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FLUOR DANIEL
SECTION
TOC
PIPING HYDRAULICS AND SPECIFICATION BOOK 1
PAGE
1
PNEUMATIC CONVEYING
DATE
8-94
PROCESS MANUAL
8.0
PNEUMATIC CONVEYING
8.1
INTRODUCTION
8.2
GAS-SOLIDS FLOW THEORY 8.2.1 General
8.3
8.2.2
Vertical Upward Flow
8.2.3
Horizontal Flow
8.2.4
Material Characteristics
8.2.5
Design Calculation Methods
TYPES OF PNEUMATIC CONVEYING SYSTEMS 8.3.1 Dilute Phase Systems 8.3.2
8.4
8.5
8.6
Dense Phase Systems
SYSTEM SELECTION AND DESIGN 8.4.1 System Type 8.4.2
Pipeline Design
8.4.3
Mode of Operation
8.4.4
Solids Feeder
8.4.5
Air Mover
8.4.6
Gas-Solid Separation Equipment
8.4.7
Solids Storage
8.4.8
Factors Affecting System Design
SAFETY CONSIDERATIONS 8.5.1 Introduction 8.5.2
Dust Explosions - General
8.5.3
Sizing of Vents - Basic Methods
8.5.4
Factors Affecting Estimation of Vent Size
8.5.5
Venting Considerations for Pneumatic Conveying Equipment
8.5.6
Control of Ignition
8.5.7
Inerting
REFERENCES, CODES AND STANDARDS
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8.7
8.8
APPENDICES 8.7.1 Appendix I: Design Calculation Methods 8.7.2
Appendix 2 :
8.7.3
Appendix 3: Fluor Daniel Shortcut Calculation Method
8.7.4
Appendix 4: Fluor Daniel Modified Allied Flotronics Method
8.7.5
Appendix 5: Fischer-Gerchow Method
8.7.6
Appendix 6: Fan Engineering Method
8.7.7
Appendix 7A: Konno and Saito Correlation (FPS Units)
8.7.8
Appendix 8
8.7.9
Appendix 9: Bulk Solid Material Characteristics
8.7.10
Appendix 10: Not Used.
8.7.11
Appendix 11
8.7.12
Appendix 12
8.7.13
Appendix 13: Sieves
8.7.14
Appendix 14: Not used
8.7.15
Appendix 15: Not used
8.7.16
Appendix 16: Not used
8.7.17
Appendix 17A: Airlock Size and RPM Calculation
8.7.18
Appendix 18A: Diverter Valve Application Chart(a)
8.7.19
Appendix 19A: Filter Air-to-Cloth Ratio Selection A:C = (AxBxCxDxE):1
8.7.20
Appendix 20: Properties of Common Vapors and Gases
8.7.21
Appendix 21: Altitude - Pressure - Temperature - Density Table of air
8.7.22
Appendix 22: Economics
8.7.23
Appendix 23: Fundamental Burning Velocities of Selected Gases and Dusts
8.7.24
Appendix 24: Fire Hazard Properties of Selected Liquids, Gases and Volatile Solids
8.7.25
Appendix 25: Defining the Limits of Hazardous (Classified) Locations For Compliance with National Electrical Code
8.7.26
Appendix 26: Explosion Properties of Dusts
8.7.27
Appendix 27: Equipment Data Sheets - Process Input
8.7.28
Appendix 28: Sample Specification
INDEXES TO FIGURES AND TABLES (NARRATIVE AND APPENDICES) 8.8.1 Index of Figures 8.8.2
Index of Tables
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PNEUMATIC CONVEYING 8.1
INTRODUCTION Pneumatic conveying is widely used in the process industries for the handling of dry bulk solid materials, in powdered, granular or pelletized form. Pneumatic Conveying vs. Mechanical Systems Advantages over Mechanical
Fewer moving parts
Compact layout in product section
Multiple pickups/discharges
Completely enclosed
Heat/cool/dry/blend
Disadvantages
Low efficiency
High velocity attrits and erodes
Inert or dry gas needed to prevent explosions or moisture pickup
There are two broad types of systems, dilute phase and dense phase. Dense Phase vs. Dilute Phase Advantages of Dense Over Dilute Phase
Reduced wear from abrasive products
Reduced breakage for friable products
Reduced skins and fines for polymers
Disadvantages
Requires multiple systems for multiple pickups
Pneumatic conveying systems have a variety of applications including unloading of stockpiles, feeding raw materials to process units and transferring product to or from storage bins.
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This manual is intended to provide a guide towards establishing a logical basis for the preliminary selection and specification of a conveying system, and to enable informed evaluation of alternative tenders by conveying system vendors. A valuable published work on the subject is the "Pneumatic Conveying Design Guide" by David Mills. It contains an exhaustive treatment of conveyer design and a wealth of experimental data. This document has drawn upon Mills' work and other published and unpublished data. A few selected articles are listed at the end of this manual and provide additional insight into the design and operation of pneumatic conveying systems. Stokes' Law states that the terminal velocity of a particle falling through a fluid is determined by the particle density, diameter, shape, and fluid properties such as density and viscosity. Translated into pneumatic conveying terms, a flowing gas will drag particles with it above a gas velocity which is characteristic of the solid particle and gas physical properties, and particle shape. This characteristic gas velocity is known as the saltation velocity. Particles traveling above the saltation velocity are suspended in stream flow with the gas, or are entrained in the gas stream. System pressure drop is the sum of the energy losses in the system. These losses are described by an energy balance, and include terms for gas acceleration, solids acceleration, gas friction loss, solids friction loss, and static losses in vertical flow. In pneumatic conveying systems, this energy balance describes a two-phase compressible flow system, and is therefore usually a trialand-error calculation procedure. All available procedures are approximations, have dependence upon average solids material characteristics, which can vary widely, making design calculations difficult to make with certainty. Inexperienced engineers should apply these methods with caution. The approaches presented in this manual will yield suitably conservative estimates, but must be verified by either direct experience with the material in question, or laboratory tests. 8.2
GAS-SOLIDS FLOW THEORY 8.2.1
General An appreciation of the nature of two-phase gas-solid flow within an enclosed duct is needed to understand the flow regimes in pneumatic conveying. A pneumatic conveying system is generally made up of sections of straight pipe, some of which are vertically oriented and normally carry solid material in an upward direction, and some which are horizontally oriented and provide for flow in lateral, horizontal directions. There is a distinct difference in the flow and transport characteristics of gas-solid systems between vertical and horizontal flow. This can be seen in the analyses presented below. It is also recognizable in plant operations in the form of line vibrations which may occur at too high a solids loading or too low a gas flow rate.
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Figure 8-1 VERTICAL CONVEYING PHASE DIAGRAM
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8.2.2
Vertical Upward Flow The phase diagram in vertical conveying is illustrated in Figure 8-1. It consists of a plot of pressure drop per unit length versus superficial gas velocity, with the specific solid flow rate as a parameter, and is most conveniently drawn on loglog coordinate paper. Such a phase diagram is specific for a given conveying fluid density and viscosity, for a given pipe size and for a given density and particle size of the conveyed material. Representation on such a plot indicates the bounds within which a vertical conveying line may operate and the attendant pressure drop and required gas rate. The curve for the empty pipe represents a lower bound; the dilute suspension "fluidization" curve represents another boundary (essentially the free fall or terminal velocity of the largest particle in the material to be conveyed), and the available pressure drop represents an upper bound. Within this area vertical pneumatic conveying may be carried out, with the following main types of flow being identified:
Dilute Phase Flow - At low solid-gas ratios the particles are carried upwards in the flowing gas steam as a uniform suspension.
Dense Phase Flow - Occurs at higher solid-gas ratios and may be either slugging or non-slugging. Heavy/coarse particles tend to be carried upward as a series of slugs. Small/light particles may be transported upward without slugging but with a large amount of internal recirculation occurring.
Moving Bed Flow - The product is transported upwards as a packed column, with very little internal circulation.
The transition from dilute phase to dense phase conveying is not always clear, particularly when dealing with materials of wide particle size distribution in which the largest particles might slowly accumulate at a bend near the bottom of a vertical line (if the velocity is only sufficient to carry up the fines in dilute phase flow) until they form a slug, bridging the pipe, and are then blown up momentarily as another slug begins to accumulate at the bottom. Such operation might go undetected if the slugs form rapidly enough or if the total line pressure drop is large enough to overshadow the fluctuation it would cause in the discharge pressure of the air mover. Ideally the transition from dilute to slugging dense phase vertical flow for a uniform particle size material would appear as illustrated in Figure 8-1 where W1, W2 etc., represent increasing specific solid flux rates in units of mass flowrate times the total pipe cross sectional area. At some high gas velocity represented by Point A, the introduction of solids at a rate W2 results in a pressure drop greater than that necessary to push the gas alone through the pipe. As the gas velocity is lowered, the pressure drop decreases, following a path nearly parallel to that of the curve for the empty pipe. When the velocity has decreased to around Point B there is a slower decline in pressure drop with further reductions in gas velocity. This is a consequence of the slowing down of the particles and of the resulting increase in the density of the suspension in the pipe. The
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particles travel up the pipe at a lower velocity than the gas. This velocity difference, or "slip", is related to their free fall or terminal velocity in the gas medium. If gas were passing up the pipe at a superficial velocity equal to the particle's free fall or terminal velocity then the particle could (theoretically) be held in suspension, moving neither upward nor downward. Thus, as the superficial velocity is reduced from Point A to Point B, the particles slow down significantly. Since the net mass flowrate W, remains constant, the flowing density or holdup must increase. This increased particle holdup, or inventory, or suspension density, is reflected in the pressure drop; the frictional pressure drop becomes negligible at low velocity, but the holdup or inventory pressure drop increases, and predominates as the superficial velocity decreases from Point B to Point C. As the suspension density increases, the distance between particles decreases. When, as illustrated in Figure 8-2, this distance decreases to the point where a downstream particle gets into the wake of its following neighbor, it drops into this wake and falls, touching its upstream neighbor, and thus effectively presents a larger binary to the flowing gas stream. The stream cannot support this larger particle and hence the entire suspension collapses to the bottom of the pipe. The velocity at which this collapse of the dilute suspension occurs is referred to as the choking velocity. Choking velocity, as illustrated in Figure 8-1 is a function of the solid flowrate W; the greater the mass flowrate the higher the velocity needed to maintain the particles sufficiently distant from each other to avoid precipitating the choking condition. If choking occurs while a continuous feed of solids is maintained at a rate W1, the solids build up, starting at the lower end of the vertical pipe, until the inventory reaches a point where slug flow (dense phase) becomes the steady state mode. This sequence of events is illustrated schematically in Figure 8-3. No good correlations for dense phase flow in vertical pipes exist (especially for "dune" type flow), although the Particulate Solids Research Institute (PSRI) is investigating this area. 8.2.3
Horizontal Flow The phase diagram for horizontal conveying is more complex than that described for vertical conveying, because it is dependent on the deaeration characteristics of the solids being conveyed. In a vertical pipe when the solids slow down or approach choking, they cannot fall to rest; they can only fall head-on into the oncoming gas stream. In a horizontal pipe when the solids slow down, they can sink to the bottom of the conveying line and either remain there as stationary solids, still pushed along by the conveying gas as an aerated mass, or be pushed through the pipe as deaerated slugs. As particles drop out, a layer of material builds up, which moves in wave or "dune" flow along the bottom of the conveying pipe, with particles in stream flow in the gas stream above the salted layer. As velocities drop lower, the dunes fill the pipe forming pistons. Since
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gas density decreases and therefore velocity increases as the gas flows through the conveying system, it is possible to transition from dense to dilute phase flow in the system. The flow regime is dependent upon the solids flowrate, the gas velocity and the solids' deaeration characteristic. The pressure drop per unit length of pipe length differs depending upon the mode of the conveying, whether as a dilute suspension, a dense aerated mass, or slug flow. The various types of flow regimes as well as pipeline pressure drop versus air velocity for horizontal and vertical pipe are shown in Figure 8-4A. Additionally, Figure 8-4B presents five modes of gas-solids flow in horizontal pipes. Consider first a simple situation involving conveying a relatively coarse material of uniform particle size with air through a horizontal line; the corresponding phase diagram, again on a log-log grid, is illustrated in Figure 8-4. The Curve AB represents the pressure drop for the gas only and the accuracy and reliability of prediction of the conveying pressure drop depends on the reliability in predicting the Curve AB. If at some relatively high gas velocity solids are constantly introduced into the line at a rate W1, an increased pressure drop will be necessary to propel the gas-solids mixture through the line, as represented by Point C in Figure 8-4. As gas velocity is reduced, the flowing frictional resistance decreases and the observed pressure drop decreases along the Curve CD. However, as gas velocity decreases the particle velocities also decrease, until at some sufficiently low gas velocity, represented by Point D, the particles "salt" out, or settle out, on the bottom surface of the pipe. The velocity at which this occurs is termed the "saltation velocity"; it is a function of the gas and solids characteristics and also of the pipe size. When dealing with relatively coarse and uniform particle sizes, saltation is generally accompanied by a rapid filling up of the pipe to nearly half its cross section. Thereafter, steady state conveying proceeds in the open space above the salted layer. As gas velocity is further reduced, the salted layer becomes deeper, thereby further restricting the pipe area and resulting in a rising pressure drop as along Curve EF. Comparing Figure 8-4 for horizontal flow, with Figure 8-1 for vertical flow, it becomes evident that in the case of vertical flow the particle free fall or terminal velocity represents an ultimate lower velocity limit below which essentially no dilute phase vertical conveying can occur; in the case of horizontal flow there must also exist some similar lower limit. The lower limit in horizontal conveying must be the minimum velocity necessary to convey a single particle through the pipe without having it salt out; i.e., the single-particle saltation velocity or the saltation velocity at zero loading.
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Figure 8-2 CHOKING VELOCITY PHENOMENA
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Figure 8-3 SCHEMATIC OF SOLID BUILD-UP FROM DILUTE TO DENSE PHASE
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Figure 8-4A FLOW REGIMES & PRESSURE DROP FOR HORIZONTAL AND VERTICAL PIPELINES
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Figure 8-4B MODES OF COCURRENT GAS-SOLIDS FLOW IN HORIZONTAL PIPES
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Figure 8-4 HORIZONTAL CONVEYING PHASE DIAGRAM
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As applicable to pneumatic conveying, the effective single particle saltation velocity is that velocity at which the particle will travel through the pipe, occasionally hitting the walls, such that the contact is minimal and not normally detectable. Measurement of single particle saltation velocities reveals that there are several distinct velocity criteria applicable to concurrent fluid particle flow when a particle is dropped into a stream flowing through a pipe: a) The minimum velocity needed to move the particle, though without transporting it an appreciable distance before it finally comes to rest (presumably related to the particles' orientation in its most stable position of rest). b) The minimum velocity required to transport a particle by rolling or bouncing along the bottom of the pipe. c) The minimum velocity required to transport an injected particle, without saltation, in fully suspended flow. d) The minimum velocity required to pick up a particle from rest on the bottom of the pipe and transport it. e) The minimum velocity required to pick up a particle from a layer of particles and transport it through the pipe. f) Conditions a to e correspond to increasing velocities in that order. Practical considerations suggest that criteria c and e are the most significant in horizontal conveying. In general, criterion e corresponds to a superficial velocity 2 - 2½ times that of criterion c. Criterion c is considered to correspond to the single particle saltation velocity which, as illustrated in Figure 8-4, represents the minimum conveying velocity in horizontal pipes, analogous to the choking velocity in Figure 8-1. The factor of 2 - 2½ between criteria c and e is in agreement with observations that when saltation occurs the pipe fills up nearly half full (doubling the velocity in the space above the salted layer) before steady state conveying is restored. 8.2.4
Material Characteristics There are two primary considerations in determining the practicability of and the design of pneumatic conveying system; first is the material's characteristics, and second is the system's design parameters. Material characteristics can vary widely in the same material in ways which can significantly impact pneumatic conveying systems. Bulk or apparent density is the uncompressed apparent density of the solids. True density is the actual density of the material without void space in between the particles. Bulk density includes the void space, which lowers the density of the powder when compared to the solid itself. If the bulk density is variable (aeration is greater or lesser), the feed rate into a pneumatic conveying system can vary greatly, particularly in systems which are fed volumetrically. Feed rate variation can cause surging,
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which if extreme could plug the system. Particle size and distribution can also cause the bulk density to vary since fine materials become aerated more readily, lowering the bulk density. Fine materials may work in one conveying system, but not in another. For example, fine materials may not perform well in piston type dense phase systems over long distances. Some materials readily break into smaller particles (i.e., are friable). This tendency may reduce the value of the material or cause excessive losses. Low velocity dense phase systems can be used to reduce this type of degradation. Particle shape will affect system selection as well. Efficiency of conveying and separation equipment is affected by particle shape. Long, thin particles such as fibers cannot be separated efficiently using a cyclone. They are carried through with the gas. These particles must be filtered. Materials with a high moisture content can stick inside piping causing plugs, clog rotary valves and blind filters such as dust collectors. Cohesive powders can act like moist powders since the particles may form large agglomerates with pressure. Some powders, especially refractories, are highly abrasive. Abrasive powders are typically handled in dense phase systems, which have low velocities. Low velocity reduces wear. Refractory liners, and special fittings such as vortex elbows or blinded tee elbows are used to control wear in dilute phase systems. Other considerations include whether the material is toxic, carcinogenic, an irritant, flammable, hygroscopic, or explosive. Most organic and metal powders are explosive or flammable when fine enough. A summary of design problems, the principle effects of a materials characteristics, and the design approach to solve the design problem follows.
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Design Problem Principle Effects
Approach to Solution
Flow Characteristics
Power consumption; uniformity Velocity control; use of of operation. feeders.
Attrition (Degradation)
Product damage; change in flow Reduce bends; lower characteristics; increase in velocity; dense phase explosive hazard. conveying . Power consumption; tendency Velocity control. to aerate. Component sizing.
Bulk Density Particle Size
Power consumption; build-up in Velocity control. ducts. Filter efficiency. design.
Abrasiveness
Accelerated component wear.
Moisture Sensitivity
Caking in spoilage.
Toxicity
Personnel hazard.
Vacuum systems.
Temperature Sensitivity
Product damage.
Cool conveying medium.
Chemical Activity
Corrosion; contamination.
Material of construction.
Odors
Spoilage of foods.
Special filters.
storage;
Filter
Velocity control.
product Dry conveying medium; ventilation in storage.
This table is taken from the lecture notes by Hendrik Colijn, Consulting Engineer, Transportation & Material Handling Services, for a "Pneumatic Conveying Systems" course. 8.2.5
Design Calculation Methods Dilute phase design calculation methods include the Zenz-Othmer method, the Fischer-Gerchow method, the Fan Engineering method, the short-cut method used at Fluor Daniel, the Modified Allied Flotronics method and the Konno-Saito correlation recommended by PSRI. All of these methods involve some form of energy balance equation analogous to the Bernoulli equation in fluid hydraulics. The Fischer-Gerchow and Fan Engineering methods focus on a momentum equation which use empirical material friction factors. These material factors are usually proportional to the tangent of the angle of repose. The Kenz-Othmer and Konno-Saito methods use the gas frictional loss and a material to gas loading ratio, avoiding the empirical factors, but producing conservative solutions:
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a) Fluor Daniel Short-cut Method b) Modified Allied Flotronics Method (Modified by Fluor Daniel Houston) c) Fischer-Gerchow Method d) Fan Engineering Method e) Konno-Saito Method (PSRI) f) Zenz-Othmer Method (Solt) Dense phase design calculation methods include various graphical phase diagram methods, the Zenz-Other method (for two-phase "dune" or "wave" flow), and the PSRI method (for "slug" or "piston" flow). a) Phase Diagram Method (Graphical) b) Zenz-Othmer Method (Solt) c) PSRI Method The three basic parameters calculated for pneumatic conveying systems are conveying line size, system pressure drop, and gas mover horsepower. The various calculation methods as well as example problems are included in Appendix 8.7. 8.3
TYPES OF PNEUMATIC CONVEYING SYSTEMS In pressure systems a source of pressurized gas is positioned at the supply end of the system. Pressure is used to push gas through the conveying system through the pick-up point, and a cyclone or dust collector which disengages the solids from the flowing gas at the solids destination. The gas is discharged directly to the atmosphere. Pressure systems may operate in dilute, dense, or some combination flow regime. Pressure sources include fans, rotary lobe blowers, centrifugal blowers and various types of compressors The solids flow capacity and ultimate conveying distance will be limited by the pressure the source is able to supply. The conveying gas may be air or some inert gas such as nitrogen, carbon monoxide, carbon dioxide, or argon. In vacuum systems a fan or blower is positioned on the discharge end of the system. A vacuum is pulled on the conveying system through the pick-up (material feed) point, and a cyclone or dust collector which disengages the solids from the flowing gas at the solids destination. The gas is exhausted from the flowing gas at the solids destination. The gas is exhausted from the fan or blower to atmosphere. Vacuum systems are typically dilute phase systems using fans or rotary lobe blowers to provide the vacuum. Small systems may use regenerative blowers as well. Dense phase vacuum conveying may be used over short distances.
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Closed systems are used to limit the make-up of inert gas or conditioned air required for some systems. These systems can be operated in pressure or vacuum, but are typically operated with a minimum system pressure just over ambient atmospheric pressure with inert atmospheres. Setting a slightly positive minimum system pressure ensures that the system will leak out, keeping air (oxygen) from entering the system. These systems can be treated the same as the pressure system, except that the fan, blower, or compressor discharges through the system, ending at the suction, instead of exhausting to atmosphere. System pressure is controlled by bleeding excess gas and adding make-up at the system minimum pressure point, typically at the fan, blower, or compressor suction. Temperature is controlled by an aftercooler at the discharge of the fan, blower or compressor. It is important in designing closed loop systems that the design pressures of bins, hoppers, silos, and solids disengagement equipment such as cyclones and dust collectors be considered carefully. Typically such equipment is a very low design pressure (-4" W.C. to +12" W.C.). Locate bins, hoppers, and silos at or near the system low pressure point in order to minimize the required design pressure. Dust collectors and cyclones are readily available with design pressures up to +100" W.C., but typically are limited to 30" W.C. All these vessels and equipment may be designed for much higher pressures at much greater expense. Combination (vacuum/pressure) systems use vacuum on the feed end of the system, and pressure on the discharge end. Low pressure systems using fans may at times pass solids along with the gas through the fan. Material handling fans are prone to high maintenance due to wear. Most combined systems require a rotary lobe blower, which cannot tolerate particulates. The material is filtered through a dust collector, and then re-fed to the pressure side of the system. Pneumatic conveying systems are broadly divided into dilute and dense phase systems. 8.3.1
Dilute Phase Systems In dilute phase systems a material feeder introduces solid particles into a gas stream, which is either created by a source of positive air pressure, or induced by a source of vacuum. The kinetic energy of the airstream is converted into dynamic pressure and aerodynamic lift, and the particles are fluidized and accelerated to form a suspension. The mass ratio of solid-gas in the suspension defined as the phase density, is less than 10:1. At the destination the particles must be separated from the gas stream. A variety of mechanisms may be used for feeding the material into the gas stream. Rotary valves are the most common, although blowing seals, venturi feeders and screw feeders have also been used. Material feeders are potential sources of gas leakage from the system and their influence upon system selection and design is discussed in Section 8.4.4. The gas-solid separation devices used include cyclones, fabric filters and, in some applications, elutriators. The selection of separation devices is primarily dependent upon the product characteristics, as discussed in Section 8.4.6.
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The minimum conveying velocities required to achieve dilute phase flow are typically in the range 13-15 m/sec. Volumetric expansion with declining pressure along the pipe may therefore yield conveying velocities of the order of 40 m/sec at the outlet. Most bulk solids can be conveyed in the dilute phase mode; the effect of particle characteristics and size distribution upon the suitability for dilute and dense phase conveyance is critical. Figure 8-5a shows dilute phase flow at velocities slightly above the minimum conveying velocity; a strand of particles skips along the bottom of the pipe, whilst the particles above this region are in fully suspended flow. Figure 8-5b illustrates flow at higher velocities where the particles have formed a completely uniform suspension. Dilute phase systems may be broken down into the following categories:
Positive pressure systems
Vacuum systems
Combination vacuum-pressure systems
They may be further divided into open and closed systems. a) Positive Pressure Systems Positive pressure systems involve a gas mover forcing gas through a pipe into which the product is introduced, fluidized and accelerated. At the destination a gas-solid separator removes the bulk solid from the gas. Positive pressure systems usually have a pressure not exceeding 14.5 psig/1 barg and utilize either:
Axial or centrifugal fans; or
Twin lobed or positive displacement blowers
Air mover selection is discussed in Section 8.4.5. Positive pressure systems are especially suited for delivery to multiple destinations. Diverter valves may be used to select the direction of flow from several alternative routes. Positive pressure systems are not recommended where several sources feed the same conveying line via rotary valves, because the air leakage (and energy loss) through the valves can be significant compared to the total air volume required for conveying. A simple positive pressure system is depicted in Figure 8-6.
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Figure 8-5
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b) Vacuum Systems Vacuum systems operate according to the same principle as positive pressure systems, except the solids are conveyed by an air flow induced on the suction side of the air mover see Figure 8-7. Centrifugal fans or twin-lobed rotary blowers are usually used in such systems. The conveying line pressure drop for vacuum systems is limited to 7 psia/0.5 bara max. (there will be additional pressure drop due to the gas solid separation equipment). As a result they cannot achieve the throughputs or distances possible for an equivalent positive pressure system. The lower air density in vacuum systems means piping and equipment are generally larger than for pressure systems with the same conveying rate. Feed hopper walls are thicker when they are subjected to vacuum. Properly feeding the conveyor from the hopper reduces the potential for hopper wall collapse. Vacuum systems need complex pipework and isolation valves. Vacuum systems are less commonly found in multipoint discharge systems because they are more prone to "make up" than positive pressure systems. Despite such disadvantages vacuum systems are ideally suited for a variety of uses, such as vacuuming up material from stockpiles, ship unloading, and cleaning up product spills. Vacuum systems have been successfully used in multipoint discharge systems in batching applications such as with dry ingredients or micro-ingredient blending. Each receiver is manifolded to a common vacuum source and has its own vacuum valve. The number of receivers that can be on-line simultaneously is limited only by the vacuum source size. They are superior to positive pressure systems for transferring product from several sources to a single destination. Leakage across rotary valves is relatively insubstantial when compared with positive pressure systems because of the small pressure differential across the valves when in vacuum service. The fact that leakage is inward is also advantageous, enabling the handling of toxic, odorous or radioactive materials. Air ingress must be prevented if it at all possible. However, at many points it is probably unavoidable (e.g., at flexible piping sections used in ship unloading). Air ingress will alter the balance of conveying air velocities and must be accounted for in the specification of the air mover. c) Combination Vacuum-Pressure Systems Combined vacuum-pressure systems have the advantage of being suitable for transferring product from multiple sources to multiple destinations. The source hoppers may be isolated by knife gate valves, the destinations selected by diverter valves. There are several types. The air mover serves as both an exhaust and blower. Particle degradation and erosion make it unwise to convey the product through the air mover, although this has been done in
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Figures 8-6 and 8-7 POSITIVE LOW PRESS & VAC SYSTEM
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some applications. As single blower "pull-push" systems tend to be undersized, they have a history of being heavy maintenance items. On no account should product be passed through a Roots type or a Gardner Denver (PD lobe type) blower. Instead it should be bypassed using an intermediate storage hopper with its own filter and feed device as depicted in Figure 8-8 and Figure 8-8A. Conservatively size the air mover, especially when using fans, and also ensure low air-to-cloth ratios in the filters. Dual combined systems separate the positive and negative pressure system by means of an intermediate vessel and enable the optimum equipment item for each service to be specified. Selection of a liquid ring vacuum pump and a screw or reciprocating compressor, instead of the single twin-lobe rotary blower usually used in single systems, would enable transport over a greater distance. A schematic of a dual combined system appears in Figure 8-9 and Figure 8-9A. The different pressures in the two parts of the system influence the air volume and therefore velocity; the different air densities influence the minimum conveying air velocities. Therefore, for an equivalent solids flowrate, different pipeline diameters may be required in the two different parts of the system. d) Closed Circuit Systems Most pneumatic conveying systems draw air from the atmosphere and discharge it to the atmosphere (via appropriate filtration equipment to protect the air mover from damage, the product from contamination and the environment from pollution). This arrangement is adequate for most transport duties because the product itself is enclosed, and pollution may be eliminated by correct design of gas-solid separators and vents. In a closed system the discharge gas is recycled from the vent back to the air mover suction. This recirculation of the conveying medium to (generally air or nitrogen) reduces the demand to a small makeup supply compensate for leakage. Where the product characteristics dictate the use of a conveying medium other than air, economic considerations will favor conservation of the gas in a closed system. If the product is explosive in air, or would be contaminated/degraded by exposure to air, an alternative medium must be used. Nitrogen is the most common alternative medium. Other circumstances which may necessitate the use of a closed system include the transport of radioactive, toxic or odorous products. The effect of the product characteristics and of the conveying medium on system selection is discussed further in Section 8.4.
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Figure 8-8 "PULL-PUSH" CONVEYING, ONE PRIME MOVER
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Figures 8-8A "PULL-PUSH" CONVEYING SYSTEM VACUUM PRESSURE WITH ONE PRIME MOVER
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Figure 8-9 "PULL-PUSH" CONVEYING, TWO PRIME MOVERS
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8.3.2
Dense Phase Systems The British Standard draft definition is as follows: "Dense phase conveying occurs when products are conveyed through all or part of the pipeline with air velocities lower than those required for dilute phase conveying and at phase densities equivalent to those found in fluidized flow". The phase density is defined as the solidsto-gas loading ratio by weight. Dense phase systems usually operate at pressures in the range of 15-90 psig/16 barg, with gas velocities of typically 3-33 ft/sec/1-10 m/sec. Initial gas velocities and velocities at the exit greater than 10 m/sec have been observed. Streams with phase densities of 40 and above are considered to be in dense phase flow. Systems operating at phase densities up to 300:1 have been designed. Dense phase systems have several advantages over dilute phase systems. They are generally more efficient, achieving higher product throughputs at lower gas flowrates and thereby reducing energy costs. The tendency for particle breakup is also reduced at lower gas flowrates. The lower volumetric flowrates enable the use of smaller air movers, piping sizes and separators. Higher pressure operation enables conveying over much greater distances (than the few hundred meters attainable by dilute phase systems) with some dense phase systems transporting product as far as 3,000 m. In most dense phase systems solids are fed to the conveying pipe using a vessel called a "blow tank" or transporter. Blow tanks/transporters usually operate at pressures above 1 barg; in such cases they must be designed according to the ASME code for Pressure Vessels, Section VIII, Division 1. They, together with the required instrumentation and control, are therefore a relatively expensive component. Similarly, the higher pressure means that the Roots type blowers common in dilute phase applications are usually inadequate for dense phase systems. Instead more expensive compressors must be used, unless the gas consumption is low enough to be accommodated by the plant air system. The transport mechanism at such low velocities is shown in Figure 8-10. In horizontal flow (a) Particles are metered into the pipe and remain on the bottom because the air velocity is too low to overcome the frictional resistance, R. (b) the particle dune increases in cross section as more particles are fed into the pipe. As the height of the dune increases so does the air resistance force, W. (c) the dune moves in the direction of air flow and spreads out and other dunes collide with it forming a larger dune. The pipe cross section is reduced, the velocity increases and the dune moves along the pipe. In vertical flow (a) an individual particle settles when the air velocity v falls below the terminal velocity WS of the particle. (b) the pressure of more particles in the same cross section of pipe reduces the gas flow area and therefore increases the velocity. (c) when a sufficient number of particles are present the effective air velocity between the particles exceeds the terminal velocity, WS, and the group of particles is lifted. (d) in effect, when conveying bulk granular
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solids, a slug flow pattern develops. Unlike dilute systems, many materials cannot be successfully conveyed in the dense phase. The particles most suitable for dense phase conveying are those with a narrow particle size distribution and good air retention properties. Granular products, especially those with a high percentage of fines, generally cannot be transported in the dense phase because their low permeability leads to blockages. Theoretical modelling of dense phase flow behavior is extremely difficult and for reliable design the use of test rigs and scale up techniques is essential. a) Blow Tank/Transporter Systems 1) General Principles
The most common type of dense phase system is based on the blow tank or transporter. Essentially a blow tank/transporter is a pressure vessel which is charged with material, pressurized and discharged batchwise into a pipeline. The filling and discharging cycle must then be repeated. While it is inherently a batch process it may be adapted for continuous operation by using twin pressure vessels either in series or parallel, as discussed below. When specifying batch systems, however, state the average pseudo-continuous rate required as such to the vendor who will recommend the approximate blow tank system size and cycle time. 2) Single Plug Blow Tanks 3) The simplest form of blow tank, Figure 8-11 only has valves to isolate
the tank from the supply hopper and the vent line. The blow tank starts to pressurize as soon as the vent line is closed, and both the tank and line must be pressurized before any material is delivered. The material is pushed into the line as a single plug, usually via a bottom discharge. No separate conveying air is used and fluidizing air is not usually supplied to the vessel. Towards the end of the cycle the tank and line must be depressured to enable charging of the tanks for the next cycle. The time spent pressurizing and depressurizing the system reduces the proportion of the cycle that is spent actually conveying product. Therefore, to achieve a given time-averaged transfer rate the actual transfer rate must be higher (Figure 8-12). The ratio of the mean to peak transfer rates may be increased (thereby reducing the peak transfer rate required to achieve a given mean transfer rate) by:
Increasing vessel size
Fitting valves to the discharge line and (if fitted) supplementary air line
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It is desirable to reduce the peak transfer rate required to meet a given service because it is this rate that provides the sizing basis for the equipment. By increasing the vessel size and hence the amount of product conveyed per cycle also increases the proportion of the cycle spent conveying. A balance must be met between the rate cycling and the blow tank/transporter size. The fitting of valves to the discharge line and supplementary air supply line (if fitted) enables rapid pressurization and depressurization. The tank may be rapidly pressurized if all the air available is used and discharge is prevented until the required steady state pressure is reached. Depressurization time is reduced by isolating the tank from the conveying line, closing the discharge line valve and opening the vent line valve immediately upon its emptying. This is also advantageous because it prevents the large volume of air in the blow tank from rapidly expanding through the conveying line once the plug has been discharged from the pipeline. The very high air velocities that otherwise result could cause severe erosion problems during this pipework venting process and subject bends (especially blank tee-pieces) to very high forces; pipework must be well supported in such circumstances.The "rapid expansion" problem does not exist in systems that have been designed to maintain product in the line between blow tank/transporter fillings. The air supply used to pressurize the blow tank is usually also used to fluidize the tank contents and thereby facilitate discharge. The fluidizing membrane is usually porous plastic, porous ceramic or filter cloth sandwiched between two perforated metal plates or rubber "pulsers." A secondary air supply is frequently fed into the conveying line just downstream of the tank. More recently, however, 80-90 % of the air is fed along the total length of the line. This supplementary air is useful if the material has poor air retention properties, and is essential for good control. Where the secondary air supply is fed into the conveying line just downstream of the tank, the discharge rate may be controlled by proportioning the air supply between the fluidizing and supplementary air lines (Figure 8-13).
Increased product flow is obtained by increasing the fraction of the total gas rate that is supplied to the blow tank.
Reduced product flow is obtained by increasing the fraction of the total gas rate that is supplied as supplementary air.
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Blow tanks/transporters may be classified as top discharge or bottom discharge, depending upon the direction in which the product is discharged. Top discharge tanks have an internal discharge pipe positioned above the fluidizing membrane (typically by 1.2 in/30 mm for powdered materials) as shown in Figure 8-14. Top discharge tanks achieve the highest feed rates and enable better control; they are best suited to fluidizable powders with low air permeability and good air retention properties. However, with top discharge tanks the contents are never completely discharged. If complete discharge is essential (e.g., for conveying accurately weighed batches or if contamination between different batches must be avoided) bottom discharge operation is necessary. Bottom discharge tanks used not to have fluidizing membranes; the material being gravity fed into the pipeline. Current designs, however, have fluidizing membranes. They are recommended for granular materials for which top discharge is unsuited because the high permeability may preclude build up of sufficient lift. The pressure drops across the discharge section of blow tanks must be accounted for in specification of the air mover. In general, Bottom Discharge Tanks Top Discharge Tanks
< 1.5 psi/0.1 bar > 1.5 psi/0.1 bar
Large top discharge tanks may have the pressure drop reduced by removing the mixture from the side. 4) Pulse Phase ("Air Knife") Systems
A pulse phase system involves a blow tank discharging a stream of material into the conveying line. Intermittent timed air injection from an "air knife" at the pipe entrance divides the stream into a series of discrete plugs as illustrated in Figure 8-15. For powdery materials with poor air retention properties a long plug will tend to block the pipeline. By chopping the material into shorter plugs the friction between the particles and the pipe wall is reduced and blockage may be avoided. The main problem with conveying materials of this type occurs in vertical pipes where the material does not form plugs, and the air velocity is below the choking velocity; the material builds up and chokes the pipe. Layout is particularly influential in this situation. The use of short risers will enable plugs to build up and then be conveyed as a mass-flow slug when the pressure differential exceeds the frictional forces and gravity. Some authorities (e.g., Krambrock, 1983) have questioned the utility of this mode of conveying, asserting that the transport of compact plugs requires significantly larger forces than for the transport of material in duning flow mode.
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Figure 8-10 DENSE PHASE SYSTEM TRANSPORT MECHANISM AT LOW VELOCITY
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Figure 8-11 SINGLE PLUG BLOW TANK
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Figure 8-12 MATERIAL FLOWRATE AGAINST TIME FOR A SINGLE PLUG BLOW TANK SYSTEM
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Figure 8-13 AIR SUPPLY PROPORTIONED BETWEEN THE FLUIDIZING AND SUPPLEMENTARY AIR LINES TO IMPROVE CONTROL
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Figure 8-14 TOP DISCHARGE BLOW TANK SHOWING INTERNAL DISCHARGE PIPE POSITIONED ABOVE FLUIDIZING MEMBRANE
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This use of timed pulse air injection has been recommended for products with the following characteristics:
Granular/plastic pellets
Narrow size distribution
High air permeability
Low air retention
It should be noted that fine materials with very low air retention characteristics may be unsuitable for dense phase flow altogether. In designing such a system, the air knife must be located sufficiently close to the blow tank to ensure that the discharge line pressure drop is not excessive, but far enough from the tank to avoid impeding the plug formation. 5) Plug Control Systems
Numerous proprietary dense phase systems have been developed for transport of solids at very low velocities over long distances, based upon various means of controlling plug formation to avoid blockage. Three approaches have been used in the design of plug control systems:
Plug Prevention with Injection of Secondary Air
Plug Elimination using Bypassing Air
Plug Prevention using Controlled Secondary Air
Plug Prevention with Injection of Secondary Air Secondary air may be supplied along the length of the conveying line either via a perforated tube or via a bypass (Figure 8-16). This may fluidize the product and help prevent plugging. If however a plug does manage to form, the air will follow the path of least resistance into the line, entering downstream of the plug without affecting it. Over longer conveying distances the air velocity increases excessively due to expansion of the gases resulting in a higher pressure drop and air consumption unless the pipeline size is stepped up appropriately. This method is best suited to transporting readily fluidizable materials at high solid- gas ratios.
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Plug Elimination using Bypassing Air The conveying pipe may be fitted with either an internal or external bypass, as shown in Figure 8-17. During normal operation little air flows through the branch pipe. When a plug forms air will bypass it until it has reached the point in the plug where the air pressure exceeds the resistance by the downstream section of the plug. In this way the plug is split into sections, disintegrating progressively from the downstream to upstream end. This system enables very low velocities to be used for the transport of free flowing bulk materials. It is especially useful for powdery and pulverized materials with low air permeability and high air retention. An external bypass may be used if the material is damaged by an internal bypass. It cannot be used for fine cohesive product because the bypass would become plugged. Abrasive solids also create problems by severely eroding the bypass, in which air velocities are relatively high.
Figure 8-15 PULSE PHASE ("AIR KNIFE") SYSTEM DIVIDES THE STREAM INTO DISCRETE PLUGS
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Plug Prevention by Controlled Secondary Air This system is designed for the transport of fine, adhesive/caking bulk materials at very low air velocities. To keep the pressure and conveying velocities as low as possible, solids plugs must be quickly detected and destroyed without increasing the conveying gas volume. Air boosters are positioned either at strategic locations (i.e., bends) along the conveying line, or at regular intervals 10-50 ft/3-15 m apart depending upon the materials being conveyed (Figure 8-18). They sense the pressure at each stage and adjust the booster pressure downstream to keep the material flowing and prevent back pressures in the system from developing. Booster valves-unlike bypass systems - add air to the line and therefore increase the conveying air velocity. The valves only admit air when and where it is required. Such systems, if properly designed for an appropriate product, offer low maintenance and long service life despite their relative sophistication. 6) Continuous Operation Using Dual Blow Tanks
Single blow tank systems operate in a batch mode. As discussed above, to achieve a given time-averaged product flowrate, a higher rate must prevail during the steady-state section of the cycle. The pipeline diameter and air requirements must be based upon this higher rate. The use of dual blow tanks enables almost continuous operation and the timeaverage flowrate approaches the steady state flowrate. As a result, the pipeline diameter, air requirements etc., are lower than for single blow tank systems - although a second pressure vessel is required. The cost may still be competitive with that for single blow tank systems because the continuous nature of the operation may enable the duty to be achieved with smaller blow tanks. In single tank systems the blow tank size tends to be larger in order to increase the ratio of average to peak conveying rates. Dual blow tank systems may be configured with the pressure vessels either in parallel or in series.
Parallel Blow Tanks A parallel blow system is depicted in Figure 8-19. Note that each blow tank requires a dedicated set of discharge, vent and isolation valves. Whilst one blow tank is being discharged, its twin is being depressured, filled and repressured, ready for discharge when the first tank is empty. An automatic control system is required to ensure correct timing and sequencing. In this way almost continuous conveying is achieved through the shared pipeline.
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Figure 8-16 PLUG PREVENTION WITH INJECTION OF SECONDARY AIR
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Figure 8-17 PLUG ELIMINATION USING BYPASSING AIR
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Figure 8-18 PLUG PREVENTION BY CONTROLLED SECONDARY AIR
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For a given mass of material conveying "continuously" uses less air as efficiency is increased, provided adequate control logic is in place to keep the material flowing.
Series Blow Tanks Continuous blow tank operation may also be achieved by two pressure tanks vertically in line beneath a supply hopper as shown in Figure 8-20. The intermediate vessel is used as an airlock for transferring material between them. This vessel is filled from the hopper and pressurized to the same pressure as the blow tank (usually by a pressure balance line from the blow tank). The isolation valve to the blow tank is opened, the blow tank topped up with product, and the valve closed. The transfer tank is then vented and refilled. In this way a continuous flow of material is maintained. The plot plan may influence the choice between parallel and series blow tanks, with parallel systems occupying the most floor space but series systems requiring substantial headroom.
b) Air Mixing Systems Gas mixing systems handle fluidizable, pulverized, powdered and granular materials. Gas and product are mixed at the entrance to the conveying line, to yield high solid-gas ratios. Two types of these systems have been developed: 1) Screw Feeder with Air Jet
A variable pitch screw feeds material from a hopper to a mixing chamber into which high pressure air jets are directed. Material is then discharged into the conveying line (Figure 8-21A). Pressures up to 40 psig/2.8 barg may be achieved. 2) Air Swept Double Entry Rotary Feeders
Product trapped in the vaned pockets of a rotary feeder is mixed directly with high pressure air entering each pocket through air ports built into the end bells of the feeder (Figure 8-21B). The pocket of material is then blown into the pipeline by the trapped air. The system operates at pressures up to about 20 psig/1.4 barg.
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Figure 8-19 PARALLEL BLOW TANKS
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Figure 8-20 CONTINUOUS BLOW TANK OPERATION WITH TWO PRESSURE TANKS IN LINE BENEATH A SUPPLY HOPPER
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Figure 8-21A SCREW FEEDER WITH AIR JET
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c) High Pressure Rotary Valve Systems At least one vendor offers a dense phase pneumatic transport system based upon high pressure rotary valves instead of the usual blow tank-type feeders. Rotary valves are available rated for differential pressures of up to 50 psi/3.5 bar, with special attention given to minimizing the air leakage that usually precludes the use of high pressure systems. Operational differences with dense phase blow tank systems include:
8.4
Product flowrate is controlled by setting the valve rotation speed, not by splitting the conveying air into two parts.
Rotary valve systems allow continuous conveying from a single vessel.
Air leakage occurs from rotary valves but not from blow tanks. This air leakage must be compensated for to ensure that the average velocity at the end of conveying line remains constant, even as the leakage rate changes with changing differential pressure across the valve.
SYSTEM SELECTION AND DESIGN The objective in undertaking the selection and design of a pneumatic conveying system is to provide the means for the reliable and economical transfer of a given bulk material at a specified rate over a given distance. In selecting the most suitable system for a given service numerous interrelated issues must be resolved - the system type (open or closed), system pressure (positive or negative), mode of flow (dilute or dense phase), type of operation (batch or continuous), and the types of feed and gas-solid separation systems. The key parameters influencing those issues are the properties and conveying characteristics of the product to be transferred and the conveying distance and layout involved. In the "Pneumatic Conveying Design Guide" by David Mills, a method is presented which should yield the most economical and suitable system in circumstances where there are no constraints on selection. Client preferences and constraints such as space limitations may limit the choices available. The guidelines below borrow heavily from Mills' treatment of conveyor selection. The stages in the specification of a pneumatic conveying system are as follows: a) Select Basic Type of System
(8.4.1)
b) Design Pipeline
(8.4.2)
c) Select Mode of Operation
(8.4.3)
d) Select Feeder
(8.4.4)
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e) Select Air Mover
(8.4.5)
f) Select Gas-Solid Separation System
(8.4.6)
g) Design Solids Storage
(8.4.7)
h) Factors Affecting System Design
(8.4.8)
The order of the decision stages will change as external constraints dictate that a particular type of equipment must be included in or excluded from the selection. The decision stages are discussed below in the preferred order (i.e., assuming there are no constraints), although in all cases they involve a degree of iteration. A summary of the advantages and disadvantages as well as process conditions for the various types of systems is shown in Figures 8-22A through F. Pneumatic Conveying Systems are being used today for products which a few years ago would have been handled exclusively by mechanical means. In spite of this, however, it is still the "conventional" products which make up the bulk of the systems installed and consequently provide the most extensive design information. Most Pneumatic Conveyor manufacturers favor a certain method of conveying or a certain component applied to a variety of methods. This is understandable as it is at least an attempt at partial standardization. We try to be impartial in our selections, but we do have a tendency to stay away from rotary air locks unless they are definitely indicated. The following comments shown in Figure 8-22F must, therefore, reflect our preferences and prejudices and should be used as a guide rather than an indictment! If the product you are interested in is not listed, ask the mechanical department for assistance. 8.4.1
System Type The first choices are concerned with whether an open or closed system is required, and whether a positive or negative pressure system should be used. a) Open and Closed Systems The material properties usually decide whether the system should be open or closed. Open systems are preferred because of their lower capital cost and minimal complexity. In many cases the proper design of gas-solid separators and vents is sufficient to prevent pollution. Open systems should therefore be used except where a closed system is necessary for economic, environmental or safety reasons.
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Closed systems usually involve recirculation of the discharge gas back to the air mover suction. This recirculation of the conveying medium reduces the demand to a small makeup supply to compensate for leakage. The volume of exhaust requiring filtration is substantially reduced, with only a small bleed stream required. Closed systems are best suited to continuous operation. Closed systems are used where a closely controlled environment is required. For instance, hygroscopic materials must be transported in dry air and may be conveyed in a closed system to minimize the air drier duty. In other cases the material may react (sometimes explosively) with air, necessitating the use of an alternative, inert conveying medium. Nitrogen is the most common gas for this purpose. Economics usually dictate that conveying media other than air are conserved in a closed system. Materials with an excessive dust content may be transported in a closed system to minimize the size and cost of the exhaust filtration system. Toxic or radioactive materials must be transported in closed systems and comprehensive measures taken to ensure that leakage to the environment does not occur. b) System Pressure The choice between the following systems must be made:
Positive pressure systems
Negative pressure (vacuum) systems
Combined negative-positive pressure systems
Dual combined systems
The distinctions between those systems were described in Section 8.3. To briefly summarize: Positive pressure systems are:
Suited to the widest range of solids feeders.
Capable of long distance conveying at high operating pressures.
Ideal for feeding multiple destinations from a single source via diverter valves.
Inadequate for feeding from multiple sources in series because air leakage across several solids feeders may be excessive.
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Figure 8-22A SYSTEM DESIGN AND SELECTION
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Figure 8-22B SYSTEM DESIGN AND SELECTION
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Figure 8-22C SYSTEM DESIGN AND SELECTION
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Figure 8-22D SYSTEM DESIGN AND SELECTION
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Figure 8-22E SYSTEM DESIGN AND SELECTION
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Figure 8-22F DESIGN CONDITIONS FOR CONVEYING VARIOUS SOLIDS MATERIALS PRODUCT
CONVEYING METHOD
CEMENT
ABRASION PROBLEM Yes
USUALLY PRES SURE Usually pressure
FLOUR
CORROSION PROBLEM
FRIABILITY PROBLEM
No
None ALMOST NIL
No
Food product -
None
Yes, in some air/material concentrations
watch for contamination
WHEAT CORN
&
EXPLOSION HAZARD
Vacuum or Pressure
Mild
No
Yes
Yes, in some concentrations
Vacuum or pressure
Severe
No
Some, if
None
Vacuum or pressure
No
ALUM
Vacuum or pressure
No
AMMONIUM
Vacuum or pressure
SAND PLASTIC PELLETS
NITRATE MALT SALT
coated None
Yes, usually due to static build-up
Some
None
Slight
No
Yes
Yes, if in pellet form
Yes
Vacuum or pressure
Mild
No
Yes
Yes, in some
Vacuum or pressure
Moderate
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Watch for contamination
concentrations Yes
With some Grades
No
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Figure 8-22F DESIGN CONDITIONS FOR CONVEYING VARIOUS SOLIDS MATERIALS LONG RADIUS BENDS RECOMMENDED Steel sch. 40 pipe or rubber hose
TYPICAL CONVEYING RATE 100 FT. 40 T.P.H. thru 4" line @ 15 P.S.I.
USE OF ROTARY AIR LOCKS Not recommended
None
Same mat'l. conveying line
25 T.P.H. thru 4" line @ 15 P.S.I.
Recommended if vented adequately
Some
Steel sch. 40 pipe
15 T.P.H. thru 4" line @ 8 P.S.I.
Recommended
Some if coated
10 T.P.H. thru 4" line @ 10 P.S.I.
Not recommended
Yes
Can be used
Some
Recommended
Not excessive
With some grades
Stainless steel min. 1/8" wall
10 T.P.H. thru 4" line @ 5 P.S.I. 10 T.P.H. thru 4" line @ 8 P.S.I. 10 T.P.H. thru 4" line @ 6 P.S.I. 7 1/2 T.P.H. thru 4" line @ 4 P.S.I. 18 T.P.H. thru 4" line @ 12 P.S.I.
Recommended if properly designed Not recommended
Some
Heavy wall rubber hose or wear pocket elbows Same mat'l as conveying line Same mat'l as conveying line As for conveying line Steel sch. 40 pipe
Can be used
Yes
SEGREGATION PROBLEM None
None Possible Possible
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as
DUSTING PROBLEMS Surprisingly little, if min. req'd. air flow used Yes, should be trapped in dust collector Not excessive but dust collectors usual Can be noticeable Minimal
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Figure 8-22F DESIGN CONDITIONS FOR CONVEYING VARIOUS SOLIDS MATERIALS REMARKS High density (.2 to .4 S.C.F.M. 1b. of material) pressure systems usual. Pumps like viscous fluid when aerated. Systems in use operating at 100 P.S.I. Look out if line plugs - usually must be disassembled. Use of Rotary air locks precludes high pressure systems. If R.A.L.'s used, should be blow thru, type for satisfactory clean out. Pressure pod systems for flour operate similar to cement systems but less air req'd. Free flowing product. Feeds & conveys well. Does not fluidize - must be blown thru line (1 to 2 S.C.F.M./lb. of material common). Handles equally well in pressure or vacuum system. R.A.L. systems most common. Maximum pressure usually 8-10 P.S.I. Abrasion biggest problem. Heavy wall pipe should be used for straight runs. High air velocities (6000 ft./min.) req'd. for sharp sands. Hose or wear pocket elbows will combat abrasion. Air locks should have controlled feed inlet. Pressures should be kept low to minimize velocity and temp. gradients. Special conveying lines often used to eliminate streamer formation. Conveys well. Usually can be stopped in line and re-started. Alum. hardens and glazes on rubbing surfaces. Air locks, if used, need large clearances. Often coats inside of pipelines. Usually handled in pellet (prill) form. Must be kept from contact with oil (explosion hazard). Air locks should, therefore, have outboard bearings. Handles well, but air flows usually kept low to minimize breakage. Otherwise, conveys similar to wheat. Corrosion main problem. Air locks, if used, should be stainless steel. Conveying lines usually aluminum. Requires min. 5000 ft./min. air velocity for steady flow. Fine salt harder to convey than coarse grades.
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Figure 8-22F DESIGN CONDITIONS FOR CONVEYING VARIOUS SOLIDS MATERIALS CONVEYING
ABRASION
CORROSION
FRIABILITY
EXPLOSION
PRODUCT
METHOD
PROBLEM
PROBLEM
PROBLEM
HAZARD
SUGAR
Vacuum or
Yes
Food prod. -
Some
Yes, in some
Pressure LIME (pulverized) LIMESTONE 3/4" / 1 1/4"
No
No
Usually pressure
Yes
Some
No
No
Moderate
Yes
Yes
Yes
No
Yes
No
No
Usually pressure
PLASTIC RESIN CLAY
trations
Some
SODA ASH
(heavy"
contamination Moderate
Vacuum pressure
SODA ASH
dust concen-
Usually pressure
FERTILIZER
(light)
watch for
or
Vacuum pressure
or
Slight
Yes
Yes
No
Vacuum pressure
or
Slight
Watch for contamination
No
Yes
No
No
No
No
Usually pressure
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Figure 8-22F DESIGN CONDITIONS FOR CONVEYING VARIOUS SOLIDS MATERIALS LONG RADIUS
TYPICAL
SEGREGATION
BENDS
CONVEYING
USE OF ROTARY
DUSTING
PROBLEM
RECOMMENDED
RATE 100 FT.
AIR LOCKS
PROBLEMS
Some
Stainless steel min.
30 T.P.H. thru 6" line @ 6 P.S.I.
Can be used but not recommended
Yes
30 T.P.H. thru 4" line @ 15 P.S.I.
Possible
Yes
1/8" wall No
As for conveying line
No
Sch. 40 steel pipe
28 T.P.H. thru 5" line @ 6 P.S.I
Not recommended
Yes
Yes
Sch. 40 pipe
18 T.P.H. thru 4" line @ 12 P.S.I.
Not recommended
Yes
No
As for conveying
18 T.P.H. thru 4" line @ 9 P.S.I.
Possible
Yes
12 T.P.H. thru 4" line @ 7 P.S.I.
Possible
Yes
Stainless steel min. 1/8" wall
7 1/2 T.P.H. thru 3" line @ 9 P.S.I.
Not recommended
Yes
As for conveying
30 T.P.H. thru 4" line @ 14 P.S.I.
Not recommended
Yes
line Yes
As for conveying line
Some
No
line
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Figure 8-22F DESIGN CONDITIONS FOR CONVEYING VARIOUS SOLIDS MATERIALS
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Advanced dense phase systems (e.g., pulse phase and plug control systems) are capable of transferring many products that are unsuited to conventional dense phase transport. They are especially suited to low velocity transport of friable/abrasive products, offering lower operating costs but at a higher initial capital cost.
Negative pressure (vacuum) systems are:
Ideal for drawing product from multiple sources because air leakage across the feeders is minimal.
Inward leakage prevents the escape of fines, dust etc., an essential requirement when transporting toxic or radioactive products.
Limited in pressure differential and conveying distance.
Combined negative-positive pressure systems are:
Ideal for transferring a product from multiple sources to multiple destinations.
Limited in pressure differential and conveying distance.
Dual combined systems are:
Able to convey over greater distances than normal combined systems.
More efficient than combined systems because the duty is split into a positive and negative half, enabling the optimum blower and exhaust types to be specified for each half.
c) Other Design Considerations Other considerations include system leakage, and system layout. Leakage, either into vacuum systems or out from pressure systems, must be added to that required for conveying when sizing the gas supplier. Diverter valves and rotary valves all leak through the seals. Additionally, rotary valves displace gas as they rotate. Leakage in very high pressure (>40 psig) becomes very large. Typically blow pots are used at pressures greater than 40 psig to reduce leakage. Other leak points (such as at flanges) also occur. Equipment arrangement is typically dictated by the process. However, some choices can be influenced by the requirements of the pneumatic conveying system. Plant Design System 3-D modeling enables the process engineer to optimize process layout including the conveying system to minimize run lengths and numbers of sweeps, lowering the ultimate system pressure drop, and therefore gas and horsepower requirements. Typical guidelines for piping layout include allowing for a minimum straight run before the first
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sweep in a system, or between horizontal-to-vertical sweeps, avoidance of inclined lines, and minimization of the number of sweeps. A minimum distance of 200 pipe diameters or 15 feet (whichever is smaller) is required to allow the gas and the solids to reaccelerate after a bend or a pick-up point. Diverter valves are counted as 30 o bends. Sub-90 o bends are ratioed directly as a fraction of the 90 o bend. While maximum vertical runs are limited by the available pressure drop, typical limits are about 100 ft total vertical distance for medium pressure systems. Inclines are more complex than either vertical or horizontal runs due to solids recycle. The maximum pressure drop (and recycle) occurs at an incline of 45 o. While maximum vertical runs are limited by the available pressure drop, typical limits are about 100 ft total vertical distance for medium pressure ((+/-2 %) from Calculated, try again. 24) Trial 2, Guess Pressure Differential = 3.0 Psi
Trial 2 Calculated System Pressure Drop = 3.05 Psi
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8.7.5
Appendix 5: Fischer-Gerchow Method The Fischer-Gerchow method calculates the gas friction loss and the solids moving loss. The total system loss is the total of these two losses. Air friction losses are normally read from tables or charts using the average gas velocity. A pressure drop and gas density must be assumed at the beginning, and then checked against the final total. The procedure is a trial and error procedure. Solids losses include acceleration losses, elevation losses, horizontal losses, and elbow (fitting) losses. Assumptions a) 8" schedule 10 conveying line b) 4,000 ft./min. pickup velocity c) 6,000 ft./min. endpoint velocity d) Endpoint air is standard condition (i.e., 14.7 psia and 70 °F) e) Example problem conditions in Appendix 2 1) Calculate air flow rate: 2
(4,000 ft./min.)(0.378 ft. ) = 1,512 Acfm at pickup point 2
(6,000 ft./min.)(0.378 ft. ) = 2,268 Scfm at the endpoint 2) Calculate Solids Acceleration Loss (E1):
Average velocity = (4,000 ft./min.+6,000 ft./min.)/2 = 5,000 ft./min. E1 = Mv2/2g = 50,000 lb./hr.(5,000 ft./min.)2/ ((60 min./hr.)2(32.2 ft./sec.2)) = 89,825 ft.-lb./min. 3) Calculate Solids Elevation Loss (E2):
E2 = ML = 50,000 lb./hr.(75 ft./60 min./hr.) = 62,475 ft.-lb./min. 4) Calculate Horizontal Loss (E3):
E3 = ML = 50,000 lb./hr.(150 ft.)(0.625) = 78,094 ft.-lb./min. where: f(s) = solids friction factor = tangent of angel of repose; The angle of repose for LDPE is 32o, so Tan 32o = 0.625
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5) Calculate Fitting Loss (E4):
E4
= =
where: L = n =
(Mv2/gR)(L)(f(s))n 50,000 lb./hr.(5,000 ft./min.2/((60 min./hr.) (32.2 ft./sec.2(8 ft.) x (2)PI(R/4)(0.625)5 = 882,100 ft.-lb./min. bend length = 2PI(R/4) number of equivalent bends = 4+((30o+15o+45o)/90o) = 5
6) Total Solids Conveying Loss:
E5
=
E1 + E2 + E3 + E4 = 1,112,494 ft.-lb./min.; Q
=
2,268 Scfm from (1)
Press. Loss =
=
1,112,494ft lb / min Scfm InW.C. min 2,268Scfmx5.2ft lb
94.33 In. W.C. = 3.41 psi
7) Air Only Frictional Loss for Gas Supply Pipe:
Assume Total System Pressure Drop = 5.0 Psi p(g)
= = =
Gas Density 29(14.7 Psia+5 Psig)/(10.73 Psia-ft.3/lb.-Mole°R(459.7 °R+70 °F)) 0.1 lb./ft.3 at the start of the system
From the friction loss chart (Figure 28), at 1,512 Acfm (or 4,000 ft./min.) and an 8.3 pipe I.D., loss = 3.1 In. W.C. per 100 ft. Fitting loss, from Fluor Chart 101C-9 in Process Manual Vol. V, for 90o miters in 45o increments. (See Section 5.0 of Hydraulics Book 2 for currently used methodology). Ks = 0.356, so the loss = =
(3+(45°/90°))0.356(4,000 ft./min./ 60 min./hr.)2(0.1 lb./ft.3/9,270) 0.057 psi
Using 20 % Safety Factor, Loss = 1.2(0.57 Psi) = 0.06 Psi = 1.66 In. W.C. Total Air Friction Loss = (3.1 In. W.C./100 ft.)(140 ft.)+1.66 In. W.C. = 6 In. W.C.
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8) Air Only Frictional Loss for Material Pipe:
Endpoint Air Flow = 2,268 Scfm p(g) = 29(14.7 Psi+(5 Psig/2))/(10.73 Psia-ft.3/lb.-Mole°R(459.7 °R+70 °F)) = 0.88 lb./ft.3 average From the friction loss chart (Figure 28), at 2,268 Scfm (or 6,000 ft./min.) and an 8.3 pipe I.D., loss = 6.45 In. W.C. per 100 ft. Fitting loss, from Fluor Chart 101C-10 in Process Manual Vol. V, for an 8 ft. radius bend, at 8 ft. x 12/8 = 12, so Ks = 0.10 (extrapolated to R/D = 12), So the Loss = (4+((30o+15o+45o)/90o))0.1(6,000 ft./min./60 min./hr.)2(0.088 lb./ft.3/9,2 70) = 0.47 Psi Using 20 % Safety Factor, Loss = 1.2(0.047 Psi) = 0.06 Psi = 1.58 In. W.C. Total Air Friction Loss = (6.45 In. W.C./100 ft.)225 ft.+1.58 In W.C. = 16.1 In. W.C. 9) Inlet and Exit Losses:
Allow 3 In. W.C. for each of (1) pickup tee, (1) receiver inlet and (1) receiver exit So, Total = 9 In. W.C. 10) Summary:
Solids Losses: Air Pipe Loss: Air Loss: Inlet/Outlet Loss:
3.4 Psi = 94.33 In. W.C. 6.0 In. W.C. 16.1 In. W.C. 9.0 In. W.C.
Total Pressure Drop = 125.43 In. W.C. = 4.53 Psi 11) Check Solids to Air Ratio at the Receiver:
(50,000 lb./hr./60 min./hr.)(2,268 Scfm (0.75 lb./Sft.3)) = 4.9 to 1 12) Check Pickup Velocity:
2,268 Scfm (14.7 Psia)/(14.7 Psia+4.53 Psi) = 1,734 ft.3/min. 1,734 ft.3/min./0.378 ft.2= 4,587 ft./min.
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4,000 ft./min. was assumed; assume a new pickup velocity of 4,500 ft./min. 13) Repeating trial with 4,500 ft./min. pickup velocity:
Total Pressure Drop = 4.89 Psi, Pickup Velocity = 4.503 ft./min. 14) Size Blower:
Add Blower Discharge Muffler Loss: Add Blower Discharge Cooler Loss:` Add Blower Discharge Filter Loss:
5 In. W.C. 5 In. W.C. 5 In. W.C.
Total Miscellaneous Losses:
15 In. W.C.
Blower Discharge Pressure = 4.89 Psi+(15/27.68) Psi = 5.43 Psi (5.43)27.68(1,212,116)/(33,000(102.78)) = 53.74 bHp Assume a blower efficiency of 75 %; So blower motor = 53.74/0.75 = 71.65 Hp Assume a blower service factor of 15 % So blower motor = 71.65(1.15) = 82.4 Hp, therefore use a 100 Hp motor. For Size 18 Rotary Valve, Air Leakage is 120 Scfm at 5 Psi Pressure Differential. The Total Air Flow is 2,268 Scfm+120 Scfm = 2,388 Scfm Add Blower Inlet Filter Loss: 5 In. W.C. Thus at blower inlet: 2,388(14.7)/(14.7 - (5/27.68)) = 2,418 Acfm Blower Suction Pressure = 14.52 Psia Blower Discharge Pressure = 20.13 Psia Blower Differential Pressure = 5.61 Psi 8.7.6
Appendix 6: Fan Engineering Method The Fan Engineering method uses an assumed pickup velocity and pipe size to calculate the solids to gas ratio, or loading and gas volume. Principles of aerodynamics are used to calculate the particle floating velocity, and the particle velocity relative to the gas. Energy equations are then used to determine the solids and gas frictional losses. The total system loss is the total of these two losses. Air friction losses are normally read from tables or charts using the average gas velocity. A pressure drop and gas density must be assumed at the beginning, and then checked against the final total. The procedure is a trial and
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error procedure. Solids losses include acceleration losses, elevation losses, horizontal losses, and elbow (fitting) losses. Assumptions a) 8" schedule 10 conveying line b) Endpoint air is at standard condition (i.e., 14.7 psia and 70 oF) c) Example problem conditions in Appendix 2. 1) Calculate Floating Velocity:
Assume Total System Pressure Drop = 5.0 Psi p(g)= = =
Gas Density 29 (14.7 Psia+5 Psig)/(10.73 Psia-Ft.3/lb.-Moleo R(459.7 oR+70 oF)) 0.1 lb./ft.3 at the start of the system
Vf = (4gp(b)D(p)/(3fdp(g)))1/2 = (4(32.174 ft./sec.2)(35 lb./ft.3)(0.01 ft.)/(3(0.5)(0.1 lb./ft.3)))1/2 = 17.3 ft./sec. = 1,040 ft./min. 2) Pickup Velocity:
From Figure 8-44, "Dilute Phase Conveying Velocities" chart, for 1/8" 3 diameter pellets and a bulk density of 35 lbs./ft. the pickup velocity is 4,800 ft./min. 3) Calculate the Relative Solids Velocity:
Vr (horizontal run)
= = =
Vf(0.18+(0.000065Va)) 1,040(0.18+(0.000065(0.48) 512 ft./min.
4) Calculate the Solids Velocity:
Vm (horizontal) = 4,800-512 = 4,288 ft./min. Vm (vertical) = 4,800-1,040 = 3,760 ft./min. 5) Calculate Solids Lift Loss:
Assume the same solids to gas loading as in the Fischer-Gerchow example above; R = 4.62 lb. Solids/lb. Gas
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Lift Loss = TPI = RL/69.4 = (4.62)75/69.4 = 4.99 In. W.C. 6) Calculate Solids Acceleration Loss:
a) Loss for Pickup from Rest: TPA1 = = =
RVm2/(2g69.4) 4.62 lb. Solids/lb. Gas (4,288 ft./min./ 60 min./hr.)2/ (2(32.2 ft./sec.2)69.4) 5.28 In. W.C.
b) Loss for Reacceleration from First Bend (Lift): Velocity = 0.8 (4,288 ft./min.) = 3,430 ft./min. Must Reaccelerate to 3,760 ft./min. TPA2 = = =
2
2
R(Vm2 -Vm1 )/(2g69.4) 2 4.62 lb. Solids/lb. Gas((4,288/60) 2 2 2 2 -(3,430/60) ft. /sec. )/(2(32.2 ft./sec. )69.4) 0.68 In. W.C.
c) Loss for Reacceleration from Second Bend (Horizontal): Velocity = 0.8 (3,760 ft./min.) = 3,008 ft./min. Must Reaccelerate to 4,288 ft./min. TPA3 = = =
2
2
R(Vm2 -Vm1 )/(2g69.4) 2 4.62 lb. Solids/lb. Gas((4,288/60) 2 2 2 2 -(3,008/60) ft. /sec. )/(2(32.2 ft./sec. )69.4) 2.68 In. W.C.
d) Loss for Reacceleration from Last Three Bends (Horizontal): Velocity = 0.8 (4,288 ft./min.) = 3,430 ft./min. Must Reaccelerate to 4,288 ft./min. TPA4 - 6
= = =
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2
2
3(R(Vm2 -Vm1 )/(2g69.4)) 2 (3)4.62 lb. Solids/lb. Gas ((4,288/60) 2 2 2 2 -(3,430/60) ft. /sec. )/(2(32.2 ft./sec. )69.4) 5.70 In. W.C.
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8.0
PIPING HYDRAULICS AND SPECIFICATION BOOK 1
PAGE
157
PNEUMATIC CONVEYING
DATE
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PROCESS MANUAL
e) Total Loss for Reacceleration: TPA Total = 14.34 In. W.C. 7) Horizontal Losses:
TPH = fRL/69.4; Use same f as for Fischer-Gerchow, f = 0.625 TPH = (0.625)4.62 lb. Solids/lb. Gas(150 ft.)/69.4 = 6.24 In. W.C. 8) Total Losses for Bends: 2
fR Vm PI/(2g69.4) (0.625)4.62 lb. Solids/lb. Gas (4,288ft./min./ 2 2 60 ft./sec.) PI/(2(322 ft./sec. )69.4) 10.37 In. W.C./Bend
TP(90) = = =
Total Loss = 5 Bends(10.37 In. W.C./Bend) = 51.85 In. W.C. 9) Total Solids Losses = 77.42 In. W.C. (2.8 Psi) 10) Total System Pressure Drop:
Total Solids Losses = 77.42 In. W.C. = 2.8 Psi Total Gas Only Losses = 1.18 Psi (Same as Fischer-Gerchow) Total System Pressure Drop = 3.98 Psi 8.7.7
Appendix 7A: Konno and Saito Correlation (FPS Units)d
P
1 Ug2 g
2gc
2
3
G S VS
2f gUg2L
gc
g CD
4 0.057Ug g L
gD0.5
where:
GS Ug g
and 1
This chart taken from Particulate Solids Research "Desktop Design Manual"
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5
G SL VS
gL
6
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8.0
PIPING HYDRAULICS AND SPECIFICATION BOOK 1
PAGE
158
PNEUMATIC CONVEYING
DATE
8-94
PROCESS MANUAL
D f g gc
= = = =
Tube diameter, ft. Fanning friction factor, (-) 2 gravitational constant, 32.2 ft./s -2 gravitational conversion constant, 32.2 lb.m-ft./(lb.lb.f )
GS L Ug VS
= = = =
Solids mass flux, lb./s-ft. Pipe length, ft. Superficial gas velocity, ft./s Solids gas velocity, ft./s
P
g
= =
Pressure drop, lb/ft. 3 Gas density, lb./ft.
1 2 3 4 5 6
= = = = = =
Pressure drop due to fluid acceleration Pressure drop due to acceleration of solids Fluid-pipe friction pressure drop Solids-pipe friction pressure drop Pressure drop due to static head of solids Pressure drop due to static head of gas (important only at high pressures)
2
2
Note: If the solids and the gas are already accelerated, terms 1 and 2 should be omitted from the calculation. Also, terms 5 and 6 should be omitted when applying the correlation to horizontal flow. PSRI Choking Velocity Correlation U ch U t gd p
Gs U ch f
0.35
D dp
0.35
p f
0.10
where: Uch Ut
= =
Choking Velocity, ft./s or m/s Single Particle Terminal Velocity, ft./s or m/s
g D Gs
= = =
gravitational constant, 32.2 ft./s or 9.81 m/s Diameter of the Conveying Line, ft. or m 2 2 Solids Mass Flux, lb./ft. -s or kg/m -s
f
=
Gas Density, lb./ft. or kg/m
p
=
Particle Density, lb/ft or kg/m
dp
=
Particle Size, ft. or m
2
3
3
Accuracy: Within ±30 %
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3 3
2
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8.0
PIPING HYDRAULICS AND SPECIFICATION BOOK 1
PAGE
159
PNEUMATIC CONVEYING
DATE
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PROCESS MANUAL
Parameter Ranges: 8 0 1 1.2 55
< < < < <
3400 m 700 psig
dp P Gs D rp
2
250 lb./ft. -s 12 in. 490 lb./ft.
3
0 0 3.2 881
< < < <
P Gs D rp
< < < <
48 bar 2
1220 kg/m -s 30.5 cm 3
7849 kg/m
Note: 1) 1. Predicts data for all Geldart Groups 2) For dp 1.0), particle surface tension = s = 0.3*1000*(Vt^2)*D(p)m*p(g)*0.3048*0.3048*0.3048*16.01846 Y Vt = 11.89 p(g) = 0.58 D(P)m = 0.0104 s= 384.6762
(ft./sec.) 3 (lb./ft. ) (Ft.) (Dynes/cm)
Y calc 11.94 (ft./sec.) (IDEAL GAS LAW) 387.5035
(Dynes/cm)
System Type: Materials with surface tensions greater than 10 dynes/cm form strong, selfsustaining slugs. Simple systems are recommended. Materials with surface tensions between 10 and 0.2 dynes/cm form weak slugs. Bypass systems are recommended. Materials with surface tensions below 0.2 do not readily form slugs on their own. A pulsed system is recommended. The surface tension for this material is 387.5035
(Dynes/cm)
The example above exhibits surface tensions above 10.0 dynes/cm, suggesting a simple system is recommended.
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SECTION
8.0
PIPING HYDRAULICS AND SPECIFICATION BOOK 1
PAGE
180
PNEUMATIC CONVEYING
DATE
8-94
PROCESS MANUAL
Minimum Pipe Diameter: For "coarse powders" (surface tensions > 0.2 dynes/cm), Dt = 8.71*(((3600*m)/(p(b)))^0.4) m= p(b) = Dt =
13.89 35 6.02
(lb./sec.) 3 (lb./ft. ) (Inches)
For "fine powders" (surface tensions
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