Reactor with gradients

Understanding. As electrochemical reactors with gradients of species, temperature, and potential in all dimensions and over a broad range of scales from nanometers to meters, fuel cells are complex devices. Changing a single parameter (e.g., the gas humidity in a PEMFC) can result in effects on the scale of reaction kinetics and other parameters, all the way to temperature distribution in a fuel ceU stack. This multitude of effects, as well as their consequences as felt in important parameters such as efficiency or power density, is difficult or impossible to comprehend without modeling approaches. 

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

We turn now to the numerical solution of Equations (9.1) and (9.3). The solutions are necessarily simultaneous. Equation (9.1) is not needed for an isothermal reactor since, with a flat velocity profile and in the absence of a temperature profile, radial gradients in concentration do not arise and the model is equivalent to piston flow. Unmixed feed streams are an exception to this statement. By writing versions of Equation (9.1) for each component, we can model reactors with unmixed feed provided radial symmetry is preserved. Problem 9.1 describes a situation where this is possible. 

Adiabatic Reactors. Like isothermal reactors, adiabatic reactors with a flat velocity profile will have no radial gradients in temperature or composition. There are axial gradients, and the axial dispersion model, including its extension to temperature in Section 9.4, can account for axial mixing. As a practical matter, it is difficult to build a small adiabatic reactor. Wall temperatures must be controlled to simulate the adiabatic temperature profile in the reactor, and guard heaters may be needed at the inlet and outlet to avoid losses by radiation. Even so, it is hkely that uncertainties in the temperature profile will mask the relatively small effects of axial dispersion. 

Steady-state reactors with ideal flow pattern. In an ideal isothermal tubular pZi/g-yZovv reactor (PFR) there is no axial mixing and there are no radial concentration or velocity gradients (see also Section 5.4.3). The tubular PFR can be operated as an integral reactor or as a differential reactor. The terms integral and differential concern the observed conversions and yields. The differential mode of reactor operation can be achieved by using a shallow bed of catalyst particles. The mass-balance equation (see Table 5.4-3) can then be replaced with finite differences ... 

There will be velocity gradients in the radial direction so all fluid elements will not have the same residence time in the reactor. Under turbulent flow conditions in reactors with large length to diameter ratios, any disparities between observed values and model predictions arising from this factor should be small. For short reactors and/or laminar flow conditions the disparities can be appreciable. Some of the techniques used in the analysis of isothermal tubular reactors that deviate from plug flow are treated in Chapter 11. 

For gas phase heterogeneous catalytic reactions, the continuous-flow integral catalytic reactors with packed catalyst bed have been exclusively used [61-91]. Continuous or short pulsed-radiation (milliseconds) was applied in catalytic studies (see Sect. 10.3.2). To avoid the creation of temperature gradients in the catalyst bed, a single-mode radiation system can be recommended. A typical example of the most advanced laboratory-scale microwave, continuous single-mode catalytic reactor has been described by Roussy et al. [79] and is shown in Figs. 10.4 and... 

The heat and material balances of a reactor with radial and axial gradients are stated in problem P8.01.04. In terms of fractional connversion, f, and for a first order reaction they are,... 

As discussed in previous chapters, the phase behavior with changing temperature and pressure may be strongly influenced by small concentration gradients in multi-component systems already. Therefore, experimental control should take this into account. It is a common practice to use reactors with glass or sapphire windows. The transition of an inhomogeneous multiphase system to a homogeneous one can be observed visually as cloud point (Sect. 2.2, with the pressure and temperature values being monitored. 

In Sect. 3.2, the development of the design equation for the tubular reactor with plug flow was based on the assumption that velocity and concentration gradients do not exist in the direction perpendiculeir to fluid flow. In industrial tubular reactors, turbulent flow is usually desirable since it is accompanied by effective heat and mass transfer and when turbulent flow takes place, the deviation from true plug flow is not great. However, especially in dealing with liquids of high viscosity, it may not be possible to achieve turbulent flow with a reasonable pressure drop and laminar flow must then be tolerated. 

The arguments advanced in Sect. 3.2.3 apply equally well to a continuous stirred tank reactor. With a reversible exothermic reaction and a fixed mean residence time, t, there is an optimum temperature for operation of a continuous stirred tank reactor. Since the conditions in an ideal stirred tank are, by definition, uniform, there is no opportunity to employ a temperature gradient, as with the plug-flow reactor, to achieve an even better performance. 

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... 

For low values of x, noticeable temperature gradients may establish inside the reactor, with a consequent worsening of the controller performance. This effect depends on the sensor location as well. As an example, when temperature is measured in peripheral compartments, the higher temperatures established in the reactor core, i.e., in the proximity of the stirrer, are ignored. As a consequence, the average reaction rate and the rate of heat production are underestimated, so that the resulting control action is less effective in counteracting possible runaway phenomena. 

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. The simplest model of a tubular reactor, the plug-flow reactor at steady state is kinetically identical to a batch reactor. The time variable in the batch reactor is transformed into the distance variable by the velocity. An axial temperature gradient can be imposed on the tubular reactor as indicated by Gilles and Schuchmann (22) to obtain the same effects as a temperature program with time in a batch reactor. Even recycle with a plug flow reactor, treated by Kilkson (35) for stepwise addition without termination and condensation, could be duplicated in a batch reactor with holdback between batches. 

This gradient quickly disappears across the reactor with a constantly increasing hydrogen content with tunnel length. 

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