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Pneumatic transport Basic definition – using gas to transport a particulate solid through a pipeline –Ex: grain, flour, plastic, pulverized coal Two modes –Dilute phase – particles are fully suspended, like entrainment in FB but deliberate, solids less than 1 % by volume, lots of pumping req’d –Dense phase – particles not suspended, loading > 30 % by volume, lots of interparticle interactions

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Phase diagram for dilute phase vertical pneu. transport (after Rhodes, p. 141, Fig 6.1) p/ L Superficial gas velocity U A B G = 0 G = G 2 > G 1 G = G 1 U ch for G 1 Uch, lowest velocity at which dilute phase transport line can be operated if solids feed rate is G1 Static head of solids dominates Friction resistance dominates

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Phase diagram for dilute phase horizontal pneu. transport (after Rhodes, p. 142, Fig 6.2) p/ L Superficial gas velocity U A B G = 0 G = G 2 > G 1 G = G 1 U salt for G 1 Saltation, solids begin to settle out in the bottom of the pipe

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Definitions Superficial gas velocity U fs = Q f (gas volumetric flow) /A (cross sectional area of pipe) Superficial solids velocity U ps = Q p /A (Q p = volumetric flow of solids) Actual gas velocity U f = Q f /A (void fraction) Actual particle velocity U p = Q p /[A(1- )]

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Important relationships Mass flow rate of particles Mass flow of fluid Solids loading = M p /M f

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Pressure drop in pneumatic transport Contributors to pressure drop 1.Gas acceleration (gas acting on gas) 2.Particle acceleration (gas acting on particles) 3.Gas/pipe friction wall friction 4.Solids/pipe friction “ 5.Static head of solidsfighting gravity 6.Static head of gas“ Not considered: interparticle forces

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Force balance on pipe Net force acting on pipe contents rate of increase in momentum of contents = Pressure - gas/wall - solids wall - gravity = rate of increase in force friction force friction forcemomentum of gas + rate of increase in momentum solids F fw and F pw are gas to wall and solids to wall friction force respectively, L = pipe length, = angle of pipe with horizontal What happens for steady state? Horizontal flow?

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Terms and physical meaning (you match them up): 1.Total pressure drop 2.Gas acceleration (gas acting on gas) 3.Particle acceleration (gas acting on particles) 4.Gas/pipe friction wall friction 5.Solids/pipe friction wall friction 6.Static head of solidsfighting gravity 7.Static head of gasfighting gravity

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Tools to calculate pressure drop Correlations for F pw For vertical transport [G = solids mass flux, mass particles/(area x time)] Horizontal transport where and For gas/wall friction pressure drop, calculate with friction factor assuming it is independent of presence of particles.

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Simple method for s.s. horizontal From Particle Technology by Orr (1966) Ratio of total pressure loss due to solids/air system ( Pt) to total pressure loss due to only air flowing ( Pa) R = mass of solid material mass of air k is an empirically derived coefficient

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Generally problematic. Solids that may be in suspension in vert/horiz transport may salt out as they go around bends. Worst case: vertical going to horizontal blinded tees recommended if bends are unavoidable No reliable correlations exist for bend pressure drops. Only a rough rule of thumb: Bend P = P for 7.5 m of vertical pipe under same flow conditions Bends

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For more info (and movies!) http://www.erpt.org/014Q/rhoe-00.htm

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