Modeling and control of size distribution processes. Andreas Johansson
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1 Modeling and control of size distribution processes Andreas Johansson Control Engineering Group Department of Computer Science, Electrical and Space Engineering
2 Agenda Size distribution processes Modeling of comminution processes Cone crusher modeling Continuous approach Discrete approach Cone crusher control The pelletizing process
3 Size distribution process or Particulate process Outcome: A size distribution of particles Examples: Chemical industry: Crystallization and Emulsion polymerization Biochemistry: Cell growth Pharmaceutics: Granulation Mineral processing: Comminution (Crushing, grinding) and pelletizing Modeling: Population balance
4 Comminution processes Crusher Size reduction: From ~1m to mm Power consumption: Up to 1 MW Efficiency: ~1 % Grinding mill Size reduction: From a few cm to µm Power consumption: Up to 3 MW Efficiency: ~1 %
5 The cone crusher Crushes rocks of size <15 cm into size less than.5~2 cm Power consumption: ~1 kw Main manipulated variables Closed side setting (CSS) Rotational speed Possible measurements Mass flow of product Power draw Size distribution of feed and product from 3D image data (Thurley 29) Feeder Mantle Chamber Bowl CSS
6 Particle size distribution Distribution: Total mass of particles of sieve size <D Example: Rosin-Rammler 1.5 Size distribution Density function: P (D) Size classes Discrete density function: The 1st difference of the distribution D Density function and discrete density function Size (mm)
7 Breaking of particles Selection function s The probability of a particle to be broken in a single breakage event Example from Kapur (1971) Selection function Progeny size distribution Breakage function B The size distribution of progeny particles when a particle is broken Example from King (21) Size (mm) D 2
8 Motion of particles Classification function c The probability of a particle to be retained Example from King (21) for a cone crusher 1 Classification function Size (mm) CSS
9 Continuous approach A small volume element dv = Ady Logarithmic particle size λ with D = D e -λ Density function of material of size λ at level y and time t: χ(t,y, λ) Define x(t,y,λ) = ρa(y,t)χ(t,y,λ) Level interval Y = (y,y+dy) Size interval Λ = (λ, λ-dλ) Mass of material in the control volume C = Y Λ: x(t,y,λ)dydλ A dv
10 Particle velocity Assumption (simplified from Evertsson 1999): Free falling during fraction η of each rotation Time of one rotation T=1/w Distance travelled during time ηt S = g(ηt) 2 /2 Mean velocity v = S/T = gη 2 T 2 /2T = gη 2 /2w Free falling Pinched
11 Material transport Fraction of material size λ at level y and time t that is qualified to move downwards Material entering the control volume Control volume dλ dy v(t)dt Material leaving the control volume v(t) Net increase in the control volume using 1 st order Taylor approximation
12 Material breakage Fraction of broken particles of size D 1 resulting between size D and D+δD 1 Progeny size distribution.5 In logarithmic size D 1 Size (mm) D+δD Mass of particles of all sizes ending up with size D
13 Population balance Breakage events per second (rotational velocity): w(t) Density function of material in the control volume at time t+dt Letting dt and dropping the arguments (Johansson 29)
14 Inputs 4 3 D63 (mm) CSS (mm) Rot. speed (RPS) Simulations Simulation results Decreased Closed Side setting results in smaller product Decreased rotational speed gives less dispersion of product size Mass flow density 5 Feed CSS = 25 mm, w = 8 RPS CSS = 15 mm, w = 8 RPS 4 3 CSS = 15 mm, w = 6.5 RPS kg/s Size (mm) Size (mm) Size (mm) kg/s Time (s) Feed mass flow density Time (s) Product mass flow density Time (s) Mass flow Feed Product Time (s)
15 Discrete approach Multi-zone approach Fixed number of crushing zones i=1..n Population balance for each zone Discrete size distribution Size densities are represented by vectors (X i, Z i, U i ) Breakage, classification, and selection are matrices (B i, C i, S i )
16 Model features Capacity limitation in each zone Recycling of oversized output Feed composed of material with different hardness Feed Cone Crusher Screen Over Size Under Size
17 Simulation: Dynamics D63 Input [mm] Time [s] ω [rps] Time [s] CSS [mm] 4 2 Throughput [kg/s] Time [s] Time [s]
18 Simulations: Steady-state Total Throughput [Kg/s] Throughput [Kg/s] max ω [rps] CSS [mm] Eccentric Speed ω [rps]
19 Simulation of closed loop control Controlled variable: Fraction f of material inside specific size interval Manipulated variable: Rotational speed ω PI Controller Discrete density function Size (mm CSS [mm] Soft material.[%] Fraction f and setpoint[%] ω [rps] Time [s] Time [s] Time [s] Time [s]
20 Simulation with screen Production maximum Feed 7 Throughput [Kg/s] Cone Crusher Screen 2 Over Size 15 ω [rps] CSS [mm] 4 Under Size
21 Online optimization Crushing objectives Aggregate industry: Produce a certain size (sand, gravel, etc.) Other mineral processing: Feed later comminution stages (mills) Control objectives Maximizing throughput in certain size class Minimizing size of the output Minimizing energy consumption Etc. Online optimization of control objectives Khalids licentiate seminar this winter
22 Iron ore production at LKAB Malmberget Run-of-mine ore Primary crushing Secondary crushing Grinding Magnetic separation Grinding Magnetic separation Grinding Magnetic separation Dewatering Bentonite blending Rolling drum Sintering Iron ore pellets
23 The pelletizing process Finely grinded iron ore and water is rolled into balls inside a rolling drum Undersized balls are returned into the rolling drum Oversized balls are returned to earlier process stages Correctly sized balls go into the sintering furnace Grinded iron ore Water Rolling drums Screen Reflow of undersize pellets Green pellets
24 Desirable properties of the pelletization process Narrow size distribution of the pellets Rapid growth in the rolling drum Requires a bimodal input size distribution (nuclei+coating) Rapid growth => decreased undersize reflow => less nuclei => slower growth Oscillation! High pellets strength Affected by water addition Water addition also affects growth rate Conclusion: Future research
25 Future work Crusher Obtain measurement data for model validation and parameter identification Model power consumption and wear Algorithms for online optimization of the operation Pelletizing Literature study on modeling and control Modeling and simulation
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