Plug flow reactor radial temperature gradients

The flow patterns, composition profiles, and temperature profiles in a real tubular reactor can often be quite complex. Temperature and composition gradients can exist in both the axial and radial dimensions. Flow can be laminar or turbulent. Axial diffusion and conduction can occur. All of these potential complexities are eliminated when the plug flow assumption is made. A plug flow tubular reactor (PFR) assumes that the process fluid moves with a uniform velocity profile over the entire cross-sectional area of the reactor and no radial gradients exist. This assumption is fairly reasonable for adiabatic reactors. But for nonadiabatic reactors, radial temperature gradients are inherent features. If tube diameters are kept small, the plug flow assumption in more correct. Nevertheless the PFR can be used for many systems, and this idealized tubular reactor will be assumed in the examples considered in this book. We also assume that there is no axial conduction or diffusion. 

A steady-state heat balance for a plug flow reactor with no radial temperature gradients is given by ... 

The solution of Eq. (173) poses a rather formidable task in general. Thus the dispersed plug-flow model has not been as extensively studied as the axial-dispersed plug-flow model. Actually, if there are no initial radial gradients in C, the radial terms will be identically zero, and Eq. (173) will reduce to the simpler Eq. (167). Thus for a simple isothermal reactor, the dispersed plug flow model is not useful. Its greatest use is for either nonisothermal reactions with radial temperature gradients or tube wall catalysed reactions. Of course, if the reactants were not introduced uniformly across a plane the model could be used, but this would not be a common practice. Paneth and Herzfeld (P2) have used this model for a first order wall catalysed reaction. The boundary conditions used were the same as those discussed for tracer measurements for radial dispersion coefficients in Section II,C,3,b, except that at the wall. 

With Heat Transfer. The tubular reactor is constructed in a similar way as a tube-in-shell heat exchanger or a fired furnace. Process fluid flows inside the tubes and is cooled or heated by the heat transfer medium within the shell. Radial temperature gradients are inherent in tubular reactors with heat transfer, so the plug flow assumption... 

Tubular reactors, which may be open or packed with catalyst, are considered ideal if there is plug flow of fluid and there are no radial gradients of temperature, concentration, or velocity. In plug-flow reactors, or PFRs, there are axial gradients of concentration and perhaps also axial gradients of temperature and pressure, but in the ideal PFR there is no axial diffusion or conduction. 

Equations (4.10.125) and (4.10.126) are extensions of the equations for an ideal plug flow reactor, Eqs. (4.10.69) and (4.10.70), to a tubular fixed bed reactor with radial gradients of temperature and concentration and hence include the factors considering the dispersion of mass and heat. (Note that we now use the term fm.effPb instead of ras used for homogeneous reactions.)... 

A maximum reactor temperature of 500 K is used in this study. This maximum temperature occurs at the exit of the adiabatic reactor under steady-state conditions. Plug flow is assumed with no radial gradients in concentrations or temperatures and no axial diffusion or conduction. 

Gas-phase reacdotis are carried out primarily in tubular reactors where the flow is generally turbulent. By assuming that there is no dispersion and ttiere are no radial gradients in either temperature, velocity, or concentration, we can model the flow in the reactor as plug-flow. Laminar reactors are discussed in Chapter 13 and dispersion effects in Chapter 14. The differential form of the design equation... 

The following assumptions are made (1) Ozone and flue gas are thoroughly mixed in a short distance using a proper distributor. (2) Gas moves in plug flow. (3) Gas follows ideal gas law. (4) There are no radial gradients of temperature, concentration, and density. (5) The reactor is operating at steady state. 

To carry out an exothermic reaction in a tubular reactor under nearly isothermal conditions, a small diameter is needed to give a high ratio of surface area to volume. The reactor could be made from sections of jacketed pipe or from a long coil immersed in a cooling bath. The following analysis is for a constant jacket temperature, and the liquid is assumed to be in plug flow, with no radial gradients of temperature or concentration and no axial conduction or diffusion. 

More complex is the plug-flow tubular reactor (PFR or PFTR), in which the composition of the fluid, flowing as a plug, gradually changes down the length of the reactor, with no composition or temperature gradients in the radial direction. Furthermore, mass- and heat-transfer... 

All simulators provide one-dimensional, plug-flow models that neglect axial dispersion Thus, there are no radial gradients of temperature, composition, or pressure and mass diffusion and heat conduction do not occur in the axial direction. Operation of the reactor can bt adiabatic, isothermal, or nonadiabatic, nonisothermal. For the latter, heat transfer to or fron the reacting mixture occurs along the length of the reactor. 

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