Low mass velocity

In order to develop the above burn-out mechanism further, it will be necessary to know more about the entrainment and deposition processes occurring. Experimentally, it is likely that these processes will be very difficult to measure separately and under conditions comparable to those prevailing in a boiling channel. From analysis of their film flow-rate data, Staniforth et al. (S8) have deduced that under burn-out conditions, the deposition of liquid droplets from the vapor core plays an important part in reinforcing the liquid film, particularly at high mass velocities. At low mass velocities, they conclude that deposition and entrainment rates must be nearly equal, and, therefore, since a thin liquid film can be expected to be tenacious and give rise to very little entrainment, they argue that both deposition and entrainment tend to zero near the burn-out location with low mass velocities. 

With the 18-in. wrap, and with the bearing pads, there was a tendency for the burn-out flux to increase slightly at low mass velocities otherwise there was no significant effect. 

Rl. Randles, J., A theory of burnout in heated channels at low mass velocities, AEEW-R279, H.M. Stationery Office, London (1963). 

It is desirable to have a low mass velocity through the bed to minimize blower energy requirements, so the 75 ftVmin ft value will be used. Normal eonversions in adiabatie eonverters are 70% in the first stage and an additional 18% in the second. Using Eklund s Reymersholm catalyst, solution of the adiabatic reactor problem at the end of the chapter shows that these conversions require 1550 ft (23 in. deep) in the first stage and 2360 ft (35 in. deep) in the seeond. As a result, in our eooled tubular reactor, we shall use a total catalyst volume of 3910 fU. 

Schuler s investigations were made at temperatures as high as 400°C and with large temperature gradients. At low mass velocities the radiation contribution to was of the order of 10 to 15%. Hence an approximate equation such as Eq. (13-26) is satisfactory for estimating Iq., except for reactions at very high temperatures. 

In summary, once a coking heater starts plugging up with coke deposits, it is futile to try to keep going at reduced feed rates. Coking is accelerated because of the low mass velocities, and downtime is lengthened by the excessive coke accumulations. 

Low mass velocity Feed interruptions Stuttering resid flow Loss of velocity steam Sodium salts Light resid Foamovers... 

In general, the recommendation for adiabatic trickle bed reactors is to avoid internals that obstruct flow and to try to prevent localized partial plugging of the bed through good flow distribution. For reactions that require heat transfer radially through a wall such as in tubular reactors, it is recommended that the pilot plant reactor be run at conditions similar to the commercial reactor. Tests at the low mass velocities typical for pilot plants may be too conservative to get an economic design. 

The global glucose oxidation rate in a low mass velocity trickle bed was found by Tsukamoto, Morita and Okada [78] to be higher than for a liquid full reactor in which the liquid was presaturated with oxygen. The catalyst was an activated charcoal impregnated with immobilized enzymes. The charcoal was 0.055 and 0.011 cm in size. The reactor was 2.1 cm I.D. and 27 cm long. 

Low Mass Velocity Downflow Reactors with Fine Diluent... 

The low mass velocity expression suggests that for a given reactor length the logarithm of the ratio of the inlet to the outlet concentration of the key component should be inversely proportional to the 0.68 power of the space velocity. This, however, was not confirmed by subsequent studies by Paraskos et al [54], and Montagna et al [50], [51]). It does represent the data of Henry and Gilbert [23]. Hence, it can be concluded that the exponent on the bed length and space velocity varies with the feedstock and perhaps catalyst activity. 

The principle causes for channelling are non-uniform catalyst loading, low mass velocity, poor or defective distributor and catalyst fouling. These are discussed below. 

Low mass velocity. As suggested by laboratory studies discussed in Section 2, poor catalyst contact of liquid is to be expected for mass velocities below 1.4 kg/m ... 

Consider first a dilute phase pneumatic transfer system operating at high velocity and relatively low mass flow density. As discussed in 6-3.1 this... 

Figure 8 shows that increasing the heat flux at constant mass velocity causes the peak in wall temperature to increase and to move towards lower enthalpy or steam quality values. The increase in peak temperature is thus due not only to a higher heat flux, which demands a higher temperature difference across the vapor film at the wall, but to a lower flow velocity in the tube as the peaks move into regions of reduced quality. The latter effect of lower flow velocity is probably the dominant factor in giving fast burn-out its characteristically rapid and often destructive temperature rise, for, as stated earlier, fast burn-out is usually observed at conditions of subcooled or low quality boiling. 

The above conclusion must certainly be taken with a measure of reserve as regards the mass velocity, for at very low velocities it appears reasonable to expect that the relative motion between vapor and liquid in a boiling channel will be affected sufficiently to influence the burn-out flux. Barnett s conclusion also applies to simple channels, whereas Fig. 35 discussed in Section VIII,C shows that a rod-bundle system placed in a horizontal position is likely to incur a reduction in the burn-out flux at mass velocities less than 0.5 x 106 lb/hr-ft2, presumably on account of flow stratification. Furthermore, gravitational effects induced in a boiling channel by such means as swirlers placed inside a round tube can certainly increase the burn-out flux as shown by Bundy et al. (B23), Howard (H10), and Moeck et al. (Ml5). 

Aladyev et al. (A4) refer to specific tests using two tubes with wall thickness of 0.016 and 0.079 in., and they report no noticeable effect on the burnout flux, but details of the tests are not given. Lee (LI) examined the question of wall thickness using two uniformly heated tube lengths with water at 1000 psia, and his results for a mass velocity of 1.5 x 106 lb/hr-ft2 are shown in Fig. 15. It can be seen that with the 68-in. tube there is no difference between a wall thickness of 0.034 in. and a thickness of 0.082 in. With the 34-in. tube, however, the thicker wall gives about 7 % higher burn-out flux values at low... 

The characteristic that has been called the low-velocity regime (M2) would have been observed at a much earlier stage if burn-out data had existed for experiments covering a very wide range of mass velocities with the other system parameters fixed. Even today there is no really good direct example of... 

The main characteristics of the effect of mass velocity are shown in Fig. 28. One interesting feature, curve (2), is a rapid rise of burn-out flux in the low-velocity regime to a value which thereafter remains practically independent of mass velocity. The primary condition which tends to induce this effect is a low value of Ah, but the pressure and Ljd ratio are also important. At 1000 psia, for example, the Ljd ratio must be less than about 100. The influence of the Ljd ratio was shown in Fig. 26. 

The computer-optimized y values obtained for a number of conditions are given in Table VI. It can be seen that the first condition assumes simple power functions only and a value for B strictly in compliance with Eq. (18). The rms error achieved is good, but marked improvements are obtained by relaxing the equations for A and B in stages, as shown, the final result giving a much better rms error. It was not necessary in the analysis to separate the data into low- and high-velocity regimes, as was the case for round-tube data, since the lowest mass velocity is not so low as to cause difficulty. 

Especially for the electrons, the fluid model has the advantage of a lower computational effort than the PIC/MC method. Their low mass (high values of the transport coefficients) and consequent high velocities give rise to small time steps in the numerical simulation (uAf < Aa) if a so-called explicit method is used. This restriction is easily eliminated within the fluid model by use of an implicit method. Also, the electron density is strongly coupled with the electric field, which results in numerical Instabilities. This requires a simultaneous implicit solution of the Poisson equation for the electric field and the transport equation for the electron density. This solution can be deployed within the fluid model and gives a considerable reduction of computational effort as compared to a nonsi-multaneous solution procedure [179]. Within the PIC method, only fully explicit methods can be applied. 

Because of the large mass of the nucleus and the low recoil velocity involved, we may use the nonrelativistic approximation... 

The density here refers to the spatial coordinate, i.e. the concentration of the reaction product, and is not to be confused with the D(vx,vy,vz) in previous sections which refers to the center-of-mass velocity space. Laser spectroscopic detection methods in general measure the number of product particles within the detection volume rather than a flux, which is proportional to the reaction rate, emerging from it. Thus, products recoiling at low laboratory velocities will be detected more efficiently than those with higher velocities. The correction for this laboratory velocity-dependent detection efficiency is called a density-to-flux transformation.40 It is a 3D space- and time-resolved problem and is usually treated by a Monte Carlo simulation.41,42... 

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