Equilibrium-limited reaction systems

In this configuration, the membrane reactor is used as an extractor and the main advantages achieved are increased yield of the extracted product and increased conversion. This kind of membrane reactors, as shown in Figure 33.1, can be used in all equilibrium-limited reaction systems. 

A porous matrix is sandwiched between two membranes. The matrix supports a liquid-phase catalyst. For the reaction A -> B, membrane 1 passes A but resists B, and membrane 2 passes both freely the function of membrane 2 is to encapsulate the catalyst solution. Reactant A is fed external to membrane 1 the concentration of A drops across the catalyst as it is consumed by reaction, due to diffusional resistance. The product diffuses to the right, reactant A does not. The benefits of this reactor are the liquid phase is encapsulated, the catalyst is separated from the product stream, the product is separated from the reactant, it provides a higher gas-liquid interfacial area, and a product is removed from an equilibrium-limited reaction. The authors suggested that the system be implemented as a shell-and-tube configuration using two different hollow-fiber membranes. 

Water was also the targeted species in two other reacting systems that will be discussed next. Both of them correspond to the synthesis of tertiary ethers, that is, typical examples of equilibrium-limited reactions where the conversion is generally low due to the limits imposed by thermodynamic equilibrium and where the presence of water has a strong inhibiting effect on the catalytic activity [274,275]. Therefore, these examples could be also included in the next section of conversion enhancement by inhibitors removal. 

In recent decades, one of the new technologies used for carrying out the H2O decomposition is MR technology. The MR is a single unit operation, integrating both membrane-based separation and reaction. The MR has a great role in enhancement of selectivity/yield in case of equilibrium-limited reactions (Kar et al., 2012 Sanchez and Tsotsis, 1996). This system is presented in two different styles, as shown in Figure 7.5. 

In hybrid systems different processes are coupled, for example, reaction and separation by membranes, adsorption, or distillation. This could lead to a reduction of the investment costs as two different functions are combined in one vessel, and one process step is eliminated. For example, a reactor with a catalyst and a membrane may be used or a distillation column with a catalytic packing, which could also lead to an optimal heat integration. Other benefits depend on the specific reaction. For example, equilibrium-limited reactions would benefit if a product is continuously removed in situ, which leads to an enhanced yield beyond the equilibrium. ... 

A silica membrane reactor will be efficient and effective therefore, when the membrane, working at full capacity, is able to process all the H2 produced by the reaction. This situation arises when the DaPe = 1 and simulations for silica membrane reactors for the water gas shift (WGS) reaction have indeed demonstrated that maximum CO conversion was achieved at DaPe close to 1 (Battersby et al., 2006 Ikuhara et al, 2007). Thus the DaPe number is a valuable metric to evaluate the potential performance of a membrane reactor and a valuable, yet simple, design tool to ensure that both the reactor and membrane components work together for maximum efficacy. However, the DaPe number does not take into account the selectivity of the membrane which obviously does affect the membrane reactor performance. Both experimental and simulation studies have shown that higher permeation results in higher conversion and product yield enhancements (Battersby et al., 2006 Boutikos and Nikolakis, 2010 Lim et al., 2010).That is not to say that a membrane with a low selectivity cannot be successfully utilized in a membrane reactor set-up. Provided the membrane has nominal selectivity for the desired products over reactants, the conversion of equilibrium-limited reactions will be enhanced in a membrane reactor system. However, the product purity will remain dilute and thus additional operational and capital expenditure will be required for further downstream processing. If the membrane is unable to separate gases then the system behaves as a packed bed reactor. 

SR of alcohols has been widely studied in conventional reactor systems for hydrogen production. Bio-derived alcohols can be utilised as the raw materials for hydrogen production. Alcohols have high H/C ratio and hydrogen can be produced at low operating temperatures compared to methane reforming. In scientific literature most studies deal with catalyst development and catalyst performance in SR reactions. Moreover, SR is an equilibrium limited reaction. In MRs, conversion values beyond the equilibrium conversion can be achieved through the shift effect . Most of the studies related... 

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-... 

Approaches to the determination of the concentration-dependent terms in expressions for reversible reactions are often based on a simplification of the expression to limiting cases. By starting with a mixture containing reactants alone and terminating the study while the reaction system is still very far from equilibrium, one may use an initial rate study to determine the concentration dependence of the forward reaction. In similar fashion one may start with mixtures containing only the reaction products and use the initial rates of the reverse reaction to determine the concentration dependence of this part of the rate expression. Additional simplifications in these initial rate studies may arise from the use of stoichiometric ratios of reactants and/or products. At other times the use of a vast... 

The aromatic hydrogenation reactions are reversible and at normal hydrotreating conditions, the equilibrium limits to achieve complete conversion. Low temperatures and higher pressures favor the aromatic saturation. The carbon atoms of a multi-ring system are hydrogenated in sequential steps, each one being equilibrium limited, as well. 

In this contribution, we describe and illustrate the latest generalizations and developments[1]-[3] of a theory of recent formulation[4]-[6] for the study of chemical reactions in solution. This theory combines the powerful interpretive framework of Valence Bond (VB) theory [7] — so well known to chemists — with a dielectric continuum description of the solvent. The latter includes the quantization of the solvent electronic polarization[5, 6] and also accounts for nonequilibrium solvation effects. Compared to earlier, related efforts[4]-[6], [8]-[10], the theory [l]-[3] includes the boundary conditions on the solute cavity in a fashion related to that of Tomasi[ll] for equilibrium problems, and can be applied to reaction systems which require more than two VB states for their description, namely bimolecular Sjy2 reactions ],[8](b),[12],[13] X + RY XR + Y, acid ionizations[8](a),[14] HA +B —> A + HB+, and Menschutkin reactions[7](b), among other reactions. Compared to the various reaction field theories in use[ll],[15]-[21] (some of which are discussed in the present volume), the theory is distinguished by its quantization of the solvent electronic polarization (which in general leads to deviations from a Self-consistent limiting behavior), the inclusion of nonequilibrium solvation — so important for chemical reactions, and the VB perspective. Further historical perspective and discussion of connections to other work may be found in Ref.[l],... 

Based on the Langmuir-Hinshelwood expression derived for a unimolecular reaction system (6) Rate =k Ks (substrate) /[I + Ks (substrate)], Table 3 shows boththe apparent kinetic rate and the substrate concentration were used to fit against the model. Results show that the initial rate is zero-order in substrate and first order in hydrogen concentration. In the case of the Schiff s base hydrogenation, limited aldehyde adsorption on the surface was assumed in this analysis. Table 3 shows a comparison of the adsorption equilibrium and the rate constant used for evaluating the catalytic surface. 

There are some common characteristics for gas-phase reaction systems that form the basis for understanding and describing the chemical behavior. In this section we will discuss some basic definitions and terms that are useful in kinetics, such as reaction order, molec-ularity, chain carriers, rate-limiting steps, steady-state and partial equilibrium approximations, and coupled/competitive reactions. 

Three conditions must be fulfilled obtain complete conversion of the reactants, H2 and CI2. The first condition is that thermal equilibrium of the system be favorable. This condition is fulfilled at low and intermediate temperatures, where formation of the product HC1 is thermodynamically favored. At very high temperatures, equilibrium favors the reactants, and thereby serves to limit the fractional conversion. The second requirement is that the overall reaction rate be nonnegligible. There are numerous examples of chemical systems where a reaction does not occur within reasonable time scales, even though it is thermodynamically favored. To initiate reaction, the temperature of the H2-CI2 mixture must be above some critical value. The third condition for full conversion is that the chain terminating reaction steps not become dominant. In a chain reaction system, as opposed to a chain-branching system discussed below, the reaction progress is very sensitive to the competition between chain initiation and chain termination. This competition determines the amount of chain carriers (batons) in the system and thereby the rate of conversion of reactants. 

Complexity in multiphase processes arises predominantly from the coupling of chemical reaction rates to mass transfer rates. Only in special circumstances does the overall reaction rate bear a simple relationship to the limiting chemical reaction rate. Thus, for studies of the chemical reaction mechanism, for which true chemical rates are required allied to known reactant concentrations at the reaction site, the study technique must properly differentiate the mass transfer and chemical reaction components of the overall rate. The coupling can be influenced by several physical factors, and may differently affect the desired process and undesired competing processes. Process selectivities, which are determined by relative chemical reaction rates (see Chapter 2), can thenbe modulated by the physical characteristics of the reaction system. These physical characteristics can be equilibrium related, in particular to reactant and product solubilities or distribution coefficients, or maybe related to the mass transfer properties imposed on the reaction by the flow properties of the system. 

To address these limitations to the commercial evaluation and implementation of C02 as a substitute solvent, we (1) present a methodology to measure and model high-pressure phase behavior of C02-based reaction systems using minimal experimental data and (2) present a new computational technique for high-pressure phase equilibrium calculations that provides a guarantee of the correct solution to the flash problem. 

Finally, there may be a few opportunities for closecoupling of reaction and adsorption systems to overcome thermodynamic-equilibrium limitations or to enhance selectivity by operating with low conversions per pass. Reaction types... 

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