Block Flow Chart of a Typical Particle Processing System

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2 Block Flow Chart of a Typical Particle Processing System Raw materials (R) uxiliary materials (H) Balance boundary of material, energy, information and costs flows Raw materials E I E I E I E I E I E I Store (R) Store (H) Raw material processing Material conversion Product Material Product B separation Waste Product formulation Store () Store (B) Store (W) Main product Waste Information (I) Energy (E) Costs (K) I E I E E I I E E I I I I uxiliary material supply E I E I Store (W) E I I uxiliary material processing H E I Recycling process (Reuse) E H I Byproduct Information Energy Proceeds

3 Hierarchic Order of Particle Conversion Processes Macroprocess (in process chamber of apparatus) Process group: Comminution Mixing Chemical reaction Storage Separation Drying gglomer pparatus & machine level dsorption films Subprocess (charact zone of process chamber) Material, energy, momentum transport Particle beds Particle swarms Continuum level Microprocess (smallest material element of process chamber) Material, energy, momentum transport fixed surface area sl, g variable surface area process determ sl, g Diluted in fluids, contact points ss variable contact area, process determin ss Particle level s solid l liquid g gas physicochemical basis of conversion Diffusion (nondirectional random transport) Convection (directional transport) De/gglomeration (creat/distruct of interactions) Moleculare level Fundamentals see: H Schubert, W Fratscher und R Kind, Zur Herausbildung einer einheitlichen Modellierungsstrategie in der Verfahrenstechnik, Chem Technik 35 (1980)

4 c) Element with one input and one output stream feed m pass through m P product d) Element with one input and two output streams feed Basic Elements of Processing Systems a) Element with one input stream feed m b) Element with one output stream source m store store separation sink m P product m P1 m P2 product m with multiple product streams m P1 m separation m P2 m P3 separat stage 1 e) Element with two input streams and one output stream feed m 1 m 2 mixing m P product m P1 separat stage 2 m P2 m P3

5 Basic Structures or Element Combinations of Processing Systems 1 Sequential combinations a) Cocurrent combination element 1 (stage 1) element 2 (stage 2) stage 1 stage 2 b) Countercurrent combination stage 1 stage 2 2 Bypass arrangements a) general element 1 element 2 element 3 b) with cocurrent elements (units) stage 1 stage 2 stage 3 c) with countercurrent elements (units) stage 1 stage 2 stage 3

6 Basic Structures or Element Combinations of Processing Systems 3 Parallel arrangement a) input side b) output side element 2a element 1a element 1 element 2 element 2b element 1b c) input and output side element 2a element 1 (stage 1) element 3 element 2b 4 Feedback arrangement, circuit element 2 feed element 1 product 5 Combination of feedbacks element 4 element 2 feed element 1 element 3 product

7 Combination of Comminution and Classification Units Block flow charts of sequential arrangements: a) Element with one input and one output stream m comminution m Fines m comminution 1 comminution 2 m Fines b) Element with one input and two output streams m m Coarse or m F1 m Fines or m F2 or with multiple product streams (fractions i) m m Coarse or m F1 m Fines1 or m F2 m Fines2 or m F F1 F2 F3 F4

8 Combination of Classification Units number of variants: N = (2 n)! n! (n+1)! n machines or classifiers n + 1 product fractions F n+1 1) n N e g 5 structur variants of 3 classifiers to produce n+1 = 4 fractions F 1 F 4 Sequential or cascade arrangements of 3 units: F1 F2 F3 F4 2) F1 F2 F4 F3 F1 F2 3) F3 F4 4) F1 F2 F4 F3 5) Parallel arrangement of n 1 = 2 units: F1 F2 F3 F4

9 Sequential Combination of Comminution and Classification Units Block flow charts: a) Preclassification + Coarse comminution Fines 1 Fines 2 b) Precomminution + comminution Coarse Fines c) Pre and subsequent comminution comminution 1 Coarse + comminution 2 Fines 1 Fines 2 d) Parallel arrangement of subsequent and comminution Coarse + comminution 1 1 Fines comminution 2 2 Fines 1 Fines 2 Fines 3 Technical flow charts (PIflow charts): crushers mills F F F F a) simple pass through without b) pass through with 1 precrusher (jaw crusher); 2 machine 3 recrusher (flat cone crusher) a) simple pass through b) pass through with classifier 1 multichamber mill; 2 premill (singlechamber mill); 3 finish mill for fines (doublechamber mill); 4 classifier with circulating air

10 Combination of Comminution and Classification Units Block flow charts of feedback arrangements and circuits: a) Feedback of coarse feedback of coarse m Coarse bzw m Feedback + comminution m m F Fines b) Feedback of fines Feedback of fines Coarse + comminution Fines 1 c) Preclassification unit preclassification 1 + Coarse feedback of coarse comminution 2 Fines 1 + Fines 2 d) Precomminution unit feedback of coarse precomminution comminution 2 comminution 1 Fines + Fines

11 Evaluation of Residence Time Distribution of Processes page 1 1 Batch process a) Cummulative residence time distribution F( τ) b) Frequency distribution f(τ) 1 F( 0 R f 0 R 2 Continuous processes with ideal residence time distribution Block flow chart: tracer 1 0 tracer a) ideal plug flow channel (piston flow, ideal replacement) 0 b) ideal continuous mixer c) cascade of ideal continuous mixers 3 1 st and 2 nd moment of residence time distribution a) mean residence time (complete initial moment) b) variance of residence time distribution (2 nd central moment)

12 Evaluation of Residence Time Distribution of Processes page 2 4 Normalized frequency distribution of residence time m f( / m ) for cascades of ideal mixers with various stage numbers n at constant total mean residence time m = n m,n = const m f ( m) 1,5 1,0 0,5 n n= with mean residence time of one stage (unit): 0 0,5 1,0 1,5 2,0 2,5 5 Cummulative residence time distribution F ( / m ) for cascades of ideal mixers with various stage numbers n 1 0,8 m F( / m ) 0,6 0,4 0,2 n= m n = 1 ideal mixer ideal replacement 6 Flow channel (pipe) with axial redispersion Bodenstein number of particles v' v axial dispersion (diffusion) coefficient of particles x ideal mixer ideal replacement

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