ENERGY REQUIREMENTS FOR DILUTE PHASE CONVEYING

The energy required for conveying can conveniently be considered in two parts: that required for the flow of the air alone, and the additional energy necessitated by the presence of the particles. It should be noted, however, that the fluid friction will itself be somewhat modified for the following reasons: the total cross-sectional area will not be available for the flow of fluid; the pattern of turbulence will be affected by the solids; and the pressure distribution through the pipeline will be different, and hence the gas density at a given point will be affected by the solids.

The presence of the solids is responsible for an increased pressure gradient for a number of reasons. If the particles are introduced from a hopper, they will have a lower forward velocity than the fluid and therefore have to be accelerated.

Because the relative velocity is greatest near the feed point and progressively falls as the particles are accelerated, their velocity will initially increase rapidly and, as the particles approach their limiting velocities, the acceleration will become very small.

The pressure drop due to acceleration is therefore greatest near the feed point. Similarly, when solids are transported round a bend, they are retarded and the pressure gradient in the line following the bend is increased as a result of the need to accelerate the particles again.

In pneumatic conveying, the air is expanding continuously along the line and therefore the solid velocity is also increasing. Secondly, work must be done against the action of the earth's gravitational field because the particles must be lifted from the bottom of the pipe each time they drop.

Finally, particles will collide with one another and with the walls of the pipe, and therefore their velocities will fall and they will need to be accelerated again. Collisions between particles will be less frequent and result in less energy loss than impacts with the wall, because the relative velocity is much lower in the former case.

The transference of energy from the gas to the particles arises from the existence of a relative velocity. The particles will always be travelling at a lower velocity than the gas. The loss of energy by a particle will generally occur on collision and. thus be a. discontinuous process.

The acceleration of the particle will be a gradual process occurring after each collision, the rate of transfer of energy falling off as the particle approaches the gas velocity.

The accelerating force exerted by the fluid on the particle will be a function of the properties of the gas, the shape and size of the particle, and the relative velocity, it will also depend on the dispersion of the particles over the cross-section and the shielding of individual particles.

The process is complex and therefore it is not possible to develop a precise analytical treatment, but it is obviously important: to know the velocity of the particles.