As simple as the definition of pneumatic conveying is, so difficult is the physical description and the calculation of this technology.

Many articles, reports, thesis’s, which describe sometimes a specific part of pneumatic conveying and a number of books are published, describing an overview of the derived formulas, manual calculation examples and built installations

All the published information is valuable in itself, but never resulted in an overall, complete description of all the physical events and the interactions that take place in pneumatic conveying.

This is also expressed by the high number of regression formula that pop-up in the pneumatic conveying papers.

Sometimes, a regression formula suggests an underlying physical law, but is not always recognized as such.

Comparing publication results is also very difficult, because of the mixed use of SI-units (which is a coherent system of units) and Imperial units.

Dr.-ING Manfred Weber, Karlsruhe, Germany, wrote a book about pneumatic conveying in 1973, in which he described pneumatic conveying in a scientific way, based on equilibrium of forces, Newton laws, energy laws, continuity laws, Bernoulli law, physical properties of gas (gas laws) and material properties (density, size).

The purpose of the book was to set a common theory for pneumatic conveying, based on only a mathematical description of physics.

This work can be considered as the start of a structured research of pneumatic conveying and as a guideline and a basis, which could be adapted for individual cases.

Today, approx. 45 years later, there are a lot of papers, publications, reports etc. and many installations built, but still the overall, integral description of pneumatic conveying, accepted by the industry and universities, is not yet commonly available.

CFD computer programs generate amazing results in visualizing pneumatic conveying, but are not easy to use for designing an installation, including feeders, compressors, filters, etc..

Let alone to use a CFD program to figure out the optimum combination of compressor type, pipe diameter and pressure drop.

A universal and integral description of a pneumatic conveying installation calculation program must have the following properties, capabilities and possibilities.

- Based on universal, physical laws

- The same formulas for vacuum conveying and pressure conveying

- Calculate gas pressure drops

- Calculate gas velocities

- Calculate various feeder systems

- Calculate various conveying gas supplies (sonic choke, pressure reducer, compressor type) characteristics

- Calculate material/gas separators (filters, cyclones)

- Calculate material velocities

- Calculate heat exchanges

- Calculate temperature changes

- Calculate sedimentation

- Calculate condensation

- Calculate energies

- Calculate bend friction and bend material velocity losses

- Calculate the existing partial gas pressure drops.

- Calculate the material related gas pressure drop

- Calculate gas supply line and vent line pressure drops

- Can calculate a Zenz diagram

- Inputs for ambient conditions and back pressure at end of conveying pipe line.

- Installation Quick modeling for vacuum- and pressure installations (including ship unloaders) for first assessment.

- Applicable for

- Transfer laboratory test to real installations without scaling

- Internal database for compressors and materials and calculated installations.

- System performance calculations (accounting for pressurizing tanks and purging pipeline)

- System evaluation

- Pneumatic conveying research

- Designing

- Silo pressure equalization during purging.

- Required aeration volumes and pressures

Back in 1980, when I had to renovate 4 pneumatic grain unloaders with an increased unloading capacity of 400 tons per suction pipe and the book of Dr.-ING Manfred Weber was 5 years old,

I started my own theory building, encouraged by the scientific/practical approach of Dr.-ING Manfred Weber.

Over the last 37 years, the developed algorithm was fine-tuned by testing many real scale installations in grains, seeds, derivatives, cement, fly ash, alumina, coal, bentonite, barite and many other materials.

The derived formulas and mathematical, involved work is written down in an eight hundred plus document.

This effort resulted in the foundation of www.yarca.nl , offering pneumatic calculation services.

The question in the title of this thread is now answered with a definite

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.

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.

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.

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. ]]>