Design methods for dilute phase pneumatic conveying linesShortcut calculation for sizing dilute phase conveying lines 

Pneumatic
Transport
Types of pneumatic transport Conveying phases Dilute Phase transport Dense Phase transport Air mover Roots Blower After Cooler Airlock Rotary Valve Product inlet / Injector Piping Pickup
velocity
Conveying speed / velocity Air volumetric and mass flowrate Pipe Equivalent Length Solids velocity in pipe Bends Solids Breakage Shortcut calculation Pressure drop dilute phase Pipe Diameter or Bore
Design methods
Pipe Blockage
Powder Buildup
Selecting dilute or dense
phase
Horizontal Conveying
Vertical Conveying

1. Method and limitationThe method presented is simplified, it proposes a short calculation path and an abascus 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 preproject, 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. 2. CalculationThere 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 velocityU_{min} is known from pilot plant trial. Alternatively, it is possible to evaluate the saltation velocity U_{salt} and apprimate U_{min} = U_{salt} Pickup velocity U_{pickup} must be significantly higher than U_{min} in order to have a stable transport and avoid blockages. A 20% margin is generally safe. U_{pickup} = 1.2*U_{min} Pipe boreD is assumed Solids Load ratioTo start the calculation, a τ = 5 is generally a good guess. Air volumetric flowrateAt the beginning of the line, the air volumetric flowrate necessary to excess the pickup 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 = U_{pickup}, can be calculated with : With :  U_{pickup} = 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). ρ_{air_pickup} = P.M/RT The air conveying velocity at the end of the line can then be calculated : With :  m_{air} 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)  M_{air} the molecular weight of air (kg/mol)  R = 8.314 J/mol/K Mean velocityThe mean velocity can be determined from the chosen pickup velocity and the calculated air velocity at the end of the line. U_{g} = (U_{pickup} + U_{end})/2 Pipe equivalent lengthThe pipe equivalent length can be estimated in this shortcut method by L_{e} = L_{h}+2*L_{v}+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 calculationThe 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 abascus presented below, knowing the mean air velocity U_{g} 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 IterationThe pressure drop is then calculated by multiplying ΔP/L by the equivalent length of the pipe L_{e}. 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, pickup 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. ExampleDuring the course of a preproject, 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 velocityFor crystal sugar, the conveying air must be at least 16 m/s. Pickup velocityConsidering a 20% margin on the minimum air velocity, the pickup velocity is designed at 16*1.2=19.2 m/s Pipe boreFrom previous experiences a 80 mm diameter pipe looks to be a reasonable approximation to the Engineer. Solids load ratioA solids load ratio of 5 is generally safe for dilute phase conveying line. Pressure dropThe estimated pressure drop is 300 mbar for the line, from previous experiences as well Air flowrateThe air flowrate can be calculated thanks to pickup velocity, pipe diameter and density of air at the pickup point. The blower will be equipped with an aftercooler to regulate temperature at 25 degrees. Q_{air_pickup} = U_{pickup} * π * D^{2} / 4 = 19.2 * π * 0.08^{2} / 4 = 0.0965 m3/s which gives 347 m3/h ρ_{air_pickup} = P.M/RT = (101315+30000) * 29 / 8.314 * (273.15+25) = 1536 g/m3 = 1.536 kg/m3 m_{air} = 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. Q_{air_end} = 533.5/1.24 = 430 m3/h which gives U_{end} = 430/(π * 0.08^{2} / 4)/3600 = 23.8 m/s The average air velocity U_{g} = (U_{pickup} + U_{end})/2 = 21.5 m/s Pipe equivalent length L_{e} = 40+2*10+5*4 = 80 m Pressure drop calculation
is calculated from the abascus with U_{g} = 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. 
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