Tubular temperature profile

Because the characteristic of tubular reactors approximates plug-flow, they are used if careful control of residence time is important, as in the case where there are multiple reactions in series. High surface area to volume ratios are possible, which is an advantage if high rates of heat transfer are required. It is sometimes possible to approach isothermal conditions or a predetermined temperature profile by careful design of the heat transfer arrangements. 

Plug Flow Reactor (PFR) A plug flow reactor is a tubular reactor where the feed is continuously introduced at one end and the products continuously removed from the other end. The concentration/temperature profile in the reactor varies with position. 

The need to keep a concave temperature profile for a tubular reactor can be derived from the former multi-stage adiabatic reactor example. For this, the total catalyst volume is divided into more and more stages, keeping the flow cross-section and mass flow rate unchanged. It is not too difficult to realize that at multiple small stages and with similar small intercoolers this should become something like a cooled tubular reactor. Mathematically the requirement for a multi-stage reactor can be manipulated to a different form ... 

Continuous Polymerizations As previously mentioned, fifteen continuous polymerizations in the tubular reactor were performed at different flow rates (i.e. (Nj g) ) with twelve runs using identical formulations and three runs having different emulsifier and initiator concentrations. A summary of the experimental runs is presented in Table IV and the styrene conversion vs reaction time data are presented graphically in Figures 7 to 9. It is important to note that the measurements of pressure and temperature profiles, flow rate and the latex properties indicated that steady state operation was reached after a period corresponding to twice the residence time in the tubular reactor. This agrees with Ghosh s results ). 

Figure 1. Typical reactor temperature profile for continuous addition polymerization a plug-flow tubular reactor. Kinetic parameters for the initiator 1 = 10 ppm Ea = 32.921 kcal/mol In = 26.492 In sec f = 0.5. Reactor parameter [(4hT r)/ (DpCp)] = 5148.2. [(Cp) = heat capacity of the reaction mixture (p) = density of the reaction mixture (h) = overall heat-transfer coefficient (Tf) = reactor jacket temperature (r) = reactor residence time (D) = reactor diameter].

The ability to manipulate reactor temperature profile in the polymerization tubular reactor is very important since it directly relates to conversion and resin product properties. This is often done by using different initiators at various concentrations and at different reactor jacket temperature. The reactor temperature response in terms of the difference between the jacket temperature and the peak temperature (0=Tp-Tj) is plotted in Figure 2 as a function of the jacket temperature for various inlet initiator concentrations. The temperature response not only depends on the jacket temperature but also, for certain combinations of the variables, it is very sensitive to the jacket temperature. 

FIGURE 13.8 Temperature profiles using a simplified model of a tubular reactor with pure styrene feed = 135 C and = 20°C. The parameter is the tube diameter in meters. 

It should be emphasized that for ideal tubular reactors, it is the total volume per unit of feed that determines the conversion level achieved. The ratio of the length of the tube to its diameter is irrelevant, provided that plug flow is maintained and that one uses the same flow rates and pressure-temperature profiles expressed in terms of reactor volume elements. 

This problem indicates the considerations that enter into the design of a tubular reactor for an endothermic reaction. The necessity of supplying thermal energy to the reactor contents at an elevated temperature implies that the heat transfer considerations will be particularly important in determining the longitudinal temperature profile of the reacting fluid. This problem is based on an article by Fair and Rase (1). 

Tubular flow units, like the CSTR, usually are operated at steady state. It is not always easy to measure the temperature profile accurately. In some high temperature operations, the coil is immersed in a fluidized sand bed or lead bath so there is fairly good temperature control. Sometimes it is felt desirable to do the laboratory work in a tubular unit if the commercial unit is to be of that type, but rate data from any kind of equipment are adaptable to the design of PFR. 

Fig. 26. Temperature profiles through an adiabatic tubular reactor with heat exchange between inlet and outlet streams.

A final mode of heat transfer in tubular reactors is the feed-cooled reactor, where the hot products from the reactor are cooled by the feed before it enters the reactor. As shown in Figure S-22, the cold feed in the jacket is preheated by the reaction in the inner tube or a heat exchanger is used for this purpose before the reactor. Temperature profiles for feed cooling are shown in Figure 5-22. 

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.

A conventional flow apparatus shown in Figure 1 was used. It consisted of gas-flow controlling devices, tubular reactor in an electric furnace, Liebig condenser, liquid trap, etc. The temperature profile along the longitudinal axis of the reactor was measured by a thermocouple. The reaction zone is defined here as the part of the reactor above 350°C. The reaction temperature means the highest temperature in the reaction zone. 

Figure 17.23. Representative temperature profiles in reaction systems (see also Figs. 17.20, 17.21(d), 17.22(d), 17.30(c), 17.34, and 17.35). (a) A jacketed tubular reactor, (b) Burner and reactor for high temperature pyrolysis of hydrocarbons (Ullmann, 1973, Vol. 3, p. 355) (c) A catalytic reactor system in which the feed is preheated to starting temperature and product is properly adjusted exo- and endothermic profiles, (d) Reactor with built-in heat exchange between feed and product and with external temperature adjustment exo- and endothermic profiles.

The essential feature of an autothermal reactor system is the feedback of reaction heat to raise the temperature and hence the reaction rate of the incoming reactant stream. Figure 1.6 shows a number of ways in which this can occur. With a tubular reactor the feedback may be achieved by external heat exchange, as in the reactor shown in Fig. 1.6a, or by internal heat exchange as in Fig. 1.6b. Both of these are catalytic reactors their thermal characteristics are discussed in more detail in Chapter 3, Section 3.6.2. Being catalytic the reaction can only take place in that part of the reactor which holds the catalyst, so the temperature profile has the form... 

Fig. 1.16. Laboratory-scale reproduction of adiabatic tubular reactor temperature profile...

Here we consider a nonisothermal, nonadiabatic tubular reactor as a distributed system. Our objective is to find its steady-state concentration and temperature profiles. 

A typical example of a tubular reactor for one-step processing of a newly synthesized polymer is described in a number of patents.183,184 This device consists of a high-pressure tube with the temperature profile regulated along its length. An extrusion die is mounted at the outlet end of the reactor. Continuous feeding is provided by a piston pump. 

Lockett M., Simmons M.J.H., Kendall K. (2004) CFD to predict temperature profile for scale up of micro-tubular SOFC stacks. Journal of Power Sources 131, 243-246. 

This equation allows calculating the temperature profile in a polytropic tubular reactor. 

A tubular reactor is to be designed in such a way that it can be stopped safely. The reaction mass is thermally instable and a decomposition reaction with a high energetic potential may be triggered if heat accumulation conditions occur. The time to maximum rate under adiabatic conditions of the decomposition is 24 hours at 200 °C. The activation energy of the decomposition is 100 kj mol-1. The operating temperature of the reactor is 120 °C. Determine the maximum diameter of the reactor tubes, resulting in a stable temperature profile, in case the reactor is suddenly stopped at 120 °C. 

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. 

Figure 5.20 shows the temperature profiles in the cooled tubular reactor for the optimum designs with the two catalysts. The optimum recycle flowrate is larger with the expensive catalyst, as expected, which yields an optimum inlet temperature that is higher. 

The system is subjected to several disturbances. The program faces numerical problems if these disturbances are too large. Figure 6.73 illustrates the erratic temperature profile that results when these numerical problems occur. The countercurrent model appears to be more prone to numerical problems than any of the other tubular reactor models. As a result the magnitudes of some of the disturbances are smaller than in the other cases. 

Figure 1 Schematic representation of the temperature profile of a tubular steam reformer as a function of time on stream...

FIG. 19-13 Noncatalytic gas-phase reactions, (a) Steam cracking of light hydrocarbons in a tubular fired heater, (b) Pebble heater for the fixation of nitrogen from air. (c) Flame reactor for the production of acetylene from hydrocarbon gases or naphthas. [Patton, Grubb, and Stephenson, Pet. Ref. 37(11) 180 (1958).] d Flame reactor for acetylene from light hydrocarbons (BASF), (e) Temperature profiles in a flame reactor for acetylene (Ullmann Encyclopadie der Technischen Chemie, vol. 3, Verlag Chemie, 1973, p. 335). 

A theoretical and experimental study of multiplicity and transient axial profiles in adiabatic and non-adiabatic fixed bed tubular reactors has been performed. A classification of possible adiabatic operation is presented and is extended to the nonadiabatic case. The catalytic oxidation of CO occurring on a Pt/alumina catalyst has been used as a model reaction. Unlike the adiabatic operation the speed of the propagating temperature wave in a nonadiabatic bed depends on its axial position. For certain inlet CO concentration multiplicity of temperature fronts have been observed. For a downstream moving wave large fluctuation of the wave velocity, hot spot temperature and exit conversion have been measured. For certain operating conditions erratic behavior of temperature profiles in the reactor has been observed. 

A mathematical model was developed, able to predict monomer conversion and temperature profiles of industrial tubular reactors for the production of low-density polyethylene, in different operating conditions. 

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