Principle of equilibrated gas

The formation of whisker carbon cannot be tolerated in a tubular reformer. The important question is whether or not carbon is formed, and not the rate at which it may be formed. In terms of the growth mechanism, it means to extend the induction period (to in Equation 5.1) to infinity. This is achieved by keeping the steady-state activity of carbon smaller than one (refer to Section 5.2.4). The carbon formation depends on the kinetic balance between the surface reaction of the adsorbed hydrocarbon with oxygen species and the further dissociation of the hydrocarbon into adsorbed carbon atoms, which can nucleate to whisker carbon. However, this approach is complex and there is a need for simple guidelines using simple thermodynamic calculations. 

By use of Reaction R6 in Table 5.2 the carbon formation check for the methane decomposition reaction can be written as  

The carbon limits are a function of the atomic ratios 0/C, H/C and inert/C and of total pressure. As the gas is at equilibrium, it is necessary to consider only one of the carbon-forming Reactions R6-R8 in Table 5.2, provided that the whisker stmcture (p ) is independent of the carbonforming reaction. 

The principle of equilibrated gas is justified by the low effectiveness factor of the reforming reaction, which implies that the gas inside most of the catalyst particle is nearly at thermodynamic equilibrium. The data in Table 5.4 supports this assumption. A series of TGA tests were carried out to determine the critical H2O/CH4 for onset of carbon formation [389], The results shown in the table support the principle of equilibrated gas . The calculated affinity for carbon formation (-AG°) from the equilibrated gas (approximately 4 kJ/mol) from graphite data is comparable with the deviation to be expected from the effect of the whisker structure. 

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On linear heating, CF from this study initiates at 400 - 420°C and proceeds to 670°C (Tm), at which point CF changes to GAS. The reverse transition of GAS to CF takes place at T , during linear cooling. Thus, the principle of equilibrated gas [1] can be applied to our system and T, can be taken as a thermodynamic equilibrium temperature. 

At a given temperature and for a given hydrocarbon feed, carbon will be formed below a critical steam to carbon ratio (15), the carbon limit A in Fig. 5. It can be shown that this critical steam to carbon ratio increases with temperature. By promotion of the catalyst, it is possible to push this limit to the thermodynamic carbon limit B reflecting the principle of equilibrated gas (4,15) ... 

Figure 5.15 Carbon limit diagram. Principle of equilibrated gas. Carbon is formed for conditions to the left of the curves. Curves 1 and 2 represent graphite data and whisker carbon (Appendix 2), respectively. The dotted hnes show feed gas compositions leading to product gas with indicated H2/CO ratios [152]. Reproduced with the permission of...

Figure 5.17 Principle of equilibrated gas. Carbon limit temperatures and Ni-crystal size [382]. Conditions H20/CFLt=1.8, C02/CH =2.2, P=18 bar abs.

The effect of particle size on carbon limits from principle of equilibrated gas is also illustrated in Figure 5.17, representing conditions for an industrial oxo-syngas plant [382]. Graphite data predicts carbon formation, whereas carbon-free operation was obtained with a catalyst with nickel particles less than 250 run. 

The principle of equilibrated gas is no law of nature. It is possible to break the thermodynamic limit. This can be done by using noble metals [396] or by using a sulphur passivated catalyst as practiced in the SPARG process [390] (refer to Section 5.5). Examples are shown in Figure 2.18. 

The higher hydrocarbons may lead to carbon formation by all three mechanisms (Table 5.1). Thermod5mamics will predict carbon formation as long as the higher hydrocarbons are present. Carbon may be stable in a steady state in spite of the principle of equilibrated gas (refer to Section 5.2.4). 

The risk of carbon (or gum) formation from higher hydroearbons can be analysed separately from the potential for carbon predicted by the principle of equilibrated gas . 

A pilot test was carried out with naphtha as feed. The critical H20/CnHm was assessed to be around 1.3. As shown in Figure 5.33, it was possible to operate at a H2O/CnHm=1.0 in the feed gas by using a hot (ejector) recycle, which brought H20/CnHm up to 1.6. The principle of equilibrated gas predicts carbon-free operation above O/C=0.9. 

Figure 5.8). Therefore, the sulphur passivation is not able to inhibit carbon formation from an equilibrated gas with affinity for carbon formation, i.e. Ihe principle of equilibrated gas works if the gas is equilibrated.

The principle of equilibrated gas shows potential for carbon > 540°C (whisker carbon data). The potential for carbon increases throughout the catalyst bed and carbon is formed when the gas approaches equilibrium. Carbon was formed from the equilibrated gas at the centre of the catalyst pellet above 750°C and 850°C with 7 and 18 vol ppm H2S in the feed gas, respectively. In the outer shell of the pellet the steady-state situation prevails, resulting in -AGe less than the approximately 30 kJ/mol necessary for nucleation of carbon. 

For gases with high H/C (typically steam reforming), there is an upper temperature limit above which the principle of equilibrated gas predicts carbon. 

Figure 5.48 Carbon limits and sulphur passivated reformer. The principle of equilibrated gas predicts an upper carbon hmit for gases with high H/C and a lower carbon limit for...

The first case is represented for instance by the Midrex process for reducing gas (refer to Section 2.4.3). Table 5.7 shows results [390] from laboratory tests simulating the Midrex process [490]. The actual feed gas shows potential for carbon (-AGc at inlet>0 for T<840°C). The principle of equilibrated gas predicts carbon (-AGc<0 for T<890°C). The results indicate that carbon formation is eliminated above 0s=approximately 0.8. 

In the case of steam reforming (the second situation for sulphur passivated reforming), it is not possible to operate under conditions where the principle of equilibrated gas shows potential for carbon because the centre of the pellet will have equilibrated gas (refer to Example 5.3). However, with the sulphur passivation it is possible to operate at conditions under which the principle of actual gas predicts carbon because of the high (-AGc) overpotential required for nucleation of carbon (Figure 5.47). 

In case a non-linear triatomic gas obeys the principle of equilibration of energies, the molar heat capacity, calculated ... 

The prineiple of equilibrated gas predicts conditions where carbon formation is expected (except for noble metals and SPARG). It does not guarantee that carbon is not formed if the principle predicts no potential in the equilibrated gas. 

The pCOj electrode was first described in 1957 by Stow and later improved to its presently used form by Severinghaus The basic principle of operation relies on equilibration of COj with an aqueous solution. The change in pH in the aqueous solution associated with the equilibration due to carbonic acid formation (H2CO3) is measured and varies with log pCO2] It should be pointed out here that these measurements (and likewise for the pO electrode described below) give CO2 tension not concentration. To obtain concentration, Henry s Law of gas solubUity must be applied. However, for most medical and biological applications the knowledge of the gas tension is sufficient. 

Methanol synthesis from C02 (Equation [1]) and CO (Equation [2]) is mildly exothermic and results in volumetric contraction. Methanol steam reforming (MSR) refers to the inverse of reaction (1), and the inverse of reaction (2) is conventionally referred to as methanol decomposition - an undesired side reaction to MSR. The slightly endothermic reverse water-gas shift (rWGS) reaction (Equation [3]) occurs as a side reaction to methanol synthesis and MSR. According to Le Chatelier s principle, high pressures and low temperatures would favor methanol synthesis, whereas the opposite set of conditions would favor MSR and methanol decomposition. It should be noted that any two of the three reactions are linearly independent and therefore sufficient in describing the compositions of equilibrated mixtures. 

Fig. 5.5. (A) Scheme of a flow digestion system and the principle of pressure equilibration A pressure reactor, B heating zone, C cooling zone, D digestion coil, E cooling device, F connection for gas supply, G restrictor tube, H collector vial, I temperature sensor, J high-pressure pump, K injection valve, L sample loop, M sample, N and O peristaltic pumps. (Reproduced with permission of the American Chemical Society.) (B) Manifold for dynamic microwave-assisted extraction I solvent, 2 pump, 3 microwave oven, 4 extraction chamber, 5 temperature set-point controller, 6 thermocouple, 7 fluorescence detector, 8 recording device, 9 restrictor, 10 extractor. (Reproduced with permission of Elsevier.)...

A possible weakness in this approach is the assumption of a biological equilibrium. Yet it is remarkable, when a general anaesthetic is being administered to a patient, how rapidly equilibration seems to occur. If the flow of anaesthetic gas is turned down, that patient at once achieves a measure of consciousness, and when the former flow-rate is resumed, the patient is very quickly back on the lower plane of anaesthesia. Actually, because of the complexity of the systems concerned, these are only steady states but, to a first approximation, Ferguson felt justified in treating them as equilibria, in order to make use of simple thermodynamic principles. 

Conducting Pd/C- HjO labeling reactions in the presence of a small amount of hydrogen gas results in a more active catalyst , as can pretreatment of the catalyst with NaBH . Nevertheless, elevated temperatures are still required (110 C for nucleosides, 110-180 °C for N-heterocycles, > 140 °C for aU but the benzylic positions of aralkylic compounds) . The catalytic hydrogen gas rapidly becomes equilibrated with solvent deuterium . Very dilute tritiated water was used as proof of principle , but this method would not be practical in its current form for the preparation of high specific activity compounds because it requires neat water as solvent/labeling source. 

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