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Conveyed Material Influences

1 INTRODUCTION

Although the performance of a pipeline with air only can be predicted reliably, theaddition of material to the flow of air changes the situation entirely. This was illus-trated in Chapter 5 where the conveying characteristics of a number of differentmaterials were presented. These were used to illustrate the differences in convey-ing capability between different materials, and the very wide differences that canexist between materials that can be conveyed in dense phase and those that cannot.

In this chapter these conveying characteristics are developed further to illus-trate the influence of conveying air velocity, and hence air flow rate, in more de-tail. Power requirements and specific energy are also considered, so that the influ-ence of velocity can be considered in more meaningful terms. This will also pro-vide a better basis for comparison between dilute and dense phase conveying ca-pability and provide a basis on which pneumatic conveying can be compared withalternative methods of conveying.

Pipeline bore and conveying distance are then considered. Pipeline bore isimportant because of the major influence that it has on the conveying capability ofa pipeline. Conveying distance is generally the most problematical of all the vari-ables. Conveying distance will nearly always be different from one situation to thenext, and hence the pressure gradient will also be different. It is essentially the

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

210 Chapter 7

pressure gradient that will dictate the solids loading ratio at which a material canbe conveyed through a pipeline, as was illustrated in Figures 4.23 and 24. Then formaterials that have very good air retention properties, such as cement, the mini-mum conveying air velocity varies with solids loading ratio, as was illustrated inFigure 4.6.

2 MATERIAL COMPARISONS

Various materials were compared in Chapter 4 in terms of their conveying capabil-ity and the broad divisions that result between materials that can be conveyed indense phase and those that can not. In this section the differences are examined interms of conveying air velocities, power requirements and specific energy. Forcontinuity the three materials considered earlier are examined further. The materi-als were cement, sandy alumina and polyethylene pellets. Conveying characteris-tics for cement were presented in Figure 4.5b and are reproduced here in Figure7.1 for reference.

All three materials were conveyed through the Figure 4.2 pipeline whichwas 165 ft long of two inch nominal bore and included nine 90° bends. Similardata for the alumina and polyethylene pellets from Figures 4.8b and 12b are simi-larly reproduced in Figures 7.2 and 3. To allow visual comparisons to be made thesame axes have been used for all three materials and conveying line pressure dropvalues up to 25 lbf/in2 have been considered in each case.

Pressure Drop 160 120

Solids LoadingRatio

20

10

40 80 120

Free Air Flow Rate - itVmin

160

Figure 7.1 Conveying characteristics for cement.


Material Conveying 211

30

20

t-3 10

Solids LoadingRatio

Conveying Line PressureDrop - lbf/in2

NO GO AREA

ConveyingLimit

40 80 120 160 200

Free Air Flow Rate - ft/min

Figure 7.2 Conveying characteristics for sandy alumina.

The data, therefore, relates to positive pressure conveying. A relatively highpressure has been used in order to accentuate the differences between the materialsconsidered. The same differences, however, will exist in negative pressure con-veying and so the analysis undertaken, and the results obtained, will differ littlebetween positive pressure and vacuum conveying.

ooo

cdOi

o

30

20

g 10'C

<Dta

Solids LoadingRatio

30


NO GO AREA

ConveyingLimit

40 80 120 160Free Air Flow Rate - ft'/min

200

Figure 7.3 Conveying characteristics for polyethylene pellets.


212 Chapter 7

2.1 Conveying Air Velocity

Since conveying air velocity is such an important parameter this is consideredfirst. Conveying line inlet air velocity is one of the basic design parameters for apneumatic conveying system and so it is this value that is plotted. This is purely amathematical process.

The relevant model for plotting velocity on the conveying characteristicswas developed in Chapter 5 at Equation 10 and is re-presented here:

F = 0-1925pd2C

ftVmin (1)

where Vn = volumetric flow rate of free air - ftVmin

p = conveying air pressure - lbf/in2 absoluted = pipeline bore - inC = conveying air velocity - ft/min

and T = absolute temperature of air - R

Pipeline bore and air temperature will be known, and so for a given value ofconveying air velocity, the corresponding value of free air flow rate for given val-ues of conveying line inlet air pressure can be evaluated. By this means lines ofconstant value of conveying line inlet air velocity can be plotted. Such a plot forcement is presented in Figure 7.4.

160 120,100

Solids LoadingRatio

Conveying Line InletAir Velocity - ft/min

40 /

,3000

40 80 120 160

Free Air Flow Rate - ft3/min

200

Figure 7.4 Conveying air velocity data for cement.



At high values of solids loading ratio the minimum conveying air velocityfor the cement is about 600 ft/min. For dilute phase, suspension flow, the mini-mum velocity is about 2000 ft/min. Between these two extremes the conveyinglimit is dictated by the relationship between minimum conveying air velocity andsolids loading ratio presented in Figure 4.7. An extremely wide range of convey-ing conditions, therefore, are available for cement. To help in the decision makingprocess, power requirements and specific energy are developed in a similar man-ner below.

The lines of constant conveying air velocity help to illustrate the problemsof compressibility with air. As conveying air pressure increases, the value of thefree air flow rate must increase in order to maintain the same value of velocity. Inmany pneumatic conveying systems there is a limit on the volumetric flow rate ofair available and so great care must be taken if material feed rate into the pipelineis increased since this will require an increase in pressure for conveying.

Because exit from the pipeline in this case is always at atmospheric pres-sure, the conveying line exit air velocity only varies with air flow rate. Conveyingline exit air velocity can be determined simply by putting p = 14-7 lbf/in2 intoEquation 7.1 to determine this value. Similar data for the sandy alumina is pre-sented in Figure 7.5.

The range of conveying conditions for this material are very limited since itis only capable of being conveyed in dilute phase, suspension flow. The conveyinglimit, dictated by the combination of a fixed value of minimum conveying air ve-locity and the compressibility of the air, significantly reduces the operating enve-lope for this type of material.

ooo

30 Conveying Line Inlet AirVelocity - ft/min

Solids LoadingRatio

Conveying Line Pressuredrop - ibfin

c5B!_o

3 to.x>*^->Cl' ^—~'

..•'5000

..6000

0 40 80 120 160 200Free Air Flow Rate - fVVrnin

Figure 7.5 Conveying air velocity data for sandy alumina.


214 Chapter 7

g30o

o

10

O03

Conveying Line Inlet AirVelocity - ft/min

Solids Loading/ Ratio

30Conveying Line Pressure

Drop - Ibf/in

40 80 120 160Free Air Flow Rate - ftVmin

200

Figure 7.6 Conveying air velocity data for polyethylene pellets.

As a consequence, changes in material feed rate, and hence pressure, have amuch greater effect in dilute phase conveying than they do in dense phase. Similardata for the polyethylene pellets is presented in Figure 7.6.

Although this material is capable of being conveyed at very low velocity,and hence in dense phase, the operating area available for dense phase conveyingis also very limited. The minimum conveying air velocity for this material for di-lute phase conveying will be about 3000 ft/min. Because of the positive slope tothe conveying limit curve only a narrow band, at low material flow rates, is avail-able for operation between these two limits. It is interesting that the 3000 ft/minvelocity curve approximately passes through the maximum value point on eachconstant pressure drop line.

2.2 Power Requirements

Pneumatic conveying has a certain reputation for high power requirements, cer-tainly with regard to dilute phase conveying, and so this is explored with regard tothe three materials being investigated. The relevant model for plotting power re-quirements on the conveying characteristics was developed in Chapter 3 at Equa-tion 6 and is re-presented here:

Power = 0-128 V hp (2)

where VQ = air flow rate at free air conditions - ftVmin

p2 = compressor delivery pressureand pi = compressor inlet pressure

- Ibf/in abs- Ibf/in2 abs



In order to plot lines of constant power, P, it is the volumetric flow rate of

free air, Va, that needs to be the subject of the equation and so a re-arrangement

gives:

• 7-81 P ,V0 = —, r ft3/min (3)

where P = power - hp

For a given value of power, P, the corresponding value of free air flow ratefor given values of conveying line inlet air pressure can be evaluated. By thismeans lines of constant value of power required can be plotted. Such a plot forcement is presented in Figure 7.7.

Power requirements for the cement on Figure 7.7 vary from a minimum ofabout 2 hp to a maximum of 25 hp. This shows the influence of air flow rate, andhence conveying air velocity very well. With a conveying line pressure drop of 25Ibf7in2, for example, 34,000 Ib/h of cement can be conveyed with 5 hp and 20,000Ib/h can be conveyed with the same 25 lbf/in2, but 25 hp. This represents a fivefold increase in power for a 40% reduction in cement flow rate. It is generally rec-ommended that a system be designed with a conveying line inlet air velocity about20% greater than the minimum conveying air velocity value.

Solids Loading Ratio

Power Required-hp

40 80 120 160 200

Free Air Flow Rate - ftVmin

Figure 7.7 Power requirements data for cement.


216 Chapter?

This is usually a sufficient margin to allow for pulsations in material flowrate, compressor characteristics and compressibility effects. Although cement canbe conveyed at any point on the performance map it is clearly inefficient to do soat unnecessarily high air flow rates.

It is obviously necessary to know the value of the minimum conveying airvelocity and this is why conveying trials with a material are so important, particu-larly if previous experience with a material is not available. Similar data for thesandy alumina is presented in Figure 7.8.

Because of the very much higher minimum conveying air velocity with thismaterial only the bottom right hand corner exists, but it is essentially the samepattern of curves.

There is no longer any scope for the 5 hp curve to convey any substantialamount of material and capabilities are in a more ordered fashion. The slope of theconstant power curves is the same and so with 10 hp, for example, 10,000 Ib/h canbe conveyed with 140 ftVmin of free air and 2,500 Ib/h can be conveyed with 200ft3/min of free air. This represents a four-fold reduction in conveying capability fora 40% increase in air flow rate.

The 10 hp curve will ultimately reach the horizontal axis and convey noth-ing when the power is entirely taken up by transporting the air through the pipe-line. An explanation for this comes the pressure drop model for air only that wasfirst presented in a simplified form in Chapter 4 at Equation 1 and is re-presentedbelow for reference:

Solids Loading Ratio30

Power Required - hpooo

£ 20

sE.2 10


80 120 160 200

Free Air Flow Rate - If/min

Figure 7.8 Power requirements for sandy alumina.



Apf LpC2

dlbf/in2

(4)

It is the velocity term, C2, that dominates in this situation and is one of themain reasons why the constant power lines slope so steeply in this region. To con-vey more material the air flow rate needs to be reduced, but there is a conveyinglimit in the way to prevent this.

To convey more material the air pressure can be increased, provided that theair mover has the necessary capability and power, but if this is at the same air flowrate, the conveying limit is in the way once again. This is why a performance mapfor a material is so important, for it provides all the information necessary to makeall the decisions required for a successful system design. Similar data for the poly-ethylene pellets is presented in Figure 7.9.

There is little difference between the power requirements data for the poly-ethylene pellets and that for the sandy alumina. This is mainly because the operat-ing envelope for dense phase conveying with the polyethylene pellets is so small.Most of the performance data is in the dilute phase conveying region and this dif-fers little with regard to the properties of the material, regardless of whether thematerial can be conveyed in dense phase or not.

The main difference between the pellets and the alumina comes in systemoperation. If air flow rate is reduced, or pressure increased, with the pellets theconveying system will simply stall, and if the conveying conditions are changed itshould be possible to re-start with little problem.

30ooo

I 20

o

Power Required - hp


\30

25

Conveying Line PressureDrop - Ibf/irv

80 120


160 200

Figure 7.9 Power requirements data for polyethylene pellets.


218 Chapter 7

The conveying limit for the alumina, and other similar materials that canonly be conveyed in dilute phase, suspension flow, is that the conveying limit gen-erally represent pipeline blockage, and once blocked it is often a time consumingprocess to clear the pipeline and re-start.

2.3 Specific Energy

In the above examples specific cases have been taken to illustrate particular points,such as the effect of air flow rate on performance. A problem with this is thatmany other parameters change and so global comparisons are difficult to make. Abasis on which direct comparison can be made is that of specific energy. This willprovide a reliable basis for comparing different materials, such as those being il-lustrated here, and with alternative mechanical conveying systems for the givenduty.

The units of specific energy are horsepower-hour per ton of material con-veyed or hp h/ton. Specific energy data superimposed on the conveying character-istics for the cement is presented in Figure 7.10.

Specific energy, E, is simply the ratio of power required, P, in hp, to material

flow rate, m „ , in ton/h:

8 = hp h/ton (5)

30

;, so

1b.

"3 101

25

10

0-5160 120

/, 100 80

Solids Loading/Ratio

40 80 120 160


200

Figure 7.10 Specific energy data for cement.



Power requirement data was presented in Figures 7.7 to 7.9. To plot lines ofconstant specific energy simply divide power required by material flow rate andmark points on the graph that give rounded values of 0-5, 1-0, 1-5, etc. Thesepoints can then be joined to provide lines of constant specific energy. Such datafor the cement from Figure 7.7 is presented in Figure 7.10.

For the cement the specific energy data clearly identifies low velocity con-veying as being the most efficient. A wide range of specific energy values appearon Figure 7.10 but this is only because air flow rates up to 200 fWmin have beenincluded, to be consistent with the other materials being considered. For normalpurposes, and certainly for conveying, air flow rates above 80 ft3/min need not beconsidered for cement in the pipeline used. Similar data for the sandy alumina ispresented in Figure 7.11.

Specific energy data for alumina follows a similar pattern to that for the ce-ment. Values, however, are generally about five times higher and this typifies thedifference between dilute and dense phase conveying capability. The influence ofpressure is a little difficult to isolate.

Constant specific energy lines tend to run approximately parallel to the con-veying limit and so at first sight it would appear to have little effect. With highpressure air for conveying, however, stepping of the pipeline to a larger borewould be recommended.

All the data presented in this chapter is for the Figure 4.2 pipeline which issingle bore. At higher pressures, and with stepped bore pipelines, an improvementin performance would be expected.

30ooo


Specific Energy

Conveying Line Pressure

80 120 160 200

Free Air Flow Rate - fVVmin

Figure 7.11 Specific energy data for sandy alumina.


220 Chapter 7

30

20

_o 10


Specific Energy - hp h/ton I

Conveying LinePressure Drop - Ibf7in

0 40 80 120 160 200

Free Air Flow Rate - ft7min

Figure 7.12 Specific energy data for polyethylene pellets.

With regard to pressure, comparisons across a given set of conveying char-acteristics are not likely to be made. They can certainly be used to investigate theimprovement in performance for a given system, but the alternative influence ofpipeline bore is more likely to be considered when designing a new system. Pipe-line bore will be considered as a separate issue later in this chapter.

Similar specific energy data for the polyethylene pellets is presented in Fig-ure 7.12. This follows a similar pattern to that of the alumina once again. At verylow values of air flow rate specific energy values are low, but material flow ratesare also low and so a much larger bore pipeline would probably be needed toachieve the desired material flow rate.

3 INFLUENCE OF PIPELINE BORE

Pipeline bore has a major influence on conveying capacity, as has been mentionedbefore. The influence of pipeline bore on conveying rate is reasonably predictableand so to illustrate the influence that pipeline bore can have two further materialshave been selected for this purpose. One is a very fine grade of dicalcium phos-phate, which is capable of being conveyed in dense phase. The other is a coarsegrade of magnesium sulfate which can only be conveyed in dilute phase in a con-ventional conveying system. Both materials were conveyed through a 310 ft longpipeline of three inch nominal bore having nine 90° bends. A sketch of the pipe-line is given in Figure 7.13 for reference.



Pipeline:LengthBoreBendsD/d =

310ft3 in nominal9x90°16

Figure 7.13 Sketch of three inch bore pipeline.

Conveying data for the dicalcium phosphate and the magnesium sulfate con-veyed through the above pipeline are presented in Figure 7.14.

Solids LoadingRatio

Conveying LinePressure Drop

- lbf/in2

NO GO AREA 25^* ,̂ ] 0

20-

(a)

0 100 200 300 400

Free Air Flow Rate - ftVmin(b)

0 100 200 300 400Free Air Flow Rate - ft3 / min

Figure 7.14 Conveying characteristics for materials conveyed through the pipelineshown in figure 7.13. (a) Dicalcium phosphate and (b) magnesium sulfate.


222 Chapter 7

From Figure 7.14a it will be seen that the dicalcium phosphate could be con-veyed in dense phase and solids loading ratios up to about 120 were achieved. Themagnesium sulfate, however, had no dense conveying capability, the maximumvalue of solids loading ratio achieved was about 12, and the minimum value ofconveying air velocity was about 2500 ft/min.

It will also be noticed that conveying line inlet air pressures up to 30 lbf/in2

were used for both materials. The material flow rates achieved, however, werevery different and so a reduced scale has been used for the magnesium sulfate. 400fWmin of free air was available for conveying and it will be seen that within thislimit the maximum pressure that could be used for conveying was about 30 IbfVin2.Although the same horizontal axis has been used for both materials, it could wellhave been halved for the dicalcium phosphate.

3.1 Scaling Parameters

To illustrate the influence of pipeline bore on conveying capability, the conveyingdata presented in Figures 7.14a and b will be scaled to larger bore pipelines. Toisolate the influence of pipeline bore the length and geometry of the pipeline willremain the same in each case considered.

For the scale up of the conveying characteristics in respect of pipeline bore,the change in datum for the empty line will have to be taken into account. Thisprocess was considered earlier in Chapter 6 with Figure 6.5. For reference pur-poses a similar plot is presented in Figure 7.15, specifically for the Figure 7.13pipeline.

10

^ 8<4-

£

I

QJJ3c/s A

Cu

1 2l-

<

0

PipelineBore - i

0 100 200 300 400 500

Free Air Flow Rate - ftVmin x (d,/3)2

600

Figure 7.15 Influence of pipeline bore and air flow rate on empty pipeline pressuredrop for figure 7.13 pipeline.



The variation of pressure drop with air flow rate for the three inch bore pipe-line is included and so the change in datum can be obtained by taking the differ-ence between the three inch and the required bore of pipeline. It will be seen fromthis that the air only pressure drop element reduces significantly with increase inpipeline bore. For a given conveying line inlet air pressure this means that thepressure drop available for conveying material will increase slightly with increasein pipeline bore, and so it will be possible to convey more material as a conse-quence.

3.1.1 Scaling Model

Scale up of material flow rate, m „ , with respect to pipeline bore, d, can be carried

out with a reasonable degree of accuracy, if the extrapolation is not too great, onthe basis of pipe cross-sectional area, A:

mp x A oc d2 - - - - (6)

or alternatively:

m , m i

- - - c o n s t (7)

3.1.1.1 Working ModelThe working form of this scaling model is:

2x - Ib/h --- ..... (8)

where subscripts 1 and 2 relate to the appropriatepipe bores of the two pipelines

It is for this reason that the air flow rate axis on Figure 7.15 is in terms of airrequired for the three inch bore pipeline x (d2/3) . Conveying air velocities scaleup exactly and so a common axis can be used. For scaling up of the characteristicsin Figures 7.14a and b to larger bore pipelines the datum pressure drop should firstbe changed throughout by the appropriate values obtained from Figure 7.15. Mate-rial flow rates for a given air flow rate and pressure drop are then scaled in theratio of (d2/3)2.

The results of scaling the data in Figures 7.14a and b to larger bore pipelinesare presented in Figure 7.16 and 7.17. Scaling in each case has been carried out for4, 5, 6 and 8 inch bore pipelines.


224 Chapter 7

.100

200 400 600

(a)Free Air Flow Rate - ft/min

200 80 6040

(b)

0 200 400 600 800 1000

Free Air Flow Rate - ft'/min

10030-^ -80 60

40

0 - , , , . ' , , , , , ,

20

0

(c)

0 400 800 1200 1600Free Air Flow Rate - ftVmin

(d)

0 1000 2000Free Air Flow Rate - ft3/min

Figure 7.16 Conveying characteristics for dicalcium phosphate in various bore pipe-lines relating to figure 7.13. (a) 4 inch bore, (b) 5 inch bore, (c) 6 inch bore, and (d) 8 inchbore pipeline.



100

,, § 8014 o

(a)

200 400 600Free Air Flow Rate - ftVmin

(b)

200 400 600 800 1000Free Air Flow Rate - ftVmin

800 1200 1600

Free Air Flow Rate - ft/min(C)

250

200

150

100

(d)

1000 2000

Free Air Flow Rate - ft/min

Figure 7.17 Conveying characteristics for magnesium sulfate in various bore pipelinesrelating to figure 7.13. (a) 4 inch bore, (b) 5 inch bore, (c) 6 inch bore, and (d) 8 inch borepipeline.


226 Chapter 7

3.2 Scaling to Larger Bores

The scale up in terms of pipeline bore produces a set of curves that are basicallygeometrically similar for both materials, apart from the slight change due to theshift in datum for the empty line pressure drop relationship. There is, therefore,little difference in minimum conveying conditions for different pipeline bores,since similar solids loading ratios result. Air flow rates are totally different, ofcourse, as these have been scaled up in proportion to the pipeline cross-sectionalarea.

As pipeline bore increases there will be a need to increase the minimumvalue of conveying air velocity slightly because of the boundary layer effect. Asthe pipeline bore increases, the low velocity area in the boundary layer also in-creases and an increase in conveying air velocity is required to compensate and soprevent saltation.

The design department of a company installing a pneumatic conveying sys-tem are unlikely to go through this detailed process of scaling. They will knowwhat type of system they wish to supply and so will scale one or two data pointsonly. The detail is included here to illustrate the global changes, and to show howpipeline bore can influence the design and specification decisions.

If a range of pipeline bores is considered for a given material flow rate, theconveying line pressure drop required will decrease, and the air flow rate will in-crease, with increase in pipeline bore. This means that the pressure capability ofthe feeding device will reduce, but the size of the filtration plant will increase.

To illustrate the influence of pipeline bore on system design parameters, ma-terial flow rates of 80,000 Ib/h for the dicalcium phosphate and 25,000 Ib/h for themagnesium sulfate have been considered. Data has been taken from the varioussets of conveying characteristics presented and that for the dicalcium phosphate ispresented in Table 7.1.

Table 7.1 Conveying Parameters for 80,000 Ib/h of Dicalcium Phosphate

Pipeline

Bore

in

3

4

5

6

8

Air Inlet

Pressure

Psig

33

21

13

9

6

Free Air

Flow Rate

cfm

145

170

205

290

740

Solids

Loading

Ratio

-

110

102

85

60

24

Conveying Air Velocity

At Inlet

ft/min

800

800

800

900

1500

At Outlet

ft/min

2610

1950

1500

1480

2120

Power

Required

hp

22

19

17

18

32



Table 7.2 Conveying Parameters for 25,000 Ib/h of Magnesium Sulfate

Pipeline

Bore

in

3

4

5

6

8

Air Inlet

Pressure

psig

31

19

12

8

5

Free Air

Flow Rate

cfm

520

600

740

930

1400

Solids

Loading

Ratio

-

10-5

9-1

7-4

5-9

3-9

Conveying Air Velocity

At Inlet

ft/min

3000

3000

3000

3000

3000

At Outlet

ft/min

9370

6870

5420

4730

4010

Power

Required

hp

75

64

57

54

52

Similar data for the magnesium sulfate is presented in Table 7.2.

3.2.1 Influence on Pressure

These tables show that there is a wide range of air supply pressure and pipelinebore combinations that are capable of meeting any given duty for a material. Toillustrate the point with regard to the influence of pipeline bore on air supply pres-sure, the data from Tables 7.1 and 7.2 is presented graphically in Figure 7.18.

30

I01

* 20

3

•3 10

80,000 Ib/h ofDicalcium Phosphate

25,000 Ib/h ofMagnesium Sulfate

5 6Pipeline Bore - inch

Figure 7.18 Typical air pressure - pipeline bore relationships for conveying duties.


228 Chapter 7

Figure 7.18 clearly shows that there is generally no one specific set of de-sign parameters for a pneumatic conveying system. With a wide range of pipelinebore and air supply pressure combinations being capable of achieving a given ma-terial flow rate, the obvious question is which pipeline bore or air supply pressureresults in the most economical design? Plant capital costs could vary considerably,for with different pipeline bore and air supply pressures there are correspondingdifferences in feeder types, filtration requirements and air mover types, apart fromwidely different pipeline costs, and so a major case study would need to be carriedout. Power requirements, and hence operating costs, however, are largely depend-ent upon the air mover specification and so these can be determined quite easily byusing Equation 3.6.

3.2.2 Power Requirements

The approximate power requirements for the cases considered are given in Tables7.1 and 7.2, and they are presented graphically in Figure 7.19. In most cases thepower required for the air mover represents the major part of the total systempower requirements, although for screw pumps a major allowance must be madefor the screw drive.

Figure 7.19 presents interesting trends for both materials considered. This isapart from the displacement of the curves, for very different conveying duties, butthis is primarily due to the fact that the magnesium sulfate could not be conveyedin dense phase.

80 I-

60

3cre* 40

o

20

25,000 Ib/h ofMagnesium Sulfate

80,000 Ib/h ofDicalcium Phosphate

5 6Pipeline Bore- inch

Figure 7.19 Influence of pipeline bore on power requirements for given conveyingduties.



For the dicalcium phosphate all of the smaller bore pipelines give reasona-bly low values of power requirement. This is because the material is conveyed indense phase in each case. It is only with the eight inch bore pipeline that there is amarked reduction in solids loading ratio and the power requirements start to risesteeply.

For the magnesium sulfate there is a gradual reduction in power require-ments with increase in pipeline bore. This is essentially due to the change in con-veying line exit air velocity. The minimum conveying air velocity for this materialis about 2500 ft/min and so a conveying line inlet air velocity of 3000 ft/min hasbeen taken in every case.

The minor influence of pipeline bore on minimum conveying air velocityhas not been taken into account in this case. Since all the pipelines considered aresingle bore, the conveying line exit air velocity is extremely high for the smallbore pipeline options, and this has a significant effect on pressure drop and henceconveying capability.

3.2.2.1 Stepped PipelinesFor the small bore pipeline/high pressure cases considered, stepped pipelineswould generally be recommended for both the dicalcium phosphate and the mag-nesium sulfate. This would have the effect of reducing the air supply pressureneeded, and hence the power required, for the smaller bore pipeline options.

In the case of the magnesium sulfate it would have the effect of making thepower requirement curve almost into a horizontal line at about 55 hp. For the di-calcium phosphate it would probably reduce the power requirements for all thesmall bore pipelines to about 15 hp. Chapter 9 of this Handbook is devoted en-tirely to stepped pipeline systems

4 INFLUENCE OF CONVEYING DISTANCE

Conveying distance also has a major influence on conveying capacity. If convey-ing distance is increased, the material flow rate will decrease, for the same convey-ing line inlet air pressure. If the air supply pressure is increased, and the air flowrate is also increased, to cater for the compressibility effect, it will be possible toachieve the same material flow rate. Increasing the air supply pressure, however, israrely an option.

The influence of conveying distance on conveying rate is reasonably pre-dictable and so to illustrate the influence that pipeline length can have, the datapresented in Figures 7.16d and 7.17d have been selected for this purpose. Theseare the conveying characteristics for the dicalcium phosphate and the magnesiumsulfate conveyed over 310 feet. This relates to the Figure 7.13 pipeline but havinga bore of eight inches. These two materials have been chosen once again becausethe influence of conveying distance is different between materials that are capableof being conveyed in dense phase and those that can only be conveyed in dilutephase.


230 Chapter 7

4.1 Scaling Parameters

To illustrate the influence of conveying distance on conveying capability the setsof conveying data presented in Figures 7.17d and 7.18d are taken as the referencepoints and are scaled to longer length pipelines. For the scale up of the conveyingcharacteristics in respect of pipeline length, the change in datum for the empty linewill have to be taken into account.

This process was considered in Chapter 6 with Figure 6.4. For referencespurposes a similar plot is presented in Figure 7.20 for the conveying distances tobe considered.

The variation of pressure drop with air flow rate for the 310 ft long pipelineis included so that the change in datum can be obtained by taking the differencebetween the 310 ft and the required length of pipeline. It will be seen from this thatthe air only pressure drop element increases with increase in pipeline length. For agiven conveying line inlet air pressure this means that the pressure drop availablefor conveying material will reduce slightly with increase in pipeline length. Thismust be taken into account, as well as the influence of conveying distance on con-veying capability.

4.1.1 Scaling Model

Scale up of material flow rate, mp , with respect to conveying distance, L, can be

carried out with a reasonable degree of accuracy, if the extrapolation is not toogreat, on the basis of a reciprocal law model:

10

a.o

o 2

Pipeline Length -2500 1500

1000

310

1000 2000

Free Air Flow Rate - frVmin

3000 4000

Figure 7.20 Influence of pipeline length and air flow rate on empty pipeline pressuredrop for 8 inch bore pipeline.



m oc — - - (9)P TA

or alternatively:

mplLc] = mp2Le2 = Const. . . . . . . . . (io)

For a constant air flow rate and pressure dropdue to the conveyed material.

where /»„ = mass flow rate of material

and Le = equivalent length of pipeline

Conveying distance, L, is expressed in terms of an equivalent length, Le, ofthe total pipeline. This comprises the three main elements of the pipeline routingand geometry. One is the length of the horizontal sections of pipeline, the secondis the length of vertically up or down sections of pipeline, and the third relates tothe bends in the pipeline. Horizontal pipeline is taken as the reference for equiva-lent length. The influence of distance, therefore, will ultimately depend upon therouting of the pipeline. For this exercise, to illustrate the typical influence of con-veying distance as a variable, the pipeline geometry in Figure 7.13 has been used.

4.1.1.1 Working ModelThe working form of this scaling model is:

m -, = mp]x-^ Ib/h - - - - - - - - ( i i )A2

where subscripts 1 and 2 relate to the appropriatelengths of the two pipelines

4.2 Scaling to Longer Distances

In this exercise the two materials are considered separately. With pipeline boreboth the air flow rate and material flow rate axes were scaled by the same parame-ter and so the results were approximately geometrically similar. For conveyingdistance only one of the axes has to be changed and this has a considerable distort-ing effect with regard to materials capable of dense phase conveying.

4.2.1 Magnesium Sulfate

The conveying characteristics for the sodium sulfate conveyed through the 310 ftlong pipeline of 8 in bore were presented in Figure 7.17d. Results of scaling tolonger length pipelines of 8 in bore are presented in Figure 7.21.


232 Chapter 7

(a)

0 1000 2000

Free Air Flow Rate - ftVmin(b)

0 1000 2000

Free Air Flow Rate - ftYmin

1000 2000

(C) Free Air Flow Rate - ft/min

1000 2000

(a) Free Air Flow Rate - ft/min

Figure 7.21 Conveying characteristics for magnesium sulfate in pipelines of increasinglength, (a) 600 foot, (b) 1000 foot, (c) 1500 foot, and (d) 2500 foot pipeline.

Since there is no change in pipeline bore, and the same range of air supplypressures is considered, there is no change in the air flow rate axis for any of thefour conveying characteristics presented in Figure 7.21. The changes all relate tothe material flow rate axis, and hence also to the solids loading ratio values.



Over 310 ft, in Figure 7.17d, 180,000 Ib/h of material would be conveyedand the solids loading ratio would be about 15, with a conveying line pressuredrop of 30 lbf/in2. This is entirely dilute phase, suspension flow, as explained ear-lier, and the minimum conveying air velocity is about 2500 ft/min, almost regard-less of air supply pressure and conveying distance.

With the distance almost doubled to 600 ft in Figure 7.2la, and the scalingmodel being an inverse law relationship, it would be expected that the materialflow rate would drop to about half, for the same air supply pressure. It will be seenthat the material flow rate has, in fact, dropped to about 88,000 Ib/h. This slightreduction on half is mostly due to the increase in air only pressure drop, whichleaves less pressure available for the conveying of material.

If the conveying line pressure drop had been doubled to about 60 lbf/in2, inorder to compensate, and so maintain the same pressure gradient, a material flowrate close to 180,000 Ib/h would have been achieved. This is provided that the airflow rate was also increased in order to compensate for the compressibility effectof the air and thereby maintain 2500 ft/min as the minimum velocity.

It must be emphasized that if the conveying distance is doubled, the materialflow rate must be halved for the system to work within the capability of the sameair supply pressure, as illustrated with Equation 10. Double the distance for thesame material flow rate equates to double the energy required. This applies to bothdilute and dense phase conveying.

If a conveying system is extended to supply a storage silo that is furtheraway, a lower material flow rate must be expected. If a system has to supply anumber of silos at varying distances, by means of diverter valves, it is most impor-tant that this fact is taken into account. If there is no control over material feedrate, therefore, all silos will have to be fed at the lowest flow rate, corresponding tothe furthest silo, and so conveying to the nearest silo will be very inefficient.

With an extension in conveying distance to 1000 ft the maximum value ofmaterial flow rate drops further to about 52,000 Ib/h. If a much higher flow ratewere to be required over this distance there would be little option but to increasethe pipeline bore. Over a distance of 2500 ft the material flow rate drops to about18,000 Ib/h and it will be seen that the solids loading ratio is now only about l'/2which is very dilute phase. Conveying over this and very much longer distances,however, is possible and very much higher material flow rates can be achieved,but power requirements are relatively high.

4.2.2 Dicalcium Phosphate

Because of the changes that occur with materials capable of dense phase convey-ing, the reference conveying characteristics for the dicalcium phosphate conveyedover 310 ft from Figure 7.16d have been reproduced in landscape form in Figure7.22 in order to illustrate the nature of the changes more clearly for this type ofmaterial. Because the pipeline bore and air supply pressures remain the same inthis procedure there is essentially no change in air flow rate needed to maintain thesame conveying line inlet air velocity.


234 Chapter 7


\

Solids LoadingRatio

500

400

~ 300

200

100

100

30.'.

20 1

1000 2000

Free Air Flow Rale - ftVmin

3000

Figure 7.22 Conveying characteristics for dicalcium phosphate conveyed over 310 ftin 8 in bore pipeline.

With a reduction in material flow rate, however, there will be a change insolids loading ratio, as was clearly illustrated in Figure 7.21 with the magnesiumsulfate. For powdered materials that can be conveyed in dense phase, however, theminimum value of conveying air velocity is influenced quite significantly by thevalue of the solids loading ratio. This concept was introduced in Chapter 4 withFigure 4.6.

The relationship between minimum conveying air velocity and solids load-ing ratio for dicalcium phosphate is presented on Figure 7.23. That for the magne-sium sulfate is also included on Figure 7.23 for reference and comparison. FromFigure 7.22 it will be seen that very high values of solids loading ratio wereachieved, and because the conveying distance was relatively short, solids loadingratios of almost 100 were achieved with a conveying line pressure drop of only 10lbf/in2. As conveying distance increases, however, and material flow rate de-creases according to an inverse law relationship, solids loading ratios reduce quitedramatically.



3000 h.Magnesium Sulfate

Dicalcium Phosphate

0 20 80 10040 60


Figure 7.23 Minimum conveying air velocity relationships for materials used.

Conveying characteristics for the Dicalcium Phosphate conveyed over a dis-tance of 600 ft through the 8 inch bore pipeline are presented in Figure 7.24.

250

200

100

50

0

80 60 40so;

0 1000 2000 3000

Free Air Flow Rate - fiVmin

Figure 7.24 Conveying characteristics for dicalcium phosphate over 600 feet.


236 Chapter 7

With an almost doubling in conveying distance to 600 ft there is a corre-sponding halving in material flow rate capability, and hence a similar reduction insolids loading ratio. The maximum value of solids loading ratio is now well below100 and only with a conveying line pressure drop of 20 lbf/in2 is the solids loadingratio above a value of about 70. For pressures below 20 lbf/in2 there is a dramaticchange in the conveying characteristics.

In this region the pressure gradient available is not high enough to supporthigh solids loading ratio conveying and much of the area around a pressure drop of10 lbf/in2 has changed entirely to dilute phase suspension flow. As a consequencethe air flow rate required to convey with a conveying line pressure drop of 10lbf/in2 changes from about 400 ftVmin over a distance of 310 ft to about 1200ftVmin over a distance of 600 ft.

It is the relationship between minimum conveying air velocity and solidsloading ratio in Figure 7.23 that dictates these changes. As the distance increases,the material flow rate decreases and hence the solids loading ratio also decreases.With a decrease in solids loading ratio below about 90 there will have to be anincrease in conveying air velocity. In order to increase velocity there must be anincrease in air flow rate. If there is an increase in air flow rate there will be a corre-sponding reduction in solids loading ratio.

This is a slowly converging cycle and explains why, for a pressure drop of10 lbf/in2, the air flow rate required can increase by a factor of three for a doublingin conveying distance. Extreme caution must be exercised in the design of densephase conveying systems in the region where conveying line pressure gradientsare in the region of 4 to 8 lbf/in2 per 100 ft of pipeline, particularly if operatingclose to the minimum value of conveying air velocity, for a reduction in materialflow rate could result in pipeline blockage. This aspect of system operation is con-sidered in more detail in Chapter 19.

This entire process is repeated, but at higher values of air supply pressure,with the extension of the pipeline to 1000 ft in Figure 7.25. From Figure 7.25 itwill be seen that there is no dense phase conveying capability over this distance atall. The minimum conveying air velocity is about 2100 ft/min for all pressuresconsidered. The transition is still there, but at higher pressures. At a pressure ofabout 45 lbf/in2 the material could be conveyed with a very low air flow rate andat low velocity. In this case the transition to dilute phase at 30 lbf/in2 would beeven more dramatic, but in terms of ratios of air flow rates it would be about threeto one again.

With further increase in conveying distance the changes are no differentfrom those for the magnesium sulfate in Figure 7.21. Conveying is only in dilutephase and so there are no further changes in air flow rate. Conveying characteris-tics for the dicalcium phosphate conveyed over 1500 ft are given in Figure 7.26.

The influence of conveying distance on material flow rate is illustrated inFigure 7.27. The maximum material flow rate achieved through an eight inch borepipeline with a conveying line pressure drop of 30 lbf/in2 has been taken as thebasis for both the dicalcium phosphate and the magnesium sulfate. The differencein conveying capability between the two materials is typical of the differences thatcan exist between different materials, as discussed in Chapter 4.



160

o

§ 120

I 80

_gE

40C3

I I I 4 I I I I I I I I

0 1000 2000 3000Free Air Flow Rate - ftVmin


100

80

60

40

20 •

0

30

I I I f I I ! I I I I

0 1000 2000 3000Free Air Flow Rate - ft3/min



238 Chapter 7

ooo

I

a!_ou,."§

500

400

300

200

100

DicalciumPhosphate

Air Supply Pressure = 301bf/in2|Pipeline Bore = 8 inch

500 1000 1500

Conveying Distance - feet

2000 2500

Figure 7.27 Influence of conveying distance on material flow rate for materials andconveying conditions considered.

This is approximately an inverse law relationship for both materials and so itwill be seen that changes are particularly pronounced over shorter conveying dis-tances. Conveying distance, therefore, is an important parameter to take into ac-count when designing a conveying system. It is even more important if materialsare required to be conveyed over a range of distances with a common conveyingsystem.

For the dilute phase conveying of materials little change in conveying air ve-locity is required with change in distance. For materials capable of being conveyedin dense phase, however, the specification of air flow rate is particularly important.Because low velocity dense phase conveying requires a relatively high pressuregradient, and because high pressure air is not convenient to use in systems thatexhaust to atmospheric pressure, the possibility of dense phase conveying rapidlyreduces with increase in distance.

This transition from dense phase to dilute phase conveying is illustrated forthe dicalcium phosphate in an eight inch bore pipeline in Figure 7.28. The verticalaxis is that of material flow rate, but scaled by the inverse law relationship withrespect to conveying distance. The horizontal axis is that of free air flow rate in aneight inch bore pipeline. Approximate lines of constant conveying line pressuredrop are also included. These are only approximate locations for reference sincetheir location will shift slightly with respect to conveying distance.

The sloping line at low air flow rate corresponds to a conveying line inlet airvelocity of about 600 ft/min and so represents the minimum conveying limit forthe dense phase conveying of the dicalcium phosphate.



J 500or<->

^400'o

| 300

& 200

_oE 100cd

900 ft +

500 1000 1500

Free Air Flow Rate - fr/min

2000

Figure 7.28 Influence of conveying distance on air flow rate required for conveyingdicalcium phosphate.

Conveying down to this limit is possible with a high pressure gradient, typi-cally above about 10 lbf/in2 per 100 ft length of pipeline. This means that convey-ing in this region is possible with either a high conveying air pressure or with ashort conveying line.

The sloping line at high air flow rates corresponds to a conveying line inletair velocity of about 2100 ft3/min and so represents the minimum conveying limitfor the dilute phase conveying of the dicalcium phosphate. This is the minimumlimit for conveying if the conveying distance is long or the pressure available forconveying is low. These, of course, are relative terms, but Figure 7.28 illustratesthe situation with regard to dicalcium phosphate. Other materials, capable of beingconveyed in dense phase and at low velocity, will follow very similar patterns.

When conveying data for a material is extended down to the air only pres-sure drop datum, and hence zero material flow rate, as with the conveying charac-teristics presented here, most of the materials capable of being conveyed in densephase will include the transition from dense to dilute phase. That for the 310 ftlong pipeline starts the transition at a pressure of about 10 lbf/in and that for the600 ft long pipeline starts at about 20 lbf/in2. For pipelines above about 900 ft longthe transition occurs at a pressure above about 30 lbf/in . The transition generallyoccurs over a relatively narrow band of pressure drop values.

Conveying in the region between these two limits is perfectly safe, stableand viable. It is dense phase conveying. If changes in operating conditions with asystem, however, such as distance, pressure and material flow rate, result in theoperating point being close to the conveying limit that links the 600 ft/min and


240 Chapter 7

2100 ft/min limit lines, the system could become unstable and likely to block thepipeline [1].

5 OTHER PIPELINE FEATURES

It was mentioned earlier, in relation to Equation 7.10, that the equivalent length ofpipeline comprised a number of elements and that horizontal conveying distancewas just one element. The other elements include vertical sections of pipeline andpipeline bends and these will be considered in the next chapter.

REFERENCE

1. D. Mills. An investigation of the unstable region for dense phase conveyingin sliding bed flow. Proc 4th Int Conf for Conveying and Handling of Particu-late Solids. Budapest. May, 2003.


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