Axial conversion profile

Figure 5. Computed axial conversion profile with changes of variable G, (ratio of conductive to convective heat transfer)...

Figure 8. Computed axial conversion profiles for changes of variable G3 (activation energy group)...

The data in Table II pertaining to pyrolysis conditions shows that all four feedstocks were pyrolyzed under substantially similar conditions, namely steam-to-hydrocarbon weight ratios of 0.9 0.1, residence times of 0.3 sec, reactor exit pressures of 2.0 bar absolute, and reactor exit temperatures of 835°C. Care also was taken to maintain identical axial temperature profiles in the reactor for each of these runs. No unambiguous measure of substrate conversion during pyrolysis is possible for distillate feedstocks of the type used in the present experiments in terms of the empirical kinetic severity function of Zdonik et al. (5), all of the present experiments were conducted at a severity of about 2. 

With a proper choice of all individual internal flow rates in sections I to IV and the velocity of the stationary phase, the feed mixture can be completely separated. Complete separation leads to a distribution of the fluid concentrations as displayed in the axial concentration profile in Fig. 5.17. Since the TMB process reaches a steady state, it can be seen from the diagram that pure component B can be withdrawn with the extract stream. Conversely, the raffinate line contains pure component A only. 

The objective is to solve Eqs. (13-42) and (13-20) for the temperature and conversion at any point in the catalyst bed. As boundary conditions at the entrance we need the temperature and conversion profile across the diameter of the reactor. Further boundary conditions applicable at any axial location are that the conversion is flat (dx/dr = 0) at both the centerline and the wall of the tube. The temperature gradient at the centerline is zero, but the condition at the wall is determined by the heat-transfer character-... 

To quantify the effect of the incomplete mixing on reaction rates in the front of the reactor channel, this same simulation was repeated assuming second order kinetics (first order in each of the two components) and Cjj = C2j = 100 mol m. A rate constant of 1.0 X 10 m moh s was used to give an intermediate level of conversion (near 25%). This case can be compared with a simulation in which the inlet boimdary conditions were changed to assume complete mixing (50 mol m of each component across the entire inlet cross section). The axial fractional conversion profiles for these two cases (unmixed and premixed feeds) are shown in Fig. 13.4, where the unmixed feed curve is the average of the calculated values for the two components. The computed conversions for the two components were... 

Figure 3 shows the effect of feed tenperature on the axial temperature profile. In all these cases, the cyclohexene conversion is 80% with total selectivity toward cyclohexene. The hot spot tenq)erature in the bed increases proportionally to the feed temperature and does not show any runaway tendencies. This is... 

One of the inconveniences of TS-PFR methods is that it is difficult, in fact impossible, to compare conversions calculated using the fitted rate expression with raw TS-PFR data. This point was raised previously in connection with the investigation of carbon monoxide oxidation. One can simulate kinetic behaviour using the above equations and parameters to produce the expected isothermal behaviour of the system but not that observed in the experimental results that are obtained from the TS-PFR during temperature ramping. This is unavoidable and results from our lack of knowledge of the axial temperature profile in the experimental set-up. 

More tests are needed comparing measured conversions and temperature profiles with model predictions for tubular reactors. Comparisons will be easier for reactions with simple kinetics than for complex reactions such as partial oxidations. Tests should be made over a wide range of Reynolds numbers, which may require high velocities and long reactors. If kinetic data are uncertain or unavailable, the overall heat transfer coefficient for the 1-D model can be obtained from the axial temperature profile and the total heat removal [41] ... 

Figure 12.2 Axial conversion and temperature profiles for aniline production in a non-isothermal nonadiabatic reactor (model A2-a).

For given reaction conditions and residence time in a PFR, the axial concentration profile and the outlet conversion depends strongly on the ratio between mixing time and characteristic reaction time. This ratio can be interpreted as a second Damkohler number for mixing Dall. ... 

Figure 5.17 Axial temperature and conversion profile (Example 5.3).

Figure 5.19 Axial temperature (a) and conversion profile (b) in a cooled microchannel for different cooling intensity, N (rr = 1, Tg = T ).

Figure 3. (a) The space velocity distribution and (b) the axial and radial conversion profiles in a cylindirical monolith. The conversion results presented here are determined with a feed composition representative of net oxidizing conditions. 

Lattner and Harold [56] performed autothermal reforming of methanol in a relatively big fixed-bed reactor carrying 380 g BASF alumina-supported copper/zinc oxide catalyst modified with zirconia. The 01C ratio was set to 0.22 while the SIC ratio varied from 0.8 to 1.5. The axial temperature profile of the reactor, which had a length of 50 cm, was rather flat, the hot spot temperature did not exceed 280° C which was achieved by the air distribution system through porous ceramic membrane tubes. More than 95% conversion was achieved. Very low carbon dioxide formation was observed for this reactor only 0.4 vol.% was found in the reformate. However, the WHSV calculated from the data of Lattner and Harold [56] reveals a low value of only 6 l/(h gcat) for the highest CHSV of 10 000 h reported. 

Davis, Ouwerkerk and Venkatesh developed a mathematical model to predict the conversion and temperature distribution in the reactor as a function of the gas and liquid flow rates, physical properties, the feed composition of the reactive gas and carrier gas and other parameters of the system. Transverse and axial temperature profiles are calculated for the laminar flow of the liquid phase with co-current flow of a turbulent gas to establish the peak temperatures in the reactor as a function of the numerous parameters of the system. Also in this model, the reaction rate in the liquid film is considered to be controlled by the rate of transport of reactive gas from the turbulent gas mixture to the gas - liquid interface. The predicted reactor characteristics are shown to agree with large-scale reactor performance. For the calculations of the mass transfer coefficient in the gas phase, kg, Davis et al. used the same correlation as Johnson and Crynes, but multiplied the calculated values arbitrarily by a factor 2 to include the effect of ripples on the organic liquid film caused by the high SOj/air velocities in the core of the reactor. 

For adiabatic prereformers it was demonstrated [347] that the axial temperature profile could be ealculated simply from the fractional conversion of the higher hydrocarbons (naphtha), assuming all other eomponents at equilibrium. 

At 290 °C reaction temperature and a feed composition of 9 vol.% methanol and 11% water, which corresponded to S/C 1.2,65% methanol conversion could be achieved at 99% hydrogen selectivity over CuZns samples treated by acid leaching for 20 min. Under autothermal conditions, more than 25% methanol conversion was achieved at S/C 1.2 and 0/C 0.3, while the oxygen was fully converted. Later, Homy et al. improved their catalyst by doping with chromium [482]. At S/C 1.0 and 0/C 0.25, axial temperature profiles were determined over the reactor to determine the hot spot formation. The hot spot did not exceed 3 K due to the high heat conductivity ofthe brass. A fixed catalyst bed showed a hot spot of about 20 K under comparable conditions. 

Roll and Hedden developed a one-dimensional model for the semi-technical gasifier. This model describes (i) the trajectories of the reed particles, (ii) the axial temperature profiles of the gas phase and of the reactor wall, (iii) the conversion of the reed particles by pyrolysis and gasification of the char formed, and (iv) the quantity and composition of the product gas. 

Radial conversion (a) and temperature (b) profiles in two-dimensional heterogeneous model with porosity and velocity profiles, (c) Comparison of radially averaged axial temperature profiles for 2D pseudo-homogeneous and heterogeneous models, djdp = 5.8 Rep = 175 [Papageorgiou and Froment, 1995]. 

Figure 8.3. A qualitative picture of axial conversion and temperature profiles in an adiabatic tubular reactor, for an exothermic reaction.

The calculated and experimental temperature distribution is shown in Fig. 18. The fit of the axial concentration profile was even better. A perfect fit cannot be expected because of the simplified reactor model and reaction model and the use of constant average parameter values throughout the whole reactor. On the other hand, the agreement between simulation and experiment seems to be sufficient for a study of the behavior of industrial multitube reactors with larger tube diameters. It turned out that for a maximum allowable entrance temperature of 640 K and a conversion larger than 95 %, as demanded by economic considerations, the tube diameter has to be limited to 10 cm, a result that is in excellent agreement with reports on technical units. 

After the input has been read and sorted, heat transfer coefficients and other thermodunamic data are calculated at the beginning of each catalyst zone. Temperature and conversion profile in the catalyst bed is then calculated by an axial integration. The mathematical model used in the integrations is described in. This model allows in principle the determination of diffusion restrictions and calculation of effectiveness factors for each reaction in cases where several reactions take place simultaneously. In such cases the concept of effectiveness factor may become rather dubious as shown below for the methanol synthesis, and this may be reflected in difficulties in the calculations. 

Radial density gradients in FCC and other large-diameter pneumatic transfer risers reflect gas—soHd maldistributions and reduce product yields. Cold-flow units are used to measure the transverse catalyst profiles as functions of gas velocity, catalyst flux, and inlet design. Impacts of measured flow distributions have been evaluated using a simple four lump kinetic model and assuming dispersed catalyst clusters where all the reactions are assumed to occur coupled with a continuous gas phase. A 3 wt % conversion advantage is determined for injection feed around the riser circumference as compared with an axial injection design (28). 

At this point the computer takes over. Gases with several values of jacket temperature and several values of heat-transfer coefficient, or hU/kg, are examined, and also several assumptions about the temperature at the wall at the inlet. Eq. (U) with n = 0 could be used. The number of axial increments are found for several cases of 50% conversion. Two of the profiles of temperature or conversion are shown in Fig. 23-6. 

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