Jack D. Hilbert, SME | Hatch
It seems like only yesterday that Paul Solt began this series of columns in March 1989, and it seems like only this morning that I took over its primary authorship in 2010, after co-authoring the columns with Paul from 2005 through 2009. During this 32-year span, we’ve provided an approach to pneumatic conveying that’s based on our test-lab resources and, more importantly, our practical field experience, combined with the works of other academic resources and the assistance of several equipment vendors.
Our mission with these articles (and the webinar series we were fortunate enough to pioneer with PBE in 2007) has been to provide conveying system end users with the tools, reference information, and independent capability to plan new systems or optimize and troubleshoot existing systems. We’ve also tried to make readers aware of new and existing technologies that allow users to analyze the relationships between several operating parameters.
One of the “hidden treasures” of pneumatic conveying we’ve introduced you to is line stepping — the practice of increasing the conveying line diameter at various intervals downstream from the material pickup point. We first discussed this concept in PBE in 1990 and have mentioned it many times since, but with the amount of optimization and debottlenecking taking place in existing conveying systems, it seems appropriate to dedicate an entire column to this topic.
In this month’s column, I’ll explain how to determine when it’s desirable to step — or increase — the conveying line diameter in a pneumatic conveying system and how to calculate the point along the conveying line where the diameter increase should occur. You can step the line diameter in both vacuum and pressure conveying systems and in systems designed to operate in either dilute phase (stream flow) or dense phase (two-phase flow). Before discussing how to step the conveying line, it’s important to understand why stepping is beneficial in some systems.
Benefits of line stepping
When we assume a constant temperature in a pneumatic conveying system, the actual volume of the conveying air increases as the absolute pressure decreases:
Since air flows through a conveying system from higher pressure to lower pressure, the air volume constantly increases through the conveying system. This increase in volume results in a proportional increase in air and material velocity, which may exceed the desirable — or optimum — design velocity for transporting a given material. Increasing velocity causes the following negative effects: increased material degradation, increased system wear, increased system pressure drop, and reduced system capacity.
If we could design a conveying line with an ever-increasing diameter, so that the increased line cross-sectional area was proportional to the increased air volume at any given point in the system, then the velocity would be constant, creating an optimum pneumatic conveying system. However, achieving this is impossible within normal cost limits.
Instead, the best alternative is to increase the conveying line diameter to the next larger size, creating a stepped conveying line. The larger diameter line should start at a point in the system where the system pressure has reduced enough to ensure that the velocity at the point where the larger diameter line starts will be at or above the desired velocity. Typically, the original pickup velocity is a good target to use as the minimum resulting velocity immediately after a line step.
Since this approach is limited by the number of pipe sizes available, especially in the US pipe system, the difference in pressure between the system’s pickup point and its terminal end (called the absolute pressure ratio) must be large enough to maintain the desired velocity using these pipe sizes. Therefore, stepping a conveying line is only feasible when operating above 8 psig on a pressure system and above 10 inches mercury on a vacuum system. Dense-phase conveying systems that operate at pressures greater than 30 psig are candidates to consider line stepping. Contrary to what common sense may suggest, determining whether stepping is a possibility depends on the absolute pressure ratio between the system’s pickup and terminal pressures rather than the system’s length.
One drawback to consider is that stepping the conveying lines on a system that has several diverter valves near its terminal end (where the material discharges to the atmosphere) will require enlarging the valves, which may be prohibitively expensive.
A conveying system that uses a Schedule 40, 4-inch pipe where the conveying line inside diameter is 4.026 inches and the line length is 200 feet would require 1,024 scfm of air at 25 psig to convey 705 lb/min of material with a true density of 100 lb/ft3, a maximum particle size of 45 mesh (354 microns), and a median particle size of 200 mesh (74 microns). This results in a superficial air velocity at the pickup of 4,287 fpm.
Let’s consider stepping this conveying line to the Schedule 40 pipe sizes shown in Table 1. (More sizes are available if we use tubing or other pipe schedules.) We calculate the actual air volume in actual cubic feet per minute (acfm) through a given pipe diameter by multiplying the velocity — in this case, 4,287 fpm — by the pipe’s cross-sectional area in square feet.
Calculating the conveying line lengths. Of the four diameters listed, we can only step the conveying line to three. We can’t step to the 8-inch-diameter line since it would require 1,489 acfm and we’re only using 1,024 scfm.
To allow stepping, the system pressure must be reduced so that the air expands to the necessary air volume (acfm) to maintain the desired velocity. For the 6-inch line, we calculate:
We can calculate the maximum system pressures for the various pipe sizes to maintain the desired velocity as shown in Table 2.
To calculate the stepping point, we start from a known point in the conveying system, either the pickup point or the terminal end. Since this is a pressure conveying system, we know that the pressure at the system’s terminal end is 0 psig (14.7 psia). (If this were a vacuum conveying system, the pressure at the system’s pickup point would be 0 psig.)
Since we’re stepping the conveying line to larger-diameter pipe, this will either reduce system pressure or increase conveying capacity. For this example, let’s calculate how to step the conveying line using the same air volume and pressure and the same amount and type of material in the previous example while increasing the conveying capacity to 1,400 lb/min.
Length of 6-inch-diameter line. In previous columns, we’ve provided formulae for calculating the pressure drop in a pneumatic conveying line. Using a computerized version of the formulae presented earlier, we can calculate the line length for 6-inch-diameter conveying line at a conveying capacity of 1,400 lb/min, as shown in Table 3.
Thus, if the last 60 feet of conveying line has a diameter of 6 inches instead of 4 inches, the system pressure will be 2.8 psig.
Length of 5-inch-diameter line. Next, we can calculate the line length for a line diameter of 5 inches instead of 6 inches, as shown in Table 4.
Thus, the conveying system operates with the same system pressure with 60 feet of 6-inch-diameter line or 26 feet of 5-inch-diameter line. We continue by calculating the length of 5-inch-diameter line required to obtain a system pressure of 10.5 psig, as shown in Table 5.
A 105-foot length of 5-inch-diameter conveying line produces a system pressure of 10.5 psig, but since the system produces the same system pressure with 60 feet of 6-inch-diameter line or 26 feet of 5-inch-diameter line, we can achieve the same system pressure by using 79 feet of 5-inch-diameter line (105 feet – 26 feet = 79 feet) and 60 feet of 6-inch-diameter line, producing a total system length of 139 feet.
Length of 4-inch-diameter line. Next, we can calculate the length for a line diameter of 4 inches instead of 5 inches, as shown in Table 6.
As the table shows, the conveying system produces the same system pressure with 33 feet of 4-inch-diameter line or 105 feet of 5-inch-diameter line, since both produce 10.5 psig. We continue by calculating the length of 4-inch-diameter line required to produce a system pressure of 25.0 psig, as shown in Table 7.
By stepping the conveying line from 61 feet of 4-inch-diameter line to 79 feet of 5-inch-diameter line to 60 feet of 6-inch-diameter line, the system has a total length of 200 feet but can now convey 1,400 lb/min, instead of the 705 lb/min it could convey when the entire conveying line was 4 inches in diameter. The stepped conveying line also operates with the same air volume of 1,024 scfm at 25 psig.
The stepped conveying line’s other major advantage is that it greatly reduces the velocity, as shown in Table 8, reducing material degradation and system wear.
The stepped conveying line in the example discussed here changes a system that’s operating at 25 psig when conveying material at 705 lb/min with velocities between 4,287 fpm and 11,583 fpm to a system that’s operating at 13.7 psig when conveying the same number of pounds per minute with velocities between 5,995 fpm and 8,388 fpm. The same system’s capacity could be increased to operate at 25 psig when conveying 1,400 lb/min with velocities between 4,287 fpm and 6,753 fpm.
Stepping a conveying line has a greater effect when the system operating pressure or vacuum is high (above 8 psig or 10 inches mercury) and when the conveying velocities are high (above 3,000 fpm).
The analysis used here is based on equations 11.1, 11.2, and 11.10 in chapter 11 of Fluidization and Fluid-Particle Systems by Frederick A. Zenz and Donald E. Othmer (New York, Reinhold, 1960). Equation 11.1 is used for horizontal conveying when the conveying velocity is above the saltation velocity; this type of conveying is commonly called stream flow. Equation 11.2 is used for vertical conveying, and Equation 11.10 is used for horizontal conveying when the conveying velocity is below the saltation velocity but isn’t a pulsed-piston flow. While this type of conveying is typically called dense phase, the more correct term is two-phase flow.
The computerized version of the above information is PneuCalc, a software originally developed by Pneumatic Conveying Consultants but now available from Hatch (www.pneucalc.com).
For further reading
Jack Hilbert (610-657-5286) is principal consultant at Pneumatic Conveying Consultants, LLC, Schnecksville, PA, and a pneumatic conveying subject matter expert (SME) for Hatch. He holds a BS and an MS in mechanical engineering from Penn State University, State College, PA, and has more than 48 years of experience in the application, design, detailed engineering, installation, and operation of pneumatic conveying systems.
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