Steady-state catalytic chemical reactor

Heterogeneous catalytic systems offer the advantage that separation of the products from the catalyst is usually not a problem. The reacting fluid passes through a catalyst-filled reactor m the steady state, and the reaction products can be separated by standard methods. A recent innovation called catalytic distillation combines both the catalytic reaction and the separation process in the same vessel. This combination decreases the number of unit operations involved in a chemical process and has been used to make gasoline additives such as MTBE (methyl tertiai-y butyl ether). 

Steady state models of the automobile catalytic converter have been reported in the literature 138), but only a dynamic model can do justice to the demands of an urban car. The central importance of the transient thermal behavior of the reactor was pointed out by Vardi and Biller, who made a model of the pellet bed without chemical reactions as a onedimensional continuum 139). The gas and the solid are assumed to have different temperatures, with heat transfer between the phases. The equations of heat balance are ... 

Chapter 10 begins a more detailed treatment of heterogeneous reactors. This chapter continues the use of pseudohomogeneous models for steady-state, packed-bed reactors, but derives expressions for the reaction rate that reflect the underlying kinetics of surface-catalyzed reactions. The kinetic models are site-competition models that apply to a variety of catalytic systems, including the enzymatic reactions treated in Chapter 12. Here in Chapter 10, the example system is a solid-catalyzed gas reaction that is typical of the traditional chemical industry. A few important examples are listed here ... 

Another type of stability problem arises in reactors containing reactive solid or catalyst particles. During chemical reaction the particles themselves pass through various states of thermal equilibrium, and regions of instability will exist along the reactor bed. Consider, for example, a first-order catalytic reaction in an adiabatic tubular reactor and further suppose that the reactor operates in a region where there is no diffusion limitation within the particles. The steady state condition for reaction in the particle may then be expressed by equating the rate of chemical reaction to the rate of mass transfer. The rate of chemical reaction per unit reactor volume will be (1 - e)kCAi since the effectiveness factor rj is considered to be unity. From equation 3.66 the rate of mass transfer per unit volume is (1 - e) (Sx/Vp)hD(CAG CAl) so the steady state condition is ... 

The starting point of a number of theoretical studies of packed catalytic reactors, where an exothermic reaction is carried out, is an analysis of heat and mass transfer in a single porous catalyst since such system is obviously more conductive to reasonable, analytical or numerical treatment. As can be expected the mutual interaction of transport effects and chemical kinetics may give rise to multiple steady states and oscillatory behavior as well. Research on multiplicity in catalysis has been strongly influenced by the classic paper by Weisz and Hicks (5) predicting occurrence of multiple steady states caused by intrapellet heat and mass intrusions alone. The literature abounds with theoretical analysis of various aspects of this phenomenon however, there is a dearth of reported experiments in this area. Later the possiblity of oscillatory activity has been reported (6). 

In a chemical packed-bed reactor in which a highly exothermic reaction is taking place conditions may be encountered under which, for a given set of input conditions (feed rate, temperature, concentration), the exit conversion is either high or low. To the experimental study of conditions connected with the existence of multiple steady states in packed catalytic reactors has not been paid as much attention in the past as to the study of... 

We also note that the process of decay in catalytic cracking has been amply demonstrated(l)(2)(3) to be a function of the time of exposure of the catalyst to the reactants i.e. of the time on stream. Such time-dependent behaviour indicates that the kinetics of the process of catalyst decay are the same as those to be expected in a batch reaction. On reflection, it is obvious that the situation of the catalyst charge in a steady-state reactor is in fact that of a batch of reactant (the catalyst) undergoing a chemical process (catalyst decay) as a function of the time on stream i.e. the time it spends at reaction conditions - at reaction temperature and in the presence of an atmosphere of feed, products and potential poisons. 

We have already considered steady-state one-dimensional diffusion in the introductory sections 1.4.1 and 1.4.2. Chemical reactions were excluded from these discussions. We now want to consider the effect of chemical reactions, firstly the reactions that occur in a catalytic reactor. These are heterogeneous reactions, which we understand to be reactions at the contact area between a reacting medium and the catalyst. It takes place at the surface, and can therefore be formulated as a boundary condition for a mass transfer problem. In contrast homogeneous reactions take place inside the medium. Inside each volume element, depending on the temperature, composition and pressure, new chemical compounds are generated from those already present. Each volume element can therefore be seen to be a source for the production of material, corresponding to a heat source in heat conduction processes. 

As an example we will consider a catalytic reactor, Fig. 2.58, in which by a chemical reaction between a gas A and its reaction partner R, a new reaction product P is formed. The reaction partner R and the gas A are fed into the reactor, excess gas A and reaction product P are removed from the reactor. The reaction is filled with spheres, whose surfaces are covered with a catalytic material. The reaction between gas A and reactant R occurs at the catalyst surface and is accelerated due to the presence of the catalyst. In most cases the complex reaction mechanisms at the catalyst surface are not known completely, which suggests the use of very simplified models. For this we will consider a section of the catalyst surface, Fig. 2.59. On the catalyst surface x = 0 at steady-state, the same amount of gas as is generated will be transported away by diffusion. The reaction rate is equal to the diffusive flux. In general the reaction rate hA0 of a catalytic reaction depends on the concentration of the reaction partner. In the present case we assume that the reaction rate will be predominantly determined by the concentration cA(x = 0) = cA0 of gas A at the surface. For a first order reaction it is given by... 

Chemical relaxation techniques have been employed to study the rates of elementary reaction steps. The two most useful variables for the system control are the concentrations of the reactants and the reactor temperature. The dynamic responses from the system after the changes of these variables are related to the elementary steps of the catalytic processes. Chemical relaxation techniques can be divided into two general groups, which are single cycle transient analysis (SCTA) and multiple cycle transient analysis (MCTA). In SCTA, the reaction system relaxes to a new steady-state and analysis of this transition furnishes information about intermediate species. In MCTA, the system is periodically switched between two steady-states, e.g. by periodically changing the reactant concentration. 

Interaction of the dynamic properties of a catalyst, a micro-scale physic-chemical system, and the dynamic properties of the macro-scale reactor creates an opportunity to improve the performance of catalytic processes using forced unsteady-state operation. Forced dynamic operation makes it possible to generate spatio-temporal patterns of temperature, composition and catalyst states that caimot be attained under steady-state operation. 

Reactor performance is established by calculating the molar density of reactant A from a steady-state mass balance that accounts for axial convection and transverse diffusion. Chemical reaction only occurs on the well-defined catalytic surface which bounds fluid flow in the regular polygon channel. Hence, depletion of reactant A due to chemical reaction appears in the boundary conditions, but not in the mass balance which applies volumetrically throughout the homogeneous flow channel. The mass transfer equation for duct reactors is written in vector form ... 

Unlike porous pellets, it is mathematically feasible to account for chemical reaction on the well-defined catalytic surfaces that bound the flow regime in regular polygon duct reactors. A qualitative description of the boundary conditions is based on a steady-state mass balance over a differential surface element. Since convective transport vanishes on the stationary catalytic surface, the following contributions from diffusion and chemical reaction are equated, with units of moI/(areatime) ... 

---