Reactor volume tubular reactors

Some scaling factors depend on the specific type of reactor. For tubular reactors, there are scaling factors for the radius and length that together give the scaling factor for volume ... 

Packed-bed reactors are tubular reactors filled with catalyst particles. In PBRs it is the weight of catalyst W that is important, rather than the reactor volume. The derivation of the dilTerential and integral forms of the design equations for packed-bed reactors are analogous to tho.se for a PFR [cf. Equations (2-15) and (2-16)). That is. substituting Equation (2-12) for Equation (1-15) gives... 

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. 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... 

Tubular reactors have been the main tools to study continuous flow processes for vapor or gas-phase reactions. These are also used for reaction in tv o flowing phases over a solid catalyst. When the catalyst is in a fixed bed, the contact between the liquid on the outside surface of the particulate is uncertain. For slurry-type solid catalyst the residence time of the catalyst or the quantity in the reactor volume can be undefined. 

Peclet number independent of Reynolds number also means that turbulent diffusion or dispersion is directly proportional to the fluid velocity. In general, reactors that are simple in construction, (tubular reactors and adiabatic reactors) approach their ideal condition much better in commercial size then on laboratory scale. On small scale and corresponding low flows, they are handicapped by significant temperature and concentration gradients that are not even well defined. In contrast, recycle reactors and CSTRs come much closer to their ideal state in laboratory sizes than in large equipment. The energy requirement for recycle reaci ors grows with the square of the volume. This limits increases in size or applicable recycle ratios. 

These are less expensive and less troublesome than tubular reactors. All the catalyst volume needed for a given conversion is usually divided in several beds or stages. In large catalyst volumes, the stages may be in separate vessels, or in small volumes in the same vessel but divided into several trays. 

The need to keep a concave temperature profile for a tubular reactor can be derived from the former multi-stage adiabatic reactor example. For this, the total catalyst volume is divided into more and more stages, keeping the flow cross-section and mass flow rate unchanged. It is not too difficult to realize that at multiple small stages and with similar small intercoolers this should become something like a cooled tubular reactor. Mathematically the requirement for a multi-stage reactor can be manipulated to a different form ... 

If the pilot reactor is turbulent and closely approximates piston flow, the larger unit will as well. In isothermal piston flow, reactor performance is determined by the feed composition, feed temperature, and the mean residence time in the reactor. Even when piston flow is a poor approximation, these parameters are rarely, if ever, varied in the scaleup of a tubular reactor. The scaleup factor for throughput is S. To keep t constant, the inventory of mass in the system must also scale as S. When the fluid is incompressible, the volume scales with S. The general case allows the number of tubes, the tube radius, and the tube length to be changed upon scaleup ... 

Consider the gas-phase decomposition A B -b C in an isothermal tubular reactor. The tube i.d. is 1 in. There is no packing. The pressure drop is 1 psi with the outlet at atmospheric pressure. The gas flow rate is O.OSSCF/s. The molecular weights of B and C are 48 and 52, respectively. The entering gas contains 50% A and 50% inerts by volume. The operating temperature is 700°C. The cracking reaction is first order with a rate constant of 0.93 s . How long is the tube and what... 

There is an interior optimum. For this particular numerical example, it occurs when 40% of the reactor volume is in the initial CSTR and 60% is in the downstream PFR. The model reaction is chemically unrealistic but illustrates behavior that can arise with real reactions. An excellent process for the bulk polymerization of styrene consists of a CSTR followed by a tubular post-reactor. The model reaction also demonstrates a phenomenon known as washout which is important in continuous cell culture. If kt is too small, a steady-state reaction cannot be sustained even with initial spiking of component B. A continuous fermentation process will have a maximum flow rate beyond which the initial inoculum of cells will be washed out of the system. At lower flow rates, the cells reproduce fast enough to achieve and hold a steady state. 

Depart from Geometric Similarity. Adding length to a tubular reactor while keeping the diameter constant allows both volume and external area to scale as S if the liquid is incompressible. Scaling in this manner gives poor results for gas-phase reactions. The quantitative aspects of such scaleups are discussed... 

Example 5.11 The results of Table 5.1 suggest that scaling a tubular reactor with constant heat transfer per unit volume is possible, even with the further restriction that the temperature driving force be the same in the large and small units. Find the various scaling factors for this form of scaleup for turbulent liquids and apply them to the pilot reactor in Example 5.10. 

This section derives a simple version of the convective diffusion equation, applicable to tubular reactors with a one-dimensional velocity profile V (r). The starting point is Equation (1.4) applied to the differential volume element shown in Figure 8.9. The volume element is located at point (r, z) and is in the shape of a ring. Note that 0-dependence is ignored so that the results will not be applicable to systems with significant natural convection. Also, convection due to is neglected. Component A is transported by radial and axial diffusion and by axial convection. The diffusive flux is governed by Pick s law. 

Nerve gas is to be thermally decomposed by oxidation using a large excess of air in a 5-cm i.d. tubular reactor that is approximately isothermal at 620°C. The entering concentration of nerve gas is 1% by volume. The outlet concentration must be less than 1 part in lO by volume. The observed half-life for the reaction is 0.2 s. How long should the tube be for an inlet velocity of 2m/s What will be the pressure drop given an atmospheric discharge ... 

The cracking of diphenylmethane (DPM) was carried out in a continuous-flow tubular reactor. The liquid feed contained 29.5 wt.% of DPM (Fluka, >99%), 70% of n-dodecane (Aldrich, >99% solvent) and 0.5% of benzothiophene (Aldrich, 95% source of H2S, to keep the catalyst sulfided during the reaction). The temperature was 673 K and the total pressure 50 bar. The liquid feed flow rate was 16.5 ml.h and the H2 flow rate 24 l.h (STP). The catalytic bed consisted of 1.0 g of catalyst diluted with enough carborundum (Prolabo, 0.34 mm) to reach a final volume of 4 cm. The effluent of the reactor was condensed at high pressure. Liquid samples were taken at regular intervals and analyzed by gas chromatography, using an Intersmat IGC 120 FL, equipped with a flame ionization detector and a capillary column (Alltech CP-Sil-SCB). 

Consider a small element of volume, AV, of an ideal plug-flow tubular reactor, as shown in Fig. 4.6. 

Set the volumetric flow rate and feed concentration for the tank and tubular reactors to desired values. Set also the order of reaction to n = 1.01. Run for a range of fraction conversions from 0 to 0.99. Compare the required volumes for the two reactor types. 

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 ... 

Low density polyethylene is made at high pressures in one of two types of continuous reactor. Autoclave reactors are large stirred pressure vessels, which rely on chilled incoming monomer to remove the heat of polymerization. Tubular reactors consist of long tubes with diameters of approximately 2.5 cm and lengths of up to 600 m. Tubular reactors have a very high surface-to-volume ratio, which permits external cooling to remove the heat of polymerization. 

---