Equilibrium compositions multiple reactions

Most processes are catalyzed where catalysts for the reaction are known. The choice of catalyst is crucially important. Catalysts increase the rate of reaction but are unchanged in quantity and chemical composition at the end of the reaction. If the catalyst is used to accelerate a reversible reaction, it does not by itself alter the position of the equilibrium. When systems of multiple reactions are involved, the catalyst may have different effects on the rates of the different reactions. This allows catalysts to be developed which increase the rate of the desired reactions relative to the undesired reactions. Hence the choice of catalyst can have a major influence on selectivity. 

Equilibrium Compositions for Multiple Reactions. When there are two or more independent reactions. Equation (7.29) is written for each reaction ... 

The treatment of chemical reaction equilibria outlined above can be generalized to cover the situation where multiple reactions occur simultaneously. In theory one can take all conceivable reactions into account in computing the composition of a gas mixture at equilibrium. However, because of kinetic limitations on the rate of approach to equilibrium of certain reactions, one can treat many systems as if equilibrium is achieved in some reactions, but not in others. In many cases reactions that are thermodynamically possible do not, in fact, occur at appreciable rates. 

In catalytic distillation the temperature also varies with position in the column, and this will change the reaction rates and selectivities as well as the equilibrium compositions. Temperature variations between stages and vapor pressures of reactants and products can be exploited in designing for multiple-reaction processes to achieve a high selectivity to a desired product with essentially no unwanted products. 

Our final statement, therefore, for finding the equilibrium composition for multiple reactions is to solve the optimization problem... 

In the case of simple reactions, the equilibrium composition can be calculated by solving the equation (8.39) with conversion as variable for chemical transformation. On the contrary, the extent of reaction is more suitable for multiple reactions. The solution may be obtained by solving a system of algebraic equations of type (8.40). 

In a typical problem, multiple reactions are taking place in a multiphase system at fixed T and P, and we are to compute the equilibrium compositions of all phases. At this point, such calculations raise no new thermodynamic issues for example, for (R independent reactions occmrring among C species distributed between phases a and P, the problem is to solve the phase-equilibrium criteria... 

Figure 11.8 Elementary algorithm for computing equilibrium compositions from multiple reactions occurring in isothermal-isobaric, vapor-Uquid situations. This algorithm combines the Rachford-Rice method for isothermal flash with the reaction-equilibrium method in Figure 11.7.

When multiple reactions take place, each reaction provides an equilibrium condition that maybe used in the calculation of the final composition. However, it is not always obvious how many independent reactions are present. For example, in the reforming of methane by steam we may write the following four reactions that produce a mixture of carbon monoxide, carbon dioxide and hydrogen ... 

Modern-day industrial-scale facilities for hydrogen or syngas production use multiple reactions to convert carbonaceous feedstock (e.g. natural gas) into the required composition. These reactions are typically equilibrium limited and this drives the operating temperatures and pressures that are used. 

Ciric and Gu (1994) present a MINLP-based approach for the design of RD columns for systems where multiple reactions take place and/or where reactive equilibrium or thermal neutrality caimot be assured. This method is based on the combination of a rigorous tray-by-tray model and kinetic-rate-based expressions to give basic constraints of an optimization model that minimizes the total annual cost. The major variables are the number of trays in the column, the feed tray location, the temperature and composition profiles within the column, the reflux ratio, the internal flows within the column and the column diameter. 

Determine the equilibrium composition for a system with a single chemical reaction and with multiple chemical reactions given the reaction stoichiometry, temperature, and pressure. 

This discussion is meant to provide you some context for this chapter, where we cover a thermodynamic analysis of reacting systems the calculations we perform in this chapter do not account for rates of product formation. They are valid only at equilibrium, when the reactions are thermodynamically controlled. The fundamental question we wish to address is, What effect do temperature, pressure, and composition have on the equilibrium conversion in a chemically reacting system This analysis tells us nothing about the rates at which a chemical reaction will proceed. It does, however, tell us to what extent a reaction is possible. As in phase equilibria, we will use the Gibbs energy of the system to study chemical reaction equilibria. To illustrate the use of G, we will first consider a specific reaction (Section 9.2). We will then describe the general formalism for a single reaction (Sections 9.3-9.5) and multiple reactions (Sections 9.7-9.8). 

Equation (9.44) tells us the number of independent reactions, R, we need to specify among the m chemical species present. The stoichiometric constraints, s, are dictated by the inlet conditions, since the ratio of elements must stay the same. As long as the reactions we come up with are independent, solution of the multiple reaction equilibria problem will give us the equilibrium composition of the system. Indeed, if we were to chose a different set of equations, as long as they were independent and satisfied the number given by Equation (9.44), we would get the same result for equilibrium composition. 

Reaction (3). Alternatively, it can be shown that that the same value of Q would be obtained if Reactions (2) and (3) were selected as the set of independent reactions. Similarly, when we calculate equilibrium compositions of systems multiple reactions, it does not matter which set we choose as long as we consider the largest number of linearly independent chemical reactions possible for the species present. 

As an example the use of ceramic membranes for ethane dehydrogenation has been discussed (91). The construction of a commercial reactor, however, is difficult, and a sweep gas is required to shift the product composition away from equilibrium values. The achievable conversion also depends on the permeability of the membrane. Figure 7 shows the equilibrium conversion and the conversion that can be obtained from a membrane reactor by selectively removing 80% of the hydrogen produced. Another way to use membranes is only for separation and not for reaction. In this method, a conventional, multiple, fixed-bed catalytic reactor is used for the dehydrogenation. After each bed, the hydrogen is partially separated using membranes to shift the equilibrium. Since separation is independent of reaction, reaction temperature can be optimized for superior performance. Both concepts have been proven in bench-scale units, but are yet to be demonstrated in commercial reactors. 

Hence, this temperature depends on the composition of the reaction mixture, Therefore, for exothermic equilibrium reactions the temperature should be lowered as more reactant is converted, to keep the rate high. Thus this type of reaction is often carried out in multiple stages (e.g. multiple reactors or multiple zones within a reactor), each with its own temperature, adapted to the reaction mixture composition. 

---