Reactors, tubular

As shown in Table 3.1, tubular reactors could be of different types. A very large number of heterogeneous catalytic reactions are carried out in a tubular reactor of one type or another. In tubular reactors the reactant is fed in from one end of the tube with the help of a pump, and the product is removed from the other end of the tube. The other reactants, if there are any, may be introduced either at the reactor entrance in a cocurrent fashion, or from the reactor exit in a countercurrent fashion (Fig. 3.3). 

The tube is generally packed with solid catalyst and/or inert packing to force good mixing and intimate contact between the reacting liquids and the catalyst. These reactors have simple construction and are always operated in the continuous mode. These reactors are the preferred ones when there is a likelihood 

Exxon and Phillips manufacture polypropylene in tubular reactors where the monomer is in the liquid form (see Section 6.8.2). One of the manufacturing processes for polyethylene involves the use of a loop reactor that has a recycle configuration. Here, under elevated pressure and temperature, a mixture of the catalyst, comonomer, hydrogen, and a solvent are introduced from one end of the reactor. The product and the unreacted starting materials are collected at the other end, and recycled back into the reactor. 

In tubular reactors, heat is removed either by providing cooling tubes running parallel inside the reactor, or through external heat exchangers. Radial temperature gradients are normally observed in tubular reactors. In the case of exothermic reactions the temperature is maximum at the center of the tube and minimum at the tube wall. Similarly, in the case of endothermic reactions the temperature is minimum at the center of the tube and maximum at the tube wall. For highly exothermic reactions, packed bed reactors are usually avoided. 

In packed bed reactors the solid catalyst is held stationary by plates at the top and bottom of the bed. In contrast, in fluidized bed reactors, the catalyst bed is relatively loosely packed, and there is no plate at the top. Rapid fluid flow from the bottom raises the bed and ensures good mixing, leading to insignificant temperature or concentration gradients. However, due to high fluid velocity some catalyst carryover is common. 

For a constant density system, the scalar concentration Cj( ,(p,x,f) of species j in a tubular reactor of uniform cross-section Q with unidirectional laminar flow (Fig. 1) obeys the CDR equation 

Using a (radius of the pipe) and L (length of the pipe) as the characteristic lengths in the transverse and axial directions, respectively, CR as the reference concentration, and Dm R as the reference molecular diffusivity, we obtain four time scales in the system associated with convection (ic), local/transverse diffusion (tD), axial diffusion tz), and reaction (tR), 

As in the previous problems, we assume that p 1 while Da, Kj, and Pet are order-one parameters. The boundary and initial conditions on the model are given by 

We now consider some important limiting cases of this model. First, we note that when axial molecular diffusion is negligible, Eqs. (130)—(131) reduce to hyperbolic model  

Under steady-state conditions (and assuming that the inlet condition is independent of time), this two-mode model can be further simplified to 

Gas-phase reactions are carried out primarily in tubular reactors where the flo is generally turbulent. By a.ssuming that there is no dispersion and there are n radial gradients in either temperature, velocity, or concentration, we can modi the flow in the reactor as plug-flow. 

Laminar teactots are discussed in Chapter 13 and dispersion effects in Chapter The differential form of the PFR design equation 

Use this differenctial form of the PFR/PBR mote balances when there is iP. 

We shall lirsi consider the reaction to lake place as a liquid-phase reaction and then to take place as a ga.s-phase reaction. 

This equation gives the reactor volume to achieve a conversion X. Dividing by H, ( C = Wih) and solving for conversion, we find 

Many papers have been published in the last 20 years or so on modeling and simulation analysis of tubular reactors. It is difficult to make a clear statement on the validity of these analyses usually because of the lack of experimental verifications. When the velocity profile varies along the tube, a prediction of reactor performance is not much more complex theoretically, but its application to real systems is very difficult (if not impossible) because of lack of information on how the velocity profile changes along the tube at high monomer conversions (and viscosities). 

Computational fluid dynamics (CFD) approaches are emerging as alternative detailed tools for examining polymerization systems with complex mixing and reactor components. Recent examples on LDPE cases include Kolhapure and Fox [118], micromixing effects in tubular reactors Zhou etal. [119], tubular (and autoclave) reactors Wells and Ray [120], analysis of imperfect mixing effects applicable to many reactive flow systems, including LDPE autoclaves and Buchelli etal. [121], fouling effects. 

High-pressure autoclaves for LDPE production represent a special class of (usually elongated) reactors, the analysis of which is handled via combinations of well-mixed and plug flow (with recycle) reactor elements. Information and models can be found in references 122-126. 

For a practically useful tubular reactor model, the reacting (polymerizing) mixture is considered homogeneous and only axial dispersion is considered. At each specific position along the tube, perfect radial mixing and a uniform velocity profile are assumed. The tube, therefore, can be modeled as a one-dimensional tubular reactor. Also, instantaneous fluid dynamics are assumed because of the incompressibility of the liquid mixture (hence the calculation of the velocity profile is simplified). 

A mass (material) balance equation for each chemical species h is given by  

Axial mixing in reactors with predominant axial flow can also be modelled by a cascade of a large number of perfectly mixed CSTR s, as described in section 7.1.3. It appears that the residence time distribution (RTD) of a tubular reactor with axial mixing can approach the RTD of a cascade of N perfectly mixed CSTR s when the following condition applies 

Note that this equation has no physical significance It is only for first order reactions that these two models pr ict the same conversion for the same mean residence time. There is, however, an important physical difference between the two models in the cascade model there is no bacl xing from reactor number N to reactor number N-1, whereas in the model for plug flow with axial dispersion there is only one discontinuity, that is at the reactor entrance. 

In order to calculate the conversion of a reaction the axial mixing coefficient has to be known. There are ample experimental data available. In principle, the axial mixing coefficient of a component A is determined by flow conditions and by the diffusivity of A, Generally speaking, the Bodenstein number for axial mixing is a function of the Reynolds and Schmidt numbers (for definitions see eq. 4.23)  

For turbulent flow in empty tubes the following relation has been found by Taylor (1954)  

Apparently, in well developed turbulent flow in tubes the Bodenstein number is ateut 3-5. Note that the coefficient of axial mixing decreases slightly with increasing velocity of flow. 

In continuous operation mode, both feed and effluent streams flow continuously. The main characteristic of a continuous stirred tank reactor (CSTR) is the broad residence time distribution (RTD), which is characterized by a decreasing exponential function. The same behavior describes the age of the particles in the reactor and hence the particle size distribution (PSD) at the exit. Therefore, it is not possible to obtain narrow monodisperse latexes using a single CSTR. In addition, CSTRs are hable to suffer intermittent nucleations [89, 90) that lead to multimodal PSDs. This may be alleviated by using a tubular reactor before the CSTR, in which polymer particles are formed in a smooth way [91]. On the other hand, the copolymer composition is quite constant, even though it is different from that of the feed. 

From a safety point of view, tubular reactors are advantageous because they have a large area/volume ratio and hence the heat removal capacity is higher than that of the CSTR. 

The wicker-tube reactor consists of a coiled tube which meanders between solid, fixed, cylindrical supports. The heat removal capacity is high and it is claimed that the multiple changes in flow dhection allow the production of a polymer dispersion with a very low coagulum content [103,104]. 

If the feed is stopped immediately in the case of malfunction, the CSTR is uncritical the non-converted reactant is only 1%, resulting in a ATai of ca. 1 °C only. This result enhances the strength of the CSTR in its behavior after cooling failure. The CSTR is a practicable and elegant solution for the industrial performance of this fast and exothermal reaction. Since the technique is based on a stirred tank, it does not require high investment for it to be realized in a traditional multipurpose plant. 

For a given tube radius there exists a particular wall temperature that gives maximum conversions in free-radical polymerizations. This can be seen qualitatively from the following considerations. If the tube wall is loo cool, the initiator will be slowly decomposed and some of it will leave the reactor unconsumed. However, the activation energy for initiator decomposition exceeds that for consumption of monomer (Section 6.16.1), and the initiator can be entirely decomposed at low monomer conversions if the wall temperature is too high for the particular reaction system [2]. 

Theonly important current application of tubular reactors in polymer syntheses is in the production of high pressure, low density polyethylene. In tubular processes, the newer reactors typically have inside diameters about 2.5 cm and lengths of the order of I km. Ethylene, a free-radical initiator, and a chain transfer agent are injected at the tube inlet and sometimes downstream as well. The high heat of polymerization causes nonisothermal conditions with the temperature increasing towards the tube center and away from the inlet. A typical axial temperature profile peaks some distance down the tube where the bulk of the initiator has been consumed. The reactors are operated at 200-300°C and 2000-3000 atm pressure. 

The ethylene and polyethylene leave the reactor and pass into a primary separation vessel which operates at a much lower pressure than the reactor itself. Most of the ethylene (and any comonomer) is flashed off in this unit and recycled through compressors to the tube inlet. Conversion per pass is of the order of 30% with ethylene flow rates about 40,000 kg/h. 

In many cases the reactor exit valve is opened and partially closed periodically to impose a pressure and flow pulse that helps keep the tube from plugging with polymer. Substantial pressure fluctuations occur in the reactor with this mode of operation. 

The equations of momentum, heat and mass transfer obviously apply to polymer systems, and they can sometimes be solved more accurately than for systems of small molecules. The reason for this is the high viscosities that lead to laminar flow. 

Consider a homogeneous solution polymerization occurring in a circular tube. We suppose the flow to be steady, axisymmetric, and Newtonian. The equation of motion for the axial velocity component is  

For the very low Reynolds numbers typical of polymer solutions, this general equation can be closely approximated as 

The axial velocity can thus be found from knowledge of /i(r, z) which in turn can be found from knowledge of the temperature and composition field in the reactor. The above formulation allows ju to be a rapidly varying function of r, but it must vary slowly in the z direction otherwise and derivatives such as 5v /5z, which are ignored in equation (4.35) will become important. 

Whenever fi changes in the axial direction, some radial velocities must exist. Even though they may be negligible with respect to equation (4.35), they can be calculated from the continuity equation  

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Because the characteristic of tubular reactors approximates plug-flow, they are used if careful control of residence time is important, as in the case where there are multiple reactions in series. High surface area to volume ratios are possible, which is an advantage if high rates of heat transfer are required. It is sometimes possible to approach isothermal conditions or a predetermined temperature profile by careful design of the heat transfer arrangements. 

Tubular reactors, as previously stated, are also advantageous for high-pressure reactions where smaller-diameter cylindrical vessels can be used to allow thinner vessel walls. Tubular reactors should be avoided when carrying out multiphase reactions, since it is often difficult to achieve good mixing between phases. 

As an example of the application of a fixed-bed tubular reactor, consider the production of methanol. Synthesis gas (a mixture of hydrogen, carbon monoxide, and carbon dioxide) is reacted over a copper-based cat dyst. The main reactions are... 

Very strong stirring equipment is needed for mixing because of the high viscosity, and long tubular reactors with low cross-sectional area are needed for heat exchange. 

Tubular membranes Tubular modules Tubular reactors Tubulates b-Tubulin Tubulin Tuffs Tufperm Tufprene... 

In this pyrolysis, sub atmospheric partial pressures are achieved by employing a diluent such as steam. Because of the corrosive nature of the acids (HE and HCl) formed, the reactor design should include a platinum-lined tubular reactor made of nickel to allow atmospheric pressure reactions to be mn in the presence of a diluent. Because the pyrolysate contains numerous by-products that adversely affect polymerization, the TFE must be purified. Refinement of TFE is an extremely complex process, which contributes to the high cost of the monomer. Inhibitors are added to the purified monomer to avoid polymerization during storage terpenes such as t7-limonene and terpene B are effective (10). 

Economic evaluations of algal production indicate that production costs vary from 0.15 to 4.00/kg of algal product, depending on type of bioreactor, culture technique, and operating conditions (51). For systems with controlled agitation and carbonation, including raceways and tubular reactors, production costs ate estimated to range from 2.00 to 4.00/kg. 

Tubes having a wide range of bore sizes are required to operate at pressures in the region of 150—300 MPa (22—44,000 psi). SmaU bore tubes, say 3—15 mm dia, are used to supply lubricant to the packing cups of secondary compressors, initiator to reactors, etc, while larger bore tubes, say 25—75 mm bore dia, are used to connect compressors to reactors and for the constmction of coolers and tubular reactors. 

Reaction conditions depend on the composition of the bauxite ore, and particularly on whether it contains primarily gibbsite, Al(OH)2, or boehmite [1318-23-6] AlOOH. The dissolution process is conducted in large, stirred vessels or alternatively in a tubular reactor. The process originated as a batch process, but has been converted to a continuous one, using a series of stirred tank reactors or a tubular reactor. 

Fig. 4. Continuous tubular reactor design. Courtesy of BatteUe.

Other above-ground continuous flow systems have been designed and operated for SCWO processes. A system developed by ModeU Development Corp. (Modec) uses a tubular reactor and can be operated at temperatures above 500°C. It employs a pressure letdown system in which soHd, Hquids, and gases are separated prior to pressure release. This simplifies valve design and material selection on the Hquid leg. 

Manufacture and Uses. Acetoacetic esters are generally made from diketene and the corresponding alcohol as a solvent ia the presence of a catalyst. In the case of Hquid alcohols, manufacturiag is carried out by continuous reaction ia a tubular reactor with carefully adjusted feeds of diketene, alcohol, and catalyst, or alcohol—catalyst blend followed by continuous purification (Fig. 3). For soHd alcohols, an iaert solvent is used. Catalysts used iaclude strong acids, tertiary amines, salts such as sodium acetate [127-09-3], organophosphoms compounds, and organometaHic compounds (5). 

Classification of the many different encapsulation processes is usehil. Previous schemes employing the categories chemical or physical are unsatisfactory because many so-called chemical processes involve exclusively physical phenomena, whereas so-called physical processes can utilize chemical phenomena. An alternative approach is to classify all encapsulation processes as either Type A or Type B processes. Type A processes are defined as those in which capsule formation occurs entirely in a Hquid-filled stirred tank or tubular reactor. Emulsion and dispersion stabiUty play a key role in determining the success of such processes. Type B processes are processes in which capsule formation occurs because a coating is sprayed or deposited in some manner onto the surface of a Hquid or soHd core material dispersed in a gas phase or vacuum. This category also includes processes in which Hquid droplets containing core material are sprayed into a gas phase and subsequentiy solidified to produce microcapsules. Emulsion and dispersion stabilization can play a key role in the success of Type B processes also. 

LDPE is produced in either a stirred autoclave or a tubular reactor total domestic production, divided between the two systems at 45% for tubular and 55% for autoclave, is estimated to be 3.4 million metric tons per year (5). Neither process has gained a clear advantage over the other, although all new or added capacity production in the 1990s has been through the autoclave. 

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). 

Continuous-flow stirred-tank reactors ia series are simpler and easier to design for isothermal operation than are tubular reactors. Reactions with narrow operating temperature ranges or those requiring close control of reactant concentrations for optimum selectivity benefit from series arrangements. 

Flow in tubular reactors can be laminar, as with viscous fluids in small-diameter tubes, and greatly deviate from ideal plug-flow behavior, or turbulent, as with gases, and consequently closer to the ideal (Fig. 2). Turbulent flow generally is preferred to laminar flow, because mixing and heat transfer... 

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... 

Fig. 21. A low density polyethylene tubular reactor used by Phillips Petroleum (85).

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