Reactor Bodenstein number

Figure 3.12 Residence time distribution in a micro reactor which is tightened by different means. ( ) Glued reactor without catalyst coating (X) glued reactor with catalyst coating ( ) reactor with graphite joints. Calculated curves for tubular reactors with the Bodenstein number Bo = 33 (solid line) and Bo = 70 (dashed line).

Other factors limiting the overall rate can be external or internal mass transfer, or axial dispersion in a fixed-bed reactor. Pertinent dimensionless numbers are the Biot number Bi, the Damkohler number of the second kind Dan, or the Bodenstein number Bo (Eqs. (5.46)—(5.48)]. 

Table IV presents some data on liquid residence time distributions measured under conditions of hydrocracking in trickle flow. It can be seen that bed dilution with fine inert particles results in a considerable improvement in the plug-flow character of the reactor, which supports the idea that the dispersion is largely determined by the packing of fine particles. Since in the range of Re numbers of interest the Bodenstein number is approximately a constant (see Figure 4), the Peclet numbers for beds of equal length should be inversely proportional to the particle diameter. Dilution of the 1.5 mm particles with 0.2 mm particles should raise Pe by a factor of about 7, which is approximately in line with the data in Table IV.

Tanks-in-Series Model Versus Dispersion Model. We have seen that we can apply both of these one-parameter models to tubular reactors using the variance of the RTD. For first-order reactions the two models can be applied with equal ease. However, the tanks-in-series model is mathematically easier to use to obtain the effluent concentration and conversion for reaction orders other than one and for multiple reactions. However, we need to ask what would be the accuracy of using the tanks-in-series model over the dispersion model. These two models are equivalent when the Peclet-Bodenstein number is related to the number of tanks in series, n, by the equation ... 

Figure 6 shows the example of the reactor dynamics of the dispersion model calculated with a Bodenstein number of 8.8... 

Through similar representations of the residence time distribution of pipe flow reactors and ideally stirred tanks (CSTR) in series, Pawlowski [427] obtained a mutual association of the equivalent Bodenstein number BOeq = vL/DsSm of the plug flow reactor and the equivalent number Neq of the CSTR in series ... 

The dispersion in tubular reactors depends on the flow regime and is characterized by the Bodenstein number, the ratio of the axial diffusion time, tu,ax, in the reactor to the mean fluid residence time, x. 

The axial dispersion in the reactor is often expressed by the axial Peclet number, and the characteristic length, which equals the tube diameter for tubular reactors, and the particle diameter for packed-bed reactors. The Bodenstein number characterizing dispersion in the tubular reactor thus becomes the following ... 

D, which has the same dimension unit as the molecular diffusion coefficient D. Usually is much larger than because it incorporates all effects that may cause deviation from plug flow, such as radial velocity differences, eddies, or vortices. The key parameter determining the width of the RTD is the ratio between the axial dispersion time and the space-time r, which corresponds to the mean residence time in the reactor t at constant fluid density. This ratio is often called Bodenstein number Bo). 

The total amount of a nonreactive tracer injected as a Dirac pulse at the reactor entrance is given by q. The Bodenstein number, Ho, is defined as the ratio between the axial dispersion time, = L /D, and the mean residence time, t = r = L ju, which is identical to the space time for reaction mixtures with constant density. For Bo - 0 the axial dispersion time is short compared to the mean residence time resulting in complete backmixing in the reactor. For Ho oo no dispersion occurs. In practice, axial dispersion can be neglected for Ho > 100. 

Under these circumstances, a general stationary heterogeneous dispersion (PD-)model for an irreversible catalytic second order reaction between a gaseous and a liquid reactant in dimensionless form consists of the balance equations shown in Fig. 18. In this model the whole fluiddynamics are lumped into a single parameter, i.e. the Bodenstein number, here based on the reactor length. 

Large-scale hydroprocessing trickle-bed reactors normally operate under adiabatic conditions therefore, heat effects caused by the reaction must also be included. Shah [61] showed that in this case the critical Bodenstein number for elimination of axial dispersion effects is a function of a heat parameter as well as a modified Damkohler number. For low Damkohler numbers smaller critical Bodenstein numbers than in isothermal reactors are sufficient to eliminate axial dispersion in adiabatic reactors, whereas the inverse is true for large Damkohler numbers. 

Figure 3.7. The longitudinal Bodenstein number of the total pulse function, BOtot for the liquid phase of a tube-type reactor with recycling as a function of the recycle ratio, r. The evaluation of the experimental results are compared with the theoretical calculation, Equ. 3.15b. (From Moser and Steiner, 1974 and 1975).

The extremes of the reactor hydrodynamics can be characterized by the Bodenstein numbers ... 

In order to describe adequately the hydrodynamics of the experimental fixed bed reactor, it is necessary to take into account the axial dispersion in the mathematical model. The time dependent continuity equation including axial dispersion for a fixed bed reactor is given by a partial differential equation (pde) of the parabolic/hyperbolic class. These types of pde s are difficult to solve numerically, resulting in long cpu times. A way to overcome these difficulties is by describing the fixed bed reactor as a cascade of perfectly stirred tank reactors. The axial dispersion is then accounted for by the number of tanks in series. For a low degree of dispersion (Bo < 50) the number of stirred tanks, N, and the Bodenstein number. Bo, are related as N Bo/2 [8].The fixed bed reactor is now described by a system of ordinary differential equations (ode s). No radial gradients are taken into account and a onedimensional model is applied. Mass balances are developed for both the gas phase and the adsorbed phase. The reactor is considered to be isothermal. 

The constant p is a measure for the extent of axial mixing after the fluid has traveled through the reactor. Usually 2p is called the Peclet number for axial mixing. A similar dimensionless number related to the diameter J of a tube is also called the Bodenstein number ... 

Axial mixing effects in packed bed reactors (see section 45.1.1) are generally quite limited. However, they may be of practical importance for very high degrees of conversion. The Reynolds and Bodenstein numbers for packed beds are defined as follows... 

Another advantage of this reactor lies in its minor axial backmixing, due to the micromachined channels, combined with optimum mixing in each cavity. The Bodenstein number (Bo) of this reactor was determined to be >120 under reaction conditions, thus characterizing a very narrow residence time distribution and hence ideal plug flow between the cavities (Fig. 12.4). 

Assuming a height of 10 m for the axial dispersed reactor a Bodenstein number can be estimated... 

Commercial scale tubular plug flow reactors utilizing SMX and SMXL static mixer internals have now been operating for more than 20 years. These static mixer designs have demonstrated their ability to mix and achieve plug flow in large scale equipment. The residence time distribution and shear stress-temperature history are very uniform. The Bodenstein number (also sometimes known... 

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