Nonisothermal Plug Flow Reactor

In order to reduce the disparities in volume or space time requirements between an individual CSTR and a plug flow reactor, batteries or cascades of stirred tank reactors ard employed. These reactor networks consist of a number of stirred tank reactors confiected in series with the effluent from one reactor serving as the input to the next. Although the concentration is uniform within any one reactor, there is a progressive decrease in reactant concentration as ohe moves from the initial tank to the final tank in the cascade. In effect one has stepwise variations in composition as he moves from onfe CSTR to another. Figure 8.9 illustrates the stepwise variations typical of reactor cascades for different numbers of CSTR s in series. In the general nonisothermal case one will also en-... 

Numerical integration of design equation for a plug-flow reactor operated nonisotherm ally... 

The reactor system may consist of a number of reactors which can be continuous stirred tank reactors, plug flow reactors, or any representation between the two above extremes, and they may operate isothermally, adiabatically or nonisothermally. The separation system depending on the reactor system effluent may involve only liquid separation, only vapor separation or both liquid and vapor separation schemes. The liquid separation scheme may include flash units, distillation columns or trains of distillation columns, extraction units, or crystallization units. If distillation is employed, then we may have simple sharp columns, nonsharp columns, or even single complex distillation columns and complex column sequences. Also, depending on the reactor effluent characteristics, extractive distillation, azeotropic distillation, or reactive distillation may be employed. The vapor separation scheme may involve absorption columns, adsorption units,... 

In practice the heat effects associated with chemical reactions result in nonisothermal conditions. In the case of a batch reactor the temperature changes as a function of time, whereas an axial temperature profile is established in a plug flow reactor. The application of the law of conservation of energy, in a similar... 

Example 9.11 Modeling of a nonisothermal plug flow reactor Tubular reactors are not homogeneous, and may involve multiphase flows. These systems are called diffusion convection reaction systems. Consider the chemical reaction A -> bB described by a first-order kinetics with respect to the reactant A. For a nonisothermal plug flow reactor, modeling equations are derived from mass and energy balances... 

To identify the additional information necessary to design nonisothermal reactors, we consider the following example, in which a highly exothermic reaction is carried out adiabaticaUy in a plug-flow reactor. 

Up to now we have focused on the steady-state operation of nonisothermal reactors. In this section the unsteady-state energy balance wtU be developed and then applied to CSTRs, plug-flow reactors, and well-mixed batch and semibateh reactors. 

Isothermal plug flow reactor. Chapter 8, p. 118 Nonisothermal plug flow reactor. Chapter 8, p. 121. 

The design formulation of nonisothermal plug-flow reactors with multiple reactions follows the same procedure outlined in the previous section—we write design... 

For nonisothermal recycle reactors, we have to incorporate the energy balance equation to express variation in the reactor temperature. The energy balance equation is the same as that of a plug-flow reactor. 

Falling Off the Steady State 623 Nonisothermal Multiple Reactions 625 Unsteady Operation of Plug-Flow Reactors... 

Nonisothermal reactor design requires the simultaneous solution of the appropriate energy balance and the species material balances. For the batch, semi-batch, and steady-state plug-flow reactors, these balances are sets of initial-value ODEs that must be solved numerically, in very limited situations (constant thermodynamic properties, single... 

In the previous examples, we have exploited the idea of an effectiveness factor to reduce fixed-bed reactor models to the same form as plug-flow reactor models. This approach is useful and solves several important cases, but this approach is also limited and can take us only So far. In the general case, we must contend with multiple reactions that are not first order, nonconstant thermochemical properties, and nonisothermal behavior in the pellet and the fluid. For these cases, we have no alternative but to solve numerically for the temperature and species concentrations profiles in both the pellet and the bed. As a final example, we compute the numerical solution to a problem of this type. 

Figure 4.24 Plug-flow reactor in a nonisothermal reaction.

The difficulty in this is the awkward form of equation (6-140) with respect to 7). One likes to compute in sequence through the series of cells, but here we face the implicit form of Ti as a function of r, i. This is the same basic difficulty that limits the utility of the CSTR sequence as an analytical model for nonisothermal reactors. For the case here though, where we employ a relatively large value of the index n in approximation of a plug-flow reactor, and where the solution will be via numerical methods anyway, we will strong-arm the problem with the approximation T,- r,- ] in the exponentials, so that... 

It is impossible to create an isothermal process in plug flow reactors as it requires the variation of thermal transfei along the reactor length, according to the kinetics of heat emission. Therefore, plug flow reactors run under adiabatic conditions or at least imder nonisothermal mode conditions with external heat removal. The heat balance equation for steady state conditions for the micro volume of a reactor can be written in the form [4] ... 

Tubular reactor The contact time is the same for all molecules or fluid elements along the reactor when the velocity is uniform in the cross section of the tube, satisfying the plug flow. All molecules have the same velocity. Therefore, the concentration is uniform in a cross section of the tube and varies only along the reactor. In the isothermal case, the temperature remains constant in the longitudinal and radial directions. In the nonisothermal case, the temperature varies along the reactor. This reactor will be denominated ideal PFR (plug flow reactor). 

Example 9.9 Modeling of a nonisothermal plug flow reactor... 

Figure 10.21 Design and analysis procedures for adiabatic, nonisothermal plug-flow reactors affected by diffusion, chemical deactivation, and sintering. (Reprinted from Lee and Ruckenstein 1983, by courtesy of Marcel Dekker, Inc.)...

To sum up, it is sufficient to treat an adiabatic reactor as a plug-flow reactor. If the axial dispersion effect is to be included, only the heat dispersion term needs to be added. In the case of nonadiabatic, nonisothermal reactors, axial dispersion terms can be neglected in comparison to the radial dispersion terms. In addition, the radial dispersion terms can often be neglected if the radial aspect ratio is small. The conservation equations for various cases are summarized in Table 9.1. 

NONISOTHERMAL, NONADIABATIC BATCH, AND PLUG-FLOW REACTORS... 

Calculation of the volume of a nonisothermal chemical reactor usually needs the use of numerical integration. For example, consider the first order reaction A B in liquid phase, taking place in an adiabatic plug flow reactor. Pure <4 enters the reactor, and it is desired to have the conversion X, at the outlet. The volume of this reactor is given by... 

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