Mass balance catalytic reactor

The catalyst prepared above was characterized by X-ray diffraction, X-ray photoelectron and Mdssbauer spectroscopic studies. The catalytic activities were evaluated under atmospheric pressure using a conventional gas-flow system with a fixed-bed quartz reactor. The details of the reaction procedure were described elsewhere [13]. The reaction products were analyzed by an on-line gas chromatography. The mass balances for oxygen and carbon beb een the reactants and the products were checked and both were better than 95%. 

The catalytic tests were carried out in a fixed bed micro-reactor at atmospheric pressure at 540 °C. The feed composition was 2.5 vol.% of propane, 5 vol. % of ammonia and 5 vol.% of oxygen. The weight of catalyst in the reactor was varied in order to keep the number of Fe ions in the reactor constant (9 pmol of Fe atoms). Conversion, selectivity and yields were calculated on the basis of mass balance in dependence on the time of stream. 

In practice, of course, it is rare that the catalytic reactor employed for a particular process operates isothermally. More often than not, heat is generated by exothermic reactions (or absorbed by endothermic reactions) within the reactor. Consequently, it is necessary to consider what effect non-isothermal conditions have on catalytic selectivity. The influence which the simultaneous transfer of heat and mass has on the selectivity of catalytic reactions can be assessed from a mathematical model in which diffusion and chemical reactions of each component within the porous catalyst are represented by differential equations and in which heat released or absorbed by reaction is described by a heat balance equation. The boundary conditions ascribed to the problem depend on whether interparticle heat and mass transfer are considered important. To illustrate how the model is constructed, the case of two concurrent first-order reactions is considered. As pointed out in the last section, if conditions were isothermal, selectivity would not be affected by any change in diffusivity within the catalyst pellet. However, non-isothermal conditions do affect selectivity even when both competing reactions are of the same kinetic order. The conservation equations for each component are described by... 

In catalytic reactors we assume that there is no reaction in the fluid phase, and all reaction occurs on the surface of the catalyst. The surface reaction rate has the units of moles per unit area of catalyst per unit time, which we will call r". We need a homogeneous rate r to insert in the mass balances, and we can write this as... 

We summarize the rates we need in a catalytic reactor in Table 74. We always need r to insert in the relevant mass-balance equation. We must be given i- or P as functions of Cj and T from kinetic data. 

We are also concerned with gradients in composition throughout the reactor. We have thus far been concerned only with the very small gradient dCj/dz down the reactor from inlet to exit, which we encounter in the species mass balance, which we must ultimately solve. Then there is the gradient in Cj around the catalyst pellet Finally, there is the gradient within the porous catalyst pellet and around the catalytic reaction site within the pellet As we consider... 

To summarize the goal of this section, we must start with the microscopic description of the catalytic reaction, then consider diffusion in pores, and then examine the reactant composition around and within the pellet, in order finally to describe the reactor maSS-balance equations in terms of z alone. The student should understand the logic of this procedure as we go from micrscopic to macroscopic, or the following sections will be unintelligible (or even more unintelligible than usual). 

As with catalytic reactions, our task is to develop pseudohomogeneous rate expressions to insert into the relevant mass-balance equations. For ary multiphase reactor where reaction occurs at the interface between phases, the reactions are pritnarily surface reactions (rate r ), and we have to find these expressions as functions of concentrations and rate and transport coefficients and then convert them into pseudohomogeneous expressions,... 

The catalytic reactor is an example where reaction occurs only at the boundary with a solid phase, but, as long as the solid remains in the reactor and does not change, we did not need to write separate mass balances for the soHd phase because its residence time Tj is infinite. In a moving bed catalytic reactor or in a slurry or fluidized bed catalytic reactor... 

A further consequence of the upstream diffusion to the burner face could be heterogeneous reaction at the burner. Such reaction is likely on metal faces that may have catalytic activity. In this case the mass balance as stated in Eq. 16.99 must be altered by the incorporation of the surface reaction rate. In addition to the burner face in a flame configuration, an analogous situation is encountered in a stagnation-flow chemical-vapor-deposition reactor (as illustrated in Fig. 17.1). Here again, as flow rates are decreased or pressure is lowered, the enhanced diffusion tends to promote species to diffuse upstream toward the inlet manifold. 

The mass balances [Eqs. (Al) and (A2)] assume plug-flow behavior for both the gas/vapor and liquid phases. However, real flow behavior is much more complex and constitutes a fundamental issue in multiphase reactor design. It has a strong influence on the reactor performance, for example, due to back-mixing of both phases, which is responsible for significant effects on the reaction rates and product selectivity. Possible development of stagnant zones results in secondary undesired reactions. To ensure an optimum model development for CD processes, experimental studies on the nonideal flow behavior in the catalytic packing MULTIPAK are performed (168). 

The mass balance equation, expressed in moles, for the catalytic reactor is given by (see Figure 9.16) Input - Output + Production = Accumulation where, in a steady state, the accumulation is zero. 

Given any complex system of heterogeneous catalytic first order reactions the mass balance on a differential volume element of the reactor at the height h yields the following system of differential equations for the j-th reaction component i) for the bubble phase... 

To relate the reaction rate or conversion, pressure drop, and temperature variation over a catalyst bed with the operating variables of a reactor, flow rate, catalyst amount etc., so-called mass-, heat- and impulse balances are used in catalytic reaction engineering [4, 8]. This chapter assumes, however, that the catalyst bed is isothermal and the pressure drop over the bed is negligible. This leaves only mass balances for each reactant or product to be considered. For a component i this can be written for part of a catalyst bed or the whole bed as... 

The mass transfer equation is written in terms of the usual assumptions. However, it must be considered that because the concentration of the more abundant species in the flowing gas mixture (air), as well as its temperature, are constant, all the physical properties may be considered constant. The only species that changes its concentration along the reactor in measurable values is PCE. Therefore, the radial diffusion can be calculated as that of PCE in a more concentrated component, the air. This will be the governing mass transfer mechanism of PCE from the bulk of the gas stream to the catalytic boundaries and of the reaction products in the opposite direction. Since the concentrations of nitrogen and oxygen are in large excess they will not be subjected to mass transfer limitations. The reaction is assumed to occur at the catalytic wall with no contributions from the bulk of the system. Then the mass balance at any point of the reactor is... 

In fixed-bed catalytic cracking tests the proper decreasing delta coke response as catalyst-to-oil is increased is possible if a constant catalyst load and a constant feed injection rate are maintained. As CCR increases above 4 wt%, however, fixed-bed cracking methods are suspect because the mass balance drops significantly and the cracking performance can be measured better using other techniques (e.g.s., circulating pilot plants or fluidized-bed reactors). 

The abstract models can be divided into two categories, each of which can be further subdivided into three classes (Fig. 5). Some of the models consist of coverage equations only, and these models will be called surface reaction models. The remaining models use additional mass and/or heat balance equations that include assumptions about the nature of the reactor in which the catalytic reaction takes place (the reactor could be simply a catalyst pellet). These models will be called reactor-reaction models. Some of the models mentioned under the heading surface reaction models also incorporate balance equations for the reactor. However, these models need only the coverage equations to predict oscillatory behavior reactor heat and mass balances are just added to make the models more realistic [e.g., the extension of the Sales-Turner-Maple model (272) given in Aluko and Chang (273)]. Such models are therefore included under surface reaction models, which will be discussed first. 

To derive the overall kinetics of a gas/liquid-phase reaction it is required to consider a volume element at the gas/liquid interface and to set up mass balances including the mass transport processes and the catalytic reaction. These balances are either differential in time (batch reactor) or in location (continuous operation). By making suitable assumptions on the hydrodynamics and, hence, the interfacial mass transfer rates, in both phases the concentration of the reactants and products can be calculated by integration of the respective differential equations either as a function of reaction time (batch reactor) or of location (continuously operated reactor). In continuous operation, certain simplifications in setting up the balances are possible if one or all of the phases are well mixed, as in continuously stirred tank reactor, hereby the mathematical treatment is significantly simplified. 

We shall develop next a single-channel model that captures the key features of a catalytic combustor. The catalytic materials are deposited on the walls of a monolithic structure comprising a bundle of identical parallel tubes. The combustor includes a fuel distributor providing a uniform fuel/air composition and temperature over the cross section of the combustor. Natural gas, typically >98% methane, is the fuel of choice for gas turbines. Therefore, we will neglect reactions of minor components and treat the system as a methane combustion reactor. The fuel/air mixture is lean, typically 1/25 molar, which corresponds to an adiabatic temperature rise of about 950°C and to a maximum outlet temperature of 1300°C for typical compressor discharge temperatures ( 350°C). Oxygen is present in large stoichiometric excess and thus only methane mass balances are needed to solve this problem. 

It is a simple matter to demonstrate that it is the interaction of reaction, geometric, and heat-transfer requirements that limits the value of scale-up. Consider a fixed-bed catalytic reactor. Suppose that the pressure drop has no effect on the rate and that plug flow exists. The mass balance for reactant is given by Eq. (12-2) as... 

A section of a fixed-bed catalytic reactor is shown in Fig. 13-4. Consider a small volume element of radius r, width Ar, and height Ar, through which reaction mixture flows isothermally. Suppose that radial and longitudinal diffusion can be expressed by Pick s law, with and Dj as effective diffusivities, based on the total (void and nonvoid) area perpendicular to the direction of diffusion. We want to write a mass balance for a reactant over the volume element. With radial and longitudinal diffusion and longitudinal convection taken into account, the input term is... 

The consideration of thermal effects and non-isothermal conditions is particularly important for reactions for which mass transport through the membrane is activated and, therefore, depends strongly on temperature. This is, typically, the case for dense membranes like, for example, solid oxide membranes, where the molecular transport is due to ionic diffusion. A theoretical study of the partial oxidation of CH4 to synthesis gas in a membrane reactor utilizing a dense solid oxide membrane has been reported by Tsai et al. [5.22, 5.36]. These authors considered the catalytic membrane to consist of three layers a macroporous support layer and a dense perovskite film (Lai.xSrxCoi.yFeyOs.s) permeable only to oxygen on the top of which a porous catalytic layer is placed. To model such a reactor Tsai et al. [5.22, 5.36] developed a two-dimensional model considering the appropriate mass balance equations for the three membrane layers and the two reactor compartments. For the tubeside and shellside the equations were similar to equations (5.1) and... 

In any catalytic system not only chemical reactions per se but mass and heat transfer effects should be considered. For example, mass and heat transfer effects are present inside the porous catalyst particles as well as at the surrounding fluid films. In addition, heat transfer from and to the catalytic reactor gives an essential contribution to the energy balance. The core of modelling a two-phase catalytic reactor is the catalyst particle, namely simultaneous reaction and diffusion in the pores of the particle should be accounted for. These effects are completely analogous to reaction-diffusion effects in liquid films appearing in gas-liquid systems. Thus, the formulae presented in the next section are valid for both catalytic reactions and gas-liquid processes. 

Consequently, the reactor model is constituted by a system of N+1 equations, where N is the number of chemical species present in the system (NO, NO2, N2 and O2, neglecting the presence of N2O N = 4) and another unknown variable is pressure. The equations are one momentum balance (in the form of simplified Ergun Law), and four mass balance relationships. The presence of NO2 among the reaction products has been related to the catalytic activity of Cu-ZSM5 towards the oxidation of NO to NO2, as revealed by our previous investigation in similar experimental conditions [7], as well as by the present results (Fig. 1). It has been hypothesised that reaction (2) proceeds in parallel to NO decomposition, having not assumed that NO2 formation is responsible for copper reduction from Cu (inactive in decomposing NO) to Cu (the active site), as also proposed by some author [20-21,23]. 

In Section 14-8, we illustrate how a differential plug-flow mass balance near the inlet of a tubular reactor packed with porous catalytic pellets provides experimental data for quantitative evaluation of (i Hougen-watsonimitiai via equation (14-199). Hence, the data pairs include the total pressure dependence of this initial conversion rate. As illustrated by (14-96), a second-order polynomial model is appropriate. Hence,... 

The mass balance with homogeneous one-dimensional diffusion and irreversible nth-order chemical reaction provides basic information for the spatial dependence of reactant molar density within a catalytic pellet. Since this problem is based on one isolated pellet, the molar density profile can be obtained for any type of chemical kinetics. Of course, analytical solutions are available only when the rate law conforms to simple zeroth- or first-order kinetics. Numerical techniques are required to solve the mass balance when the kinetics are more complex. The rationale for developing a correlation between the effectiveness factor and intrapellet Damkohler number is based on the fact that the reactor design engineer does not want to consider details of the interplay between diffusion and chemical reaction in each catalytic pellet when these pellets are packed in a large-scale reactor. The strategy is formulated as follows ... 

---