Reactor temperature contours

Figure 2. Radial-axial velocity field and temperature contours for a rotating-disk reactor at an operating condition where a buoyancy-driven recirculation vortex has developed. The disk temperature is HOOK, the Reynolds number is 1000, Gr/Re / = 6.2, fo/f = 1.28, and L/f = 2.16. The disk radius is 4.9 cm, the spin rate is 495 rpm. The maximum axial velocity is 55.3 cm/sec. The gas is helium.

The study of the peak temperature sensitivity to the reactor operating parameters and the construction of sensitivity boundary curves for stable reactor operation were previously reported ( l). This paper presents a computer study on conceptual relationships between the conversion-product properties and the reactor operating parameters in a plug flow tubular reactor of free radical polymerization. In particular, a contour map of conversion-molecular weight relationships in a reactor of fixed size is presented and the sensitivity of its relationship to the choice of initiator system, solvent system and heat transfer system are discussed. 

Figure 5. Molecular weight-conversion contour map for various concentrations of a free-radical initiator operating in a tubular-addition polymerization reactor of fixed size. Curves were constructed using varying jacket temperatures (kinetic parameters for the initiator Ea = 32.921 Kcal/mol In k/ = 26.494 In sec f = 0.5 (------------------------) optimum operating line)...

The computer simulation study of the operation of the tubular free radical polymerization reactor has shown that the conversion and the product properties are sensitive to the operating parameters such as initiator type, jacket temperature, and heat transfer for a reactor of fixed size. The molecular weight-conversion contour map is particularly significant and it is used in this paper as a basis for a comparison of the reactor performances. 

When we want to look at the connection between the flow behavior and the amount of heat that is transferred into the fixed bed, the 3D temperature field is not the ideal tool. We can look at a contour map of the heat flux through the wall of the reactor tube. Fig. 19 actually displays a contour map of the global wall heat transfer coefficient, h0, which is defined by qw — h0(Tw-T0) where T0 is a global reference temperature. So, for constant wall temperature, qw and h0 are proportional, and their contour maps are similar. The map in Fig. 19 shows the local heat transfer coefficient at the tube wall and displays a level of detail that would be hard to obtain from experiment. The features found in the map are the result of the flow features in the bed and the packing structure of the particles. 

It is often necessary to employ more than one adiabatic reactor to achieve a desired conversion. The catalytic oxidation of SOj to SO3 is a case in point. In the first place, chemical equilibrium may have been established in the first reactor and it would be necessary to cool and/or remove the product before entering the second reactor. This, of course, is one good reason for choosing a catalyst which will function at the lowest possible temperature. Secondly, for an exothermic reaction, the temperature may rise to a point at which it is deleterious to the catalyst activity. At this point, the products from the first reactor are cooled prior to entering a second adiabatic reactor. To design such a system, it is only necessary to superimpose on the rate contours the adiabatic temperature paths for each of the reactors. The volume requirements for each reactor can then be computed from the rate contours in the same way as for a... 

Because the adiabatic reaction path is linear a graphical solution, also applicable to multi-bed reactors, is particularly apposite. (See Example 3.7 as an illustration.) If the design data are available in the form of rate data for various temperatures and conversions they may be displayed as contours of equal reaction rate in the (T, Y) plane. Figure 3.14 shows such contours upon which is superimposed an adiabatic reaction path of slope cp/(- AH) and intercept T0 on the abscissa. The reactor size may be evaluated by computing ... 

The reaction path in the T, Y plane could be plotted by solving the above set of equations with the appropriate boundary conditions. A reaction path similar to the curve ABC in Fig. 3.20 would be obtained. The size of reactor necessary to achieve a specified conversion could be assessed by tabulating points at which the reaction path crosses the constant rate contours, hence giving values of kYT which could be used to integrate the mass balance equation 3.87. The reaction path would be suitable provided the maximum temperature attained was not deleterious to the catalyst activity. 

A contour plot given in Figure 5.17 shows how TAC varies in a two-stage adiabatic reactor system with interstage cooling. The reactant ratio yRA/yRB is fixed at unity in this figure, so there are two design optimization variables, the inlet temperatures of the two reactors 7) and T2-... 

The use of the (Na-K) coolant in the first contour, with maximum temperature <400"C makes it possible to have safe normal pressure inside the reactor vessel. All structures and the configuration of die core were chosen to provide maximum nuclear and radiation safety. 

A similar analysis for the two CSTRs in series yields the DC contour maps in Figure 21.26. While the first reactor has disturbance rejection comparable to that for the single reactor, the control variable in the second reactor is saturated at steady state for the worst disturbance direction (feed rate change alone). Hence, even for perfect control in the second reactor, the temperature setpoint cannot be maintained for this disturbance. However, this is mitigated by the fact that the conversion in the second reactor is small, and hence, the offset in Ti is expected to be small. 

Figure 10.10a shows propane conversion contours obtained from 2D CFD calculations for catalytic propane combustion in a non-adiabatic microchannel for the conditions mentioned in the caption [23]. Unlike the homogeneous combustion case, the preheating and combustion zones in catalytic microburners overlap since catalytic reactions can occur on the hot catalyst surface close to the reactor entrance. Figure 10.10b shows a discontinuity in the Nu profile, similar to the homogeneous combustion problem. In this case, it happens at the boundary between the preheat-ing/combustion zone and the post-combustion zone. At this point, the bulk gas temperature (cup-mixing average) and wall temperatures cross over and the direction... 

The conclusion from this contour plot is self-evident. It is interesting to note that a temperature maximum occurs very close to the reactor entrance and then the heat is lost rapidly to the cooling jacket. For higher partial pressures, the peak can reach 1000°C. 

It will be recalled that we already defined J earlier in Chapter 1. We note from Equation 8.17 that a trajectory of slope Cp /-AH on an plot, as shown by line A in Figure 8.6a, represents the path of an adiabatic reaction. The and curves along with the adiabatic line A and the rate contours shown in the X -T plane are central to the design of an adiabatic reactor. Note that this relationship between conversion and temperature is unique to adiabatic reactors and cannot be used for any nonadiabatic situation (i.e., where heat is supplied or ranoved). 

The isothermal and optimal pathway (and any other pathway) can be compared descriptively by a plot of SO2 conversion versus temperature and the curves of equal rate (Figure 6.3.9). The shape of these contours is dear At a constant conversion, the rate first increases with temperature but then decreases as the influence of the equilibrium becomes strong. The optimal pathway to minimize the reactor size (dashed line) is the one on top of the mountains. ... 

A tube reactor of 20 m was simulated to show the performance of the reactor as a function of the length. The thermodynamic upper limit of hydrogen purity on dry basis at 10 bar total pressure and a temperature of 848 K with lithium zirconate as acceptor is 91 mole%. Very long reactors and low space velocities are required to reach the equilibrium composition due to the limitations of the C02-capture kinetics. A contour plot of the dry hydrogen fraction is shown in Fig. 11.9. It is observed that... 

Figure 3-8 presents a map of alternator load capability (solid lines) ranging from 25 to 200 kWe, reactor inlet temperature (dashed lines) with ranges from 740 to 970 K, and cycle efficiency (contour color map) with ranges from 0.08 to 0.259 for a 2-2-2s system architecture. The proposed reactor vessel material for Prometheus is a Ni-based superalloy, which is cooled by the reactor inlet flow. A design temperature of 900K is the near the limit for acceptable creep allowance. Plant operation is envisioned to control the turbine inlet temperature, by reactor reflector motion, and Brayton speed to not exceed the blue line (constant reactor inlet temperature) on Figure 3-8. 

The typical temperature and species-concentration contour map obtained by the CFD simulation are shown in Fig. 13.13.This map emphasizes that the heat supply to the catalyst bed is very important for membrane reactor performance. 

The contour map of temperature and molar fractions of three components, CfiH,2, CfiHfi and H, in the axial cross-section of the membrane reactor... 

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