The tubular reactor

The tubular reactor is a relatively common component on chemical plants. The reactants enter at one end and the products leave from the other, with a continuous variation in the composition and the temperature of the reacting mixture in between. It is common for the feed to consist of a mixture of gases, as in the case of ammonia and methanol synthesis, where the feed gas passes through a densely packed catalyst bed which promotes a number of different reactions simultaneously. 

The actual configuration of the reactor may take various forms depending on the precise requirements of the process. For example, for a high-temperature homogeneous gas-phase reaction such as naphtha cracking, the reactor may be simply a long tube in a furnace [Fig. 6(a)]. In other cases, the single tube is replaced by a number of tubes in parallel as shown in Fig. 6(b). 

The flow pattern within the reactor will depend on various factors. In a simple tubular reactor without packing at Reynolds numbers greater 

THE SIMPLEST DISTRIBUTED MODEL Example 1 The Tubular Reactor 

This is a partial differential equation, as we should expect from a plug-flow tubular reactor with a single reaction. We note in passing that the solution requires the specification of an initial distribution and a boundary, or feed, value. These are both functions (the first of z because t = 0 the second of t because z = 0) in the distributed system. Of the corresponding quantities, c0 and cin, in the lumped system, the latter is embodied in the ordinary differential equation itself and the former is the initial value. 

If we want to avoid the use of infinitesimals, we may certainly do the balance over an arbitrary section of the tube, for example, a z b. Then 

FIGURE 2 Finite and infinitesimal balances on the plug flow reactor P.  

This is true for an arbitrary section of the reactor, and it follows that, if the integrand is continuous, the integrand must also vanish everywhere (Fig. 2). For, if it did not vanish at a point of continuity, but were, for instance, positive there, then there would have to be a finite interval in which it remained positive and, no matter how small this interval might be, a and b could be chosen within it and Eq. (24) would be violated. Thus, we arrive again at Eq. (22). 

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Initiators. The degree of polymerization is controlled by the addition rate of initiator(s). Initiators (qv) are chosen primarily on the basis of half-life, the time required for one-half of the initiator to decay at a specified temperature. In general, initiators of longer half-Hves are chosen as the desired reaction temperature increases they must be well dispersed in the reactor prior to the time any substantial reaction takes place. When choosing an initiator, several factors must be considered. For the autoclave reactor, these factors include the time permitted for completion of reaction in each zone, how well the reactor is stirred, the desired reaction temperature, initiator solubiUty in the carrier, and the cost of initiator in terms of active oxygen content. For the tubular reactors, an additional factor to take into account is the position of the peak temperature along the length of the tube (9). 

Specific reactor characteristics depend on the particular use of the reactor as a laboratory, pilot plant, or industrial unit. AH reactors have in common selected characteristics of four basic reactor types the weH-stirred batch reactor, the semibatch reactor, the continuous-flow stirred-tank reactor, and the tubular reactor (Fig. 1). A reactor may be represented by or modeled after one or a combination of these. SuitabHity of a model depends on the extent to which the impacts of the reactions, and thermal and transport processes, are predicted for conditions outside of the database used in developing the model (1-4). 

Tubular Reactors. The tubular reactor is exceUent for obtaining data for fast thermal or catalytic reactions, especiaHy for gaseous feeds. With sufficient volume or catalyst, high conversions, as would take place in a large-scale unit, are obtained conversion represents the integral value of reaction over the length of the tube. Short tubes or pancake-shaped beds are used as differential reactors to obtain instantaneous reaction rates, which can be computed directly because composition changes can be treated as differential amounts. Initial reaction rates are obtained with a fresh feed. Reaction rates at... 

The epitaxy reactor is a specialized variant of the tubular reactor in which gas-phase precursors are produced and transported to a heated surface where thin crystalline films and gaseous by-products are produced by further reaction on the surface. Similar to this chemical vapor deposition (CVE)) are physical vapor depositions (PVE)) and molecular beam generated deposits. Reactor details are critical to assuring uniform, impurity-free deposits and numerous designs have evolved (Fig. 22) (89). 

Figure 3 shows a simple schematic diagram of an oxygen-based process. Ethylene, oxygen, and the recycle gas stream are combined before entering the tubular reactors. The basic equipment for the reaction system is identical to that described for the air-based process, with one exception the purge reactor system is absent and a carbon dioxide removal unit is incorporated. The CO2 removal scheme illustrated is based on a patent by Shell Oil Co. (127), and minimises the loss of valuable ethylene in the process. 

In previous studies, the main tool for process improvement was the tubular reactor. This small version of an industrial reactor tube had to be operated at less severe conditions than the industrial-size reactor. Even then, isothermal conditions could never be achieved and kinetic interpretation was ambiguous. Obviously, better tools and techniques were needed for every part of the project. In particular, a better experimental reactor had to be developed that could produce more precise results at well defined conditions. By that time many home-built recycle reactors (RRs), spinning basket reactors and other laboratory continuous stirred tank reactors (CSTRs) were in use and the subject of publications. Most of these served the original author and his reaction well but few could generate the mass velocities used in actual production units. 

The reaction section consists of the high pressure reactors filled with catalyst, and means to take away or dissipate the high heat of reaction (300-500 Btu/lb of olefin polymerized). In the tubular reactors, the catalyst is inside a multiplicity of tubes which are cooled by a steam-water condensate jacket. Thus, the heat of reaction is utilized to generate high pressure steam. In the chamber process, the catalyst is held in several beds in a drum-type reactor with feed or recycled product introduced as a quench between the individual beds. 

In the tubular reactor, a large amount of reaction heat is removed through the tube walls. 

In actual practice the temp in the region of the converging streams of the second stage reactor is kept between 90 and 120°, and the rest of the tubular reactor between 110 and 140°. 

Valve 29 in line 14 is a quick opening bypass valve which is normally closed. However, in case of an emergency shutdown, this valve can be instantly opened to shut off the supply of alcohol to the reaction zone and return the alcohol stream via line 31 to alcohol supply tank 11. Such a quick opening by-pass valve normally is not employed in the nitrating acid line, since in case of an emergency shutdown, nitrating acid is employed to sweep out the tubular reactor... 

The precondensation can be earned out continuously with the use of a tubular reactor at a temperature of 290-310°C.56 The tubular reactor is a 4-m-long coiled pipe with a diameter of 4 mm which is heated at 300°C. At the end of the pipe is a valve which is regulated so that the pressure is 1.5 bar. The residence time in the pipe is only seconds. The prepolymer obtained can be postcondensed in the solid state to a high molecular weight. 

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 ). 

The solution of Equations (5.23) or (5.24) is more straightforward when temperature and the component concentrations can be used directly as the dependent variables rather than enthalpy and the component fluxes. In any case, however, the initial values, Ti , Pi , Ui , bj ,... must be known at z = 0. Reaction rates and physical properties can then be calculated at = 0 so that the right-hand side of Equations (5.23) or (5.24) can be evaluated. This gives AT, and thus T z + Az), directly in the case of Equation (5.24) and imphcitly via the enthalpy in the case of Equation (5.23). The component equations are evaluated similarly to give a(z + Az), b(z + Az),... either directly or via the concentration fluxes as described in Section 3.1. The pressure equation is evaluated to give P(z + Az). The various auxiliary equations are used as necessary to determine quantities such as u and Ac at the new axial location. Thus, T,a,b,. .. and other necessary variables are determined at the next axial position along the tubular reactor. The axial position variable z can then be incremented and the entire procedure repeated to give temperatures and compositions at yet the next point. Thus, we march down the tube. 

Based on the results of these researchers the tubular reactor in this study has been described by the axisymmetric model using effective diffusivities given by Equation 20. 

To improve the mixing quality in the tubular reactor, Kenics type in-line static mixer reactor was employed. The in-line static mixers were designed to mix two or more fluids efficiently since an improved treinsport process such as flow division, radial eddying, flow constriction, and shear reversal eliminated the gradients in concentration, velocity and temperature. However, only 70 % conversion was achieved with one Kenics mixer unit. As shown in Table 2, five mixer units were required to achieve the maximum conversion. 

Equating the time of passage through the tubular reactor to that of the time required for the batch reaction, gives the equivalent ideal-flow tubular reactor design equation as... 

Again the entrance and exit boundary conditions must be considered. Thus the two boundary conditions at Z = 0 and Z = L are used for solution, as shown in Fig. 4.15. Note, that these boundary conditions refer to the inner side of the tubular reactor. A discontinuity in concentration at Z = 0 is apparent in Fig. 4.16. 

Figure 4.15. Convective and diffusive fluxes at the entrance (Z=0) and exit (Z=L) of the tubular reactor.

Figure 4.16. Concentration profiles in the tubular reactor for extreme and intermediate values of the dispersion number. 

The tubular reactor, steady-state design equation is of interest here. The dimensional and dimensionless forms are compared for an nth-order reaction. 

Rerun Exercise 1 for n = 2 and compare the ratio of volumes, Vtuta. Answer the question in Exercises 1, regarding the required volumes. Suppose a conversion of 90% is desired, and the flow rate to the tank reactor is to be one-half that of the tubular reactor. What would be the ratio of volumes ... 

Figure 5.73. The partial-pressure variables for the tubular reactor are shown.

Other configurations that are used include an concentric electrode setup in a tubular reactor, where the discharge still is capacitivily coupled. Also, inductive coupling has been used, with a coil surrounding the tubular reactor [146, 147]. 

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