APPLIED AND ENVIRONMENTAL MICROBIOLOGY, Jan. 1991, p. 138-145 Vol. 57, No. 1 99-224/91/1138-8$2./ Copyright 1991, Amerian Soiety for Mirobiology Temperature Effets on Baterial Leahing of Sulfide Minerals in Shake Flask Experiments LASSE AHONEN't AND OLLI H. TUOVINEN2* Department of Mirobiology, University of Helsinki, SF-71 Helsinki, Finland,' and Department of Mirobiology, The Ohio State University, 484 West 12th Avenue, Columbus, Ohio 4321-12922 Reeived 1 Otober 199/Aepted 16 Otober 199 The mirobiologial leahing of a sulfide ore sample was investigated in shake flask experiments. The ore sample ontained pyrite, pyrrhotite, pentlandite, sphalerite, and halopyrite as the main sulfide minerals. The tests were performed at eight different temperatures in the range of 4 to 37 C. The primary data were used for rate onstant alulations, based on kineti equations underlying two simplified models of leahing, i.e., a shrinking partile model and a shrinking ore model. The rate onstants thus derived were further used for the alulation of ativation energy values for some of the sulfide minerals present in the ore sample. The halopyrite leahing rates were strongly influened by the interation of temperature, ph, and redox potential. Sphalerite leahing ould be explained with the shrinking partile model. The data on pyrrhotite leahing displayed good fit with the shrinking ore model. Pyrite leahing was found to agree with the shrinking partile model. Ativation energies alulated from the rate of onstants suggested that the rate-limiting steps were different for the sulfide minerals examined; they ould be attributed to a hemial or biohemial reation rather than to diffusion ontrol. Current ommerial-sale operations involving biologial oxidation and solubilization of opper and uranium ores are arried out at ambient temperatures. In dumps, heaps, underground stopes, or in situ proesses, the prevailing temperatures may display extremes suh as those found under snow over or in elevated temperature zones. While efforts in benh and pilot studies involve inubation temperatures whih are near optimum for baterial growth and ativities, temperature ontrol measures for leah liquors are not pratied in leah mines. Temperature profiles in underground mines display wide variation depending on the depth and geology of the formation. Temperatures of <1 C are not unommon and they show little seasonal pattern. Temperature-related differenes between leah mine operations and benh studies make it diffiult to utilize laboratory data to evaluate large-sale biologial leahing proesses. We have previously determined temperature-related effets on baterial enrihment and growth with ferrous iron and elemental sulfur in the range of 4 to 37 C (1, 2). For the present work we have utilized sulfide ore samples as energy substrates for baterial enrihment studies at suboptimal and near-optimal temperatures. Differenes between ambient temperatures in leah mines and near-optimum temperature onditions in laboratory studies prompted us to determine baterial leahing rates at suboptimal temperatures. In the present paper, the results from shake flask leahing experiments are reported. These experiments were undertaken to desribe temperature effets on the kinetis of the baterial leahing of halopyrite (general formula, CuFeS2), sphalerite (ZnS), Co,Ni-pentlandite ([Co,Ni]8S9), pyrrhotite (Fe,_,S), and pyrite (FeS2) present in the ore sample. The evaluation of rate onstants requires the determination of suitable kineti equations. Two basi models were evaluated for this purpose. First, a shrinking partile model * Corresponding author. t Present address: Geologial Survey of Finland, SF-215 Espoo, Finland. 138 was tested whih assumes that the leahing rate is diretly proportional to the surfae area of the mineral. Beause ontinuous measurement of the surfae area during the experiment was not possible, the model was further simplified by replaing the surfae area with the residual mass of the mineral. This treatment makes the model formally analogous with the first-order homogeneous reation. Seond, a simplified shrinking ore model was tested whih assumes that the rate is inversely proportional to the extent of the dissolution proess and thus to the onentration of the dissolved metal. This phenomenon an be due to the formation of the produt zone. A similar kineti effet also follows when the leah liquor has to penetrate an inreasing distane inside the partile before it reahes the ontat surfae. MATERIALS AND METHODS The initial soure of the inoulum was a omposite water sample olleted from a opper mine (1). Both stati and shake flask ulture onditions were used in the initial enrihment. Enrihment experiments under stati ulture onditions were arried out at 4, 7, 1, 13, 16, 19, 28, 37, and 46 C (+ 1 C). Shake flask enrihment ultures were inubated at 7, 16, 28, and 37 C. All ultures were prepared in mineral salts media whih ontained.4 g eah of (NH4)2SO4, K2HPO4, and MgSO4 7H2 (ph 2.5) per liter. Media ontaining 1% (wt/vol) sulfide ore material were inoulated with the omposite mine water sample and inubated in shaking (18 rpm) or stati 25-ml flasks at eah test temperature. One established, the ultures were tested in shake flask leahing experiments. Dupliate flasks were used for eah test temperature, and ontrol (uninoulated) flasks were also used to estimate the hemial leahing rates. Some ultures were also tested at temperatures other than that used for original enrihments. The sulfide ore material was ground to a -59-,um size fration for the leahing experiments. Partial elemental analysis of the ore sample indiated the following elemental omposition (wt/wt): total S, 38.2%; Cu, 6.1%; Ni,.76%;
o _ 1 8 6 4 2 _. L,6O x 5 4 4) 3 I Ql 2.5 2. 1.5 1. 1 8 6._.3 so : 4 C2) * 2 37.././Zn *Ni./~ mv / Cu_ 2 41 r;zziiz~1i 2 4 28C Ni. - //-*Co /.-Cu 2 4b! mv ~~~~~~~~~~~~ mv IIIIZ~T I 2 4 19C./ *- Zn mv ~ / Ni. (i -,, l C-oy O-GWCo Cu 2 4o l.-l* 2 4 16. Zn 13 C 1 Zn NiiZn' Cu~~~~~~~~~~.._2 E r< o 2 4 6 2 4 2 4 mv mv mv J U u ji 6 O 5 4., 4 3r 2.5 2. O 1.5 1. / 2~~~~~~~~~~~~~~ 2 4 6 2 4 2 4 a Ug is N._ CO 'a -_ 4 r a. : C1 1.5: 2 4 2 4 6 FIG. 1. Leahing of sulfide ore material at the test temperatures. 139
14 AHONEN AND TUOVINEN APPL. ENVIRON. MICROBIOL. 2 18 16 o 14 /3 o N 12 28 n = 1 4I~16 6 4 4 /z.~.~ TABLE 1. Kineti parameters of opper leahing from halopyrite Temp (C) Rate onstant, k Rate (1/day) (%/day) (dyldt) t1/2 (days) 37.49.49 142 28.42.42 164 19.26.26 266 16.21.21 329 13.17.17 415 1.11.11 624 7.7.7 1,5 4.5.5 1,39 2 1f/ */:> b7_i (SCE) was used as a referene. Redox potential values (SCE sale) were initially below 4 mv and inreased to the 55- to 6-mV range when ative leahing started. At low temperatures this inrease was gradual, taking several 2 4 6 8 weeks, whereas at high temperatures the redox potential inreased within a few days. Dissolved metals (Cu, Co, Ni, and Zn) were analyzed by atomi absorption spetrometry. FIG. 2. Leahing of opper from halopyrite at eah test tem- The kineti models were evaluated with experimentally perature. Barrs indiate standard error. determined values of k whih were alulated from the metal release data. These rate onstants were determined as slopes of linear lines whih were alulated by the method of the Co,.45%; Fe, 4.4%; and SiO2, 17.3. Based on the hem- sum of the least squares. The k values are stritly valid only ial analysi s and on mineralogial examination, the ore within eah set of experiments, and a omparison of k values sample was estimated to ontain approximatelyi7% hal- for different sets of results or different metals annot be opyrite,. e7% sphalerite,.4% Co,Ni-pentlandite (Co-Ni made based on the results in the present work. -1:1), 4% v pyrite, and 2% pyrrhotite. Pyrite ontained The equations were based on a shrinking partile model.6% Co anid.2% Ni. Pyrrhotite ontained.3% Co and and a shrinking ore model. The theoretial as well as.3% Ni. Pe ntlandite ontained 23% Co and 23% Ni. Quartz experimental bases of these models have been presented was the matin gangue mineral, in assoiation with siliates previously (3, 5, 6). andl nxidsevz ore The rate equation for the shrinking partile model is The huilk,amnle was haraterized bv a relatively low aid onsumption, indiating the relative absene of alkaline ore materials. The leahing of the sulfide ore material was monitored by the determination of ph, redox potential, and soluble opper, nikel, zin, and obalt. In initial phases it was neessary to add sulfuri aid beause of the aid-onsuming harateristi of the ore, but during ative leahing periods the reations were aid produing. Redox potential was measured with a Pt eletrode; a standard alomel eletrode Temperature C 1.7 1i92i1 ph B~~~~ 8 7 o* 6 (D).)D 4 := 2 dyldt = k. (WO - y) from whih the rate onstant (k) was solved k - ln [WJWo - Y] t (2) where W is the initial onentration of the metal in the ore material, y is the extent of the dissolution proess expressed as the onentration of the dissolved metal, and t is the time (days). The rate equation for the shrinking ore model is dyldt = k'ly (3) from whih the rate onstant was solved k = yl/t (4) where k = x/-ik. Thus, there is a paraboli relationship between y and t. The half-lives of mineral dissolution (t112) were determined from the respetive rate onstants as ln 21k. The rate onstants were further used for estimation of the ativation energy (Ea) values: ln k = ln A - Ea/RT (5) where A is the Arrhenius onstant, R is the universal gas onstant, and T is the temperature in kelvin. For a plot of ln k versus 11T, the slope is equal to EaIR. The Ea values were alulated from the linear part of the Arrhenius diagrams. (1) FIG. 3. Temperature and ph relationship in the baterial leahing of halopyrite. RESULTS Leahing experiments. The primary leahing data determined as hanges in metal onentrations, redox potential,
VOL. 57, 1991 OXIDATION OF SULFIDE MINERALS 141-5. -2. r- 11- ---I -2.5 ;- C -6. + -3. - ~~~~ -7.. -3.5 - -8. A -4. L B 32 33 34 35 36 32 33 34 35 36 14/T 14/T -2. X -3.5-2.5-3. -4.5-3.5-4. -6.5f ~~~~~~~~~~~D -4.5-7.5---- 32 33 34 35 36 32 33 34 35 36 14/T 14/T FIG. 4. Arrhenius plot of rate onstants for the baterial leahing of (A) halopyrite, (B) sphalerite, (C) pyrrhotite, and (D) pyrite. o N._- o N Co Co _O n FIG. 5. Leahing of zin from sphalerite (A) and linearized plot of zin leahing (B) at eah test temperature, based on the shrinking partile model.
142 AHONEN AND TUOVINEN TABLE 2. Kineti parameters of zin leahing from sphalerite Temp Rate onstant, Correlation Rate (dy/dt) t1/2 oc)a k (1/day) oeffiient (%/day) (days) 37A.16.983 16. 4.3 28A.914.997 9.1 7.6 28B.125.996 12.5 5.5 28C.134.998 13.5 5.2 19A.15.979 1.5 6.6 16A.819.985 8.2 8.5 16B.838.969 8.4 8.3 13A.592.998 5.9 11.7 13B.551.986 5.5 12.6 1A.53.979 5. 13.8 1B.53.999 5. 13.8 7A.161.983 1.6 43. 7B.167.998 1.7 41.5 7D.411.996 4.1 16.9 4A.27.995 2.7 25.7 4B.236.999 2.4 29.4 a Letter designations indiate soure of the inoulum: A, the inoulum ulture was grown at the same temperature as used for the subulture; B, the inoulum was previously grown at 19 C; C, the inoulum was previously grown at 7 C; D, the inoulum was previously grown at 28C. and ph values as well as aid onsumption are summarized in Fig. 1 for eah test temperature. Of the metals of interest assoiated with the sulfide minerals in the ore material, zin was leahed most quantitatively. After 6 weeks, the yields of sphalerite solubilization were 9 to 1% at 16, 19, 28, and 37 C. Within this same temperature range, soluble nikel reahed 5 to 7% reovery, representing the leahing of sulfide minerals pyrrhotite, pentlandite, and pyrite. The relative realitrane of halopyrite to hemial and mirobiologial leahing was evidened by low onentrations of TABLE 3. APPL. ENVIRON. MICROBIOL. Kineti parameters of nikel dissolution, representing the leahing of pyrrhotite, and estimated time ourses = y2lk2) to reah 25, 5, and 9% dissolution of pyrrhotite (t25%, t5o%, and t%) Calulated leahing Temp Rate onstant, Correlation times (days) (oc)a k (1/day) oeffiient t25% t5%o t9% 37A.134.987 3.5 14 45 37B.125.99 4. 16 52 28A.122.996 4.2 17 55 28B.112.998 5. 2 65 28C.111.995 5.1 2 66 19A.79.992 13 5 16 16A.738.991 12 46 15 16B.777.991 1 41 13 13A.594.999 18 71 23 13B.586.988 18 73 24 1A.46.982 3 12 38 1B.361.966 48 19 62 7A.337.98 55 22 71 7B.222.976 13 5 1,6 7D.347.982 52 21 67 4A.298.974 7 28 91 4B.143.928 31 1,2 3,9 a Letter designations indiate soure of the inoulum: A, the inoulum ulture was grown at the same temperature as used for the subulture; B, the inoulum was previously grown at 19 C; C, the inoulum was previously grown at TC; D, the inoulum was previously grown at 28C. soluble opper at all test temperatures, amounting to <15% dissolution of this mineral. At the lower range of test temperatures, the leahing yields delined and the apparent leahing rates for eah metal analyzed also appeared to derease as the temperature was lowered. 1 9 A 8 a 7 " B 37 8~~~~~~~~~~ 6 i 1 4. ~~~~2~ ~ ~ ~ 1 2 4 6 8 2 4 6 8 FIG. 6. Leahing of nikel (A) and linearized plot of nikel leahing (B) at eah test temperature, based on the shrinking ore model.
VOL. 57, 1991 OXIDATION OF SULFIDE MINERALS 143 1 9 8 O 7 2 6 5 n 4 ) 3 ar 2 1 2 4 6 8 C u N :3 CO 9 8 7-6 5-4 3 2-1 - _ 2 4 FIG. 7. Leahing of obalt (A) and linearized plot of pyrite leahing (B) based on dissolved obalt onentrations and the shrinking partile model. 6 I q It an also be seen in Fig. 1 that there were onsiderable hanges in ph and redox potential values, relating to the temperature of inubation. At the higher range of test temperatures, the ore sample displayed aid-produing harateristis. The dereases in the ph an be related, by and large, to sulfuri aid prodution due to the baterial oxidation of sulfide entities in the minerals. The respetive redox potential values at around 6 mv (SCE) displayed oxidizing onditions. These values are omparable to those where the redox potential is determined by Fe3"/Fe2". In the present work, pyrrhotite and pyrite were the two major iron sulfides in addition to a minor soure of iron in the form of halopy- 1..95.9.85.-v 16 Z.8 o1.75/ o+o.55.7~~~~~~~ /.65.6.55 4g< 1 2 4 6 8 FIG. 8. Molar ratio of obalt and nikel [Co/(Co + Ni)] during leahing. rite. At the lower test temperatures, net aid onsumption prevailed beause of the lak of baterial oxidation of sulfide minerals. The redox potential values either remained at a lower level or displayed a prolonged lag period before inreasing to around 6 mv (SCE). All of these hanges TABLE 4. Kineti parameters of obalt dissolution, representing the leahing of pyrite and pentlandite Temp Rate onstant, Correlation Rate ti/2 OC)II k (1/day) oeffiient (%/day) (days) 37A.445.982 4.54 15.6 37B.37.977 3.77 18.7 28A.22.993 2.22 31.5 28B.24.993 2.42 28.9 28C.224.988 2.27 3.9 19A.88.987.88 78.8 16A.69.996.69 1 16B.823.994.83 84.5 13A.566.998.57 121 13B.563.988.57 124 1A.321.989.32 217 1B.255.975.26 267 7A.19.922.11 63 7B.124.942.12 578 7D.134.939.13 533 4A.19.951.11 63 4B.71.839.7 98 a Letter designations indiate soure of the inoulum: A, the inoulum ulture was grown at the same temperature as used for the subulture; B, the inoulum was previously grown at 19 C; C, the inoulum was previously grown at 7 C; D, the inoulum was previously grown at 28 C.
144 AHONEN AND TUOVINEN 2 18 16 6) 1 12 EO 14 8 6 *4-1 `1-1 _~ a o Zn- 2 Ni 1 2 3 4 Temperature FIG. 9. Ratios of experimentally determined rate onstants for baterial and hemial leahing (kbaterial/khemial) at the test temperature. indiated a slower baterial ativity at the lower temperature range. Leahing of halopyrite. To quantitate the temperaturedependent responses, the leahing rates were alulated separately for eah metal. These data were then taken to represent the leahing of the major sulfide minerals. The solubilization of opper at eah test temperature is shown in Fig. 2. Figure 2 shows the solubilization of opper at eah test temperature. The leahing at the higher temperature range was initially fast and subsequently delined to slower rates. At the lower temperature range the rates were initially slow and subsequently inreased to faster rates, whih appeared to remain onstant. The initially slow rates at the lower temperature range an be attributed to the lag phases preeding ative baterial leahing. These lag phases were also apparent from the slow inrease in the redox potential at low test temperatures. The solubilization of opper from halopyrite was found to be dependent on several fators in addition to the temperature. Of these, espeially the redox potential and ph were important. No effort was made to haraterize these dynami interations by statistial analysis. An example of these interative relationships in the redox potential range of >55 mv is shown in Fig. 3. The hange in the mass of halopyrite during the dissolution was taken to be negligible, and thus the leahing rates were also used as the respetive rate onstants. The k values in the ph range 2.1 to 2.5 displayed the most pronouned temperature dependene and were seleted for the estimation of the ativation energy. The kineti parameters of opper leahing are presented in Table 1. The respetive Arrhenius plot is shown in Fig. 4A and it yielded an ativation energy of 77 kj/mol. Leahing of sphalerite. Virtually omplete solubilization of zin was ahieved at >16C test temperatures (Fig. 5A). The rate of leahing was proportional to the residual zin onentration (Fig. SB), thereby representing an example of the shrinking partile model. The effet of temperature was partiularly notieable on the length of the lag period preeding the ative leahing. The kineti parameters are summarized in Table 2. The rate onstants yielded a linear Arrhenius plot (Fig. 4B) and an ativation energy value of 45 kj/mol. APPL. ENVIRON. MICROBIOL. Leahing of pyrrhotite. The baterial leahing of nikel at eah test temperature is shown in Fig. 6A. Nikel was distributed in both the pentlandite and pyrrhotite phases, with a minor amount in pyrite. Based on their relative abundane and Ni ontent, it was estimated that approximately 5% of the total Ni was in pyrrhotite. We have found that the leahing rate of pyrrhotite is higher than that of pentlandite or pyrite; this differene is also in good agreement with mineralogial investigations of leah residues (unpublished results). Thus, the initial dissolution of nikel was taken to represent the leahing of pyrrhotite in the present work. The pattern of nikel leahing displayed an initially fast phase followed by a seond, delining phase. The data were found to fit a straight-line relationship in a paraboli plot (Fig. 6B). This is representative of a shrinking ore model whih assumes that the rate of leahing is inversely proportional to the onentration of the dissolved metal. The respetive kineti parameters are listed in Table 3. The rate onstants derived with the paraboli model displayed linearity in the Arrhenius plot (Fig. 4C) and yielded an ativation energy value of 4 kj/mol. Leahing of pyrite. Pyrite leahing was evaluated indiretly based on the dissolution of obalt and on the derease in ph. Based on the relative abundane of pyrite and pentlandite and their Co ontent, it was estimated that approximately two-thirds of the total Co was assoiated with pyrite. The leahing of obalt at the test temperatures is shown in Fig. 7A. The profile of obalt leahing indiated linearity and did not resemble the same paraboli type of time ourse that was observed for nikel. The soluble obalt is related to the leahing of both pyrite and pentlandite. The molar ratio of Co/(Co + Ni) for eah temperature is shown in Fig. 8. The inreases in the ratios of Co/(Co + Ni) shown in Fig. 8 demonstrate preferential pyrite oxidation. A onstant ratio would indiate (i) preferential pentlandite oxidation or (ii) the simultaneous oxidation of both pyrite and pyrrhotite. Dereasing ratios would indiate pyrrhotite dissolution. Figure 7B demonstrates the temperature relationship of obalt dissolution, and this is onsidered to represent mainly pyrite oxidation. The kineti parameters of pyrite oxidation are summarized in Table 4. An ativation energy value of 95.5 kj/mol was estimated from the respetive Arrhenius plot shown in Fig. 4D. Of the minerals examined in this study, the baterial leahing of pyrite displayed the highest temperature dependene, as is also apparent from the high Ea value. Chemial leahing rates. The rate onstants for eah mineral in the uninoulated ontrol flasks were alulated in the same way as for the respetive inoulated experiments. A ratio of the rate onstants of the hemial and baterial leahing (kbaterial/khemiad) is shown in Fig. 9. The ratio was highest (about 12 to 15) for sphalerite. For halopyrite and pyrrhotite, the ratios were in the range of 5 to 9 and 2 to 4, respetively. These ratios were relatively independent of the test temperature. However, a strong temperature dependene was apparent with obalt, for whih the ratio inreased from about 1 at 4 C to 17 at 37 C. These ratios for obalt primarily represent the relative differenes between the baterial and hemial leahing of pyrite. DISCUSSION To our knowledge, this study is the first to report ativation energy values for baterial leahing of several minerals
VOL. 57, 1991 in one ore material. The values were different for the sulfide minerals examined. The relatively high ativation energy values for halopyrite and pyrite indiated the existene of a hemial or biohemial ontrol of the leahing proess. This ontrol is mineral speifi as otherwise the respetive ativation energy values would be the same for eah mineral. The rate-determining step an also be a mineral-speifi hemial reation, as, for example, the initial release of the metal ion from the mineral lattie. The relatively low Ea values for pyrrhotite and sphalerite suggest a mixed ontrol due to diffusion as well as a hemial or biohemial reation. Galvani oupling effets between sphalerite-pyrite or sphalerite-halopyrite may derease the kineti barriers of sphalerite oxidation. Thus, galvani effets may emphasize the role of movement of metal ions in the viinity of mineral surfae as the rate-determining steps. In general, rate-ontrolling phenomena in baterial leahing systems are poorly understood, and available experimental information on rate-limiting steps in these omplex proesses is insuffiient to evaluate the atual mehanisms. To date, mathematial models have not been developed for dynami interations, suh as those desribed in the present study between ph, redox potential, temperature, and baterial ativity toward halopyrite solubilization, ommon in baterial leahing proesses. For halopyrite, the leahing of opper was initially fast but subsequently delined to more or less onstant rates. The temperature dependene of halopyrite oxidation was partially masked by hanges in ph and redox potential. Paraboli kinetis due to the formation of produt zone have been reported previously for halopyrite (4). In the present work, the k values were estimated from those parts of the time ourses whih displayed apparent steady states as defined by omparable rates of formation and removal of the produt zone. OXIDATION OF SULFIDE MINERALS 145 A omparison of the baterial and hemial leahing rates demonstrates that the baterial atalyti effet is most pronouned for sphalerite and pyrite. The baterial atalysis of obalt leahing was distintly temperature dependent. A possible explanation for this observation is that the ratedetermining step is different for the baterial and hemial oxidation of pyrite, whereas the rate-determining steps in the leahing of the other sulfide minerals do not disriminate between the baterial and hemial reations. ACKNOWLEDGMENTS Partial funding for this work was reeived from the Ministry of Trade and Industry (Finland), Outokumpu Ltd., and the Nordisk Industrifond. We thank Petteri Hietanen for skillful tehnial assistane, Outokumpu Ltd. for ore samples and metal analyses, and Laurie Haldeman for typing the manusript. REFERENCES 1. Ahonen, L., and. H. Tuovinen. 1989. Mirobiologial oxidation of ferrous iron at low temperatures. Appi. Environ. Mirobiol. 55:312-316. 2. Ahonen, L., and. H. Tuovinen. 199. Kinetis of sulfur oxidation at suboptimal temperatures. Appl. Environ. Mirobiol. 56: 56-562. 3. Blanarte-Zurita, M. A., R. M. R. Branion, and R. W. Lawrene. 1986. Appliation of a shrinking partile model to the kinetis of mirobiologial leahing, p. 243-253. In R. W. Lawrene, R. M. R. Branion, and H. G. Ebner (ed.), Fundamental and applied biohydrometallurgy. Elsevier Siene Publishers, Amsterdam. 4. Dutriza, J. E., and R. J. MaDonald. 1974. Ferri ion as a leahing medium. Miner. Si. Eng. 6:59-1. 5. Sohn, H. Y. 1979. Fundamentals of the kinetis of heterogeneous reation systems, p. 1-42. In H. Y. Sohn and M. E. Wadsworth (ed.), Rate proesses of extrative metallurgy. Plenum Press, New York. 6. Wadsworth, M. E. 1979. Hydrometallurgial proesses, p. 133-241. In H. Y. Sohn and M. E. Wadsworth (ed.), Rate proesses of extrative metallurgy. Plenum Press, New York.