Reactor diameter

Fig. 23. Turbulent and bubbling beds scale-up comparison where increasing gas velocity, fines content, and JT/D staging can help maintain reactor efficiency as the reactor diameter increases. A 100% efficiency is equivalent to plug flow.

In cases where a large reactor operates similarly to a CSTR, fluid dynamics sometimes can be estabflshed in a smaller reactor by external recycle of product. For example, the extent of soflds back-mixing and Hquid recirculation increases with reactor diameter in a gas—Hquid—soflds reactor. Consequently, if gas and Hquid velocities are maintained constant when scaling and the same space velocities are used, then the smaller pilot unit should be of the same overall height. The net result is that the large-diameter reactor is well mixed and no temperature gradients occur even with a highly exothermic reaction. 

One goal of catalyst designers is to constmct bench-scale reactors that allow determination of performance data truly indicative of performance in a full-scale commercial reactor. This has been accompHshed in a number of areas, but in general, larger pilot-scale reactors are preferred because they can be more fully instmmented and can provide better engineering data for ultimate scale-up. In reactor selection thought must be given to parameters such as space velocity, linear velocity, and the number of catalyst bodies per reactor diameter in order to properly model heat- and mass-transfer effects. 

Bench-Scale Reactor. The bench-scale reactor is 0.81 in. i.d. and 48 in. long. The nominal feed gas rate for this unit is 30 standard cubic feet per hour (scfh) the feed gas is supplied from premixed, high-pressure gas cylinders. Except for reaction temperature, the bench-scale unit is substantially manually operated and controlled. The catalysts used in these studies were standard commercial methanation catalysts ground to a 16-20 mesh size which is compatible with the small reactor diameter. 

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].

T = temperature p = density AH = heat of reaction h = heat-transfer coefficient D = reactor diameter Cp = heat capacity Rp = polymerization rate Tj = reactor jacket temperature P = pressure... 

It is common practice to use geometric similarity in the scaleup of stirred tanks (but not tubular reactors). This means that the production-scale reactor will have the same shape as the pilot-scale reactor. All linear dimensions such as reactor diameter, impeller diameter, and liquid height will change by the same factor, Surface areas will scale as Now, what happens to tmix upon scaleup ... 

Establish ideal flow patterns This is usually assumed to be the case for plug-flow and continuously stirred tank reactors, but are all conditions for ideal mixing fulfilled For example, a rule of thumb is that the diameter d of the PFR should be at least lOx the diameter of the catalyst particles to eliminate the influence of the reactor wall. Also, the amount of catalyst should be sufficient to avoid axial gradients. Another rule is that the ratio of the bed length L to the reactor diameter d, i.e. L/d, should be >5-10. Higher values are preferable, but these may cause other problems such as temperature gradients and pressure drops. 

An impressive example of the impact of miniaturization on the explosion limit has been given for the oxyhydrogen reaction [18]. For a conventional reactor of 1 m diameter, explosive behavior sets in at 420 °C at ambient pressure (10 Pa). An explosion occurs at about 750 °C, when the reactor diameter is decreased to about 1 mm. A further reduction to 100 pm shifts the explosive regime further to higher pressures and temperatures. 

Fixed-bed reactors are used for testing commercial catalysts of larger particle sizes and to collect data for scale-up (validation of mathematical models, studying the influence of transport processes on overall reactor performance, etc.). Catalyst particles with a size ranging from 1 to 10 mm are tested using reactors of 20 to 100 mm ID. The reactor diameter can be decreased if the catalyst is diluted by fine inert particles the ratio of the reactor diameter to the size of catalyst particles then can be decreased to 3 1 (instead of the 10 to 20 recommended for fixed-bed catalytic reactors). This leads to a lower consumption of reactants. Very important for proper operation of fixed-bed reactors, both in cocurrent and countercurrent mode, is a uniform distribution of both phases over the entire cross-section of the reactor. If this is not the case, reactor performance will be significantly falsified by flow maldistribution. 

The reactor operates at a temperature 270 °C and a pressure of 2.5 bara. The reactor diameter is 10 m. Hydrogen is used in large excess in the reaction, and for the purposes of this exercise the properties of the gas may be taken as those of hydrogen at the reactor conditions. The density of the catalyst particles is 1800 kg/m3. 

The reactor design in terms of ratio of the diameter of the immersion transducer to reactor diameter, liquid height, position of the transducers and characteristics of the cell plays a important role in deciding the cavitational activity distribution and hence the efficacy of sonochemical reactors for the specific application. Based on a critical analysis of the existing literature, following important design related information can be recommended ... 

With an increase in the diameter of immersion transducer relative to the reactor diameter, the cavitational activity increases till an optimum ratio, usually dependent on the application [51,52], The ratio mainly affects the level of turbulent... 

The flow conditions (mass velocity, reactor diameter, etc.). 

Figure 1. Apparent reaction-rate constant vs. reactor diameter and bed height. (From Frye etal., 1958.)...

Figure 4. CO conversion in Hydrocol reaction for several reactor diameters. (From Volk et al., 1962.)...

Understanding the effect of reactor diameter on the volumetric mass transfer coefficient is critical to successful scale up. In studies of a three-phase fluidized bed bioreactor using soft polyurethane particles, Karamanev et al. (1992) found that for a classical fluidized bed bioreactor, kxa could either increase or decrease with a change in reactor diameter, depending on solids holdup, but for a draft tube fluidized bed bioreactor, kxa always increased with increased reactor diameter. 

Steinfeld et al. [133] demonstrated the technical feasibility of solar decomposition of methane using a reactor with a fluidized bed of catalyst particulates. Experimentation was conducted at the Paul Scherrer Institute (PSI, Switzerland) solar furnace delivering up to 15 kW with a peak concentration ratio of 3500 sun. A quartz reactor (diameter 2 cm) with a fluidized bed of Ni (90%)/Al2O3 catalyst and alumina grains was positioned in the focus of the solar furnace. The direct irradiation of the catalyst provided effective heat transfer to the reaction zone. The temperature was maintained below 577°C to prevent rapid deactivation of the catalyst. The outlet gas composition corresponded to 40% conversion of methane to H2 in a single pass. Concentrated solar radiation was used as a source of high-temperature process heat for the production of hydrogen and filamentous... 

In Section I, we mentioned that the TFM can simulate fluidized beds at engineering scales (height 1-2 m), and that the large-scale industrial fluidized-bed reactors (diameter 1-5m, height 3-20m) are still far beyond its capabilities. Clearly, it would be highly desirable to predict the properties of gas-solid flows at the industrial scale however at present, there is no fully evolved model— based on fundamental principles—which is capable of this. In this section, we outline some new ideas in this direction that have been developed both at the... 

Note the different ds in these problems. While d always signifies diameter, D is reactor diameter (or diameter of a cylinder or sphere because that notation is used in mass transfer rather than the radius R), dp is the diameter of a single pore, and d is the diameter of a single tube in a tube waU reactor. 

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