##### Procedure

The location of the equivalent operating point on the conveying characteristics for the test pipeline needs to be established first, taking account of the pressure and air flow rate requirements. Scaling is conveniently carried out in two stages. In the first stage scaling is with respect to conveying distance, and this includes both pipeline orienta- tion and bends. In the second stage the scaling is with respect to pipeline bore.

Air only pressure drop values need to be established and so this procedure is also included. In this case, as the pipeline is longer and will be of a larger bore the two effects are likely to cancel each other. If there is likely to be a noticeable difference between the two it would always be recommended that this should be taken into account. Appropriate equations, derived earlier in the Design Guide, are reproduced where required for convenient reference.

###### Operating point

The operating point on the conveying characteristics for the test pipeline on Figure 16.1 must first be identified. At 1.6 bar the minimum air flow rate is about 0.021 kg/s and so the operating point will correspond with an air flow rate 20 per cent higher at 0.025 kg/s. The corresponding material flow rate is approximately 12.8 tonne/h. This is shown on Figure 16.6 and is identified as point (a) as a first estimate.

###### Conveying line inlet air velocity

The minimum conveying air velocity, *C*min, corresponding to the conveying limit for a pressure drop of 1.6 bar can be determined by using Equation (9.20), reproduced here as Equation (16.1).

###### Taking the conveying line exit air pressure, *p*2, to be standard atmospheric pressure of 101 300 N/m2, the pipeline friction factor, *f*, to be 0.0045, the length of the test pipeline,

*L*, as 50 m, the air flow rate as determined above at 0.025 kg/s, *R *for air = 287 J/kg · K, the air temperature *T *= 288 K and the test pipeline bore, *d *of 0.053 m, gives:

As will be seen this is negligible and not really worthwhile taking into account. This is because it is for very low velocity conveying in a relatively short pipeline. For high velocity dilute phase conveying in a long pipeline it would be essential that this should be taken into account.

**Note**

For greater accuracy with this air only pressure drop value, if it is be required, an allowance for the bends in the pipeline should also be included. If Equation (10.9) is used for the purpose and a value for *k *for the bends of 0.2 is taken from Figure 10.6 it will be seen that the equivalent length for all nine bends will come to about 5.4 m. This value should be added to the actual pipeline length of 50 m and used in Equation (16.2).

###### Equivalent lengths

The equivalent length of a pipeline for the conveying of material takes the length of horizontal pipeline as the reference value. To this is added an equivalent length of straight horizontal pipeline, both for the vertically up sections of pipeline and for the bends in the pipeline. These two elements were considered in Chapter 14 on ‘Pipeline scaling parameters’.

For vertically up elements of pipeline in Section 14.6 it was shown that the scaling parameter was two, so that the length of the vertically up sections of pipeline is simply doubled. No significant influence of conveying conditions were found and so it is applied universally to dilute and dense phase conveying. For pipeline bends in Section 14.5 it was shown that the equivalent length of the bends could be related to the con- veying line inlet air velocity and the analysis reported provides the basis of the relationship presented in Figure 16.4. It was found that the equivalent length of pipe bends varied little with bend geometry, being reasonably consistent over a *D/d *range from about four to forty. For very short radius bends, and blind tee bends in particular, how- ever, the equivalent length would be very much greater.

The equivalent length of a pipeline, *L*e, therefore, can be expressed as:

where *h *is the total length of horizontal sections of pipeline; *v*, the total length of ver- tically up sections of pipeline; *N*, the total number of bends in pipeline and *b*, the equivalent length of each bend.

###### Test pipeline

A sketch of the test pipeline is given in Figure 16.2 and from this it will be seen that the equivalent length of the test pipeline, *L*e1, is:

There is no significant vertical lift and there are nine bends in the test pipeline. With a conveying line inlet air velocity of 3.6 m/s the equivalent length of the bends, from Figure 16.4, is about 11⁄2 m each.

###### Plant pipeline

A sketch of the plant pipeline is given in Figure 16.3 and from this it will be seen that the equivalent length of the plant pipeline, *L*e2, is:

The actual length of the plant pipeline is 155 m and it is this length that needs to be used to evaluate the air only pressure drop for the plant pipeline having the same bore as the test pipeline. Neglecting the effect of the bends once again and substituting the length of 155 m in place of 50 m into Equation (16.2) (this is the only parameter to change in this equation), gives:

Although this is three times greater than that for the test pipeline, as would be expected, it is still insignificant in terms of the 1.6 bar conveying line pressure drop value. The increase in the air only pressure drop from 0.009 bar to 0.027 bar means that 0.018 bar less pressure is available for conveying material.

This loss in pressure of 0.018 bar should be deducted from the 1.6 bar, which gives

1.582 bar, and it is this value that should be used on Figure 16.6 in order to determine the material flow rate to be used for scaling purposes. Once again, for low velocity high pressure conveying, these pressure drop terms are insignificant, but for long dis- tance, high velocity, low pressure conveying these terms will be significant and will have to be taken into account. This will be illustrated in the next case study in the next chapter.

###### Scaling for length

The scaling model for pipeline length is given in Equation (14.4) and is reproduced here in Equation (16.4):

The two equivalent lengths were determined immediately above, and the material flow rate for the test pipeline was obtained from Figure 16.6; 4.12 tonne/h is the mate- rial flow rate that would be expected, for the same conveying line pressure drop and air flow rate, if the pipeline had the same bore as the test pipeline, neglecting the effect of the air only pressure drop.

Before considering the options from this result the conveying parameters need to be checked.

###### Conveying conditions – check

A check needs to be made at this point to evaluate the new value of solids loading ratio. This needs to be done in order to determine whether the material can still be con- veyed in dense phase, since the operating point for scaling is based on a conveying line inlet air velocity of 3.6 m/s and an air mass flow rate of 0.025 kg/s. The new solids loading ratio, from Equation (1.3), will be:

From Figure 16.5 it will be seen that at a solids loading ratio of 45 the minimum value of conveying air velocity is about 4.5 m/s and not 3.0 and so the initial operating point identified on Figure 16.6 is not valid for scaling. As a consequence an operating point on Figure 16.6 having a conveying line inlet air velocity much higher than 1.2 X 4.5 = 5.4 m/s will be required to compensate.

###### Conveying conditions – re-calculate

As the check failed at this point it is necessary to return to the operating point on Figure 16.6 and locate a new operating point. From the benefit of the first calculation it would be suggested that a value of conveying line inlet air velocity of about 8 m/s should be tried. This is identified on Figure 16.6 as point (b). The new operating point needs to be a large increase on the first, for in the solids loading ratio term the material flow rate will remain approximately the same, while the air mass flow increases significantly.

From Figure 16.6 the new material flow rate for the test pipeline is now 12.0 tonne/h and the new air flow rate is 0.052 kg/s. Although the air flow rate is very much higher the air only pressure drop values will still be very small, in comparison with the conveying line pressure drop, and so can be neglected once again. The equivalent length of the bends, from Figure 16.4, however, is very much greater. These have increased from

1.6 m/bend for a conveying line inlet air velocity of 3.6 m/s, to 6.1 m/bend for the con- veying line inlet air velocity of 8 m/s.

The revised equivalent length for the test pipeline has increased from 50 m to 105 m, and that for the plant pipeline of 53 mm bore has increased from 199 m to 227 m. With these new values in Equation (16.4) the revised material flow rate of

12.0 tonne/h becomes 5.55 tonne/h for the plant pipeline of 53 mm bore. The revised solids loading ratio will be:

From Figure 16.5 it will be seen that the minimum conveying air velocity correspon- ding to a solids loading ratio of 30 is about 6.3 m/s. With a 20 per cent safety margin this gives a conveying line inlet air velocity of about 7.6 m/s. Since the revised calcu- lation was based on a conveying line inlet air velocity of 8.0 m/s this is higher than necessary but reasonably close for the calculation to proceed.

###### Scaling for bore

A scaling model for pipeline bore is given in Equation (14.8). This is in terms of the material flow rate that will be achieved if the diameter of the pipeline is increased to a given value. In this case the material flow rate has been specified and so the appro- priate diameter of pipeline is required. The appropriate equation can be obtained by re-arranging Equation (14.8) and this is presented in Equation (16.5).

188 mm bore pipeline is not an option, of course, and so the possible options need to be considered:

1. If 70 tonne/h is not critical a 150 mm bore pipeline could be considered. Using Equation (14.8) gives a material flow rate of 44 tonne/h.

2. If a 200 mm bore pipeline is chosen the material flow rate that could be achieved would be about 79 tonne/h.

3. The flow rate of 70 tonne/h could be achieved in a 150 mm bore pipeline if a higher conveying line pressure drop was to be used. With a higher pressure drop the cement could be conveyed at a higher solids loading ratio and this would mean that a lower conveying line inlet air velocity could be used.

4. The flow rate of 70 tonne/h could be achieved in the 200 mm bore pipeline with a lower conveying line pressure drop. With a lower material flow rate, however, the solids loading ratio will be lower and there could be a risk of blocking the pipeline. This situation was considered with Figure 13.6.

5. It is possible that 70 tonne/h could be achieved with a 1.6 bar pressure drop in a 150 mm bore pipeline if it were to be stepped to 200 mm part way along its length.

In assessing tender proposals for such a system, where a design might come on the border-line of pipeline bores, or pressure rating for different components, it is essential that the design options be interrogated in order to determine what margins have been incorporated.

###### Air requirements

An air supply pressure of 2 bar gauge was selected at the outset, along with a convey- ing line pressure drop of 1.6 bar, and so the free air flow and an approximate value for the power supply are now required.

###### Air flow rate

The air flow rate will be evaluated for the 200 mm bore pipeline, assuming that the air supply pressure will be about 1.6 bar gauge. The equations for evaluating air flow rate were developed in Chapter 9. The design here is based on a conveying line inlet air veloc- ity of 8.0 m/s and Equation (9.10), reproduced here as Equation (16.6) is appropriate:

This is the volumetric flow rate of the air at free air conditions, which are the reference conditions required for the specification of a compressor.