**Eric Maynard** | Jenike & Johanson

Dilute-phase pneumatic conveying systems are fairly simple as they’re made up of four components to move material and air through a pipeline: the air mover, solids feeder, pipeline, and separator. While each component plays a part, the air mover carries a lot of the system’s responsibilities in transporting the material. Choosing the correct air mover for your system involves many considerations. This article focuses on estimating the pneumatic conveying line’s total pressure drop, which is vital to selecting a suitable air mover for your system and application.

Pneumatic conveying is an important and practical form of bulk solids transport that has applications in almost every industry. The range of materials that can be transported is extensive. Powders and granular materials of nearly every type can be conveyed, including finished products like sludge pellets (from a municipal wastewater treatment plant for example), candy, and pressed metal parts as well as stringy materials, such as chopped fiber and metal turnings.

A pneumatic conveying system consists of four basic components: the air (or gas) mover, solids feeder, pipeline, and separator. While these components’ placements may vary depending on whether the system is operating in a vacuum or pressure conveying mode, their basic functions remain the same.

The air mover provides the proper airflow rate required for material transport at the right velocity and pressure. The solids feeder introduces the solid particles at a controlled rate into the pipeline where they are mixed with the conveying air. Positive-pressure systems require devices to feed material from atmospheric pressure into a pressurized pipeline, while vacuum systems need to minimize air leakage into the pipeline as this can create conveying problems. The pipeline consists of straight sections, both horizontal and vertical, connected together with bends. In the separator, the solids are decelerated and recovered from the airstream in which they have been transported and then stored in a silo or fed into another piece of equipment or process. The air is typically released into the atmosphere. In closed-loop systems, the inert gas is recirculated after being cleaned and often cooled to limit a gradual increase in operating temperature, which happens due to the pressurization cycle reusing the same gas over and over. Controls, instrumentation, and safety equipment are also commonly integrated with the pneumatic conveying system.

A key element you must consider for pneumatic conveying design is the air mover, which may be a compressor, centrifugal fan, or positive-displacement (PD) blower. If you don’t select the proper air mover for your planned pneumatic conveying system, then the airflow — and hence velocity — may be compromised and could allow for buildup, line plugging, and erratic system performance at best. The system pressure drop, or pressure loss, during air and solids transport through the entire conveying line is critical to estimate as this will help you select a suitable air mover.

The following worked example is focused on system pressure drop estimation and doesn’t focus on troubleshooting common pneumatic conveying problems^{1} like abrasive wear, particle attrition, rate limits, buildup, or plugging. Additionally, a suitable minimum conveying velocity determination isn’t covered in the worked example but can typically be found through pilot lab testing and scaling of the results or through the use of reliable historical performance data, such as with dilute-phase conveying of cement or flour.

**Pneumatic conveying terminology**

There are numerous terms describing air (or gas) and solids flow and pressure conditions within a pneumatic conveying system, and understanding some basic terminology before embarking on designing a system is necessary. Here are some commonly used definitions and other information that can be helpful.

Conveying systems can be configured and classified in a number of ways depending on their function, operating pressure (positive, negative, combined, or closed-loop), and operating pressure magnitude. Perhaps the most common, and often misunderstood, descriptions are dilute-phase conveying and dense-phase conveying, which refer to the solids concentration inside the pipeline. Conveying can occur over a wide range of conditions bounded on one end by gas alone with no entrained solids and on the other end by a completely full pipe where the solids are essentially extruded through the line. Dust collection systems are an example of conveying systems that operate at very low solids loading where the performance is governed almost entirely by the gas flow.**Dilute-phase conveying. **This occurs when particles are conveyed in the gas stream at a velocity that’s greater than the saltation and choking velocities. This type of system is often referred to as a *stream-flow system* because particles are fully suspended in the gas stream. Most bulk solids can be conveyed in dilute-phase mode. However, potential adverse effects, such as pipeline wear or particle attrition, could result due to high conveying velocity. The term “dilute phase” also refers to the solids loading within the conveying line. Typically, a dilute-phase line conveys less than 15 pounds of solids per pound of gas at a relatively low pressure (generally less than 15 psig).**Dense-phase conveying. **This occurs when particles are conveyed in the gas stream at a velocity that’s less than the saltation velocity. Two general modes of flow can result in dense phase and are referred to as *plug* or *piston-flow* and *moving-bed (dune) flow*. Only certain bulk solids can be efficiently conveyed in these two dense-phase modes. In plug flow, coarse, permeable bulk solids like pellets or coffee beans can be reliably conveyed, whereas with moving-bed flow, fine, impermeable bulk solids like cement or pulverized fuel ash can be effectively conveyed. The term “dense phase” also refers to the solids loading within the conveying line. Typically, a dense-phase line conveys greater than 15 pounds of solids per pound of gas at a higher pressure (generally greater than 15 psig) than a dilute-phase system. Major advantages of a dense-phase system versus a dilute-phase system include reduced conveying gas velocity (yielding less pipeline wear and particle damage), lower gas requirements, lower operating (energy) costs, and the ability to convey long distances.**Pressure versus vacuum systems.** A positive-pressure conveying system uses gas pressure above atmospheric pressure to entrain the bulk solids and transport the material to either one or multiple destinations (often at atmospheric pressure). Conversely, a vacuum conveying system picks up solids at near atmospheric pressure, often from multiple locations, and discharges the material into a vessel that’s at a pressure less than atmospheric (hence the name “vacuum”). Positive-pressure systems can operate at high-pressure levels and convey materials over long distances, such as up to a few thousand feet. Vacuum systems are typically limited to transporting material less than 300 feet, though some systems have greater capabilities. Vacuum systems also are well-suited for handling dusty or toxic materials, given that any leakage in the pipeline will be inward. There are specialized systems that incorporate features of both positive- and negative-pressure conditions, such as pull–push systems used in ship and railcar unloading equipment.

# Worked example

For this example, consider the design of a positive-pressure dilute-phase pneumatic conveying system that must transport powder at 10,000 lb/h using ambient air. Based on a preliminary layout, the pipeline and equipment arrangement is shown in **Figure 1**. Assume two 90-degree elbows are used with a radius-to-diameter (r-to-d) ratio of 4, the conveying line’s terminal point is at atmospheric pressure, and no leakage occurs with the rotary valve.

Use the general solution algorithm steps below to estimate the system’s pressure loss from conveying the air and solids. Ultimately, this calculation will help you to determine what air mover type is required to provide the necessary conveying velocity for the solids as well as the air mover’s ability to respond to the pressure drop.

- Calculate air mass flowrate.
- Calculate pipeline diameter required for desired minimum conveying velocity.
- Calculate total pressure drop.
- Calculate new air density and velocity at pickup.
- Recalculate air mass flowrate, pipeline diameter, and total pressure drop based on new air density.
- Select a suitable air mover.

# Minimum conveying velocity

Let’s assume that through pneumatic conveying tests, the minimum conveying velocity, *u _{min}*, for this material ranges from 60 to 70 ft/s over a range of solids loading conditions. This is perhaps the most important velocity for the pneumatic conveying system designer. This is the minimum velocity that must exist in a given pneumatic conveying system for a given material to move to prevent plugging the pipeline. In dilute-phase conveying, whereby all of the solids are suspended in the moving airstream, an air velocity of approximately 50 ft/s (3,000 fpm) is a

*lower bound*for fine and low-density powders. Lower bound is the value that’s less than or equal to every element of a data set. It’s well-documented that larger particles with higher particle densities require a higher minimum conveying velocity

^{2}to prevent saltation (when solids settle in a horizontal conveying line) and choking (when solids stall in a vertical conveying line). Another important velocity to be aware of is choking velocity, which is the gas velocity at which the particles conveyed upward in a vertical pipeline begin to approach their free-fall velocity. Approaching the particles’ free-fall velocity results in the material no longer conveying upward but instead collapsing into a fluidized-bed (refluxing) condition.

Commonly, an air velocity, *u _{air}*, of 70 ft/s (4,200 fpm) is selected for many powders and granular solids in a dilute-phase conveying mode, so we’ll use this as the minimum conveying velocity. However, selecting a suitable velocity is critical, since too low of a value can result in line plugging and too high of a value increases pressure drop at velocity squared (u

^{2}) and the potential for line wear and particle attrition at velocity cubed (u

^{3}). Ideally, pilot-scale testing with a representative material subjected to an anticipated solids loading range will help to determine the appropriate minimum conveying velocity. For this example, assume the solids friction factor,

*λ*

*s*, is 0.02 and the solids loading ratio,

*, is 7 (based on stable pneumatic conveying results). Assuming the conveying air is 70ºF at sea level conditions, use an air density,*

*ϕ**ρ*

*, of 0.075 lb*

_{air}_{m}/ft

^{3}, where

*lb*is pounds of mass, and a dynamic air viscosity,

_{m}*μ*

*, of 0.000012 lb*

_{air}_{m}/ft s.

# Step 1: Calculate air mass flowrate

Using **Equation 1**, calculate the air mass flowrate, *ṁ** _{air}*, using the solids loading ratio,

*ϕ*,

*7*, and the desired solids mass flowrate,

*ṁ*, of 10,000 lb/h.

_{solids}**Equation 1**

For a pneumatic conveying system to reliably operate in a stable manner, the solids feed into the conveying line must be controlled.^{3} Frequently, problems of nonuniform feed into the pneumatic conveying lines are thought to be problems with the pneumatic conveying system itself, whereas the problem actually lies with the upstream equipment.

Feeding solids into a positive-pressure system requires a means of sealing against the pressure in the pipeline. Devices used for this purpose include rotary valves, double flap gates, specially designed sealing screws, and venturi nozzles. Some of these devices (rotary valves and sealing screws) control the solids flowrate into the line, hence they’re truly feeders, while others (double flap gates and venturi nozzles) only provide a pressure seal but don’t meter solids.

# Step 2: Calculate pipeline diameter

Using **Equation 2**, which is the *law of continuity* from fluid mechanics, calculate the pipeline diameter, *D*, with the specified minimum conveying velocity, *u _{min}*, of 70 ft/s. The law of continuity means that what flows into a defined volume in a defined time, minus what flows out of that volume in that time, must accumulate in that volume.

**Equation 2**

where *A _{pipe}* is the pipeline cross-sectional area. When applying the 3.72-inch pipe diameter results to ANSI’s steel pipe specification schedule 40, we see that we need to select a 3.5-inch schedule 40 pipe with an internal diameter equal to 3.548 inches (rounded up to 3.55 inches for simplicity). Proceeding with the calculations,

*D*now represents internal diameter, which is 3.55 inches. At this smaller internal diameter, the air velocity,

*u*, will be slightly higher (77 ft/s) based on the ratio of the diameters squared.

_{air}# Step 3: Calculate total pressure drop

The major forces involved in dilute-phase conveying of bulk solids in an airstream are:

- Friction between moving air against pipeline wall
- Friction between moving solids against pipeline wall
- Force required to move air through vertical pipeline sections
- Force required to lift solids through vertical pipeline sections
- Force required to accelerate solids from feedpoint velocity to conveying velocity

In consideration of these forces, **Equation 3** provides the total pressure drop, *Δ**P _{total}*, for a system, including a term for additional losses, such as with an air and solids separator. For this example, we’ll assume the pressure loss for the equipment is negligible.

**Equation 3**

where *Δ**P*_{air} is the pressure loss from the air moving through the pipeline, *Δ**P _{solids}* is the pressure loss from the solids acceleration, and

*Δ*

*P*is the pressure loss from one piece of equipment to another (for example, the piping from the blower to the feedpoint or a diverter valve in the conveying line). Again, because that pressure loss is such a small amount compared to the rest of the pressure losses and this is a simplified equation, we’ll disregard it for this equation. The pressure loss for the air moving through the pipeline can be found using the Darcy-Weisbach relationship shown in

_{equipment}**Equation 4**. The “knowns” in this equation are velocity,

*u*; air density,

_{air}*ρ*

*; and pipeline internal diameter,*

_{air}*D*, from

**Equation 2**. The “unknowns” are air friction factor, ƒ, and equivalent line length,

*L*.

**Equation 4**

The air friction factor, ƒ, can be determined through the use of the Moody diagram^{4} or the Colebrook equation for laminar and turbulent flow through pipes, where the relative pipe internal roughness and Reynold’s number are known. The relative roughness is the ratio of absolute roughness to pipeline diameter. A typical value for absolute roughness for a smooth bore steel pipeline is 0.0005 feet. Thus, a relative roughness of 0.0017 feet results from this example. The Reynold’s number, *Re*, which is the non-dimensional ratio of air inertial-to-viscous forces, can be calculated with **Equation 5**.

**Equation 5**

Remember, *D* now equals the pipeline’s internal diameter of 3.548 inches, which has been rounded up to 3.55 for this article. Using the Reynold’s number and the relative roughness, a pipeline air friction factor of 0.023 is estimated.

The length term in **Darcy’s equation (4)** can be either equivalent or actual pipeline length, depending on the calculation need. The total equivalent length, *Leq*, accounts for horizontal and vertical pipelines that the air will flow through, plus an estimated equivalent length for short and long radius bends. For this example with two elbows having a radius-to-diameter ratio of 4 and an equivalent length of 15 diameters for each, this results in each elbow being 4.5 feet or a total of 9 feet extra conveying equivalent length. Therefore, the total equivalent length, *Leq*, becomes 50 feet + 30 feet + 50 feet + 9 feet (from elbows) = 139 feet (with the equivalent line length, *L*, of 130 feet without the elbows). An excellent reference for equivalent lengths for pipeline elbows and their various forms can be found in S. Dhodapkar, P. Solt, G. Klinzing’s paper “Understanding bends in pneumatic conveying systems.”^{5}

Using this information, we can estimate the pressure loss from air only in the system and solve **Equation 4**.

**Equation 4**

Note the important conversion that’s needed from pounds of mass,* lb _{m}*, to pounds of force,

*lb*

_{ƒ}, which can be accomplished through the use of the gravitational constant,

*g*, which is shown as

_{c}*32.2 lb*⋅

_{m}/ft ÷ lb_{ƒ}*s*below. See

^{2}**Equation 6**.

**Equation 6**

Now we need to return to the solids-component pressure losses, as given in **Equation 7**.

**Equation 7**

where *ΔP _{accel.}* is the pressure loss from the solids acceleration,

*ΔP*is the pressure loss from the solids friction,

_{friction}*ΔP*is the pressure loss for the solids through the bends, and

_{bends}*ΔP*is the pressure loss for the solids lift or the vertical pipelines where solids need to be carried upward. The pressure loss from acceleration of the solids can be found using

_{lift }**Equation 8**, with an assumed

*slip ratio*of solids-to-air of 0.5, shown as

*u*below. The slip ratio refers to the ratio of the air-phase velocity to the liquid-phase velocity. Because of the drag forces between the flowing air and the solids, the particle velocity will always be lower than the air velocity. Commonly, the slip ratio ranges from 0.5 to 0.9. Heavier and more coarse particles (for example, gravel) will have a slip ratio of 0.5 or less, and lighter and finer powders (for example, talc) will have a value closer to 0.8. Again, use the gravitational constant,

_{air}/2*g*, to resolve the force and mass units.

_{c}**Equation 8**

where *u _{air}* is the new air velocity of 77 ft/s based on the pipeline’s smaller internal diameter determined in

**Equation 2**and

*v*is the solids-to-air slip ratio of

_{solids}*u*.

_{air}/2The pressure loss from the solids friction can be found using **Equation 9**.

**Equation 9**

where *λ**s* is the solids friction factor. Note the significant pressure loss from friction from moving the solids through the pipeline (2.95 psi) compared to only moving the air (0.52 psi) — about one-fifth!

Next, calculate the pressure loss for the solids through the bends, *Δ**P _{bends}*, (

**Equation 10**) and for the solids lift,

*Δ*

*P*, (

_{lift}**Equation 11**). Please note, now that we’re calculating for solids and not air, we’re estimating the

*Δ*

*P*as the product of friction through the pipeline divided into 130-foot increments, shown as 2.95 psi/130 ft below, then multiplied by the elbow equivalent length, shown as

_{bends}*Leq*below, of 9 feet.

**Equation 10**

**Equation 11**

where *g* is universal gravity of 32.2 ft/s^{2} and *Δz* is the vertical height needed to lift solids up 30 feet. Again, consider the units conversion needed for force and mass resolution using the gravitational constant, *g _{c}*, to resolve.

**Equation 11**

Now the solids pressure loss can be totaled, as below.

**Equation 7**

Then, the total pressure loss, *Δ**P _{total}*, can be found from the solids and air components together. As stated previously, assume the pressure loss for the equipment is negligible.

**Equation 3**

Additional pressure loss could be included due to the air and solids separator, additional piping before the solids infeed, or after solids disengagement. Typically, for air and solids separators, a pressure loss of 6 inches water gauge is considered.

# Step 4: Calculate new air density and velocity at pickup

After the total pressure drop is calculated, the air velocity, *u _{air}*, at the solids’ feedpoint needs to be recalculated due to the higher pressure than initially assumed at atmospheric conditions and corresponding air density.

**Equations 12**and

**13**provide the new air density,

*ρ*, and new air velocity,

_{air,new}*u*, and calculations are based on the pressure drop determined in step 3. Remember to use absolute pressure and temperature (when appropriate) in these calculations.

_{new}**Equation 12**

where *ρ _{1}* is the initial air density at the system’s start and

*ρ*is the air density recalculated at the solids feedpoint;

_{2}*P*is the initial pressure at the system’s start and

_{1}*P*is the pressure recalculated at the solids feedpoint;

_{2}*RT*is the gas constant (

*R*) and the gas temperature (

*T*), and

*RT*

_{1}and

*RT*refer to locations in control volume;

_{2}*P*is the new pressure calculated from

_{new}*P*; and

_{2}/ P_{1}*P*is atmospheric pressure.

_{atm}**Equation 13**

where *A _{1}* and

*A*are the pipeline cross-sectional area at the system’s start and at the solids feedpoint, respectively; and

_{2}*u*and

_{1}*u*are the air velocity at system start and the air velocity at the solids feedpoint, respectively.

_{2}Note that the recalculated velocity, *u _{new}*, is lower than the initial specified velocity of 70 ft/s. This demonstrates the compressibility effects for the air, which can also be affected by temperature changes as well. If testing has shown that 70 ft/s is required to avoid line buildup and plugging, then you’ll be required to revisit this algorithm with a higher initial velocity to compensate for the air compression (and reduced volume and velocity at the pickup point). The pickup velocity is the gas velocity at the pickup point of the conveying system where solids are introduced into the conveying gas stream. When used in a research connotation, this is the gas velocity necessary to pick up, suspend, entrain, or detach particles at rest in a settled layer on the bottom of a horizontal pipeline.

If the air velocity is calculated to be too high (especially toward the end of the line due to the air density dropping), consider *line stepping*. Line stepping can be achieved by increasing the pipeline’s internal diameter at discrete points, thereby locally reducing the air velocity. Be cautious to not reduce the velocity to a point where either saltation occurs or an unstable conveying regime exists.

# Step 5: Recalculate air mass flowrate, pipeline diameter, and total pressure drop based on new air density

A more accurate calculation method involves an iterative procedure that’s performed in discrete steps along the pipeline to account for the change in air density and velocity. For brevity, the reiteration isn’t covered in this article.

# Step 6: Select a suitable air mover

Now that we have determined the rates for each variable, we can figure out the volumetric airflow rate. The volumetric airflow rate, *Q*, can be found with **Equation 14**, assuming approximately 60 ft/s velocity is sufficient. We can assume this because as stated at the beginning of this article, the minimum conveying velocity for this material ranges from 60 to 70 ft/s.

**Equation 14**

Now that we have a rough estimate of the dilute-phase pneumatic conveying system’s pressure, we can determine what air mover would be the best for this system. Earlier in this article, we mentioned three air movers: a compressor, centrifugal fan, or positive-displacement (PD) blower. Typically, for pressures less than 3 psig, a radial blade centrifugal fan can be used. The most common fans used in dust collection applications are machines that typically have maximum pressure ratings on the order of 0.7 to 1.5 psig. Because we have a pressure of 4.5 psig, a centrifugal fan wouldn’t meet the pressure resistance requirement for the system.

When line pressures exceed 15 psig, a compressor (such as a sliding vane, liquid-ring, rotary screw, or reciprocating) is normally used. A compressor is usually run at 30 to 100 psig, so having this air mover produce compressed air at only 5 psig or so is a waste of energy.

For pressures between 3 and 15 psig, a Roots-type PD blower is often used. One of the key features of this PD blower type is that it provides a nearly constant air volume delivery over its operating pressure range. This is important since airflow control in pneumatic conveying systems is critical for stable operation.

Thus, a PD rotary lobe blower is suitable for this application. A centrifugal fan isn’t likely to be a good candidate for this application due to the total pressure drop calculation (or estimation). Furthermore, a compressor is overkill. Air mover equipment vendors have performance curves available, which demonstrate operating ranges for the machine under specified conditions, such as pressure, temperature, operation speed, and others.

The step-by-step calculation method for estimating pressure loss through a dilute-phase conveying line will assist personnel with proper air mover selection, which is the heart of the pneumatic conveying system. Adopting a total system view, understanding not only the pneumatic conveying system’s operation but also its interaction with the solids handling equipment upstream and downstream, should also be carefully considered.

**PBE**

# References

- E. Maynard, “Troubleshooting and solving problems with your pneumatic conveying system,”
*Chemical Engineering Progress*, June 2010. - F. Cabrejos, G. Klinzing, “Minimum conveying velocity in horizontal pneumatic transport and the pickup and saltation mechanisms of solid particles,”
*Bulk Solids Handling*, Vol. 14, No. 3, July/September 1994, pp. 541-550. - E. Maynard, J. Khambekar, “Proper feeding of pneumatic conveying lines,”
*Powder and Bulk Engineering*, July, 2011. - L. Moody, “Friction factors for pipe flow,”
*Transactions of the ASME*, 66, 8, Nov. 1944, pp. 671-684. - S. Dhodapkar, P. Solt, G. Klinzing, “Understanding bends in pneumatic conveying systems,”
*Chemical Engineering*, April 2009.

**For further reading**

Find more information on this topic in articles listed under “Pneumatic conveying” and “Solids flow” in our article archive.

**Eric Maynard **(978-649-3300) is a vice president at Jenike & Johanson Inc. He’s been with the company for 25 years and has worked on more than 750 projects, designing handling systems for materials including chemicals, plastics, foods, pharmaceuticals, coal, cement, and more. He’s also a principal instructor for the AIChE bulk solids handling and pneumatic conveying courses and a special expert on NFPA Combustible Dust Committees 652 and 654.

**Jenike & Johanson • Tyngsboro, MA978-649-3300 • www.jenike.com**

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