Pneumatic transportBasic definition using gas to transport a particulate solid through a pipelineEx: grain, flour, plastic, pulverized coal Two modesDilute phase particles are fully suspended, like entrainment in FB but deliberate, solids less than 1 % by volume, lots of pumping reqdDense phase particles not suspended, loading > 30 % by volume, lots of interparticle interactions

Phase diagram for dilute phase vertical pneu. transport(after Rhodes, p. 141, Fig 6.1)p/LSuperficial gas velocity UABG = 0G = G2 > G1G = G1Uch for G1Uch, lowest velocity at which dilute phase transport line can be operated if solids feed rate is G1Static head of solids dominatesFriction resistance dominates

Phase diagram for dilute phase horizontal pneu. transport(after Rhodes, p. 142, Fig 6.2)p/LSuperficial gas velocity UABG = 0G = G2 > G1G = G1Usalt for G1Saltation, solids begin to settle out in the bottom of the pipe

DefinitionsSuperficial gas velocity Ufs = Qf (gas volumetric flow) /A (cross sectional area of pipe)Superficial solids velocity Ups = Qp/A (Qp = volumetric flow of solids)Actual gas velocity Uf = Qf/Ae (void fraction)Actual particle velocity Up = Qp/[A(1-e)]

Important relationshipsMass flow rate of particles

Mass flow of fluid

Solids loading = Mp/Mf

Pressure drop in pneumatic transportContributors to pressure dropGas acceleration (gas acting on gas)Particle acceleration (gas acting on particles)Gas/pipe friction wall frictionSolids/pipe friction Static head of solidsfighting gravityStatic head of gasNot considered: interparticle forces

Force balance on pipeNet force acting on pipe contentsrate of increase in momentum of contents=

Pressure - gas/wall - solids wall - gravity = rate of increase in force friction force friction forcemomentum of gas + rateof increase in momentum solidsFfw and Fpw are gas to wall and solids to wall friction force respectively, L = pipe length, = angle of pipe with horizontalWhat happens for steady state? Horizontal flow?

Terms and physical meaning (you match them up):Total pressure dropGas acceleration (gas acting on gas)Particle acceleration (gas acting on particles)Gas/pipe friction wall frictionSolids/pipe friction wall frictionStatic head of solidsfighting gravityStatic head of gasfighting gravity

Tools to calculate pressure dropCorrelations for FpwFor vertical transport [G = solids mass flux, mass particles/(area x time)]

Horizontal transport

whereand

For gas/wall friction pressure drop, calculate with friction factor assuming it is independent of presence of particles.

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

Chart2

1.15

2.14

3.11

3.5

3.5

coefficient k, dimensionless

superficial velocity, ft/min

coefficient k, dimensionless

k as a function of superficial velocity

Sheet1

superficial velocity, ft/mincoefficient k, dimensionless

20001.15

30002.14

40003.11

50003.5

60003.5

Sheet1

coefficient k, dimensionless

superficial velocity, ft/min

coefficient k, dimensionless

k as a function of superficial velocity

Sheet2

Sheet3

BendsGenerally 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 ifbends are unavoidableNo reliable correlations exist for bend pressure drops. Only a rough rule of thumb: Bend DP = DP for 7.5 m of vertical pipe under same flow conditions

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