Based on long term experience and a scientific approach of the physics, a mathematical algorithm is developed for this purpose.

The developed computer program covers multiple objectives:

-          Design and calculation of new installations

-          Evaluation of existing installations

-          Basis for research of pneumatic conveying and material properties

-          Vacuum- and pressure conveying

A pneumatic conveying system comprises a number of basic components:

-          Compressor

-          Feeder system

-          Booster compressor

-          Conveying route

-          Filter- receiver system

Each of these components can be a selection of one of the many available technologies, which have their own specific influence on the pneumatic conveying performance.

The various applications where pneumatic conveying is used are:

-          Ship unloading

-          Bulk truck unloading

-          Powder injection into chemical processes

-          Storage

-          Internal material transport

The developed computer software is built to be able to perform a pneumatic conveying calculation, based on:

-          Geometrical description of the conveying route.

-          Pneumatic conveying characteristics of the material

-          Selection of compressor(type)

-          Selection of booster(type

-          Selection of conveying gas

-          Ambient conditions

-          Selection of feeder(type)

Additionally design support

-          Ship size data

-          Altitude air conditions

-          Conversion of English units to ISO units

-          Standard pipe selection

-          Particle size distribution

-          Compressor properties calculation from compressor tables

-          Sonic chokes

-          Critical pressure reducers

-          Vacuum nozzle snorkel calculations

-          Cyclone calculations

-          Humidity and condensation calculations

After calculating, the output results are:

-          Gas velocities

-          Material velocities

-          Pipeline capacity

-          System capacity

-          Solid Loading Ratios

-          Pressure(drops)

-          Temperatures

-          Residence times

-          Used power

-          Differentiated and overall energy consumption

-          Checking the chance of choking

-          Condensation calculation

-          Capacity curve = function(pressure drop)

-          Zenz curve (manually repeated calculations) 

Calculation of pneumatic systems using gas as carrying medium

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 changing velocities of the carrying gas and the particles and a change in the gas conditions (p,V,T) 

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=0,001 sec)

The physical laws involved in this algorithm are :

-          Newton laws

-          Bernoulli laws

-          Law of conservation of energy

-          Thermal 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 dLn 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 dLn+1), covering the distance from location 2 to location 3.

The output of section dLn is used as the input for section dLn+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)

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

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.

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.

Services.

Yarca pneumatic software bv offers pneumatic conveying calculation reports for a large range of installations and materials.

The calculations serve installation designs and evaluation of technical and operational performance. 

Conclusions are complemented with the theoretical description of the underlying physics.