Fixed critical tube diameter

If the true pipe diameter is only 10% smaller than the critical diameter, the Ci-dependent term of Equ.(4-148) already amoimts to 0.85, and it approaches 1 if the safety distance is made greater. If a cooling intensity is demanded for fixed-bed reactors which is determined for a fixed value of 1 for the Ci-dependent term, then this can only be advantageous for process safety, especially for a design with close proximity of true and critical tube diameter. 

However, the high activity together with the exothermic reaction makes reactor design critically important to ensure effective heat removal. Tubular fixed bed reactors (TFBR) are particularly vulnerable to thermal damage, so tube diameters are limited to prevent heat transfer problems. This leads to an expensive reactor as a large number of small tubes have to be used. 

Effect of Pressure. For fixed mass flux, tube diameter, tube length, and inlet subcooling, the critical heat flux initially increases with increasing pressure and then decreases with pressure approaching zero as the critical pressure is approached. 

In order to exclude the ignition of a fixed bed tube reactor in the middle of the pipe reliably, the pipe diameter must be smaller than the critical diameter dc- This diameter is defined as ... 

A second criterion for the safe operation of a cooled fixed-bed reactor is obtained from Equ.(4-136). If the demand is fulfilled that the true tube diameter must not exceed the critical diameter, then this allows a distinct maximal temperature difference between maximum and wall temperature only. Mathematically this is obtained by setting d equal to dc resulting in Ci = 1 and inserting this into Equ.(4-136). 

Figure 12 shows some results of pressure drop measurements over a 1-m-long internally finned round tube (4-mm internal diameter, six fins, fm height 1 mm, fin thickness 0.5 mm) with a cutoff angle at the bottom end of 60 . With n-decane as the liquid and air at ambient temperature and pressure as the gas, the pressure drop increases steadily with increasing gas velocity until a certain critical gas velocity is reached. Below this critical velocity, the pressure drop is low, viz., orders of magnitude lower than in a fixed bed of catalyst under comparable conditions. It can also be seen that under these conditions the superficial velocity of the liquid in the internally finned tube has little effect on the pressure drop. 

The asymptotic nature of the friction factor is clearly brought out in Fig. 10.24, which shows the measured fully established friction factors taken in three tubes of differing diameters as a function of the Weissenberg number based on the Powell-Eyring relaxation time for fixed values of the Reynolds number for aqueous solutions of polyacrylamide. The critical Weissenberg number for friction (Ws), is seen to be on the order of 5 to 10. When the Weissenberg number exceeds 10, it is clear that the fully developed friction factor is a function only of the Reynolds number. 

The second inlet option is to use a critical oriflce, which is essentially a small hole drilled into a metal plate which allows air to enter the drift tube at a fixed rate. Providing the pressure on the downstream side of the orifice is more than a factor of two lower than on the upstream side, gas enters at the speed of sound and the flow rate cannot be increased any further. Such conditions are easily achieved in PTR-MS, where the gas usually enters at atmospheric pressure into a drift tube with a pressure near to 1 mbar. Clearly the diameter of the aperture in the critical oriflce plate must be compatible with the pumping speed of the system in order to maintain the desired drift tube pressure, but an orifice of a few tens of microns is typical. A clear advantage of a critical oriflce inlet is its simplicity but the flow rate through the orifice is sensitive to fluctuations in the temperature and pressure on the upstream side, so is not ideal in applications where such fluctuations might occur. 

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