Gas-Solid Flows
1
INTRODUCTION
There is essentially no limit to the capability or a pneumatic conveying system for the conveying of dry bulk particulate materials. Almost any material can be conveyed and high material flow rates can be achieved over long distances. There are, however, practical limitations and these are mainly imposed by the fact that the conveying medium, being a gas, is compressible. The limiting parameters are then mainly the economic ones of scale and power requirements. Conveying capability depends mainly upon five parameters. These are pipe bore, conveying distance, pressure available, conveying air velocity and material properties. The influence of many of these variables is reasonably predictable but that of the conveyed material is not fully understood at present. 1.1
Pipeline Bore
The major influence on material flow rate is that of pipeline bore. If a greater material flow rate is required it can always be achieved by increasing the pipeline bore, generally regardless of the other parameters. In a larger bore pipeline a larger cross sectional area is available and this usually equates to the capability of conveying more material.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
108 1.2
Chapter 4 Conveying Distance
In common with the single phase flow of liquids and gases, conveying line pressure drop is approximately directly proportional to distance. Long distance conveying, therefore, tends to equate to high pressure, particularly if a high material flow rate is required. For the majority of conveying applications, however, it is not convenient to use high pressures. As a consequence, long distance, with respect to pneumatic conveying, means about one mile. This limitation, and means of extending distance capability, are discussed at various points in this handbook. In this chapter the basic fundamentals are considered. 1.3
Pressure Available
Although air, and other gases, can be compressed to very high pressures, it is not generally convenient to use air at very high pressure. The reason for this is that air is compressible and so its volumetric flow rate constantly increases as the pressure decreases. In hydraulic conveying, pressures in excess of 2000 lbf/in 2 can be used so that materials can be conveyed over distances of 70 miles and more with a single stage. With water being essentially incompressible, changes in the velocity of the water over this distance are not very significant. In pneumatic conveying, air at pressures above about 15 lbf/in 2 gauge is generally considered to be 'high pressure', as mentioned in Chapter 1. With air at 15 lbf/in 2 expanding to atmospheric pressure, for example, the conveying air velocity will double over the length of the pipeline. Although the air expansion can be accommodated to a certain extent by stepping the pipeline to a larger bore part way along its length, this is a complex design procedure. As a consequence, air pressures above 100 lbf/in 2 gauge are rarely used for pneumatic conveying systems that deliver materials to reception points at atmospheric pressure. Where pneumatic conveying systems are required to deliver materials into reactors and vessels that are maintained at pressure, however, high air supply pressures can be used, and 300 lbf/in 2 is not unusual. With a high back pressure the expansion of the air is significantly limited and relatively few, if any, steps would be required in the pipeline. It is on this basis that staged pneumatic conveying systems would be designed for very long distance conveying. 1.4
Conveying Air Velocity
The parameter here is volumetric flow rate, for this has to be quoted, along with supply pressure, when specifying a blower, compressor or exhauster for a pneumatic conveying system. The critical design parameter with respect to pneumatic conveying, however, is conveying air velocity, and more particularly, conveying line inlet air velocity or pick-up velocity. Since the air expands along the length of the pipeline it will always be a minimum at the material feed point at the start of the pipeline, in a single bore pipeline, regardless of whether it is a positive pressure or a vacuum conveying system.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Gas-Solid Flows
109
In a single bore pipeline the velocity will be a maximum at the end of the pipeline. It is the value of the minimum velocity of the air that is critical to the successful operation of a pneumatic conveying system. Volumetric flow rate, of course, is given simply by multiplying conveying air velocity by pipe section area. In this process, however, the correct velocity has to be used and this is considered in detail in the next chapter on 'Air Requirements'. The minimum value of conveying air velocity depends to a large extent on the properties of the bulk particulate material to be conveyed and the mode of conveying. For dilute phase conveying this velocity is typically about 3000 ft/min, although this does depend upon particle size, shape and density, as will be discussed. For dense phase conveying the minimum velocity is about 600 ft/min. For fine powders that are capable of being conveyed in dense phase the minimum value of conveying air velocity also depends upon the concentration of the material in the air, or the solids loading ratio, and this will be considered in detail in this chapter. In dilute phase conveying the particles are conveyed in suspension in the air and this relatively high value of velocity is due, in part, to the large difference in density between the particles and the air. In hydraulic conveying typical velocities for suspension flow are only about 300 ft/min, but the difference in density between water and particles is very little in comparison. The difference in density between water and air is about 800:1. Since the difference in conveying medium velocity is only of the order of about 10:1 it will be seen that the pressure of the air, and hence its density, will not have a major effect on the value of minimum conveying air velocity for general pneumatic conveying. 1.5
Material Properties
The properties of the conveyed material have a major influence on the conveying capability of a pneumatic conveying system. It is the properties of the material that dictate whether the material can be conveyed in dense phase in a conventional conveying system, and the minimum value of conveying air velocity required. For this reason the conveying characteristics of many different materials are presented and featured in order to illustrate the importance and significance of material properties. Although it is the properties of the bulk material, such as particle size and size distribution, particle shape and shape distribution, and particle density that are important in this respect, at this point in time it is the measurable properties of materials in bulk that are more fully understood, These include air-material interactions, such as air retention and permeability, and are more convenient to use. In general, materials that have either good air retention or good permeability will be capable of being conveyed in dense phase and at low velocity in a conventional conveying system. Materials that have neither good air retention nor good permeability will be limited to dilute phase suspension flow.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
110
Chapter 4
7.5.7 Dense Phase Conveying There are two main mechanisms of low velocity, dense phase flow. For materials that have good air retention, the material tends to be conveyed as a fluidized mass. In a horizontal pipeline the vast majority of the material will flow along the bottom of the pipeline, rather like water, with air above, but carrying very little material. At a solids loading ratio of about 150 the pipeline is approximately half full. For dense phase flows there is a distinct pulsing of the flow, with the material flowing smoothly and then suddenly stopping for a second or two and then flowing smoothly again. In vertically upward flow, the flow of material also pulses, and for the second that the flow halts the material falls momentarily back down the vertical pipe. For materials that have good permeability the material tends to be conveyed in plugs through the pipeline. The plugs fill the full bore of the pipeline and are separated by short air gaps. As the conveying air velocity is reduced, the air gap between the plugs gradually fills with material along the bottom of the pipeline and the plug ultimately moves as a ripple along the top of an almost static bed of material. As the air flow rate reduces, to give very low conveying air velocities, the material flow rate also reduces. Materials composed almost entirely of large mono-sized particles, such as polyethylene and nylon pellets, peanuts, and certain grains and seeds, convey very well in plug flow. In dilute phase conveying, nylons and polymers can suffer damage in the formation of angel hairs, and grains and seeds may not germinate as a consequence of damage caused at the high velocities necessary for conveying. Because of the very high permeability necessary, air will readily permeate through the material while it is being conveyed and so maximum values of solids loading ratios will typically be about 30. 2
MATERIAL CONVEYING CHARACTERISTICS
If a pneumatic conveying system is to be designed to ensure satisfactory operation, and to achieve maximum efficiency, it is necessary to know the conveying characteristics of the material to be handled. The conveying characteristics will tell a designer what the minimum conveying velocity is for the material, whether there is an optimum velocity at which the material can be conveyed, and what pipeline diameter and air mover rating will be required for a given material flow rate and conveying distance. Alternatively, for an existing pneumatic conveying plant, the appropriate conveying characteristics will tell a designer what flow rate to expect if it is necessary to convey a different material, and whether the air flow rate is satisfactory. Conveying characteristics can also be used to check and optimize an existing plant if it is not operating satisfactorily. In order to be able to specify a pipe size and compressor rating for a required duty it is necessary to have information on the conveying characteristics of
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Gas-Solid Flows
111
the material. If sufficient previous experience with a material is available, such that the conveying characteristics for the material are already established, it should be possible to base a design on the known information. If previous experience with a material is not available, or is not sufficient for a full investigation, it will be necessary to carry out pneumatic conveying trials with the material. These should be planned such that they will provide data on the relationships between material flow rate, air flow rate and conveying line pressure drop, over as wide a range of conveying conditions as can be achieved with the material. The trials should also provide information on the minimum conveying air velocity for the material and how this is influenced by conveying conditions. This is particularly important in the case of dense phase conveying, for the differences in conveying characteristics between materials can be very much greater than those for dilute phase conveying. If the investigation is to cover the entire range of conveying modes with the material, then the previous experience must be available over a similar range of conveying conditions. Scale up in terms of air supply pressure, pipe bore, conveying distance and pipeline geometry from existing data is reasonably predictable, provided that the extrapolation is not extended too far. Scale up in terms of mode of conveying, into regions of much higher solids loading ratios and lower conveying air velocities, however, should not be attempted unless evidence of the potential of the material for such conveying is available. 2.1
Conveying Mode
With high pressure air, conveying is possible in the dense phase mode, provided that the material is capable of being conveyed in this mode. It is the influence of material properties on the possible mode of conveying, as well as differences in material flow rates achieved for identical conveying conditions, that makes it essential for conveying trials to be carried out with an untried material before designing a pneumatic conveying system. In conveying tests with high pressure air there is an additional need, therefore, to establish the limits of conveying and this may be over a very wide range of conveying conditions. In addition to material properties, conveying distance can have a significant influence on the solids loading ratio at which a material can be conveyed, and hence mode of conveying that is possible. The influencing factor here is simply pressure gradient, and this will limit conveying potential regardless of the capabilities of the material. This aspect of conveying pipeline performance is considered in more detail in Chapter 8. 2.1,1
The A ir Only Datum
In order to illustrate how conveying characteristics can be used it is necessary to show first how they are built up and to examine the influence of the main variables.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
112
Chapter 4
30
40
80
120
160
200
Free Air Flow Rate - ftVmin Figure 4.1
Air only pressure drop data for pipeline shown in figure 4.2.
The simplest starting point is to consider the air only flowing through the pipeline. If a graph is drawn of pressure drop against air flow rate for a conveying line the result will be similar to that shown in Figure 4.1. The data in Figure 4.1 relates to a 165 ft long pipeline of 2 inch nominal bore which includes nine ninety degree bends. Details of the pipeline are presented in Figure 4.2. This pipeline was used for conveying many of the materials for which conveying characteristics are presented in the first part of this chapter, and several subsequent chapters. As a consequence, both the pipeline in Figure 4.2, and the air only pressure drop datum in Figure 4.1, will serve as a reference for much of the data that follows. The line representing the air only pressure drop on Figure 4.1 is effectively the lower limit for conveying and will appear on subsequent graphs with a zero to indicate that this is the datum for conveying and represents a material flow rate of Olb/h. It will be seen from Figure 4.1 that the air only pressure drop increases markedly with increase in air flow rate. When material is added to the air in the pipeline, at any given value of air flow rate, there will be an increase in pressure. This is as a consequence of the drag force of the air on the particles to enable them to be conveyed through the pipeline. The air, however, has to be at a velocity that is sufficiently high to convey the material, otherwise the particles will not convey, and a build up of such material could cause blockage of the pipeline.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Gas-Solid Flows
113
Pipeline: 165 ft long 2 inch nominal bore 9 * 90° bends D/d = 24
Figure 4.2
Details of pipeline used for conveying trials.
In some situations, when fine dust is fed into a pipeline, there will be a slight reduction in pressure drop, and this relates to modification of the boundary layer. The flow rates of material involved are very small and have no relevance to pneumatic conveying. It will be seen from Figure 4.1 that if an air mover having a low pressure capability is to be employed, the pressure drop available for conveying material will be very limited, particularly if a high air flow rate is required for dilute phase conveying. Pipeline bore, of course, can be increased in order to compensate if the pressure available for conveying is limited. 2.1.1.1 Pressure Drop Evaluation Figure 4.1 relates to single phase flow and the analysis of such flows is well established and quite straightforward. The pressure drop, Ap, for a fluid of density p, flowing through a pipeline of a given diameter, d, and length, L, can be determined from Darcy's Equation:
fLpC2 Ap
a
d
lbf/in 2
-
-
(1)
where / is the friction factor, which is a function of the Reynolds number for the flow and the pipe wall roughness, and C is the mean velocity of the flow - ft/min It can be seen from this mathematical model, which is presented in more detail in Chapter 6 on 'The Air Only Datum', that pressure drop follows a square law relationship with respect to velocity. This means that if the velocity is doubled the
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
114
Chapter 4
pressure drop will increase by a factor of approximately four. Velocity, therefore, is a very important parameter in this work and so in graphical representations of experimental results and data, velocity needs to be represented on one of the axes. 2.7.2 Conveying Air Velocity A major problem with using velocity, however, is that it is not an independent variable. Gases are compressible and their densities vary with both pressure and temperature. Since density decreases with decrease in pressure, the velocity of the conveying gas will gradually increase along the length of a constant bore pipeline. In Figure 4.1 it will be noticed that free air flow rate has been used instead of velocity. Velocity, however, can be determined quite easily from the volumetric flow rate by use of the two following equations: D V\ r\
T •M
_
fD T . V2
T *2
_
D V0 ^0
.-T*.
T -'0
where p = absolute pressure of air
- lbf/in 2
V = volumetric flow rate of air and T = absolute temperature of air and the subscripts relate to: 1 = conveying line inlet 2 = conveying line exit 0 = free air conditions
- ftVmin - R(°F + 460)
and for a circular pipeline:
C =
576 V —
ft/min
- - - - - . . . . -
where C = conveying air velocity and d = pipeline bore
(3)
- ft/min - inch
This shows quite clearly how velocity is influenced by both gas pressure and temperature, for a given volumetric flow rate of free air, and that for any given set of conditions the gas velocity can be evaluated quite easily. These equations are developed further in the next chapter. In Figure 4.3 a graph is presented that will allow the conveying air velocity to be evaluated for any given free air flow rate and conveying air pressure for conveying data relating to Figures 4.1 and 2. Conveying air velocity values up to about 6000 ft/min have been considered as this is ideally the maximum value that should normally be employed in dilute phase conveying.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
115
Gas-Solid Flows
Conveying Air Pressure - Ibf/in 2 gauge
6000 L
c
I L 4000
_o
Atmospheric Pressure = 14-7 Ibf7in 2 absolute
> •= 2000 c o U
Pipeline Bore = 2 in nominal Air Temperature = 60 F 40
80
120
160
200
Free Air Flow Rate - ft/min Figure 4.3 The influence of air flow rate and pressure on conveying air velocity for test pipeline and data. 2.2
Pneumatic Conveying
If a small quantity of a granular or powdered material is fed into a gas stream at a steady rate there will be an increase in the conveying line pressure drop, above the air only value, if the gas flow rate remains constant. For a given material the magnitude of this increase depends upon the concentration of the material in the gas. As the material flow rate into the conveying line increases, therefore, the conveying line pressure drop will also increase. In a two phase flow system consisting of a gas and solid particles conveyed in suspension, part of the pressure drop is due to the gas alone and part is due to the conveying of the particles in the gas stream. In such a two phase flow the particles are conveyed at a velocity below that of the conveying gas. There is, therefore, a drag force exerted on the particles by the gas. For dilute phase, suspension flow, this drag force is the main contributor to the conveying line pressure drop, whether it is accelerating the particles from the feed point or conveying them through straight pipeline or around bends, and so it is not surprising that different materials will behave very differently. These differences will be highlighted in this chapter, and they will be a major theme through the handbook. 2.2.7 Slip Velocity The difference in velocity between the conveying gas and the particles is called the slip velocity. The magnitude of the slip velocity will depend upon the size, shape
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
116
Chapter 4
and density of the particles. For horizontal conveying, low density 20 micron sized particles are likely to be conveyed at about 90% of the velocity of the conveying gas, and for high density 1000 micron sized particles the value will be about 50%. A typical representative value for the velocity of powdered materials is about 85% of the gas velocity for horizontal conveying and 75% of the gas velocity for conveying vertically up. 2.2.2
Cases Considered
The influence of particle concentration on conveying line pressure drop over a wide range of conveying air flow rates, and hence velocities, is illustrated with three very different materials. These are ordinary portland cement, a sandy grade of alumina and polyethylene pellets. They are representative of materials capable of the range of conveying modes discussed above and so are used to illustrate the conveying characteristics typical of these three groups of material. Identical sets of axes have been used for presenting the conveying data for each of the three materials so that direct visual comparisons can be made between the conveying capabilities of the three materials. Each of the three materials considered was conveyed through the pipeline shown in Figure 4.2. 200 ftVmin of free air was available at a pressure of 100 Ibf/in 2 gauge, although the maximum value of pressure employed for conveying any of the materials was limited to about 40 Ibf/in" gauge. A top discharge blow tank was used to feed each of the materials into the pipeline. It should be emphasized that the data presented here for the various materials relates only to the materials tested and to this particular pipeline. This aspect of the problem is considered in more detail in Chapters 7 and 8 where scaling parameters are presented, which will allow the conveying data presented here to be scaled to any other pipeline required. 2.3
The Conveying of Cement
Pressure drop data for the cement is presented in Figure 4.4. This is a graph of conveying line pressure drop plotted against free air flow rate, and lines of constant cement flow rate have been drawn as the family of curves. Within the limit of the 30 Ibf/in2 pressure drop the cement was conveyed at flow rates up to about 35,000 Ib/h through this two inch nominal bore pipeline. 2.3.1 Conveying Limits The zero line at the bottom of the graph is the curve representing the variation of conveying line pressure drop with air flow rate for air only, which comes from Figure 4.1 for the pipeline used. This, therefore, represents the lower limit with respect to the material conveying capacity for the given system. Apart from the lower limit of zero for material conveying capacity, there are three other limitations on the plot in Figure 4.4.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
117
Gas-Solid Flows
Material Flow Rate - I b / h * 1000
30
Q
30
20
0. o
10 c o U
0
0
40
80
120
160
200
Free Air Flow Rate - ItVmin Figure 4.4
Pressure drop data for cement.
The first is the limit on the right hand side of the graph, but this is set only by the volumetric capacity of the compressor or blower used. This was 200 ftVmin, and by reference to Figure 4.3 it will be seen that conveying air velocities are up to about 8000 ft/min at the end of the pipeline. For the majority of pneumatic conveying systems this is considered to be the upper limit. This upper limit is partly influenced by problems of material degradation and bend erosion in the conveying line, but it is mainly due to the adverse effect on the conveying line pressure drop and hence material flow rate. This aspect of the problem is considered in more detail in the next section. In terms of the overall conveying characteristics, the shape of the curves is quite clearly established within this maximum limit. The second limit is that at the top of the graph and this is set by the pressure rating of the compressor or blower used. Once again this is not a physical limit, for if air is available at a higher pressure, it can be used for conveying, but it would normally be recommended that the pipeline be stepped to a larger bore in order to limit the very high values of conveying air velocity. This aspect of system design is considered in Chapter 9. The third is the limit on the left hand side of the graph and this represents the approximate safe minimum conditions for successful conveying with the material. The lines actually terminate and conveying is not possible in the area to the left at lower air flow rates. This limit is governed by a complex combination of material properties, material concentration and conveying distance, and is considered in more detail later in this section.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Chapter 4
118
Any attempt to convey with a lower air flow rate would result in blockage of the pipeline, in a conventional conveying system. This is because the air flow rate would be below the minimum required to convey the material. The terminology employed for these situations is choking, when conveying vertically up, and saltation when conveying horizontally. 2.3.2
Conveying Air Velocity
Effects
An alternative way of presenting the conveying data on Figure 4.4 is to plot the material flow rate against the air flow rate and to have a series of curves at a constant value of the conveying line pressure drop. Such a plot is presented in Figure 4.5a. Although the air only datum is lost, this alternative plot shows the influence of excessively high conveying air velocities very well. The lines of constant pressure drop can be seen to slope quite steeply to the air flow rate axis, and hence to zero material flow rate at very high air flow rates, and hence velocities. This is because of the square law relationship of pressure drop with respect to velocity, presented in Equation 1 for air only, but which approximately applies to suspension flow for high velocity dilute phase conveying. Conveying Line Pressure Drop - Ibt7in2
60
Solids Loading Ratio
60
\
Conveying
35
,50
o 50 o o
30
40
> 40 40
GO
I
I 30
AREA
730
Conveying Limit
Bi
.220 ~ is
° 20
fcu
is 'C
