Wall-temperature profiles, tubular reactor

In this work, thermal cracking reactors of ethylene plants are investigated dynamically. The main attention is given to the cracking coil. The modelling of the furnace itself is not considered.The tubular reactor is modelled by assuming the external wall temperature profile or heat flux profile of the coil. There is no report on dynamic analysis of this type of reactor in the literature except Jackman and Arises work (12). The literature is mainly interested in the steady state modelling of these reactors and control. 

Example 8.9 Find the temperature distribution in a laminar flow, tubular heat exchanger having a uniform inlet temperature and constant wall temperature Twall- Ignore the temperature dependence of viscosity so that the velocity profile is parabolic everywhere in the reactor. Use art/P = 0.4 and report your results in terms of the dimensionless temperature... 

Figure 5-23 Plots of reactant and temperature profiles versus axial position z and radial position JC in a wall-cooled tubular reactor. The reactor can exhibit a hot spot near the center where the rate is high and cooling is least.

Under smooth fluidization the motion, heat capacity, and small size of the particles result in a remarkably uniform temperature throughout the bed. Radial gradients, so important in fixed beds, are negligible. The transfer of heat to or from the reactor can be considered by assuming that a finite heat-transfer coefficient exists at the wall, and that the temperature across the bed is uniform. This situation is depicted in Fig. 13-18, where curve c applies to the fluidized bed. For comparison, curve b represents a homogeneous tubular reactor in turbulent flow, where the temperature profile is not so flat as in the fluidized bed but is still more uniform than for the packed bed, case (a). ... 

Hence, conversion and temperature profiles in a plug-flow tubular reactor with constant outer wall temperature are simulated by solving two coupled first-order ODEs that represent mass and thermal energy balances at high Peclet numbers. They are summarized here for completeness in terms of a generic rate law 3R when only one chemical reaction occurs ... 

Simulation of tubular steam reformers and a comparison with industrial data are shown in many references, such as [250], In most cases the simulations are based on measured outer tube-wall temperatures. In [181] a basic furnace model is used, whereas in [525] a radiation model similar to the one in Section 3.3.6 is used. In both cases catalyst effectiveness factor profiles are shown. Similar simulations using the combined two-dimensional fixed-bed reactor, and the furnace and catalyst particle models described in the previous chapters are shown below using the operating conditions and geometry for the simple steam reforming furnace in the hydrogen plant. Examples 1.3, 2.1 and 3.2. Similar to [181] and [525], the intrinsic kinetic expressions used are the Xu and Froment expressions [525] from Section 3.5.2, but with the parameters from [541]. 

Two-Dimensional Model of a Wall-Cooled Fixed Bed Reactor Radial heat transport is an important factor in wall-cooled (or heated) reactors, particularly if we have a strong exothermic reaction with the danger of a temperature runaway. Figure 4.10.67 shows a typical radial temperature profile in a cooled tubular fixed... 

The main problems related to the use of the tubular-flow reactor are caused by the deviations from ideal flow conditions, entrance and exit effects, heating and cooling rates and effects of heat of reaction on the temperature profiles and on the temperature difference between the reactants and the reactor wall. The heat transfer limitations can be very significant if the reactor diameter is not very small and if temperatures above 600°C are employed. Another problem arises from the difficulty in the evaluation of the actual reaction time, because of the increase in volume of the reacting mixture with temperature and conversion. 

Fig. 8 shows a typical temperatur profile in a tubular packed bed reactor. Profiles like this have been measured for example by Seidel (46). Near the wall there is a very steep temperature gradient. This observation suggests the introduction of a so called wall heat transfer coefficient... 

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