Product Distribution under Steady-State Conditions

Product Distribution under Steady-State Conditions 

As mentioned in the Introduction, we can distinguish simple FT catalysts, producing hydrocarbons exclusively with ruthenium as the outstanding example, and complex FT catalysts, such as promoted iron, wherein the steady-state metallic, oxidic, and carbidic phases can coexist. With the latter catalysts the product is a cocktail containing various oxygenates, in particular primary alcohols, as well as hydrocarbons. 

Following the approach of separating variables, we shall review here the models appropriate to describe the distribution of products over simple FT catalysts only. The products then consist of paraffins and a-olefins with essentially unbranched carbon chains. As paraffins and olefins can easily be interconverted under FT conditions, the information most pertinent to the reaction mechanism has to be derived from the distribution with respect to the chain length. The formation of alcohols is briefly reviewed in Section VI. 

Basically, two models can be visualized to rationalize chain length distributions in the absence of secondary reactions  

Chain growth through lateral reaction between building blocks populating the catalyst surface. 

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Product Distribution under Steady-State Conditions.169... 

Isomerization probably occurs primarily via i Rh(CO)L2 prior to capture by CO in step 9. After i CORh(CO)2L2 forms by further steps 10 and 14, getting back to i Rh(CO)L2 by the reverse of steps 14, 10, and 9 seems unlikely, especially under CO and H2 pressure. This conclusion is supported by isotopic-labeling studies by Pino. If steps 9 and 4 are essentially irreversible, then the RCHO/R CHO ratio will primarily depend on the steady-state concentration ratio of i Rh(CO)L2 to i Rh(CO)L2. If 4 and kg are similart, then fcs, kg, and the relative stabilities (K /Kg) of i Rh(CO)L2 and R Rh(CO)L2 will determine the aldehyde product distribution. Steric crowding in the branched alkyl complex is no doubt a major factor in destabilizing it compared to the linear alkyl as early recognized by Evans, Osborn, and Wilkinsonthe increased crowding of phosphines relative to carbonyls accounts for the increased yields of desired linear products in both the Rh and Co hydroformylation systems. Electronic factors no doubt also play a role, and in fact most dominate the product distribution with styrene, where R Rh(CO)L2 capture by CO is favored over R Rh(CO)L2. The question is, to what extent is the ratio [R Rh(CO)L2]/[R Rh(CO)L2] kinetically or thermodynamically controlled under steady-state conditions ... 

Unlike continuous systems, batch operations do not run under steady-state conditions, and their performance varies with time. As discussed in Chapter 2, the important issues with batch systems are the optimal scheduling of different equipment to produce a variety of products and the determination of optimal cycle times for batch processes. Therefore, the optimization of batch operations often involves determining the best processing time for a certain operation, the best time at which a certain action should take place, or the best distribution of actions over a period of time. The optimization of batch processes is, in itself, a very broad topic and certainly beyond the scope of this section of this chapter. Rather than try to address the many interesting problems in this field, the approach here is to illustrate several inportant concepts through the use of exanples. The interested reader is encouraged to read further into this subject [7-101. 

Kinetically, the overall dissolution process consists of carrier transport in the semiconductor, electrochemical reactions at the interface, and mass transport of the reactants and reaction products in the electrolyte. Also, toe are a number of reactions involved at the interface and these reactions consist of several steps and subreactions. At any given time the dissolution kinetics can be controlled by any one or several of these steps. The distribution of reactions along a pore bottom under a steady-state condition during pore propagation must be such that pore walls are relatively less active than the pore tip. Then, the dissolution reactions are concentrated at the pore tip resulting in the preferential dissolution and formation of pores. The formation of pores is the consequence of spatially and temporally distributed reactions. 

Under ideal condition, when an isothermal CSTR is operating at steady state (SS) in a totally micro-mixing condition, the PS product will be homogeneous having a perfect ZO polydispersity (the Schultz-Flory distribution). Deviations from ideality have been theoretically studied by operating CSTR processes under non-steady state conditions with fort peritxlic operation [70]. The effects of an independent sinusoidal forcing of the monomer and the initiator feed concentrations results in theoretical control of the polydispersity. 

Mechanism. The thermal cracking of hydrocarbons proceeds via a free-radical mechanism (20). Siace that discovery, many reaction schemes have been proposed for various hydrocarbon feeds (21—24). Siace radicals are neutral species with a short life, their concentrations under reaction conditions are extremely small. Therefore, the iategration of continuity equations involving radical and molecular species requires special iategration algorithms (25). An approximate method known as pseudo steady-state approximation has been used ia chemical kinetics for many years (26,27). The errors associated with various approximations ia predicting the product distribution have been given (28). 

Similar ideas can be applied to formaldehyde oxidation. For bulk formaldehyde oxidation, we found predominant formic acid formation under current reaction conditions rather than CO2 formation. Hence, it cannot be ruled out, and may even be realistic, that formaldehyde is first oxidized to formic acid, which can subsequently be oxidized to CO2. The steady-state product distribution at 0.6 V is much more favorable for such a mechanism as in the case of methanol oxidation. On the other hand, because of the high efficiency of COad formation from formaldehyde, this process is likely to proceed directly from formaldehyde adsorption rather than via formation and re-adsorption of formic acid. Alternatively, the second oxygen can be introduced via formaldehyde hydration to methylene glycol, which could be further oxidized to formic acid and finally to CO2 (see the next paragraph). 

Case B. Suppose, more realistically, that the catalyst undergoes a known, experimentally determined, rate of attrition as a function of particle size (Zenz, 1971 Zenz Kelleher, 1980). The particle loss rate from the cyclone system will now approach and finally equal the rate of production of 0 to 10 micron particles by attrition from all the larger sizes. To maintain reactor inventory, this loss rate will be replaced, at an equal rate, with fresh catalyst. Since the rate of attrition of any size particle depends on its concentration in the stream subjected to the attrition (as finer particles effectively cushion the coarser), and since the loss is replaced with fresh catalyst (containing the coarsest), the bed size distribution will reach a steady state between 10 and 150 microns in which the mean size, as well as all sizes smaller than the largest, will now be decreased from what would have prevailed under conditions of zero attrition. 

Steady-state operation was quickly achieved under SCF conditions and the SCF-FT process has a marked effect on the hydrocarbon product distribution with a shift to higher carbon number products owing to enhanced heat and mass transfer from the catalyst surface. In addition, an obvious difference in the olefin content was observed where the 1-olefin content in the SCF phase was always higher than in the gas phase. Based on the experimental observations, a mechanistic explanation is provided for the difference of the reaction behavior under supercritical and gas-phase environments. 

Careful analysis of the reaction products in the HDN of the 2,6-lutidine (2,6-dimethylpyridine) and the 2,6-lupetidine (2,6-dimethylpiperidine) allowed Ledoux et al.37 to conclude that under these low pressure conditions (1 atm H2, 5-10 Torr amine, in a steady state flow system, at 300°C on Mo03/A1203 in a fixed-bed reactor) the hydrogenated product is not the intermediate for the HDN of the aromatic compound because the distributions of the products obtained by the reaction of the two amines are fundamentally different. 2,6-Lutidine gives at initial conversion 60% toluene, 21% C3 + C4 and 8% olefinic n-C7, while 2,6-lupetidine gives only 18% toluene, 4% C3 + C4 but 69% of olefinic n-C7. Under the same experimental conditions (but at 380°C), analysis of the pyridine and piperidine HDN products38 shows that... 

Based on the results of Dalla Betta and co-workers, it is clear that the steady-state activity of a completely sulfur-poisoned Ni or Ru methanation catalyst is 102-104 times lower than that of the fresh catalyst. However, a typical industrial methanation process would more probably involve a catalyst only partly poisoned by sulfur. Bartholomew and co-workers (23, 113, 157) attempted to assess how sulfur poisoning of only a portion of the catalyst would affect its activity/selectivity properties in fixed-bed and fluidized-bed reactors. Data in Table XII show the effects on specific activity and product distribution of partially presulfided Co/A1203 and Ni/Al203 catalysts in a fixed bed. Catalysts were presulfided with 10 ppm H2S at 725 K, and reaction was carried out with sulfur-free feedgas. Corresponding data are listed in Table XIII for catalysts partially presulfided and then studied in a fluidized-bed reactor under the same conditions. The decrease in H2 uptake... 

The situation when the gas is isotopically scrambled, however, is very different and indeed the experimentally observed measured quantity is also very different. When the gas is isotopically scrambled, one does not measure these specific ratios of rate constants. Instead, a statistical steady-state, such as Q -F OO QOO QO + O and in the above example O + QQ OQQ OQ + Q, exists at all energies, and now the energy distribution of the vibrationally excited intermediates is that which is dictated by the steady-state equations for the above reactions, and not by that of a vibrationally hot intermediate formed solely via one channel. Under such conditions all energies of the intermediate are statistically accessible, if not from one side of the reaction intermediate then from the other. Phrased differently, the isotopic composition of the collisionally stabilized product Q3 or QO2 or will typically differ from that of the vibrationally excited species Q or QO2, since the intrinsic lifetime of the latter is isotope-dependent, as discussed in [15]. The usual RRKM-type pressure-dependent rate expression and conventional isotope effect results, modified by the nonstatistical effect discussed earlier [15]. 

The experimental approach was outlined in Sec. 2.3. HyperthermaJ beams of energy selected Ar atoms or N2 molecules were directed at polymer surfaces that were continously bathed with the effluent of a low pressure RF plasma source of oxygen atoms (see Fig. 7). Interaction of the effusive 0-atom beam with polymer samples produced both CO and CO 2 continuously, and data were collected under conditions of steady-state oxidation, as verified by the unchanging signals from CO and CO2 in the mass spectrometer. Product TOF distributions were collected at m/z = 28(CO+) and 44(002 ), following impingement of hyperthermaJ beam pulses on polymer surfaces that had reached a steady state of oxidation. 

C Hft/NOy -I- hv Exposure Experiment. The steady state reactant and product distribution in this experiment contained a complex mixture of oxidants whose concentrations were, in general, much larger than those that occur under ambient conditions but likely contains many of the air pollutants that are present during smog conditions (Table II). 

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