In many industrial processes and transport, materials have to be stored and moved from one location to another location. For long distances, e.g. from one country to another country (or continents), modalities are used e.g. ships, aircraft, trains, trucks, etc.

Where changes are made in the transport (or storage) modality, various technologies are used to move the material from one modality to the other modality.

The basic applied technologies are :

• mechanical systems
• grabs
• screws
• belt conveyers
• buckets
• etc.

• Carrying medium systems
• Hydraulic systems using liquids as carrying edium
• Pneumatic systems using gas as carrying medium

The bulk handling sector over the world is a key player in economics as it handles all kinds of commodities such as cereals, seeds, derivatives, cement, ore, coal, etc., which are processed in the industry to other commodities, which have to be transported and handled again.

To manufacture all the necessary equipment for the bulk handling alone a whole industry exists. The magnitude of financial investment is tremendous as well as the operating cost involved.

The importance of economic handling is not only a matter of the handlers, but also to third parties such as the transport sector.

The technology of bulk handling equipment is crucial to all the involved parties and therefore it is of the upmost importance that the bulk handling industry employs the best engineers and operators, who design, develop, build, calculate, operate the installations and do research and document their achieved knowledge and experience.

One sector of bulk handling is the pneumatic unloading and conveying of cereals, seeds, derivatives and powdery products such as cement, fly ash, bentonite, etc.

The first pneumatic unloaders were built around 1900. In 1975, there were still, steam driven, floating grain unloaders operating in the ports of Rotterdam and Antwerp. Unloaders, which even dated back from 1904.

How these installations were calculated is not really known as the manufacturers did not reveal their knowledge publicly for obvious (commercial) reasons. Trial and error must have played a significant role in the beginning of this industry.

Calculating a pneumatic system was, before computers were introduced, done by applying practice parameters, based on field data from built machines.

Example 1975

Calculation grain unloader anno 1975

Set Capcity grain                                 440                  tons/hr

Bulk density grain                                0,75                tons/m3

Suction height (elevation)                     30                    m

Air displacement pump                        500                  m3/min

Vacuum air pump                                0,4                   bar

Absolute pressure vacuum pump          0,6                   bar

air density                                            1,2                   kg/m3

pressure drop nozzle                            0,16                 bar

Nozzle diameter                                  0,45                 m

Cross section nozzle                            0,1590             m2

Grain volume                                       9,778               m3/min
(Capacity/grain density/60)

Air volume at nozzle                            357,1               m3/min
(Air displ pump * abs press pump /(1-press drop nozzle))

Transport volume after nozzle               367                  m3/min
(Grain volume + Airvolume at nozzle)

Grain mass                                          7333                kg/min (capacity *1000/60)

Air mass                                              360                  kg/min
(Air displ pump * abs press pump * 1,2)

Transport mass after nozzle                  7693                kg/min (Grain mass + Air mass)

Specific density mixture                       20,97               kg/m3 (Transport mass after nozzle / Transport volume after nozzle)

Mean velocity of
mixture after nozzle                              2307                m/min
38,45              m/sec
(Transport volume after nozzle / Cross section nozzle)

Pressure drop nozzle                           1577                mmWC
11,98              cmHg
(specific density mixture * mean velocity^2 / (2 * 9,83))

pressure drop miscellaneous                  5                      cmHg

pressure drop vacuum pump                30,4                 cmHg
(Vacuum air pump * 76)

Available pressure drop elevation 1       3,416               cmHg
(press. drop vacuum pump – press, drop nozzle –
press, drop misc.)

Elevation per available press. drop        2,2361             m/cmHg (elevation / available pressure drop elevation)

Loading factor from diagram                24,45               kg/m3 (Loading factor = function (elevation per available pressure drop))

Calculated Capacity                            440,1               tons/hr
(60 * loading factor from diagram * air displ vacuum pump * (1- vacuum))

Table loading factor kg/m3 = function (elevation per available pressure drop)

Loading factor  elevation/cmHg
16                               3.6
17                               3.44
18                               3.28
19                               3.16
20                               3.0
21                               2.84
22                               2.64
23                               2.48
24                               2.26
25                               2.04
26                               1.74
27                               1.35
By changing the figures in this calculation, an iteration process is executed until the set capacity equals the calculated capacity The calculation can be started by assuming the pressure drop over the nozzle at 0.15 bar.

If a parameter is not known, assume this parameter and vary until an optimum is found.

It is clear, that this method is not really accurate, nor gives it a scientific insight how the physics of pneumatic conveying work.

Calculation of Pneumatic Systems using Gas as Carrying Media

Since computers are available, it became possible to build an algorithm that can execute calculations in a time domain, whereby the conveying length is divided in differential pipe lengths, which are derived from the elapsed time increment.

The physical principle of this technology is:
A gas flow in a pipeline will induce a force on a particle, which is present in the gas flow. This force (if of sufficient value) will accelerate and/or move that particle in the direction of the flow. (Impulse of air is transferred to particles) The particle is moved from location 1 to location 2.

Between pipe location 1 and pipe location 2 , impulse is transferred from the gas to the particles and to friction.

This transferred impulse is used for:

• acceleration of particles
• collisions between particles and from the particles to the wall
• elevation of  the particles
• keeping the particles in suspension
• air friction

Bends are calculated only for product kinetic energy losses by friction against the outer wall and air friction pressure drop. The calculation of velocity losses in a bend are depending on the orientation of the bend in relation to the product flow.

There are 5 bend orientations to be considered:

• vertical upwards to horizontal       (type 1)
• horizontal to vertical downwards   (type 2)
• vertical downwards to horizontal   (type 3)
• horizontal to vertical upwards       (type 4)
• horizontal to horizontal                (type 5)

All these energy transfers result in a change in the gas conditions (p,V,T) and changing velocities of the carrying gas and the particles.

All these energies, velocity changes and gas conditions can be calculated and combined into a calculation algorithm.

This algorithm calculates in the time domain (dt=0,01 sec)

The physical laws involved in this algorithm are:

• Newton laws
• Bernoulli laws
• Law of conservation of energy
• Thermo dynamic laws

From the original (start) conditions, the changes in those conditions are calculated for a time period  of dt. Using the average velocity over the period dt, the covered length dL_n can be calculated. At the end of this calculation the energy, acquired by the particles, can be calculated.

By adding those changes to the begin conditions at location 1, the conditions at location 2 can be calculated for the particles as well as for the gas.

From there, the calculation is repeated for the next interval of time dt (and length dL_n+1), covering the distance from location 2 to location 3.
The output of section dL_n is used as the input for section dL_n+1.
This procedure is executed until the end of the whole installation is reached.

All the conditions at the intake of a pneumatic conveying system are known. Therefore the intake is chosen as the start of the calculation.

In vacuum- and pressure pneumatic conveying calculations, the used product properties are identical. The only difference is the mass flow, generated by a compressor in vacuum mode or pressure mode.

The calculation result should be the capacity at a certain pressure drop.

However, both these values are not known. To calculate the capacity, the pressure drop must be set and the capacity must be iterated from a guessed value. The calculated pressure drop from a “wrong” guess will be different from the set pressure drop. Therefore the capacity guess is renewed in such a way that the new, to be calculated, pressure drop, approaches the set pressure drop. This iteration ends when the calculated pressure drop equals the set pressure drop. The capacity that resulted in this pressure drop equality is the wanted value. (Input and output are consistent) (Notice the similarity of the iteration process with the example 1975)

This iteration can also be executed, whereby the capacity is set and the pressure drop is iterated.

Example of a computer calculation 2007

Example of a modern computer calculation 2008

The computer program is originally written in Q-basic under DOS and still operates, although some features are now lost under Windows

By changing the program from Q-basic to VisualBasic, the screens appear in a Windows form and more Windows features can be applied, but the program algorithm stays the same.

A very important feature of this algorithm is that performance data from existing installations can be used to determine the product loss factors for certain products. That opens the opportunity to build a database of various products that can be conveyed pneumatically and be calculated. As the used physics are basic, the calculations work as well as in pressure mode as in vacuum mode with the same formals, product parameters and product loss factors. (Adaptations are made for the different behavior of the gas pumps in pressure mode and vacuum mode)

As the pneumatic conveying calculation is basic, the calculation program can be extended with many other features s.a. booster application, rotary locks, high back pressure at the end of the conveying pipe line, heat exchange along the conveying pipe line, energy consumption per conveyed ton, Δp-filter control, double kettle performance, sedimentation detection, 2 pipelines feeding one pipeline, etc. Also it becomes now possible to evaluate product pneumatic conveying properties from field data and tests and also investigating operating machines for functioning. (Defects were found, just by calculating the actual situation).

Based on the properties of pneumatic conveying, derived from the above described theory, the used technology is chosen. The used technology and operational procedures are also depending on the type of application and product.

The above only describes the calculation of pneumatic conveying based on physics. The connection between theory and practice is made by measured and calculated parameters from field installations. In addition to this theory, there are many technological issues to be addressed, ranging from compressor technology to the structural integrity of a complete unloader as well as PLC controls, hydraulics, pneumatics, electric drives motors, diesel engines, filter technology, ship technology, soil mechanics (product flow), maintenance, methods of operation, etc.

The mathematical approach with the field verification (resulting in many corrections and extra features), documented description and creating the computational software is (was) a matter of many years of persistent labor but worthwhile. This approach also resulted in a better and still growing understanding of the pneumatic conveying technology. The influence of the various parameters and there effects (sometimes hidden by counter action) was revealed step by step.

July, 2008
Teus Tuinenburg
The Netherlands