A Model of the Dump Leaching Process That Incorporates Oxygen Balance, Heat Balance, Ancl Air Convection

A Model of the Dump Leaching Process that Incorporates Oxygen Balance, Heat Balance, ancl Air Convection

L. M. CATHLES AND J. A. APPS

A one dimensional, nonsteady-state model of the copper waste dump leaching process has been developed which incorporates both chemistry and physics. The model is based upon three equations relating oxygen balance, heat balance, and air convection. It assumes that the dump is composed of an aggregate of rock particles containing nonsulfide copper minerals and the sulfides, chalcopyrite and pyrite. Leaching occurs through chemical and diffusion controlled processes in which pyrite and chalcopyrite are oxidized by ferric ions in the lixiviant. Oxygen, the primary oxidant, is transported into the dump by means of air convection and oxidizes ferrous ion through bacterial catalysis. The heat generated by the oxidation of the sulfides promotes air convection. The model was used to simulate the leaching of copper from a small test dump, and excellent agreement with field measurements was obtained. The model predicts that the most important variables affecting copper recovery from the test dump are dump height, pyrite concentration, copper grade, and lixiviant application rate.

THE leaching of low-grade copper-bearing waste has heat generation, fluid flow and other transport phe- been practiced either by accident or through design nomena relating to the leaching process must also be for several hundred years. During the last fifty years, considered. A leaching system cannot be considered increasing attention has been paid to the systematic in a steady state, because all factors involved in the leaching of low-grade waste resulting from the open leaching process change progressively as a function pit mining of porphyry copper deposits in the western of time. United States. By now, this activity is yielding an im- In this paper we have developed a one-dimensional portant secondary source of domestic copper, t Indeed, model of the nonsteady-state dump leaching system. some mining operations have been planned and are We have applied this model to a small test dump con- operating exclusively from the production of copper structed and leached at the Utah Copper Division of obtained from leaching. Many of these operations are Kennecott Copper Corporation. To our knowledge only exploiting oxide copper deposits where copper is read- two other attempts have been made to integrate the ily leached by the application of dilute sulfuric acid. diverse aspects of dump leaching into a coherent all- Low-grade waste discarded as a result of open pit embracing model. %3 While we do not feel that the mining of porphyry copper deposits is dumped in gul- model presented in this paper is the final answer to lies surrounding the deposit. The disposal site is de- a clarification of the dump leaching process, we be- termined primarily by the convenience of the site to lieve that it forms a basis upon which subsequent re- the mining operation, and is not usually based on con- search in this area might be coordinated. siderations necessary for optimum leaching. In the western United States several billion tons of waste has accumulated in this manner. During the last decade, many people have become A MODEL OF THE DUMP LEACHING conscious of the fact that this enormous resource of PROCESS copper is not being exploited effectively because in- Initial Assumptions sufficient attention is being paid to those factors which could lead to improved design and layout of waste Sulfides must be oxidized before their metal values dumps. It is believed that if the leaching process may be put into solution. The conceptual basis of the were completely understood, then it would be possible model of dump leaching presented here is simply that to design and leach copper from waste dumps in a far the exothermic sulfide oxidation reactions generate more efficient manner than is currentIy being prac- heat and consume oxygen from the air, and by so do- ticed. The problem is a large one. Not only must the ing drive air convection through the dump. This air chemistry of leaching be understood, including both convection is the only significant source of oxidant to kinetic and thermodynamic aspects, but the effect of the dump. A system is envisioned in which a countercurrent L. M. CATHLES is a senior geophysicist at the Ledgemont Labora- interlocking flow of air and water passes through an tory, Kennecott Copper Corporation, Lexington, Massachusetts. J. A. APPS, formerly a scientist at the Metal Mining Division Research Cen- aggregate of rock fragments, as shown in Fig. 1. ter, Kennecott Copper Corporation, Salt Lake City, Utah, is now staff The oxygen leaves the gas phase within the dump scientist, Energy and Environment Division, Lawrence Berkeley La- by dissolving in the liquid phase where it oxidizes boratory, University of California, Berkeley, California. ferrous to ferric iron through the agency of bacteria. Manuscript submitted February 5, 1975. The ferric iron diffuses into the ore fragments and

METALLURGICAL TRANSACTIONS B VOLUME 6B, DECEMBER 1975-617 oxidizes the sulfide minerals:* Acid, Fe *+ and heat

*At 1/5 atmosphere PO: and the temperatures involved in dump leaching, Fe*~ F 0 2 GAS oxygen is not very soluble in water (<8.6 • 10-3 g/1 ). Typical ferric iron concentrations in leach dumps run ~1 g]l. These relative concentrations ensure Fe~ will be the oxidizing agent in the diffusion controlled processes envisioned above. are produced along with Cu ++. o o o For the purposes of our model, we have assumed the formation of a leached rim which is separated from the unreacted core by a sharp boundary, as shown in Fig. 2. As the leached rim grows the rate of leaching drops because of longer diffusion paths and a shrinking reaction zone. Evidence for a shrink- SULFIDE BLEBS ~~/~ LIQUID PHASE ing core has been supported observationally by Braun, Lewis and Wadsworth 4 and by Madsen, Wadsworth and Groves. ~ Theoretical arguments also support the ex- istence of a sharp boundary for the conditions of our Fig. 2--Idealization of the leaching of a single waste partic|e. model (see Eq. [11]). For those reasons we will later employ the mathematical formulation of the so called "shrinking core model", as developed by Braun, Lewis gram of chalcopyrite copper leached, the following and Wadsworth. However, we recognize that there are number of grams of 02 will be consumed: many conditions in which a sharp boundary between g O z consumed = (1.25 + 1.75 FPY) g chalcopyrite the leached rim and the unreacted core boundary is not observed because of variable reaction rates of Cu leached [3] the sulfides, acid gangue interaction, sulfide concen- Actually the amount of oxygen consumed per gram of tration, grain size of sulfides and gangue minerals, chalcopyrite copper leached is somewhat greater than and porosity of the rock. A generalized model, taking this, if account is taken of the oxidant required to pre- account of several of these factors has been developed cipitate, as jarosite (KFe3(SO4)2(OH)6), the iron ex- by Bartlett. 6 changed for copper during cementation (2.5 lb Fe/lb Most low-grade waste, from which copper is leached, Cu) and the iron produced in leaching the chalcopyrite is derived from the outer pyritic halo of porphyry cop- and pyrite. The precipitation of cemetation iron within per deposits, where the copper-bearing sulfide is chal- the dump must clearly be taken into account even copyrite. 7 We assume that chalcopyrite and pyrite are though the source of the iron is outside the dump. the principal sulfide minerals and that they oxidize in Further, if the excess acid produced by the oxidation a waste dump environment in the following manner: of pyrite is neutralized by reaction with gangue of bio- 0/2 + ~ CuFeS 2 + ~ (2H + + SO~-) -- -~ (Cu *+ + SO~-) tite composition* additional iron is generated, oxidized, + ~(Fe +~ + SO~-) + -~ H20 + ~S [1] *Biotite has been found to be more reactive by a factor of~100 than other gangue minerals in a porphyry copper intrusive. Calcite, the only other highly reactive mineral likely to occur, is usually present only in minor amounts. O~ + ~ FeS 2 + 7 H20 -- 2 (Fe++ + SO~-) and precipitated. Withthese additions Eq. [3] becomes: +~-2 (2H § + SO~-). [2] g O z consumed = (1.75 + 1.91 FPY) g chalcopyrite Evidence that these are the oxidation mechanisms for the two sulfides comes from studies by Wadsworth. 8 Cu leached [4] Observations by Stephens 9 show that sulfur is a prod- Waste material typically contains 10 to 100 moles of uct of the oxidation of sulfides in waste dumps. It can pyrite for every mole of sulfide copper. Thus pyrite be seen that for every mole (64 g) of chalcopyrite is by far the most important oxidant consumer if it is leached, 5/2 mole (5/2 932 g) of oxygen will be con- oxidized in proportion to its molar ratio to sulfide sumed. If FPY moles of pyrite are leached per mole copper. of sulfide copper, an additional 7/2 FPY moles (7/2 Because leach solutions cannot carry significant 932 9FPY g) of O z will be consumed. Thus for every oxidant with them as they move through the dump, air is the main source of oxidant within a dump. A liter of air contains 0.28 g 02 9Fig. 3 shows that Eq. [4] requires far more air than water to flow through a _l waste dump if the effluent solutions are to contain the copper concentrations typically observed. For the particular dump we shall consider, at least 80 times more air passed through the dump than water 9That is, for each liter of leaching solution leaving the dump with a net gain of 0.25 g/1 (2 lb. Cu/1000 gal.) copper, 80 liters of air are required to supply the oxidant necessary for the chemical reactions involved. CONVECTIVE FLOW OF AIR Eqs. [1] and [2] not only tell us the amount of oxidant UP THROUGH THE DUMP consumed per gram of copper leached, but also the Fig. l--Countercurrent interlocking flow of air and water heat generated per gram of copper leached 9(The ent- through a leach dump. The flow of water is usually inter- halpy of reaction, A/-/R, of Eq. [11 is approximately mittant.

618-VOLUME 6B, DECEMBER 1975 METALLURGICAL TRANSACTIONS B 4oo! too of 02 transport into a waste dump. In this respect our model differs from that of Harris, 2 whose pseudo-par- 3801- ~ 95 ticulate leaching case assumes that Oa transport into 360- MIDAS TESTDUMPq /_ 90 a dump occurs primarily by diffusion through the inter- stices of the particles. 340 - F' - 85 In the next section we generalize Eqs. [4] and [5] 320 - 80 slightly to take into account copper sulfides other than chalcopyrite. We then develop the rate equations re- 300! - 75 lating copper extraction with oxygen uptake and heat 8 280 - 70 generation. We show that these rate equations are governed by the chemical and diffusional processes oc- < 260! - 65 Z rr curring during the leaching of waste particles in the 240i - 60 ,,<, rr dump. Finally, we derive three equations describing 22G 66 ~ oxygen balance, heat balance and convective air flow which are the basis for our one dimensional model. 2oc 60 ,= rr I- 1- LIJ I-- Formulation of a One Dimensional Model 160 40 < ~ Because sulfide leaching is usually dominated by the 0 .J ,40 as ~ leaching of pyrite, Eqs. [4] and [5] are quite easy to IJ- generalize. Provided FPY is taken as the moles of rr 120 30 ~ < ws pyrite oxidized per mole of sulfide copper oxidized, 100 25 ,~ and provided FPY is greater than ~4, Eqs. [4] and [5] will hold to good approximation even if sulfide min- 80 20 O erals other than chalcopyrite are present. 60 15 rr We assume sulfide oxidation takes place in a dump , only where the air filled pores of the dump contain 40 10 oxygen and that the oxidation proceeds at a rate inde- 20 5 pendent of the actual oxygen concentration. Unpub-

6.22 ( , , , , , , , , , , lished studies of the bacterial oxidation of waste dump 5 10 15 20 25 30 36 40 46 60 leaching solutions with air, conducted by the second author, have shown that the bacterial oxidation rate MOLES py/MOLE SULFIDE Cu LEACHED (FPY) of ferrous iron is essentially independent of oxygen FPY Fig. 3--Graph relating the air flow through a dump to the concentration in the air until the concentration falls ratio of the moles of pyrite leached to sulfate copper leached below 1 pct. More recent studies by the second author (FPY), for a typical effluent copper concentration. involving the uptake of oxygen by wetted mine waste show that oxygen uptake is substantially independent of oxygen partial pressure for the same range of oxy- - 108.8 kcal;* AHR for Eq. [2] is - 94.9 kcal). If we gen concentrations. * 1 kcal = 4.1868 kJ. By contrast nonsulfide copper is leached with acid again take into account the heat consumed in the pre- alone. Acid generated by pyrite oxidation anywhere cipitation of jarosite, require acid and iron balance, in the dump is recirculated through the dump in nor- and assume 2.5 lb. Fe are exchanged per pound of Cu mal operation. Therefore, nonsulfide copper leaching at the precipitation plant: should take place everywhere in the dump at a rate independent of the presence or absence of nearby kilocatories produced = (2.89 + 5.41FPY) g chalco- oxygen. pyrite Cu leached [5] Suppose the fraction of sulfide copper remaining in the dump after some leaching is Xs, and the fraction Again it can be seen pyrite oxidation will, in all proba- of nonsulfide copper in the dump is XNs. Let the orig- bility, be the most sig-nificant source of heat. The rate inal sulfide copper grade be G s and the original non- at which a waste dump heats up is a direct measure of sulfide copper grade be GNS. Then the rate at which FP Y. copper is leached from the dump, fftCu , may be ex- Eqs. [4] and [5] contain the fundamentals of a model pressed as: of the dump leaching process. Sulfide oxidation reactions consume oxygen from the air in a dump. Since / dX S dX S \ O~ is a heavy component in air, the oxygen depleted ~cu = pR(1 - ~ ) its -a-i-- + cNs -ag-)" [6] air is lighter. Since water vapor is a light component of air, saturation of the air inside a dump with water Similarly the rate of oxygen consumption, 6tO2 , and the vapor wilt also produce buoyant forces. Buoyant forces rate of heat generation fftA, may be expressed, from tend to produce air convection. Furthermore, the oxi- Eqs. [4] and [5]: dation reactions are exothermic, which also promotes air convection. A AT of 20~ produces buoyant forces dxs two or ten times larger than complete oxygen deple- ~o2 = pR(1- ,#)Gs-~- (1.75 + 1.91s [7] tion or complete water vapor saturation, respectively. For normally observed permeabilities, air convec- dXs tion rather than diffusion is the principal mechanism 6{A = PR(1- r (2.89 + 5.41FPY) [8]

METALLURGICAL TRANSACTIONS B VOLUME 6B. DECEMBER 1975-619 OR, the density of the rock waste, is commonly about 2.7 g/cm~; 4,, the interblock porosity of the dump is Table I. Parameters Used for the Determination of ToS and rcs ~25 pct; PR(1- ~p), the bulk density of the dump as a whole, is equivalent to 1.7 tons/yd '~, Parameter Description Value The rate of leaching, dX 8/dr and dXNs/dt , may be de- a Radius of waste particle 1-5 cm R scribed also in terms of leaching from a waste particle. /2malf Surface area of sulfide mineralization per ~80 cm -~ Let us suppose that the leaching of a sulfide-bearing unit volume of waste DL Diffusion constant of Fe~ in water ~2 X 10 -s cm:/s particle is governed by an equation of the form: FPY Moles of pyrite reached per mole and sulfide 47 copper leached - ko. %ulf[ox]z = 0 [9a] Gs Sulfide copper grade 0.;8 wt pet K Oxidant required to leach a unit volume of 0.444 g/cm 3 G waste particle and that [Ox] l just outside the ore particle is a known kox First order rate constant for the oxidation ~--I0 -v cm/s function of time. The symbols given are defined in of pyrite by Fe~ [Ox] Concentration of Fe~ in leaching solution 10 -3 g/cm 3 Table I. Tortuosity of diffusion channels ~5 For a simple one-dimensional case, Eq. [9a] be- 6 Reation skin septh (see Eq. [1 I]) Calculated value = comes: 0.142 cm Porosity of waste through which diffusion 4 X 10 -2 D'ol ~ R l 32[0X] Rl can take place kox u,f[o ]Rl : 0 [9b] T / 3x e

Satisfying the boundary conditions [Ox] ~ = [Ox] l X=0 I"DS = 1590 mo.* In addition, T c and ~'D may be given and [Ox]~ x~ O, the solution is *1 mo=3Id. R [ Ox] e a temperature dependence: d[Ox]z x=0 [10] -r(T) = ~(T = 0~ EXP (1000 P E ~ T R (273) (273 +T)/ [16] Where 5 = reaction skin depth = - -~-~Dox ~R [11] * koxT Rasulf This introduces activation energies E*DS, E*CS, EDNS,* ECN S. From the literature ~~ reasonable ~esses for The reaction skin depth is the distance into the particle where the oxidant concentration has fallen to 1/e EDS and EDN S would be 5.0 kcal/mol. E*CS and ECN s might range from 14.0 kcal/mol to 20.0 kcal/mol, the its initial value. Since by hypothesis the rate of oxida- activation energies reported for the leaching of py- tion reaction is proportional to oxidant concentration. rite 1~, ~z and for chalcopyrite. ~3 5 is a measure of the distance into the ore particle that significant chemical reaction takes place. Given values for TDS , "rC5 , ~'DIVS, "teNS, Eqs. [12] and [13] determine the rate of leaching at any point Using values given in Table I. 5 = 0.142 cm. The in the dump at any stage of leaching. XNS and X S reaction skin depth is therefore thin, relative to the can be updated after each increment of model leach- average size particle diameter. Leaching of a parti- ing. Model time increments may be taken as short as cle can, therefore, be described in terms of the so- desired. called shrinking core model which is of a similar form The most serious approximation in Eqs. [12] and to that developed by Braun, Lewis and Wadsworth. 4 [13] is probably the assumption that the dump is com- dXs - 3x s" posed of waste particles only of one size. This may - [121 not be as serious an approximation as it might at first seem, given the tendency of small ore particles _ .,t x-z/3 to clump together and leach as if they were a larger dXv s ---Ns [13] aggregate, and the tendency for large ore particles 1/3 y1/3 dt 61DNSXNs (1 -- "'NS' + TeNs to have large enough cracks that they leach like somewhat smaller particles.l~ where ~-D is the time required to leach a waste parti- Furthermore, recent work has also shown that cop- cle completely when the process is solely diffusion per recovery rates from operating dumps at Kenne- controlled, and ~'C the time to leach a waste particle cott's Bingham mine can be correlated quite well with completely when the process is controlled by the de- laboratory studies of copper recovery from similar creasing surface area of the shrinking unleached core. material when the mean particle size of the waste, ~'C and "i"D can be computed theoretically from the fol- as found in the dump, is compared with laboratory lowing relations: leaching studies. The heat balance in a waste dump may be described ga [14] rcs = ko.~ a n ,~ 5 [Ox] by: - SUl[ aT PTCT at - -- (PlClVl + pgCgVg).VT + 6~A TDS = 6[Ox]D' ox*R + KTVZT [17a]

Using the values given in Table I, "rCS = 903 mo, and where p and C are the density and heat capacity of the

620-VOLUME 6B, DECEMBER 1975 METALLURGICAL TRANSACTIONS B total dump (subscript T) and the liquid (subscript l) application was used, an approximation that has been and gas (subscript A*) phase of the dump. V l is the shown valid so long as the leach cycle is less than Darcy liquid velocity (i.e. cm ~ water/cm" dump sur- three months. As will be discussed later the ambient face-s passed through the dump). V~ is the darcy air temperature was varied seasonally in a manner ap- velocity through the dump (i.e. cm a air/cm-" dump propriate to the location of the dump (temperature area-s). KT, the thermal conductivity of the dump is measurements were available from a mine station). taken to be 5 • I0 -3 cal/cm.~ 9s. For calculation, The surface temperature of the dump was also varied pTCT = 0.6, plCl = 1.0, and pg.Cg = 1.3 • 10 -3 (0.126 seasonally but at a higher average temperature and + 0.0283T), where T is the temperature of the dump. over a more restricted range. Air convection kept This last expression takes into account the thermal the dump surface warmer than the surroundings. Snow effects of evaporation. It is assumed the air in the was observed to melt more quickly on the dump than dump is always saturated with water; account is taken in the surrounding areas. of the increase in water saturation values with in- Given a set of parameters and operating procedures creasing air temperature, T, and the effect, through (rate of application of water), the finite difference the latent heat of vaporization, this would have on the model computes the leach history of the model dump. heat capacity or heat carrying ability of air. The dump is considered to be broken into N layers. For a one dimensional dump (i.e. air and water flow The percent copper leached per month (or the efflu- restricted to be vertical only), Eq. [17b] simplifies to: ent copper heads) can be computed easily:

OT aT ~2T fracti~lOemo =dXToTdt (2"68x10~ ~-o) =2"68x pTCT ~ = (PlClVl -- pgCgVg)-~- + ~A + KT 0?. z

[17b] ---d-t-- + G S dt E [22] One dimensional convective air flow through a dump dump N(Gs + GIGS) may be described:

kAVE AP [181 Vg- I~g H HEADS [g/1 Cu] = OR(1- 4,)H

H is the height of the dump, t~g is the viscosity of air + Cs -~--/ . looo [23] = 1.9 • 10 -4 poise.* AP is the pressure drop across the d---Y-- dump NVl *l poise = 0.1 Pa'S. dump. &P may be expressed as: The cumulative pet leached, 1 - XTO T is just: AP = PoogoHEHi(a(T i) r i + ~ (1 -- ion]g)) [19] (GNs XNs + Gs X S) fraction Cu leached = 1 ~ [24] i GNS + G S Here Poo is the density of air at STP, go is the gravita- tional constant, ffi = Hi/H, is the normalized thickness The next section compares the rate of leaching and of the ith incremental level of the dump. a(T i) is the the cumulative leaching of a test dump to the rate of temperature dependent coefficient of thermal expan- Ieaching and cumulative leaching computed by the sion which, like the heat capacity, includes the effects model through Eqs. [22] and [24]. of changing water vapor saturation. 13 is a coefficient which describes the decrease in air density due to oxygen depletion (~ = 2.83 x 10-2). [6~]g = [O,.]g/[o2]~Tp. CALIBRATION OF THE MODEL kAVE, the average permeability of the dump, may be Fig. 4 shows a cross section of the Midas test dump, expressed: built of mine waste with normal size distribution by 1 the Utah Copper Division of Kennecott Copper Corpor- kAV : E [201 ation at Bingham Canyon, Utah. The dump is about 400 ft long, 200 ft wide. The average depth is 20 ft with a

Any distance, zi, from the base of the dump, where fresh air is assumed to enter, the oxygen concentra- r C' tion in the dump will be: t C9 e8 C;' c6 C5 C4 C3 C2 c1 TEST HOLES

[ je = 1 [2I] r 7100J Eqs. [17b], [18], and [21] represent a model of the - TEMPERATURE OISTRIBUTION - Section C-C' dump leaching process that includes both physics (air > ! convection) and chemistry. The equations can be solved lr~ C9 D~ C7 C5 C5 C4 C3 C2 C1 TEST HOLES ' /-.~,~= 9-.- ~~~~~~~-'-- ' ..... using an implicit finite difference scheme in which the 7140 o dump is considered to be broken into N layers. The method used was to start the dump leaching at some 7100~ ~ " starting temperature and loop between Eqs. [18] and OXYGEN DISTRIBUTION ~ Section C-C' [21] until a steady state O 2 profile and air velocity was attained. Then Eq. [17b] was used to determine 50 0 0 log HORZ. ~, VERT. SCAL~ the temperature of the dump at t + At. At was gener- Fig. 4--August 1969 temperature and oxygen distribution in ally taken to be one month. The average rate of fluid a section through the Midas test dump, METALLURGICAL TRANSACTIONS g VOLUME6B DECEMBER 1975-621 maximum depth of 40 ft. Fifty-eight leaching ponds T (mo) = 10~ 1O.cos ((mo - 1)~/6) cover the top of the dump. The waste tonnage beneath the ponds is about 93,000 tons (assuming 1.7 tons/y@) where mo runs from 1 to 12 and is the number of the The waste itself is 60 pet quartzite and 40 pet biotite calendar month. Thus the top surface of the clump was gTanite. The average grade of the waste is 0.145 pct assumed to vary seasonally between 32~ and 68~ copper. 80 pet of the copper was sulfide, dominantly (0~ and 20~ a slightly more restricted and hotter chalcopyrite; the rest was nonsulfide copper. range than the ambient temperature variation of 19~ Leaching of the dump began on April 9, 1969. Prior to 63~ (-7~ to 17~ to this, there had been some runnoff through the dump The temperature at the base of the test dump was but very low copper extraction. Fig. 5 shows that observed to fluctuate somewhat. The assumption of a leaching after water application was slow at first, in- constant 20~ basal temperature is a matter of con- creased rapidly to a maximum about five months after venience and is probably subject to some error. Both the start of leaching, and then fell steadily, with some boundary conditions are plausible. Subsequentwork fluctuations that appear correlated with the season has shown these assumptions to be quite reasonable. (maximum in summer). Fig. 4 shows that by August The starting temperature of the model dump was 1969 the internal dump temperature had risen to 130~ 10~ The Midas test dump was built in winter so the (54~ There was substantial oxygen depletion as the dump was initially at least this cold. air convected through the dump. It can also be seen Fig. 6 compares the calibrated model leaching his- that the air conveeted in along the high permeability tory to the leaching history of the Midas test dump base of the dump and then up through the dump--the shown in Fig. 5. The match in general is quite good. one dimensional model is appropriate for this case. In addition to the leaching history similarity, the model As time went on the location of maximum dump tem- dump reached 51~ internal temperature by August perature shifted from the far end of the dump (as shown 1969 and then decreased in temperature to about 14~ in Fig. 4) to about the same distance from the near end. as did the far end of the Midas test dump. In August The parameters used in the model are listed in Table 1969 the effuent oxygen concentration was 9 pct, in II. good agreement with observation (see Fig. 4). The The following thermal boundary conditions were values of rCS and r DC are quite close to the values chosen. The base of the dump was fixed at 20~ The anticipated from Eqs. [14] and [15] (compare Tables top surface temperature was allowed to vary: I and II). The initial rise in extraction rate is due to the heat- ing up of the dump. This feature is not peculiar to the Midas test dump, and can be observed in the leaching 2.4 1 1 ] I l 1 i I I 1 I I I I 24 history of many dumps. The fall in leaching rate after 23 2.3 the first seven months of leaching is clue to the fact 2.2 22 the more accessible copper has been leached and Fe+++ 2.1 21 must diffuse through already leached areas to reach

2,0 20 the remaining copper. The fall in dump temperature also contributes to the decline in leaching rate. 1.9 19

1.8 18 o VARIATIONS FROM THE BASE d 1.7 17 o. z MODEL 1,6 16 0 It is of interest to vary the model parameters to see z" 1.5 MIDAS TEST DUMP 15 < o UCD 14 what effect they may have on the rate of copper extrac- k- 1.4 o x < ge uJ r,.. 1.3 /~ of Data 13 l- uJ ,,x 1.2 12 O Table II. Parameters Used for the Model Shown in Fig, 6 ,,=, 1.1 \\ o 1.0 10 Parameter Description Value u \ k- < .9 g H Height of dump 670 cm (22 ft) .8 \ 8 FPY Moles pyrite leached/mole Cu leached 47 < o k' Dump permeability k AVE l0 "s cm 2 ( 1000 0z .7 \\ 7 darcys) .6 \\N 6 V/ Rate of water application 2.26 X I0 "s cm3/ .5 # 5 cm 2 dump's (0.02 gal/ft 2' h) Gs Dump sulfide copper grade 0.t 16 wt pct .3 3 GNS Dump nonsulfide copper grade 0.029 wt pct TDS Diffusional sulfide leach time (20~ 1700 mo .2 2 7"CS Leach time for sulfide copper under surface 200 mo .'Y ~1 area rate control (20~ Diffusionai nonsuIfide Ieach time (20~ 500 mo I I I I i i I I I I [ t ?DNS 2 4 6 8 10 12 2 4 6 8 10 12 2 4 6 7"CNS Leach time for nonsulfide copper under 300 mo f// surface area rate control (20~ -- 69 -- DATE -- 70 -- E DS, E DNS Activation energies for diffusion 5.0 kcal/mol Fig. 5--The rate of extraction and cumulative extraction of ECS, E~NS Activation energies for chemical leaching 18.0 kcal/mol copper from the Midas test dump, using a five-month run- reactions ning average.

622-VOLUME 6B, DECEMBER 1975 METALLURGICAL TRANSACTIONS B MIDAS TEST DUMP 5 MONTH RUNNING AVERAGE been included, as yet. in the model. Secondly. not all 2.d 24.0 the parameters listed in Table III are mutually inde- 2.: 23.0 pendent. For example, increasing FPY at a constant

2., 22.0 sulfide copper grade will cause "rDS to increase substantially. LastIy, the combination of parameters that 2.1 21.0 successfully models the Midas test dump is not neces- 20.0 2.( sarily a unique set or the correct set. Data from more 15 19.0 than one test dump is needed to resolve these uncertain- 1.[ 18.0 ties. The most critical uncertainties are probably the d 1.1 17.0 chemical activation energies and FPY (see Table II). The lack of dependence of Ieach rate on permeability 1.f 10.0 z" o simply indicates the dump was shaIlow and permeable z" 15.0 o (J enough not to be oxygen starved anywhere. Had the F- 1.4 14.0 a: dump been thicker (~ 100 ft.), a significant dependence ee k- 1.3 13.0 xm of leach rate on permeability would be noted. x 1.2 12.0 re 1.1 11.0 o CONCLUSIONS 1.0 10.0 m >_. From the discussion presented it can be concluded: 9.0 ~" .9 < 1) Air convection is an important part of the dump .8 8.0 leaching process and must be accounted for in any re .7 7.0 successful model of this process (Fig. 3). .6 6.0 2) Exothermic oxidation reactions heat up waste

.5 5.0 dumps with time (Fig. 4). Any leaching model that is to be applicable to real dumps must account for the .4 4.0 temperature dependence of the leaching process. .3 3.0 3) A simple model that requires energy, mass and .2 2.0 momentum balance, and that derives rate control from .1 1.0 a temperature dependent shrinking core model and a single "average" waste particle diameter (Eqs. [12], 4 6 8 10 12 2 4 6 8 10 12 2 4 6 8 [13], [16]) has proved remarkably successful in ac- 969 - DATE - 70 - counting for the most important observed features of Fig. 6--Comparison of observed and calculated Midas test dump copper leaching behavior. the leaching history of a well studied test dump (Fig. 6). 4) Dump height, lixiviant application rate and dump permeability are the most important factors affecting the rate of copper leaching that are accessible to op- Table III. The Effect of Parameter Variation on Copper Recovery erational alteration. (Table III and discussion in text). After 24 Months of Leaching

Increase in Copper Recovered ACKNOWLEDGMENTS Parameter Variation in 24 Months, Pct The authors would like to thank Kennecott Copper H J +10 8.9 FPY J +10 6.2 Corporation for permission to publish this paper. In fDS --10 6.2 particular, the authors would also like to thank the G s J +10 4.8 Messrs. W. D. Southard, A. D. Pernichele and B. P. E~S + 10 2.7 Ream of Utah Copper Division for permission to use res - 10 1.8 the Midas test dump data as a base case for this study. Vt ,/ -10 1.3 Enough recognition cannot be given to the extensive. TDNs -- 10 1.3 E~s + 10 0.9 careful work of these individuals and others that was GNS +10 0.9 required to collect the high quality data so easily cited rCNs -- I 0 0.4 in this paper. E3N s + 10 0.4 Parts of this paper were presented at the 78th Na- Starting Temp +10 0.4 tional Meeting of the American Institute of Chemical E~NS + 10 0.0 k' +10 0.0 Engineers in a Symposium Section on Modeling and -10 -0.4 Analysis of Dump and In-Situ Leaching Operations, August 19, 1974 in Salt Lake City, Utah.

tion. Table III lists the parameters of Table II and NOMENCLATURE shows the percent increase in copper extraction after a : radius of a waste particle, [cm] a R twenty four months of leaching that results from a 10 sulf : surface area of sulfide mineralization pct alteration in the listed parameter. The parameters per unit volume of waste, [cm -I] that are checked affect the rate of leaching primarily % : heat capacity of gas phase in dump in- by allowing the dump to attain higher temperatures. cluding effects of variable water satu- The reader is cautioned that the variations in leach ration, [g/cm 3] rate shown in Table III are based only on what is in the C : heat capacity of mobile liquid phase in model. Much may go on in a waste dump that has not dump, [cal/g ~

METALLURGICAL TRANSACTIONS B VOLUME 6B, DECEMBER 1975 623 C T : heat capacity of dump as a whole, ing in the dump or a given layer of the [cal/g ~ dump, [-] : diffusion constant of oxidant in water, z i : distance o[ center of ith layer of dump D OX~ [cm2/s] from base of dump, [cm] EDS, EDNS : activation energies describing, through Eq. [16], the temperature dependence of GREEK LETTERS "1"0.9, tONS, [kcal/mole] a : coefficient of thermal expansion of air : activation energies describing, through including effects of changing water vapor Eq. [16], the temperature dependence of saturation. [-] ,r C S , T C NS, [kcal/mole] /3 : coefficient describing the chainge in air FPY : moles of pyrite leached per mole of sul- density due to oxygen depletion. (See fide copper leached [-] Eq. [191), [-] GS : initial copper sulfide grade of dump, 6 :reaction skin depth, [cm] [wt fraction Cu] /~g : viscosity of the gas phase in the dump, GNS : initial copper nonsulfide grade of dump, [wt fraction Cu] PR : density of waste particles, [g/cm 3] go : g-cavitationaI acceleration, [cm/s e] PT : density of the dump as a whole ("Total" H : height of dump, [cm] dump) (PT = PR [1- ~p]), [g/cm 3] : thickness of ith layer of dump, [cm] Pl : density of liquid phase of dump (water), H i : dimensionless thickness of ith layer of [g/cm 3} dump hr i = H i/H, [-] 0g : density of gas phase in dump including Mt R : enthalpy of reaction, [kcaI] effect of variable water vapor saturation, KAVE : oxidant required to Ieach waste particIe, [g/cm3l [g/cm 3 particle ] Poo : density of air at standard temperature KT : thermal conductivity of dump as a whole and pressure, [g/cm 3] (total dump), [cal/cm ~ s] TDS , rDN s : time to leach typical waste particle com- k' : intrinsic permeability of the dump, [cm 2] pletely of sulfide or nonsulfide copper k : average permeability of the dump assuming rate of leaching is limited by (i Darcy ~ 10-8 cmZ), [cm 2] diffusion of oxidant or acid into the par- kox : chemical rate constant characterizing ticle, [mo] reaction of oxidant and sulfide minerals, .rcs ' .rCN S : time to leach typical waste particle com- [cm/s] pletely of sulfide or nonsulfide copper N : number of layers into which dump has assuming the rate of leaching is con- been arbitrarily broken for sake of com- trolled by the shrinking surface area of putation (usually 30), [-] the sulfide or non-sulfide copper ("chem- fOx] : concentration of oxidant, [g/cm 3] ical" control), [mo] [ o~t~r p : concentration of oxygen in air under : interblock porosity of dump (usually standard conditions of temperature and ~25 pct), [-] pressure, [g/cm 3] ~ : porosity of waste through which diffusion [%] g : concentration of oxygen in gas phase of can take place, [-] dumps, [g/cm 3] [02] g : normalized oxygen concentration in gas phase of dump [o2]g = [02]g/[o~]gTp, [-] REFERENCES ~P : pressure drop across (bottom to [6p-) the 1. H. W. Sheffer and L. G. Evans: Bureau of Minesl.C., 1968, no. 8341, 57 pp. dump (106 dynes/cm 2 ~ 1 atmosphere), 2. J. A. Harris: Proc. Australian Inst. Mining Met., 1969, no. 230, pp. 81-92. [dyn/cm 2] 3. R..I. Roman, B. R. Benner, and G. W. Becket: SME-AIME Trans., 1974, rot. : gas constant 2), [cal/~ 256, pp. 247-52. R (~ 4. R. L. Braun, A. E. Lewis, and M. E. Wadsworth: Solution MiningSymposium, 6~A : rate of heat generation, [kcal/cm3dump s] Chapt. 21, pp. 295-323, American Institute of Mining, Metallurgical and 6/02 : rate of oxygen consumption, Petroleum Engineers Inc., New York, 1974. [g Oa/cm dump-s] 5. B. W. Madsen, M. E. Wadsworth, and R. D. Groves: SME-AIME Trans., 1975, fftCu : rate of copper leaching [g Cu/ema-dump s] vol. 258, pp. 69-74. T : temperature of dump at any partieuIar 6. R. W. Barflett: Proceedings o/the b~ternational Symposium on Hydro- metallurgy, Chapt. 14, pp. 331-74, American Institute of Mining, Metallurgical location. Temperature of water, rock, and Petroleum Engineers Inc., New York, 1973. and gas phases assumed identical, [~ 7. J. D. Lowelland J. M. Guilberu Econ. GeoL, 1970, vol. 65, pp. 373-408. : tortuosity of diffusion channels, [-] 8. M. E. Wadsworth: Universityof Utah, Salt Lake City, Utah, personal com- % : darcy gas velocity through dump, munication, 1974. [cm 3 gas/cm 2 dump ar ca. s ] 9. J. D. Stephens: Kennecott Copper Corporation, Salt Lake City, Utah, personal communication, 1974. : darcy velocity of water passing through V l 10. Y. T. Auck and M. E. Wadsworth: Proceedings of the International Sym- the dump. Average rate over application posium on ftydrometallurgy, Chapt. 25, pp. 645-700, American Institute of periods and rest cycles is used. Mining, Metallurgicaland Petroleum Engineers Inc., New York, 1973, [cm 3 water/era"dump surface, s] 1t. C. T_ Mathews and R. G. Robins: Aust. Chem. Eng., 1972, pp. 21-25. : fraction of initial nonsulfide copper re- 12. E. E. Smith and K. S. Shumate: Water Pollution Control Research Series XNS 14010 FPS 02/70, U.S. Department of the Interior, Federal Water Wuality maining in dump or given layer of dump, Administration. 1970. [-] 13. A. E. Lewisand R. L. Braun: UCRL.73284 preprint, Lawrence Livermore XS : fraction of initial sulfide copper remain- Laboratory, January 1972.

624-VOLUME 6B, DECEMBER 1975 METALLURGICAL TRANSACTIONS B