With pneumatic conveying performance of materials varying as widely as the sample shown in Figure 4.38, it is not surprising that the scope and accuracy of computer-aided design programs is limited. Many manufacturing companies that serve a wide range of industries generally make a point of listing in their advertising material, a vast number of different materials that they have experience of conveying. Most reputable manufacturing companies will have a test facility, specifically for the purpose of testing clients’ materials. This will generally be offered as a ‘free’ service and the client will be invited to witness the conveying trials to show that their material can be conveyed reliably.
It is unlikely that the geometry of the test facility will match that of the plant pipeline to be built, but with the use of appropriate scaling parameters such differences can be accounted for. With regard to the pipeline these differences include: pipeline bore; horizontal and vertical lengths; number, location and geometry of bends in the pipeline; and pipeline material. With regard to conveying conditions, conveying line pressure drop, conveying air velocity and solids loading ratio of the conveyed material can all have an influence on the conveying performance of the pipeline. With regard to the conveyed material there is mean particle size and size distribution, particle shape and particle density. If tests are carried out with a specific material, it is possible that the computer program will not have to take particle properties into account, but such a program could not possibly be used for another material, or even a different grade of the same material, with any degree of reliability.
The potential influence of material grade is illustrated in Figure 4.39, where conveying data for both a coarse and a fine grade of fly ash are compared (Mills & Agarwal 2001).
Fly ash comes from the combustion of pulverised coal in a boiler. The resulting ash is mostly carried over with the combustion gases. The coarse ash soon drops out of suspension
Air mass flow rate (kg/s) Air mass flow rate (kg/s)
Fly ash flow rate (tonne/h) Fly ash flow rate (tonne/h)
24
Figure 4.39 Conveying data for fly ash. (a) Coarse grade; (b) fine grade.
in the economiser and air pre-heater hoppers but the fine ash has to be physically removed by electrostatic precipitators. Both grades of ash were conveyed through the same pipeline in Figure 4.38 and it will be seen that the coarse grade had no dense phase conveying potential at all. There were also very marked differences in material flow rates achieved.
4.5.1 Conveying air velocity
Conveying air velocity is clearly important and that at the material feed point into the pipeline is critical. A problem comes in evaluation of this velocity, for compressors are specified in terms of a given quantity of air being delivered at a given pressure, and the reference point for each is different. The volumetric flow rate of the air delivered, ˙V0, is that at ‘free air conditions’ (standard atmospheric pressure and temperature) and this will generally be close to that at the pipeline exit. The delivery pressure will be close to that at the pipeline inlet. Compressibility, therefore, must be taken into account.
The basic equation here is the Ideal Gas Law:
p ˙V = ˙maRT (4.2)
The inclusion of the characteristic gas constant, R, in this equation means that this equation can be used for any gas. Nitrogen, carbon dioxide, superheated steam and many other gases are often used for pneumatic conveying. The following equations, however, are derived in terms of air only. If any other gas is employed the equations will have to be re-worked with the appropriate value of R.
From this equation is derived:
p1V˙1
T1
= p2V˙2
T2
(4.3) This applies for any gas and is essentially a continuity equation for the conveying system and pipeline.
The volumetric flow rate of the air (or any other gas) at any point can be obtained from:
V˙ =πd2
4 × C m3/s (4.4)
4.5.2 Compressor specification
A conveying line inlet air velocity, C1, will need to be specified for the given material and conveying conditions, and a pipeline bore, d, will also need to be evaluated. By re-arranging the above equations and substituting for constants (including R) and free air conditions it can be shown that:
V˙0= 2.23 × p1d2C1
T1
m3/s (4.5)
This is the volumetric flow rate of air required for conveying the material through the pipeline. To this may need to be added an allowance for any leakage of air across the material feeding device.
The air supply pressure to be specified will be p1plus allowances for any pressure drops, such as that between the compressor and the material feed point into the pipeline.
It should be emphasised that absolute values of both pressure and temperature must always be used in all of the above equations.
4.5.3 Solids loading ratio
Solids loading ratio,φ, as mentioned earlier, is the dimensionless ratio of the mass flow rate of the material conveyed divided by the mass flow rate of the air used to convey the material.
Air flow rate is almost exclusively expressed in terms of a volumetric flow rate and so air mass flow rate is most conveniently derived from the conveying line inlet air conditions. A further re-arrangement of the above equations gives:
m˙a= 2.74 × p1d2C1
T1
kg/s (4.6)
This then gives the solids loading ratio as:
φ = m˙p
3.6 ˙ma
(4.7) since material flow rate is traditionally expressed in terms of tonne per hour.
1.2
0.8
0.4
00 0.04 0.08 0.12 0.16 0.20 0.24
Conveying line pressure drop (bar)
Air mass flow rate (kg/s) Material flow rate (tonne/h)
Air only 6
4
2
0 8
Figure 4.40 Typical pressure drop relationship for pipeline with material flow.
4.5.4 The air only datum
The pressure drop required to convey the air alone through the pipeline provides a datum for the conveying system. Only when the conveying line pressure drop exceeds this datum value will any material be conveyed, but then the greater the excess over this datum pressure drop the greater will be the material flow rate. This is illustrated in Figure 4.40, with the zero material flow rate line being the air only pressure drop for the pipeline.
This air only pressure drop can be calculated reliably from basic fluid mechanics. The equation used here is that derived by Darcy:
p = 4 f L
d ×ρ C2
2 N/m2 (4.8)
The friction factor, f , is a function of the Reynolds number, Re, for the flow and the pipe wall roughness, and can be obtained from a Moody chart. Because air is compressible, both air velocity and air density will vary along the length of the pipeline and so Equation (4.8) should be integrated between limits in order to get an accurate value. This would be recommended in any situation where the air only pressure drop represents a high proportion of the available pressure drop for conveying, such as for long distance conveying.
It will be seen from Figure 4.40 that there is approximately a square law relationship between pressure drop and velocity. Conveying line inlet air velocity values, therefore, should not be too high or there will be an adverse effect on conveying performance, as will also be seen from Figure 4.40. The conveyed material in Figure 4.40 was a granular grade of potassium chloride and so was only capable of dilute phase conveying. The pipeline used was 95 m long, of 81 mm bore, with nine 90◦long radius bends and was almost entirely in the horizontal plane.
4.5.5 Acceleration pressure drop
The material that is fed into the pipeline will essentially have zero velocity at the feed point and so will have to be accelerated to its terminal velocity at the end of the pipeline. The pressure drop for this can be approximated with:
pacc= (1 + φ) ×ρ2C22
2 N/m2 (4.9)
The density and velocity terms are those of the air at the end of the pipeline. The approxi-mations lie in the fact that the air will have an initial velocity, and the terminal velocity of the material will be below that of the air, the actual velocity depending upon particle size, shape and density.
4.5.6 Scaling parameters
If conveying data for a given material is available, from a test pipeline or another plant pipeline, this data can be scaled to that for any other plant pipeline. Any differences in pipeline length, bore, orientation and number of bends between the two pipelines can be taken into account by means of scaling parameters. Any data coming from another pipeline will automatically include pressure drop elements for straight pipeline, bends, air only and acceleration, and so it will be a matter of determining the differences in values between the two pipelines. The evaluation can be carried out in three parts, with one for the air only, another for the acceleration and the third for all the pipeline elements, such as straight sections and bends, considered in terms of an equivalent pipeline length.
4.5.6.1 Conveying mode In scaling from one set of pipeline data to another, on no account should the conveying limits derived for the new pipeline exceed those of the original data, unless there is positive evidence that the material is capable. This means that the conveying line inlet air velocity derived should not be lower than that for the data to be scaled. If the pressure gradient available for the new pipeline is greater than that for which the original data was derived, the solids loading ratio may be much higher (see Figure 4.34), and hence a much lower conveying line inlet air velocity may appear possible (see Figure 4.33). If a material has no natural dense phase conveying potential, however, there will be no possibility of conveying the material at a lower velocity, and hence in dense phase, if a higher pressure gradient is available, unless there is a change in the type of conveying system used.
4.5.6.2 Equivalent length The equivalent length of a pipeline is taken in terms of the length of straight horizontal pipeline. This means that all straight horizontal sections of pipe in a pipeline can be added together and effectively have a weighting of unity.
4.5.6.3 Vertical pipeline For material flows vertically up the pressure drop will be ap-proximately double that for horizontal pipeline. For vertically upward pipeline, therefore, it is recommended that the length of vertically up sections is doubled to provide an equivalent length (Mills 2004; Mills et al. 2004).
For material flows vertically down the pressure gradient can be positive or negative, depending upon the value of solids loading ratio at which the material is conveyed. For
dilute phase flows there is generally a pressure drop for the pipeline but for dense phase flows, with air retentive materials, there is usually a pressure rise (Mills 2004; Mills et al.
2004). If the pipeline system to be designed has any significant length of vertically downward flow, great care will have to be exercised with the design process.
It is generally recommended that inclined sections of pipeline, particularly for vertically upward flow, should be avoided and that only horizontal and vertical sections should be employed in any pipeline routing. The minimum conveying air velocity required for inclined pipeline sections can be higher than that for horizontal and vertically up sections of pipeline, and so are more vulnerable to pipeline blockage. The pressure gradient in such inclined sections is also generally higher than that for horizontal pipeline.
4.5.6.4 Pipeline bends Data for the equivalent length of pipeline bends was given in Figure 4.35. Although the data relates to bends having a bend diameter, D, to pipeline bore, d, ratio of about 24:1, it is generally considered that the relationship holds for D/d ratios down to about 3:1 (Mills 2004; Mills et al. 2004). Below this, and certainly for blind tees (see Figure 4.28c), the equivalent length can be much greater.
Although bends provide pneumatic conveying systems considerable flexibility in routing, there is a considerable penalty to pay in terms of pressure drop, and hence conveying capability. The equivalent length in Figure 4.35 is in terms of conveying line inlet air velocity and it will be seen that for dilute phase conveying, bend losses can be very significant. The total loss due to the bends is the value from Figure 4.35 multiplied by the total number of bends in the pipeline, and so every effort should be made to keep the number of bends in a pipeline to a minimum.
Little data is available for 45◦ and other bends. Because the primary impact of the conveyed material in making the turn is the major cause of the material retardation, and hence its subsequent re-acceleration (see Figure 4.29), bend angle is not likely to have a major influence.
4.5.7 Scaling model
The scaling model for equivalent length is in terms of material flow rate:
m˙p2 = ˙mp1×Le1
Le2
tonne/h (4.10)
This is an inverse law relationship and so for a given air supply pressure, and hence energy value, if the length of pipeline is doubled, for example, there will be an approximate halving of the material flow rate. If scaling is to a longer pipeline there will be an additional loss to take into account, because of the increase in air only pressure drop for the pipeline, for pipeline length is on the top line of Equation (4.8).
4.5.7.1 Pipeline bore If a high material flow rate is required it is likely that a larger pipeline bore will be needed. This scaling can be carried out independently of equivalent length. Although a higher conveying line pressure drop will give an improvement in perfor-mance, it will generally be small in comparison to that which can be obtained by increasing pipeline bore. If a larger bore pipeline is used there is likely to be an additional bonus, for the air only pressure drop for the pipeline will be lower, since pipeline bore is on the bottom
Minimum conveying air velocity (m/s)
0 20 40 60 80 100
16
12
8
4
0
Solids loading ratio (dimensionless) Potassium sulphate
Ordinary portland cement
Figure 4.41 Conveying limits for materials considered.
line of Equation (4.8). The scaling model for pipeline bore is:
m˙p2 = ˙mp1×
d2
d1
2
tonne/h (4.11)
4.5.7.2 Scaling influences When designing a pneumatic conveying system to achieve a given material flow rate over a specified conveying route there is always a wide selection of conveying parameters that can be employed. If a large bore pipeline is selected, then a low pressure will be required and if a high pressure is used, then a smaller bore pipeline will meet the duty. There is an almost infinite combination of pipeline bore and air pressure combinations that could be used, limited only by the availability of pipeline in regular increments in size of bore, and an upper limit on air supply pressure of about 5 bar gauge, for positive pressure conveying systems delivering materials to reception points at atmospheric pressure, due to the problems of air expansion.
Where there is such a choice available in selecting conveying parameters the question arises as to the possible influence on power requirements, since this does tend to be rather high for pneumatic conveying systems. For materials that can be conveyed in dense phase there is the additional question of conveying capability if a high pressure air supply is not employed. To illustrate these points ordinary portland cement, being typical of powdered materials, and potassium sulphate, being typical of granular materials, are used. Cement has very good air retention properties and is capable of being conveyed in dense phase and hence at low velocity, whereas the potassium sulphate considered is a coarse granular material and can only be conveyed in dilute phase suspension flow. The conveying limits for these materials are presented in Figure 4.41.
Conveying data for the two materials was obtained from a pipeline 95 m long, of 81 mm bore and included nine long radius 90◦ bends. The influence of pipeline bore only is in-vestigated, with a material flow rate of 40 tonne/h for the cement and 12 tonne/h for the potassium sulphate considered by way of example. The results are shown in Figure 4.42.
With a wide range of pipeline bore and air supply pressure combinations capable of achieving a given material flow rate, the obvious question is which bore or air supply
Pipeline bore (mm) Potassium sulphate
(12 tonne/h)
Cement (40 tonne/h)
Air supply pressure (bar gauge)
3
2
1
0
80 100 120 140 160 180 200 220
Figure 4.42 Influence of pipeline bore on air supply pressure for given parameters.
pressure results in the most economical design? Plant capital costs could vary considerably, for with different pipeline bore and air supply pressures there are differences in feeder types, filtration requirements and air mover types, apart from widely different pipeline costs, and so a major case study would need to be carried out. Power requirements, and hence operating costs, however, are largely dependent upon the air mover specification and so these can be determined quite easily by using Equation (4.1).
The approximate power requirements for the cases considered are presented in Figure 4.43. In most cases the power required for the air mover represents the major part
Pipeline bore (mm) Potassium sulphate
(12 tonne/h)
Cement (40 tonne/h)
Power required (kW)
120
100
80
60
40
20
0
80 100 120 140 160 180 200 220
Figure 4.43 Influence of pipeline bore on power requirements for given parameters.
of the total system power required, although for screw pumps a major allowance must also be made for the screw drive. Figure 4.43 presents an interesting trend for both of the ma-terials considered. For the cement the smallest bore pipeline is clearly the best, but for the potassium sulphate it is the largest bore pipeline.
For the potassium sulphate the decrease in power requirements with increase in pipeline bore can be explained in terms of the decrease in velocity through the pipeline. With a conveying line inlet air pressure of 3.2 bar gauge the conveying line exit air velocity will be about 68 m/s, and this reduces to 27 m/s with the much lower air supply pressure required for the 200 mm bore pipeline. Pressure drop increases significantly with increase in conveying air velocity and so the pipeline with the lowest velocity profile will generally give the lowest power requirement for a material such as potassium sulphate.
For the cement the increase in power with increase in pipeline bore can also be explained in terms of velocity profiles, but in this case it is values of conveying line inlet air velocity that are relevant. Since cement is capable of being conveyed in dense phase, the relationship between minimum velocity and solids loading ratio, as shown in Figure 4.41, dictates. In an 81 mm bore pipeline the inlet velocity is only 4.2 m/s, since the solids loading ratio is 109. In the 200 mm bore pipeline the solids loading ratio is reduced to 14 and so the inlet air velocity is 12.0 m/s.
The above relationship holds equally for negative pressure conveying systems. Because of the natural limit on conveying line pressure drop available, however, the situation is limited to short distance conveying.
4.5.8 Scaling procedure
The primary objective of a system design is generally to achieve the given material flow rate.
The first stage in the design process, therefore, is to scale the available data approximately to the required conveying distance using Equation (4.10). For this it will be necessary to evaluate or specify a value for the conveying line inlet air velocity. With both pressure drop and pipeline bore having an influence on material flow rate a decision will have to be made both on the air supply pressure, or vacuum, and the pipeline bore. In the first instance a linear relationship can be used for conveying line pressure drop and Equation (4.11) for
The first stage in the design process, therefore, is to scale the available data approximately to the required conveying distance using Equation (4.10). For this it will be necessary to evaluate or specify a value for the conveying line inlet air velocity. With both pressure drop and pipeline bore having an influence on material flow rate a decision will have to be made both on the air supply pressure, or vacuum, and the pipeline bore. In the first instance a linear relationship can be used for conveying line pressure drop and Equation (4.11) for