80
where Cmm = minimum conveying air velocity - ft/min and
Material having dilute phase conveying capability only
2000 Material with dense phase conveying capability
g 1000 u
20
40
60
80
100
Solids Loading Ratio Figure 16.1 Relationship between minimum conveying air velocity and solids loading ratio for different materials.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Quick Check Methods
453
For a material that is not capable of being conveyed in dense phase, such as granular materials having both poor air retention and poor permeability, the conveying limits are defined approximately by: Cmm =
2300 to 3200 ft/min
(for all
(8)
A graphical representation, for typical materials, of these relationships between minimum conveying air velocity and solids loading ratio is also included on Figure 16.1. For most purposes, the use of this graph probably provides the quickest means of determining the necessary value, but for anyone wanting to program the analysis, Equations 7 and 8 are offered for this purpose. Design would generally be based on a conveying line inlet air velocity, C/, 20% greater than the minimum conveying air velocity, C,,,,,,:
C, 2.3.2
= 1-2
ft/min
(9)
Solids Loading Ratio
An approximate relationship between pressure drop and solids loading ratio, for dilute phase conveying, is presented in Figure 16.2. The relationship is based upon the assumption that the curves on Figure 16.2 are equi-spaced with respect to conveying line pressure drop. For many materials conveyed in dilute phase this is a reasonable approximation.
Air Flow Rate - V0 Figure 16.2 Influence of solids loading ratio and air flow rate on conveying line pressure drop for dilute phase suspension How.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Chapter 16
454
A mathematical expression for this is:
(10)
where Apc and Ap,,
conveying line pressure drop - Ibf/irT air only pressure drop - Ibf/in 2
2.3.3 Material Flow Rale Now from Equation I :
mP m. Directly equating these two expressions for solids loading ratio gives:
mp =
Ib/h
(11)
If air mass flow rate, ma , is not a convenient parameter, Equation 11 can be expressed in an alternative form, in terms of air pressure, p, and velocity, C, by substituting a combination of Equations 3 and 5 to give:
mP
p nd C 4 RT
Ib/h
Another alternative is to substitute solids loading ratio, , from Equation 10 into Equation 4, which gives:
mp =
p C d2 67-9 T
Ib/h
Pipeline inlet conditions are the most convenient to use here. 2.3.3.1 Negative Pressure Systems For vacuum systems the pressure, p, will be atmospheric.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
(12)
455
Quick Check Methods
2.3.3.2 Positive Pressure Systems For positive pressure systems the pressure, p, in Equation 12 will be equal to the conveying line pressure drop, A/?c, plus atmospheric pressure, which is:
where A/? r = conveying line pressure drop - lbf/in 2 and paln, = atmospheric pressure - lbf/in 2 2. 3. 4 Pipeline Bore By substituting the solids loading ratio, (/), from Equation 10 into Equation 5, the expression can be in terms of the pipeline bore required:
d
A/?,,
= 8-24
in
(13)
P The situation for both positive and negative pressure systems is the same as above. 2.3.5 A ir Supply Pressure Alternatively, the expression can be in terms of the pressure required to convey the material. Substituting the solids loading ratio, 0, from Equation 10 into Equation 6 gives:
p
= 67-9
T
lbf/in 2 abs
-
(14)
C d' Pipeline inlet conditions are again the most convenient to use. 2.3.5.1 Negative Pressure Systems For negative pressure systems the pressure, p, will be atmospheric and hence Apc can be determined, which is the value required in this case. Re-arranging Equation 14 and expressing in terms of pipeline inlet conditions for this case gives:
67-9
m d ~
. + 1 | lbf/in 2
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
(15)
Chapter 16
456
2.3.5.2 Positive Pressure Systems For a positive pressure system: A/7C
=
Pa,
Substituting this into Equation 14 and expressing in terms of pipeline inlet conditions gives:
mp =
PllPl
67'9
This is a quadratic equation, the solution to which is:
2
P
212mpTl&pa (16)
\Patm
Palm
Note: This will give the correct root. 2.3.6
Air Only Pressure Drop
Since the air only pressure drop, Apa, features prominently in all of these models, a convenient expression for this pressure drop is required. An expression that will give the air only pressure drop in terms of conveying line inlet, or exit, air velocity is needed. These models were derived in detail in Chapter 6 on The Air Only Datum. 2.3.6.1 Negative Pressure Systems For negative pressure systems the expression also needs to be in terms of the inlet air pressure, p / , since this is generally known (usually atmospheric). Such an expression was developed at Equation 6.20 and is:
,05 j_
lbf/in-
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
(17)
457
Quick Check Methods
2.3.6.2 Positive Pressure Systems For positive pressure systems the expression needs to be in terms of the exit pressure, p2, since this is generally known (usually atmospheric). Such an expression was developed at Equation 6.17 and is:
,0-5 1+
-1
Ibf/irT
(18)
Pipeline Features This quick check method does not take pipeline features such as vertical sections and bends into account very well. Bends are a particular problem because the equivalent length with material flow increases by an order of magnitude above the air only value. This is where the accuracy of the method can be improved, if conveying data is available, and constants are applied to the component parts of the pipeline for fine tuning. 2.3.7.1 Vertical Conveying The models presented so far relate essentially to horizontal pipelines. Most pneumatic conveying systems, however, will include a vertical lift and so this needs to be taken into account. The pressure drop in vertical conveying over a very wide range of solids loading ratio values, is approximately double that for horizontal conveying. Sections of vertical conveying in a pipeline, therefore, can most conveniently be accounted for by working in terms of an equivalent length and allowing double for vertical lifts. This equivalent length needs to be incorporated in the actual pipeline length in the preceding equations. 2.3.7.2 Pipeline Bends A model to give the equivalent length of a bend in terms of straight pipeline was presented in Chapter 6 at Equation 9:
k d
(19)
487 For a radiused 90° bend, k is typically about 0-15 (see Figure 6.6) and an average value of friction factor,/, is about 0-004 (see Figure 6.3). For a 6 inch bore pipeline, therefore, the equivalent length of a bend is approximately 4-7 ft. The performance of bends within pneumatic conveying systems was considered in Chapter 8 and equivalent lengths were presented in Figure 8.18. From this it is evident that a constant needs to be applied to the bend loss coefficient and a multiplying factor of three is suggested by way of compromise. With conveying data for a particular material this is a particular area for fine tuning.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
458
2.4
Chapter 16
Procedure
To illustrate the method it is proposed to use the same example as employed in the previous chapter to demonstrate the procedure with regard to scaling parameters for dilute phase conveying. This was to investigate the conveying potential of the pipeline system illustrated in Figure 15.12 of 8 inch bore for the conveying of granular coal. The pipeline routing included a total of 570 feet of horizontal pipeline, 80 feet of vertically up pipeline and eight 90° bends. It was proposed that a conveying line inlet air pressure of 12 psig should be used, with atmospheric pressure at 14-7 psia. The minimum conveying air velocity for the coal was given as 2600 ft/min and with a 20% margin the conveying line inlet air velocity was taken as 3120 ft/min. It will assumed that the temperature of the air and coal are 520 R (60°F) throughout. 2.4.1 Air Only Pressure Drop The starting point in the process is to evaluate the air only pressure drop, Apa, for the pipeline and potential conveying parameters. Possibly the best equation for the air only pressure drop for the given situation is Equation 18 presented above, and this is repeated below for reference:
Ibf/in"
P2
- - -
(20)
The terms in this equation are as follows: ...i P2 = 14-7 Ibf/in 2 absolute. This is the conveying line exit air pressure, which is atmospheric pressure. C? = 5660 ft/min. This is the conveying line exit air velocity. The conveying line inlet air velocity is given above as 3120 ft/min and C2 can be calculated using Equations 5.1 and 5.5. P R = 53'3 ft Ibf/lb Rand is the characteristic gas constant for air. See TableS.l. ij T2 = 520 R. This is the absolute value of conveying line exit air temperature, given above. gL. = 32'2 ft lb/lbfs~. This is the gravitational constant. \y = the constant relating to pipeline geometry: The pipeline head loss coefficient, i//, was presented in Chapter 6 with Equation 6.1 1 and is presented below for reference:
W
=
-1 -9-375 d 450
(dimensionless)
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
-
- - -
(21)
459
Quick Check Methods The terms in this equation are as follows:
/ = 0-004. This is the pipeline friction coefficient. This is derived from Figure 6.3, having evaluated the Reynolds number for the flow (see Chapter 6 section 2. 1 .4) in the usual way. ! L = 730 feet. This is the equivalent length of the straight sections of pipeline, comprising 570 ft of horizontal pipeline and 80 ft of vertically up pipeline. [Lf = Lh + 2Lt] d = 8 inch. This is the diameter of the pipeline. Zk = 3-6. This is the loss coefficient for all the bends in the pipeline. For an individual bend the value of k for air is about 0-15 (see Figure 6.6). There are 8 bends in the pipeline and it was recommended above that this loss coefficient should be multiplied by a factor of three. Substituting the above set of values into Equation 21 gives \$i = 0-0469. Substituting this value for if/ and the previous set of values into Equation 20 gives:
=
14-7
=
1-65 lbf/in 2
0-0469x5660 2 8x53-3x460x32-2
2. 4. 2 Material Flow Rate Since the diameter of the pipeline is specified as 8 inch and the system is to operate with an air supply pressure of 12 psig, it is the material flow rate that needs to be evaluated. This is given by Equation 1 1, and requires a value for the air mass flow rate in Ib/h. This can be determined by re-arranging Equation 5.4 and substituting V from Equation 5.2, since a value for volumetric flow rate has not yet been evaluated:
p n d2Cx60 m = 4RT
Ib/h
(22)
Taking conveying line inlet air conditions and substituting the above values gives:
26-7x^x82x3120x60 -
4x53-3x520 = 9065 Ib/h
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
460
Chapter 16
Substituting these values into Equation 11 gives:
m
"
- 9065 [ —-1 11.65 =
56,900 Ib/h
In the case study presented in the previous chapter, using conveying data and scaling parameters, a material flow rate of about 71,600 Ib/h was evaluated for the conveying of granular coal. Since the method used here makes no reference to the type of material being conveyed, a 20% error is to be expected. 3
UNIVERSAL CONVEYING CHARACTERISTICS METHOD
The pressure required to convey a material through a pipeline can be divided into a number of component parts. The most important are the straight pipeline sections and the bends. For each of these elements there are a multitude of sub variables that can have an influence, but their incorporation necessarily adds to the complication of the process. A compromise is clearly needed in order to provide a Quick Check Method [1|. 3.1
Straight Pipeline
Figure 16.3 is a graph of material flow rate plotted against air flow rate, which is the usual form for presenting conveying characteristics for materials. In this case the family of curves that are drawn are lines of constant pressure gradient in Ibf/in 2 per 100 ft of pipeline. The data was initially derived from conveying trials with barite and cement, but has since been found to be reasonably close to that for many other materials. Data in this form has been presented for both horizontal and vertical pipeline runs in earlier sections, notably in Chapters 8 and 15. 3.1.1 Horizontal Pipeline The data in Figure 16.3 represents the pressure gradient for conveying material through straight horizontal pipeline of 2 inch bore. As will be seen, it covers both dilute and dense phase conveying, with a smooth transition between the two. This Quick Check Method is based on the use of this data and so it will be seen that there is no specific reference to material type. It must be recognized, therefore, that this is also strictly a first approximation method only, but it will provide an entirely different means of obtaining a quick check solution. To the pressure drop for conveying the material must be added the pressure drop for the air, and this will be considered later. The effect of pipeline bore must also be considered, and this, of course, is also related to the air flow rate.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
461
Quick Check Methods
Solids Loading Ratio ---.
240 200 160 120 \ll \i 15/14 13 50
40
oi
100
Pressure Gradient - lbf/in 2 per 100 ft
30
o 20
20
10
10
0 0
40
80
120
160
200
Free Air Flow Rate - ft'/min Figure 16.3
Pressure gradient data for horizontal conveying in 2 ineh bore pipeline.
Straight vertical pipeline sections are another element that requires to be taken into account, but these can conveniently be incorporated with Figure 16.3, as will be seen. Pipeline bends are a completely separate issue and will be dealt with later. 3. 1.2
Vertically Up Pipeline
For flow vertically up, it has been found that the pressure gradient is approximately double that for horizontal conveying, as reported in Chapter 8, and that this applies over an extremely wide range of solids loading ratios. To take account of vertically up sections of pipeline, therefore, the pressure gradient values on Figure 16.3 simply need to be doubled for any operating point on the chart. For flows in vertically down sections of pipeline the situation is very different, as discussed in Chapter 8. In dense phase flows there is a pressure recovery, such that the pressure gradient has a negative value. For dilute phase flows, however, there is a pressure loss. The transition between the two occurs at a solids loading ratio of about 35 and at this value materials can be conveyed vertically down with no pressure drop at all. Figure 16.3, therefore, cannot be used in this case, as discussed in section 3.2 of Chapter 8.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
462
3.2
Chapter 16
Pipeline Bore
Material flow rate varies approximately in proportion to pipe section area, and hence in terms of (diameter)2. Air flow rate, to maintain the same velocity in a pipeline of different bore, varies in exactly the same way. To determine the pressure gradient for flow in a pipeline having a bore different from that of the reference data in Figure 16.3, both the material and air flow rates should be adjusted in proportion to (d2/2)2, where d 2 is the diameter of the plant pipeline in inches. It will be noted, therefore, that there will be no change in the value of the solids loading ratio. It must be appreciated that along the length of a pipeline, as the pressure drops and the conveying air velocity increases, the pressure gradient is likely to increase. In Figure 16.3 a single value is given for the entire pipeline. This value can be taken to be an average for the pipeline, but it is another feature that reinforces the point that this is only an approximate method. 3.2.1 Stepped Pipelines When high pressure air is employed it is usual to increase the bore of the pipeline to a larger diameter along the length of the pipeline. This technique was considered in some detail in Chapter 9. By this means the very high velocities that will result towards the end of a single bore pipeline, from the expansion of the air, can be prevented. By this means it is often possible to gain a significant increase in performance of the pipeline. The pressure drop in a stepped pipeline can be evaluated in exactly the same way as outlined above. A critical point in stepped bore pipelines is the location of the steps along the length of the pipeline. At each step in the pipeline the conveying air velocity must not be allowed to fall below a given minimum value. The solution, therefore, will be an iterative one since the velocity of the air at the step depends upon the pressure at the step. 3.3
Pipeline Bends
Pressure drop data for bends in pipelines is presented in Figure 16.4. This is an identical plot to that in Figure 16.3 and covers exactly the same range of conveying conditions. The pressure drop in this case is for an individual bend in the pipeline and hence is in Ibf/in" per bend. The data given in Figure 16.4 relates to 90° radiused bends in a 2 inch bore pipeline. This is also data that was derived from conveying trials with barite and cement that has since been found to be reasonablyclose to that for other materials. 3.3.1 Bend Geometry As mentioned earlier, it has been found that this pressure drop relationship varies little over a range of D/d (bend diameter to pipe bore) ratios from about 5 to 30.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Quick Check Methods
463
Solids loading ratio
60
60
50 o o o
Pressure Gradient - tbf/in 2 per 100ft _0 U,
13 20 a
10
0
40
80
120
160
200
Free Air Flow Rate - ft'/min Figure 16.4
Pressure drop data for 90° radius bends in 2 inch bore pipeline.
It has been found that the pressure drop in very sharp or short radius bends, and particularly blind tee bends, however, is significantly higher and so an appropriate allowance should be made if any such bend has to be used, or is found to be fitted into an existing pipeline. Little data exists for bends other than those having an angle of 90° and so it is suggested that the data in Figure 16.4 is used for all bends, since 90° bends are likely to be in the majority in any pipeline. In the absence of any reliable data on the influence of pipeline bore it is suggested that the data in Figure 16.4 is used for all bends, regardless of pipeline bore. For larger bore pipelines the material and air flow rates will have to be scaled in the same way as outlined for the straight pipeline in Figure 16.3. 3.4
Air Only Pressure Drop
As mentioned earlier, the data in Figure 16.3 relates only to the conveying of the material through the pipeline, and so the pressure drop required for the air alone must be added. In Figure 16.5 the influence of pipeline bore on this pressure drop for 500 ft long pipelines is presented to illustrate the potential influence of this variable and is similar to that shown earlier in Figure 6.5.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Chapter 16
464
Pipeline Bore - 1
Pipe! -500
Conveying Line Exit Air Velocity - ft/min 1000
2000 40
Figure 16.5 drop.
3000
4000
5000
6000
7000
80 120 160 Free Air Flow Rate - ftVmin * (d 2 /2) 2
8000
9000 200
Influence of pipeline bore and air flow rate on the empty pipeline pressure
Figure 16.5 shows the influence of air flow rate and pipeline bore on conveying line pressure drop for a representative pipeline length of 500 ft. Since pipe bore is on the bottom of Equation 6.3, pressure drop deceases with increase in pipeline bore. Figure 16.5 is presented by way of illustration. The air only pressure drop for any pipeline can be evaluated as illustrated above in section 2.4.1 and the models presented in Chapter 6. It will be seen that conveying line exit air velocity has been added to the horizontal axis for reference. Conveying line inlet air velocity is the critical design parameter, but this cannot be added conveniently because it is also a function of the conveying line inlet air pressure. Because a range of pipeline bores are represented on this plot, the air flow rate is in terms of that for the reference 2 inch bore pipeline x (d2/2)2. From Figure 16.5 it will be seen that the air only pressure drop can be quite significant, and particularly so for long, small bore, pipelines. As there are many variables in this pressure drop relationship it is probably best to evaluate the pressure drop mathematically on an individual basis, using the models presented in Chapter 6, as mentioned above Another graph, plotted for 4 inch bore pipelines, is presented in Figure 16.6 to illustrate the influence of pipeline length, with the pressure drop relationship being presented for 100 and 1000 ft long pipelines, as well as the 500 ft long pipeline of 4 inch bore. This is similar to that shown above in Figure 16.5 and also includes both air flow rate and conveying line exit air velocity on the horizontal axis.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Quick Check Methods
465
1000
Pipeline Length - ft
10
,g
Pipeline Bfrre - 4 inert
-O
T 6 a I §4
! -. 500
100
Conveying Line Exit Air Velocity - ft/min 3000 4000 5000 6000 7000 8000
1000 2000 40
80
120
160
9000
200
2
Free Air Flow Rate - fVVrnin x (d2/2) Figure 16.6 drop. 3.5
Influence of pipeline length and air flow rate on empty pipeline pressure
Conveying Parameters
Many of the conveying parameters to be taken into account in the analysis are similar to those presented above for the previous method. 5.5.7 Pick-Up Velocity System design decisions have always to be made with regard to a value of the conveying line inlet air velocity to be employed. This is critical to the success of any pneumatic conveying system. The data presented in Figure 16.1 and Equations 7 to 9 is equally valid here by way of guidance in determining a value for pick-up velocity. Once again it must be emphasized that if the material is capable of being conveyed at low velocity in dense phase, then the influence of solids loading ratio will additionally have to be taken into account. 3.5.2 Influence of Distance and Pressure The design method presented here is an iterative process, and particularly so for dense phase conveying where the conveying line inlet air velocity is a function of the solids loading ratio. Solids loading ratio is an important parameter in this process, and so the potential influence of conveying distance and air supply pressure on the solids loading ratio is presented in Figures 16.7 and 16.8. These graphs were presented earlier in Figures 4.27 and 4.28 to illustrate the potential capability of pneumatic conveying systems.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Chapter 16
466
150 100 80
60
40
15
I°
200 300 Conveying Distance - ft
tx
-10
100 80 60
40
400
500
30
Figure 16.7 The influence of air supply pressure and conveying distance on solids loading ratio for low pressure conveying systems.
60
ISO
100
80
60 30
