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16 / July 2021 powderbulk.com PBE PNEUMATIC POINTS TO PONDER 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 fol- lowing negative effects: increased material degradation, increased system wear, increased system pressure drop, and reduced sys- tem capacity. If we could design a convey- ing line with an ever-increasing diameter, so that the increased line cross-sectional area was propor- tional 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. Jack D. Hilbert, SME, Hatch Pneumatic conveying line stepping I t 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 col- umns 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 technol- ogies 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 vari- ous 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 convey- ing 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 benefi- cial in some systems. Benefits of line stepping When we assume a constant tem- perature in a pneumatic conveying system, the actual volume of the conveying air increases as the abso- lute pressure decreases: absolute pressure 1 x volume 1 = absolute pressure 2 x volume 2 or volume 2 = volume 1 x absolute pressure 1 absolute pressure 2 Since air flows through a conveying system from higher pressure to lower pressure, the air volume constantly increases 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.