Yang Fluidization, Solids Handling, and Processing

Dense Phase Conveying 695

3.0BASIC PHYSICS

A starting model can be selected depending on the type of dense phase transport. Modeling a homogeneous dense phase would use the same approach as dilute phase with a new frictional term. This approach would have two contributions due to the gas alone and the linear combination with the solids contribution.

Mathur and Klinzing (1981) have developed a frictional term to account for the solids pressure drop which is meant for high loading systems (μL= 10 to 50). Their expression for fs is

where the pressure drop for the solid contribution is

A work by Stegmaier (1978) has also developed a friction factor associated with the solids flow. This expression is

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Weber (1973) has developed a simple expression for dense phase which can be written as

where β = sinα + μRcosα

μR = coefficient of sliding friction

Wen and Simon (1959) have recommended an overall expression that lumps the air and solids pressure contributions together.

where W - lb/ft2s

Vg - ft/s

The Wen and Simon expression has often been used to calculate the pressure loss in systems where one has a high concentration material at the bottom of the pipeline. This type of flow is often called two-phase flow. Wirth and Molerus (1986) have termed this two-phase flow as strand flow and have developed a technique to predict the pressure loss in such flows. Using Figs. 18 and 19 one can follow the procedure:

(i) Calculate the friction number Fri from

where ε = voidage of strand (0.4)

fr = coefficient of sliding friction = 0.6

(ii)The loading µl is set and ρ µ/[ρp(1 - ε )] is calculated.

(iii)These values locate a point on the Fig. 18 and from the ordinate the reduced pressure drop can be found.

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these analyses, a moving packed bed model was proposed using the theory of soil mechanics. An experimental study by Dickson et al. (1978) showed how a plug moved by mechanical means requires a force that increases exponentially with plug length. A simple force balance for a cohesive powder inclined in a plug at an angle of α can be given as

Konrad was the first to address the issue of pulsed piston transport using the properties of the solids as they slide through the pipe in a plug-like motion. The friction generated in such systems often can be likened to bin and hopper flow and design, requiring shear stress measurements such as carried out by the Jenike shear stress unit. The final expression using the Konrad approach can be written for horizontal flow as

Eq. (13)

The stress terms F´ at the front of the plug and B´ at the back of the plug, dependent on the pressure drop and powder properties, can be developed from a momentum balance but often times they are set equal to each other. Using the momentum balance

The term c´ is zero for cohesionless powders such as plastic pellets. As one sees, there are several parameters that need to be measured specifically

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for the particular material conveying. This type of data is difficult to generalize which makes pulse piston modeling particularly difficult. Other investigators have studied the pulse piston flow operation (Legel and Swedes, Lippert, Aziz and Klinzing, 1988). Pulse piston operations are often demonstrated at trade shows where plastic pellets are used to demonstrate the concept. Plastic pellets are unique materials in that they can actually form their own pulsed pistons without special feeding devices. Cohesive materials require special feeder arrangements as has been seen in the specific examples shown above.

Weber (1973) has put forth a rather simple approach to pulsed piston modeling which couples the gas and solid behavior. The expression that Weber suggested is given in Eq. (9). One notes that this expression has an exponential decay of the pressure as the plug length decreases. This behavior has often been seen in industrial operations.

A series of studies were performed by Borzone and Klinzing (1987), Gu and Klinzing (1989) and Aziz and Klinzing (1990) on plug flow of coal. In order to transport plugs of fine materials, especially in the vertical case, it is necessary to have an sudden application of pressure so that the transport gas does not leak through the plug. It is very apparent that there exists a minimum plug length for material transport in this mode or else there will be a breakthrough of the gas leaving a mound of material on the bottom of the pipe. Their modeling was confined to modifying the work of Konrad for cohesive flow, as well as that of Weber. Good agreement was seen between the experiment and model as shown in Fig. 21. When increased pipe diameters were studied in vertical flow, the minimum plug length did not vary significantly with pipe diameter while the maximum plug lengths decreased with pipe diameter to maintain stable plugs. The vertical plugs were dominated by the gravitational force. The concept of plug length and optimum operation is one that often is of concern. Aziz, in his study of fine coal, found that there is a minimum plug length that will form in order to convey in the piston model. This minimum condition is of interest in the design of any pulse piston operation. Unfortunately, the ability to predict such a minimum length is lacking. Known powder properties are essential to predict the minimum plug lengths. Figure 22 shows the various modes of collapse of the horizontal plugs when the plug length is below the minimum value. It has also been observed by Aziz that a layer of material can be deposited on the bottom of the pipe and a plug-like flow will move with this as its base, thus transporting in a half-plug mode. The pressure drop across a plug can be represented by a straight line behavior as predicted by the

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Figure 26. Plug and air gap flow behavior with distance.

Recently Min (1994) under the direction of Wypych has experimentally studied the conveying of plastic particles and wheat over a sizable distance in the pulsed piston operation. The results that they obtained experimentally agree qualitatively with the model suggested by Plasynski et al. and Destoop. Figure 27 exhibits this length of the air gap as a function of air or solids flow rates at constant air or solids mass flow. There is design strategy for this type of flow that can be suggested.

Tsuji et al. (1990) have modeled the flow of plastic pellets in the plug mode with discrete dynamics following the behavior of each particle. The use of a dash pot/spring arrangement to account for the friction was employed. Their results show remarkable agreement with the actual behavior of real systems. Figure 28 shows these flow patterns. Using models to account for turbulent gas-solid mixtures, Sinclair (1994) has developed a technique that could have promise for the dense phase transport.

Further analysis of plug flow has been given by Destoop and Russell (1995) with a simulated computer model for catalyst and polymer materials. The model was developed based on piston-like flow of plugs separated by plugs of gas. The model has been employed taking into account the product grade, temperature, flow rates and line configuration.