General state diagram for pneumatic conveying

Verification and improvement with the help of operational data from industrial positive pressure conveying installations

Ing (grad) Manfred Heyde

Content

1 Introduction 1 2 Software 1 3 state diagram for pneumatic conveying 2 4 operating data of industrial pneumatic conveying equipment 5 5 Improved state diagram and computer program 9 5.1 Sketch of the dense phase region 11 6 Pneumatic conveying at high temperatures 12 7 References 14

1 Introduction Flow behaviour of moving bulk materials, including heat and mass transfer, was described by the author on the basis of common physical principles [1]: http://www.epubli.de/shop/autor/Manfred-Heyde/3168 Many published measurement results could be summarized with the help of suitable algorithms and graphic representations, for example, the mass flow from hoppers, the heat exchange and the catalytic gas phase reaction in fluidized beds, the pressure loss and the heat transfer of turbulent flow through pipes, as well as the flow condition and the pressure loss in pneumatic conveying lines.

2 Software A computer program, that includes a database, allows the quick and direct use of the developed algorithms for evaluation and design of processes, apparatuses and equipment. This free software is written in Visual Basic and runs even under Windows 7 (32 bit). It includes the main results. The german version can be downloaded from the following link: https://skydrive.live.com/redir.aspx?cid=0239e78e2f136dde&resid=239E78E2F136DDE!340&authkey=s60rZ0M*8fA%24 A english version of the software can be downloaded from the following link:

https://skydrive.live.com/#cid=0239E78E2F136DDE&id=239E78E2F136DDE%21936

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3 State diagram for pneumatic conveying The construction of the universal state diagram, originally used by the software to calculate the operating conditions in pneumatic conveying lines, is based on the evaluation of data sets from industrial installations and on the results of a number of scientific studies. The used data sets from industrial conveying installations were published by Muschelknautz and Krambrock [2] as well as Muschelknautz and Wojahn[3]. On the abscissa of the graphic is the well-known dimensionless Reynolds number Re plotted. The ordinate shows another dimensionless expression, that comes from a physical model for the turbulent pipe flow [1], and that will be hereinafter referred to as K-number. K is mainly formed by the pressure loss, the length of pipe, the pipe diameter as well as the dynamic viscosity of the conveying gas. In the current model represents K the ratio of pipe diameter and wall-related "Mischungsweglänge". The diagram is an implicit representation of the physical parameters, so that for the determination of the pressure loss an iterative calculation is required. As regards the flow conditions which occur, we can distinguish dilute phase with a distinct state of minimum pressure loss as well as dense phase. In between of these areas there lies a transitional area with unstable flow conditions. The bulk materials that were conveyed under dense phase conditions had particle sizes of at most 350 microns, possibly 700 microns. The maximum throughput for dense phase flow was 19.5 / h. In contrast, two systems with throughputs of 35 t / h (soda) and 50 t / h (fly ash) do not operate in dense phase, but on the boundary of dilute phase, the so-called choke line. Otherwise, in dilute phase working installations are almost exclusively installed for bulk solids with particle sizes in mm-range.

The state diagram shows also, that in dense phase along the lines of equal solid throughputs different operating conditions are possible, with corresponding changes in the amount of the

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gas or the gas velocity as well as the pressure drop. For a scale-up the question remains, which conditions a comparable operating point of the subsequent production line must meet.

An example for the wide range of variation of the operating conditions can be found in a publication by Krambrock [4]. This publication also contains a diagram, that represents the maximum possible throughput of PE granules as a function of the flow rate and the tube diameter, with the pressure loss as parameter. These functional relationships are in the state diagram represented by the left/upper boundary line. With the help of the information of Krambrock the only indicated current boundary can readily be precised.

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4 operating data of industrial pneumatic conveying systems The operating conditions of industrial bulk solid conveyor lines, that are listed in the following table, come exclusively from the bulk-online Forums: http://forum.bulk-online.com/forumdisplay.php?11-Pneumatic-Conveying

( ) = calculated values, µ = solid / gas ratio

Table 1: Operating conditions of industrial installations (1) data set coming from the following bulk-online thread: http://forum.bulk-online.com/showthread.php?4754-Pneumatic-Conveying-of-PP In this installation is the measured pressure loss of 0.3 bar about 0.1 bar bigger than the calculated value for the minimum pressure loss in dilute phase. This surplus is surely caused by the 8 (not specified) pipe bends of the conveying line. (2) data set coming from the following bulk-online thread: http://forum.bulk-online.com/showthread.php?3348-Conveying-of-LLDPE-Granules These operating data fit extremely well in the scheme of the dense phase, although the particle size of

Nr. Produkt dp50

µm

L

m

h

m

D

mm

&Ms

t/h

&Mg

Nm3/h

∆∆∆∆p

bar

u

m/s

µ

-

1 PP pellets (1) (4000) 36.5 15.2 150 14 ca 2010 0.3 (30) (6)

2 LLDPE Granules (2) (mm) 100 -- 300 60 -- (0.41) (10.3) 20

3 Cement (3) -- 216 40 ca 285 85 ca 6000 1.6 -- --

4 Polycarbonat:

Powder & Pellets (4)

-- / 2500 50 + 60 15 + 20 100/125 6 / 7 ca 1700 1(0.73) (38) (3)

5 Expanded Perlite (5) 28.5 35.2 28.3 83 3,28 ca 280 0.25 -- (9.35)

6 PTA (6) 130 120 40 150 90 3000 2.66 (27.5) (24)

7 PP Pellets (7) -- 140 22 (187) 30 ca 2700 0.66 (21) (10)

8 Rapeseed (8) 2500 230 10 206 12 (2700) 0.4 (21.5) (3.6)

9 PET Virgin Chips (9) (>12700) 40 20 80 1.5 (ca 570) 0.15 (32) (2)

10 Cement (10) -- 176 -- 50 7.63 (233) 3.15 (18) (26)

11 Spent Cell Liner (11) -- 85 -- 77 2.5 (230) (0.3) (13) (9)

12 Cement (12) -- 132 55 250 120 ca 4200 1.7 (14.5) (24)

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this material, in contrast to the fine-grained solids, which are commonly conveyed under such conditions, lies in millimeter range. There were observed no general operational problems, except of vibrations at pipe bends, which lead the flow vertically upwards. In regard to the terminal velocity of particles with a size of 4 mm is the actual gas velocity too low. So, material can accumulate themselves in the pipe bends and possibly develop a behaviour like a pulsating spouting bed, and thus generate vibrations. (3) data set coming from the following bulk-online thread: http://forum.bulk-online.com/showthread.php?7057-Pneumatic-Transport-Cement-Pipeline-Pigging The operating data of this system offered the opportunity to determine the boundary of dense flow more accurately, because the operating conditions are lying exactly on this line. For a gas temperature of 125 ° C and a bulk solid throughput of 85 t / h, the calculation on the basis of the improved coordinates (no longer equal to those of the original state diagram) yields the following values: 7060 kg / h for the gas flow and 1.66 bar for the pressure loss. In this thread was also an increase to 100 t / h solids throughput discussed; according to my calculations, however, this requires a gas flow of 7860 kg / h at a pressure loss of 1.92 bar, for which the installed compressor capacity does not suffice. (4) data set coming from the following bulk-online thread:

http://forum.bulk-online.com/showthread.php?21119-Increasing-the-Conveying-Capacity (5) data set coming from the following bulk-online thread: http://forum.bulk-online.com/showthread.php?16367-Optimisation-of-a-Pneumatic-Conveying-Line After the program's calculation lies the operating point of this installation on the boundary of dilute phase, the so-called choke line. (6) data set coming from the following bulk-online thread: http://forum.bulk-online.com/showthread.php?7259-Conveying-of-PTA After the calculation lies the operating point of this installation also on the boundary of dilute phase, the so-called choke line. The operational pressure loss is equal to the calculated value, when a (unconfirmed) gas temperature of 90 °C is used.

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(7) data set coming from the following bulk-online thread: http://forum.bulk-online.com/showthread.php?4797-PP-Pellet-Conveying-Problem This operating point lies close to the so-called choke line of the dilute phase. For this operation conditions yields the calculation a slightly smaller gas flow rate and looks as follows:

The average gas velocity is much smaller than for the conveying of PP pellets in the installation No. 1 of Table 1. (8) data set coming from the following bulk-online thread: http://forum.bulk-online.com/showthread.php?5655-Pneumatic-Conveying-of-Rapeseed This is another good example, to verify the calculated results. For a bulk solid throughput of 12 t / h yields the calculation for the condition of minimum pressure loss in dilute phase a value of 0.36 bar. This value lies near the pressure difference of 0.4 bar of the blower, what the possible solids throughput accordingly limits.

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(9) data set coming from the following bulk-online thread: http://forum.bulk-online.com/showthread.php?4794-Why-Is-Throughput-Reduced As usual for bulk materials with large particle diameters, the gas velocity is much higher than the calculated value for the minimum pressure loss in dilute phase: 32 m/s instead of 14 m/s. However, the bulk solid throughput is too small for such a gas velocity, and I am also of the opinion, that the reason for this is the poorly functioning material feed. The fan is designed for pressures up to 0.5 bar at a gas flow rate of 700 m3 / h and would be able, to handle a much higher bulk solid throughput. The calculation result for the current bulk solid throughput of 1.5 t / h is as follows:

(10) data set coming from the following bulk-online thread: http://forum.bulk-online.com/showthread.php?5597-Typical-Solids-Friction-Factor-for-Cement The calculation results for the choke condition on the boundary of the dilute phase for a (unconfirmed) gas temperature of 110 ° C are identic to the operating data:

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(11) For completeness, here are added the operating conditions for the conveying of used, very abrasive cell liner: http://forum.bulk-online.com/showthread.php?5437-Lean-Phase-Conveying-of-Abrasive-Cell-Liner The information for this system are not complete, However, the calculated pressure loss of 30 kPa for the choking conditions fits quite well to the blower specification of 40 or 60 kPa. (12) data set coming from the following bulk-online thread: http://forum.bulk-online.com/showthread.php?3709-Determinining-Pneumatic-Conveying-Parameters The operating point lies a little left hand from the boundary of the dense phase. The estimated values for the parameters K and Re of the state diagram are 450 and 450,000. The calculation results for gas flow rate and the pressure drop confirm the assumptions.

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5 Improved state diagram and computer program The main concern of the state diagram is the universal and clear presentation of the operating data of industrial conveying installations with their large number of parameters. For this purpose a large number of published data from industry and research was added into the coordinate system. They form the skeleton of the state diagram and reveal the areas of dilute phase and dense phase conveying as well as their boundaries. There are three characteristic conveying states, that lie in the diagram on particular lines. Two of the states are the pressure loss minimum in dilute phase as well as the boundary to the transition area, the so-called choking line. The third one is the boundary of dense phase on the other side of the transition area, the position of which was determined by the aid of the operational data No. 3 in Table 1 more accurately. From the data of dense phase conveying was derived in addition an estimation for frequently used pipe diameters as ratio to the bulk material throughput. In order to facilitate the estimation of the sizes of conveying lines, the software helps, as mentioned, in determining a usable pipe diameter. Furthermore, can be determined on the basis of the design data, the relevant parameters for the three characteristic conveying states. The respective values are being calculated by means of simple mathematical equations for the respective straight lines. For all other possible operating points, the respective parameters can be read from the state diagram. However, the left border line of the display, which represents the boundary of the bulk solid movement, is only indicated, but may be precised, as described above. For the calculations of conditions in dilute phase uses the program its default pipe diameter and corrects the calculation result in the case of deviations from the actual diameter. This correction has been found to be necessary during the recalculation of the used literature data, , but it is surely not particularly sophisticated. For bulk solids with big particles is the gas velocity in some cases bigger than the velocity at the point of minimum pressure loss in dilute phase: for example, 38 m / s instead of 21 m / s for the installation No. 4 (2.5 mm) in Table 1. In dense phase the operating points are distributed over the entire range. This opens up the possibility to draw lines of constant bulk solids throughput. Originally, the maximum bulk solid throughput was 19.5 t / h. Fortunately, the installation No. 3 offered the opportunity for an expansion of the throughputs and the accurate determination of the position of the boundary of the dense phase region, because this operating point lies exactly on this line. As already described above, yields the calculation on the basis of the new coordinates (which are no longer those of the original in the state diagram registered correspond) for a gas temperature of 125 ° C and a bulk solid flow of 85 t / h the following result: 7060 kg / h for the gas flow and 1.66 bar for the pressure loss. Once again here is the attention being focused on the installation No. 2 in Table 1. These operating data fit extremely well in the scheme of the dense phase, although the particle size of this material, in contrast to the fine-grained solids, which are commonly conveyed under such conditions, lies in millimeter range. There were observed no general operational problems, except of vibrations at pipe bends, which lead the flow vertically upwards. In regard to the terminal velocity of particles with a size of 4 mm is the actual gas velocity too low. So, material can accumulate themselves in the pipe bends and possibly develop a behaviour like a pulsating spouting bed, and thus generate vibrations. -------------------------------- *) In the case of horizontal conveyor lines with vertical pipe sections must for the steady

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conveying state an equivalent length be used. For this, the value for the whole vertical pipe length is being enlarged by a factor between 1.7 and 2.0. After the product was fed into the pipeline, and after pipe bends, the bulk solids are accelerated to their terminal velocity. The energy required for this is removed from the air stream, so that an additional pressure loss occurs, which, in case of short conveying lines, can become the majority. Reference values for the size of this additional pressure losses can be found in the literature. After the product feeder in horizontal pipelines, for the acceleration of 1 kg of solid per kg of air, depending on the particle diameters, the following pressure losses are required: 250 N/m2 (dp = 8000 microns) or 550 N/m2 (dp = 1000 microns) [5]. These values apply to a gas velocity of 20 m / s and a particle density of 1000 kg/m3. For the straight up directed conveying of bulk solids are about 100 N/m2 required for the acceleration of 1 kg of solids per kg of air[6]. This value was determined at a gas velocity of 23 m / s and for a particle density of 2600 kg/m3. The required pressure losses for the acceleration of the bulk solids increases itself in general with decreasing settling velocities of the particles. The reason lies in the fact that smaller or

lighter particles at constant mass flow have higher end speeds. In the flow through pipe bends, the bulk solid is by the centrifugal forces pressed outward and moves along the pipe wall . This results in increased friction between the particles and the tube wall, so that the velocity of the material decrease. In the subsequent straight pipe line, the solid is then again accelerated to the speed of the steady state. In this way, the pressure loss ∆pKr is generated. After Schuchart [7], the additional pressure drop ∆pKr for horizontal deflections depends on the ratio between pipe bend

radius R and tube diameter D. The diagram depicts the related pressure loss for the pipe bend in relation to the related pressure loss in a straight pipe for air with and without solids loading dependent of 2R / D. For the frequently used ratio of 10 for 2R / D the pressure drop for the pure air flow is by a factor of 2 bigger and that of the bulk solid conveying by a factor of 15 bigger than in a straight pipe. However, it remains unclear, whether the specified ratios can be applied to the here for steady conveying conditions calculated pressure losses. An estimation on the basis of the calculated and the measured pressure drops of the installation 1 in Table 1, for which eight bends have been given, indicates rather factors half as large or even smaller. Certainly, the properties of the particles and the surface conditions of the pipe bends play also a role. **) In the evaluated data of industrial installations were no evidence of additional influences, which are dependent of the conveyed bulk solids. The only relevant parameter is the bulk solid throughput. Also could no other physical similarities be discovered, which are connected with the bulk solid properties in some way, and possibly exist in form of hidden parameters. Even the oft-cited solid / gas ratio turned out to be unusable. A factor, which is in this context closest to a parameter, is the bulk solid throughput related to the cross-sectional area of the pipe.

Dependence of the pressure loss

ratio on the diameter ratio 2R / D

in horizontal pipe bends [7]

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5.1 Sketch of the dense phase area This is the graphic for the dense phase area of the state diagram, which was improved by using the here analyzed operating data . The on the border to the transition area lying endpoints of the lines of equal bulk solid throughput were calculated by the appropriate modified software program.

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6 Pneumatic conveying at high temperatures

Operating data for industrial pneumatic conveyor lines that are operated at high gas temperatures are to be found at the following Internet address:

http://www.enviro-engineering.de/pdf/InjektorenBauformenVariantenUndAnwendungen.pdf

( ) = Calculated values, µ = solid / gas ratio

Table 2: Operating data of industrial installations with high gas temperatures

(1) As in other installations for the transport of bulk materials with large particles, the gas velocity in this conveying line is by a factor of 1.6 higher than those, calculated for the minimum pressure loss in dilute phase. The extrapolation from the calculated operating point of minimum pressure loss gives values of 100 000 and 25 for the parameters Re and K. The calculation results look like this.

Nr. Product dp50

µm

L

m

h

m

D

mm

&Ms

t/h

&Mg

Nm3/h

∆∆∆∆p

bar

u

m/s

µ

-

1 Ash (1) / 80 °C 0-3000 20 25 80 0.6 ca 350 (0.14) (23.6) (ca 1.5)

2 Ash (2) / 250°C 0-1000 11 15 178 6.5 ca 750 (0.133) (16.5) 6.5

3 Cement (3) / 125 °C -- 216 40 ca 285 85 ca 6000 1.6 -- --

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(2) The data of this conveying system describe the operating condition at a gas temperature of 250 ° C, which due to a longer cooling period of the ash under the actual operating temperature of 450 ° C lies. The measured ash throughput of 6.5 t / h is assessed as being surprisingly high. The calculation for this condition results in a pressure loss of 0.133 bar at a gas flow of approximately 1000 kg / h.

The following calculation results describe now the situation at the actual operating temperature of 450 ° C and at the same pressure loss. The gas flow rate lies at about 900 kg / h, while the ash throughput at this gas temperature is reduced to a value of 3500 kg / h; this value corresponds exactly to the design conditions of the conveying line.

(3) This is once again the installation No. 3 of Table 1 with the corresponding interpretation: The operating data of this system offered the opportunity to determine the boundary of dense flow more accurately, because the operating conditions are lying exactly on this line. For a gas temperature of 125 ° C and a bulk solid throughput of 85 t / h, the calculation on the basis of the improved coordinates (no longer equal to those of the original state diagram) yields the following values: 7060 kg / h for the gas flow and 1.66 bar for the pressure loss. In this thread was also an increase to 100 t / h solids throughput discussed; according to my calculations, however, this requires a gas flow of 7860 kg / h at a pressure loss of 1.92 bar, for which the installed compressor capacity does not suffice.

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7 References [1] Heyde, M.: Fluidisieren von Schüttgütern. epubli GmbH, Berlin, 2011. ISBN 978-3-8442-

1270-9. [2] Muschelknautz, E.; und W. Krambrock: Vereinfachte Berechnung horizontaler

pneumatischer Förderleitungen bei hoher Gutbeladung mit feinkörnigen Partikeln. Chem.-Ing.-Tech. 41(1969)21, S.1164-1172.

[3] Muschelknautz, E.; und H. Wojahn: VDI-Wärmeatlas 1973, Kap Lh. [4] Krambrock, W.: Dichtstromförderung. Chem.-Ing.-Tech. 54(1982)9, S.793-803. [5] Siegel, W.: VDI-Forschungsheft 538: Experimentelle Untersuchung zur pneumatischen

Förderung körniger Stoffe in waagerechten Rohren und Überprüfung der Ähnlichkeitsgesetze. Düsseldorf: VDI-Verlag, 1970.

[6] Kerker, L.: Druckverlust und Partikelgeschwindigkeit bei der vertikalen Gas-Feststoff-Strömung. vt "verfahrenstechnik" 11(1977)9, S.549-559.

[7] Schuchart, P.: Widerstandsgesetz beim Transport in Rohrkrümmern. Chem.-Ing.-Tech. 40(1968)21/22, S.1060-1067.