Design methods for dilute phase pneumatic conveying lines

Shortcut calculation for sizing dilute phase conveying lines

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

1. Method and limitation

The method presented is simplified, it proposes a short calculation path and an abacus to have an idea of the sizing of the line (diameter, air flow, pressure drop for a target conveying rate of a material). This is useful in pre-project, or to check an existing conveying line on the spot. However, it is not an accurate methodology and should therefore not be used for the detail design of an installation. Detail design should be carried out by a specialized company having more developed calculation codes and preferably be based on test data.

The model is given only for understanding the sensitivities of some process levers like solids load ratio, velocity...etc... but cannot be used for design, use of the model for other purposes is at the user own risk.

2. Calculation

There are different variations to the method, depending on the knowledge the designer has of the product and of pneumatic conveying. For this page, it will be assumed that the minimum air velocity for the material conveyed and that the pipe diameter is assumed from a previous experience (or is known if an existing line is the object of the study).

Minimum air velocity

Umin is known from pilot plant trial. Alternatively, it is possible to evaluate the saltation velocity Usalt and apprimate Umin = Usalt

Pick-up velocity

Upickup must be significantly higher than Umin in order to have a stable transport and avoid blockages. A 20% margin is generally safe.

Upickup = 1.2*Umin

Pipe bore

D is assumed

To start the calculation, a τ = 5 is generally a good guess.

Air volumetric flowrate

At the beginning of the line, the air volumetric flowrate necessary to excess the pick-up speed can be calculated by assuming the expected design pressure drop, for example 400 mbar in pressure dilute phase or 300 mbar in vacuum dilute phase. The pressure drop assumption is important as iterations will be done on this value.

The air volumetric flowrate at the conditions of pressure and temperature at the beginning of the line, with U = Upickup, can be calculated with :

With :
- Upickup = air conveying velocity at the inlet of product (m/s)
- d = diameter of pipe at inlet of product (m)

The air volumetric flowrate must be converted in a mass flowrate by calculating the volumetric mass of air at the beginning of the line. For a vacuum conveying line, the pressure is atmospheric while for a pressure conveying line the pressure is often equal to (atm + pressure drop).

ρair_pickup = P.M/RT

The air conveying velocity at the end of the line can then be calculated :

With :
- mair the air mass flowrate (kg/h)
- P the pressure at the end of the line (Pa), usually atm for pressure conveying and (atm - pressure drop) in vacuum conveying
- T the temperature of the air at the end of the line (K)
- Mair the molecular weight of air (kg/mol)
- R = 8.314 J/mol/K

Mean velocity

The mean velocity can be determined from the chosen pick-up velocity and the calculated air velocity at the end of the line.

Ug = (Upickup + Uend)/2

Pipe equivalent length

The pipe equivalent length can be estimated in this shortcut method by Le = Lh+2*Lv+5*NB

With :

- Le = equivalent length of the pipe (m)
- Lh = length of horizontal pipe in the whole pipe layout (m)
- Lv = length of vertical pipe in the whole pipe layout (m)
- NB = number of bends

Pressure drop calculation

The following formula is used to estimate the pressure drop in this simplified calculation method :

With :

Which represents the pressure drop of the air only in pipe. It can be determined thanks to the abacus presented below, knowing the mean air velocity Ug and the pipe diameter.

Which represents the influence of the solids load on the pressure drop. It can be calculated thanks to the solids loading ratio τ assumed previously.

ΔP/L is given in mmCE/m and should be converted to more convenient unit, for example bar

Iteration

The pressure drop is then calculated by multiplying ΔP/L by the equivalent length of the pipe Le. It is then necessary to compare the result of the calculation to the initial assumption of the pressure drop. If those 2 are significantly different, it is necessary to restart the calculation with a new assumption of pressure drop. If the gap in between the 2 values is high or impossible to have the assumption and the calculation result equal, it means that another assumption must be changed, typically the pipe diameter or the solids load ratio.

1. Assume pipe diameter, solids load ratio, pick-up velocity

2. Assume pressure drop

3. Calculate pressure drop

4. Check calculated pressure drop = hypothesis on pressure drop. If not, back to step 2, assume new pressure drop, or step 1, assume new diameter and or solids load ratio, if yes, go step 5

5. End of calculation

3. Example

During the course of a pre-project, an engineer wishes to roughly estimate the design of a pneumatic conveying line in order to approximate a cost necessary for a CAPEX request.

The pneumatic conveying line is meant to transport 2000 kg/h of crystal sugar over 50 m (40 m horizontal, 10 m vertical and 4 bends). The line will be a pressure lean phase pneumatic conveying with a blower at the beginning of the line. The engineer runs through the shortcut calculation method given above.

Minimum air velocity

For crystal sugar, the conveying air must be at least 16 m/s.

Pick-up velocity

Considering a 20% margin on the minimum air velocity, the pick-up velocity is designed at 16*1.2=19.2 m/s

Pipe bore

From previous experiences a 80 mm diameter pipe looks to be a reasonable approximation to the Engineer.

A solids load ratio of 5 is generally safe for dilute phase conveying line.

Pressure drop

The estimated pressure drop is 300 mbar for the line, from previous experiences as well

Air flowrate

The air flowrate can be calculated thanks to pick-up velocity, pipe diameter and density of air at the pick-up point. The blower will be equipped with an aftercooler to regulate temperature at 25 degrees.

Qair_pickup = Upickup * π * D2 / 4 = 19.2 * π * 0.082 / 4 = 0.0965 m3/s which gives 347 m3/h

ρair_pickup = P.M/RT = (101315+30000) * 29 / 8.314 * (273.15+25) = 1536 g/m3 = 1.536 kg/m3

mair = 347*1.536 = 533.5 kg/h

At the end of the line, the receiver is at atmospheric pressure, thus the volumetric weight of air is 1.24 kg/m3.

Qair_end = 533.5/1.24 = 430 m3/h which gives Uend = 430/(π * 0.082 / 4)/3600 = 23.8 m/s

The average air velocity Ug = (Upickup + Uend)/2 = 21.5 m/s

Pipe equivalent length

Le = 40+2*10+5*4 = 80 m

Pressure drop calculation

is calculated from the abascus with Ug = 21.5 m/s and d=80 mm, which gives 8.5 mmCE/m

is calculated from a solids ratio of 5, which gives 2.825

ΔP/L = 8.5*2.825 = 24.0125 mmCE/m

ΔP = 11.325 * 80 = 1921 mmCE/m

In bar, the pressure drop is 0.192 bar. This is much less than 300 mbar assumed previously, the calculation should therefore be done again by assuming a new pressure drop, maybe 200 mbar. This big gap may show as well that the pipe diameter is oversized and a new attempt could be done with d=60 mm.

With these new data, the pressure drop is 316 mbar which is pretty consistant with the 300 mbar assumed. At 2 t/h, a solids load ratio of 5 and an air flowrate at pickup condition of 195 m3/h, with a pipe of 60 mm diameter and the layout given, the pressure drop is expected to be around 316 mbar.

Dilute phase conveying shortcut calculator file : Excel Calculation sheet for shortcut pressure drop calculation in dilute pneumatic conveying

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