Numerical modeling and optimization of product selectivity and catalyst activity in Fischer-Tropsch synthesis via response surface methodology: Cobalt carbide particle size and ratio effects
Graphical abstract
Introduction
The excessive emission of greenhouse gases from transportation vehicles, as well as decreasing fossil fuel reserves results in a rising demand for alternative and clean transportation fuels [1]. Fischer-Tropsch (FT) synthesis is a well-studied catalytic process of producing such fuels from the synthesis gas, a mixture of hydrogen and carbon monoxide gases. The process produces a wide range of products, among which paraffins, olefins and alcohols are the most abundant compound classes. The synthesis reactions of these products are as follows [2]:
Paraffins:
Olefins:
Alcohols:
C5+ paraffins, low- and intermediate-molecular-weight olefins, and C20+ linear hydrocarbons provide useful feeds in refining processes leading to fuels and petrochemicals [3]. Hence, increasing the selectivity of these desirable products is of utmost importance. The control of catalyst properties and operating conditions plays a vital role in the FT selectivity manipulation [[4], [5], [6], [7], [8], [9], [10]]. The metallic Co particle size effects on the FT synthesis performance of cobalt based catalyst supported with different materials have been widely investigated [[11], [12], [13], [14]]. Bezemer et al. studied the effects of cobalt particle size in the range of 2.6–27 nm at low (1 bar) and high pressures (35 bar) over an inert graphitic carbon nanofiber supported catalyst and found that the turnover frequency (TOF) was independent of cobalt particle size for the catalysts with particle sizes larger than 6 nm (1 bar) and 8 nm (35 bar) [11]. However, both the selectivity and activity were strongly influenced by the cobalt particle size for catalysts having smaller cobalt particles. Diaz et al. also investigated carbon-nanofiber supported cobalt catalysts and reported that the carbon-nanofiber synthesized at lower temperature (723 K) having the lowest particle size of 13.9 nm exhibited the highest C5+ selectivity of about 90% compared to other two supports (≈13% and ≈15%) with higher particle sizes (32.8 nm and 36.4 nm) that were synthesized at higher temperatures (873 K and 1023 K) [12]. However, the same catalyst showed the low catalytic activity. Borg et al. reported an optimum cobalt particle size range of 7–8 nm for alumina-supported cobalt catalysts, at which the maximum C5+ selectivity was observed [13].
Despite the fact that a great deal of studies have been carried out to investigate the effect of catalyst properties and operating conditions on the FT selectivity and activity, there are only a few research works in the literature that investigate such effects and the significance of each factor, as well as the interaction of the factors by means of statistical models. The conventional method of optimizing a process involves monitoring the influence of one variable at a time on a response, while keeping other factors constant [15]. The major drawback of this one-factor at-a-time (OFAT) method is that it does not include the interactive effects of variables, which results in inadequate optimization towards response [16]. Furthermore, the number of experiments carried out to conduct the research is increased resulting in an increase of time and cost. In contrast, design of experiments (DOE) based on the response surface methodology (RSM) makes it possible to vary several factors simultaneously [17]. Compared to OFAT, DOE requires fewer resources for the same amount of obtained data. RSM is one of the useful multivariate statistic techniques for optimization. RSM is a set of statistical and mathematical techniques, which is useful for developing, improving, and optimizing processes [[18], [19], [20], [21]]. This methodology could be used to model or optimize any response, which is affected by the levels of one or more quantitative factors [22]. Hence, such statistical approach can evaluate the interaction effects between factors and estimates combination of levels to obtain better optimum conditions [16]. However, before the RSM is applied, it is necessary to choose an experimental design that determines which experiments should be conducted in the studied experimental region [15,23]. There are various design types in RSM, such as central composite, Box-Behnken and historical data design. The main difference between the historical data design and other types of designs is that it is useful in terms of defining the design points using all or some of the available data [24].
A few studies explore the effect of operation conditions on FT selectivity based on the statistical models developed by means of RSM [[25], [26], [27], [28], [29], [30]]. Riyahin et al. fitted cubic polynomial to the experimental data obtained over iron-based catalyst by taking temperature, pressure, synthesis gas feed molar ratios and space velocity as predictor variables and found that the C5+ selectivity increases with increasing pressure ratio ( and decreasing temperature [25]. The same authors further studied the effects of temperature, pressure and space velocity on the FT product distribution over Re promoted and supported cobalt based-catalyst by means of the Box-Behnken design of RSM, for which reported that the selectivity of heavier key raw hydrocarbons could be increased by using lower temperature, pressure and space velocity ranges [26]. The importance of temperature, time on stream, partial pressure of and was examined through product selectivity models for iron-based catalyst by Atashi et al. [27]. The partial pressure of hydrogen gas was found to be the most important parameter having an effect on the selectivity model, while the interaction between temperature and the partial pressure of was found to be the most important interaction. In other extended research, Atashi et al. developed eight selectivity models for five different products, including methane, light hydrocarbons, gasoline, diesel and wax, on the basis of three independent factors, namely reduction temperature, time on stream and ratio inlet gas. It was reported that the ratio was the most effective factor for the diesel selectivity, while the reduction temperature for the selectivity of all other hydrocarbon products [28].
These studies were carried out based on the data which had been obtained over only the same catalyst, which make it impossible to explore the effect of catalyst parameters via the statistical models. The present study aims to develop statistical models for the FT product selectivity and catalyst activity through the historical data design of RSM to investigate the effects of cobalt carbide particle size and usage ratio effects and by using built models to find optimum conditions to maximize the selectivity of desired range of products and catalyst activity. The analysis is performed based on the experimental data collected at three different usage ratio levels over seven cobalt-based catalysts with different cobalt carbide particle sizes [31]. Hence, the predictor variables are cobalt carbide particle size and the usage ratio. Five separate models were developed for five different responses, namely methane (CH4) selectivity, light olefins (C2C4) selectivity, long-chain hydrocarbons (C5+) selectivity, cobalt time yield (CTY) and turnover frequency (TOF). The single- and multi-objective optimization were performed based on the derived models in order to find the optimum conditions for minimizing the undesirable products and maximizing the desirable products, as well as the catalyst activity are also analyzed in this paper.
Section snippets
Methodology
The experimental data used in this research was obtained from the work of Dai et al. [31]. The experimental procedures were described by the authors and the abbreviated procedures are summarized here. The study was focused on the effect of particle size on the catalytic performance of catalysts with different cobalt loading in the range of 0.5 wt% to 20 wt%. The catalysts were prepared by means of incipient wetness impregnation method. The support material was with average
Results and discussion
This study aims to investigate the effects of cobalt carbide particle size and usage ratio on five different responses, including methane, light olefins and long-chain hydrocarbons selectivity, as well as cobalt time yield and turnover frequency, through statistical models by developing via response surface methodology. The experimental and predicted responses are in good agreement, which are tabulated in Table 2.
The ANOVA results are presented in Table 3, in which SE coefficient, F-value,
Conclusion
The response surface methodology was applied in this study to investigate the effects of cobalt carbide particle size and usage ratio on the FT synthesis product selectivity and activity. The statistical models were developed to predict the relationship between the predictor variables and five different responses, namely CH4, C2C4 and C5+ selectivity, as well as cobalt time yield (CTY) and turnover frequency (TOF). The model improvement was carried out for each model based on the ANOVA results.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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