DYNAMICS OF LEACHING A UNIFORMLY FISSURED ORE BODY A. A. Ignatov and S. A. Proskurin

Predicting the relation between the mining-geological characteristics of an ore body and the process conditions for extracting metals by leaching requires a study of the laws governing the rate of the physico-chemical processes in the ore body in respect of both location and time [i]. This is most frequently based on experimental data obtained by leaching ore particles packed in a column. The results are presented as interpolated empirical Eqs., applicable to the particular type of ore within the range of the experimental conditions [2, 3]. Analytical methods have been used by [4-6] to study the dynamics of leaching of a single ore sample under specified limiting conditions of mass transfer. In the present work, mathematical simulation was used to study the dynamics of mass transfer during the percolation of a reagent solution through a packing of coarse ore particles. The uniformly fissured ore body was represented by a cubic packing of spherical particles of constant radius, formed from a chemically inert silicate cement with a uniformly distributed soluble mineral component. The rate of percolation of the reagent through the packing was constant. The proposed model can be used to find the conditions for underground hydrodynamic leaching [7]. In the extension of the work [8], the mass transfer Eqs. were integrated, assuming a simple diffusion mechanism, but in the present work, the rate of non-catalytic solid-liquid reaction was deduced on the basis of both the kinetics of dissolution of the mineral component of the ore and the rate of diffusion of the dissolved substance. Let us assume that a nonrversible reaction takes place inside each particle of the packing in the endless spherical layer separating the zones of reacting and nonreacting components of the ore. In the course of leaching, the radius of the reacting layer is gradually reduced. Let the Eq. of the reaction between the reagent A(£) and the mineral component of the ore B(s ) occur without a change in volume, then v,Act ~+vtB~ s~ -~ vml]cP-r~+ v w W ,

(i)

where ~(p_p) is the mineral component of the ore, and W is the nonmineral reaction product. Migration of the dissolved component in the solid-liquid system is defined by the conditions for the mass transfer equations which can be written in the following dimensionless forms:

0~= 0"-~=

1 D= 0 [ O~a~

~
r ~ V A Or ~r Tr J'

O~X~t,:

--&- + VTK aC~t

aC a

r =

,~>0;

-.2'M~,(C,,--C~,I,.=,), .

_

.-.

•

""

O~0;

-~ - / t vt ~l,=C-: -c > O; O~m OoCA= ~ Z , O < X < t ; ~: j;-r = Or'

r =

OC a

t: ~

.----' Bi~. ( C a - - C o , ) , "

x = O : Cm=O, CA

O~.~X~
(2) (3)

(5) (6)

(7)

CA

~ = o: P . = c~,= o~ ~ = i

(8)

Magadan. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 6, pp. 104-110, November-December, 1986. Original article submitteed April 7, 1986. 512

0038-5581/86/2206-0512

$12.50

O 1987 Plenum Publishing Corporation

where

C~=---.-, ca " X =

T

VA~A . v-~,' J°m-- v,~lt m m

C~=--;-; cot ;

=

V=D---~; " VA~ A

P'=--; vt~t

.

cA

M=

c:=

;

=

Dm

~D A

Pdr~

Bi =~¢',PO,i

kPo

~, Po

r=

;

g;

DAt

and the index a = A indicates the reagent, and a = H the minera ! component; CA, CA, concentrations of the reagent in the stream and in the particle; Cm, Cm, concentrations of the mineral component in the stream and in the Rorous zone of the particle; C~, concentration of the saturated mineral component solution; C~, concentration of the reagent at the inlet; D, P0, radial coordinate and the external radius of the particle; x, L, longitudinal coordinate and the length of the packing; t, time; g, radius of the dissolution front in the particle; v, rate of solution flow; DA, Dm, diffusion coefficients for the reagent and the dissolved mineral component; k, velocity constant of the heterogeneous reaction; 7B, density of the mineral component of the ore; e, porosity of the packing; ~, porosity of the leached zone of the particle, or the volumetric proportion of the mineral component Bs; Ssp = 3(1 - E)/00, external surface area of the particle in unit volume of packing; 8A, 8m, coefficients of mass transfer, for the reagent and the mineral component, between the particles and the stream; vi, ~i, stoichiometric coefficients and molecular weight of the reactants (i = A, B, ~, or

W). Let us make a few comments. Equation (3) defines the transfer of the dissolved components in the voids of the packing, for high values of the Peclet diffusion number (Pe D = vo0/D A >> I). The kinetic Eq. (4) defines the dynamics of the surface reaction ~ = ~(T), between the leaching and nonleaching zones of the particles. Boundary conditions of the type (5) are valid for an unsaturated mineral componen ! solution (Cm|r= ~ < i). For a saturated solution, boundary conditions of the first type Cm{r= ~ = i, 0 =¢ X & I, are used, but the reagent concentration profile is found from boundary'conditions of the second order: r

~:-~;=-~7'

O
In deriving the mass transfer equations, a linear relation between the porosity of the parti cle M, the coefficients of active diffusion and mass transfer, was assumed. A more complex model for determining the coefficients [9] does not appear from a numerical integration of Eqs. (2)-(8) to be limiting. The area of the reaction surface in the particle was calculated from S s = 4~g2~. The value CX is the minimum concentration of the reagent, at the external surface of the particle, which will produce a saturated solution of the mineral component by the surface reaction. The value of C~ can be found from the mass balance for the reactants:

0;.1

&m

"

For the proposed linear approximation of the concentration profile in the leached zone, and a diffusion controlled process, we have:

;m=¢

;*= 0; , .

"D

The numerical solution of Eqs. (2)-(8) for various conditions was obtained by integral-interpolation [i0]. Two point boundary conditions for Eq. (2) were solved by implicit prediction, with an error 0(~r 2, AT), where ~r, fit are the uniform steps of the particle radius and time grids. The equation of transfer into the stream (3) was integrated implicitly with a first-order accuracy 0(fiX, ~T), where AX is the step in the longitudinal grid of the packing. These methods were completely insensitive to errors of rounding and ensured the maintenance of the material balance in the packing. In order to avoid the iterative processes in the integration of the nonlinear systems (2)-(8), the first part of 513

0,;-

?

o

iv

~o

~o

.z

Fig. i. Relation between Z and $ for the same kinetic ratio ~ / x B (I) or diffusion ratio T~/T B (2] c?mponents of the total leaching time: C~ = 0.8; V = 1.0; Bi A = 10 4 . Eq. (4) was based on the solution of Eq. (2) for the previous time section. Special tests showed that these methods could be used to evaluate the parameters with a first-order accuracy. The mass-transfer equations were integrated in the following order. The concentration profiles CA, CA in the particles and in the stream wer_e calculated for a sequence of time sections. The results were used to find the profile Cm, C~. If C m r=g > I, then, for a difm fusion controlled mechanism, the values of Cm, C_m were recalculated for the boundary condition Cmlr= ~ = i, so as to match the Cm, C m and CA, C A profiles. An algorithm was developed on this basis for calculating the process parameters on a BESM- 6 computer. The fraction of the mineral component extracted from the packing was calculated from the equation

~l(t)=

mn~t)

o •

mm t,

where ram(t)=

S~V[em(L,t')dt' is

the mass of the mineral component removed from the packing by

0

the stream up to the time t, and m~ = SL(I- E)~yt(Pt/Pm) is the maximum possible value of mm(t) with complete leaching, S is the cross-sectional area of the packing, Cm(L, t') is the concentration of the mineral component at the packing outlet at the time t'. A comparative analysis of the theoretical results was made under conditions such that the error of the integral process performance, n(t), did not exceed l-2Z. The performance of the algorithm for integrating Eqs. (2)-(8) was established by determining the limiting conditions for leaching a single particle [5, 6]. Calculation of the process coefficients for strictly internal diffusion or kinetic mechanisms showed that the leaching parameters could be evaluated theoretically with an error not exceeding I%. It will be noted that the number Z, used in Eq. (5), is the ratio of the duration of the process in a single particle under an internal diffusion mechanism to that under a kinetic mechanism. The relative contributions of these processes to the time of leaching is shown in Fig. i. For small values of Z, the time for complete extraction Tt tends to the value ~ for a full kinetic mechanism. At higher values of Z, ~t tends to the time of leaching •~ ~or a full diffusional mechanism. Let us apply the above methods to study the leaching of chalcocite with sulfuric acid saturated with oxygen. If we take into account the low rate of mass transfer in the hydrometallurgical extraction of nonferrous metal ores, the calculations are of considerable practical help in selecting, from a detailed calculation of the reaction mechanism, a method for accelerating the complex mass transfer process. For the reaction + H20, C u , S + H , S O 4 ÷ - f 5 0 , - + . 2CuSO, . ,

514

J ~6

o,6-

o,2o

a,4

a,,8

x

~

o

o,8

z

Fig. 3

Fig. 2

Fig. 2. Concentration profile of reagent in voids of packing during leaching: i) • = 99.2; 2) • = 198; 3) T = 248; C~ = 1.0; V = 0.125; B~ = 25. Fig. 3. Longitudinal profile of nonreacted p a r t of mineral component in packing during leaching: I) x = 99.2; 2) x = 248; 3) • = 347.2; C~ = 1.0; V = 0.125; Z = 16.5; B~ = 25.

3O0-

I00-

L

6

o

CA

2,5

s

45

CA

Fig. 5

Fig. 4

Fig. 4. Relation between time of complete leaching of packing and inlet concentration of reagent C~: i) V = 0.125; 2) V = 1.0; Z = 14.5; B~ = 25. Fig. 5. Relation between consumption X and inlet concentration C~ of the reagent: i) V = 0.125; V = 1.0; Z = 14.5; B~ = 25. which takes place in two stages, the velocity constant k for the dissolution of the chalcocite is determined by the velocity constant of the first stage of the reaction, since the intermediate mineral, covellite (CuS), in the presence of oxygen is oxidized at a much greater rate than the rate of the first stage of the reaction. Typical values of the physicochemical constants are: Dry,= | 0 7 ' . m t ] h ; ' D , == iO-5 m ! / h ; " "" "

, ; # 2 4 0 kg ,; 6 =8

gm';k = 5 .,t0-4 roth;

~, == ,5650 k g . / m ' ; p , ' = 0 , 6 t 7 ;

/~m=,, 0 , 3 0 6 ;

p+=2,5.

$ ==0,35;

{0 "t m; L="5,0m;

z = 0,05; v = 0,01 m/h; ~, ----I0-' m/h. Some interesting features and time, the rate of sorption can be explained. In general, leached zone, a reaction zone,

of the dynamics of the reagent, the packing can and a nonleached

of the reagent concentration profile in space and the formation of soluble reaction products be divided into three zones: a completely ore zone. Sorption of the reagent converts

515

the mineral component B s into a soluble form N(p_p), creating a boundary in the middle zone which gradually expands, and the nonleached zone shrinks. In the nonleached zone, the reagent concentration falls to zero, since the reagent is completely used up in the middle zone. With a low rate of solution percolation through the voids of the packing, typical concentration profiles in the direction of flow through the packing, and the proportions of nonleached mineral component B s are shown in Figs. 2 and 3. On the basis of similar profiles, it is not difficult to calculate the speed of movement of the leaching boundary. With increasing reagent inlet concentration and rate of reagent flow, the fronts of the CA(X)/C ~, ~(X) profiles become more sloping and the zone of active reaction occupies a greater part of the total length of the packing. The relation between the time for complete leaching of the packing, Tt, and the rate of flow and inlet concentration of the reagent solution, has been studied (Fig. 4). It was established that, in general, the rate of reagent solution flow had a significant effect on the value of Tt, particularly for small values of C~ (C~ ~ i). With increasing rate of flow, the time of leaching approached a lower limiting value,-equ@l to the time to leach a single particle i~mlersed in a solution of constant concentration C~. With increasing values of C~, the time of leaching of the packing tended to a limit, equal to the time of leaching a single particle by a diffusion controlled mechanism. Under these conditions, the concentration at the surface reached a saturation value, C* m" A study of the relation between the values of Tt, C~, and V has shown that measures to reduce the total reagent consumption and hence improve the efficiency of utilization of the reagent, can be deduced from the expression: Z=

.,(~--e)xYtP t c ~ '

where t t is the time for leaching, corresponding to the time T t. The numerator of this expression is proportional to the minimum expenditure of reagent for leaching the mineral component from the packing; the denominator is the mass of reagent entering the packing. It will be seen from Fig. 5, that increasing the reagent concentration (C~ 2) and the rate of percolation (V > 0.i) will cause a sharp drop in the efficiency of reagent utilization. Under normal conditions, the rate of solution flow should be small (V < 0.i) and the reagent concentration high. This will reduce the reagent expenditure and the leaching time. The method can be used to study the process under the following conditions: (a) in packings of sufficient length to generate a saturated solution which will reduce the rate of leaching; (b) with variable reagent expenditure, to reduce the adverse effect of the saturated solution and improve the reagent utilization and other process conditions; (c) when the heterogeneous reaction produces both soluble and insoluble compounds. CONCLUSIONS i. Dimensionless criteria and numbers have been derived, the numerical values of which determine the mass transfer processes during the percolation leaching of a packing of coarse ore particles. The rate of chemical dissolution and the mechanism of transfer of the mineral into a soluble form have been considered. 2. As an example, the leaching of a copper sulfide ore with sulfuric acid has been studied, and the relation between the efficiency of utilization of the reagent, the initial reagent concentration and the rate of percolation has been established. LITERATURE CITED i. 2. 3.

4.

516

D. M. Bronnikov and A. A. Spivak, "Major problems of geotechnology," Fiz.-Tekh. Probl. Razrab. Polezn. Iskop. (1982). V. G. Bakhurov, S. G. Vecherkin, and I. K. Lutsenko, in: Underground Leaching of Uranium Ores [in Russian], Atomizdat, Moscow (1969). A. Grizo, "Leaching of a low-grade chalcocite-covellite ore containing iron in sulfuric acid: influence of pH and particle size on kinetics of copper leaching," Hydrometallurgy, !, No. 8 (1982). B. W. Madsen, M. E. Wadsworth, and R. D. Groves, "Application of a mixed kinetics model to leaching of low-grade copper sulfide ores," Trans. Soc. Min. Eng. AIME, !, No. 258 (1975),

5.

6. 7. 8. 9. I0.

G. A. Aksel'rud and V. I. Lysyanskii, in: Extraction (Solid-Liquid Systems) [in Russian], Khimiya, Leningrad (1974). O. Levenshpil', in: Engineering Design of Chemical Processes [in Russian], Khimiya, Moscow (1969). G. D. Lisovskii and D. P. Lobanov, in: Heap and Underground Leaching of Metals [in Russian], Nedra, Moscow (1982). A. A. Ignatov and A. B. Ptitsyn, "Simulated dynamics of leaching nonferrous metal ore," Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 4 (1985). Ch. Satterfil'd, in: Mass Transfer in Heterogeneous Catalysis [in Russian], Khimiya, Moscow (1976). A. A. Samarskii, in: Introduction to Theory of Differential Systems [in Russian], Nauka, Moscow (1971).

517