Inlet void fraction

Lisseter and Fowler (1992) have derived a simple set of equations for bubbly flow through a vertical tube. They have shown that under steady flow conditions, the void fraction will relax from its inlet value to an asymptotic value within only a short distance from the inlet. They have obtained a relationship between the inlet void fraction and the imposed pressure drop and derived a simple expression for the equihbrium void fraction. They have also considered the wall friction in their analysis of bubbly flows. 

Combined gas and vapor mass fraction, x = 0.551 Specific volume of combined gas and vapor, = 0.0752 m /kg Specific volume of two-phase system, = 0.0422 m /kg Inlet void fraction, a (Equation 4.74) = 0.982... 

Inlet void fraction Omega parameter Nonflashing critical pressure ratio Flashing critical pressure ratio Critical pressure Type of flow... 

The void fraction data obtained in micro-channels and conventional size channels showed significant differences depending on the channel cross-section and inlet geometry. For the micro-channel with a diameter of 100 pm, the effects of the inlet geometry and gas-liquid mixing method on the void fraction were seen to be quite strong, while the conventional size channels have shown a much smaller effect of inlet geometry on the void fraction. 

Thus, similar void fraction data can be obtained in micro-channels and conventional size channels, but the micro-channel void fraction can be sensitive to the inlet geometry and deviate significantly from the Armand correlation. 

For a micro-channel connected to a 100 pm T-junction the Lockhart-Martinelli model correlated well with the data, however, different C-values were needed to correlate well with all the data for the conventional size channels. In contrast, when the 100 pm micro-channel was connected to a reducing inlet section, the data could be fit by a single value of C = 0.24, and no mass velocity effect could be observed. When the T-junction diameter was increased to 500 pm, the best-fit C-value for the 100 pm micro-channel again dropped to a value of 0.24. Thus, as in the void fraction data, the friction pressure drop data in micro-channels and conventional size channels are similar, but for micro-channels, significantly different data can be obtained depending on the inlet geometry. 

Kawahara et al. (2002) presented void fraction data obtained in a 100 pm micro-channel connected to a reducing inlet section and T-junction section. The superficial velocities are Uqs = 0.1-60m/s for gas, and fAs = 0.02-4 m/s for liquid. The void fraction data obtained with a T-junction inlet showed a linear relationship between the void fraction and volumetric quality, in agreement with the homogeneous model predictions. On the contrary, the void fraction data from the reducing section inlet experiments showed a non-linear void fraction-to-volumetric quality relationship ... 

The molar ratio of steam to ethylbenzene at the inlet is 9 1. The bed is 1 m in length and the void fraction is 0.5. The inlet pressure is set at 1 atm and the outlet pressure is adjusted to give a superficial velocity of 9 m/s at the tube inlet. (The real design problem would specify the downstream pressure and the mass flow rate.) The particle Reynolds number is 100 based on the inlet conditions 4 x 10 Pa s). Find the conversion, pressure, and velocity at the tube outlet, assuming isothermal operation. 

In the model equations, A represents the cross sectional area of reactor, a is the mole fraction of combustor fuel gas, C is the molar concentration of component gas, Cp the heat capacity of insulation and F is the molar flow rate of feed. The AH denotes the heat of reaction, L is the reactor length, P is the reactor pressure, R is the gas constant, T represents the temperature of gas, U is the overall heat transfer coefficient, v represents velocity of gas, W is the reactor width, and z denotes the reactor distance from the inlet. The Greek letters, e is the void fraction of catalyst bed, p the molar density of gas, and rj is the stoichiometric coefficient of reaction. The subscript, c, cat, r, b and a represent the combustor, catalyst, reformer, the insulation, and ambient, respectively. The obtained PDE model is solved using Finite Difference Method (FDM). 

In a contact sulphuric acid plant the secondary converter is a tray type converter, 2.3 m in diameter with the catalyst arranged in three layers, each 0.45 m thick. The catalyst is in the form of cylindrical pellets 9.5 mm in diameter and 9.5 mm long. The void fraction is 0.35. The gas enters the converter at 675 K and leaves at 720 K. Its inlet composition is ... 

Alternatively, the mean of G (calculated at the relief pressure) and G (calculated at the maximum accumulated pressure) can be used. Since Leung s method assumes that the reactor contents are homogeneous during relief, the consistent assumption for the vapour fraction at inlet to the relief system (needed to calculate G) is that it is the same as the average for the reactor, i.e. at the inlet to the relief system the void fraction is given by ... 

The void fraction at the inlet to the relief system will be estimated assuming the reactor contains a homogeneous two-phase mixture. This is consistent with the assumptions of the relief sizing method used. 

One of the most significant, parameters describing the inlet condition is the phase split at this position. This can be described by either the mass fraction of gas/ vapour, x, or the volume (void) fraction, a. These two parameters are related ... 

A schematic process flow sheet is shown in Figure 2. Inlet gas, a mixture of methane, hydrogen and carbon monoxide at 100°F and 500 psia (stream 1) is successively cooled to -140°C by the outlet gas stream from the absorber and some recycle gas. The absorber is a packed column of 1-in. berl saddles with 50% void fraction. The rich liquid from the bottom of the absorber is heat exchanged with the bottom liquid from the stripper. The stripper is also a packed column with 1-in. berl saddles. The dissolved methane, hydrogen, and carbon monoxide is stripped out by heating at the bottom of the stripper. The outlet gas stream from the stripper is heated in a heat exchanger by a recycle gas stream and is further compressed to produce the final methane product at 100°F and 1000 psia. 

The reactor is of the heat-exchanger type with catalyst and tubes and rising steam outside. In this project we consider spherical catalyst particles of 5 mm diameter and a bed void fraction of 45%, which offers a good trade-off between efficiency and lower pressure drop. The gas inlet pressure is 10 bar. We aim at a pressure drop less than 15% of the operating pressure, namely a maximum of 1.5 bar. 

Wall effect gives rise to radial heterogeneity. Although Soo (1989), Ding et al. (1992) and Ding and Gidaspow (1990) proposed boundary conditions for their models, it is still considered necessary to measure relevant parameters near the wall, such as fluid velocity, particle velocity, and void fraction. Inlet and outlet effects are even more difficult to generalize, and will therefore be discussed only in a qualitative sense. 

Here A0 and E are the frequency factor and the activation energy for the reaction, respectively, Rg is the universal gas constant, 7] is the reactor inlet temperature pG and pi are the gas and liquid densities, respectively, Cpr. and CpL are the gas and liquid heat capacities respectively, V0G and U0L are the superficial gas and liquid velocities respectively, e. is the void fraction of the undiluted catalyst, r is the space time, C-, is the reactor inlet concentration of the reactant, m is the order of the reaction, and A7/r is the heat of reaction. The results shown in Figs. 4-5... 

It is clear that a behavior such as the one shown in Fig. 6-4 is caused by plugging of the catalyst bed by solids deposition. The plugging causes the bed void fraction to decrease. Some speculations on the modes of deposition can be made from analysis of the plugging material. This material consists primarily of oxides of iron in the form of loose particles and is densely deposited in the inlet portion of the reactor. The material is probably carried by the fluid while it is flowing through rusted pipelines. As the reaction proceeds, bed plugging in an HDS reactor also occurs as a result of metal deposits, both nickel and vanadium, and coking of the catalyst. 

The voidage value at a particular level represents the average voids over the spout cross section at that level. The upper limit of spout level covered by the data is the surface of the bed proper, no measurements having been made in the fountain above the bed. In all cases, the voidage is seen to decrease with increasing distance from the inlet orifice, from 100% at the orifice to its lowest value at the top, but the gradients and the lowest values of vary widely for the different systems studied, the latter ranging from 0.70 to 0.99 in Fig, 25. For beds in which H = it would be expected that the void fraction at the top of the spout would be somewhat closer to that of a loosely packed bed than 0.70. 

The pressure Pout, which is produced at the outlet, enables the current distribution over the WP surface to be changed. This is associated, to a large degree, with the fact that the gas bubble size decreases with an increase in Pout- The void fraction and its effect on the current distribution decrease. At a certain ratio between the inlet pressure and Pout, the nonuniformity of the current distribution may be significantly reduced. 

If there is no change of density during the reaction, the concentration can be suitably measured in moles per unit volume and the linear velocity will be denoted by if reactor is packed, the velocity v is taken to be the volume flow rate divided by the total cross-sectional area of the reactor. (The mean velocity through the interstices of the packed bed is v/e, where is the void fraction.) Also, let c/z) be the concentration of at a distance z from the inlet and r(ej, T) be the pseudo-homogeneous reaction rate in moles per unit reactor volume per unit time. If is the cross-sectional area of the reactor then in a unit of time... 

W = required relief rate, kg/s X = mass fraction of vapor at inlet a = void fraction in vessel... 

These calculations require knowledge of column void fraction (5) fractional pore volume of the stationary phase (e) capacity factors ( /) or distribution coefficients (K,) dispersitivity or diffusivity of the solute ( >) and initial and inlet column conditions. The determination of k, is described in reference 5. Knowledge of limits for sample volume, elution volume, and column length for a given target of product purity and recovery allows a best-case estimate of throughput, eluent volumes, and support costs using correlations described previously (5). 

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