磷矿选矿文献-外文文献部分2009-investigating the effect of some operating parameters on phosphate flotation kinetics by neural network

1、Advanced Powder Technology 20 (2009) 355360Original PaperInvestigating the effect of some operating parameters on phosphateotation kinetics by neural networkS. Al-ThyabatFaculty of Mining and Environmental Engineering, Al-Hussein Bin Talal University, Maan, P.O. Box 20, Jordana r t i c l e i n f oa

2、b s t r a c tArticle history:Received 31 October 2008Received in revised form 26 December 2008 Accepted 20 January 2009Articial neural network (ANN) was used to simulate the effect of feed mean size, collector dosage, and impeller speed on otation kinetic. Simulation were conducted using multi layer

3、 feed forward neural net- work assuming that otation is following rst order kinetic model.Simulation results showed that otation rate constant (K) exponentially increased with increasing par- ticle size up to a certain limit where it then decreased sharply. On the contrary, otation rate constant (K)

4、 was inversely proportional with collector dosage but gradually increased with increasing impeller rota- tional speed.2009 Published by Elsevier B.V. on behalf of The Society of Powder Technology Japan. All rightsreserved.Keywords: Flotation kinetic Neural network Froth otation Particle size Impelle

5、r speed Collector dosagePhosphate beneciationR mass of TCP inconcentrate1. Introduction100%2mass of TCP in feedPhosphate whichis an importantconstituent of fertilizersFlotation kinetics in mechanical otation (average bubble size600 lm) depend to large extents on the hydrodynamic of otation cell. Flo

6、tation micro-process such as bubbleparticle collision, bub- bleparticle attachment and detachment, air and solid dispersion, and rising of loaded bubbles are all occurred in high turbulence medium with Reynolds number of order (106107) where Reynolds number for mechanical otation cells is given by E

7、q. (3). Therefore, turbulence hydrodynamic is the decisive factor in modelling ota- tion operating parameters. By analogy with stirring tanks, experi- mental results of many researchers supported the claim that the active region for otation micro process is that with high energy dissipation rate, i.

8、e., near impeller stream 810:industry is mainly produced by beneciation of phosphate rock. Froth otation is one of the common methods in phosphate rock processing, where, almost two thirds of the world production is being upgraded by oatation 1.Understanding the macro and micro processes of otation

9、is one of the main challenges in current minerals industry research. Flotation sub-processes are complex and not fully understood yet. Therefore, development of mathematical models which pre- dict otation performance (recovery and grade) from rst princi- ples is still a big challenge 25.Most of the

10、research work found in the literature assumed rst order kinetic model when describing batch otation process. As shown in Eq. (1), otation rate constant K represent all otationRe qPBND23lPBmicro-processes (bubbleparticle detachment) 6,7:collision,attachmentandwhere N is impeller rotational speed, lPB

11、 is pulp density (particle bubble aggregate), and D impeller diameter.In minerals otation, otation rate (velocity) is a collective term used to describe otation mechanisms namely, particlebubble collision (Pc) particlebubble attachment (Pa), particlebubble detachment (1Pd). Extensive research were c

12、onducted to deter- mine the values of these probabilities using DLVO, extended -DLVO and turbulence theories 8,1114.Schubert 12 proposed the following model (Eq. (4) to calcu- late the probability of particlesbubble collision per unit volumeR R11eKt 1R is recovery at time t, Ris the maximum mineral

13、recovery. Recov-1ery is given by Eq. (2) where TCP is tricalcium phosphate Ca3 (PO4)2 (1% P2O5 = 2.184% TCP.)E-mail addresses: .jo, althyabatyahoo.co.uk0921-8831/$ - see front matter 2009 Published by Elsevier B.V. on behalf of The Society of Powder Technology Japan. All rights r

14、eserved. doi:10.1016/j.apt.2009.01.004Contents lists available at ScienceDirectAdvanced Powder Technologyjournal homepage: /locate/apt356S. Al-Thyabat / Advanced Powder Technology 20 (2009) 355360in a unit time. In this model Schubert emphasized the requirement of sufcient collision

15、between particles and bubbles for successful attachments. He concluded that the maximum collision occur near impeller stream where energy dissipation rate (energy input (w) per pulp unit mass).qparameters of classical rst order kinetic models (ultimate recov- ery, rate constant and time correction c

16、onstant) are not constant but function of otation operating parameters. He developed a sta- tistical model to predict each of classical model parameter as a function air ow rate, froth thickness and feed grade. The author developed what he called modied kinetic model which is used in reducing the ef

17、fect of uctuation in feed grade on otation performance.Mowla et al. 16 studied the effect of some operating parame- ters on reverse otation of hematite from silica sand. Assuming rst order kinetic model, the authors reported that otation kinetic rate constant increased as the feed mean size (d50) in

18、creased, i.e., longer time required to oat coarse particles. According to the authors this may due to the capability of smaller particles to oat easier and faster than larger ones.The effect of particle size on otation performance was also studied by Vieira and Peres 17 who studied the effect of par

19、ticles size on reverse otation of quartz using different dosages of differ- ent cationic collectors and pH levels. The authors found that recov- ery of ne particles otation increased with the increase of collector dosage until a certain limit whereas any increase above that limit was ineffective. Ac

20、cording to the authors the reason may due to the equilibrium between ionized and molecular species in the pulp at that point.Deglon 18 studied the effect of agitation in mechanical ota- tion cell on the otation performance of South African platinum ores. The author results emphasised the effect of a

21、gitation level measured in impeller speed on cell hydrodynamics which affect otation micro processes. He found that in general the increase in the level of agitation increase otation rate/recovery but signif- icantly decrease concentrate grade. The reason might be the entrainment of unwanted gangue

22、in otation froth.Westhuizen and Deglon 19 developed a mathematical model to correlate impeller critical speed of induced-air mechanical cell with particle size, solids percent, solid density, aeration rate, and liquid viscosity. Testing the effect of particle size under different variation of aerati

23、ons and solids concentration, the authors found that 1 s criterion for solids suspension in otation cell is nonlinear- ly proportional to impeller speed. Validation of their results with those obtained by Schubert 20, the authors claimed that they found exact similarity in proportionally exponent. O

24、n the other hand, the authors found that aeration measured by its supercial gas velocity is linearly proportional with critical impeller speed. They reported the increase of critical impeller speed with the in- crease in aeration rate to the effect of aeration on the reduction in power draw which de

25、teriorate solid suspension.Using articial neural network (ANN) in minerals industry oper- ations was a subject of extensive research since 1990s 2123. Dif- ferent researchers utilized the interpolation capability of ANN to study the effect of operating parameters on froth otation perfor- mance. In c

26、urrent work, the effect of Feed means size, collector dosage, and impeller speed on otation rate constant (K) was ex- plored. ANN model were developed by training and validation of the network with the results of 35 otation experiments. The ANN was then used to predict otation performance, and otati

27、on rate constant at different combinations of operating parameters.Dv 2 Dd2Pc 5 NP NB45PBPBdPB 0:5 dP dB!1=9 7q2=3e4d iDqDv20:336qFiV3FwhereNPq 2concentration of particles in otation pulp concentration of bubbles in otation pulpNBroot mean square between particlesroot mean square between bubbles(rms

28、)ofrelativeturbulentvelocityDPq2(rms)ofrelativeturbulentvelocityDPdPBeDq qF VFdiameter of bubblesparticles aggregateenergy dissipation rate (input power (Kw)/mass of the pulp)density difference between particles and uid density of the uidkinematic viscosity of the uidLuttrell and Yoon 13 simplied Eq

29、. (4) and dened particle collision probability as function of particle and bubble diameters (Eq. (7)2dp dBPc A7where A is a parameter function of Reynolds number (Re).Once particle collide with bubble, the efciency of particle attachment depends on bubbleparticle contact time and the interaction for

30、ces. Amand 14 showed that contact time required for successful attachment is greater than the sum of thinning time (tf) required for uid lamella around particle, rupture time (tR) for the lamella, and time required to form stable aggregate (ts).Yoon and Mao 11 used the extended DLVO theory to descri

31、be the nature of interaction forces between particle and bubble during the contact time. The total forces are the sum of electrostatic forces, Van Der waals (dispersion) forces, and hydrophobic forces. Attachment and detachment forces are the forces required to break energy barriers between bubblepa

32、rticles as given by Eqs. (8) and (9): E1 Ek wd E1P exp8aPd exp9Ekwhere E1 is the energy barrier, Ek is the kinetic energy of attach- ment, and wd is the work of adhesion.For rst order otation kinetic, the probability of particles col- lection to concentrate (recovery) is the multiplication of previo

33、us probabilities as shown in Eq. (10):2. Experimentalk ZPcPa1 Pd10Flotation feed used in experiments was siliceous phosphate ob- tained from Eshydia Mine in south of Jordan. The feed was pre- pared by agitating and scrubbing in 3-liter Denver D-12 otation cell for 3 min at 57% solids and 1050 RPM. C

34、hemical analysis of the nal feed was 17.9% P2O5 and 50.68% AI (acid insoluble, i.e., the gangue which is mainly silica).where Z is number of particles and bubbles in unit volume per unit time.Correlating otation kinetic represented by otation rate con- stant (K) with otation operating parameters was

35、 the subject of extensive research work in recent years. Cilek 15 reported thatS. Al-Thyabat / Advanced Powder Technology 20 (2009) 355360357Table 1Flotation experiments results.3. Neural network design and simulationArticial neural network (ANN) is an attempt to simulate the basic functions of biol

36、ogical brain in order to perform complex functions by computer systems such as classifying objects, match- ing patterns, and predicting the future based on past information. In this work, Multi layer Feed forward-back propagation ANN was used. This type of network consists of multiple layers of diff

37、er- ent number of neurons which are connected by nonlinear transfer functions in order to predict linear and nonlinear relationships be- tween input and output vectors 24,25. They called feed forward since ow of information is only allowable in forward direction.The architecture of this type of ANN

38、is shown in Fig. 1.Number of layers and their neurons are usually determined by trial and error. In a previous work, it was found that ANN architec- ture of 9 11 5 9 2 is suitable for simulating the effect of feed size, impeller speed, and collector dosage on otation recovery and grade 26. This mean

39、s that the network consists of four input lay- ers of 9, 11, 5, and 9 neurons, respectively and one output layer with two neurons (grade and recovery). In this work the same net- work architecture was used to test the effect of mentioned param- eters on otation kinetics. The output of current networ

40、k was otation kinetic rate and otation separation efciency.The results of 25 experiments were randomly chosen to simu- late the previous Network while the rest (10 experiments) were used for validation. ANN training and validation performance is shown in Fig. 2.After ANN training and validation, ota

41、tion performance was simulated. The range of feed mean size, collector dosage, and impeller speed were divided into 100 equal parts, i.e., feed mean size, collector dosage, and impeller speed was increased by an increment of 7.8 lm, 0.0056 kg/TOF, 4.04 RPM, respectively. This was conducted in order

42、to investigate the general trend of otation kinetic and separation efciency with the increase of operating parameters.As shown in Fig. 3, otation rate remains constant with the in- crease in operating parameters to certain limit where it increased sharply then leveled up at high operating parameters

43、.The gure also showed that at low values of operating parame- ters otation separation was high while otation rate constant was low. On the contrary, at high values of operating parameters, ota- tion rate constant was high while separation efciency was low. This may interpreted as follows: as particl

44、e size increased the probability of collisions between particles and bubbles increased so the collection (recovery) of particles by bubbles is expected to increased but because particles become more heavier (bigger) their time of otation become longer (low otation rate). However, it seems that the i

45、ncrease in agitation (impeller speed) increase par- ticles otation rate and compensate for the increase in particle size. The increase in collector dosage affects the selectivity and in- creased the recovery of gangue to concentrate which reduces sep- aration efciency. On the contrary, higher agitat

46、ion (impeller speed) override the increase in particles size which shortens theConstant otation parameters.Depressant (sodium silicate) = 5 kg/TOF; pH 9. TOF: ton of feed.Flotation experiments were conducted in 3-liter Denver ota- tion cell using 500 g of phosphate sample (specic gravity 2.7).In eac

47、h experiment, otation recovery, concentrate grade, and o- tation time were recorded. The results are shown in Table 1. Fatty acid (tall oil) was used as phosphate collector, sodium silicate as silica depressant, while sodium hydroxide to modify pulp PH.Flotation kinetic constant was calculated from

48、rst order ota- tion kinetic equation shown previously assuming the following theoretical boundary conditions: R(t = 0) = 0 and R(t = 1) = 100 at the beginning and end of otation, respectively while separation efciency was calculated from otation recovery (R) and concen- trate grade using Eq. (11):Se

49、paration efficiency SE RTCP RGangue100%11Fig. 1. ANN architecture.Exp.Feed meanCollectorImpellerFlotationKineticSeparation no.size (lm)dosagespeedtime (s)constantefciency(kg/TOF)(RPM)K (1/s)(%)17500.901200360.111276.2025530.561200360.072774.0237500.781200350.097873.7642770.561200410.065862.8157500.5

50、61200310.093980.6562770.781200420.074961.8878540.901200350.081382.3682770.901200380.083546.0692771.121200460.060858.41102770.671200390.102061.29118541.121200390.096885.35125530.781200370.093571.13135530.901200400.092864.45145531.011200390.096445.56157501.121200460.096965.59165530.901100340.071566.18

51、177501.121100390.089769.85185531.121100390.085772.16197500.781500290.106868.80205530.781500240.045157.89215530.901500220.103566.29225531.121500290.112857.52233800.561200330.046573.40243800.901200340.083059.34253800.781200320.117670.2626790.671200440.026358.46273801.121200370.082570.07283800.90110050

52、0.076172.25293801.121100390.096569.98303800.781100390.068188.07313800.901500240.073865.46323801.121500320.081176.57335530.781100420.084968.27347500.901100400.104574.08353800.781500370.099687.64358S. Al-Thyabat / Advanced Powder Technology 20 (2009) 355360Fig. 2. Training results for experimental dat

53、a. MSE: mean squared error, epoch: number of training.Fig. 5. The effect of collector dosage on otation performance (feed size = 463 lm, impeller speed = 1298 rev/min).Fig. 6. The effect of impeller speed on otation performance (collector dos- age = 0.8731 kg/TOF, feed size = 463 lm).Fig. 3. ANN sim

54、ulation results (kinetic constant: 1/s; SE%).time required for particles to report to concentrate (higher ota- tion rate). The increase in collector dosage and agitation reduce o- tation selectivity which in turn reduce separation efciency.However, to study the effect of each operating parameter, si

55、m- ulation was conducted by increasing each parameter while the other parameters were held constant. The results of simulation are shown in Figs. 46.Fig. 4 shows that otation rate constant (K) increased exponen- tially with increasing particle size up to a certain limit where itdecreased sharply. Th

56、is may due to the increase in pulp dispersant as coarse particles increase (the pulp become more diluted) which increase bubbleparticle collisions. However, the increase of parti- cle size to a certain limit encourages the detachment of particles from loaded bubbles which in turn causes the rate constant to de- crease. On the other hand, separation efciency increased with increasing feed mean size. This may due to the decrease in entrain- ment of nes as particle size increase although the expected de- crease in otation recovery as th