Flory equation, product distributions

The product distribution frcm the Fischer-Tropsch reaction on 5 is shown in Table I. It is similar but not identical to that obtained over other cobalt catalysts (18-21,48, 49). The relatively low amount of methane production (73 mol T when compared with other metals and the abnormally low amount of ethane are typical (6). The distribution of hydrocarbons over other cobalt catalysts has been found to fit the Schulz-Flory equation [indicative of a polymerization-type process (6)]. The Schulz-Flory equation in logarithmic form is... 

Flory polymerization kinetics (4). Henrici-Olive and Olivd (5) proposed the use of the related equation of Schulz (6). Over the last decade the Flory equation has been used frequently to describe product distributions in FT synthesis. The Friedel-Anderson (i) or Flory (4) approaches apply when the rates of propagation and termination are independent of carbon number. We do not attempt here to discuss all previous research on FT product distributions except to say that the literature contains many examples of product distributions that obey Flory kinetics within relative narrow carbon number ranges and many that do not. 

The F-T synthesis typically follows polymerization kinetics. The Anderson-Schulz-Flory equation describes the product distribution ... 

FT synthesis product distributions can be described by equations first developed for polymerization kinetics (31). Flory product distributions (31)... 

Concurrent with FTS mechanism studies, product distribution models were developed based on the analysis of product composition. Friedel and Anderson28 29 in the 1950s published the Anderson-Schulz-Flory (ASF) distribution model to predict the wide range of products yielded from FTS. The equation is shown as follows ... 

Product distribution from the Fischer-Tropsch unit is generally regarded as being approximated by the Anderson-Schulz-Flory equation ... 

Tavakoli A, Kargari A, Sohrabi M Apphcation of Anderson-Schtilz-Flory (ASF) equation in the product distribution of slurry phase FT synthesis rvith nanosized iron catalysts, Chem EngJ 136(2-3) 358-363, 2008. 

The production of hydrocarbons using traditional F-T catalysts is governed by chain growth (polymerization) kinetics. The theoretical equation describing the distribution of hydrocarbon products, commonly referred to as the Anderson-Schulz-Flory (ASF) equation, is... 

Batch Polymerization. Batch polymerization with this mechanism was first treated by Flory (19) using a statistical development. The same results were obtained by Biesenberger (8) using a kinetic analysis with an analytical solution. This was also one of the cases treated by Kilkson (35) using Z-transforms. In the simple cases, his result reduces to the Flory, or random, MWD with the dispersion index of 2. In more complex cases, he solves directly for the moments of the distribution. The Z-transform is probably the most powerful tool for solving condensation MWD problems the convolution theorem allows the nonlinear product terms in the kinetic equation to be handled conveniently. 

As mentioned in Section 4,5, the assumption of a mechanistic scheme accord ing to Equations (23) (26) is supported by the elegant experiments carried out by Pettit who obtained Fischer-Tropsch products with a typical Schulz-Flory distribution when reacting CH3N3/H1 over transition metals [125] and by the work by Biloen and Sachtler using catalysts precovered by C (109-1II]. 

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