5x 10 9 m2 s1 and encounter distance of 0.5 nm, significant differences are noted between the kinetic theory and diffusion equation approaches [286]. In all cases, the diffusion equation leads to a faster rate of reaction. In their measurements of the recombination rate of iodine atoms in hydrocarbon solvents, Langhoff et al. [293] have noted that the diffusion equation analysis consistently predicts a faster rate of iodine atom recombination than is actually measured. Thus there is already some experimental support for the value of the kinetic theory approach compared with the diffusion equation analysis. Further developments cannot fail to be exciting. 

There are a number of possible approaches to the calculation of influences of finite-rate chemistry on diffusion flames. Known rates of elementary reaction steps may be employed in the full set of conservation equations, with solutions sought by numerical integration (for example, [171]). Complexities of diffusion-flame problems cause this approach to be difficult to pursue and motivate searches for simplifications of the chemical kinetics [172]. Numerical integrations that have been performed mainly employ one-step (first in [107]) or two-step [173] approximations to the kinetics. Appropriate one-step approximations are realistic for limited purposes over restricted ranges of conditions. However, there are important aspects of flame structure (for example, soot-concentration profiles) that cannot be described by one-step, overall, kinetic schemes, and one of the major currently outstanding diffusion-flame problems is to develop better simplified kinetic models for hydrocarbon diffusion flames that are capable of predicting results such as observed correlations [172] for concentration profiles of nonequilibrium species. 

The theory of rotation effects on prolate luminescent molecules in solution and its experimental verification have been developed and compared. Generalized diffusion equations for the rotational motion of an asymmetric rigid motor have been used to given an expression for steady-state fluorescence depolarization. " The radiationless transition from the first excited singlet state of Eosin has been measured by optoacoustic relaxation, and the absolute fluorescence quantum yields of organic dyes in poly(vinyl alcohol) have also been measured by the photoacoustic method. The accuracy of the method has been discussed in the latter paper. Actinometry in flash photolysis experiments has been assisted by new measurements on the extinction coefficient of triplet benzophenone. Matrix-isolation fluorescence spectrometry has been used to detect polycyclic aromatic hydrocarbons from gas chromatography. ... 

A value of c equal to 0.3, previously used to describe FT selectivity data on Ru catalysts (4), was also chosen here to describe the behavior of cobalt catalysts. This equation for hydrocarbon diffusion in melts reflects the strong influence of molecular size in reptation and entanglement models of transport in such systems (IJ6). Our model also requires the input of intrinsic values for jSn (given by the asymptotic j8r), jSo, j8r, and j8s, measured independently. After such parameters are specified, the model yields a non-Flory carbon number distribution of increasingly paraffinic hydrocarbons that agrees well with our experimental observations (Fig. 16). 

Diffusion coefficients of hydrocarbons are less influenced by temperature than those of alcohols and diethyl ether, for which the dependence is close to that observed in a normal gas-in-gas diffusion. Equation 17 was derived for strong sorbable gases thus, this equation could not be used for n-hexane isotherms in the higher temperature range, where the isotherm is almost linear. 

Details of the neutralization process following radiation-induced primary charge separation may be examined via the medium of ultrafast techniques now employed in studies of luminescence decay processes. As an example, the form of luminescence decay curves of dilute organic scintillator in aliphatic hydrocarbon solution excited by x-ray pulses of about 0.5-1.0 nsec, duration is attributed (in previous papers) to neutralization processes involving ions. The relation, t cc r3, for the time required for neutralization of an ion pair of initial separation r, when applied to such curves, leads to a distribution function of ion-pair separations. A more appropriate and desirable approach involves solution of a diffusion equation (which includes a Coulomb interaction term) for various initial conditions. Such solutions are obtained by computer techniques employed in analogy to corresponding electrical networks. The results indicate that the tocr3 law affords a fair description of the decay if the initial distribution can be assumed to be broad. 

ABSTRACT. The principle features of the frequency-response i paratus developed at Imperial College is described. The apparatus has been used in both its a) full and b) single-step frequency modes to determine the diffiisivities of various hydrocarbons in silicalite-1. Die effect of temperature and loading of sorbate in the silicalite-1 has been ascertained. The effect of the introduction of A1 atoms into the framework of silicalite-1 on the diffusivity of benzene has been detmnined. The diffusion of benzene in NaX has been studied and diffusion coefficients obtained which agree with NMR pulsed field gradient measurements, n-Butane and 2-butyne hydrocarbons were found to generate out-of-phase response curves by the full FR method which could only be fitted by introducing two diffusion coefficients into the solution of the appropriate diffusion equation. 

Based on the assumption of equi-molar counter diffusion, analytical expression for concentration overpotential is possible when H2 is used as fuel [76]. However, the situation is more complex when CH4 or other hydrocarbons are used as fuel. When any fuel other than pure H2 or CO is used as the anode stream, numerous chemical reactions proceed in the porous anode and one has to resort to numerical methods to evaluate the concentration overpotential. The most appropriate approach is to solve the porous media problem as a reaction-diffusion equation. But to reduce the numerical intensity of the problem many researchers do adhere to the simple analytical expression derived for H2 even for the case of hydrocarbons [81]. 

If the pore-mechanism applies, the rate of permeation should be related to the probability at which pores of sufficient size and depth appear in the bilayer. The correlation is given by the semi-empirical model of Hamilton and Kaler [150], which predicts a much stronger dependence on the thickness d of the membrane than the solubility-diffusion model (proportional to exp(-d) instead of the 1 Id dependence given in equation (14)). This has been confirmed for potassium by experiments with bilayers composed of lipids with different hydrocarbon chain lengths [148], The sensitivity to the solute size, however, is in the model of Hamilton and Kaler much less pronounced than in the solubility-diffusion model. 

The solution procedure to this equation is the same as described for the temporal isothermal species equations described above. In addition, the associated temperature sensitivity equation can be simply obtained by taking the derivative of Eq. (2.87) with respect to each of the input parameters to the model. The governing equations for similar types of homogeneous reaction systems can be developed for constant volume systems, and stirred and plug flow reactors as described in Chapters 3 and 4 and elsewhere [31-37], The solution to homogeneous systems described by Eq. (2.81) and Eq. (2.87) are often used to study reaction mechanisms in the absence of mass diffusion. These equations (or very similar ones) can approximate the chemical kinetics in flow reactor and shock tube experiments, which are frequently used for developing hydrocarbon combustion reaction mechanisms. 

The Mallard-Le Chatelier development for the laminar flame speed permits one to determine the general trends with pressure and temperature. When an overall rate expression is used to approximate real hydrocarbon oxidation kinetics experimental results, the activation energy of the overall process is found to be quite high—of the order of 160kJ/mol. Thus, the exponential in the flame speed equation is quite sensitive to variations in the flame temperature. This sensitivity is the dominant temperature effect on flame speed. There is also, of course, an effect of temperature on the diffusivity generally, the dif-fusivity is considered to vary with the temperature to the 1.75 power. 

On the other hand, if the rate constant for the quenching step exceeds that expected for a diffusion-controlled process, a modification of the parameters in the Debye equation is indicated. Either the diffusion coefficient D as given by the Stokes-Einstein equation is not applicable because the bulk viscosity is different from the microviscosity experienced, by the quencher (e.g. quenching of aromatic hydrocarbons by O, in paraffin solvents) or the encounter radius RAb is much greater than the gas-kinetic collision radius. In the latter case a long-range quenching... 

The theoretical lines in Figure 2 are calculated assuming constant values of D0 with the derivative d In p/d In c calculated from the best fitting theoretical equilibrium isotherm (Equation 8). The theoretical lines give an adequate representation of the experimental data suggesting that the concentration dependence of the diffusivity is caused by the nonlinearity of the relationship between sorbate activity and concentration as defined by the equilibrium isotherm. The diffusivity data for other hydrocarbons showed similar trends, and in no case was there evidence of a concentration-dependent mobility. Similar observations have been reported by Barrer and Davies for diffusion in H-chabazite (7). 

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