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Kinetic model for batch bacterial dissolution of pyrite particles by Thiobacillus ferrooxidans
Chemical En&emimg F’rinted
Sclencr. Vol. 47, No. I, pp. 133-139,
1992.
cm-2509p2
in Chat Britain.
0
KINETIC
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1991 Pemo
Press plc
MODEL FOR BATCH BACTERIAL DISSOLUTION OF PYRITE PARTICLES BY THXOBACILLUS FERROOXIDANS
SATORU ASAI, YASUHIRO KONISHI and KATUYA YOSHIDA Department of Chemical Engineering,University of Osaka Prefecture, 804 Mozu-Umemachi 4-cho, Sakai, Osaka 591,Japan (Received for publication
16 May 1991)
Abstrnet-The kinetics of the bacterial dissolution of pure pyrite (Fe&) particles by Thiobaci~fusfirrooxidamswas studied at di&rent initial particle sizes in a well-mixed batch reactor. Experimental studies were ma& on the adsorption of bacteria on pyrite particles as well as the bacterial dissolution of pyrite. The
Langmuir isothermwas usedto fit the adsorption data. The equilibriumconstantin the Langmuir equation was independentof the particle size, whereas the maximum adsorption capacity per unit weight of pyrite increased with decreasing particle sire. A rate expression for the kinetics of bacterial growth and pyrite
dissolution was derived, taking into account the effect of initial particle size. The kinetic parameters appearing in the rate equations, the growth yield and specific growth rate of adsorbed bacteria, were evaluated by curve-matching, using the experimental data obtained at different initial particle sizes. The evaluated kinetic parameters were found to be independent of the initial particle size. This kinetic model was successfully used to predict the bacterial dissolution behavior for the dil%mnt operating variables, i.e. the initial particle size, the initial cell concentration and the initial pyrite-liquid loading ratio.
INTRODUCTION
It is widely accepted that certain bacteria play a major role in most leaching operations for metal sulfides. One of the most important bacteria in the sulfide leaching is an acidophilic chemoautotrophic bacterium, Thiobacillus fmooxidans, which can multiply with mineral sulfur as a solid substrate. The bacterial leaching is referred to as the microbial oxidation of metal sulfide. The bacterial leaching techniques are applied to the recovery of copper and uranium from low-grade ores and the removal of pyritic sulfur from coal (microbial desulfurization). In spite of the abundant amount of information available on bacterial leaching, the growth kinetics of bacteria attached on the mineral surface are poorly understood. In a previous paper (Konishi et al., 1990) a mathematical model was developed to describe the kinetics of the batch growth of T. fmooxidans on pure pyrite (Fe&) and the subsequent dissolution of pyrite. The previous paper described the development of the model, along with an evaluation of key parameters appearing in the rate equations (the specific growth rate and growth yield of bacteria attached on pyrite) from experimental data. The emphasis in the previous work was laid on the fact that, during the bacterial dissolution process, the number of attached bacteria was related to the number of free cells through the Langmuir adsorption isotherm, and that, furthermore, the growth rate of adsorbed bacteria was proportional to the product of the number of adsorbed cells and the fraction of solid surface unoccupied by cells. However, the effect of particle size on the growth kinetics has not yet been addressed experimentally and theoretically.
The purpose of this work is to obtain kinetic data on the bacterial dissolution of pure pyrite by T. ferrooxidans using different particle size fractions, to take into account the effect of particle size into the previous kinetic model (Konishi et al., 1990), and to consider the influences of various operating variables on the bacterial dissolution rate in a batch bioreactor.
EXPERIhIENTAL
SECTION
For the kinetic analysis of bacterial growth and pyrite dissolution, it is important to estimate the number of bacteria attached on the pyrite surface. Adsorption experiments are a useful means of estimating the number of attached bacteria. Thus, the following experimental studies were made on the adsorption of T. ferrooxidans on pyrite particles as well as on the bacterial dissolution of pyrite.
Materials
The pyrite used in this study was a natural mineral of high purity (95% Fe&). The mineral was ground and was then sieved to obtain three different size fractions, 53-63 pm, 63-88 pm and 149-177 pm. Thiobacillus ferrooxidans was obtained from Dowa Yanahara Mine, Japan. The original strain was transfered to 9 K liquid medium (Silverman and Lundgren, 1959) supplemented with 1 W/V % FeS,, in order to adapt the cells to the particular pyrite. The adapted strain of T. fmooxidans showed a dramatic reduction of lag time for the batch cultivation, as pointed out by HofFmann et al. (1981). The inoculum age of about 10 days was used in the following adsorption and dissolution runs.
133
134
SATORU
ASAI
et al.
Apparatus and procedure In the adsorption experiments, an accurately weighted amount of pyrite particles (0.5 and 1.0 g) was mixed with 100 cm3 of iron-free 9 K liquid medium at pH = 2 in a flask. The initial number of cells in the liquid phase was varied from 8.80 x 1O1’ to 1.15 x 1015cells/m3. The flask was shaked at 30°C for three hours. After the adsorption equilibrium of T. ferrooxiduns was reached, the number of cells in the liquid phase was counted with Toma’s Hematometer, according to the procedure proposed by Imai et al. (1970). The number of cells adsorbed on pyrite was determined from the difference of the number of cells in the liquid phase before and after adsorption, since the adsorption of cells to the flask wall was found to be negligible. The dissolution reactor was an air sparged agitated vessel of 600 cm3. The reactor was operated batchwise with respect to the liquid, and the liquid stirrer was driven at 500 l/min. Air was continuously fed into the liquid at 2000 cm3/min. The liquid temperature was 30°C. A dissolution run was initiated by inoculating 5cm3 of an active culture of T. ferrooxiduns to 500 cm3 of the modified 9 K medium with the initial iron concentration of around 0.3 kg/m3 and the initial pH = 2. The initial cell number ranged from 1.02 x lOi to 2.53 x 1014 cells/m3. After that 5 g of pyrite of the desired size was added to the liquid medium, and this is taken as zero time. As the dissolution proceeds, the pH value was controlled at the initial value by adding a small amount of KOH solution. The liquid samples were withdrawn from the bioreactor for analysis. The number of cells in the liquid was counted by using Toma’s Hematometer, and the concentrations of total iron and ferrous iron were determined by redox titration_ In some runs, the solution samples were analyzed for sulfate ions by the EDTA-Ba method (Iritani and Tanaka, 1958).
EXPERIMENTAL
BESULTS
XL x
IO-l4
@olIslm3)
Fig. 1. Isotherms for the adsorption of i’%bbaciillrs fmooxidans on pyrite particles at &&rent particle diameters DPO’ curves given in Fig. 1 represent the Langmuir isotherms predicted from eq. (l), using the evaluated values of X4, and K,. For each particle size. the Langmuir isotherm provides a valid fit to the experimental data. Table 1 lists the values of X,,,, and K, evaluated for the particle sizes covered in this work, along with previous data for particle size fraction of 25-44 pm (Konishi et al., 1990). The adsorption equilibrium constant K, is practically independent of the particle size, whereas the maximum adsorption capacity X_,, per unit mass of pyrite decreases with increasing particle size. The decrease in X,,,, is presumably explained by considering a decrease in the specific surface area, reflected by an increase in the particle size.
Bacterial dissolution Preliminary experiments revealed that the chemical oxidation of pyrite by ferric iron can be neglected under the present experimental conditions. During the bacterial dissolution, therefore, the following direct microbial action is believed to take place: 2FeS, + 70, + 2HsO -* 2Fe2+ + 4SOi-
+ 4H+
Adsorption equilibrium Isotherms for the adsorption of T. ferrooxtians on pyrite obtained at three different sizes are presented in Fig. 1, where the concentration X, of adsorbed bacteria are plotted against the concentration X, of free bacteria in the liquid phase. It is evident that, as the particle becomes small, the amount of adsorbed bacteria increases. The equilibrium isotherm data at each particle size is characterized by a monotonic approach to a limiting adsorption amount, indicating that the data can be modeled by the Langmuir equatiom X, = KAXA,XLI(~
+ &XL)
(1)
where X,,,, is the maximum adsorption capacity per unit weight of pyrite and KA is the adsorption equilibrium constant. Since a plot of XL/X, vs XL at each particle size gave a straight line, the two constants X,_ and KA were evaluated from the slope and intercept of the best fitting lines, respectively. The solid
(a) The ferrous iron formed is immediately oxidized to the ferric iron according to the liquid-phase reaction
catalyzed by T. ferrooxidans: 4Fe2+ + O2 + 4H+ +4Fe3+
+ 2HsO
(b)
Figure 2 shows the relative release of both total iron and sulfate from pyrite into the liquid phase, which was measured during the bacterial dissolution. The molar concentration of sulfate formed, {SO:- } is 2 times that of iron leached, {Fe}, e z,,, where (SO:-}, and {Fe},, denote the Y~-,‘oy initial concentrations. This experimental result indicates that the bacterial leaching of iron and sulfur from pyrite proceeds stoichiometrlcally, according to reaction (a). In addition, all the leached iron was found to be present as ferric iron, as expected from reaction (b). Figures 3 and 4 show time courses of total iron concentration [Fe]= and free bacteria concentration
Kinetic model for batch bacterial dissolution
13s
of pyrite particlcJ
Table 1. Effect of particle size on maximum adsorption capacity X,,, adsorption equilibrium constant K,. and growth yield YA of adsorbed bacteria Particle X&X 10-t” (cells/kg-FeS,) 25-44 53-63 63-88 149-177
x 10’s (m3/cells)
K,
6.61t 2.50 1.41 0.912
Y” x lo-“’ (cells/kg-Fe&)
4.68 t 3.58 4.03 5.29
3.30’ 3.61 3.30 3.88
+ Konishi et al. (1990).
o 53-83pm A 83-88pm c 149-177gm 2.0 -
Fig. 2. Relative release of iron and sulfur during bacterial dissolution at initial pyrite-liquid loading ratio W,/V = 10 kg/ms, initial particle sire Dr,, = 53-63 ,nm, initial cell initial iron conconcentration X,, = 0.72 x lot’ alls/mg, centration {Fe},, = 10.8 mol/m3. and initial sulfate coneentration {SO:- Je = 48.4 mol/m”.
XL in the liquid phase. It is evident that, after a brief lag phase, the dissolution of pyrite takes place with an increase in the concentration of free bacteria in the liquid phase. The significant increase in the concentration of free bacteria with respect to time is likely to be due to the release of bacteria from the pyrite surface. This idea comes from the fact that the growth rate of T. jkrooxidans adsorbed on pyrite is much higher than that of free bacteria suspended in the liquid (Konishi et al.. 1990). Figures 3 and 4 demonstrate that the kinetics of bacterial growth and dissolution are markedly affected by the initial particle size LIP0 of pyrite as a solid substrate. The amount of iron dissolved and the number of free bacteria increase greatly with decreasing initial particle size. Although the concentration of adsorbed cells cannot be easily measured, it may be considered from the adsorption isotherms observed in this work (Fig. 1) that the number of adsorbed cells per unit weight of pyrite increases with decreasing the initial particle sixe. Thus it can be concluded that an increase in the capacity of pyrite to adsorb bacteria, reflected by a decrease in the particle size, gives an increase in the rates of bacterial growth and subsequent pyrite dissolution.
OoO
15
10
5
Time ways)
Fig. 3. Time course of total iron concentration [Fe]= in the liquid phase at initial pyrite-liquid loading ratio W,/V = 10 kg/m3, initial iron concentration [Fe]rc = 0.3100.380 kg/m3 and initial CA1 concentration XTO = 1.02 K 1014-2.53 x lOz4 cells/m3 (effect of initial particle diameter D,.,,). Solid curves were computed from mathematicd model described in the text.
ANALYSJS
OF KINETIC
DATA
A kinetic model was developed to describe the batch growth in the dissolution of pyrite caused by direct microbial action (Konishi et al., 1990). According to the previous model, the total growth rate is expressed as the sum of the growth rate R, of bacteria adsorbed on the solid surface and the rate R, of bacteria suspended in the liquid phase: (dX,/dt)
= RA + RL
(2)
- @‘a
(3)
with XT = X,( W,/V)(l
RA = pAXXAf3v(WO/V)(i RL = P‘XL(1 0. = (X&
- #)
- X_4)/X&
+ (I - 4)X,
- a)‘,’
(4) (5) (6)
136
SATORU
Ash41
where X, is the concentration of total bacteria per unit volume of solid-liquid mixture, pA is the specific growth rate of adsorbed bacteria, W, is the initial weight of pyrite, V is the volume of solid-liquid mixture, I$ is the volume fraction of pyrite in the solid-liquid mixture, and a is the fraction of pyrite dissolved. It should be noted that the term (1 - ~1)~‘~ in eqs (3) and (4) is used to represent a decrease in the surface area of pyrite particles due to dissolu~on. The kinetic model emphasizes that the growth rate. RA of adsorbed bacteria depends on the fraction 0, of adsorption sites unoccupied by bacteria. The growth rate R, is proportional to the dissolution rate of pyrite as a solid substrate: R, = - (Y,/V)(dW/dt)
(7)
where W is the weight of pyrite at any time. The growth yield Y, of bacteria on pyritic sulfur is defined as: r, = [(XT - X,,)
v -
a%fm/(~Wo)
et al.
:
15
Inflg.3
Sydmlssmeas 0
I
I
I
5
I
I
lo
I 15
Tl m e (days) Fig. 4. Time course of concentration X, of fee cells in the liquid phase at initial pyrite-liquid loading ratio W,/V = 10 kg/m’. initial iron concentration [Fe&, = 0.3100.380 kg/m3 and initial cell concentration XT0 = 1.02 x 10”-2.53 x 1Ol4 cells/m3 (effect of initial particle diameter L&-,). Solid curves.were computed from mathematical model described in the text.
(8) Y, is the growth yield of bacteria on ferrous iron and j- is the weight fraction of iron is pyrite. Since the ferrous iron formed in reaction (a) is readily oxidized through reaction (b), the net formation rate of ferrous iron can be assumed to be zero: where
(1 - +)(d[Fe*‘]/dQ
= - (f/V)(dW/dr)
- RJ&
= 0.
(9)
Combining eqs (2), (4)-(7) and (9) and rearranging gives the final expression for the total growth rate as: (dX,/dQ
= PAXA(~ - X,lX,,J(w,l~)(l
- 01)~‘~
x (1 +fY,/r,)-
(IO)
The time-variation of the total iron concentration [Fe]= in the liquid phase can be related to the total growth rate by combining eqs (2), (7) and (9): (1 -
dMKWT/W = - (f/WdWW = [A’( 5 +fY,)l(dX,/W.
(11)
Since the adsorption rate of bacteria is much higher than the rates of bacterial growth and dissolution, the adsorption equilibrium can be considered to be achieved during the dissolution process. Consequently, the concentration X, of adsorbed bacteria can be eliminated by writing it in terms of the Langmuir adsorption isotherm. eq. (1). This is an important point because the surface concentration X, cannot be easily measured and the appearance in the performance equation must be avoided. Eliminating the unknown X, from eqs (1) and (3) and rearranging gives the following expression for the total cell concentration XT as a function of liquid-phase cell concentration X, alone: XL = CJ{(l -
- 9) - K,X,
((1 -
9) -
K,X,
Fig. 5. Evaluation of growth yield YA of T. ferrooxidans Adsorbedon pyrite particles (effect of initial particle diameter Dpo). The conditions are the same as in Fig. 3.
The above-mentioned performance equations were used to evaluate the growth yields Y, and the specific growth rate pA from the experimental data obtained at different initial particle sizes (Figs 3 and 4). The adsorption parameters X_,_ and K, used in the evaluation
are listed in Table
1. The val&s
off, 4 and
YL, were taken as the same values used in the pr& vious work, i.e. f = 0.466, C/J = 0 and Y, = 3.49 x 1OL3 cells/kg-Fe2+, respectively (Konishi et al., 1990). To evaluate the growth yield YA, graphical technique was used. The data in Figs 3 and 4 are replotted on log-log scale in Fig. 5 in the form sug-
gested by eq. (8). The values of XT were evaluated from eq., (12). Although the difference in the three lines cannot be regarded as significant, the growth yield Y,
+ K,X,,(W,/V)(l
- c#‘3>z + 4(1 -
+ KAXA,JWO/VU
-
&)KAXT
42’3}1/{2(1- $)KA}-
(12)
Kinetic model for batch bacterial di~olution of pyrite particles of each particle size was evaluated from the intercept of lines. and is given in Table 1. It is evident that the particle size of pyrite has little effect on the growth yield of bacteria adsorbed on pyrite. Furthermore, to find a value of specific growth rate pA that provides a At of data, the differential equations, eqs (10) and (1 l), were solved numerically by using the Runge-Kutta method, with the help of eqs (l), (8) and (12). Figures 3 and 4 compare the kinetic data with the numerical solutions obtained for three different initial particle sizes, using a value of F(” of 2.5d-’ and the length of the lag phase of O.Bd, which have been previously evaluated for pyrite of 25-44 pm (Konishi et cl.. 1990). The calculated curve at each particle size gives a good fit with the experimental data, indicating that the speci6c growth rate of adsorbed bacteria is pL1 = 2.5 d-‘, regardless of the particle size or the specific surface area of particles.
where
DISCUSSION The performance equations (B), (LO)-(12) permit us to predict the kinetics for the bacterial dissolution of pyrite of any particle sixes. The key parameters pA, Y, and K, in the performance equations are independent of particle size. However, the key parameter X,_ is affected by the change in particle size because X,_ is conveniently defined as the maximum adsorption capacity based on the unit weight of pyrite. Actually, the surface of pyrite particles plays an important role in the adsorption and growth of bacteria during the dissolution process. Thus, a more common way to express the maximum capacity of pyrite to cell adsorption is in terms of a new parameter X, having the units of cells per surface area. The two kinds of parameters, X,_ (cells/kg-Fe&) and X,_ (celIs/ ma-FeS,), are related through the equation: X.4_ = (JIX,,IP)(~P,,)
(13)
where + is the specific shape factor, and p is the density of particle. The experimeutal data for XAm in Table 1 are plotted on log-log scale as a function of . _ parttcle size D,.,, in Fig. 6, along with the data for the adsorption equilibrium constant K,. The data points for X,_ are correlated by a line with the slope of - 1, giving support to the constancy of $X., in eq. (13). Assuming that the particle diameter is represented by the screen opening, the constant @X,/p is determined as 1.46 x lo9 cells m/kg from the intercept of the line. Consequently, the performance equations contain the implicit effect of the initial particle size Now using eqs (1) and (13), the rate expressions 2;. and (12) for the total growth rate can bc trausfomled to: (dX,/dt)
= PA~CK_,XJ(~
+ KAXL)~I(~
+f K/ YA) 114)
and x,
=
CJ{(l -
#) - KAXT + I&d)*
- CC1 - 4) - XAXT +
Fig. 6. Elect of initial particle diameter Dro on maximum adsorption capacity X, and equilibrium constant X, appearing in Langmuir isotherm.
+ 4(1-
6 = (SX,_lP)(l/~,*)(w,I~)(l
(16)
The rate expression (11) for the bacterial dissolution can be rewritten in terms of the dissolution fraction a, by recalling that u = ( W, - W)/ W,: dddt = @Xd~)IC(Ri/V(
YA +f&)l.
(17)
The modified performance equations were used to simulate the dissolution behavior of pyrite particles by T. ferrooxiduns in a batch bioreactor. The differential equations (14) and (17) were solved numerically with the help of eqs (l), (S), (15) and (16), using the Ruuge-Kutta method. The parameters used in the simulations are as follows: p,, = 2.5 d-l, f = 0.466, 4 = 0, $X,,,_/p = 1.46 x lo9 cells m/kg, KA = 4.40 x lo-l5 mj/adIs, YL = 3.49 x 1Ol3 cells/kgFe*+, Y, = 3.30 x lOI4 cells/kg-FeS, , respectively. The length of lag phase was assumed to be 0.8 d. Figure 7 shows a typical simulation of batch growth and pyrite dissolution for the following initial conditions: the particle size LIP0 = 20 pm, the total cell concentration XT0 = 1.0 x lOI cells/m3 and the solid-liquid ratio We/V = 10 kg/m3. The conceutration X, of adsorbed bacteria increases first rapidly and then gradually approaches the maximum value X A,; hence the fraction t?,, of adsorption sites unoccupied by cells decreases quickly during the early stages of dissolution. The competing dependences of X, and 6, is responsible for the sigmoidal shape of the X,-time curve. since the growth rate of adsorbed bacteria is proportional to the product of X, and f3,, as demonstrated by eq. (4). The increase in the liquidphase concentration X, of free bacteria mainly occurs as a result of the release of bacteria which multiply on the solid substrate. The total cell concentration X, is related to the dissolution fraction a of pyrite as a solid substrate.
+)KAXr
&@1/{2(1 - ~)KA)
- cf)2’3.
(15)
1.0 0%
10.6 u 0.2
‘0
0
10
20
20
Fig, LO.‘Model simulations @in@ and experimental data @oints) for thti eikct of initial pyrite-ti9ticI loading ratio K,lV on fraction 01 of pyrite dissolved fpammeters: DpO = 35 pm, XT0 = 5 x HP” c&s/m3). Fig. 8: Mo;d-sLsimulationsof the effe’ectof initial particle size D pIDon fraction a of pyrite dissolved (parameters: W,/ 8’ = 10 kg/m3 and X, = 1 x IOS3 c@Iis)m3).
Figure 8 shows the effect of in&id )particfe size DPD on the diesalutitin fraotiort CC. It is evident from this figure that, in a batch reactor, the time required fot a given dissolution fraction decreases sigticantly as particle size times small_ This simulation result agrees with not only the present experimental data but also previous observations that the rate of bacterial dissolution is alinost doubled when ‘C&Y part&& size of copper sulfide is reduced from 177-125 to less than 62 pm [Ehrtich and Fox, 1967). Based on the present kinetic model, therefore, the effect of particle size on bacterial dissolution can be explained by a change in the capacity of pyrite for cell adsorption. Figure 9 shows the elect of initial cell cancentration XT0 on the dissolution fraction s as a function of time. There is a slight effect on going from XT0 - 1 x 10’3 to X rD = 1 x lOi cells/m3, except for the initial period up to abowt fwe days. This is consistent with an ex~r~rne~tal observation that the rate of bacterial pyrite dissolution is nc)t considerably affected by the initial ceU concentration (Konishi et &, 1990). It should be noted, furthermore, from the mocfel simulatim in Fig%9 that further increase of
XT0 from 1 x ifY4 to f x WS cellslm3 gives rise to a decline in dissolution fraction E. In this ease, the concentration XA of adsorbed bacteria remains almost constant at the maximum capacity XA,, resulting in the marked decrease in the vacant fraction 8, of adsorption sites. F&us, iu view of the influenoe of vacant fraction 0, on the growth rate, too large an inoouiation.of cells has a negative effect on the batterial dissolution sate. This simulation result is consistent with the experimental data of Razz& and Trussell (f963), who reported that the existence of cells in excess of the optimal number in the inoculum decreased the amount of copper leached from chalcopyrite in a given time. Figure 10 shows model simulations for the effect of initial pyrite-liquid loading ratio W,[Y on the dissdution fraction a, along with experimental data obtained in the previous work (Konishi et al., 1980). The experimeutai data are weff described by the solid cnrves predicted from the model, which indicate that the dissolution fradion Q decreases with increasing the initial soEd--liquid ratio. According to the canputation, a remarkable decrease in the vacant fraction 0, of adsorption sites, mused by art increase in the concentration of adsorbed bacteria, is responsible for the lowerina of the ~ssolution fraction.
Kinetic
model
for batch bacterial
CONCLUSIONS
bacterial dissolution of pyrite particles by Thiobucillusfmooxidans was kinetically studied in a wellmixed batch reactor. Experiments were performed on both the adsorption of bacteria on pyrite and the bacterial dissolution, using different particle size fractions of pyrite. The experimental data for absorption equilibrium were analyzed to determine two parameters in the Langrnuir isotherm (Table 1). The equilibrium constant for cell adsorption was independent of the particle size, whereas the maximum adsorption capacity based on the unit weight of pyrite was inversely proportional to the particle diameter. The observed dissolution rates increased with decreasing the initial particle size. A modified kinetic model, which allows for the effect of initial particle size, was
dissolution
X‘
The
developed. The parameters G and c(~appearing in the model were evaluated from the experimental data. The growth yield & and the specific growth rate Pi of adsorbed bacteria were evaluated as U, = (3.30-3.88) x 1Ol4 cells/kg-FeS, and pA = 2.5 d-l, regardless of the particle size. The kinetic model, eqs (14)-(17X allowed us to establish the respective e&&s of the three operating variables, i.e. initial particle size, initial ccl! concentration and the initial solid-liquid loading ratio. authors are indebted to Dowa Mining Co., Ltd. for supplying the pyrite minerals and the strain of Thiobacillus ferrooxidans.
Acknowledgement-The
X, X
1‘0
% Q
lYeIT {Fe), {SO:-
of pyrite particles
concentration of bacteria suspended in the liquid phase, cells/m3-liquid concentration of bacteria in total solid-liquid mixture, cells/m3-mixture initial GonFentration of total bacteria iu solid-liquid mixture, cells/m’-mixture growth yield of bacteria on pyritic sulfur, cells/kg-FeSZ growth yield of bacteria on ferrous iron, cells/kg-Fe*+ concentration of total iron in liquid phase. kg/m3-liquid molar concentration of total iron in liquid phase, mo1/m3-liquid ) molar concentration of sulfate ion in liquid phase, mol/m3-liquid
Greek letters fraction of pyrite dissolved, dimensionless z parameter defined by eq. (16), cells/m3 fraction of adsorption sites unoccupied by 0” cells, dimensionless specific growth rate of bacteria on solid surPA face, d - 1 specific growth rate of bacteria in liquid Pl. phase, d-l density of solid particles, kg/m3 P volume fraction of solid particles in 4 solid-liquid mixture, dimensionless specific shape factor of solid particles, ti dimensionless
NOTATION
7-O KA R.4
RL t V W Wo X, X Am X 6n
CES
47:1-5
initial diameter of solid particle, m weight fraction of iron in pyrite, dimensionless equilibrium constant for cell adsorption, m3/ceUs growth rate of bacteria adsorbed on solid surface, cells/dm”-mixture growth rate of bacteria suspended in the liquid phase, cells/dm3-mixture time, d volume of solid-liquid mixture, m3 weight of pyrite, kg initial weight of pyrite, kg concentration of bacteria adsorbed on solid surface, cells/kg-solid maximum adsorption capacity per unit weight of solid particles, cells/kg-solid maximum adsorption capacity per unit surface area of solid particles, cells/m’
139
REFERENCES
Ehrlich, H. L. and Fox, S. I., 1967, Environmental
effects on
bact&ial copper extraction from low-grade copper sulfide ores. Biotechnol. Bioengng 9.471-485. Hoffmann, M. R., Faust, B. C., Panda, F. A., Koo, H. H. and Tsuchiya, H. M., 1981, Kinetics of the removal of iron pyrite from coal by microbial catalysis. Appl. EntGron. Microbial. 42, 259-271. Imai, K., Sugio, T. and Tano, T., 1970, A new method for the determination of the cell number of iron-oxidizing batteria in iron containing media. Hakko Kyokaishi (J.
Ferment. Assoc., Japan) 28,404-406. Iritani, N. and Tanaka, T., 1958, Volumetric analysis of sulfate ion using EDTA-Ba. Jpn. Anal. 7, 4246. Konishi, Y., Asai, S. and Katoh, H., 1990, Bacterial dissolution of pyrite by Thiobacillus ferrooxidans. Bioprocess
Engng 5.231-237. Razz&, W. E. and Trussel, P., 1963, Isolation and properties of an iron-oxidizing Thiobacillus. J. Bacterial. 85, 595603. Silverman, M. P. and Lundgren, D. G., 1959, Studies on the chemoautotrophic iron bacterium Ferrobacillus ferrooxiduns. I. &I improved medium and a harvesting procedure for securing high cell yields. J. Buctetiol. 77,
642-647.
Sclencr. Vol. 47, No. I, pp. 133-139,
1992.
cm-2509p2
in Chat Britain.
0
KINETIC
s5.00 + 0.00
1991 Pemo
Press plc
MODEL FOR BATCH BACTERIAL DISSOLUTION OF PYRITE PARTICLES BY THXOBACILLUS FERROOXIDANS
SATORU ASAI, YASUHIRO KONISHI and KATUYA YOSHIDA Department of Chemical Engineering,University of Osaka Prefecture, 804 Mozu-Umemachi 4-cho, Sakai, Osaka 591,Japan (Received for publication
16 May 1991)
Abstrnet-The kinetics of the bacterial dissolution of pure pyrite (Fe&) particles by Thiobaci~fusfirrooxidamswas studied at di&rent initial particle sizes in a well-mixed batch reactor. Experimental studies were ma& on the adsorption of bacteria on pyrite particles as well as the bacterial dissolution of pyrite. The
Langmuir isothermwas usedto fit the adsorption data. The equilibriumconstantin the Langmuir equation was independentof the particle size, whereas the maximum adsorption capacity per unit weight of pyrite increased with decreasing particle sire. A rate expression for the kinetics of bacterial growth and pyrite
dissolution was derived, taking into account the effect of initial particle size. The kinetic parameters appearing in the rate equations, the growth yield and specific growth rate of adsorbed bacteria, were evaluated by curve-matching, using the experimental data obtained at different initial particle sizes. The evaluated kinetic parameters were found to be independent of the initial particle size. This kinetic model was successfully used to predict the bacterial dissolution behavior for the dil%mnt operating variables, i.e. the initial particle size, the initial cell concentration and the initial pyrite-liquid loading ratio.
INTRODUCTION
It is widely accepted that certain bacteria play a major role in most leaching operations for metal sulfides. One of the most important bacteria in the sulfide leaching is an acidophilic chemoautotrophic bacterium, Thiobacillus fmooxidans, which can multiply with mineral sulfur as a solid substrate. The bacterial leaching is referred to as the microbial oxidation of metal sulfide. The bacterial leaching techniques are applied to the recovery of copper and uranium from low-grade ores and the removal of pyritic sulfur from coal (microbial desulfurization). In spite of the abundant amount of information available on bacterial leaching, the growth kinetics of bacteria attached on the mineral surface are poorly understood. In a previous paper (Konishi et al., 1990) a mathematical model was developed to describe the kinetics of the batch growth of T. fmooxidans on pure pyrite (Fe&) and the subsequent dissolution of pyrite. The previous paper described the development of the model, along with an evaluation of key parameters appearing in the rate equations (the specific growth rate and growth yield of bacteria attached on pyrite) from experimental data. The emphasis in the previous work was laid on the fact that, during the bacterial dissolution process, the number of attached bacteria was related to the number of free cells through the Langmuir adsorption isotherm, and that, furthermore, the growth rate of adsorbed bacteria was proportional to the product of the number of adsorbed cells and the fraction of solid surface unoccupied by cells. However, the effect of particle size on the growth kinetics has not yet been addressed experimentally and theoretically.
The purpose of this work is to obtain kinetic data on the bacterial dissolution of pure pyrite by T. ferrooxidans using different particle size fractions, to take into account the effect of particle size into the previous kinetic model (Konishi et al., 1990), and to consider the influences of various operating variables on the bacterial dissolution rate in a batch bioreactor.
EXPERIhIENTAL
SECTION
For the kinetic analysis of bacterial growth and pyrite dissolution, it is important to estimate the number of bacteria attached on the pyrite surface. Adsorption experiments are a useful means of estimating the number of attached bacteria. Thus, the following experimental studies were made on the adsorption of T. ferrooxidans on pyrite particles as well as on the bacterial dissolution of pyrite.
Materials
The pyrite used in this study was a natural mineral of high purity (95% Fe&). The mineral was ground and was then sieved to obtain three different size fractions, 53-63 pm, 63-88 pm and 149-177 pm. Thiobacillus ferrooxidans was obtained from Dowa Yanahara Mine, Japan. The original strain was transfered to 9 K liquid medium (Silverman and Lundgren, 1959) supplemented with 1 W/V % FeS,, in order to adapt the cells to the particular pyrite. The adapted strain of T. fmooxidans showed a dramatic reduction of lag time for the batch cultivation, as pointed out by HofFmann et al. (1981). The inoculum age of about 10 days was used in the following adsorption and dissolution runs.
133
134
SATORU
ASAI
et al.
Apparatus and procedure In the adsorption experiments, an accurately weighted amount of pyrite particles (0.5 and 1.0 g) was mixed with 100 cm3 of iron-free 9 K liquid medium at pH = 2 in a flask. The initial number of cells in the liquid phase was varied from 8.80 x 1O1’ to 1.15 x 1015cells/m3. The flask was shaked at 30°C for three hours. After the adsorption equilibrium of T. ferrooxiduns was reached, the number of cells in the liquid phase was counted with Toma’s Hematometer, according to the procedure proposed by Imai et al. (1970). The number of cells adsorbed on pyrite was determined from the difference of the number of cells in the liquid phase before and after adsorption, since the adsorption of cells to the flask wall was found to be negligible. The dissolution reactor was an air sparged agitated vessel of 600 cm3. The reactor was operated batchwise with respect to the liquid, and the liquid stirrer was driven at 500 l/min. Air was continuously fed into the liquid at 2000 cm3/min. The liquid temperature was 30°C. A dissolution run was initiated by inoculating 5cm3 of an active culture of T. ferrooxiduns to 500 cm3 of the modified 9 K medium with the initial iron concentration of around 0.3 kg/m3 and the initial pH = 2. The initial cell number ranged from 1.02 x lOi to 2.53 x 1014 cells/m3. After that 5 g of pyrite of the desired size was added to the liquid medium, and this is taken as zero time. As the dissolution proceeds, the pH value was controlled at the initial value by adding a small amount of KOH solution. The liquid samples were withdrawn from the bioreactor for analysis. The number of cells in the liquid was counted by using Toma’s Hematometer, and the concentrations of total iron and ferrous iron were determined by redox titration_ In some runs, the solution samples were analyzed for sulfate ions by the EDTA-Ba method (Iritani and Tanaka, 1958).
EXPERIMENTAL
BESULTS
XL x
IO-l4
@olIslm3)
Fig. 1. Isotherms for the adsorption of i’%bbaciillrs fmooxidans on pyrite particles at &&rent particle diameters DPO’ curves given in Fig. 1 represent the Langmuir isotherms predicted from eq. (l), using the evaluated values of X4, and K,. For each particle size. the Langmuir isotherm provides a valid fit to the experimental data. Table 1 lists the values of X,,,, and K, evaluated for the particle sizes covered in this work, along with previous data for particle size fraction of 25-44 pm (Konishi et al., 1990). The adsorption equilibrium constant K, is practically independent of the particle size, whereas the maximum adsorption capacity X_,, per unit mass of pyrite decreases with increasing particle size. The decrease in X,,,, is presumably explained by considering a decrease in the specific surface area, reflected by an increase in the particle size.
Bacterial dissolution Preliminary experiments revealed that the chemical oxidation of pyrite by ferric iron can be neglected under the present experimental conditions. During the bacterial dissolution, therefore, the following direct microbial action is believed to take place: 2FeS, + 70, + 2HsO -* 2Fe2+ + 4SOi-
+ 4H+
Adsorption equilibrium Isotherms for the adsorption of T. ferrooxtians on pyrite obtained at three different sizes are presented in Fig. 1, where the concentration X, of adsorbed bacteria are plotted against the concentration X, of free bacteria in the liquid phase. It is evident that, as the particle becomes small, the amount of adsorbed bacteria increases. The equilibrium isotherm data at each particle size is characterized by a monotonic approach to a limiting adsorption amount, indicating that the data can be modeled by the Langmuir equatiom X, = KAXA,XLI(~
+ &XL)
(1)
where X,,,, is the maximum adsorption capacity per unit weight of pyrite and KA is the adsorption equilibrium constant. Since a plot of XL/X, vs XL at each particle size gave a straight line, the two constants X,_ and KA were evaluated from the slope and intercept of the best fitting lines, respectively. The solid
(a) The ferrous iron formed is immediately oxidized to the ferric iron according to the liquid-phase reaction
catalyzed by T. ferrooxidans: 4Fe2+ + O2 + 4H+ +4Fe3+
+ 2HsO
(b)
Figure 2 shows the relative release of both total iron and sulfate from pyrite into the liquid phase, which was measured during the bacterial dissolution. The molar concentration of sulfate formed, {SO:- } is 2 times that of iron leached, {Fe}, e z,,, where (SO:-}, and {Fe},, denote the Y~-,‘oy initial concentrations. This experimental result indicates that the bacterial leaching of iron and sulfur from pyrite proceeds stoichiometrlcally, according to reaction (a). In addition, all the leached iron was found to be present as ferric iron, as expected from reaction (b). Figures 3 and 4 show time courses of total iron concentration [Fe]= and free bacteria concentration
Kinetic model for batch bacterial dissolution
13s
of pyrite particlcJ
Table 1. Effect of particle size on maximum adsorption capacity X,,, adsorption equilibrium constant K,. and growth yield YA of adsorbed bacteria Particle X&X 10-t” (cells/kg-FeS,) 25-44 53-63 63-88 149-177
x 10’s (m3/cells)
K,
6.61t 2.50 1.41 0.912
Y” x lo-“’ (cells/kg-Fe&)
4.68 t 3.58 4.03 5.29
3.30’ 3.61 3.30 3.88
+ Konishi et al. (1990).
o 53-83pm A 83-88pm c 149-177gm 2.0 -
Fig. 2. Relative release of iron and sulfur during bacterial dissolution at initial pyrite-liquid loading ratio W,/V = 10 kg/ms, initial particle sire Dr,, = 53-63 ,nm, initial cell initial iron conconcentration X,, = 0.72 x lot’ alls/mg, centration {Fe},, = 10.8 mol/m3. and initial sulfate coneentration {SO:- Je = 48.4 mol/m”.
XL in the liquid phase. It is evident that, after a brief lag phase, the dissolution of pyrite takes place with an increase in the concentration of free bacteria in the liquid phase. The significant increase in the concentration of free bacteria with respect to time is likely to be due to the release of bacteria from the pyrite surface. This idea comes from the fact that the growth rate of T. jkrooxidans adsorbed on pyrite is much higher than that of free bacteria suspended in the liquid (Konishi et al.. 1990). Figures 3 and 4 demonstrate that the kinetics of bacterial growth and dissolution are markedly affected by the initial particle size LIP0 of pyrite as a solid substrate. The amount of iron dissolved and the number of free bacteria increase greatly with decreasing initial particle size. Although the concentration of adsorbed cells cannot be easily measured, it may be considered from the adsorption isotherms observed in this work (Fig. 1) that the number of adsorbed cells per unit weight of pyrite increases with decreasing the initial particle sixe. Thus it can be concluded that an increase in the capacity of pyrite to adsorb bacteria, reflected by a decrease in the particle size, gives an increase in the rates of bacterial growth and subsequent pyrite dissolution.
OoO
15
10
5
Time ways)
Fig. 3. Time course of total iron concentration [Fe]= in the liquid phase at initial pyrite-liquid loading ratio W,/V = 10 kg/m3, initial iron concentration [Fe]rc = 0.3100.380 kg/m3 and initial CA1 concentration XTO = 1.02 K 1014-2.53 x lOz4 cells/m3 (effect of initial particle diameter D,.,,). Solid curves were computed from mathematicd model described in the text.
ANALYSJS
OF KINETIC
DATA
A kinetic model was developed to describe the batch growth in the dissolution of pyrite caused by direct microbial action (Konishi et al., 1990). According to the previous model, the total growth rate is expressed as the sum of the growth rate R, of bacteria adsorbed on the solid surface and the rate R, of bacteria suspended in the liquid phase: (dX,/dt)
= RA + RL
(2)
- @‘a
(3)
with XT = X,( W,/V)(l
RA = pAXXAf3v(WO/V)(i RL = P‘XL(1 0. = (X&
- #)
- X_4)/X&
+ (I - 4)X,
- a)‘,’
(4) (5) (6)
136
SATORU
Ash41
where X, is the concentration of total bacteria per unit volume of solid-liquid mixture, pA is the specific growth rate of adsorbed bacteria, W, is the initial weight of pyrite, V is the volume of solid-liquid mixture, I$ is the volume fraction of pyrite in the solid-liquid mixture, and a is the fraction of pyrite dissolved. It should be noted that the term (1 - ~1)~‘~ in eqs (3) and (4) is used to represent a decrease in the surface area of pyrite particles due to dissolu~on. The kinetic model emphasizes that the growth rate. RA of adsorbed bacteria depends on the fraction 0, of adsorption sites unoccupied by bacteria. The growth rate R, is proportional to the dissolution rate of pyrite as a solid substrate: R, = - (Y,/V)(dW/dt)
(7)
where W is the weight of pyrite at any time. The growth yield Y, of bacteria on pyritic sulfur is defined as: r, = [(XT - X,,)
v -
a%fm/(~Wo)
et al.
:
15
Inflg.3
Sydmlssmeas 0
I
I
I
5
I
I
lo
I 15
Tl m e (days) Fig. 4. Time course of concentration X, of fee cells in the liquid phase at initial pyrite-liquid loading ratio W,/V = 10 kg/m’. initial iron concentration [Fe&, = 0.3100.380 kg/m3 and initial cell concentration XT0 = 1.02 x 10”-2.53 x 1Ol4 cells/m3 (effect of initial particle diameter L&-,). Solid curves.were computed from mathematical model described in the text.
(8) Y, is the growth yield of bacteria on ferrous iron and j- is the weight fraction of iron is pyrite. Since the ferrous iron formed in reaction (a) is readily oxidized through reaction (b), the net formation rate of ferrous iron can be assumed to be zero: where
(1 - +)(d[Fe*‘]/dQ
= - (f/V)(dW/dr)
- RJ&
= 0.
(9)
Combining eqs (2), (4)-(7) and (9) and rearranging gives the final expression for the total growth rate as: (dX,/dQ
= PAXA(~ - X,lX,,J(w,l~)(l
- 01)~‘~
x (1 +fY,/r,)-
(IO)
The time-variation of the total iron concentration [Fe]= in the liquid phase can be related to the total growth rate by combining eqs (2), (7) and (9): (1 -
dMKWT/W = - (f/WdWW = [A’( 5 +fY,)l(dX,/W.
(11)
Since the adsorption rate of bacteria is much higher than the rates of bacterial growth and dissolution, the adsorption equilibrium can be considered to be achieved during the dissolution process. Consequently, the concentration X, of adsorbed bacteria can be eliminated by writing it in terms of the Langmuir adsorption isotherm. eq. (1). This is an important point because the surface concentration X, cannot be easily measured and the appearance in the performance equation must be avoided. Eliminating the unknown X, from eqs (1) and (3) and rearranging gives the following expression for the total cell concentration XT as a function of liquid-phase cell concentration X, alone: XL = CJ{(l -
- 9) - K,X,
((1 -
9) -
K,X,
Fig. 5. Evaluation of growth yield YA of T. ferrooxidans Adsorbedon pyrite particles (effect of initial particle diameter Dpo). The conditions are the same as in Fig. 3.
The above-mentioned performance equations were used to evaluate the growth yields Y, and the specific growth rate pA from the experimental data obtained at different initial particle sizes (Figs 3 and 4). The adsorption parameters X_,_ and K, used in the evaluation
are listed in Table
1. The val&s
off, 4 and
YL, were taken as the same values used in the pr& vious work, i.e. f = 0.466, C/J = 0 and Y, = 3.49 x 1OL3 cells/kg-Fe2+, respectively (Konishi et al., 1990). To evaluate the growth yield YA, graphical technique was used. The data in Figs 3 and 4 are replotted on log-log scale in Fig. 5 in the form sug-
gested by eq. (8). The values of XT were evaluated from eq., (12). Although the difference in the three lines cannot be regarded as significant, the growth yield Y,
+ K,X,,(W,/V)(l
- c#‘3>z + 4(1 -
+ KAXA,JWO/VU
-
&)KAXT
42’3}1/{2(1- $)KA}-
(12)
Kinetic model for batch bacterial di~olution of pyrite particles of each particle size was evaluated from the intercept of lines. and is given in Table 1. It is evident that the particle size of pyrite has little effect on the growth yield of bacteria adsorbed on pyrite. Furthermore, to find a value of specific growth rate pA that provides a At of data, the differential equations, eqs (10) and (1 l), were solved numerically by using the Runge-Kutta method, with the help of eqs (l), (8) and (12). Figures 3 and 4 compare the kinetic data with the numerical solutions obtained for three different initial particle sizes, using a value of F(” of 2.5d-’ and the length of the lag phase of O.Bd, which have been previously evaluated for pyrite of 25-44 pm (Konishi et cl.. 1990). The calculated curve at each particle size gives a good fit with the experimental data, indicating that the speci6c growth rate of adsorbed bacteria is pL1 = 2.5 d-‘, regardless of the particle size or the specific surface area of particles.
where
DISCUSSION The performance equations (B), (LO)-(12) permit us to predict the kinetics for the bacterial dissolution of pyrite of any particle sixes. The key parameters pA, Y, and K, in the performance equations are independent of particle size. However, the key parameter X,_ is affected by the change in particle size because X,_ is conveniently defined as the maximum adsorption capacity based on the unit weight of pyrite. Actually, the surface of pyrite particles plays an important role in the adsorption and growth of bacteria during the dissolution process. Thus, a more common way to express the maximum capacity of pyrite to cell adsorption is in terms of a new parameter X, having the units of cells per surface area. The two kinds of parameters, X,_ (cells/kg-Fe&) and X,_ (celIs/ ma-FeS,), are related through the equation: X.4_ = (JIX,,IP)(~P,,)
(13)
where + is the specific shape factor, and p is the density of particle. The experimeutal data for XAm in Table 1 are plotted on log-log scale as a function of . _ parttcle size D,.,, in Fig. 6, along with the data for the adsorption equilibrium constant K,. The data points for X,_ are correlated by a line with the slope of - 1, giving support to the constancy of $X., in eq. (13). Assuming that the particle diameter is represented by the screen opening, the constant @X,/p is determined as 1.46 x lo9 cells m/kg from the intercept of the line. Consequently, the performance equations contain the implicit effect of the initial particle size Now using eqs (1) and (13), the rate expressions 2;. and (12) for the total growth rate can bc trausfomled to: (dX,/dt)
= PA~CK_,XJ(~
+ KAXL)~I(~
+f K/ YA) 114)
and x,
=
CJ{(l -
#) - KAXT + I&d)*
- CC1 - 4) - XAXT +
Fig. 6. Elect of initial particle diameter Dro on maximum adsorption capacity X, and equilibrium constant X, appearing in Langmuir isotherm.
+ 4(1-
6 = (SX,_lP)(l/~,*)(w,I~)(l
(16)
The rate expression (11) for the bacterial dissolution can be rewritten in terms of the dissolution fraction a, by recalling that u = ( W, - W)/ W,: dddt = @Xd~)IC(Ri/V(
YA +f&)l.
(17)
The modified performance equations were used to simulate the dissolution behavior of pyrite particles by T. ferrooxiduns in a batch bioreactor. The differential equations (14) and (17) were solved numerically with the help of eqs (l), (S), (15) and (16), using the Ruuge-Kutta method. The parameters used in the simulations are as follows: p,, = 2.5 d-l, f = 0.466, 4 = 0, $X,,,_/p = 1.46 x lo9 cells m/kg, KA = 4.40 x lo-l5 mj/adIs, YL = 3.49 x 1Ol3 cells/kgFe*+, Y, = 3.30 x lOI4 cells/kg-FeS, , respectively. The length of lag phase was assumed to be 0.8 d. Figure 7 shows a typical simulation of batch growth and pyrite dissolution for the following initial conditions: the particle size LIP0 = 20 pm, the total cell concentration XT0 = 1.0 x lOI cells/m3 and the solid-liquid ratio We/V = 10 kg/m3. The conceutration X, of adsorbed bacteria increases first rapidly and then gradually approaches the maximum value X A,; hence the fraction t?,, of adsorption sites unoccupied by cells decreases quickly during the early stages of dissolution. The competing dependences of X, and 6, is responsible for the sigmoidal shape of the X,-time curve. since the growth rate of adsorbed bacteria is proportional to the product of X, and f3,, as demonstrated by eq. (4). The increase in the liquidphase concentration X, of free bacteria mainly occurs as a result of the release of bacteria which multiply on the solid substrate. The total cell concentration X, is related to the dissolution fraction a of pyrite as a solid substrate.
+)KAXr
&@1/{2(1 - ~)KA)
- cf)2’3.
(15)
1.0 0%
10.6 u 0.2
‘0
0
10
20
20
Fig, LO.‘Model simulations @in@ and experimental data @oints) for thti eikct of initial pyrite-ti9ticI loading ratio K,lV on fraction 01 of pyrite dissolved fpammeters: DpO = 35 pm, XT0 = 5 x HP” c&s/m3). Fig. 8: Mo;d-sLsimulationsof the effe’ectof initial particle size D pIDon fraction a of pyrite dissolved (parameters: W,/ 8’ = 10 kg/m3 and X, = 1 x IOS3 c@Iis)m3).
Figure 8 shows the effect of in&id )particfe size DPD on the diesalutitin fraotiort CC. It is evident from this figure that, in a batch reactor, the time required fot a given dissolution fraction decreases sigticantly as particle size times small_ This simulation result agrees with not only the present experimental data but also previous observations that the rate of bacterial dissolution is alinost doubled when ‘C&Y part&& size of copper sulfide is reduced from 177-125 to less than 62 pm [Ehrtich and Fox, 1967). Based on the present kinetic model, therefore, the effect of particle size on bacterial dissolution can be explained by a change in the capacity of pyrite for cell adsorption. Figure 9 shows the elect of initial cell cancentration XT0 on the dissolution fraction s as a function of time. There is a slight effect on going from XT0 - 1 x 10’3 to X rD = 1 x lOi cells/m3, except for the initial period up to abowt fwe days. This is consistent with an ex~r~rne~tal observation that the rate of bacterial pyrite dissolution is nc)t considerably affected by the initial ceU concentration (Konishi et &, 1990). It should be noted, furthermore, from the mocfel simulatim in Fig%9 that further increase of
XT0 from 1 x ifY4 to f x WS cellslm3 gives rise to a decline in dissolution fraction E. In this ease, the concentration XA of adsorbed bacteria remains almost constant at the maximum capacity XA,, resulting in the marked decrease in the vacant fraction 8, of adsorption sites. F&us, iu view of the influenoe of vacant fraction 0, on the growth rate, too large an inoouiation.of cells has a negative effect on the batterial dissolution sate. This simulation result is consistent with the experimental data of Razz& and Trussell (f963), who reported that the existence of cells in excess of the optimal number in the inoculum decreased the amount of copper leached from chalcopyrite in a given time. Figure 10 shows model simulations for the effect of initial pyrite-liquid loading ratio W,[Y on the dissdution fraction a, along with experimental data obtained in the previous work (Konishi et al., 1980). The experimeutai data are weff described by the solid cnrves predicted from the model, which indicate that the dissolution fradion Q decreases with increasing the initial soEd--liquid ratio. According to the canputation, a remarkable decrease in the vacant fraction 0, of adsorption sites, mused by art increase in the concentration of adsorbed bacteria, is responsible for the lowerina of the ~ssolution fraction.
Kinetic
model
for batch bacterial
CONCLUSIONS
bacterial dissolution of pyrite particles by Thiobucillusfmooxidans was kinetically studied in a wellmixed batch reactor. Experiments were performed on both the adsorption of bacteria on pyrite and the bacterial dissolution, using different particle size fractions of pyrite. The experimental data for absorption equilibrium were analyzed to determine two parameters in the Langrnuir isotherm (Table 1). The equilibrium constant for cell adsorption was independent of the particle size, whereas the maximum adsorption capacity based on the unit weight of pyrite was inversely proportional to the particle diameter. The observed dissolution rates increased with decreasing the initial particle size. A modified kinetic model, which allows for the effect of initial particle size, was
dissolution
X‘
The
developed. The parameters G and c(~appearing in the model were evaluated from the experimental data. The growth yield & and the specific growth rate Pi of adsorbed bacteria were evaluated as U, = (3.30-3.88) x 1Ol4 cells/kg-FeS, and pA = 2.5 d-l, regardless of the particle size. The kinetic model, eqs (14)-(17X allowed us to establish the respective e&&s of the three operating variables, i.e. initial particle size, initial ccl! concentration and the initial solid-liquid loading ratio. authors are indebted to Dowa Mining Co., Ltd. for supplying the pyrite minerals and the strain of Thiobacillus ferrooxidans.
Acknowledgement-The
X, X
1‘0
% Q
lYeIT {Fe), {SO:-
of pyrite particles
concentration of bacteria suspended in the liquid phase, cells/m3-liquid concentration of bacteria in total solid-liquid mixture, cells/m3-mixture initial GonFentration of total bacteria iu solid-liquid mixture, cells/m’-mixture growth yield of bacteria on pyritic sulfur, cells/kg-FeSZ growth yield of bacteria on ferrous iron, cells/kg-Fe*+ concentration of total iron in liquid phase. kg/m3-liquid molar concentration of total iron in liquid phase, mo1/m3-liquid ) molar concentration of sulfate ion in liquid phase, mol/m3-liquid
Greek letters fraction of pyrite dissolved, dimensionless z parameter defined by eq. (16), cells/m3 fraction of adsorption sites unoccupied by 0” cells, dimensionless specific growth rate of bacteria on solid surPA face, d - 1 specific growth rate of bacteria in liquid Pl. phase, d-l density of solid particles, kg/m3 P volume fraction of solid particles in 4 solid-liquid mixture, dimensionless specific shape factor of solid particles, ti dimensionless
NOTATION
7-O KA R.4
RL t V W Wo X, X Am X 6n
CES
47:1-5
initial diameter of solid particle, m weight fraction of iron in pyrite, dimensionless equilibrium constant for cell adsorption, m3/ceUs growth rate of bacteria adsorbed on solid surface, cells/dm”-mixture growth rate of bacteria suspended in the liquid phase, cells/dm3-mixture time, d volume of solid-liquid mixture, m3 weight of pyrite, kg initial weight of pyrite, kg concentration of bacteria adsorbed on solid surface, cells/kg-solid maximum adsorption capacity per unit weight of solid particles, cells/kg-solid maximum adsorption capacity per unit surface area of solid particles, cells/m’
139
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effects on
bact&ial copper extraction from low-grade copper sulfide ores. Biotechnol. Bioengng 9.471-485. Hoffmann, M. R., Faust, B. C., Panda, F. A., Koo, H. H. and Tsuchiya, H. M., 1981, Kinetics of the removal of iron pyrite from coal by microbial catalysis. Appl. EntGron. Microbial. 42, 259-271. Imai, K., Sugio, T. and Tano, T., 1970, A new method for the determination of the cell number of iron-oxidizing batteria in iron containing media. Hakko Kyokaishi (J.
Ferment. Assoc., Japan) 28,404-406. Iritani, N. and Tanaka, T., 1958, Volumetric analysis of sulfate ion using EDTA-Ba. Jpn. Anal. 7, 4246. Konishi, Y., Asai, S. and Katoh, H., 1990, Bacterial dissolution of pyrite by Thiobacillus ferrooxidans. Bioprocess
Engng 5.231-237. Razz&, W. E. and Trussel, P., 1963, Isolation and properties of an iron-oxidizing Thiobacillus. J. Bacterial. 85, 595603. Silverman, M. P. and Lundgren, D. G., 1959, Studies on the chemoautotrophic iron bacterium Ferrobacillus ferrooxiduns. I. &I improved medium and a harvesting procedure for securing high cell yields. J. Buctetiol. 77,
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