Solids distribution

Two types of probe have commonly been used conductivity and optical. Both types of probes and the associated instrumentation are commercially available, but care should be taken to ensure that the probe and instrumentation are suitable for a particular application. The dimensions of the measuring volume should be at least an order of magnitnde greater than the dimensions of the solid particles, and the probe should allow free flow through the measuring volume. If these criteria cannot be met, inaccurate measurements will result, and a custom-built probe may have to be used. 

Attempts to close a solids mass balance using these approaches generally fail nnless the solids are very well distributed throughout the vessel. It is very difficult to measure accurately the quantity of any unsuspended solids on the vessel base. This problem is most acnte if visual observations are not possible. The nnmber of locations in the vessel at which measurements are made will nsnally be limited for practical reasons. This lack of spatial resolution will lead to inaccnrate measurements being made in regions where there are high solids concentration gradients. 

At high solids concentrations, visual observations become difficult The solids screen most of the vessel from view. If a process with a high solids concentration is being investigated, observations at lower solids concentrations will aid in understanding the mixing mechanisms. However, observations should stiU be carried out at high solids concentration since the flow patterns in the vessel often vary considerably with solids concentration. 

The measured electrical conductivity of the probe volume will vary as the solids concentration in the probe volume changes. Generally, the measured conductivity is linearly related to the volume fraction of solids over a wide range of solids concentrations  

The measured conductivity may change not only as a result of solids concentration, but also due to changes in the fluid temperature and to impurities dissolving in the fluid. During use it is essential to measure temperature accurately and to correct for any changes. The following expression can be used  

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Computation fluid mixing and computational fluid dynamic techniques have increasingly been used to elucidate solids distribution in agitated vessels [44],... 

Liquid-solid distributions are involved in ion-exchange and other adsorption-based separation processes, separation processes based on crystallization or precipitation, flotation processes for ore dressing, and smelting processes. 

Examples of the formation of volatile metal compounds or complexes leading to separations based on gas-liquid and gas-solid distribution are much rarer. 

Horio, M., Morshita, K., Tachibana, O., and Murata, M., Solid Distribution and Movement in Circulating Fluidized Beds, Circ. Fluid. Bed Tech. II, 147— 154 (1988)... 

Figure 15. Assessing lateral solids distribution by baffles.

Figure 16 shows two cases for lateral solids distribution, a fairly uniform distribution illustrated on the left-hand side, and a relatively concentrated distribution near the center source, shown on the right-hand side. It is clear that for both cases, areaa, represents the excess of solids over the average for w near the central feed, at the expense of deficit for areaa2 near the peripheral region. Graphically the nonuniformity index is thus... 

From a practical point of view, for improved solids distribution, the indications are for innovative design of obstructing structures next to the wall to break the falling sheet of solids in order to equalize their flow pattern across the column through repeated redistribution. 

Figure 6. Histograms of the nearest-neighbor mass spacing distribution for hadron states with same quantum numbers. Curves represent the Poisson (dashed) and Wigner (solid) distributions. Taken from Ref. (Pascalutsa, 2003).

In beds of both coarse and fine solids one may observe a somewhat different solid distribution with height—a distinct difference between dense and lean regions and a sharp dense phase surface, as shown in Fig. 20.14. This behavior is more typical of fluidized combustors, not catalytic reaction systems. 

Consider a first-order reaction in a fluidized bed, where we have plug-flow for the gas through the bed, while the distribution of solids across the cross-section of the bed is uniform. In general, the solution of this model, under the additional assumption of uniform solids distribution throughout the reactor, is... 

K denotes the equilibrium constant, C is in moles dm 3 of solution, and the coefficients A depend upon T but not on C. This isotherm equation approaches Henry s law as C becomes small enough and has already been shown adequate, for a suitable choice and number of coefficients A, to represent experimental isotherms well (4, 6, 20). One to three such coefficients were needed according to the rectangularity of the isotherms. It lends itself to thermodynamic analysis of gas-solid distribution equi-... 

Carson and Katz noted that their experimental hydrate composition changed at different temperatures and pressures in a manner indicative of a solid solution of mixtures, rather than segregated macroscopic quantities of pure hydrocarbons within the hydrate. The concept of a solid solution enabled the notion of the mole fraction of a guest component in the solid phase hydrate mixture, on a water-free basis. Carson and Katz defined a vapor-solid distribution coefficient (KVSi) for each component as... 

This overall average value is close to the values obtained by CT scanning. Considering the error associated with the measurement of small amount of the displaced water, this indicates that CT provides adequate measurements of the solids distribution in the bed despite its small values. 

Fig. 6. Determination of solid distribution at three axial positions (a) cross-sectional distribution (b) azimuthally averaged solids holdup and (c) overall solids holdup. The horizontal line indicates experimentally determined solids fraction.

The acceleration is a direct measure to the dynamic factors. However, there are few reports, if not to say none, about that for meso-scale structures. In a recent attempt, Meng et al. (2009) made use of the multiple sensors of an X-ray computerized tomography (CT) to measure the cluster accelerations. Instead of the conventional use of CT for cross-sectionally scanning the solids distribution, they erected the X-ray fan-beam and the sensors to follow the vertical movement of clusters... 

Figure 11 A typical snapshot of the simulated solids distribution at the wall of the ETH CFB, along with the axial profile of the cross-sectionally averaged solids volume fraction and the radial profiles of time-average solids volume fraction and solids velocity (pp = 1400 kg/m3, dp = 60 m, Ug = 3.5 m/s, H0 = 1.7 m).

Figure 19 An industrial MIP reactor and the relevant simulation results of solids distribution.

Figure 22 shows a snapshot of the solids distribution at the walls of the whole boiler. Below the secondary air inlets, clearly a dense bottom was formed. Above that, the dilute top region was predicted with various forms of clusters, most of which flow down along the wall as shown by the vector slice at the side wall. At the loop-seal valves, dense bottom regions were formed with bubbles. The solids captured by the cyclone were also in forms of certain kind of dynamic aggregates, falling down spirally along the wall. Unfortunately there is no data we can use to verify such complex phenomena. Obviously more efforts are needed to measure the flow behavior in such a hot facility. 

Figure 22 Snapshot of the solids distribution at all the walls together with a slice of the solids velocity vectors at the side wall.

Figure 24 The seesaw phenomenon by instantaneous solids distribution in the boiler at simulation time of (a) No. 28.9 s and (b) No. 38.7s. The red circles indicate high solids volume fraction on the top wall of the furnace (Zhang et al., 2010).

Martinsen, P. and Schaare, P. (1998) Measuring soluble solids distribution in kiwifruit using near-infrared imaging spectroscopy. Postharvest Biol. Technol. 14,271-81. 

A comprehensive account of radial voidage distribution requires a recognition of the lateral movement of solids in addition to their axial movement. One of the most important and yet least understood aspects of riser hydrodynamics is the lateral solids distribution mechanism [Kwauk, 1992]. Typical experimental findings for the radial voidage... 

Figure 6 Solid distributions at upstream and downstream of a horizontal pipe with different solids loading (McKee et al., 1995a).

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