# Design method for dense phase pneumatic conveying lines

## Scale-up calculation from pilot tests

Section summary
1. Method and limitations
2. Calculation
3. Example

## 1. Method and limitations

There are few existing methods published to calculate dense phase pneumatic conveying systems but most of the knowledge here stays with specialized suppliers. Anyway, if dilute phase pneumatic conveying lines can be sized pretty confidently thanks to models, it is less true for dense phase conveying, thus pilot plant tests are almost every time conducted in order to design a new installation and to control / adjust model results. The calculations below are showing how to scale up - or scale down in some cases - the pilot plant results in order to design an industrial line, it focuses especially on the parameters to be kept constant.

## 2. Calculation

In order to have meaningful test results, the following must be ensured :

- The test line has a similar length, but most importantly a similar number of bends as the industrial line

- The solids load ratio is similar to what is planned for the industrial line

- The pick-up speed and end of line speed are determined and kept equal for both test line and industrial line

From there, the pressure observed during the tests should be the same industrially and the industrial actual line actual need in conveying air and actual throughput can be calculated thanks to the following formula :

## 3. Example

A trial is organized to design an industrial dense phase pneumatic conveying line for a material that is sensitive to breakage. The industrial line must be able to convey 8 t/h, the pipe layout is 50 m including 15 m vertical and has 5 bends.

The design needs to know the following :

Industrial line
Diameter D = ?
Solids load ratio %tau = ?
Air flow = ?
Upickup = ? Uend = ?
Conveying pressure = ?

A pilot plant test is carried out on a line featuring a diameter 60 mm. The layout is 50 m, with only 5 m elevation but 5 bends. The tests confirm the possibility to convey dense phase the materials. The tests results are given below :

Pilot Plant results
Product conveying rate = 2000 kg/h
Conveying pressure = 1.2 bar g, temperature = 20c
Air flowrate = 67 Nm3/h

The following calculation can then be performed :
- Qair = 67*1/2.2 = 30.5 m3/h
- Upickup = 30.5/(π*0.062/4) / 3600 = 3 m/s
- mair = 67*1.2 = 80 kg/h
- τ = 2000/80 = 25
The material flow and air relative to the pipe section are conserved through scale up.

For the example D = (8000/2000*0.06^2)^0.5 = 0.12 m
The air conveying velocity is conserved in between the pilot test and the industrial installation, thus the air flow can be calculated :
Qair = Upickup * Sindus = 3 * π * D^2 /4 = 122 m3/h at 1.2 bar g
This gives 267 Nm3/h

In summary

Pilot Plant test results Industrial line design
Pneumatic conveying line capacity = 2000 kg/h Pneumatic conveying line capacity = 8000 kg/h
d = 60 mm D = 120 mm
Upickup = 3 m/s
Uend = 6 m/s
Upickup = 3 m/s
Uend = 6 m/s
Pressure = 1.2 bar g Pressure = 1.2 bar g
Air flow = 67 Nm3/h Air flow = 267 Nm3/h
Layout = 50 m incl 5 m vertical and 5 bends Layout = 50 m inlc 15 m vertical and 5 bends

Note that the industrial line having a higher elevation than the test plant, the designer should consider an additional pressure generated by the column of product to lift and adjust the calculation - not detailed here.

You can access the calculation Excel sheet here

As mentionned above, dense phase conveying is always a delicate conveying process and a design should always be done with a recognized company, the procedure above being only for awareness and not detail design,

This scale-up procedure can also be used in dilute phase.

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