Axial temperature profile

Figure 10. Axial temperature profiles during methanation Top, experiment HGR-13 and bottom, experiment HGR-14...

With decreasing cell size, the temperature difference between the wall of the cell and the eatalyst partiele in the cell would decrease to zero. For sufficiently small cell dimensions, we may assume the two temperatures are the same. In this case, the heat conduction through the wall becomes dominant and affects the axial temperature profile. As the external heat exchange is absent and the outside of the reactor is normally insulated, the temperature profile is flat along the direction transverse to the reactant flow, and the conditions in all channels are identical to each other. The energy balance is... 

A main objective of the work of Hardt et al. was to study the influence of heat transfer on the achievable molar flux per unit reactor volume of the product species. They compared unstructured channels to channels containing micro fins such as shown in Figure 2.31. Heat transfer enhancement due to micro fins resulted in a different axial temperature profile with a higher outlet temperature in the reaction gas channel. Owing to this effect and by virtue of the temperature dependence... 

Equation 21.5-6 is in a form to determine the axial temperature profile through the catalyst bed. To determine W firm equation 21.54, however, we transform 21.5-6 to relate /A and T, corresponding to equation (D) in Example 15-7 for adiabatic operation... 

The growth rate is quite sensitive to the axial temperature profile. An axial temperature profile that increases along the reactor because it improves the deposition uniformity is commonly used in industry. The temperature of each successive zone in the furnace (defined by the furnace elements in Figure E14.5a) can be adjusted by voltage applied to variac heaters. The zone temperatures are assumed constant within each zone, T-,j = 1,..., ntv where ntz is the number of temperature zones to be used,... 

Fig. 3 The inlet temperatures were set at 350, 425 and 500 for these axial temperature profiles.

Area 300 is controlled using a distributed control system (DCS). The DCS monitors and controls all aspects of the SCWO process, including the ignition system, the reactor pressure, the pressure drop across the transpiring wall, the reactor axial temperature profile, the effluent system, and the evaporation/crystallization system. Each of these control functions is accomplished using a network of pressure, flow, temperature, and analytical sensors linked to control valves through DCS control loops. The measurements of reactor pressure and the pressure differential across the reactor liner are especially important since they determine when shutdowns are needed. Reactor pressure and temperature measurements are important because they can indicate unstable operation that causes incomplete reaction. 

An empirical model that describes the axial temperature profile was developed by Cox and Fenner [30] based on the research performed by Edmondson [31]. The model is as follows ... 

Fig. 11. Axial temperature profile in cooled fixed-bed catalytic reactor.

Figure 4 shows the effect of a 10% drop in the inlet gas temperature (from 573 to 515.7 K) on the axial temperature profiles within the reactor for standard type I operating conditions. Although the inlet gas temperature is reduced, the cooling jacket temperature remains unchanged (Tw = 573 K),... 

Figure 28 shows comparisons of the transient gas and solid axial temperature profiles for a step-input change with the full model and the reduced models. The figure shows negligible differences between the profiles at times as short as 10 sec. Concentration results (not shown) show even smaller discrepancies between the profiles. Additional simulations are not shown since all showed minimal differences between the solutions using the different linear models. Thus for the methanation system, Marshall s model reduction provides an accurate 2Nth-order reduced state-space representation of the original 5/Vth-order linear model. 

Fig. 28. Transient axial temperature profiles during start-up, type I conditions.

A detailed experimental exploration of temperature profiles in the reactor packed with the CuO catalyst showed near at the extinction boundary three steady-state axial temperature profiles which were easily reproducible (Fig. 19). There is no simple explanation of these effects so far 55). 

The volumetric liquid holdup, 4>L, depends on the gas/vapor and liquid flows and is calculated via empirical correlations (e.g., Ref. 65). For the determination of axial temperature profiles, differential energy balances are formulated, including the product of the liquid molar holdup and the specific enthalpy as energy capacity. The energy balances written for continuous systems are as follows ... 

Example 5.5 Continuous Heating of a Thin Sheet Consider a thin polymer sheet infinite in the x direction, moving at constant velocity Vq in the negative x direction (Fig. E5.5). The sheet exchanges heat with the surroundings, which is at T = T0, by convection. At x = 0, there is a plane source of heat of intensity q per unit cross-sectional area. Thus the heat source is moving relative to the sheet. It is more convenient, however, to have the coordinate system located at the source. Our objective is to calculate the axial temperature profile T(x) and the intensity of the heat source to achieve a given maximum temperature. We assume that the sheet is thin, that temperature at any x is uniform, and that the thermophysical properties are constant. 

Fig. 1.24. Steady-state, axial temperature profiles for the gasoline reformerin Figure 1.21. (a) High load 33 kWi Hv (b) low load 3 kWlhv ...

Steady State Axial Temperature Profiles In Wall Cooled Fixed Bed Reactors... 

Figure 10. Axial temperature profiles in a wall cooled reactor. Conditions yC,He = 0.005 T — 613 K and Rep = 20. Key , measured points -------, calculated with uniform flow and---, calcu-...

Figure 11. Axial temperature profiles in a wall cooled reactor. Conditions and key are the same as in Figure 10.

The catalytic CO oxidation by pure oxygen was selected as a model reaction. The Pt/alumina catalyst In the form of 3.4 mm spherical pellets was used. The CO used In this study was obtained by a thermal decomposition of formic acid In a hot sulphuric acid. The reactor was constructed by three coaxial glass tubes. Through the outer jacket silicon oil was pumped, while air was blown through the inner jacket as a cooling medium. The catalyst was placed in the central part of the tube. The axial temperature profiles were measured by a thermocouple moving axially in a thermowell. Gas analysis was performed by an infrared analyzer or by a thermal conductivity cell. [7]. 

A detailed experimental study of operating conditions in a nonadiabatic fixed bed reactor revealed that for certain inlet conditions oscillatory or erratic behavior of temperature profiles can be observed [23]. To follow this phenomenon local thermocouple temperature reading and axial temperature profiles were monitored. The results of measurements are reported in Fig. 3. 

Although two reactors are shown in Figure 1, they were not used simultaneously. The reactor shown in the center was the fixed bed reactor which is of primary interest in this contribution. It consisted of a 12.7 mm diameter X 250 mm long steel tube packed with 40/50 mesh catalyst (0.3 mm average particle diameter). The reactor was heated by a nichrome wire coil and was well insulated. The coil spacing was adjusted and was packed in insulation with the intent of making the reactor crudely adiabatic. A variac controlled heater on the reactor inlet and a thermocouple sensor kept the feed to the reactor at the nominal reaction (or feed inlet) temperature of 400°C. The tube of the fixed-bed, reactor was fitted with 12 thermocouples to record the axial temperature profile in the bed (Figure 1). 

Steady-State Behaviour The dashed line in Figure 2 shows a typical experimental axial temperature profile for conditions listed in Table I. The banded region in the vicinity of the hot spot includes those points (labelled a, b and c) in which radial temperature profiles were also measured using moving thermocouples. There, the upper and lower lines represent the highest measured temperature and the wall temperature, respectively, at those axial points. 

Figure 2. Typical steady-state axial temperature profiles. Key -A-A-, simulated catalyst surface temperature -V-V-, simulated gas temperature and...

The sensitivity of the axial temperature profile to the feed and salt bath temperatures is shown in Figures 6 and 7, respectively. Figure 6 shows the response to a ramp decrease in the feed temperature by 2 C over a period of 10 minutes. For small perturbations (up to 5°C), the hot spot travels downstream and passes through a maximum value before reaching its new steady-state. When the disturbance is reversed, the hot spot moves upstream in a similar manner and returns to the former steady-state. 

Heat transfer studies on fixed beds have almost invariably been made on tubes of large diameter by measuring radial temperature profiles (1). The correlations so obtained involve large extrapolations of tube diameter and are of questionable validity in the design of many industrial reactors, involving the use of narrow tubes. In such beds it is only possible to measure an axial temperature profile, usually that along the central axis (2), from which an overall heat transfer coefficient (U) can be determined. The overall heat transfer coefficient (U) can be then used in one--dimensional reactor models to obtain a preliminary impression of longitudinal product and temperature distributions. 

Some measured axial temperature profiles are displayed in Fig. 2 at various air flow rates. The data are plotted as ln0vs. bed depth z, where 0=Tg-T(z), and z is the axial distance measured from the top of the reactor tube (Fig. 1). At bed depths between 20 and 30 cms. radial temperature and velocity profiles become fully developed and all the plots become linear. The overall heat transfer coefficient (U) can then be obtained simply from the slope of the lines, since... 

In practice the heat effects associated with chemical reactions result in nonisothermal conditions. In the case of a batch reactor the temperature changes as a function of time, whereas an axial temperature profile is established in a plug flow reactor. The application of the law of conservation of energy, in a similar... 

The liquid is initially distributed by means of four small 1/16" pipes. An inert bed, realized with inert alumina pellets, ensured preheating, liquid saturation and an uniform distribution of both fluids. The reactor is provided with an axial thermocouple well. A sliding thermocouple can be moved along the bed axis allowing to measure the axial temperature profile and to check the isothermal operation of the reactor. 

Figure 3. Representative Axial Temperature Profiles Start Up Run 6 Low Benzene.

---