## Pneumatic conveying installation calculation methods

The gas pressure drop of a pneumatic conveying system in relation to the conveyed material rate is determined in a number of ways over time.

1) Trial and error
This is probably the way how the design of pneumatic conveying started in the early days.
From the “built as designed” installations, field measurements were, combined with physical principles, used to generate regression formulas, in which the size of the installation and the product were captured, for further design.

2) Influence of material: Δp=(1+K)*gas pressure drop + additional pressure drops
From built installations, the K-factor (accounting for the presence of material) was calculated back from the observed performance.
Bends and vertical sections are accounted for by equivalent lengths.

This method is somewhat more refined, as the Factor is a function of the velocity head.
This function, which is derived from lab tests is considered valid for all, chosen, pipe diameters.
By dividing the considered pipeline in shorter sections, the effect of an increasing velocity head along the pipeline or a decreasing velocity head after an increase in pipe diameter, the calculation result increases in accuracy.
Bends and vertical sections are accounted for by equivalent lengths.

4) Lab test with scaling up + additional pressure drops.
This method is widely used and the applied scaling techniques are numerous and are often complemented with company corrections.
Bends and vertical sections are accounted for by equivalent lengths.

5) Calculating partial pressure drops of all installation components.
This approach is based on the involved energy, delivered by the expanding gas for the partial energies (pressure drops) which can be calculated by applying the physical laws.
a. Law of conservation of energy
b. Gas laws
c. Newton laws
d. Thermodynamic laws
e. Bernoulli law
In addition, the extra pressure drops are calculated separately.
The material pressure related pressure drop requires material related “Solid Loss Factor”, which cannot be calculated.
However, for the material related pressure drop, a formula can be made, in which the “Solid Loss Factor” is incorporated.
From field- or test measurements, the “Solid Loss Factor” can be calculated back.
For new design calculations this “Solid Loss Factor” in combination with the formula, which is used for the derivation, can be applied to calculate the material related pressure drop.

The calculation methods, mentioned under 1)..4) were developed before the introduction of computers.
When computers became available, the “old” calculation methods were programmed as they were.
These calculations were automated, rather than that the computing power was used to improve the calculation algorithm.

When computers became available (1980), the first calculation algorithm with numeric integration and iteration was developed for vacuum grain unloaders.
This is the calculation method from Yarca pneumatic conveying software (www.yarca.nl), mentioned under 5)
Since then, the algorithm was extended with many additional calculation features, s.a.
- Installation modeling of all components
- sedimentation detection
- condensation
- heat exchanges
- temperature changes
- compressor properties
- feeding devices
- booster application
- back pressure
- Air/Nitrogen
- tank feeding pressure drop
- filters/cyclones
- pressure tank systems
- pressure tank / silo pressure equalization
- material velocity calculation
- bend velocity calculations
- energy consumption calculations.
- System performance calculations
- Zenz diagram calculation (manual)
- Data base of materials
- Data base of compressors and vacuum pumps with volume calculations as a function of the pressure drop
- Calculation iteration to:
o fixed pressure to capacity
o fixed capacity to pressure
o fixed capacity + fixed pressure drop to “Solid Loss Factor”
o etc.
- etc.

Whether a software program is representing the real physics of pneumatic conveying, is expressed in its ability to calculate the Zenz diagram.

Pneumatic conveying software must also be user friendly, whereby all required data are entered in a structured way into the program and all relevant calculation results are displayed.
(Tell the program what you want, push the button and get the results)

The many pneumatic conveying calculation methods are mostly kept within the companies for commercial reasons.