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Design method for dense phase pneumatic conveying lines

Scale-up calculation from pilot tests

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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)
5. Published methods for dense phase pneumatic conveying design - Dense phase pressure drop calculation

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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's pipe 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 mass flow by unit of pipe cross sectional area is kept constant :

m_pindus/S_indus = m_ppilot/S_pilot

The air flow can then be calculated by

Q_{air_indus_N} = S_indus * u_pick-up * ρ / ρ_N in Nm³/h

With :

m_pindus = mass flow of the product SCALED UP in kg/h
m_ppilot = mass flow of the product OBSERVED in pilot plant in kg/h
S_indus = pipe section SCALED up in m²
S_pilot = 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
Q_{air_indus_N} = air flow SCALED up in Nm³/h
u_{pick_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
ρ_N = 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 :

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 :

The following calculation can then be performed :

• Q_air = 67*1/2.2 = 30.5 m³/h
• U_pickup = 30.5/(π*0.06²/4) / 3600 = 3 m/s
• m_air = 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 :
Q_air = U_pickup * S_indus = 3 * π * D² /4 = 122 m³/h at 1.2 bar g
This gives 267 Nm³/h

In summary

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.

4. Dense phase Excel calculation tool (scale up)

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, to have a rough idea of the scale up, and not detail design.

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

5. Published methods for dense phase pneumatic conveying design - Dense phase pressure drop calculation

Design calculation methods for dense phase conveying, which comes back to calculating the pressure drop of a dense phase pneumatic conveying system given a pipe layout, materials properties and flowrate, is usually not detailed in bulk solids handling books, with few exceptions, at least from what the author of this website could read. It is therefore particularly difficult for Engineers outside of specialized companies producing those system, to perform even some rough designs of dense phase pneumatic conveying systems. This paragraph attempts to perform a literature review of the published method or research for dense phase pneumatic conveying that may interest Engineers working on this field :

Author	Book, article title or thesis	Year	Description
Sprouse and Schuman	Dense-Phase Feeding of Pulverized Coal in Uniform Plug Flow (AICHE Journal)	1983	Specifically for dense phase continuous flow (piston flow)
Luis Sancheza, Nestor A. Vasqueza, George E. Klinzing, Shrikant Dhodapkarb	Evaluation of models and correlations for pressure drop estimation in dense phase pneumatic conveying and an experimental analysis (Powder Technology)	2005	Review several models, the Mi model is the one most in accordance with the set of data
Bo Mi	B. Mi, Low-velocity pneumatic transportation of bulk solids	1994	Proposes a model for horizontal dense phase conveying
Geldart and Ling	Dense Phase Conveying of Fine Coal at High Total Pressures (Powder Technology)	1990	Model for dense phase conveying
G.E. Klinzing, F. Rizk, R. Marcus, L.S. Leung	Pneumatic Conveying of Solids: A theoretical and practical approach (Springer)	2010	Parts of the book are touching the dense phase pneumatic conveying of solids
Mills	Pneumatic Conveying Design Guide (Butterworths) page 421	2013	Mills is applying the Universal Conveying method to dense phase conveying, these are relatively high capacity and pressure though