Superficial velocity calculations

The amount of level swell is correlated with the superficial velocity, jg, of gas or vapour at the surface of the liquid. Superficial velocity is the volumetric flow of gas or vapour, divided by the vessel cross-sectional area (i.e., with no attempt to account for the fraction of the cross-sectional area occupied by liquid). Within a particular flow regime, level swell increases with increasing superficial velocity. 

Accurate prediction of the degree of level swell requires computer simulation141. However, conservative estimates can be made to predict superficial velocity for the following cases  

For these approximations, the superficial velocity calculation is different in each case. 

In order to predict the beginning of two-phase relief and whether two-phase or single-phase relief should be assumed for relief sizing, the superficial velocity is calculated from the rate at which the chemical reaction generates gas and/or vapour. (The use of this approximation overestimates the superficial velocity.) 

The calculation will usually be performed at the relief pressure. If the superficial velocity, calculated above for the gas and vapour generated by the reaction, does not cause two-phase relief, then the relief system can safely be sized for single-phase gas or vapour relief (provided the mixture is not inherently foamy). The above method should not be used to decide whether two-phase relief would actually 

---

Computer Models, The actual residence time for waste destmction can be quite different from the superficial value calculated by dividing the chamber volume by the volumetric flow rate. The large activation energies for chemical reaction, and the sensitivity of reaction rates to oxidant concentration, mean that the presence of cold spots or oxidant deficient zones render such subvolumes ineffective. Poor flow patterns, ie, dead zones and bypassing, can also contribute to loss of effective volume. The tools of computational fluid dynamics (qv) are useful in assessing the extent to which the actual profiles of velocity, temperature, and oxidant concentration deviate from the ideal (40). 

For estimating purposes for direct-heat drying applications, it can be assumed that the average exit-gas temperature leaving the sohds bed wih approach the final solids discharge temperature on an ordi-naiy unit carrying a 5- to 15-cm-deep bed. Calculation of the heat load and selec tion of an inlet-air temperature and superficial velocity (Table 12-32) will then permit approximate sizing, provided an approximation of the minimum required retention time can be made. 

Calculation of the target efficiency T o of an isolated fiber in an air stream having a superficial velocity the same as that in the filter... 

Assuming an eluent viscosity of 1 cP, K can be read from Table 2.1 and the theoretical linear velocity of an eluent at any given pressure can be calculated. For the less rigid Sephadex G types, the maximum operating pressures at which the relation between superficial velocity and applied pressure is still linear are given in Table 2.1. Exceeding the pressures listed will result in bead compression, a reduction in pore volume, and a decreased flow rate. 

Water temperature of bulk -water, °F Superficial velocity, based on cross-section area of empty column, ft/sec Calculated or estimated maximum superficial vapor velocity, ft/sec... 

Calculate the gas hold-up for an agitated and aerated system with power input of 18 hp in an 80 m3 vessel with gas superficial velocity of 2.6 m-rniif1. 

The bubble voidage in the draft tube, ebr, was calculated on the basis of the velocity of a rising gas slug relative to its surrounding solids. The total gas superficial velocity in the draft tube, lJjn can be derived to be... 

The velocity calculated by dividing the volumetric flow rate by the whole cross-sectional area of the bed is known as the superficial velocity u. The mean velocity within the interstices of the bed is then ub = ule. 

The flow pattern is primarily determined by the particle Reynolds number, which is about 100 in the industrial converter (superficial velocity 0.35-0.55 Nm/s), but in order to improve the accuracy of the comparison of different catalysts, higher flow rates are also included. Although theoretical correlations can be used for extrapolating the measured pressure drops for a new shape to the industrial operation temperature, a more reliable method is to calculate the pressure drop from industrial experience for well-known shapes, e g. 10-mm ring, and assume the same relative pressure drop as in the cold measurements. 

If Eq. (9.20) for the relative velocity v,. is used to calculate the superficial velocity, one obtains the equations for calculating the phase flow velocities at the flooding point ... 

Figure 3.11 Nomogram for calculation of maximum production rate as a fimction of superficial velocity, bed height and air inlet temperature. From De Michelis and Calvelo (1985), by permission of the Institute of Food Technologists, USA.

Here, it has to be noted that for calculating the Peclet number in fixed beds, the actual velocity has to be used, i.e. the interstitial velocity, which influences the degree of mixing. In slurry bubble column reactors, the real velocity of the fluid is the bubble velocity, which is much higher than the gas superficial velocity. The mean bubble rise velocity for a batch liquid is (eq (3.201))... 

The experiments for the specified study have been made in the pulsing flow regime. This is stated in the original article, and it is evident by calculating the liquid and gas mass superficial velocities, which are... 

All calculations can be repeated for the other superficial velocities and the results are shown in Figure 5.22. 

Hydrodynamics The particle size can be evaluated from the superficial velocity at incipient fluidization fm and the Ergun equation by trial and error (eq. (3.451)). For this calculation, we need the bed porosity at incipient fluidization for the assumed particle size, which can be evaluated by using the relationship of Broadhurt and Becker (eq. (3.466)). Note, that the resulting value cannot be lower than the fixed-bed porosity. Since we assume spherical particles, a reasonable value of bed porosity is 0.41. This procedure results in a particle size of 0.077 mm and sfm = 0.47. 

Figure A3.3 (see below) is a plot of the average void fraction in the vessel versus the calculated superficial velocity. This may also be of use in assessing flow regime. If the bubbly flow correlation predicts a void fraction greater than 1, then it is not physically realistic. If, for this case, the small-scale test has indicated that the fluid is not inherently foamy, then the churn-turbulent regime is likely.

In order to predict the end of two-phase relief, the superficial velocity should be calculated based on the rate of depressurisation by the pressure relief system. (The size of the relief system will have to be known or guessed at this stage). 

The decision about whether relief will be two-phase or single-phase gas or vapour only can be made once an average void fraction in the swelled liquid, a, has been calculated using the methods above, with the gas/ vapour superficial velocity obtained from equation (A3.1). The decision is made by comparing a with the initial void fraction in the vessel, aR. 

A void fraction, a, should be calculated using the methods above, and with the superficial velocity, jg, calculated from equation (A3.2). This void fraction represents the final void fraction in the reactor at the end of two-phase venting. Thus ... 

In order to use the sizing method, the reactor, void fraction, aD, at which total vapour/ liquid disengagement is expected at the maximum accumulated pressure, must first be evaluated. This may be done by level swell calculation (see Annex 3) or by small-scale experiment with the same vapour superficial velocity as will occur at plant-scale (see Annex 2). Equation (A5.7)can then be used to find the relief area ... 

Before using the method, the void fraction at disengagement must be evaluated at conditions corresponding to the maximum accumulated pressure during relief. This can be done by level swell calculation (see A3.3) or possibly by a small-scale experiment that uses depressurisation to achieve the same vapour superficial velocity as in the full-scale reactor during relief (see Annex 2). The required relief rate can then be calculated fromt31 ... 

Carbon dioxide at an inlet concentration of 0.1 mole per cent is to be removed from an air stream at a total pressure of 1 bar by bubbling through a 0.0SM (0.05 kmol/m3) solution of NaOH at 20°C in a bubble column. The caustic soda solution passes through the column at such a rate that its composition is not significantly affected by the absorption. The superficial velocity of the gas will be 0.06 m/s. The ratio of outlet concentration of C02 in the air to inlet concentration is to be calculated for the following cases the height of the gas-liquid dispersion will be 1.5 m in each case ... 

Note that the actual diameter of the column does not appear in the calculation because the gas rate is expressed as a superficial velocity however, plug flow for the large column would be extremely improbable.)... 

---