Conveyed Material Influences

Transcription

1 Conveyed Material Influences 1 INTRODUCTION Although the performance of a pipeline with air only can be predicted reliably, the addition of material to the flow of air changes the situation entirely. This was illustrated in Chapter 5 where the conveying characteristics of a number of different materials were presented. These were used to illustrate the differences in conveying capability between different materials, and the very wide differences that can exist between materials that can be conveyed in dense phase and those that can not. In this chapter these conveying characteristics are developed further to illustrate the influence of conveying air velocity, and hence air flow rate, in more detail. Power requirements and specific energy are also considered, so that the influence of velocity can be considered in more meaningful terms. This will also provide a better basis for comparison between dilute and dense phase conveying capability and provide a basis on which pneumatic conveying can be compared with alternative methods of conveying. Pipeline bore and conveying distance are then considered. Pipeline bore is important because of the major influence that it has on the conveying capability of a pipeline. Conveying distance is generally the most problematical of all the variables. Conveying distance will nearly always be different from one situation to the next, and hence the pressure gradient will also be different. It is essentially the

2 pressure gradient that will dictate the solids loading ratio at which a material can be conveyed through a pipeline, as was illustrated in Figures 4.23 and 24. Then for materials that have very good air retention properties, such as cement, the minimum conveying air velocity varies with solids loading ratio, as was illustrated in Figure MATERIAL COMPARISONS Various materials were compared in Chapter 4 in terms of their conveying capability and the broad divisions that result between materials that can be conveyed in dense phase and those that can not. In this section the differences are examined in terms of conveying air velocities, power requirements and specific energy. For continuity the three materials considered earlier are examined further. The materials were cement, sandy alumina and polyethylene pellets. Conveying characteristics for cement were presented in Figure 4.5b and are reproduced here in Figure 7.1 for reference. All three materials were conveyed through the Figure 4.2 pipeline which was 165 ft long of two inch nominal bore and included nine 90 bends. Similar data for the alumina and polyethylene pellets from Figures 4.8b and 12b are similarly reproduced in Figures 7.2 and 3. To allow visual comparisons to be made the same axes have been used for all three materials and conveying line pressure drop values up to 25 lbf/in 2 have been considered in each case. Pressure Drop Solids Loading Ratio Free Air Flow Rate - itvmin 160 Figure 7.1 Conveying characteristics for cement.

3 Material Conveying t Conveying Limit Conveying Line Pressure Drop - lbf/in 2 NO GO AREA Solids Loading Ratio Free Air Flow Rate - ft/min Figure 7.2 Conveying characteristics for sandy alumina. The data, therefore, relates to positive pressure conveying. A relatively high pressure has been used in order to accentuate the differences between the materials considered. The same differences, however, will exist in negative pressure conveying and so the analysis undertaken, and the results obtained, will differ little between positive pressure and vacuum conveying. o oo 30 Conveying Line Pressure Drop - lbf/in 2 Solids Loading Ratio 30 cd Oi o 20 g 10 'C <D ta Conveying Limit NO GO AREA Free Air Flow Rate - ft'/min 200 Figure 7.3 Conveying characteristics for polyethylene pellets.

4 2.1 Conveying Air Velocity Since conveying air velocity is such an important parameter this is considered first. Conveying line inlet air velocity is one of the basic design parameters for a pneumatic conveying system and so it is this value that is plotted. This is purely a mathematical process. The relevant model for plotting velocity on the conveying characteristics was developed in Chapter 5 at Equation 10 and is re-presented here: F = pd2 C ftvmin (1) where V n = volumetric flow rate of free air - ftvmin p = conveying air pressure - lbf/in 2 absolute d = pipeline bore - in C = 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 of conveying air velocity, the corresponding value of free air flow rate for given values of conveying line inlet air pressure can be evaluated. By this means lines of constant value of conveying line inlet air velocity can be plotted. Such a plot for cement is presented in Figure ,100 Solids Loading Ratio Conveying Line Inlet Air Velocity - ft/min 40 /, Free Air Flow Rate - ft 3 /min 200 Figure 7.4 Conveying air velocity data for cement.

5 At high values of solids loading ratio the minimum conveying air velocity for the cement is about 600 ft/min. For dilute phase, suspension flow, the minimum velocity is about 2000 ft/min. Between these two extremes the conveying limit is dictated by the relationship between minimum conveying air velocity and solids loading ratio presented in Figure 4.7. An extremely wide range of conveying conditions, therefore, are available for cement. To help in the decision making process, power requirements and specific energy are developed in a similar manner below. The lines of constant conveying air velocity help to illustrate the problems of compressibility with air. As conveying air pressure increases, the value of the free air flow rate must increase in order to maintain the same value of velocity. In many pneumatic conveying systems there is a limit on the volumetric flow rate of air available and so great care must be taken if material feed rate into the pipeline is increased since this will require an increase in pressure for conveying. Because exit from the pipeline in this case is always at atmospheric pressure, the conveying line exit air velocity only varies with air flow rate. Conveying line exit air velocity can be determined simply by putting p = 14-7 lbf/in 2 into Equation 7.1 to determine this value. Similar data for the sandy alumina is presented in Figure 7.5. The range of conveying conditions for this material are very limited since it is only capable of being conveyed in dilute phase, suspension flow. The conveying limit, dictated by the combination of a fixed value of minimum conveying air velocity and the compressibility of the air, significantly reduces the operating envelope for this type of material. 30 Conveying Line Inlet Air o Velocity - ft/min Solids Loading Ratio c5 B! _o 3 to Conveying Line Pressure drop - ibfin.x>*^->cl' ^ ~'.. ' Free Air Flow Rate - fvvrnin Figure 7.5 Conveying air velocity data for sandy alumina.

6 g30 o Conveying Line Pressure Drop - Ibf/in Conveying Line Inlet Air Velocity - ft/min Solids Loading / Ratio 30 o 10 O Free 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 a much greater effect in dilute phase conveying than they do in dense phase. Similar data 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 conveying is also very limited. The minimum conveying air velocity for this material for dilute phase conveying will be about 3000 ft/min. Because of the positive slope to the conveying limit curve only a narrow band, at low material flow rates, is available for operation between these two limits. It is interesting that the 3000 ft/min velocity curve approximately passes through the maximum value point on each constant pressure drop line. 2.2 Power Requirements Pneumatic conveying has a certain reputation for high power requirements, certainly with regard to dilute phase conveying, and so this is explored with regard to the three materials being investigated. The relevant model for plotting power requirements on the conveying characteristics was developed in Chapter 3 at Equation 6 and is re-presented here: Power = V hp (2) where V Q = air flow rate at free air conditions - ftvmin p 2 and pi = compressor delivery pressure = compressor inlet pressure - Ibf/in abs - Ibf/in 2 abs

7 In order to plot lines of constant power, P, it is the volumetric flow rate of free air, V a, that needs to be the subject of the equation and so a re-arrangement gives: 7-81 P, V 0 =, r ft 3 /min (3) where P = power - hp For a given value of power, P, the corresponding value of free air flow rate for given values of conveying line inlet air pressure can be evaluated. By this means lines of constant value of power required can be plotted. Such a plot for cement is presented in Figure 7.7. Power requirements for the cement on Figure 7.7 vary from a minimum of about 2 hp to a maximum of 25 hp. This shows the influence of air flow rate, and hence conveying air velocity very well. With a conveying line pressure drop of 25 Ibf7in 2, for example, 34,000 Ib/h of cement can be conveyed with 5 hp and 20,000 Ib/h can be conveyed with the same 25 lbf/in 2, but 25 hp. This represents a five fold increase in power for a 40% reduction in cement flow rate. It is generally recommended that a system be designed with a conveying line inlet air velocity about 20% greater than the minimum conveying air velocity value. Solids Loading Ratio Power Required -hp Free Air Flow Rate - ftvmin Figure 7.7 Power requirements data for cement.

8 This is usually a sufficient margin to allow for pulsations in material flow rate, compressor characteristics and compressibility effects. Although cement can be conveyed at any point on the performance map it is clearly inefficient to do so at unnecessarily high air flow rates. It is obviously necessary to know the value of the minimum conveying air velocity and this is why conveying trials with a material are so important, particularly if previous experience with a material is not available. Similar data for the sandy alumina is presented in Figure 7.8. Because of the very much higher minimum conveying air velocity with this material only the bottom right hand corner exists, but it is essentially the same pattern of curves. There is no longer any scope for the 5 hp curve to convey any substantial amount of material and capabilities are in a more ordered fashion. The slope of the constant power curves is the same and so with 10 hp, for example, 10,000 Ib/h can be conveyed with 140 ftvmin of free air and 2,500 Ib/h can be conveyed with 200 ft 3 /min of free air. This represents a four-fold reduction in conveying capability for a 40% increase in air flow rate. The 10 hp curve will ultimately reach the horizontal axis and convey nothing when the power is entirely taken up by transporting the air through the pipeline. An explanation for this comes the pressure drop model for air only that was first presented in a simplified form in Chapter 4 at Equation 1 and is re-presented below for reference: o 30 Power Required - hp Solids Loading Ratio 20 Conveying Line Pressure Drop - lbf/in 2 s E Free Air Flow Rate - If/min Figure 7.8 Power requirements for sandy alumina.

9 Ap f LpC 2 d lbf/in 2 (4) It is the velocity term, C 2, that dominates in this situation and is one of the main reasons why the constant power lines slope so steeply in this region. To convey more material the air flow rate needs to be reduced, but there is a conveying limit in the way to prevent this. To convey more material the air pressure can be increased, provided that the air mover has the necessary capability and power, but if this is at the same air flow rate, the conveying limit is in the way once again. This is why a performance map for a material is so important, for it provides all the information necessary to make all the decisions required for a successful system design. Similar data for the polyethylene pellets is presented in Figure 7.9. There is little difference between the power requirements data for the polyethylene pellets and that for the sandy alumina. This is mainly because the operating 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 differs little with regard to the properties of the material, regardless of whether the material can be conveyed in dense phase or not. The main difference between the pellets and the alumina comes in system operation. If air flow rate is reduced, or pressure increased, with the pellets the conveying system will simply stall, and if the conveying conditions are changed it should be possible to re-start with little problem. o 30 I 20 Conveying Line Pressure Drop - Ibf/irv Solids Loading Ratio Power Required - hp \ o Free Air Flow Rate - ftvmin Figure 7.9 Power requirements data for polyethylene pellets.

10 The conveying limit for the alumina, and other similar materials that can only be conveyed in dilute phase, suspension flow, is that the conveying limit generally represent pipeline blockage, and once blocked it is often a time consuming process 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 that many other parameters change and so global comparisons are difficult to make. A basis on which direct comparison can be made is that of specific energy. This will provide a reliable basis for comparing different materials, such as those being illustrated here, and with alternative mechanical conveying systems for the given duty. The units of specific energy are horsepower-hour per ton of material conveyed or hp h/ton. Specific energy data superimposed on the conveying characteristics for the cement is presented in Figure 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) /, Solids Loading /Ratio 30 ;, so 1 b. " Free Air Flow Rate - ftvmin Figure 7.10 Specific energy data for cement.

11 Power requirement data was presented in Figures 7.7 to 7.9. To plot lines of constant specific energy simply divide power required by material flow rate and mark points on the graph that give rounded values of 0-5, 1-0, 1-5, etc. These points can then be joined to provide lines of constant specific energy. Such data for the cement from Figure 7.7 is presented in Figure For the cement the specific energy data clearly identifies low velocity conveying as being the most efficient. A wide range of specific energy values appear on Figure 7.10 but this is only because air flow rates up to 200 fwmin have been included, to be consistent with the other materials being considered. For normal purposes, and certainly for conveying, air flow rates above 80 ft 3 /min need not be considered for cement in the pipeline used. Similar data for the sandy alumina is presented in Figure Specific energy data for alumina follows a similar pattern to that for the cement. Values, however, are generally about five times higher and this typifies the difference between dilute and dense phase conveying capability. The influence of pressure is a little difficult to isolate. Constant specific energy lines tend to run approximately parallel to the conveying limit and so at first sight it would appear to have little effect. With high pressure air for conveying, however, stepping of the pipeline to a larger bore would be recommended. All the data presented in this chapter is for the Figure 4.2 pipeline which is single bore. At higher pressures, and with stepped bore pipelines, an improvement in performance would be expected. o 30 Conveying Line Pressure Specific Energy Solids Loading Ratio Free Air Flow Rate - fvvmin Figure 7.11 Specific energy data for sandy alumina.

12 30 20 Conveying Line Pressure Drop - Ibf7in Specific Energy - hp h/ton Solids Loading Ratio I _o Figure 7.12 Free Air Flow Rate - ft7min Specific energy data for polyethylene pellets. With regard to pressure, comparisons across a given set of conveying characteristics are not likely to be made. They can certainly be used to investigate the improvement in performance for a given system, but the alternative influence of pipeline bore is more likely to be considered when designing a new system. Pipeline bore will be considered as a separate issue later in this chapter. Similar specific energy data for the polyethylene pellets is presented in Figure This follows a similar pattern to that of the alumina once again. At very low values of air flow rate specific energy values are low, but material flow rates are also low and so a much larger bore pipeline would probably be needed to achieve the desired material flow rate. 3 INFLUENCE OF PIPELINE BORE Pipeline bore has a major influence on conveying capacity, as has been mentioned before. The influence of pipeline bore on conveying rate is reasonably predictable and so to illustrate the influence that pipeline bore can have two further materials have been selected for this purpose. One is a very fine grade of dicalcium phosphate, which is capable of being conveyed in dense phase. The other is a coarse grade of magnesium sulfate which can only be conveyed in dilute phase in a conventional conveying system. Both materials were conveyed through a 310 ft long pipeline of three inch nominal bore having nine 90 bends. A sketch of the pipeline is given in Figure 7.13 for reference.

13 Pipeline: Length Bore Bends D/d = 310ft 3 in nominal 9x90 16 Figure 7.13 Sketch of three inch bore pipeline. Conveying data for the dicalcium phosphate and the magnesium sulfate conveyed through the above pipeline are presented in Figure Conveying Line Pressure Drop - lbf/in 2 Solids Loading Ratio NO GO AREA 25^*^, ] (a) Free Air Flow Rate - ftvmin (b) Free Air Flow Rate - ft 3 / min Figure 7.14 Conveying characteristics for materials conveyed through the pipeline shown in figure (a) Dicalcium phosphate and (b) magnesium sulfate.

14 From Figure 7.14a it will be seen that the dicalcium phosphate could be conveyed in dense phase and solids loading ratios up to about 120 were achieved. The magnesium sulfate, however, had no dense conveying capability, the maximum value of solids loading ratio achieved was about 12, and the minimum value of conveying air velocity was about 2500 ft/min. It will also be noticed that conveying line inlet air pressures up to 30 lbf/in 2 were used for both materials. The material flow rates achieved, however, were very different and so a reduced scale has been used for the magnesium sulfate. 400 fwmin of free air was available for conveying and it will be seen that within this limit the maximum pressure that could be used for conveying was about 30 IbfVin 2. Although the same horizontal axis has been used for both materials, it could well have been halved for the dicalcium phosphate. 3.1 Scaling Parameters To illustrate the influence of pipeline bore on conveying capability, the conveying data presented in Figures 7.14a and b will be scaled to larger bore pipelines. To isolate the influence of pipeline bore the length and geometry of the pipeline will remain 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. This process was considered earlier in Chapter 6 with Figure 6.5. For reference purposes a similar plot is presented in Figure 7.15, specifically for the Figure 7.13 pipeline. 10 Pipeline Bore - i ^ <4-8 I Q JJ 3 c/s A Cu 1 2 l- < Free Air Flow Rate - ftvmin x (d,/3) 2 Figure 7.15 Influence of pipeline bore and air flow rate on empty pipeline pressure drop for figure 7.13 pipeline.

15 The variation of pressure drop with air flow rate for the three inch bore pipeline is included and so the change in datum can be obtained by taking the difference between the three inch and the required bore of pipeline. It will be seen from this that the air only pressure drop element reduces significantly with increase in pipeline bore. For a given conveying line inlet air pressure this means that the pressure drop available for conveying material will increase slightly with increase in pipeline bore, and so it will be possible to convey more material as a consequence 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, on the basis of pipe cross-sectional area, A: m p x A oc d (6) or alternatively: m, m i const (7) Working Model The working form of this scaling model is: 2 x - Ib/h (8) where subscripts 1 and 2 relate to the appropriate pipe bores of the two pipelines It is for this reason that the air flow rate axis on Figure 7.15 is in terms of air required for the three inch bore pipeline x (d 2 /3). Conveying air velocities scale up exactly and so a common axis can be used. For scaling up of the characteristics in Figures 7.14a and b to larger bore pipelines the datum pressure drop should first be changed throughout by the appropriate values obtained from Figure Material flow rates for a given air flow rate and pressure drop are then scaled in the ratio of (d 2 /3) 2. The results of scaling the data in Figures 7.14a and b to larger bore pipelines are presented in Figure 7.16 and Scaling in each case has been carried out for 4, 5, 6 and 8 inch bore pipelines.

16 (a) Free Air Flow Rate - ft/min (b) Free Air Flow Rate - ft'/min ^ (c) Free Air Flow Rate - ftvmin (d) 0 -,,,.',,,,,, Free Air Flow Rate - ft 3 /min Figure 7.16 Conveying characteristics for dicalcium phosphate in various bore pipelines relating to figure (a) 4 inch bore, (b) 5 inch bore, (c) 6 inch bore, and (d) 8 inch bore pipeline.

17 100,, o (a) Free Air Flow Rate - ftvmin (b) Free Air Flow Rate - ftvmin (C) Free Air Flow Rate - ft/min (d) Free Air Flow Rate - ft/min Figure 7.17 Conveying characteristics for magnesium sulfate in various bore pipelines relating to figure (a) 4 inch bore, (b) 5 inch bore, (c) 6 inch bore, and (d) 8 inch bore pipeline.

18 3.2 Scaling to Larger Bores The scale up in terms of pipeline bore produces a set of curves that are basically geometrically similar for both materials, apart from the slight change due to the shift 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, of course, as these have been scaled up in proportion to the pipeline cross-sectional area. As pipeline bore increases there will be a need to increase the minimum value of conveying air velocity slightly because of the boundary layer effect. As the pipeline bore increases, the low velocity area in the boundary layer also increases and an increase in conveying air velocity is required to compensate and so prevent saltation. The design department of a company installing a pneumatic conveying system are unlikely to go through this detailed process of scaling. They will know what type of system they wish to supply and so will scale one or two data points only. The detail is included here to illustrate the global changes, and to show how pipeline bore can influence the design and specification decisions. If a range of pipeline bores is considered for a given material flow rate, the conveying line pressure drop required will decrease, and the air flow rate will increase, with increase in pipeline bore. This means that the pressure capability of the feeding device will reduce, but the size of the filtration plant will increase. To illustrate the influence of pipeline bore on system design parameters, material flow rates of 80,000 Ib/h for the dicalcium phosphate and 25,000 Ib/h for the magnesium sulfate have been considered. Data has been taken from the various sets of conveying characteristics presented and that for the dicalcium phosphate is presented in Table 7.1. Table 7.1 Conveying Parameters for 80,000 Ib/h of Dicalcium Phosphate Pipeline Air Inlet Free Air Solids Conveying Air Velocity Power Bore Pressure Flow Rate Loading Required Ratio At Inlet At Outlet in Psig cfm - ft/min ft/min hp

19 Table 7.2 Conveying Parameters for 25,000 Ib/h of Magnesium Sulfate Pipeline Air Inlet Free Air Solids Conveying Air Velocity Power Bore Pressure Flow Rate Loading Required in psig cfm Ratio - At Inlet ft/min At Outlet ft/min hp Similar data for the magnesium sulfate is presented in Table Influence on Pressure These tables show that there is a wide range of air supply pressure and pipeline bore combinations that are capable of meeting any given duty for a material. To illustrate the point with regard to the influence of pipeline bore on air supply pressure, the data from Tables 7.1 and 7.2 is presented graphically in Figure I01 80,000 Ib/h of Dicalcium Phosphate * ,000 Ib/h of Magnesium Sulfate 5 6 Pipeline Bore - inch Figure 7.18 Typical air pressure - pipeline bore relationships for conveying duties.

20 Figure 7.18 clearly shows that there is generally no one specific set of design parameters for a pneumatic conveying system. With a wide range of pipeline bore and air supply pressure combinations being capable of achieving a given material flow rate, the obvious question is which pipeline bore or air supply pressure results in the most economical design? Plant capital costs could vary considerably, for with different pipeline bore and air supply pressures there are corresponding 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 Power Requirements The approximate power requirements for the cases considered are given in Tables 7.1 and 7.2, and they are presented graphically in Figure In most cases the power required for the air mover represents the major part of the total system power requirements, although for screw pumps a major allowance must be made for the screw drive. Figure 7.19 presents interesting trends for both materials considered. This is apart from the displacement of the curves, for very different conveying duties, but this is primarily due to the fact that the magnesium sulfate could not be conveyed in dense phase. 80 I ,000 Ib/h of Magnesium Sulfate 3 cr e* 40 o 80,000 Ib/h of Dicalcium Phosphate Pipeline Bore- inch Figure 7.19 duties. Influence of pipeline bore on power requirements for given conveying

21 For the dicalcium phosphate all of the smaller bore pipelines give reasonably low values of power requirement. This is because the material is conveyed in dense phase in each case. It is only with the eight inch bore pipeline that there is a marked reduction in solids loading ratio and the power requirements start to rise steeply. For the magnesium sulfate there is a gradual reduction in power requirements with increase in pipeline bore. This is essentially due to the change in conveying line exit air velocity. The minimum conveying air velocity for this material is about 2500 ft/min and so a conveying line inlet air velocity of 3000 ft/min has been taken in every case. The minor influence of pipeline bore on minimum conveying air velocity has not been taken into account in this case. Since all the pipelines considered are single bore, the conveying line exit air velocity is extremely high for the small bore pipeline options, and this has a significant effect on pressure drop and hence conveying capability Stepped Pipelines For the small bore pipeline/high pressure cases considered, stepped pipelines would generally be recommended for both the dicalcium phosphate and the magnesium sulfate. This would have the effect of reducing the air supply pressure needed, 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 the power requirement curve almost into a horizontal line at about 55 hp. For the dicalcium phosphate it would probably reduce the power requirements for all the small bore pipelines to about 15 hp. Chapter 9 of this Handbook is devoted entirely to stepped pipeline systems 4 INFLUENCE OF CONVEYING DISTANCE Conveying distance also has a major influence on conveying capacity. If conveying distance is increased, the material flow rate will decrease, for the same conveying line inlet air pressure. If the air supply pressure is increased, and the air flow rate is also increased, to cater for the compressibility effect, it will be possible to achieve the same material flow rate. Increasing the air supply pressure, however, is rarely an option. The influence of conveying distance on conveying rate is reasonably predictable and so to illustrate the influence that pipeline length can have, the data presented in Figures 7.16d and 7.17d have been selected for this purpose. These are the conveying characteristics for the dicalcium phosphate and the magnesium sulfate conveyed over 310 feet. This relates to the Figure 7.13 pipeline but having a bore of eight inches. These two materials have been chosen once again because the influence of conveying distance is different between materials that are capable of being conveyed in dense phase and those that can only be conveyed in dilute phase.

22 4.1 Scaling Parameters To illustrate the influence of conveying distance on conveying capability the sets of conveying data presented in Figures 7.17d and 7.18d are taken as the reference points and are scaled to longer length pipelines. For the scale up of the conveying characteristics in respect of pipeline length, the change in datum for the empty line will have to be taken into account. This process was considered in Chapter 6 with Figure 6.4. For references purposes a similar plot is presented in Figure 7.20 for the conveying distances to be considered. The variation of pressure drop with air flow rate for the 310 ft long pipeline is included so that the change in datum can be obtained by taking the difference between the 310 ft and the required length of pipeline. It will be seen from this that the air only pressure drop element increases with increase in pipeline length. For a given conveying line inlet air pressure this means that the pressure drop available for conveying material will reduce slightly with increase in pipeline length. This must be taken into account, as well as the influence of conveying distance on conveying capability Scaling Model Scale up of material flow rate, m p, with respect to conveying distance, L, can be carried out with a reasonable degree of accuracy, if the extrapolation is not too great, on the basis of a reciprocal law model: 10 Pipeline Length a. o 1000 o Free Air Flow Rate - frvmin Figure 7.20 Influence of pipeline length and air flow rate on empty pipeline pressure drop for 8 inch bore pipeline.

23 m oc - - (9) P T A or alternatively: m pl L c] = m p2 L e2 = Const.... (io) For a constant air flow rate and pressure drop due to the conveyed material. where /» = mass flow rate of material and L e = equivalent length of pipeline Conveying distance, L, is expressed in terms of an equivalent length, L e, of the total pipeline. This comprises the three main elements of the pipeline routing and geometry. One is the length of the horizontal sections of pipeline, the second is the length of vertically up or down sections of pipeline, and the third relates to the bends in the pipeline. Horizontal pipeline is taken as the reference for equivalent length. The influence of distance, therefore, will ultimately depend upon the routing of the pipeline. For this exercise, to illustrate the typical influence of conveying distance as a variable, the pipeline geometry in Figure 7.13 has been used Working Model The working form of this scaling model is: m -, = m p] x-^ Ib/h (ii) A Scaling to Longer Distances where subscripts 1 and 2 relate to the appropriate lengths of the two pipelines In this exercise the two materials are considered separately. With pipeline bore both the air flow rate and material flow rate axes were scaled by the same parameter and so the results were approximately geometrically similar. For conveying distance only one of the axes has to be changed and this has a considerable distorting effect with regard to materials capable of dense phase conveying Magnesium Sulfate The conveying characteristics for the sodium sulfate conveyed through the 310 ft long pipeline of 8 in bore were presented in Figure 7.17d. Results of scaling to longer length pipelines of 8 in bore are presented in Figure 7.21.

24 (a) Free Air Flow Rate - ftvmin (b) Free Air Flow Rate - ftymin (C) Free Air Flow Rate - ft/min (a) Free Air Flow Rate - ft/min Figure 7.21 Conveying characteristics for magnesium sulfate in pipelines of increasing length, (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 supply pressures is considered, there is no change in the air flow rate axis for any of the four conveying characteristics presented in Figure The changes all relate to the material flow rate axis, and hence also to the solids loading ratio values.

25 Over 310 ft, in Figure 7.17d, 180,000 Ib/h of material would be conveyed and the solids loading ratio would be about 15, with a conveying line pressure drop of 30 lbf/in 2. This is entirely dilute phase, suspension flow, as explained earlier, and the minimum conveying air velocity is about 2500 ft/min, almost regardless of air supply pressure and conveying distance. With the distance almost doubled to 600 ft in Figure 7.2la, and the scaling model being an inverse law relationship, it would be expected that the material flow rate would drop to about half, for the same air supply pressure. It will be seen that the material flow rate has, in fact, dropped to about 88,000 Ib/h. This slight reduction on half is mostly due to the increase in air only pressure drop, which leaves less pressure available for the conveying of material. If the conveying line pressure drop had been doubled to about 60 lbf/in 2, in order to compensate, and so maintain the same pressure gradient, a material flow rate close to 180,000 Ib/h would have been achieved. This is provided that the air flow rate was also increased in order to compensate for the compressibility effect of the air and thereby maintain 2500 ft/min as the minimum velocity. It must be emphasized that if the conveying distance is doubled, the material flow rate must be halved for the system to work within the capability of the same air supply pressure, as illustrated with Equation 10. Double the distance for the same material flow rate equates to double the energy required. This applies to both dilute and dense phase conveying. If a conveying system is extended to supply a storage silo that is further away, a lower material flow rate must be expected. If a system has to supply a number of silos at varying distances, by means of diverter valves, it is most important that this fact is taken into account. If there is no control over material feed rate, therefore, all silos will have to be fed at the lowest flow rate, corresponding to the 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 of material flow rate drops further to about 52,000 Ib/h. If a much higher flow rate were to be required over this distance there would be little option but to increase the pipeline bore. Over a distance of 2500 ft the material flow rate drops to about 18,000 Ib/h and it will be seen that the solids loading ratio is now only about l'/2 which 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 Dicalcium Phosphate Because of the changes that occur with materials capable of dense phase conveying, the reference conveying characteristics for the dicalcium phosphate conveyed over 310 ft from Figure 7.16d have been reproduced in landscape form in Figure 7.22 in order to illustrate the nature of the changes more clearly for this type of material. Because the pipeline bore and air supply pressures remain the same in this procedure there is essentially no change in air flow rate needed to maintain the same conveying line inlet air velocity.

26 500 Conveying Line Pressure Drop - lbf/in 2 \ 30.'. 100 Solids Loading Ratio 400 ~ Free Air Flow Rale - ftvmin Figure 7.22 Conveying characteristics for dicalcium phosphate conveyed over 310 ft in 8 in bore pipeline. With a reduction in material flow rate, however, there will be a change in solids loading ratio, as was clearly illustrated in Figure 7.21 with the magnesium sulfate. For powdered materials that can be conveyed in dense phase, however, the minimum value of conveying air velocity is influenced quite significantly by the value of the solids loading ratio. This concept was introduced in Chapter 4 with Figure 4.6. The relationship between minimum conveying air velocity and solids loading ratio for dicalcium phosphate is presented on Figure That for the magnesium sulfate is also included on Figure 7.23 for reference and comparison. From Figure 7.22 it will be seen that very high values of solids loading ratio were achieved, and because the conveying distance was relatively short, solids loading ratios of almost 100 were achieved with a conveying line pressure drop of only 10 lbf/in 2. As conveying distance increases, however, and material flow rate decreases according to an inverse law relationship, solids loading ratios reduce quite dramatically.

27 3000 h.magnesium Sulfate Dicalcium Phosphate Solids Loading Ratio Figure 7.23 Minimum conveying air velocity relationships for materials used. Conveying characteristics for the Dicalcium Phosphate conveyed over a distance of 600 ft through the 8 inch bore pipeline are presented in Figure so; Free Air Flow Rate - fivmin Figure 7.24 Conveying characteristics for dicalcium phosphate over 600 feet.

28 With an almost doubling in conveying distance to 600 ft there is a corresponding halving in material flow rate capability, and hence a similar reduction in solids loading ratio. The maximum value of solids loading ratio is now well below 100 and only with a conveying line pressure drop of 20 lbf/in 2 is the solids loading ratio above a value of about 70. For pressures below 20 lbf/in 2 there is a dramatic change in the conveying characteristics. In this region the pressure gradient available is not high enough to support high solids loading ratio conveying and much of the area around a pressure drop of 10 lbf/in 2 has changed entirely to dilute phase suspension flow. As a consequence the air flow rate required to convey with a conveying line pressure drop of 10 lbf/in 2 changes from about 400 ftvmin over a distance of 310 ft to about 1200 ftvmin over a distance of 600 ft. It is the relationship between minimum conveying air velocity and solids loading 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 an increase in conveying air velocity. In order to increase velocity there must be an increase in air flow rate. If there is an increase in air flow rate there will be a corresponding reduction in solids loading ratio. This is a slowly converging cycle and explains why, for a pressure drop of 10 lbf/in 2, the air flow rate required can increase by a factor of three for a doubling in conveying distance. Extreme caution must be exercised in the design of dense phase conveying systems in the region where conveying line pressure gradients are in the region of 4 to 8 lbf/in 2 per 100 ft of pipeline, particularly if operating close to the minimum value of conveying air velocity, for a reduction in material flow rate could result in pipeline blockage. This aspect of system operation is considered 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 From Figure 7.25 it will be seen that there is no dense phase conveying capability over this distance at all. The minimum conveying air velocity is about 2100 ft/min for all pressures considered. The transition is still there, but at higher pressures. At a pressure of about 45 lbf/in 2 the material could be conveyed with a very low air flow rate and at low velocity. In this case the transition to dilute phase at 30 lbf/in 2 would be even more dramatic, but in terms of ratios of air flow rates it would be about three to one again. With further increase in conveying distance the changes are no different from those for the magnesium sulfate in Figure Conveying is only in dilute phase and so there are no further changes in air flow rate. Conveying characteristics for the dicalcium phosphate conveyed over 1500 ft are given in Figure The influence of conveying distance on material flow rate is illustrated in Figure The maximum material flow rate achieved through an eight inch bore pipeline with a conveying line pressure drop of 30 lbf/in 2 has been taken as the basis for both the dicalcium phosphate and the magnesium sulfate. The difference in conveying capability between the two materials is typical of the differences that can exist between different materials, as discussed in Chapter 4.

29 160 o 120 I 80 _g E C3 40 I I I 4 I I I I I I I I Free Air Flow Rate - ftvmin Figure 7.25 Conveying characteristics for dicalcium phosphate over 1000 feet I I I f I I! I I I I Free Air Flow Rate - ft 3 /min Figure 7.26 Conveying characteristics for dicalcium phosphate over 1500 feet.

30 238 Chapter 7 o I 300 a! _o u,." Dicalcium Phosphate Air Supply Pressure = 301bf/in 2 Pipeline Bore = 8 inch Conveying Distance - feet Figure 7.27 Influence of conveying distance on material flow rate for materials and conveying conditions considered. This is approximately an inverse law relationship for both materials and so it will be seen that changes are particularly pronounced over shorter conveying distances. Conveying distance, therefore, is an important parameter to take into account when designing a conveying system. It is even more important if materials are required to be conveyed over a range of distances with a common conveying system. For the dilute phase conveying of materials little change in conveying air velocity is required with change in distance. For materials capable of being conveyed in dense phase, however, the specification of air flow rate is particularly important. Because low velocity dense phase conveying requires a relatively high pressure gradient, and because high pressure air is not convenient to use in systems that exhaust to atmospheric pressure, the possibility of dense phase conveying rapidly reduces with increase in distance. This transition from dense phase to dilute phase conveying is illustrated for the dicalcium phosphate in an eight inch bore pipeline in Figure The vertical axis is that of material flow rate, but scaled by the inverse law relationship with respect to conveying distance. The horizontal axis is that of free air flow rate in an eight inch bore pipeline. Approximate lines of constant conveying line pressure drop are also included. These are only approximate locations for reference since their location will shift slightly with respect to conveying distance. The sloping line at low air flow rate corresponds to a conveying line inlet air velocity of about 600 ft/min and so represents the minimum conveying limit for the dense phase conveying of the dicalcium phosphate.

31 J 500 o r<-> ^400 'o 900 ft & 200 _o E 100 cd Free Air Flow Rate - fr/min Figure 7.28 Influence of conveying distance on air flow rate required for conveying dicalcium phosphate. Conveying down to this limit is possible with a high pressure gradient, typically above about 10 lbf/in 2 per 100 ft length of pipeline. This means that conveying in this region is possible with either a high conveying air pressure or with a short conveying line. The sloping line at high air flow rates corresponds to a conveying line inlet air velocity of about 2100 ft 3 /min and so represents the minimum conveying limit for the dilute phase conveying of the dicalcium phosphate. This is the minimum limit for conveying if the conveying distance is long or the pressure available for conveying is low. These, of course, are relative terms, but Figure 7.28 illustrates the situation with regard to dicalcium phosphate. Other materials, capable of being conveyed 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 pressure drop datum, and hence zero material flow rate, as with the conveying characteristics presented here, most of the materials capable of being conveyed in dense phase will include the transition from dense to dilute phase. That for the 310 ft long pipeline starts the transition at a pressure of about 10 lbf/in and that for the 600 ft long pipeline starts at about 20 lbf/in 2. For pipelines above about 900 ft long the transition occurs at a pressure above about 30 lbf/in. The transition generally occurs over a relatively narrow band of pressure drop values. Conveying in the region between these two limits is perfectly safe, stable and viable. It is dense phase conveying. If changes in operating conditions with a system, however, such as distance, pressure and material flow rate, result in the operating point being close to the conveying limit that links the 600 ft/min and

32 2100 ft/min limit lines, the system could become unstable and likely to block the pipeline [1]. 5 OTHER PIPELINE FEATURES It was mentioned earlier, in relation to Equation 7.10, that the equivalent length of pipeline comprised a number of elements and that horizontal conveying distance was just one element. The other elements include vertical sections of pipeline and pipeline bends and these will be considered in the next chapter. REFERENCE 1. D. Mills. An investigation of the unstable region for dense phase conveying in sliding bed flow. Proc 4 th Int Conf for Conveying and Handling of Particulate Solids. Budapest. May, 2003.