saltpeter extraction and modelling of caliche mineral heap leaching

Available online at www.sciencedirect.com

(2008) 103–114www.elsevier.com/locate/hydromet

Hydrometallurgy 90

Saltpeter extraction and modelling of caliche mineral heap leaching

John A. Valencia a, David A. Méndez a, Jessica Y. Cueto b, Luis A. Cisternas a,b,⁎

a Department of Chemical Engineering, Universidad de Antofagasta, Antofagasta, Chileb Center for Mining Scientific Research and Technology (CICITEM), Antofagasta, Chile

Received 11 April 2007; received in revised form 26 September 2007; accepted 2 October 2007Available online 11 October 2007

Abstract

The leaching of heaped Caliche minerals represents a valid alternative for the saltpeter extraction, giving good recovery levelswith excellent economic projections and technical results when compared with existing technology. This study reports onexperimental tests of the leaching of this mineral in columns in which we determined the recovery of nitrate and magnesium atdifferent heights through the bed of the mineral. The columns were sampled at three different heights, recovering the strongsolution from sample ports at each height and calculating the recoveries of the target materials at each height. These variables wereanalyzed as a function of time and irrigation ratio, thus obtaining empirical kinetic expressions. A simple mathematical model wasconstructed which represented the leaching process for the solutes, considering the variation in height of the bed of the leachedmineral. The model showed a good fit for predicting the concentration of nitrate and magnesium.© 2007 Elsevier B.V. All rights reserved.

Keywords: Heap leaching; Caliche; Sodium nitrate

1. Introduction

Saltpeter is a white salt which is translucent and bright,composed primarily of sodium nitrate. It forms thin crustson the surfaces of rocks and walls of the mineral and oftenforms a superficial horizon of some soils in Chile(Pokorny and Maturana, 1997), Spain, Iran, Egypt, andIndia. Saltpeter is commercially important as a fertilizer,food preservative, in glass manufacture, and in somemedicines as a diuretic. It was historically important in themanufacture of gunpowder, and is currently used inexplosives, fireworks (rockets), and matches, as well as inmetallurgical smelting agents. It is an important raw

⁎ Corresponding author. Department of Chemical Engineering,Universidad de Antofagasta, Antofagasta, Chile.

E-mail address: [email protected] (L.A. Cisternas).

0304-386X/$ - see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.hydromet.2007.10.001

material for obtaining nitrogen in the manufacture ofcertain compounds such as nitric acid, and as an oxidizingagent in many industrial chemical processes.

The main procedures for the extraction of nitrate fromcaliche mineral were worked out by Pedro Gamboni(a Chilean) in 1853. Twenty years later the Englishmechanical engineer James T. Humberstone adapted acountercurrent leaching process originally developed byShank for obtaining soda ash by the LeBlanc process. Thelatter method allows processing caliche minerals contain-ing 15%nitrates. After the invention of synthetic saltpeter,the Shank process became uneconomical, and wasreplaced by a cold leaching process developed byGuggenheim in the 1920's. Presently, this process isonly used at two worksites, including Maria Elena andPedro de Valdivia in northern Chile. More detailedinformation in this area has been presented by the study ofWisniak and Garces (2001).

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http://dx.doi.org/10.1016/j.hydromet.2007.10.001

Nomenclature

A Column cross-sectional areaa Parameter Eq. (2)b Parameter Eq. (2)Cj,i Concentration of species j in section ihi Height of section iH Initial height of each sectionkj,i Solution constant of species j in section i, m/hL Total height of the columnl Mean particle size, mmm Parameter of Rosin Ramler modeln Constant in Eq. (11)qi Flow of solution exiting section iqi Flow of solution exiting columnRji Radius of soluble particle j in section iRi Particle radius in section irr Irrigation ratio, m3/tonR Initial radius of soluble particlesSi Section iVsi Cylindrical volume of section iVGi Volume of insoluble particles in section iVji Volume of soluble particles j in section ix Particle size, mmzi Adimensional height section i

Greek lettersα A dimensional concentrationβ Equation parameter 18γ Equation parameter 17ρ Densityξi Relative porosity of section iσ Adimensional radiusθi Delay time in section iτ Adimensional time

Subscripti Sectionj Soluble species

Superscripte Experimentals Saturation

104 J.A. Valencia et al. / Hydrometallurgy 90 (2008) 103–114

A current existing demand on the world market forlow grade saltpeter in fertilizer manufacture haspromoted the exploitation of caliche mineral in theTarapacá and Antofagasta regions of Chile. This led tomodifications in the original methods of extracting

nitrate. Since 1990 the leaching process has been usedon heaps of the mineral at Pampa Blanca, Chile,similarly to that used with some other metals (Dixon andHendrix, 1993; Qin et al., 2007; Wan and LeVier, 2003;Cariaga et al., 2005), with the leaching agent for caliche

Table 1Results of chemical analyses of the caliche mineral for columnleaching in the present study in untreated form (RAW) and classifiedinto particles N9.53 mm (CLASS.)

Element Unit Raw Class

I2 ppm 647 509Insoluble % 54.94 60.19Na % 9.36 8.08K % 0.99 0.73Ca % 2.10 1.50Mg % 0.78 0.70Cl % 4.60 3.85SO4 % 14.97 12.55NO3 % 10.15 8.80CO3 % 0.03 0.05KClO4 % b0.1 b0.1Moisture % 2.23 3.20Ionic balance −0.39 −0.94

105J.A. Valencia et al. / Hydrometallurgy 90 (2008) 103–114

being water. The leaching of piled minerals represents avalid alternative, with excellent economic and techno-logical possibilities and good levels of recovery whencompared with current extraction technology andtransformation of the product.

The leaching of heaps consists of feeding the solventonto a mass of mineral having a determined grade, sothat the solvent percolates through the mineral, carryingaway the solute. The enriched solution is recovered fromthe base of the mineral mass which rests on animpermeable mineral or plastic-covered base.

The leaching of caliche differs specifically from theleaching of copper and precious metals minerals. Withcaliche there are several soluble species while in the caseof copper and gold minerals there are few. In the case ofcopper and gold minerals, dissolution occurs through achemical reaction and the resulting solutions are diluted;in the case of caliche, dissolution is by simple solubilityand the final solutions must be concentrated.

The objective of the present research is to study theprocess of leaching of caliche heaps, with particularattention to the recovery of nitrate and magnesium. Thelatter is important because it is a control variable in thecaliche leaching process. The objective was pursued byestablishing experimental tests and then developing amathematical model representing the leaching processwhich would allow better understanding of the phe-nomena involved, and leading to new possibilities forimproving the technology.

2. Experiment

2.1. Materials and equipment

Testing was carried out in columns using calichemineral from the Antofagasta Region of Chile. Specificchemical analyses were carried out on the types and gradevalues of materials composing the mineral. Analyticalmethodology applied included volumetric oxidation–reduction for iodine (I2), gravimetry for the insolublesand sulphate (SO4), atomic absorption spectrometry (AA)for sodium, potassium, calcium, and managanese (AA;Varian Corp., model 220FS instrument), precipitationvolumetry for chlorine (Cl−), nitrate (NO3) and perchlorate(KClO4) were measured by molecular absorption using aUNICAMCorp. model UV2 instrument, carbonate (CO3)by acid–base volumetry, and moisture by difference inweight. The results are shown in Table 1 (raw column).

Mineralogical composition was determined usingX-ray diffraction using a Siemens model 5000 automat-ed and computerized diffractometer. This analysisprovided a general impression of the species more or

less abundant in the sample; abundant species were thoseoccurring at above 5% and the less abundant speciesthose occurring below this percentage.

The goniometer used was a vertical Braga–Brentano,with a wave-length radiation of 15,406 Å (CuKα1). Thesecondary monochromator was of graphite, with 1 mm/1 mm/0.1 mm slits. The scanning range was between 3and 79° (2θ), time interval 1.0 s, and the database usedwas that of the International Center of Diffraction Data(ICDD). The main species observed included: nitrate(NaNO3), halite (NaCl), sodium anorthite ((Ca,Na)(SiAl)4O8) and quartz (SiO2). The minor speciesincluded: anhydrite (CaSO4), glauberite (Na2Ca(SO4)2), loeweite ([Na12 Mg7(SO4)13] 15H2O), calcite(CaCO3), polyhalite (K2Ca2 Mg(SO4)4 2H2O), prober-tite (NaCa(B5O7)(OH)4 3H2O), gypsum (CaSO4 2H2O)and illite–montmorillonite (insoluble clay).

A granulometric analysis of the mineral was carriedout using the following Tyler screens: 1″, 3/4″, 1/2″, 5,8, 20, 30, 70 and 100. The results obtained are shown inFig. 1, together with the results of fits to the distributionof particle size proposed in the Rosin–Ramler model(see Macías-Garcia et al., 2004), where x represents theparticle size in millimeters (mm), l is the mean size ofthe particle and m is the adjustable parameter charac-teristic of the particle distribution.

Accumulated k Retanied ¼ exp � xl

� �mh ið1Þ

In the case of the caliche analyzed, the value of l was12.156 mm, and of m was 1.624, with a correlationfactor R2 =0.9943 and an estimated standard error of0.0282.

Preliminary leaching tests were carried out in columnswhich demonstrated that large amounts of fine material

Fig. 1. Experimentally obtained granulometric particle size distribution (PSD) of caliche mineral of the present study compared with the theoreticalRosin–Ramler distribution (Macías-Garcia et al., 2004).

Fig. 2. Schematic diagram of equipment used in the experiment.


was formed, causing problems due to channeling, and totransport of the fines. In order to avoid these problemswe decided to classify the mineral to be leached, loadingthe columns with material having particle sizes greaterthan 3/8 inch (9.53 mm). In order to determine theeffect of the classification procedure, the chemical com-position of the mineral was re-determined, producing theresults presented in Table 1. No significant differenceswere found between the initial results (raw) and thosepresented (class.) in Table 1. The preliminary tests werealso used to estimate the time required for the mineral tobe completely wetted prior to beginning the leachingproper; the time required for this was 10 h for the totalmineral loaded.

2.2. Procedure

Leaching tests were carried out following methodstypically used by the industry (NEN 7343, 1995), butusing water as the leaching solution. The procedures forstorage and transport of the solids used were based onCEMA (Conveyor Equipment Manufacturer Associa-tion) and ASTM (American Society for Testing andMaterials) norms.

CEMA indicates that the criterion of the dimensionof the experimental model can be a cylindrical recipientwith a diameter of about 20 times the particle diameter.Thus for carrying out the tests a column was used withan internal diameter of 200 mm since more than 89% ofthe mineral loaded had a diameter of less than 20 mm.

In order to simulate a leaching process for columns ofdifferent heights, a column was prepared which wasdivided into three different heights of the mineral, where

samples of the leaching solution could be removed fromthe column at each of the three heights. Enrichedsolution samples extracted from each height could then

Table 3Results of chemical analyses on residue of leached caliche mineralremaining in the leaching column

Element Unit Content

I2 ppm 37Insolubles % 88.86Na % 0.09K % 0.26Ca % 2.38Mg % 0.14Cl % 0.01SO4 % 6.23NO3 % 0.06CO3 % 0.00KClO4 % b0.1Moisture % 17.54Ionic balance −1.41


be analyzed for concentrations and recoveries of nitrateand magnesium. Divisions of the mineral at the differentheights in the column were established by installing aperforated plexiglass plate and a drain bib at each heightfrom which samples of the leaching solution could beextracted. A pad of glass wool was installed at each levelof the mineral to prevent the movement of fines fromone level to the next.

The experimental scheme is shown in Fig. 2, andTable 2 lists the disposition of the mineral moduleswhich define the different heights in the column.

A low flow rate of water (4.8 l/h m2) was deliveredby a peristaltic pump in order to minimize transport offine particles by the leaching flow. The tests werecarried out at room temperature, using potable water at atemperature of about 25°C.

The mineral in the columns was irrigated at first untilcompletely wetting the entire bed and then the solutionwas maintained without draining up to 10 hours, whichwas the period selected based on preliminary tests, sothat the dissolving fluid at the exit port from each heightwould be the same as that entering and would reduce theeffect of absorption of moisture by the mineral. This wasthen followed by continuous dropwise irrigation. Thewater was fed into the first module, from which it wasdrained (solution from height 1), then directed into thesecond module (solution from height 2), and finally intothe third (height 3).

Continuous monitoring was carried out, takingsamples every 12 hours from the outputs of eachmodule. After 250 h of irrigation, entry of water intomodule #1 was stopped and the leaching solution wasallowed to flow until each module had been drained.Representative bed samples were then taken from eachmodule in order to make mineralogical analyses of theresidue, determine which salts had been leached, andmaking other analyses of the solutions.

Table 3 shows the results of chemical analyses of theleached mineral residue left in the column. This samplewas prepared from a composite of subsamples ofresidues at each of the levels. Assays of nitrate andmagnesium for each level are given in Table 4.

The results of the chemical analyses of the leachedmineral showed that since most of the soluble species hadbeen removed, the percentage of insolubles in the residue

Table 2Characteristics of leached modules

Height (modules) Column height, mm Mass of caliche loaded, Kg.

1 910 27.202 1820 54.403 2730 81.60

increased from 60.19 to 88.86%. The percentage recoveryof nitrate reached 95.62%, magnesium 94.59%, sulfate68.28%, iodine 95.35% and chloride 99.83%. The X-rayanalysis showed the species in major abundance in theresidue were quartz (SiO2), bassanite (CaSO4∙0.5H2O)and sodium anorthite [(Ca, Na)(Al, Si)4O8]. The lesserabundant species included orthoclase (KAlSi3O8), calcite(CaCO3), Mg-vermiculite [(Mg2.36Fe0.48Al0.16)(Al1.28Si2.72)O10(OH)2(H2O)6 Mg], montmorillonite [Ca0.2(Al,Mg)2Si4O10(OH)24H2O], probertite [NaCa(B5O7)(OH)43H2O], kaolinite [Al2Si2O5(OH)4], loeweite [Na12 Mg7(SO4)13∙15H2O],moscovite [KAl2(Si3Al)O10(OH,F)2] andgypsum (CaSO4∙2H2O).

When comparing the mineralogical results from theleached residue with those in the original mineral sample,it can be seen in that the species containing the nitratedisappeared from the more and less abundant speciesresulting in a total recovery of nitrate of over 95%. In thecase of the magnesium, the species which contained thiselement in the raw mineral were loeweite and polyhalite.The first of these remained present in the residue (probablypartially dissolved), but the polyhalite was completelydissolved. It was apparent that the dissolution kinetics ofloeweite and polihalite were different, governing thesolution behavior of the magnesium as noted in assays ofthe strong solution from different levels, which gave twodifferent solubility rate curves for magnesium.

3. Results and discussion

3.1. Leaching recovery as a function of irrigation time

The percentage recovery of nitrate and magnesium weredetermined from the initial grade value of the mineral and fromthe final analysis of the leached residues in each module. Thetrends in percentages of recovery of nitrate are shown in Fig. 3as a function of irrigation time.

Table 4Results of column leaching tests and estimations of percentages of recovery as a function of residue assays

Height Irrigationtime, h

IrrigationRatiom3/ton

Heightof residuemm

Mass ofresiduekg

Residue assays,% %, Recovery

NO3 Mg NO3 Mg

1 250 1.36 600 17.39 1.41 0.046 89.75 95.802 336 0.92 1200 34.74 0.60 0.058 95.65 94.683 420 0.76 1800 34.74 0.60 0.141 95.62 87.16


The nitrate recovery curves showed that excellent percen-tages of recovery were obtained at heights 2 and 3 (Table 4)when compared with the recovery obtained at the lowestheight. The best dissolution was observed at the lowest height(Height 1) during the initial hours of irrigation. The lesseramount of recovery obtained at the first height can beexplained by the fact that the leaching time was less than atthe others levels, resulting in less dissolution of the nitrateat the lower level. This is shown by the lower levels of nitratein the leached residues in Table 4, it is also possible todetermine the final height of each mineral leached, as thisdecreases by 34% compared with the initial, and the mass ofthe gravel decreases by 36% compared with the initial mass ofmineral loaded. These percentages are approximately the samefor each height of mineral.

The concept of the kinetic as mentioned above is moreclearly demonstrated by analysis of the magnesium results(Fig. 4). That is, solution of the magnesium was more rapid inthe lower portion of the column. Nevertheless, there was adifference between the magnitude of solution of the magne-sium and that of nitrate, as in the case of magnesium therecovery is greater at Height 1 although the irrigation time atthis height was less than in the others as shown in Table 4.

3.2. Leaching recovery as a function of irrigation ratio

A more detailed analysis of the behavior of the recovery ofnitrate and magnesium is obtained when it is observed as a

Fig. 3. Percentage recovery of nitrate (NO3) from different

function of irrigation ratio. The term irrigation ratio, rr,represents the quotient between the volume of the leachingsolution fed and the tonnage of mineral being irrigated, iswidely used in the mining industry instead of leaching time,since the operational conditions may vary and the leachingtime may be a variable, which is difficult to quantify. Incontrast, the volume of leaching solvent is easily quantified.The irrigation ratios obtained in the test were less at Heights 2and 3, since they represented double and triple the mass thatcontained at Height 1.

With respect to the recovery of nitrate as a function ofirrigation ratio (Fig. 5), it can be noted that at the greatestheight, the kinetic begins slowly until reaching an irrigationratio near 0.3 m3/ton, then beginning to accelerate untilreaching and exceeding the kinetic curves of Heights 2 and 3.The contrary case is observed at the lowest level (Height 1)which shows a rapid kinetic with the lowest irrigation ratios,but as these increase, the kinetic slows, becoming practicallyconstant for irrigation ratios greater than 1.2 m3/ton. As mightbe expected, in the middle level (Height 2), there isintermediate behavior between the two extremes mentioned.Nevertheless, the greatest recovery is obtained from the middlelevel, and this can be attributed to the fact that a sufficientirrigation ratio is not obtained at the greatest height (Height 3)for obtaining a greater nitrate recovery5.

The behavior of the recovery of magnesium as a function ofthe irrigation ratio (Fig. 6) at the lowest level (Height 1) hasthe more rapid kinetic, which is subsequently reached by the

heights in the column as a function of irrigation time.

Fig. 4. Percentage recovery of magnesium (Mg) from the column at different heights as a function of irrigation time.


kinetics of the other levels, although these do not produce thesame recovery as the first, since they never achieve anirrigation ratio of greater than 1.0 m3/ton.

The experimental data were fit to empirical expressions,finding that the following models provided satisfactory fits forall the heights:

Recovery ¼ 1� exp �a � rrb� � ð2Þ

Where rr is the irrigation ratio. The parameters a and b ofempirical expression 2 are given in Table 5, together with thecoefficient of fit R2 and a standard error estimated for each ofthe fits. The parameters were obtained by linearizingexpression 2, and fitting the data to a straight line.

3.3. Leaching model

Models have been found in the literature which haveanalyzed the heap leaching process, considering unreactedcore model with generation of ash (see for example da Silva,2004 and KNona and Liddell, 2005). Therefore those works

Fig. 5. Experimental recovery of nitrate (NO3) and

have not included the variation of particle size withoutgeneration of ash, with which is generated a decrease in theheight of the bed as we wish to demonstrate as follows.

We will consider that the column is cylindrical in section,and represents an element of volume within the heap. Thiscylinder is then subdivided into i sections, with the volume ofeach section represented by VS,i equal to the volume of acylinder, i.e. VS,i=A hi, where hi is the height of the cylindricalsection and A represents the transverse area of the bed. Thelength of the column L, can vary as the reaction proceeds aswill be seen below. Fig. 7 shows the division of the columninto sections which have an input flow of q0 to its upperportion and output flow qL from its lower portion. Dissolutionof one or various species occurs in each section.

The model developed below considers the followingassumptions:

1. A plug flow through the mineral bed is assumed, althoughdue to the mathematical complexity of the resolution, themodel is represented by completely mixed reactors in serieswith a time delay. In this way, for each given section, a

kinetic fit, as a function of irrigation ratio.

Fig. 6. Experimental recovery of magnesium (Mg) and kinetic fit, as a function of irrigation ratio.


completely mixed reactors with a time delay was considered.In this work only 1 section for height was necessary.

2. It is assumed that the solid to be leached occurs as particles ofpure mineral without mixtures of insoluble materials or othersoluble species, also, that the insoluble particles do notcontain soluble materials and thus do not take part in theleaching process.

3. For the soluble particles, it is assumed that dissolvingeffects the shrinking of spherical particles, without theproduction of ash, so that the particles progressivelydecrease in size, and with this there is a variation in theheight of the bed, which decreases with leaching of thematerial. The leaching of nitrate from caliche generateslittle residue, and few deposits (this differs from theleaching of copper sulfide minerals where residues aregenerated and deposits are formed due to the formation ofsulfur on the gangue and even on the mineral).

4. For simplicity it is considered that the porosity of the bed isconstant, even though the porosity of the mineral changesdue to removal of soluble species, and there are variationsin the height of the bed. The geometry of the solublemineral particles was considered to be spherical.

5. The temperature for any effect was considered constant,that is, no consideration was given to salt solubility,changes in density, and kinetics of the dissolution resultingfrom temperature changes.

6. The size distribution of the mineral particles to be leachedwas not considered. A single mean particle size was

Table 5Parameters for the recovery fit of nitrate (NO3) and magnesiumleaching of caliche mineral in columns at different heights

Height Nitrate Magnesium

a b R2 a b R2

1 2.01 0.70 0.96 2.25 0.99 0.992 3.94 1.19 0.99 3.01 1.20 1.003 3.91 1.32 0.99 2.59 1.20 1.00

assumed. This was done in order to obtain a simpleleaching model, and considering that the leaching processis carried out considering uniform particle sizes to avoid,on one hand, obstructing the passage of the solution by fineparticles, and on the other hand, decreasing the percentageof recovery due to the presence of larger particles.

7. The saturation concentration of a determinate speciesdepends on the other dissolved species and therefore itsthe changes in the time. The saturation concentration formagnesium was assumed to be 20 g/L. and for NO3 250 g/L as determined by experimentally saturating a solutionwith the initial mineral.

Fig. 8 shows a section which assumes the existence ofspherical particles of gangue (insolubles) and soluble specieshaving the same initial radius. The section has a total volume ofVS,I, which represents the sum of the volume of the insolubleparticles VG,i, plus the volume of the soluble particles,PJ

j¼1 Vj;i, and the volume of the interstitial solution, Vi.

Fig. 7. Division of the leaching column into sections.


The relation between volume Vi and VS,i is given by theporosity, ξi.

ni ¼Vi

VS;ið4Þ

ni ¼Vi

VG;i þPJj¼1

Vj;i þ Vi

ð5Þ

It is assumed that the particles are spherical, and thus, thevolume of each type of particle that will be leached in thesection of the column is:

Vj;i ¼ Nj;i43pr3j;i ð6Þ

Where Nj,i is the number of particles of species j containedin volume VS,i , whose particle radius is rj,i.

The porosity of the bed may change with time, in relation tochange in the volume of the solution Vi and less species whichare dissolved Vj,i. Nevertheless, in the present study it isassumed that the porosity is constant and equal at a mean valueduring the leaching. This supposition is required to maintainthe simplicity of the equations of the model.

Deriving Vj,i with time, following Eq. (6), we obtain:

dVj;i

dt¼ 4pNj;ir

2j;i

drj;idt

ð7Þ

Using Eq. (5) and replacing Eq. (7) it can be shown that:

dVi

dt¼ 4pni

1� ni

XJj¼1

Nj;ir2j;i

drj;idt

ð8Þ

For convenience, it is taken into account that Vi=ξiAhi. Thus,in changing the volume of the solution, we also change theheight of the cylindrical section hi, since it is considered that the

Fig. 8. A Distribution of the material in a cylindrical section of the column pria cylindrical section of the column after a time period during which leaching

particle dissolves radially, thus causing a lowering in the heightof the bed.

Adhidt

¼ 4p1� ni

XJj¼1

Nj;ir2j;i

drj;idt

ð9Þ

Eq. (9) shows the change of hi depends of the instantaneousparticle dissolution area and the change of particle size, wherethe initial condition for height is hi(0)=Hi. It is reasonable toconsider that each section has the same initial height andtherefore hi(0)=H. Later will be demonstrated particle sizedecreases over time, and therefore we expect hi decreases.

The variation in radius of leached particles is related to thesupposition that these particles dissolve without leaving ash, andtheir size becomes reduced radially. Simultaneously, the rate inmass reduction of each particle is proportional to the surface areaavailable for the dissolution and to the n power of the difference inconcentration between the particle surface (saturation concentra-tion, Cj

s) and the concentration in the bed (Cj,i), following asolution mechanism shown in Fig. 9 for a single particle. If wedefine the mass of a single particle as follows:

43qjpr

3j;i ð10Þ

With a constant particle density ρ ji, the change in the massof the particle is:

4pqjr2j;i

drj;idt

¼ �kj4pr2j;i Cs

j � Cj;i

� �nð11Þ

Simplifying,

qjdrj;idt

¼ �kj Csj � Cj;i

� �nð12Þ

Where kj is a dissolution constant or mass transfer coef-ficient in m/h, n is a constant (a value of 0.6 was assumed inthis work), Cj

s is the saturation concentration of j and Cj,i is theconcentration of chemical species j in volume Vi, and where

or to initiation of leaching of species, t=0. B Distribution of material inof species has begun, t≠0.

Fig. 9. Transient balance of material of a particle in being dissolved.


the initial condition for size is rj,i(0)=Rj,i. In general we canconsider that all the sections have the same initial particle size,this mean rj,i(0)=Rj. Also in this work all soluble species jhave the same initial particle size and therefore rj,i(0)=R. InEq. (12), the negative sign implies that the mass is becomingsmaller, and is contributing to the volume of solution Vi.

Based on the equations obtained, it is possible to conceiveof each cylindrical section of the column as a completelymixed reactor which functions in a quasi-steady state, due tothe change in the volume of the solution. For a section i, thematerial balance for each dissolved species can be writtenassuming the controlling volume is the solution that carriesaway the dissolved species, thus having a positive sign for theexpression of the reaction speed. The material balance is asfollows:

ddt

ViCj;i

� � ¼ qi�1Cj;i�1

þ 4pNj;ikjr2j;i Cs

j � Cj;i

� �n�qiCj;i ð13Þ

In this equation, qi represents the flow of solution which exitsthe present section i, while qi−1 is that which comes from thepreceding section. Considering that qi−1=qi=q and Vi=ξiAhi,the definitive expression remains in the following form:

niACj;idhidt

þ niAhidCj;i

dt¼ qCj;i�1 þ 4pNj;ikjr

2j;i

� Csj � Cj;i

� �n�qCj;i ð14Þ

Simulation were developed that indicate that the volumetricflow rate changes between 0.07% and 0.36%, confirming theprevious supposition. In this last equation, we also have toconsider a delay θi for Cj,I, specific for each section of thecolumn.

Since the variation in height depends on changes in thevolume of the dissolved species, we must write this samematerial balance for all the species susceptible to beingdissolved.

Eq. (14) shows an integral-differential equation which is nolinear. This equation gives Cj, i(t) under initial condition Cj,i(0)=Cjs. Replacing it in Eq. (12) rj,i(t) may be obtained and then

replace this last function in Eq. (9) to obtain hi(t).Eqs. (9), (12) and (14) can be re-written as a function of the

following adimensional variables:

aj;i ¼ Cj;i

Csjzi ¼ hi

Hrj;i ¼ rj;i

Rjs ¼ qt

AHð15Þ

From which is obtained

dzids

¼XJj¼1

gj;ir2j;i

drj;ids

ð16Þ

drj;ids

¼ �bj 1� aj;i� �n ð17Þ

aj;idzids

þ zidaj;ids

¼ 1niaj;i�1 þ kj;ir

2j;i 1� aj;i� �n� 1

niaj;i ð18Þ

with

aj;i 0ð Þ ¼ 1 zi 0ð Þ ¼ 1 rj;i 0ð Þ ¼ 1

where

gj;i ¼4pNj;iR3

j

1� nið ÞAH bj ¼kjCsn

j AH

qjRjq

kj;i ¼4pNj;ikjR2

j Cs n�1ð Þj

qni

ð19Þ

It should be observed that parameter γj,i represents thefraction of the volume occupied by the soluble species j insection i. Also, parameter βj,i represents two ratios, the ratio ofdissolving speed of the soluble species to the velocity of thesolution, and the ratio between the saturation concentrationand the density of the soluble species. Then the equationscan be interpreted as follows: the height (Eq. (16)) of thepile decreases as the fraction of the volume of each speciesdecreases, and that the area of each particle decreases atthe speed of decrease in the radius of the soluble particles.The radii of the soluble particles decrease (Eq. (17)) as theconcentration of the solution decreases, and depends on theratio between the velocity of solution and percolation of thesolution.

We determined the change in concentration Cj, solvingEqs. (9), (12) and (14) using the Runge–Kutta method(Bequette, 1998). For the case of nitrate obtained from theexperiments carried out and from the model (Fig. (10)), theparameters which were input for resolution of the model were:the dissolution constant 0.2 (m/h)(kg/m3)0.4 for the solution ofthe nitrate and 0.01 (m/h) (kg/m3)0.4 for the magnesium, whichwere obtained through iterations of the model until finding avalue which fit the data of the model to experimentally ob-tained values; the initial mineral particle size to be leached was6.35 ∙10−3 m, the feed flow to the columns was 1.14 ∙104 m3/h,the porosity of the bed was considered to be 0.2, which was

Fig. 10. Results from the variable height model showing the experimental concentrations of nitrate (NO3) for the three heights analyzed.


estimated considering that the initial porosity of the bed was0.4. The initial value of the porosity of the mineral wasobtained by direct measurement of the quotient of the volumeof the recipient and the volume of the mineral which wascalculated from the mass of the mineral loaded and its density.Only one section for height was used in this work. The lagtimes were 0 for NO3 and Mg in height 1, 30 and 12.5 for NO3

and Mg in height 2, 70 and 25 for NO3 and Mg in height 3.These lag times are only a fraction of the experimental lagtimes (25 and 0 for NO3 and Mg in height 1, 100 and 25 forNO3 and Mg in height 2, and 225 and 50 for NO3 and Mg inheight 3). Therefore it is clear that saturation is really the causelag time response in the effluent concentration curves of Figs.10 and 11.

The results are shown in Figs. 10 and 11. In general there is agood agreement between the model and the experimental values.The lag times occur since the solution becomes saturated withthe soluble species and thus the leaching occurs in the segmentsof the columns, also, although probably less significant, due tothe percolation time in the column. To this, we note that as the

Fig. 11. Results from the variable height model showing the experimental

solution lowers through the bed it increases in concentration untilreaching saturation, without having extracted all the nitrate andmagnesium in the upper part of the column. It should be notedthat the results of the model fit better with the nitrate experi-mental data, which is attributable to the fact that the nitrateclosely follows the assumptions of the model. In the case of themagnesium concentrations, Fig. 11, since this species was foundto be containedwithin 2mineralogical species and as they do nothave the same solution kinetic, the model hasmore difficulties toadapt to its experimental data.

When analyzing the specific case of the leaching of nitratefollowing the model, it is possible to verify the decrease inheight and radius of the particles resulting from thisphenomenon. This is also verified experimentally (Tables 2and 4). Nevertheless the decrease in height resulting in thismodel only represent the dissolution of NO3 and Mg andtherefore does not prove to be the same as in a real scenario(34.1%) since the former does not consider the change inporosity and the dissolution of other salts contained in themineral which produce greater decreases in the height, since

concentrations of Magnesium (Mg) for the three heights analyzed.

Table 6Deviation of the relative error of the concentrations obtained by themodel, versus the experimental concentrations

Height NO3 Mg

1 0.79 0.422 0.19 0.143 0.11 0.20


the caliche is a mineral whose composition contains more than40% material soluble in water at room temperature.

The model supposes that the extraction occurs as a functionof the radius of the mineral particle, and due to the difference insaturation concentration and solution in the interstices of thebed. The resolution of the preceding is adjusted to the behaviorof the solution contained within the bed, validating the pro-posed supposition.

The relative error of Eq. 20, produced by the model isshown in Table 6, where Cn is the concentration in the modeland Cn

e is the experimental concentration, and N is the numberof data. Thus the relative mean error for the NO3 is about 15%for the last two heights, while that for Mg is about 25%. Theeffluent concentration in the first height has high deviation, butit can be considered that the behavior is delayed. These errorscan be considered acceptable, considering the simplicity of themodel, and the simplifications carried out.

Relative error ¼ 1N

XNn

jCn � Cenj

Cen

ð20Þ

4. Conclusions

The tests of column leaching provide examples ofa valid technique for the kinetic analysis of the leachingprocess in heaps of soluble species. The variation carriedout in the development of this study included division ofthe mineral bed into three different heights which wasdone in order to understand the variation in concentrationof the leaching solution at different heights in the column.It was possible then to evaluate and adjust correlationswhich were convenient for recovery of the species, andestablishing empirical kinetic expressions for the behaviorof nitrate and magnesium each height.

The results show that it is possible to leach caliche forthe extraction of saltpeter using water as a leachingagent to give extractions above 90% with irrigationratios of 0.8 m3/ton. The height of the pile decreasessignificantly with leaching (ca. 34%) since the solublespecies make up an important percentage of the mineral.

The model developed was fit to experimentallyobtained values for nitrate and magnesium concentra-tions, for the three bed heights analyzed. The resultsare better for leaching NO3 than for Mg; this is explainedin part because the NO3 occurs as only one type of

mineralogical species, while the Mg is present as twosoluble minerals. The analysis of the residue shows thatpractically all of the NO3 (nitrate) was leached, while oneof the Mg minerals was completely leached (polyhalite),and part of the other (loeweite) was not leached.

This study is the first approximation of modelingwith variation in height, which could be complementedin future studies by including the size distribution of themineral loaded, variation in porosity in the column, andthe interactive effects of solution of one species onanother. Of these factors, probably the most important isthe variation in porosity over time, since the particleschange significantly in size during the leaching process.

Acknowledgments

The authors wish to thank CONICYT for supportthrough Fondecyt Project 1020892. Luis Cisternasthanks Mr. Patricio Pinto Gallardo (SKM Minmetal)for his expert technical assistance in carrying out theleaching experiments.

References

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saltpeter extraction and modelling of caliche mineral heap leaching

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