Cobalt Fischer–Tropsch Catalyst Deactivation Modeled Using Generalized Power Law Expressions

Abstract

Ten sets of deactivation data from five previously reported studies of cobalt Fischer–Tropsch synthesis (FTS) catalysts were found to be modeled well using concentration-independent first and second order generalized power law expressions (GPLEs) which predict that activity approaches a non-zero asymptote. Concentration dependencies of reactants and products were generally not addressed in the model regressions, although selected simulations which incorporated CO, H₂, and/or H₂O concentrations in deactivation rate equations showed very little or no dependence on concentrations of these species. For reaction temperatures in the range of 220–230 °C, pressures of 15–30 bar, and H₂/CO ratios of 1.6–2.6, first order and second order deactivation rate constants average 0.12 ± 0.06 and 0.11 ± 0.05 day⁻¹, respectively. Limiting (asymptotic) activities are largely in the range of 30–40 % of initial activity based on the generally superior extrapolations of second order GPLE. This consistency is impressive considering significant differences among catalyst properties and operating conditions in the five studies that apparently involve different mechanisms of deactivation, including sintering, carbon formation, and/or cobalt aluminate formation. Second order models predict significant longevity for cobalt FTS catalysts; for example, based on the 2nd order models, normalized activities for commercial catalysts in two different pilot slurry reactor facilities are projected to be 56 and 45 % of initial activity after 200 days on stream. For two of the previous studies providing data over periods of 40–55 days, it was possible to identify two different causes of deactivation, one rapid (reaching completion in 10–20 days) and one slow (apparently continuing beyond 40–50 days). A method was developed for calculating first and second order model parameters for the two regions of operation. Rapid activity loss (path 1) is observed for either sintering or Co surface aluminate formation, while poisoning/fouling by deposited carbon or coke (path 2) occurs relatively slowly over the entire process run of 40–55 days and is the dominant mechanism after 10–20 days for both sets of data. The results show that simple GPLE models are surprisingly generally useful for predicting activity versus time behavior of supported cobalt FTS catalysts under typical process conditions.

Appendix

An analogous form of Eq. 1 can be written specifically to describe sintering, as follows:

$$- \frac{{d\left( {\frac{D}{{D_{0} }}} \right)}}{dt} = k_{s} \left( {\frac{D}{{D_{0} }} - \frac{{D_{eq} }}{{D_{0} }}} \right)^{m}$$

(7)

where D is the metal dispersion as a function of time, D₀ is the initial dispersion, D_eq is the dispersion at long times (equilibrium), k_s is the sintering rate constant, and m is the order of the sintering process.

Assuming concentration independence of the deactivation rate, the solution to Eq. 7 for first order (d = 1) deactivation process is of the form:

$$\frac{D(t)}{{D_{0} }} = \left( {1 - \frac{{D_{eq} }}{{D_{0} }}} \right)\exp \left( { - k_{s1} t} \right) + \frac{{D_{eq} }}{{D_{0} }}$$

(8)

while for Eq. 2 with second order deactivation (m = 2), the solution is

$$\frac{D(t)}{{D_{0} }} = \left( {k_{s2} t - \left(1 - \frac{{D_{eq} }}{{D_{0} }}\right)^{ - 1} } \right)^{ - 1} + \frac{{D_{eq} }}{{D_{0} }}$$

(9)

The assumption of the concentration independence of the deactivation rate for a thermal sintering process is justified since this is typically only a function of temperature. However, the temperatures used in most FT reactors are generally below any expected mobility due to thermal effects, at least as determined by heuristics such as the Tamman and Hüttig temperatures, respectively defined as 0.5 and 0.3 of the melting point (T_m) of the material. Near the Hüttig temperature, atoms at defects will become mobile, while near the Tamman temperature, bulk atoms begin to be mobile. Since T_m for cobalt metal is 1,495 °C [69], Tamman and Hüttig temperatures are 611 °C (0.5T_m = 884 K) and 257 °C (0.3T_m = 530 K) respectively. Hüttig and Tamman temperatures are defined for bulk materials; clearly, surface thermodynamic properties for dispersed nanoparticles are different compared to the bulk, although defects and surfaces may have some similarities. Since the Hüttig temperature is 257 °C and reactor temperatures commonly associated with cobalt FT catalysis of 200–230 °C are significantly lower, thermal sintering is not likely to be a major deactivation mechanism under FTS conditions. Rather, sintering caused by adsorbate–surface interactions that we refer to here as chemical-assisted sintering are more likely to explain the observed sintering. Chemical-assisted sintering of Ni/alumina catalysts in methanation due to formation of volatile Ni(CO)₄ followed by its decomposition downstream to large Ni crystallites has been well documented [1-Ch.5, 62]. Similarly, formation of volatile or mobile surface carbonyl species, (Co₂(CO)₈, or mobile Co(OH)_x surface species [41, 42] could similarly explain sintering of Co catalysts during FTS, although these species would probably be thermally unstable at typical reaction temperatures [69]) and would hence be short-lived. Wilson and de Groot [67] reported that under high pressure (4 bar, H₂/CO = 2) and moderate temperature (523 K) conditions, single crystal Co (0001) surfaces restructured significantly due to interaction with the CO. More recently, Parkinson et al. [68] have shown that chemical-assisted sintering occurs at room temperature for palladium supported on magnetite under ultra-high vacuum conditions at a CO partial pressure of only 5 × 10⁻¹⁰ mbar. However, as previously discussed, most of the GPLE deactivation models in this paper are not significantly improved by including reactant or product concentrations. This insensitivity is possibly due to the partial pressure of CO under reaction conditions greatly exceeding that needed to saturate the available surface with Co carbonyls.