Equilibrium Limitations

The ensemble density p g(p d ) of a mixing system does not approach its equilibrium limit in die pointwise sense. It is only in a coarse-grained sense that the average of p g(p,. d ) over a region i in. S approaches a limit to the equilibrium ensemble density as t —> oo for each fixed i . 

An important point about kinetics of cyclic reactions is tliat if an overall reaction proceeds via a sequence of elementary steps in a cycle (e.g., figure C2.7.2), some of tliese steps may be equilibrium limited so tliat tliey can proceed at most to only minute conversions. Nevertlieless, if a step subsequent to one tliat is so limited is characterized by a large enough rate constant, tlien tire equilibrium-limited step may still be fast enough for tire overall cycle to proceed rapidly. Thus, tire step following an equilibrium-limited step in tire cycle pulls tire cycle along—it drains tire intennediate tliat can fonn in only a low concentration because of an equilibrium limitation and allows tire overall reaction (tire cycle) to proceed rapidly. A good catalyst accelerates tire steps tliat most need a boost. 

Process Applications The production of esters from alcohols and carboxylic acids illustrates many of the principles of reactive distillation as applied to equilibrium-limited systems. The equilibrium constants for esterification reactions are usually relatively close to unity. Large excesses of alcohols must be used to obtain acceptable yields with large recycles. In a reactive-distiUation scheme, the reac-... 

Data on the gas-liquid or vapor-liquid equilibrium for the system at hand. If absorption, stripping, and distillation operations are considered equilibrium-limited processes, which is the usual approach, these data are critical for determining the maximum possible separation. In some cases, the operations are are considerea rate-based (see Sec. 13) but require knowledge of eqmlibrium at the phase interface. Other data required include physical properties such as viscosity and density and thermodynamic properties such as enthalpy. Section 2 deals with sources of such data. 

Reac tion (27-37) can occur in parallel with the methanol reactions, thereby overcoming the equilibrium limitation on methanol formation. Higher alcohols can also be formed, as illustrated by Reaction (27-25), which is apphcable to the formation of either linear or branched alcohols. 

All of the above reactions are reversible, with the exception of hydrocracking, so that thermodynamic equilibrium limitations are important considerations. To the extent possible, therefore, operating conditions are selected which will minimize equilibrium restrictions on conversion to aromatics. This conversion is favored at higher temperatures and lower operating pressures. 

Methane is unique among hydrocarbons in being thermodynamically stable with respect to its elements. It follows that pyrolytic reactions to convert it to other hydrocarbons are energetically unfavourable and will be strongly equilibrium-limited. This is in marked contrast to the boranes where mild thermolysis of B2H6 or B4H10, for example, readily yields mixtures of the higher boranes (p. 164). Vast natural reserves of CH4 gas exist but much is wasted... 

A promoted nickel type catalyst contained in the reactor tubes is used at temperature and pressure ranges of 700-800°C and 30-50 atmospheres, respectively. The reforming reaction is equilibrium limited. It is favored at high temperatures, low pressures, and a high steam to carbon ratio. These conditions minimize methane slip at the reformer outlet and yield an equilibrium mixture that is rich in hydrogen. ... 

Because beta-scission is mono-molecular and cracking is endothermic, the cracking rate is favored by high temperatures and is not equilibrium-limited. 

Equilibrium-Limited Reactor. This system is the basis for most practical, commercial methanation plants. It is safe from the standpoint... 

Kinetically Limited Process. Basically, this system limits the temperature rise of each adiabatically operated reactor to safe levels by using high enough space velocities to ensure only partial approach to equilibrium. The exit gases from each reactor are cooled in external waste heat boilers, then passed forward to the next reactor, and so forth. This resembles the equilibrium-limited reactor system as shown in Figure 8, except, of course, that the catalyst beds are much smaller. 

The possible advantages of this system over the equilibrium-limited reactor system are smaller catalyst beds, lower gas recycle requirements, and lower capital requirements. The possible disadvantages of this system are (a) practically no turn-down since any turn-down would be equivalent to decreased space velocities, closer approach to equilibrium, and higher temperature rises (b) maldistribution of gases across the bed would give rise to excessive temperature rises in zones of low flow and (c) considerably shortened catalyst life because of possible high local or zonal temperature and, concurrently, greater chances for carbon laydown. 

In chemical processing the most fundamental constraint is that of the thermodynamics of the system. This constraint defines both the heat balance of the process and whether or not the processes in the reactor will be equilibrium limited. These constraints will limit the range of chemical engineering solutions to the problems of designing an economically viable process that can be found. 

The novel approach finally taken was to conduct the reaction and purification steps in a reactor-distillation column in which methyl acetate could be made with no additional purification steps and with no unconverted reactant streams. Since the reaction is reversible and equilibrium-limited, high conversion of one reactant can be achieved only with a large excess of the other. However, if the reacting mixture is allowed to flash, the conversion is increased by removal of the methyl acetate from the liquid phase. With the reactants flowing countercurrently in a sequence of... 

A by-product comes out of solution or is intentionally removed to avoid an equilibrium limitation. 

Semibatch or fully continuous operation with continuous removal of a by-product gas is also common. It is an important technique for relieving an equilibrium limitation, e.g., by-product water in an esterification. The pressure in the vapor space can be reduced or a dry, inert gas can be sparged to increase Ai and lower a, thereby increasing mass transfer and lowering u/ so that the forward reaction can proceed. 

The finishing reactors used for PET and other equilibrium-limited polymerizations pose a classic scaleup problem. Small amounts of the condensation product are removed using devolatilizers (rotating-disk reactors) that create surface area mechanically. They scale as... 

Membranes in catalysis can be used to improve selectivity and conversion of a chemical reaction, improve stability and lifetime of the catalyst, and improve the safety of operation. The most well-known example is in situ removal of products of an equilibrium-limited reaction. However, many more ways of application of a membrane can be thought of [1-3], such as using the membrane as a reactant distributor to control the reactant concentration levels in the reactor, or performing catalysis inside the membrane and having control over reactant feed and product removal. 

Membranes can be applied to catalysis in different ways. In most of the literature reports, the membrane is used on the reactor level (centimeter to meter scale) enclosing the reaction mixture (Figure 10.3). In most cases, the membrane is used as an inert permselective barrier in an equilibrium-limited reaction where at least one of the desired products is removed in situ to shift the extent of the reaction past the thermodynamic equilibrium. 

To develop the rate equations suitable for process modeling and reactor design, experimental data have been analyzed on the basis of the postulated reaction mechanism [2] given in Table 1. Here the formation of polymer is excluded because it is not detected under our experimental conditions. All of the reactions are equilibrium-limited and the net rates for the formation of each component with some assumptions [3] are given as follows ... 

Membrane reactors are known on the macro scale for combining reaction and separation, with additional profits for the whole process as compared with the same separate functions. Microstructured reactors with permeable membranes are used in the same way, e.g. to increase conversion above the equilibrium limit of sole reaction [8, 10, 11, 83]. One way to achieve this is by preparing thin membranes over the pores of a mesh, e.g. by thin-fihn deposition techniques, separating reactant and product streams [11]. 

Also, 1,3-dioxolane was obtained from the reaction of ethylene glycol (EG) and aqueous formaldehyde in high yield using an ion-exchange resin catalyst. In a batch mode of operation, with 50% excess EG, the conversion of formaldehyde is limited to 50% due to equilibrium limitation, whereas in batch reactive distillation, formaldehyde conversion greater than 99%... 

It is useful to combine reaction and separation for equilibrium-limited reactions and also for consecutive reactions, particularly when the desired intermediate products undergo faster undesirable reactions. The concept of extractive reactions for equilibrium-limited and consecutive reactions has been covered in Section 4.2.1. Distillation column reactors provide yet another strategy. 

Consider an equilibrium-limited esterification reaction. One way to drive the reaction to completion is to remove the water formed by the reaction selectively through a membrane. This can be an attractive strategy when higher temperatures are undesirable due to factors like colouration of the materials and formation of undesirable products even though these may be present at a low level. As another example, consider the air oxidation of cyclohexane or cyclododecane to cyclohexanone/-ol or cyclododecanone/-ol, where the product can undergo more facile oxidation to unwanted or much lower value products. Consequently, industrial processes operate at a level of less than 5% conversion. If a membrane can selectively remove cyclohexanone as it is formed, the problems mentioned above can be thwarted. However, selective polymeric membranes, which can work at oxidation temperature, have not yet been proved. 

Removal of reaction products can shift the equilibrium, forcing the reaction to go to completion. This can be effected by evaporation of products from the reaction mixture (reactive distillations), extraction (including supercritical extraction) of products from the reaction mixture (reactive extractions), or membrane processes. Counter- and cocurrent operation also falls within this category. If the reaction is equilibrium-limited or inhibited by reaction products countercurrent operation outperforms cocurrent operation. 

Quoting only first order (linear) age errors when the age plus age-error approaches the secular-equilibrium limit ... 

SA conversion increases with increasing residence time, and with increasing MeOH SA to a maximum of about 98%. It appears that the maximum conversion increases to 99% for the highest MeOH SA studied (30), consistent with an equilibrium limited reaction. The esterification reaction rate was strongly suppressed by lowering MeOH/SA ratio below 10%. 

Table VIII demonstrates the inverse relationship of conversion to S02 concentration in the feed that is a consequence of applying flow reversal to S02 oxidation using a single reactor. As the S02 concentration in the table moves from 0.8 to over 8 vol%, the conversion drops from 96-97% down to 85%. At the same time, the maximum bed temperature changes from 450 to 610°C. For an equilibrium-limited, exothermic reaction, this behavior is explained by variation of the equilibrium conversion with temperature.

---