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Hydrometallurgy49199823–46
Sulphuric acid pressure leaching of a limonitic
laterite:chemistry and kinetics
D.Georgiou,V.G.Papangelakis)
Department of Chemical Engineering and Applied Chemistry,Uni?ersity of Toronto,200College Street,
Toronto,Ontario,Canada M5S3E5
Received5November1997;revised27February1998;accepted2March1998
Abstract
Sulphuric acid pressure leaching of limonitic laterites is the process of choice to recover nickel and cobalt from equatorial lateritic ores,replacing the energy intensive pyrometallurgical methods.
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This process achieves a high nickel and cobalt extraction more than95%with a high selectivity due to simultaneous iron and aluminium dissolution and precipitation.Experiments were carried out using batch pressure leaching techniques.A titanium autoclave equipped with acid injection and sample withdrawal units was employed.Conditions close to the industrial practice were tested:pulp density30%,acid to ore ratio0.2and temperature ranging from230to2708C.Raw limonite and the evolution of the nature of solid products during leaching were characterised using transmission electron microscopy.It was observed that limonite consists of aggregates of needle-like particles of goethite compacted together.Nickel was found to be predominately associated with this phase.During leaching,goethite dissolves continuously liberating nickel whilst iron re-precipitates as dense hematite particles in solution by ex situ precipitation.Several kinetic models for porous solids were also tested.The grain model was finally proposed to best describe nickel dissolution kinetics.The rate-controlling step was suggested to be pore diffusion of sulphuric acid.q1998Elsevier Science B.V.All rights reserved.
1.Introduction
Laterites are oxide ores widely distributed in the equatorial regions.They were formed during laterization,a weathering process of ultramafic rocks that is favoured by
)Corresponding author.
0304-386X r98r$19.00q1998Elsevier Science B.V.All rights reserved.
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PII S0304-386X9800023-1
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D.Georgiou,V.G.Papangelakis r Hydrometallurgy49199823–46
warm climate and abundant https://www.doczj.com/doc/324684701.html,teritic deposits usually consist of three layers, namely the limonitic,the saprolitic and the garnieritic layer.Limonite,which comprises the top lateritic layer,is a homogeneous ore consisting mainly of goethite with which w x
nickel is associated1–3.
Sulphuric acid pressure leaching is the preferred process to recover nickel and cobalt from limonitic laterites.This is reflected by the current activity of many companies in Canada and in Australia.Although several projects for Ni and Co recovery from laterites by acid pressure leaching are now under consideration,particularly in Australia,the only plant currently employing this process is located at Moa Bay,Cuba which is operated by w x
Moa Nickel4,5.Advantages of the acid pressure leaching process include:
1.Low operational cost—sulphuric acid is a cheap raw material—and acid is
regenerated in situ.
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2.No drying and reduction steps are needed,since raw laterite‘as mined’is used.
3.High selectivity is obtained due to hydrolytic iron re-precipitation as hematite.
4.No sulphur dioxide emissions are produced.
5.Recoveries of more than95%for nickel and more than90%for cobalt can be
achieved.
The process is a‘one-pass’with respect to sulphate.As a consequence there is a large
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volume of sulphate tailings gypsum that is generated.Limonitic laterites are ideal for this process due to their low magnesia content and consequently low acid consumption w x6.The chemistry of the process was recently reviewed from an industrial perspective w x5.Sulphuric acid leaching of limonitic laterites is performed at high temperatures ?.
240–2708C in acid resistant autoclaves.Titanium has been found to be the best material of construction.At these temperatures,equilibrium vapour pressure reaches
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33–55atm.Iron and aluminium in the trivalent state,follow a dissolution–precipita-
w x
tion path,forming solid products2,7.
?Iron in the form of goethite and aluminium in the form of boehmite gibbsite,the major phase of Al in limonite,transforms during slurry heating to boehmite at around w x.
135–1558C8,9dissolve to ferric and aluminium sulphates respectively,according to reactions1and2:
FeOOH q3H q?Fe3q q2H O1?.
?s.2
AlOOH q3H q?Al3q q2H O2?.
?s.2
NiO q2H q?Ni2q q H O3?.
?s.2
CoO q2H q?Co2q q H O4?.
?s.2
Nickel and cobalt in the assumed form of‘oxides’,dissolve according to reactions3
w x
and4respectively and remain in the aqueous phase as sulphates7,10.Ferric cations hydrolyse rapidly after the dissolution of goethite,forming directly hematite according
?.
to reaction5or basic ferric sulphate reaction6,which can transform to hematite ?.
reaction7.Basic ferric sulphate formation depends upon leaching conditions and it is
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favoured by very acidic environments high sulphate contents.High temperatures
()D.Georgiou,V.G.Papangelakis r Hydrometallurgy 49199823–4625
w x though,favour the formation of hematite 11,12.These reactions cause the regeneration of the acid consumed by goethite dissolution in the first place:
2Fe 3q q 3H O ?Fe O q 6H q
5?.223?s .Fe 3q q SO 2y q H O ?FeOHSO q H q
6?.424?s .2FeOHSO q H O ?Fe O q 2SO 2y q 4H q
7?.4?s .223?s .43Al 3q q 2SO 2y q 7H O ?H O Al SO OH q 5H q
8?.?.?.?.?.6s 423342Al 3q q SO 2y q H O ?AlOHSO q H q 9?.
424?s .Aluminium cations also hydrolyse,leading to the formation of solid products.Alunite and r or basic sulphate are formed,according to reactions 8and 9respectively.High ?.temperatures above 2808C favour the formation of basic sulphate,but this can also w x form at lower temperatures if the acidity is high 10–12.Again,most of the acid consumed by boehmite dissolution is regenerated.Finally,an acid-to-ore ratio of around 0.2was found adequate for Ni and Co leaching of a limonitic laterite by previous w x investigations 7,10.
Most of the work done in the past involved bulk measurements of solution and r or solids composition after batch experimentation where all samples were obtained at the w x end of reaction period after autoclave cool down 7,10.In the present work,more accurate chemical r mineralogical analysis and experimental procedures were followed w x that enabled quantitative analysis of the chemistry and the reaction kinetics 13.In brief,the objectives of this work were:
1.Study the evolution of solution and solids chemistry during leaching.
2.Derive a simple conceptual model for nickel dissolution kinetics to be used in process
modelling studies later.
2.Experimental
2.1.The ore
The laterite used in this study was an Indonesian limonite and was provided by INCO It was a reddish-brown,clay-like solid,containing 42to 44%water.A particle size analysis was performed and is shown in Fig.1.About 50%of the total number of ?.particles had a size of less than 1m m median size of 0.97m m ,most of them falling in the range of 0.5to 1m m.The mean size of the particles was 1.70m m.Further analysis of bulk and absolute density,pore volume,pore size distribution,as well as surface area are shown in Table https://www.doczj.com/doc/324684701.html,terite is a highly porous material with very fine size pores and a high surface area.Table 2shows the average elemental composition of the Indonesian limonite,as provided by INCO Because of a suspected variability in the Ni and Co content,a sample of each reactor charge was digested in aqua regia and analysed before the material was placed in the reactor.A variability of "10%in the nominal composi-tion was thus identified.Limonite also contains traces of other elements,such as calcium,zinc and copper.The metals comprise 59%of the dried laterite;the balance
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D.Georgiou,V.G.Papangelakis r Hydrometallurgy49199823–46
Fig.1.Particle size analysis of laterite.
?.?.?.
41%is oxygen O and some hydrogen H,since oxides and hydroxides are the main components of laterite.
2.2.Experimental set-up and procedure
Leaching tests were performed in a2-l titanium autoclave,manufactured by the Parr Instrument.Temperature was controlled within"28C by a temperature control system, manipulating both an electrical heating mantle and a water-cooling stream.Agitation was provided by a titanium-made twin impeller that was magnetically driven.The autoclave was equipped with an acid injection device designed by INCO.
A certain amount of‘as mined’laterite was mixed with a pre-calculated amount of deionised water and placed in the reactor.The slurry was then heated up to a
Table1
Solid characteristics of limonitic laterite
y3
Bulk density 1.09g cm
y3
Absolute density 3.73g cm
Porosity0.708
2y1
Specific surface area64.82m g
Average pore diameter0.04m m
Table2
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Elemental composition of the laterite in wt.%of dried solids INCO
Fe Si Al Cr Ni Mg Mn S Co
47.7 3.87 1.9 1.56 1.22 1.030.970.260.14
()D.Georgiou,V.G.Papangelakis r Hydrometallurgy 49199823–4627
?.predetermined temperature in the range of 230to 2708C under continuous agitation.?Upon temperature stabilisation,a certain amount of concentrated sulphuric acid 96.wt.%,corresponding to different acid-to-ore ratios,was injected into the autoclave w x under nitrogen pressure 13.
Samples were withdrawn through a dip tube and cooled by a co-current heat exchanger.A 30m m pore graphite filter,manufactured by Union Carbide,was utilised in order to prevent solids from passing through the sampling tube.Solution aliquots were periodically withdrawn and analysed.After the end of the experiment,the solids were analysed for Ni and Co.A mass balance check on these metals was always within 1to 5%of the initial metal content.In the case of experiments performed to monitor the evolution of solids composition with time,the filter was removed.The slurry samples obtained were filtered and the solids washed and dried in an oven at about 608C for 24w x h.The dry solids were then prepared for transmission electron microscopy analysis 13.
2.3.Chemical analysis of solution
?.Flame atomic absorption spectroscopy FAAS was utilised to analyse the liquid samples,after the proper dilution,for nickel,cobalt,iron and aluminium.A fully ?.automated instrument VARIAN SpectrAA.250Plus was employed for this purpose.In w x calculating Ni and Co extraction,a volume correction formula was used 13:
i y 1i y 1
V y n C q n C YYi M ,i i M ,i
?/i s 1i s 1X s 10?.
M ,i m c r 100?.M ?.?.where V is the initial volume ml of the solution,?the volume ml of the sample i i ?.?y 1.withdrawn each time,C the concentration of M Ni,Co in sample i mg l ,m the M,i ?.initial mass of laterite in g on a dried basis added into the reactor and c the M ?.concentration of M in limonite wt.%dried solids .
FAAS analysis was followed by complexiometric determination of the free acid in w x the samples 14.The free acid measured corresponds to the total sulphate minus that ?bound to metals stoichiometrically.The metal cations present in the samples i.e.,Ni,.Al,Fe,etc.had first to be chelated in order to prevent them from reacting with sodium ?.?.hydroxide NaOH .Calcium cyclohexane-1,2-diaminetetraacetate Ca-CDTA was used w x as the chelating agent 13,14.
2.4.TEM analysis of raw ore and solid products
?.Transmission electron microscopy TEM was utilized in order to produce high magnification photos of the raw ore and the solids during leaching.It was coupled with X-ray analysis and electron diffraction for elemental and mineralogical analysis respec-tively.The sample preparation procedure was the following:a small portion of each sample was incorporated into epoxy resin that was left to harden for 24h at 658C.The samples were then thin-sectioned and y 200mesh slices of approximately 0.1m m
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D.Georgiou,V.G.Papangelakis r Hydrometallurgy49199823–46
thickness were selected and placed on to copper grids.These grids were then formvar coated and placed on brass holders.The samples were finally analysed by a TEM ?.w x
instrument Philips EM430operating at100kV15.
3.Results and discussion
3.1.Limonite characterisation
The distribution of each metal in the several mineral phases existing in limonite is described below.
3.1.1.Fe–Al–Cr
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Goethite a-FeOOH is the dominant phase of iron as revealed by electron diffraction analysis.Fig.2shows a goethite structure under TEM;Fig.2demonstrates that goethite
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is indeed highly porous consisting of aggregates of needle-like particles grains aligned and compacted together.X-ray elemental analysis showed that nickel is associated with the goethite lattice;aluminium and silicon were also present as minor constituents.The
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consistency of the presence of these elements Ni,Al,Si in the goethite lattice always at the same proportion,as testified by the same peak heights of the X-ray spectra, suggests that they exist as substituents of the goethite lattice rather than being bound on its surface by adsorption mechanisms.The substitution of trivalent iron by divalent
w x nickel seems to be facilitated by simultaneous incorporation of tetravalent silicon3.
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Fig.2.Goethite structure under TEM magnification=30,600.
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D.Georgiou,V.G.Papangelakis r Hydrometallurgy49199823–4629
Minor iron phases were also found to exist in the form of alumino-chromite ?.?.
Al Fe Cr O and maghemite g-Fe O as identified by electron diffraction analy-x1y x2423
sis.Aluminium substitutes part of iron in the goethite and chromite lattice.Aluminium
??..?.
also exists as gibbsite Al OH or aluminium oxide Al O but the presence of these
323
structures in this type of limonite was minor.Apart from chromite,chromium was also found many times to be associated with the goethite lattice.
3.1.2.Si–Mg
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Silicon exists in the goethite lattice as previously shown Fig.2.It also exists in the
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form of relatively big quartz SiO particles.Silicon with magnesium form magnesium
2
??..?
silicate particles probably as serpentine,Mg Si O OH rich in nickel Ni substitutes
3254
w x.
Mg in serpentine1,2as shown in Fig.3.However,the amount of such particles in limonite is minor.
3.1.3.Ni–Co–Mn
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As shown above,nickel is a main substituent in the goethite lattice Fig.2.It also
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exists in the magnesium silicate particles Fig.3.Nickel was also found in a third phase
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together with cobalt;possibly asbolane a manganese phase.
3.2.Leaching chemistry
One-hour leaching tests were performed first at30%solids and an acid to ore ratio ?.
a r o of0.2;the temperature range was230to2708C.Samples were regularly
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Fig.3.A magnesium-silicate structure under TEM magnification=21,000.
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D.Georgiou,V.G.Papangelakis r Hydrometallurgy49199823–46
withdrawn and analysed for iron,aluminium,nickel,cobalt and free sulphuric acid concentration.
The concentration profiles of iron and aluminium in the solution are typical of the consecutive reactions1,2,5–9as shown in Figs.4and5.Dissolution of iron is followed by rapid precipitation.At this acid level,it reaches a near-equilibrium concentration of around350mg l y1after60min of reaction time at2308C.The ‘equilibrium’concentration of iron drops to178mg l y1and64mg l y1at250and 2708C respectively.Aluminium also follows the same pattern,but its precipitation is not as fast as that of iron.At2308C aluminium requires45min of leaching time for its
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precipitation rate to overcome its dissolution rate Fig.5.This time decreases to5min and2.5min at250and2708C respectively due to a substantial increase of leaching rate with temperature.At2708C the equilibrium concentration of aluminum is reached after
y1?.
30min of reaction time at a level of around440mg l Fig.5.
Extraction curves of nickel and cobalt are shown in Figs.6and7respectively.About 90%of the nickel is extracted in20min at2508C while the same extraction is obtained in10min at2708C.The final extraction of nickel reaches the value of96to97%.On
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the other hand,temperature has no influence on cobalt extraction Fig.7.Around80% of the cobalt is extracted in10min of leaching regardless of temperature.The final extraction level reaches the value of90–91%in all cases.It appears that,at least80to 90%of cobalt exists in a rapidly leachable phase,probably asbolane.
Extraction of nickel and cobalt is not the only parameter to be considered.Selectivity, w x w x?.
defined here as the M r Fe q Al ratio M s Ni,Co in the aqueous phase after1h of ?.
leaching time to achieve maximum metal extraction,is an equally important parameter. Increasing the temperature from230up to2708C substantially improves the quality of
?the leach liquor and increases selectivity up to six times for both nickel and cobalt Fig. .8.This was expected,since temperature enhances the rate of precipitation of iron and
aluminium cations in the aqueous phase and decreases the solubility of hematite and ?.
alunite main solid products.
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Fig.4.Iron dissolution–precipitation kinetics30%solids-a r o s0.2.
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D.Georgiou,V.G.Papangelakis r Hydrometallurgy49199823–4631
?.
Fig.5.Aluminium dissolution–precipitation kinetics30%solids-a r o s0.2.
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Acidity level is expressed in two ways.First,the mass ratio of acid-to-ore dry is indicative of the stoichiometric quantity of acid placed into the reactor initially.An
w x
alternative way is to express the acidity level by the value of H SO.This value is
24 fundamentally responsible for driving the dissolution and precipitation reactions which take place,and can be followed by chemical analysis during an experiment.Although
?
the stoichiometric acid requirements of iron which consists the bulk of the solid phase .?.
—laterite are zero net acid consumption s0;see reactions1,5,6and7,nevertheless, finite acid consumption is expected during leaching due to dissolution of soluble compounds.Hence,acidity was not expected to remain constant,but to decrease.
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Fig.6.Nickel dissolution kinetics30%solids-a r o s0.2.
()
32
D.Georgiou,V.G.Papangelakis r Hydrometallurgy49199823–46
?.
Fig.7.Cobalt dissolution kinetics30%solids-a r o s0.2.
However,the hydrolytic precipitation of iron and aluminium regenerates acid,eventually leading to stabilisation of the acid concentration.
w x
As seen in Fig.9,H SO initially drops very fast and essentially remains constant
24
w x thereafter in all cases.It was decided therefore,to consider the H SO as being
24 constant during the reaction with a numerical value equal to its average.The latter value
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Fig.8.Selectivity vs.temperature after1h of leaching30%solids-a r o s0.2.
()D.Georgiou,V.G.Papangelakis r Hydrometallurgy 49199823–4633
?.Fig.9.Acidity variation with time 30%solids-a r o s 0.2.
w x was always very close to the final H SO .Average sulphuric acid concentration 24?w x .H SO was defined by the following formula:
24ave t
C d t H A 0C s 11?.
A ,ave t w x w x where,C s H SO ,C s H SO at time t,and t s time elapsed until extrac-A,ave 24ave A 24?tion reached a plateau t s 10,30,45min for 270,250and 2308C respectively at 30%.solids and a r o s 0.2.
3.3.Characterisation of reacted solids
A leaching test was performed at 30%solids,2708C and an acid-to-ore ratio of 0.2.Slurry samples were withdrawn regularly and the solids were very quickly washed,filtered and prepared for TEM analysis.Fig.10demonstrates solids before acid injection ?.and at various times during leaching magnification =122,000.There is no observable structural change of limonite during heating the slurry up to 2708C and before acid injection.It is evident from Fig.10that the aggregates of needle-like goethite particles dissolve continuously during leaching;at the same time hematite particles form in ?.?solution,and perhaps in the cavities pores of the goethite particles ex situ precipita-.tion .Finally,all needle-like goethite particles disappear and the bulk of the residue becomes filled with hematite particles.Electron diffraction analysis of the particles shown in Fig.10confirmed the above crystalline structures.Hematite particles form ?very fast and do not show observable growth during leaching their average size at 2.5.min is approximately equal to that at 30min .Their average size is 0.1to 0.3m m as w x shown in Fig.10.In previous publications 13,16,hematite particles formed after ?.leaching at a low slurry density 1%solids showed a uniform size distribution.At high ?.slurry densities 30%solids hematite particles do not appear as uniform in shape and
()
34
D.Georgiou,V.G.Papangelakis r Hydrometallurgy49199823–46
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Fig.10.Solids before and during leaching30%solids-2708C-a r o s0.2under TEM at a magnification of=122,000.
size as they appear at low slurry densities.In both cases,however,the average particle
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size was the same.Finally,basic ferric sulphate FeOHSO was not observed in any
4
solids sample.
()
D.Georgiou,V.G.Papangelakis r Hydrometallurgy49199823–4635
?
Fig.11.Alunite structure under TEM at a magnification of=30,60030%solids-2708C-a r o s0.2-30min of .
leaching.
Alunite was a secondary precipitation phase.It forms relatively big particles as the
?.?one shown in Fig.11at the end of leaching30min.This is the only solid phase in all .
of our TEM study with which sulphur was found to be associated.Hematite is also present in Fig.11.
Table3
Conditions of experiments
?.?. Experiment%Solids Temperature8C Acid r ore Agitation r.p.m. 1102300.25400
2102500.15400
3102500.25400,600
4102500.35400
5102700.25400
6222300.20450
7222300.25450
8222500.15450
9222500.20450,550,650 10222500.25450
11222700.15450
12222700.20450
13222700.25450
14302300.20600
15302500.20600
16302700.20600
()
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D.Georgiou,V.G.Papangelakis r Hydrometallurgy49199823–46
After5min of leaching,magnesium silicate structures were also found with no nickel content proving that nickel is highly leachable in this phase.Finally,all of nickel and
w x most of cobalt in the manganese phase were leached after30min of reaction15.
3.4.Kinetics of nickel dissolution
Consequently,a series of19leaching tests was performed under various conditions and an attempt was made to fit several shrinking-core-type models to Ni-extraction vs. time curves.The conditions are shown in Table3;experiments3and9were repeated under different agitation conditions.
Fig.12.Effect of agitation on nickel dissolution kinetics.
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D.Georgiou,V.G.Papangelakis r Hydrometallurgy49199823–4637
First of all,leaching tests conducted at various agitation rates—with particles always
?
at full suspension—excluded external mass transfer diffusion through the liquid .
boundary layer from being the rate-controlling step.In fact,the agitation rate had a negligible effect on the rate of nickel dissolution as shown in Fig.12.The same results also serve to demonstrate the degree of reproducibility of the experiments.
3.4.1.The shrinking core model
w x
This is the most widespread model17–19describing fluid–solid reaction kinetics of ?.
dense non-porous particles.All the standard equations of this model were tested and it
?.?
Fig.13.Fitting of nickel conversion X to several equations of the shrinking core model experiment3,Table .3.
()D.Georgiou,V.G.Papangelakis r Hydrometallurgy 49199823–46
38Table 4
Shrinking core models examined
X A t
?.1Film diffusion control-dense-constant size small particles-all geometries
?.2Chemical reaction control-dense-flat plate particles
2r 3()1y 1y X A t
?.1Film diffusion control-dense-shrinking spheres
1r 2()1y 1y X A t
?.1Film diffusion control-dense-large-shrinking spheres
?.2Chemical reaction control-dense constant size-cylindrical particles
1r 3()1y 1y X A t
?.1Chemical reaction control-dense-constant size or shrinking spheres
2r 3()()1y 31y X q 21y X A t
?.1Ash diffusion control-dense-constant size-spherical particles
?.was finally found that Eq.12which nominally describes an ‘ash diffusion control’situation of constant size spherical particles gives an excellent fit to our data:
t
2r 31y 31y X q 21y X s 12?.?.?.
t ?.where X s nickel conversion and t s time for complete reaction min .
Fig.13shows the fitting of several equations of the shrinking core model to nickel ?.?.conversion X at 10%-solids-2508C-a r o s 0.25experiment 3,Table 3.The corre-w x sponding models tested are summarised in Table 417,18.The same was repeated for ?.all experiments shown in Table 3.In all cases,Eq.12showed an excellent fit.This 2?.meant that regression coefficients R for Eq.12,always ranged between 0.9130and 0.9982with an average of 0.9774as compared to the other equations of Table 4which 2w x always scored lower R values 13.
?.?.Porosity measurements Table 1and TEM photos Fig.2though,proved that goethite particles are highly porous.Furthermore,it was found that goethite particles consist of needle-like grains compacted together which dissolve continuously during ?.leaching with no ash layer forming on their surface Fig.10.Thus,although the ??..shrinking core model Eq.12fits the mathematics,it is not consistent with the physical picture of limonite leaching.A review of fluid–solid reaction models for porous w x particles 20is thus required before proceeding further.
3.4.2.The homogeneous model
w x According to this model 21,22,the solid particle is considered to be an ensemble of small lumps distributed uniformly throughout the solid phase.The model assumes two stages of reaction:one controlled by chemical reaction and the other by diffusion.Since reaction is faster near the surface than in the interior of the particle,after a certain time the solid reactant near the surface will be completely exhausted forming an inert product ?.layer ash .As the reaction progresses,two zones appear:an outer zone in which the
()D.Georgiou,V.G.Papangelakis r Hydrometallurgy 49199823–4639
?.solid reactant is completely exhausted the diffusion zone ,and an inner zone where the ?.reaction still takes place the reaction zone .
Under the assumption that the fluid film resistance is negligible,there are two cases.Either the diffusion of a reactant A in the fluid phase through the solid,or the chemical reaction between A and the solid phase is the controlling step.In the case that diffusion of A is the slowest step,the model comes out with the following equation:
u y 2r 3s 1y 31y X q 21y X 13?.?.?.)u y
where u is dimensionless time,defined as:
y u s k C t 14?.y y A ,f ?y 1y 1.)where k l mol min is the reaction rate constant based on volume;u is a y y ?.dimensionless time for complete reaction constant ;and C is the bulk concentration
A,f ?y 1.)2
w x of the fluid reactant mol l .In this case u is proportional to R 21,22.As seen,
y P ?.?.Eq.13is identical to Eq.12,which gives an excellent fit to the experimental data.?.Again,however,the assumption of an inert product layer ash forming on the reacting ?.?.particle i.e.,hematite is not supported by the TEM photos of the solids Fig.10.
3.4.3.The uniform pore model
w x This model 20,23,24assumes that the solid contains uniform,open and completely ?.wetted cylindrical pores capillaries .The porous solid body will react in a spatially uniform manner;its physical size will not change but the consumption of the solid phase will lead to progressive enlargement of the pores,till the whole structure collapses.For ?regularly spaced,uniform cylindrical pores and with no diffusional limitations chemical .w x reaction control ,this model gives the following formula 20,24for the calculation of conversion:2′t G y 1y t r t 0
c X s 1q y 115?.
?/?/1y ′t G y 10c where ′is the initial porosity of the solid particle,and G is a structural parameter 0?.greater than zero which satisfies the following equation:
43′G y G q 1s 016?.027
The time constant t equals the time for the pore radius to become twice that at t s 0.It c is given by the following equation:
r r po m t s 17?.c r
?.?where r is the initial pore radius cm ,r is the molar density of the solid phase mol po m y 3.?y 2y 1.cm and r is the rate of reaction mol cm min .
?.?.For ′s 0.708Table 1,Eq.16gives 3real roots:G sy 3.5010,1.1665,2.3345.0The negative value is unacceptable and for G s 1.1665negative values of conversion X ?.are obtained when Eq.15is employed.Thus,the accepted root is G s 2.3345.Fig.14?.?.compares the data from the experiment 3Table 3with the predictions of Eq.15.
()D.Georgiou,V.G.Papangelakis r Hydrometallurgy 49199823–4640
?.?.Fig.14.Test of uniform pore model,Eq.15experiment 3,Table 3.
It is evident from Fig.14that the uniform pore model gives a poor fit.In addition,by using the trial-and-error method,the minimum value of t was found to be equal to 108c min,for all experimental data.This is unacceptable,since the reaction is over in less than 60min in most of the cases.Presumably,the simplicity of the geometry and r or the assumption of chemical reaction control in this model lead to the failure of the correct prediction.Unfortunately,no equation could be found in the literature regarding a uniform pore diffusion control model.
3.4.4.The random pore model
w x This model 20,25,26also assumes that the solid particles contain void elements of similar geometry,such as cylindrical capillaries or spherical voids with random intersec-tions.An analytical expression for the conversion has been obtained for chemically controlled reactions:2)k t )X s 1y exp y k t y C
18?.?/2with
k )s r s 19?.
04p L 1y ′?.00C s 20?.
2S 0
()
D.Georgiou,V.G.Papangelakis r Hydrometallurgy49199823–4641
?.
Fig.15.Conversion rate vs.conversion experiment3,Table3.
?2y1.
where s is the initial molar surface area m mol,L the initial characteristic length 00
?y3.
of a pore per unit volume m m and S the initial reaction surface area per unit
?2y3.)
volume m m.It is obvious that k and C can be obtained by multiple regression ?.?2.
of ln1y X vs.t,t,from experimental data.
?.
Eq.18was tested but negative values of the structural parameter C were obtained
?.?2.?after multiple regression of ln1y X with pairs of t,t,from all experiments Table .3.Most possibly the assumption of chemical reaction control was wrong.
In the case that diffusional limitations exist, e.g.,external mass transfer,pore diffusion or ash diffusion,complex mathematical formulas,or only numerical solutions
w x
can be obtained,as presented by Bhatia and Perlmutter26.They concluded that ?.
intrapellet pore diffusion becomes important at low values of the structural parameter ?.w x y6y3?.62 i.e.,C?026.For L-10m r m Fig.2,′s0.708,S s241.8=10m
000
y3?.?.y23
m s=r,Table1,it is calculated from Eq.20that C-6.28=10.Fig.15 s
?. shows the pattern of conversion rate vs.conversion for experiment3Table3.
?Conversion rate was calculated from the slopes of the conversion vs.time curve Fig. .w x
14for that experiment.This plot is used to test the model13,26.The same pattern of
?. conversion rate vs.conversion was obtained from all experiments Table3.The very low value of parameter C and the pattern of the previous diagram indicate that ?.w x intrapellet pore diffusion probably dominates leaching of nickel from limonites13,26.
3.4.5.The grain model
w x
According to this model24,27,28,solid particles are visualised as pellets consisting of individual dense grains compacted together.Each grain reacts individually following
()D.Georgiou,V.G.Papangelakis r Hydrometallurgy 49199823–46
42an unreacted shrinking core pattern.The fluid reactant diffuses through the interstices of the solid grains while undergoing reaction.As a result,the solid reactant is progressively depleted with a gradual decrease in the extent of reaction of the solid grains,as we move toward the centre of the pellet.When diffusion through the pores is the rate-controlling step,the model gives the following expression for spherical particles:
t )
2r 3s 1y 31y X q 21y X 21?.?.?.2s ?
where t )and s are given by the following equations:
?bkC A A ,f g )t s t 22?.
?/r F V m g g 1r 2R 3k 1y ′A ?.P g
s s 23?.
??/32D F V e g g Where F is the grain shape factor taking the values of 1,2,3for a grain shape of flat g ?2.plate,cylinder or sphere respectively.A and V are the external surface area cm and g g ?3.?.volume cm of grain respectively;R is the radius of the pellet cm ,′is the porosity P ?.?y 2y 1.of the pellet particle and k the reaction rate constant mol m min .Parameter b is ??.a stoichiometric factor b s 1from the reaction 3,where 1mol of NiO reacts with 1.?y 3.?.mol of H SO and r the molar density of solid particles mol cm .Again,Eq.2124m is similar to the one of the shrinking core model of dense particles under ash diffusion ??..control Eq.12.
?.?.?.Fig.16.Fitting of nickel conversion X to Eq.2330%solids-a r o s 0.2.