Pneumatic Conveying System with Mathcad Prime 2.0

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1 Pneumatic Conveying System with Mathcad Prime 2.0 Ahmad A. M. Allawi PTC Consultant Electrical Engineer-Power and Communications A qusetion was raised if the capacity of an existing pneumatic conveying system, conveying High Density Polyethylene (HDPE) particles, can be increased from lbm/hr to 30000lbm/hr?. The system data are given and summary results of calculations are given at the end of the worksheet. The system, simply composed of the following pipe components: Blower(1375 SCFM) and feeding+horizontal pipe (100ft)+bend+vertical pipe (50ft)+bend +horizontal pipe (325 ft)+cyclone to the atmosphere. All bends with R/D>6. The points for calculations of the system are, starting from cyclone atmospheric point (a), given by: Atmospheric point: a Horizontal pipe points: b-c bend points: c-d Vertical pipe points: d-e Bend points: e-f Horizontal pipe points: f-g Blower/Feeding points: g Note: Units in this worksheet are used everywhere which simplifies the conversions System Data Capacity Increment required for the plant capacity Q_Blower 1375 Existing blower flow rate p_blower 0.3 Pressure drop in the blower T g Gas or air (used) temt standard conditions dp 4 Particle diameter

2 dp 4 Particle diameter k Pipe roughness p_cyclone Pressure drop in the cyclone D 0.5 Pipe diameter ft V T 30.6 Terminal velocity at the feeding point 14.7 Exit pressure boundary conditions gas_constant Gas used is air ρ p 59 3 Particle desnsity M 29 Molecular weight of air g Gravity acceleration g c Constant 2 μ g Gas (air) viscosity at 68 Degree F L bc 325 Horizontal pipe length L de 50 Vertical rise pipe length L fg 100 Inlet horizontal pipe length Calculations Ponit a M ρ gstp gas_constant T 3 Gas density from ideal gas law g

3 Point b P b + p_cyclone D 2 A pipe area V gb Q_Blower Gas velocity at point b A P b ρ gb ρ gstp P b Gas (air)density at point b Re ρ gb V gb D Reynolds number μ g Gas friction factor using Churchill's equation 16 b Re a ln k Re D 16 f Re 3 2 ( a + b) 1 12 Capacity μ Solids mass- to- air ratio Q_Blower ρ gstp V 2 gb Fr

4 Fr g D V 2 T Frp g dp dp dp in ft now λ z μ 0.3 Fr 0.86 Frp 0.25 D dp must be in ft dp P bc 4 f + λ z μ L bc D ρ gb 2 2 V gb g c 144 Point c P c P b + P bc Pressure at point c Q_Blower V gc Gas velocity at point c A P c ρ gc ρ gstp P c Gas density at point c Pipe bend cd B 0.5 For R/D>6 P bend B ( 1 + μ) ρ 2 gc V gc Pressure drop in bend cd 2 g c point d P d P c + P bend Pressure at point d V gd Q_Blower Gas velocity at point d A P d ρ gd ρ gstp P d Gas density at point d V 2 gd Fr vertical pipe de

5 Fr g D λ z μ 0.3 Fr 0.86 Frp 0.25 D dp y dp0.0132ft, ρ-particles59lbm/ft^3 V p V gd y Capacity ε A ρ p V p ρ 0 ε ρ gd + ( 1 ε) ρ p Vertical pressure drop de P vert 4 f + λ z μ L de + D ρ gd 2 V gd ρ 0 L de g g c g c point e P e P vert + P d Pressure at point e V ge Q_Blower Gas velocity at point e A P e ρ ge ρ gstp P e pipe bend ef Gas density at point e P bend B ( 1 + μ) ρ 2 ge V ge Pressure drop in bend ef 2 g c point f P f P e + P bend Pressure at point f

6 P f P e + P bend Pressure at point f V gf Q_Blower gas velocity at point f A P f ρ gf ρ gstp P f gas density at point f horizontal pipe fg V 2 gf Fr g D λ z μ 0.3 Fr 0.86 Frp 0.25 D dp horizontal pressure drop fg P fg 4 f + λ z μ L fg D ρ gf 2 V gf g c P g P f + P fg V gg Q_Blower A P g ρ gg ρ gstp P g The additional acceleration P accel ρ 2 gg V gg ( μ y) g c P gtotal P g + P accel Pressure drocross the blower P in Inlet pressure to blower P blower P gtotal P in

7 P blower P gtotal P in Saltation Velocity using Rizk Correlation dp 4 HDPE particle dia. mm δ 1.44 dp ψ 1.1 dp ( ) Capacity V Saltation 3600 g D A ρ gstp Summary of the Results Pressure at the pipe point Pressure drot the pipe points P b P bc P c P vert P d P fg P e P blower P f P g Gas (air) velocity at the various points in the pipe V gb V gd V gc V ge V gf V gg

8 Saltation Velocity V Saltation Conclusion The smallest velocity in the pipe line occurs at point g94.6 ft/s, hence the velocity everywhere in the pipe line exceeds the Saltation velocity. we assume that the blower is capable of the 4.45 psi pressure increase, the velocity provided by the blower flow rate of 1375 SCFM exceeds the saltation velocity everywhere in the pipe line, therefore, the blower and the pipe line system is capable of conveying 30000lbm/hr of solids. References 1- Theory and design of dilute phase pneumatic conveying system. A.T. Agarwal USA Vol. 17 No.1 Jan/Feb Pneumatic conveying design guide 2nd ed., David Mills Elsevier. 3- Handbook of fluidization and fluid particle systems edited by Wen-Ching Yang On the prediction of pickund saltation velocities in pneumatic conveying, L.M Amarante Mesquita, Brazlian journal of chemical engineering, Vol.31 March A tutorial on pipe flow equations, Donald W. Schroeder,Jr. Aug.2001/Stoner Associates Inc. 6- Design example dilute phase pneumatic conveying. Author/publisher are not known.

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