Pneumatic Conveying System with Mathcad Prime 2.0 ahmad.allawi15@gmail.com ahmad_allawi@yahoo.com Ahmad A. M. Allawi PTC-4009681 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 20000 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 30000 Increment required for the plant capacity Q_Blower 1375 Existing blower flow rate p_blower 0.3 Pressure drop in the blower T g 68 527.67 Gas or air (used) temt standard conditions dp 4 Particle diameter
dp 4 Particle diameter k 0.00015 Pipe roughness p_cyclone 0.368 0.1807 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 10.73 3 Gas used is air ρ p 59 3 Particle desnsity M 29 Molecular weight of air g 32.2 2 Gravity acceleration g c 32.174 Constant 2 μ g 0.0000114 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 0.0753 gas_constant T 3 Gas density from ideal gas law g
Point b P b + p_cyclone 14.8807 D 2 A 0.1963 4 2 pipe area V gb Q_Blower 115.296 Gas velocity at point b A P b ρ gb ρ gstp P b 0.0762 3 Gas (air)density at point b Re ρ gb V gb D 3.8543 10 5 Reynolds number μ g Gas friction factor using Churchill's equation 16 b 37530 6.5316 10 17 Re a 2.457 ln 1 + 7 0.9 0.27 k 2.7804 10 21 Re D 16 f 2 + 8 12 1 0.0042 Re 3 2 ( a + b) 1 12 Capacity μ 4.8296 Solids mass- to- air ratio Q_Blower ρ gstp V 2 gb Fr 825.6626
Fr g D 825.6626 V 2 T Frp 2.2159 10 3 g dp dp 0.0131 dp in ft now λ z 0.082 μ 0.3 Fr 0.86 Frp 0.25 D 0.1 0.0016 dp must be in ft dp P bc 4 f + λ z μ L bc D ρ gb 2 2 V gb 1.7239 2 2 g c 144 Point c P c P b + P bc 16.6047 Pressure at point c Q_Blower V gc 103.3258 Gas velocity at point c A P c ρ gc ρ gstp P c 0.085 3 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 0.2856 Pressure drop in bend cd 2 g c point d P d P c + P bend 16.8903 Pressure at point d V gd Q_Blower 101.5785 Gas velocity at point d A P d ρ gd ρ gstp P d 0.0865 3 Gas density at point d V 2 gd Fr 640.881 vertical pipe de
Fr g D 640.881 λ z 0.082 μ 0.3 Fr 0.86 Frp 0.25 D 0.1 0.0019 dp y 1 0.123 0.0131 0.3 59 0.5 0.7427 dp0.0132ft, ρ-particles59lbm/ft^3 V p V gd y 75.4379 Capacity ε 1 0.9905 A ρ p V p ρ 0 ε ρ gd + ( 1 ε) ρ p 0.6483 3 Vertical pressure drop de P vert 4 f + λ z μ L de + D ρ gd 2 V gd ρ 0 L de g 0.4767 2 g c g c point e P e P vert + P d 17.367 Pressure at point e V ge Q_Blower 98.7904 Gas velocity at point e A P e ρ ge ρ gstp P e 0.089 3 pipe bend ef Gas density at point e P bend B ( 1 + μ) ρ 2 ge V ge 0.2731 Pressure drop in bend ef 2 g c point f P f P e + P bend 17.6401 Pressure at point f
P f P e + P bend 17.6401 Pressure at point f V gf Q_Blower 97.261 gas velocity at point f A P f ρ gf ρ gstp P f 0.0904 3 gas density at point f horizontal pipe fg V 2 gf Fr g D 587.5594 λ z 0.082 μ 0.3 Fr 0.86 Frp 0.25 D 0.1 0.0021 dp horizontal pressure drop fg P fg 4 f + λ z μ L fg D ρ gf 2 V gf 0.4949 2 g c P g P f + P fg 18.1349 V gg Q_Blower 94.6069 A P g ρ gg ρ gstp P g 0.0929 3 The additional acceleration P accel ρ 2 gg V gg ( 1 + 2 μ y) 0.7333 2 g c P gtotal P g + P accel 18.8683 Pressure drocross the blower P in 0.3 14.4 Inlet pressure to blower P blower P gtotal P in 4.4683
P blower P gtotal P in 4.4683 Saltation Velocity using Rizk Correlation dp 4 HDPE particle dia. mm δ 1.44 dp + 1.96 7.72 ψ 1.1 dp + 2.5 6.9 1 ( 6.9 + 1) Capacity 10 7.72 V Saltation 3600 g D 6.9 71.1999 A ρ gstp --------------------Summary of the Results------------------- Pressure at the pipe point Pressure drot the pipe points P b 14.8807 P bc 1.7239 P c 16.6047 P vert 0.4767 P d 16.8903 P fg 0.4949 P e 17.367 P blower 4.4683 P f 17.6401 P g 18.1349 Gas (air) velocity at the various points in the pipe V gb 115.296 V gd 101.5785 97.261 V gc 103.3258 V ge 98.7904 94.6069 V gf V gg
Saltation Velocity V Saltation 71.1999 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-2006. 2- Pneumatic conveying design guide 2nd ed., David Mills 2004- Elsevier. 3- Handbook of fluidization and fluid particle systems edited by Wen-Ching Yang 2003. 4- On the prediction of pickund saltation velocities in pneumatic conveying, L.M Amarante Mesquita, Brazlian journal of chemical engineering, Vol.31 March 2014. 5- 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.