TECHNICAL PAPERS

Application of the Shrinking Core Model for Copper Oxide Leaching

J. L. Shafer, M. L. White, and C. L. Caenepeel

Introduction

Often an in situ leach is the only practical economic method for copper recovery from small low grade oxide deposits. The decision to develop a copper property by an in situ blast and leach is strongly dependent on ore grade, tonnage, hydrology, and the copper extraction and acid consumption rates. The inherent leachability of the ore will in part determine the desired amount of fracturing of the ore deposit by the blast in order to obtain a copper extraction rate that is economical.

For the last several years Occidental Research Corp. (ORC), has undertaken a modest effort to address the question of how to best identify and determine the information necessary to predict and control the operation of an in situ leach for the economic recovery of copper.

Modelling of the Leaching Process

During the past 10 years the activity in the mathematical modelling of the leaching of copper sulfides in copper dumps and heaps has increased dramatically. The modelling of copper oxide leaching has not received as much attention. The acid leaching of non-sulfide copper minerals while chemically less complex, compared to sulfides, does generate a vertical acid

concentration gradient in the ore heap being leached due to the acid-base nature of the reaction. This is generally not observed in sulfide deposits that are biologically active, due to the buf- fering action of opposing reactions involving the generation of sulfuric acid from sulfide minerals and acid consuming host rock. Thus, the objective of ORC 's copper oxide modelling ef- forts is to determine the leaching parameters which will account for this vertical acid concentration gradient. Knowledge of this gradient will result in the correct choice of the feed acid concen- tration to the top of the ore dump or heap, such that the ef- fluent will have the desired pH.

J. L. Shafer, Member SME-AIME, is Staff Engineer for Minerals Technology Div., Exxon Research and Engineering Co. in Florham Park, New Jersey. He was formerly associated with Occidental Research Corp. Martha L. Whlte was affiliated with Occidental Research Corp. in La Verne, Calif. Chrlstopher L. Caenepeel is with the California State Polytechnic Univ. in Pomona, Calif. SME preprint 778402, SME Fall Meeting and Exhibit, St. Louis, Mo., October 1977. Manuscript Oct. 10, 1977. Discussion of this paper must be submitted, in duplicate, prior to April 30, 1979. In accordance with the Postal Service Regulations, this material has been assessed a page charge and is considered advertisement for postal purposes.

MINING ENGINEERS This page of SME-AIME Transactions follows page 70. The intervening non-Transactions pages appeared in MINING ENGINEERING.

MINING ENGINEERING 165

One of the first analytical leaching models was developed by Taylor and whe1an.l Although these authors could predict future recovery from a coarse particle leach knowing past recovery, their model could not be used in scale up work. ~ a m s 2 developed a diffusion rate controlling model which un- fortunately uses an extremely difficult to measure size distribution parameter.

Some of the most noteworthy efforts to predict the behavior of a heap or in situ leach have been made by WadsworthS and Roman, et al.4 In both of these studies both small and large column leach tests have been used to isolate important design parameters.

Reaction Zone Model

In 1972 wadsworth3 ~ublished a reaction zone model that

In this latter equation the surface reaction and pore diffusion resistances are defined by equation (6) and 7).

Once the effective surface reaction rate constant and effective pore diffusion coefficient have been evaluated equations (6) and (7) may be used to determine if the leaching rate is limited by surface reaction or pore diffusion rates or if it is a combined kinetic process.

Shrinking Core Model

correlated well with primary copper sulfide leaching data.526 Later Pohlman and 0lson7 successfully applied this same model Roman, et a1,4 have developed an unreacted shrinking core

in a kinetic study of the acid leaching of chrysocolla. Models diffusion model which is essentially a simplification of the reac- tion zone model. In essence these authors assume that the sur- similar to the reaction zone model have previously been face reaction rate constant, p, for some leaching processes is very

proposed for high temperature gas solid reactions by ~alensi8 and ~ o s s . 9

large and thus the surface reaction resistance in equation (5) and (6) is near zero. Therefore, for these processes the leaching

The reaction zone model essentially involves steady state dif- rate is pore diffusion rate controlled. The differential and in- fusion of the reactants through the previously reacted portion of

tegrated forms (assuming constant lixiviant concentration) of the ore fragment and a subsequent first order surface reaction at the shrinking core model are outlined in equations (8) and (9), the reactive particle site. The model is based on the assumptions respectively. that the rock is isotropic and that reactants and products of the leaching process are transported in the solution-filled channels d ~ ~ i = 3ne!,cH( 1-c, , )1/3 1 8 )

within the individual ore fragments. The effective area of "1 FrcGjr12 [ 1 - ( l - ~ ~ ~ ) ~ / ~ ~

mineral particles within the moving reaction zone is essentially constant and independent of the mineral particle size I - 2/3a?i - ( I - a 1 i ) 2 / 3 = 2 ~ D e C ~ t i 1 9 ) distribution. Finally, circulation of the leach solution around + c ~ i r , ~ - ' 2

the individual ore particles is sufficient so that bulk solution transport is not rate controlling.

The differential and integrated (assuming constant lixiviant Application of Mathematical Models concentration) forms of th;reaction zone kodel for a multi- particle sized ore are summarized in equations (1) and (2). As is indicated by equation (2) and (9), the reaction zone and

the shrinking core models may be easily used to predict the leaching history of a monosized leach with constant lixiviant

do - ] i = Fa 1 1- ' , J , )2 /3 111 concentration provided the key rate constants (De and /I) are

= t i erGJ:j l / 3 113, 1 ) j - 11-1 : - a ) known. Use of the models for a multiple particle sized leach Glc 1' 1 1

requires that the models be applied to each particle size ri and then the extent of reaction (ati)at any time tifor all the p&ticle

1 - 2 / 3 c 1 i - ( 1 - c J i , 2 / 3 + - [ : - (1- . :J1) ' /31 = % ( 2 i G ; K ?

sizes may be easily computed from equation (10). dlK;

J J

st, =El", a j i The constants P' and y are measures of the relative import- I

I i O )

of the rate of surface reaction and the rate of diffusion of the reactants and products within the individual ore particles. The utilization of these same models for a column leach of

These two constants are specifically defined in equations (3) and Ore yet because the

(4). lixiviant solution reacts with the individual ore particles and becomes depleted in reagent as it flows downward through the

I = ore. To account for this effect the following equation may be

6' = Zoe ( 3 ) 0s O r 0 ' 4 ' used to determine axial variation of the acid in the column.

The effective pore diffusion coefficient De is a function of the coefficient of diffusion, a sphericity factor and a factor which accounts for both particle porosity and the tortuosity of the dif- fusion path. In a similar manner the effective surface reaction rate constant, p, is dependent upon the actual surface reaction rate constant, the reaction zone thickness, and the average radius and density of the ore particle consituent being leached.

It should be pointed out that one may use equation (1) coupled with experimental data to judge the relative import- ance of the surface reaction and pore diffusion rates. This can be accomplished by rewriting equation (1) in a form that parallels the universal rate law, i.e.,

d a j i C~ - - =- - D r i v i n g F o r c e ( 5 1

d t RSR+ RPD Resistance

In essence it is assumed that the change in lixiviant concen- tration is directly proportional to the change in copper concen- tration in the same lixiviant solution. Unfortunately the propor- tionality factor aa, which is called the acid consumption num- ber, is not constant. It tends to vary with the effective particle size, the lixiviant concentration, the gangue constituents in the host rock and the extent of reaction.

At this time it must be emphasized that although all of the necessary equations for proper modelling of a copper oxide leach have been identified, their application is not necessarily straight forward because the resultant differential equations must be solved numerically. However, ~ o m a n 4 has developed a numerical analysis technique which overcomes most of the ap-

166 FEBRUARY 1979 SOCIETY OF

parent difficulties. The proposed numerical analysis methodology involves treating column leaches as a series of finite differential volumes. Vertical variation within the column in size distribution, ore grade, concentration, etc., are therefore reflected in the characteristics assigned to each differential volume. Finally the differential volumes are placed on top of one another in order to simulate the leaching history of the en- tire column.

Because this proposed numerical solution technique is designed to take into account the vertical acid concentration gradient, that portion of ORC ' s modelling efforts which verified the ability of the proposed paradigms to "model" and "predict" leaching behavior is reported here. A clear distinction is being made between the usage of the words "model" and "predict. " It is quite possible to have a mathematical expression which will "model" or correlate well with a set of leaching data-but not necessarily be able to "predict" the leaching behavior of the same ore under a different set of experimental conditions. This latter property will be the true test of the validity of a proposed paradigm.

Experimental Procedure and Method of Data Analysis

Ore Preparation-Although our preliminary test work was with monosized material in small diameter columns, it was felt that in general "leachability tests" would be best performed on muiti-particle size ore. It was rationalized that ;his would be more representative of the particle size distribution, mineralogy and physical characteristics that exist in a typical in situ leach. The rest of this paper describes the column leaching studies which were performed on a particular 2273 kg (5000 Ib) sample of minus 20.3 cm (8 in.) rock from a low grade copper oxide deposit. An 1818 kg (4000 lb) sample of this ore was crushed to -

-7.6 cm (-3 in.) and 454 kg (1000 lb) were crushed to -5.1 cm (-2 in.) with 95% -3.8 cm (-1.5 in.). Both of these samples were distributed into thirty one 208 L (55 gal) barrels with the aid of a rotating chute. Approximately 25% of the two samples was then separated out for screen and copper analysis. The - remaining ore was saved for column leach studies. Sampling statistics would indicate that to achieve a trulv re~resentative

2 .

sample of -7.6 cm (-3. in.) rock a minimum sample size of 13.6- 18.2 tons (15.0-20.0 st) would be required. Thus one can only expect to obtain an approximate head copper assay and screen analysis.

After screen analysis on the "representative sample" - every screen size was staged crushed to -0.63 cm (-y4 in.). At this point a sample was split out and set aside to back generate a composite sample of the original -7.6 cm (-3 in.) or -5.1 cm (-2 in.) ore. This was similarly repeated on -100 mesh pulverized material from each sample. These two composited samples were then used for beaker leach test to determine initial acid consumption and the relative importance of the surface reaction rate constant.

Chemical analysis of the ore indicated 0.45% total copper, 0.39% acid soluble copper and 0.45% hot acidified ferric sulfate soluble copper. Thus the bulk of the copper is non- sulfide and the sulfide which is present is not chalcopyrite. The copper minerals which have been identified are brochantite CuS04.3Cu(OH)2. The actual acid consumption by the beaker leach tests was approximately 4-5 g of acid/g copper at 60% ex- traction.

Beaker Leach Tests-A stirred vat acid leach on monosized ore was performed with the pH being maintained constant. The resulting leaching response was used to judge the relative impor- tance of the surface reaction and pore diffusion resistances as previously defined in equations (6) and (7). The results of this analysis indicate that for effective particle sizes in excess of 0.02 cm the pore diffusion resistance is dominant (82%) after the

10% of the leaching reaction. Since the pore diffusion resistance becomes more dominant with increasing particle size and since the particle sizes selected for the remaining tests were clearly in excess of 0.02 cm the remainder of the model verification study has been restricted to the shrinking core model.

Small Column Leach Tests-Two acid trickle leach tests were performed in cylindrical PVC columns 1.8 m (6 ft) by 0.15 m (6 in.). Each column was loaded with approximately 45 kg (100 lb) of -5.1 cm (-2 in.) ore. Both columns were leached with an aqueous sulfuric acid solution with a concentration of 15 g/L. To study shrinking core model over a range of conditions, the acid solution flow rate to one of the two column leach tests was established at the high flow rate (designated HFR) of 1.8 ~/rnin/mZ (0.044 gal/min/ft2). The flow rate to the second column was set at a lower flow rate (designated LFR) of 0.22 ~/rnin/rnZ (0.0054 gal/min/ft2) which is more typical for a commercial scale in situ leach. Because of this difference in lixiviant feed rate the effluent acid concentration histories from the two columns were drastically different. The HFR leach test had a nearly constant effluent acid strength of 14 g /L throughout the period of the leach while the LFR leach had for the period of the leach a uniformly increasing effluent acid strength (7 g/L after 5 days, 11 g/L after 10 days and 12 g/L af- ter 15 days).

The physical properties of the ore, the variation of the acid consumption number and the measured time variation of the extent of reaction were used with the shrinking core model to isolate the key rate constant. The effective diffusion coefficient "Den (6 X 10-8 cm2/sec for LFR test and 8 X 10-8 cm2/sec for HFR test) was obtained by selecting the calculated curve which gave the best visual fit to the HFR and LFR experimental data (Fig. 1). Since the shrinking core model does not have a func- tional dependency between lixiviant concentration and effec- tive diffusion coefficient, the two computed effective diffusion coefficients should be relatively close. The reported deviation in the two values of De was thought to be due to observed differen- ces between the "representative sample" particle size distribution which was initially used and that which was ob- tained from the post mortem ore analysis (Table 1). The LFR test data was subsequently rerun with the particle size distribution obtained from the post mortem ore analysis. It was found that the effective diffusion coefficient for the LFR test run increased to 7 X 10-8 cm2/sec.

At this time it must be noted that throughout this study the percent copper recovered has been based on total copper and not on the basis of oxide copper. The justification for this, as in- dicated in Table 1 is that the amount of sulfide copper (total copper-oxide copper) decreases to nearly the same extent as the

91 1 &,&'- f CALCULATED DATA

- W FLOW RATE

%MAN'S 'Omm. ~ r ~ o ~ ~ c m ~ / ~ ~ s

A HlOH FLOW RATE rK- , A 15 I 20 I 25 1

TIME [DAYS)

Fig. 1 -Copper recovery on small column leach test.

MINING ENGINEERS MINING ENGINEERING 167

Table 1-Screen and Copper Analyses on Ore in 15 cm (6 in.) Diameter Column

SCREEN ASSAY (Y. Cul ASSAY 1% Cut

total of oxide copper. This same post mortem copper analysis of the leached ore gives further support to the shrinking core model in that the larger particles do not leach nearly as well as the smaller ones.

Large Column Leach Test-As a true test of the validity of the shrinking core model used in this study the modelling parameters derived from the previously described small column leach tests were used to predict the behavior of a three large column (con- nected in a series) leach test. The large columns were 2.43 m (8 ft( by 0.38 m (15 in.) and each was filled with 359 kg (792 Ib) of -7.6 cm (-3 in.) ore for a total of 1078 kg (2376 Ib). The flow schematic in Fig. 2 indicates the leaching operation with the three columns connected in series. As opposed to the earlier leach tests the effluent stream from the third column was decopperized by cementation on scrap iron and subsequently reacidified for recycle back to the feed acid tank. The use of an aeration tank following the cementation column was an attempt to air oxidize the ferrous iron in solution to ferric and ferric hydroxide. This step would subsequently control iron build-up in the acid solution and provide the ferric ions essential to the leaching of the copper sulfides. As was not totally unexpected the aeration was nearly ineffective since only approximately 6% of the total iron was precipitated.

T h e feed acid rate averaged 0.23 ~ / m i n / m 2 (0.0057 gal/min/ft2, about the same as the previously described LFR test) and the feed acid concentration was varied to hopefully achieve a constant effluent pH of about 2. The modelling results from the small column leach tests were used to predict this variable feed acid concentration.

The key characteristics of the feed sulfuric acid solution are presented in Fig. 3. The seemingly irrational behavior of the

COLUMN 2 COLUYU 3

5-SbMPLING POINT

Fig. 2-Multi-column leaching system

Fig. 3-Free acid, pH, So2-2 profile for feed acids for three- column leach.

sulfate concentration and pH which both differ drastically from the clearly defined stepwise behavior of the free acid concen- tration is attributable to periodic fresh water additions to the feed acid tank. This was necessitated because of spills, evaporation, and solution removal for analytical samples. As would be expected the pH profile follows the sulfate profile even though the free acid strength may be the same due to the buf- fering effect of the sulfate and bisulfate ions. The final total iron (ferric and ferrous) concentration at the end of the leach was about 11 g/L. The concentration of the ferric in the influent for most of the leach was about 1 g/L.

Figures 4, 5 and 6 summarize the data obtained from the three column leach during the 63 days of leaching. Figure 4

'describes the acid concentration history for both the influent and effluent streams for each column. The effluent free acid concentration history, apart from reflecting the changes in feed acid concentration, also reflects fluctuations in feed acid flow rates, analytical errors, and equipment malfunction. Despite the scatter in the data the general trend of increasing effluent acid concentration for a fixed feed acid is apparent. The objec- tive was generally to feed as strong a concentration of acid as possible so that the effluent stream exiting the ore heap had the desired pH.

Figure 5 is a plot of the net copper effluent (copper out- copper in) for each column separately. There are several in- teresting observations to be made from this figure. First, columns two and three initially remove copper from solution; therefore, the net copper concentration is negative. This obser-

FEED SOLUTION COLUMN I

COLUMN 2

COLUMN 3

0 I 1 I L i I _I 0 8 16 2 4 32 4 0 4 8 56 64 72 8 0

TIME (DAYS)

Fig. 4-Acid profile vs. time three column leach.

168 FEBRUARY 1979 SOCIETY OF

COLUMN I

- - - TOP COLUMN

-. - MIDOLE COLUMN

BOTTOM COLUMN

I I I I I 10 2 0 3 0 4 0 5 0 6 0 70

TlME IDAYS)

Fig. 5-Effluent coppervs. time three column leach.

vation is consistent with the data in Fig. 4 which indicates that during this same time period there was little if any free acid in the effluent stream of these two columns. Thus for a brief initial time period copper is dissolved and then reprecipitated. Second, the maximum net concentration of copper obtained decreases as one follows the flow of solution from the first to the last column. This is obviously caused by the decreasing acid concentration seen by each column. Lastly, it must be noted that all three columns appear to have approximately the same rate of copper extraction after about the eighth day of leaching. This can be explained by the rather fortuitous counterbalancing of opposing effects. The amount of copper left to be extracted increases from column one to three, a factor favoring an in- crease in copper extraction; however, this effect is opposed by the decreasing acid concentration from column one to three.

The temporal variation of the percent copper extracted from each of the three columns separately is plotted in Fig. 6. It should be noted that 47% of the total copper was extracted in 63 days from the three columns collectively.

After acid leaching for 63 days the ore was removed from each column and then screened and each size fraction was prepared for copper analysis. Table 2 summarizes the screen and copper analysis before and after leaching. The post mortem analysis does indicate a small amount of acid decrepitation of the rock. On the basis of a material balance using the copper remaining in the leached ore and the copper as dissolved in the solution the head assay should have been 0.50% instead of the 0.45% value which was calculated on the basis of chemical analysis of a "representative" sample. To correct for this error the average head assay of the copper leached was taken as 0.50%. This was accomplished by multiplying the copper assay of each screen fraction by .50/.45 or 1.11. This appeared to be somewhat less arbitrary than setting the copper assay for all screen fraction equal to 0.50%.

Predictions

Aside from possible mitigating circumstances, an inability to predict the leaching behavior of 1078 kg (2376 lb) of -7.6 cm(-3

4 8 - COLUMN 2

0 W

COLUMN3

0 8 16 2 4 32 40 4 8 5 6 6 4

TlME ( D A Y S )

Fig. 6-Percent copper recovered vs. time three column leach.

in.) copper oxide ore in the three 2.43 X 0.38 m (8 ft X 15 in.) column leach from the leach tests on 45 kg (100 lb) of -5.1 cm (- column leach from the leach tests on 45 kg (100 lb) of -5.1 cm (-2 in.) in a 1.82 X 0.15 m (6 ft X 6 in.) column ought to infer an ;ests,which by their very nature cannot be nearly as well con- trolled. The converse is not necessarily true.

The experiment and the predicted leaching curves for the ex- traction of copper from the three column leach are presented in Fig. 7. The input to Roman's model was the "De" value (8.0 X 10-8 cmZ/sec) determined from the HFR leach since its particle size distribution was less subject to question. At the end of the 63 days of leaching 47% of the copper had actually been extracted and the shrinking core model predicted 43% (a relative error of only 8.5%). An attempt was made to model the three column leach with the shrinking core model. The effective diffusion coefficient De for the three column leach was found to be 10 X 10-8 cm2/sec. This compares rather favorably with the value of 8 X 10-8 cmz/sec obtained for the HFR leach.

The relative closeness of the value of Roman's "De" as determined for the HFR leach test, 8 X 10-8 cm2/sec and the value of 10 X 10-8 cmz/sec obtained for the three column leach indicates that the experimental differences, as summarized in Table 3, had either minimal effects or cancelled each other. The discrepancy between the two diffusion coefficients may be attributed to the fact that Roman's effective diffusion coef- ficient contains a tortuosity factor and a geometry factor (a measure of departures from sphericity) which wouldn't necessarily be the same for the -7.6 cm (-3 in.) and -5.1 cm (-2 in.) rock. Another major difference between the two leach tests was the recycle of effluent in the three column leach whereas in the HFR leach there was no recycle or sulfate build-up. As has already been illustrated in Fig. 3 recycling causes the sulfate concentration to more than double. This factor causes the pH to increase for a fixed free acid concentration. Also it is standard

Table 2-Screen and Copper Analyses on Three-Column Leach

- - -- COPPER ANALYSES I% TOTAL Cul

SCREEN SIZE

76mn5.km

5 . 0 a n ~ 2 . k

2 k m n 1 9 s m

1.9cm11.2cm

SCREEN ANALYSES IWT ?.I

l ~ l ~ l A L

MINING ENGINEERS MINING ENGINEERING 169

lHIT,AL

18.8

60 .7

5 7

6 . 0

12crn10S€m

-0.6sm

TOTAL

COLUMN I

COLUMN I

16 5

61.0

4.7

6.0

5.2

3.6

1 0 0 0

COLUMN 2

COLUMN 2

19.1

59 .8

4 . 0

6 . 2

COLUMN 3

7.2

4 .8

1000

COLUMN 3

19.2

61.5

3.9

6 .2

6.6

4 . 3

100.0

6 . 8

2 . 4

100.0

.42

5 0

4 5

Table 5-The Effect of Parameter Variation ( + 10%) on Copper Recovery

% CHANGE I N PARAMETER COPPER RECOVERY

AVE. RADIUS - 4.7

GRADE OF ORE - 4 . 0

S.G. OF ORE

ACID CONSUMPTION - 4.0

% SATURATION 0.0

% VOIDS + 1.3

ACID CONCENTRAT l ON + 4.0

FLOW RATE + 4.0

copper extraction was 4 and 8 g of sulfuric acid/g of copper, respectively. The acid consumption for the HFR and LFR column leach test at 47% extraction was 5.6 and 5.2, respec- tively. The three column leach test had an acid consumption of 4.8. The acid consumption increases as the copper extracted in- creases and thus cannot be taken as constant. These obser- vations clearly indicate that leach tests need to be designed which, apart from determining a value for the effective dif- fusion coefficient, will also determine how the acid consumption varies throughout the period of the leach.

Conclusions

The shrinking core diffusion model which does take into ac- count the vertical acid concentration gradient, is able to "model" the leaching data from three different leach tests. The ability of the model to "predict" the leaching behavior for a relatively large scale column leach test on coarse ore has been verified. However, it must be pointed out that in addition to the chemical leaching kinetics, copper recovery depends to a large extent on the "effective in-place" particle size distribution created by the blast, the permeability, and uniformity thereof, in the blast-fractured zone, and the ability to maintain solution flow with a minimum amount of channeling.

Typically the percent voids in an actual in situ leach will be only a third of what is obtained in a column leach test. Because of this there is considerable particle to particle contact and in- dividual particles will be blinded by each other. As blinding in- creases, the particles will behave like larger particles with a coar- ser apparent size distribution. lo This phenomenon has been ob- served in recent studies published by D'Andrea, et al.11 In this investigation it was demonstrated that the authors' full scale in situ operation leached drastically slower than their model prediction. In fact the observed leaching rate was less than the model would have predicted based on the average particle size prior to rubblization. Thus it may be assumed that the shrinking core kinetic model will most likely predict an upper limit for the extraction rate in a field test.

Nomenclature

a, Acid consumption number CH Concentration of Lixiviant (moles/cc)

Ccu Concentration of Copper in Lixiviant Solution (moles/cc)

De Effective diffusion coefficient (cmZ/sec) Grade of ore of particle size r j 2 Molecular wt of ore constituent being leached (g/moles)

rj Radius of particle (cm) ti Time (sec)

wj Wt function of particles of size rj

at; Predicted total fraction of ore extracted from range of particle sizes at time ti

aji Predicted fraction of ore constituent leached with particle size r. at time ti

8' Constant dedned in equation (3) - cm 0 Effective surface reaction rate constant - cm/sec y Constant defined in equation (4) - cm5/mole-sec o Molar acid consumption - moles of acid/moles of

copper e Bulk density of ore g/cc

References

l ~ a ~ l o r , J. and Whelan, P. T . , "The Leaching of Cuprous Pyrites and the Precipitation of Copper at Rio Tinto, Spain," Institution of Mining and Metallurgy Bulletin, No. 457, Nov. 1942, pp. 1-36. Z~a r r i s , J. A, , "Development of a Theoretical Approach to the Heap Leaching of Copper Sulfide Ores, " Australian Institute of Mining and Metallurgy Proceedings, No. 250, 1969, pp. 91-92. S ~ a d s w o r t h , M. E., "Rate Processes in Hydrometallurgy, " Second Tutorial Symposium on Extractive Metallurgy, Univer- sity of Utah, 1972. 4 ~ o m a n , R. J., Benner, B. R., and Becker, G. W., "Diffusion Model for Heap Leaching and I t ' s Application to Scale-up," Trans., AIME, Vol. 256, 1974, pp. 247-252. S ~ a d s e n , B. W., Wadsworth, M. E., and Grover, R. D., "Ap- plication of Mixed Kinetic Model to the Leaching of Low Grade Copper Sulfide Ore, " Trans. AIME, Vol. 258, 1975, pp. 69-74. G ~ ~ l a n , F. F., McKinney, W.A., and Pernichele, A.D., Solution Mining Symposium, Society of Mining Engineers and the Metallurgical Society of AIME, Dallas, February 25-27, 1974. Braun, R. L., Lewis, A. F., and Wadsworth, M. E., "In Place Leaching of Primary Sulfide Ores: Laboratory Leaching Data and Kinetic Model, " pp. 295-323. 7 ~ b i d . Pohlman, S. L., and Olson, F. A., "A Kinetic Study of Acid Leaching of Chrysocolla Using a Weight Loss Technique,"

446. g~alensi . G.. "Cinetique de l'oxydation de spheunules et de

oudres metalliques, " Comptes Rendes, 202, 1936, p. 309. gRoss, H., Strangway. P and Lien, H.. "Studies on Kinetics of Iron Oxide Reduction, " Canadian Metallurgical Quarterly, 8, 1969, p. 235. l o ~ o m a n , R. J., "The Limitations of Laboratory Testing and Evaluation of Dump and In Situ Leaching," presented at ANS Topical Meeting on Energy and Mineral Recovery Research, A ri11977. Golden, Colorado. lPD1Andrea. D. V., Lanon. W. C.. Chamberlain. P. G., and Olson, J. J., "Some Considerations in the Design of Blasts for In Situ Copper Leaching," Proceedings of the 17th Symposium on Rock Mechanics, Snowbird, Utah, August 1976, pp. 5B1-1 - 5B1-3.

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