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# Design method for dense phase pneumatic conveying lines

## Scale-up calculation from pilot tests

Section summary
1. Method and limitations
2. Calculation procedure of dense phase conveying system from pilot plant results
3. Example of design of dense phase conveying system
4. Dense phase Excel calculation tool (scale up)

## 1. Method and limitations

### How to design and size a dense phase pneumatic transport line ?

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.

Figure 1 : Typical dense phase conveying system

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 procedure : dense phase conveying design from pilot plant results

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

Solids load and air velocity are thus the constant for the scale up. The pipe diameter and the air volumetric flow thus need to be adjusted in consequence.

From there, the pressure observed during the tests should be the same industrially if the constant above are respected, thus industrial pipe diameter and the industrial air flow rate can be calculated the following way :

Pipe Diameter

The air flow can then be calculated by

Qair_indus_N = Sindus * upick-up * ρ / ρN in Nm3/h

With :

mpindus = mass flow of the product SCALED UP in kg/h
mppilot = mass flow of the product OBSERVED in pilot plant in kg/h
Sindus = pipe section SCALED up in m2
Spilot = pipe section USED in pilot plant in m2
D = diameter of the pipe SCALED up in m
d = diameter of the pipe USED in pilot plant in m
Qair_indus_N = air flow SCALED up in Nm3/h
upick_up = air velocity at beginning of pipe OBSERVED in pilot plant, parameter kept constant for scale up
ρ = specific weight of air a the beginning of the conveying pipe, from pressure OBSERVED in the pilot plant and ASSUMED constant in the industrial scale, in kg/m3
ρN = specific weight of air at normal conditions in kg/m3

## 3. Example of calculation to design a dense phase conveying system

### Example of sizing of dense phase conveying line from pilot plant results

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*0.062)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 * D2 /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