There are a few concerns over the popular kinetic expressions for the iron-FT reaction. Most of these equations have a first order inhibition term, implying that only one catalytic site is involved in the rate determining step of the FT reaction. Furthermore, the iron-FT rate equations differ significantly from those that have been proposed for the cobalt-based FT reaction. Lastly, it seems as if different iron-FT rate expressions are required to describe different sets of kinetic data. Consequently, the issue of iron-FT kinetics were again considered with the aim of developing a rate equation that can bring some consistency in the description of data from various kinetic studies.
2. Development of a new rate equation from existing data
A previous experimental study at Sasol has revealed that the reaction order of hydrogen in the iron-FT reaction is 0.5 rather than 1 or higher as suggested by most of the popular rate expressions. The following rate equation was found to describe the data from this study far better than the other expressions considered at the time:
rFT = PH2^0.5 PCO / (PCO + bPH2O) (1)
For the development of a new equation, this reaction order of hydrogen was retained. However, the denominator term was squared in order to account for a dual site mechanism, which is regarded to be a more plausible description of the FT reaction. Furthermore, the contribution of vacant sites was also included in the inhibition term, yielding the following equation:
rFT = PH2^0.5 PCO / (1+kPCO+bPH2O)^2 (2)
The above equation was fitted to various sets of kinetic data from Sasol and the open literature. In all cases it was surprisingly found that the effect of water on the iron-FT reaction rate was not statistically significant and that water should therefore be omitted from the expression. The new model was therefore simplified to the following form:
rFT = PH2^0.5 PCO / (1+kPCO)^2 (3)
Equation 3 could describe each set of historic data considered at least as well as (and often better than) the specific equation that was originally reported to be the most applicable, bringing more consistency to the description of iron-FT kinetics.
3. The belief of water inhibition
The above finding is in stark contradiction with the general consensus in the literature that water inhibits the rate of the iron-FT reaction. However, a critical review of the literature showed that the notion of water inhibition is highly doubtful, as it is based on inconclusive evidence. As an example, reports by Satterfield et al., namely that the co-feeding of water to the iron-FT synthesis lowered the FT reaction rate, are often cited as support for the belief of water inhibition. Closer inspection of the data revealed that the co-feeding of water diluted the reaction medium and increased the rate of water-gas-shift. The result was a significant decrease in the CO partial pressure upon water addition (up to a factor of five), but the influence that this might have had on the reaction rate was not even considered. Similarly, the other evidence presented in the literature to support the notion of water inhibition has also proven to be doubtful.
4. Experimental validation of the new kinetic model
4.1 Experimental approach
The experiments were performed in a mechanically-agitated (well-mixed) micro slurry reactor. A spray-dried precipitated iron catalyst (Ruhrchemie-type) was employed.
During the testing of various rate expressions with published (existing) kinetic data, Equations 1 and 3 were identified as the main rival models. The new experimental study was therefore primarily aimed at discriminating between these two equations. An experimental design procedure was developed which prescribed how system inputs should be varied in order to ensure that conditions are covered where the two rival models differ substantially. Briefly the approach entailed identifying operating conditions where the ratio of Equation 3 to Equation 1 varied significantly. As the two models have exactly the same reaction terms (numerators), merely the ratio of the inhibition terms (denominators) had to be considered:
Rinh = (PCO+bPH2O) / (1+kPCO)^2 (4)
A three-dimensional plot of Rinh as a function of PCO and PH2O revealed that the ratio of inhibition terms would vary extensively if the partial pressures of carbon monoxide and water were varied in a fixed ratio. This can be achieved by keeping the feed composition and conversion more or less constant, while varying the reactor pressure. This approach was considered to be far more pragmatic than prescribing specific sets of reagent partial pressures at the outlet of a CSTR where the two models would predict different reaction rates.
By varying the stirrer speed over the whole range of pressures used during the kinetic study, it could be shown that interparticle (gas-liquid and liquid-solid) mass transfer restrictions were eliminated. By means of calculation, it was shown that intraparticle diffusion limitations were also negligible.
In our experience at Sasol, the iron-FT catalyst can be notoriously unstable if operated over the wide range of process conditions normally required for a kinetic study. In order to ensure a stable intrinsic activity of the catalyst, the following methodology was employed. The reactor was essentially maintained at reference conditions during the whole experimental run and changes to other operating points were only made for short intervals. Calculations and measurements confirmed that these short intervals allowed sufficient time to ensure hydrodynamic steady state with respect to the permanent gases inside the reactor, but insufficient time for the catalyst to respond to the new conditions. The data obtained at reference conditions also confirmed that the intrinsic catalyst activity was constant throughout the run.
The results showed that the original model (Equation 1) failed completely to describe the measured reaction rates. There was a large systematic deviation in the accuracy of the model with varying operating pressure. Re-optimisation of the water coefficient yielded a significantly large negative number. This physically impossible situation indicates that this rate equation does not correctly account for the effect of water on the FT reaction rate. By applying the physical constraint that an adsorption coefficient must be non-negative, the water coefficient assumed an optimised value of 0. The omission of water from the equation reduced the model to a simple expression in hydrogen, but brought about little improvement in the model fit. Similar results were obtained for some other popular iron-FT rate equations, namely those proposed by Dry, Huff et al. and Ledakowicz et al. In all cases, it was found that the optimised coefficient values of water (or CO2) were 0. The moment these coefficients were assigned significant positive values, the models were completely unable to describe the reaction rate. The equation by Van Steen et al. was also unable to fit the kinetic data well.
To the contrary, the new model described the measured reaction rate near perfectly. Moreover, the optimised CO coefficient compared very well to the values estimated previously from historic data obtained with similar catalysts. No systematic deviations could be detected in the model fit. The slight deviations that were observed appeared to be random scatter and are probably due to experimental errors.
5. Overall conclusions
From the study, the following was found regarding the kinetics of the iron-FT reaction:
• The notion of water inhibition of the iron-FT reaction rate must be questioned. No convincing evidence could be found in the literature for this premise. The new experimental study, which was specifically designed to discriminate between equations that account for water inhibition and a new equation which does not, also indicated that there is no basis for including water in the kinetic model. • The new equation was by far the best model to describe both the historic kinetic data, as well as the data from the new experimental study. • The new model is very similar to some of the popular rate equations that have been proposed for the cobalt-FT reaction.
In view of the above, it is concluded that Equation 3 is currently the most accurate and appropriate kinetic model available for the iron-FT reaction.