Ind. Eng. Chem. Fundam. 1982, 21, 214-220
214
Region 3
(FT
[(YB)nlAI
> V) =
(V[(YBR*)n+llAl
[(YC,VI* )nlAI [(YBR)n+llN
=
+ =
(FT
- V)[YOlAl)/pB
[YOIAl
(A-36) (A-37)
-k ~ [ Y o I A -k I (Qoti V ) [ ( Y T R ) ~ + ~ ] A I ) / ( Q O-k~ I vd (A-38)
(VB[(YBR*)n+llA1
The albumin separation factors for regions 1 and 2-mode 2 are calculated from eq 14, A-2, A-16, A-21, A-32, A-33, and A-35. Equations A-15 and A-20 are also needed for region 1. The albumin separation factors for region 3mode 2 are calculated from eq 14, A-2, A-16, A-21, A-32, A-36, and A-38. Nomenclature A = effective cross sectional area of packed column, cm2 BR = bottom reservoir BP = bottom product E = strength of electric field, V/cm EPC = electropolarization chromatography F B = volume of bottom feed, cm3 F T = volume of top feed, cm3 Fo = feed volume with zero protein concentration, cm3 I A = isoelectric point of protein A IB = isoelectric point of protein B M A = total elution volume at the center of mass of protein A, cm3 M B = total elution volume at the center of mass of protein B, cm3 P, = high pH level Pz = low pH level P B = volume of bottom product, cm3 PT = volume of top product, cm3 Qo = high bulk displacement rate, cm3/min Q, = low bulk displacement rate, cm3/min Ri = retardation coefficient of component i S.F. = separation factor t = duration, min f = average duration of electric field, min +R = top reservoir TP = top product V = volume of fluid phase, cm3 V, = bottom reservoir dead volume, cm3 V T = top reservoir dead volume, cm3 v, = migration velocity, cm/min veA= migration velocity of protein A, cm/min
v,B = migration velocity of protein B, cm/min vo = bulk velocity, cm/min v, = net velocity in axial direction, cm/min W = weight fraction of the product = weight fraction of the bottom product YB = concentrationof solute in the bottom product, g-mol/cm3 YBR = concentration of solute in the bottom reservoir, gmol/cm3 yc = concentration of solute in the column (fluid phase), g-mol/cm3 yo = concentration of solute in the feed, g-mol/cm3 YT = concentration of solute in the top product, g-mol/cm3 y m = concentration of solute in the top reservoir, g-mol/cm3 Y = concentration of solute in the fluid phase, g/g Yo = concentration of solute in the feed, g/g ( ) = average value
w”,
Greek Letters = protein mobility, cm2/V-s a = overall separation factor for protein mixture
Subscripts A1 = albumin Hb = hemoglobin n = nth cycle of operation 0 = initial condition P = product m = steady-state condition Superscript * = intermediate concentration in nth cycle of operation
Literature Cited Chen, H. T.; Hsien, T. K.; Lee, H. C.; Hill, F. B. AIChE J . 1977, 23,695. Chen, H. T.; Wong, Y. W.; Wu, S. AIChE J . 1979, 25,320. Chen, H. T.; Yang, W. T.; Pancharoen, U.; Parisi, R. J. AIChEJ. 1980a, 26, 839. Chen, H. T.; Pancharoen, U.; Yang, W. T.; Kerobo, C. 0.; Parisi, R. J. Sep. Sci. Techno/. 1980b, 15, 1377. Chen, H. T.; Yang, W. T.; Wu, C. M.;Kerobo, C. 0.; Jajaiia. V. Sep. Sci. Techno/. 1981, 16, 43. Chiang, A. S.; Kmioten, E. H.; Langan, S. M.; Noble, P. T.; Reis, J. F. G.; Lightfoot, E. N. S e p . Sci. Technd. 1979, 14, 453. Oren, Y.; Soffer, A. J . Electrochem. Soc. 1978, 125,869. Sabadeli, J. E.; Sweed, N. H. Sep. Sci. 1970,5, 171. Shaffer, A. G.; Hamrin, C. E. AIChE J. 1975, 21, 782. Shah, A. B.; Reis, J. F. G.; Lightfoot, E. N.; Moore, R. E. Sep. Sci. Techno/. 1979, 14, 475. Thompson, D. W.; Bass, D. Can. J . Chem. Eng. 1974,52,345
Received for review May 4, 1981 Accepted January 18, 1982
Solids Suspension in Mixing Tanks KakuJlTojo’ and Kel Mlyanaml Department of Chemical Engineering, University of Osaka Prefecture, Sakai, Osaka 59 1, Japan
The dynamic characteristics of solids flow in slurry reactors with an axial flow agitator, a marine propeller or a vibrating disk, have been investigated both theoretlcaliy and experimentally. The dynamic and steady state solids concentration profiles have been well described by means of the axial sedimentation-dispersion model. The correlation equations for the model parameters have been also provided.
Introduction Slurries have been used in a number of industrial operations. Typical examples of these operations are hy0 196-43 13/82/ 102 1-02 1480 1.25/0
drogenation, coal liquefaction, washing crystals and leaching. In these slurry operations, the solids in the tank are required to be suspended completely throughout the 0 1982 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 21, No. 3, 1982 L IQUlD A SOLIDS
tank to attain the maximum interfacial area between the solids and liquid phases. Although it is not always the case, the homogeneous suspension in which the solids are uniformly dispersed throughovk, the tank is preferable in some operations, especially in continuous operation with solids of a wide size distribution; when the size distribution is broad, larger particles tend to reside longer in the tank than smaller ones and then the continuous operation of slurry reactors may be inferior. As concerns solids suspension in mixing tanks, the complete suspension phenomena have been extensively investigated by many researchers (Zwietering, 1958; Parlshenko et al., 1957; Zundelvich, 1977; Nagata, 1975, Tojo and Miyanami, 1981). The dynamic characteristics of slurry reactors remain unsolved so far, however, and more work is left to be done. For estimating the mass transfer or chemical reaction rates in slurry reactors,flow characteristics of all the phases involved should be taken into account. In spite of the fact that the flow pattern of the liquid phase has been intensively studied by assuming that fine solids follow the liquid motion perfectly, less attention has been paid to the solid flow characteristics. Takeba et al. (1971) reported that a considerable concentration gradient of suspended solid catalysts was observed in a multistage vibrating disk tank for hydrogenation of glucose solution with suspended Raney nickel catalysts. Recently, Bohnet and Niesmak (1979) have measured appreciable concentration gradient of suspended solids in a mixing tank containing an axial flow propeller. It is obvious that knowledge of the concentration profiles and the residence times of suspended solids is necessary for rational design and operation of slurry reactors. Argo and Cova (1965) have presented the solids concentration profiles in a bubble column and tubular reactors and analyzed the data based on a sedimentation-disperion model. Kafarov et al. (1971) have investigated the dynamics of solids flow in a stirred tank on the basis of the sedimentation-dispersion model. They found that the residence time of the solid phase differs significantly from that of the liquid phase. Blass and Cornelius (1977) have measured the residence time distribution of solids in a multistage bubble column by using a radioactive tracer and found that a mixing cell model is applicable to explanation of the distribution. Since both the solids and liquid flow patterns in mixing tanks are closely related to the agitation method employed, the effect of agitation method on the flow patterns of both phases should be studied in detail. In slurry reaction processes the concentration profiles of the suspended solids relate directly to the interfacial area between the phases involved and the resulting percent conversion. Therefore the solids concentration profile in the slurry reactor should be precisely evaluated for estimating the performance of the reactor. In addition, the dynamic characteristics of the solids flow are also of practical importance for startup and shutdown problems. A t this stage of research, however, little is known with respect to such information. In the present work, the dynamic and steady state solids concentrations in the slurry mixing tank were measured by using a photoelectric method. The experimental data were then analyzed by a sedimentation-dispersion model. Two types of axial flow agitators, a marine propeller and a vibrating disk, have been examined, although much attention has been paid to vibratory agitation because this type has potential advantages for slurry operation with respect to mechanical sealing, solids suspension performance, and solid-liquid mass transfer (Tojo et al., 1980).
215
Figure 1. Schematic diagram of the sedimentation-dispersion model.
Theory For a differential element of the reactor volume based on a one-dimensional sedimentation-dispersion model (Figure l ) , the continuity equations may be written as
for solid particles, and
ac,
ac,
at = -u- az
+
&( E L g )
- R,
(2)
for the component of A in the liquid; u is the liquid superficial velocity, uf is the solids falling velocity, and E, and EL are the dispersion coefficients for the solids phase and the liquid phase, respectively. Although the solids falling velocity ut may depend on the solids concentration, ut was assumed to be constant in the present model. This will be justified empirically in a later section. It is also assumed that the following simple, irreversible reaction takes place on the solid surface and then the mass transfer of A through the solid-liquid interface controls the overall reaction rate.
A
on the solid surface
bP
The reaction term, R,, can be expressed by (Fan et al., 1979) Ra = Gk/(ppdp)CCa (3) The boundary conditions are derived from the mass balance equations in the volume elements of the reactor bottom and top (Figure 1). dC E p z = -u(Co - C) - ufc [Z = 0 (tank bottom)] (4) dCa EL= = -u(Ca0 - C,) dC E - = -ufc PdZ EL=dCa
[Z = 0 (tank bottom)] (5)
[Z = H (tank top)]
0 [Z = H (tank top)]
(6)
(7)
Equations 1and 2 can be rewritten in dimensionless forms as follows
ax _ - -(I - 4)aT
at
'( '
+ - -ax) -
at Pep at
(8)
216
Ind. Eng. Chem. Fundam., Vol. 21, No. 3, 1982
,,/'
- *I
,
-
Parameter. P e L
,,I'
L
Pe,-24
61 1
P t I.OI
os
I
5
Pep
1
2
3 Ttme, T
4
so
IO
100
or PeL
Figure 4. Effect of Peclet numbers both in the solids and the liquid phase on the response time tgg.
, 0
I
' " . I
5
6 I O
(-1
---
-___-
Figure 2. Effect of liquid phase Peclet number on the dynamic behavior of concentrations.
x
,/'
/
Parameter
Is;
i 2
I
X
0 '
3-00
4
5
;
Time. T (-1
3 4 5 Ttme, T ( - )
6
7
Figure 5. Effect of reaction parameter 4" on dynamic behavior of concentrations.
!
Solids
Figure 3. Effect of solids phase Peclet number on the dynamic behavior of concentrations.
where X = C/Cin or C/Cout, Y = Cali& or Ca/Caout,( = Z / H , Q = uf/u, 7 = t / ( H / u ) ,Pep = u H / E p ,PeL = uH/EL, and $, = 6kH/(ppdpu)Cin.The boundary conditions become C;=1
C;=O
dX/dC; = -PefX
(10)
dY/dC; = 0
(11)
dX/dC; = (Pep - Pef)X - PepXo
(12)
dY/dC; = -Pe,(Yo - y)
(13)
Equations 8 and 9 can be solved under appropriate initial conditions; in the washout operation where the solids suspended at a steady state are withdrawn by introducing liquid with zero solids concentration continuously, the initial condition with respect to the solid particles is (Tojo et al., 1975) 1 X(5,O) = b p [ ( P e p - P e f N - 01 - Pep/Pefl 1 - Pep/Pef (14) On the other hand, the start-up problem is subject to the following initial condition
X([,0) = 0
(7 5
0)
(15)
The liquid phase initial condition is given as Y(F, 0) = 1
(16)
Equations 8 and 9 under the boundary conditions eq 10 to 13 were solved numerically by using the Runge-Kutta-Gill method. Figure 2 shows the effect of the liquid phase Peclet number, PeL, on the dynamic behavior of the reactant concentrations under the start-up condition. The solids concentration is also plotted by a dashed line. As can be seen from this figure, the percent conversion defined by (1 - Y) decreases with increasing the intensity of liquid
Somplinq position
r
Bypass
+
Discharge t o drain
Figure 6. Schematic diagram of experimental apparatus.
mixing. Figure 3 shows the effect of solids phase Peclet number, Pe , on the dynamic concentration profiles both in the liquit! phase and in the solids phase. The percent conversion is appreciably increased as the solids phase Peclet number increases. This is due to the fact that the amount of solids suspended in the tank is increased with increasing solids Peclet number and the resulting increase in solids-liquid interfacial area. Figure 4 shows the effect of the Peclet numbers, Pep and PeL, on the response time T~ at which the concentration reaches 90% of a new steady-state value. As can be seen from this figure, the time T% is hardly influenced by liquid mixing (dashed line). It can be said, therefore, that the dynamic behavior of slurry reactors may be affected only slightly by the liquid flow characteristics. However, it is markedly influenced by the solids flow characteristics. Figure 5 shows the effect of the reaction parameter, &, on the dynamic concentrations. The solid lines represent the reactant concentrations in the liquid phase and the dashed line stands for the concentration of the solids phase. Experimental Section Figure 6 shows a schematic diagram of the experimental apparatus. The measurements were carried out in 0.1-, 0.2-, and 0.3-m diameter flat-bottomed, cylindrical tanks. Two types of axial flow agitators are examined: a four-
Ind. Eng. Chem. Fundam., Vol. 21, No. 3, 1982 217 Particles
Mirror
0
Light
source
155
-~ Scale in
mm.
Figure 7. Probe for solids concentration measurement.
blade marine propeller (impeller height hi) and a vibrating disk without perforation (low part vibration, Tojo et al., 1975). Most runs were carried out in a continuous operation. At the start of a run, a known mass of solids was fed into the tank and then mixed completely, After reaching steady state, the solids concentrations at several spots in the tank were measured by using a light obscuration method. A small probe for measuring the solids concentration was developed. The detail of the probe is shown in Figure 7. If S is the cross-sectional area of the light beam, this is progreasively reduced by obscuration in its passage through the dispersion according to the following relationship -dS = KSa, dl
Table I. Experimental Conditions inside diameter of tank diameter of vibrating disk diameter of impeller (4-blade marine propeller) impeller speed impeller height liquid depth vibration frequency vibration amplitude liquid flow rate mean part. size d,, solid particles d3,, m Toyoura sands 250 P.V.C.powders 150 250 glass beads carborundum 74, 114, 175 IO
1
di dd d
10, 20, 30 10-16 4.2
cm cm cm
n
5-1 8 0.16, 0.35
1 Is
= di
cm
0.3-4.3 1-6 35-51.3
Hz
P
H f A
QL
density, pDg/cm3 2.69 1.50 2.50 3.30
cm cm 1s
settling vel., us, cmls 2.72 0.212 2.65 0.71, 1.0, 1.90
Key n(l/secJ P e p Pet 0 17.8 010 0.19
2
6.1
0
1.55
1.5
-Calculated
u
(17)
where dl is an incremental path length and up is the projected area of particles per unit volume of the dispersion expressed by
" t 0.2
-0 (Bottom)
0.4
€
2
4
3
Time,
where C, is the concentration by weight of the solids and Iiand Io are the incident illumination and the reflected illumination, respectively. The linear relationship between In (Ii/Io) and Cw/d32 according to eq 20 held when the solids concentration was less than about 10% by weight. A t the higher solids concentration, In (Ii/Io) gradually approached a maximum value and then decreased as the solids concentration increased. This was because a considerable part of light scattered by the particles is superimposed on the returning light in the higher concentration slurries. Water slurries of glass spheres (240 pm), P.V.C. spheres (150 pm), Toyoura sands, one of the Japanese standard sands (250 pm) and carborundum (76,104, and 175 pm)
.
Propeller
I
Since the area illuminated is proportional to the intensity of illumination, eq 19 becomes
1.0 (Top)
Figure 8. Axial concentration profiles of solids in the stirred tank with a marine propeller.
CN is the number concentration of particles and K is an extinction coefficient which is constant (= z) for the solid particles of d, > 10 pm (Azzopardi, 1979). Therefore eq 17 can be rewritten as
where Siis the initial cross-sectional area of the light beam, d32is the volume-surface mean diameter, and
0.8
0.6
I
5
6
(-1
Figure 9. Dynamic behavior of the solids washout concentration.
were used. All the experiments were carried out under the mixing condition in which a free-of-solids zone in the upper part of the tank was hardly generated and hindered settling did not take place. The properties of the solids and the experimental conditions are summarized in Table I. Perfect mixing in the liquid phase has been verified under the present experimental conditions by the response to a pulse of aqueous sodium chloride solution.
Results and Discussion Figure 8 shows axial concentration profiles of solids suspended in a stirred tank with the marine propeller (d/di = 0.42). The lines on this figure were computed by choosing the model parameters, Pe and Pef,so as to agree with the experimental profiles. Tke wash-out characteristics of solids suspension are shown in Figure 9. In this figure, the solid line was obtained by utilizing the combination of the model parameters so as to describe both the steady-state and the dynamic solids concentration profiles; the dashed line was calculated by using the free settling velocity u, as the particles falling velocity of the model ufand the model parameter Pep(= 0.02),by which only the steady-state concentration profile can be explained. The considerable deviation between the experi-
218
Ind. Eng. Chem. Fundam., Vol. 21, No. 3, 1982
I O
-
" A
1
Key
0 ~3 0
V
0
A
-
Calculated
c
f
'1 2\
P e p Pc 2 2 5 . 233. 65. 3 6 0 225, 450, O f I , O O 3 (cm)
(Hr)
(-)
(-)
I
A
1
~ 1 0 s sb e a d s - Water
0 2
0.4
E
06
OB
10
Ccrborundum P V C spheres
LO 4 0 5 o6 10 4
-
I
0
x* OO
Solids Toyouro sands Toyoura sands Toyoura sands Glass beads
uD/us + (dd/di )'(ZAfJ/u,
(-1
Figure 12. Correlation of Pef in the vibratory disk tank.
Figure 10. Steady-state solids concentrations in the vibratory disk tank.
s
0
02
0 1
0.3 0.4 2A/H f-)
0.5
0.6
(
7
Figure 13. Effect of 2 A j H on the coefficient of $ in eq 22. Figure 11. Dynamic behavior of the solids washout concentrations in the vibratory disk tank.
mental result and the dashed line calculated with u, implies that the free settling velocity cannot be used as the model falling velocity. Therefore the Peclet number Pe, based on the model falling velocity ut should be considered as a model parameter which depends on the experimental conditions. The steady-state and dynamic solids concentrations in the slurry tank with disk vibratory agitation are shown in Figures 10 and 11, respectively, where the calculated profiles based on the sedimentation-dispersion model are also plotted as the solid lines. It can be seen from Figure 11that the residence time distribution of the solids suspended in the mixing tank is much influenced by the mixing condition, namely, the amplitude and frequency of the vibrating disk. In reality, perfect mixing of the solids phase in slurry reactors is one special case, and therefore the perfect mixing assumption may cause significant error in evaluating the performance of the slurry readors unless the solids flow characteristics are appropriately estimated.
Correlation of Model Parameters (1) Vibratory Agitation. It is found that the dynamic characteristics of the solids flow in the vibrating disk tank are influenced by the liquid flow rate, intensity of agitation (vibrating frequency and amplitude), solids falling velocity, and tank geometries. For correlating the model parameters Pep and Pef, we made an assumption with respect to the soh& falling velocity; the flow ratio of liquid to solids u/uf, which coincides with the model parameter ratio Pep/Pef, is a function of operating conditions and tank dimensions because the solids falling velocity is retarded by axial flow generated by the vibrating disk. This axial flow rate is given by
Q,,
7F
= (2Afl,d,*
where dd is the vibrating disk diameter. Therefore the
o b ' ; "
8
n
" 12 (I/secJ
'
1'6
I
20 1
Figure 14. Correlation of model parameters, Perand Pef/Pe, in the stirred tank.
ratio of the superficial upward liquid velocity u' to the solids falling velocity uf can be expressed by u + Q,/(rdi2/4)
x=-"
=
Uf
where u, is the free settling velocity of the solids. Figure 12 shows the correlation of Pef in terms of the dimensionless group x defined by eq 21. The data are well correlated by the ratio defined by eq 21, although the correlation is clearly affected by an additional factor, namely, the amplitude to liquid depth ratio (2AIH). By taking into consideration this additional factor, the model parameter Pef has been correlated as follows Pef = J, exp(-1.18 x) (22) where J, is a function of 2A/H as shown in Figure 13. It can be seen from Figure 12 that the perfect mixing assumption for the solids phase is valid only in the case of x > 5 or high amplitude operations (2A/H > 0.6). Because the dynamic behavior of slurry reactors may be considerably influenced by the solids flow characteristics as can be expected from Figure 4, the deviation of an actual
Ind. Eny. Chem. Fundam., Vol. 21, No. 3, 1982 210
.
8 -
6 6
.
1 \-'
95
-
7.8 0 G l a s s -Water 0 e Styropor -Water
/'
:Ca[ulaied
U T 4 -
n
-
30 pet *I3
.so0
rpm
.'.
20
or
-
/
B
1200
1000
d
P '
ad
pep'pef
0
ua
c
n
i
1
u
n IC
P r o p e l l e r , B.0.16,
3
Styropor (dm=l.15mm
U
:
6.
:Calculated
n
('
. -100
' rpm '
120
0'04 0'06
008
o/I
0'12
0'14
0'16
0'18
,
1
Figure 16. Correlation of model parameters, Per and Pe,/Pef (Bohnt and Niesmak's data).
:
u c 4 -
0'02
:
2.
i' I
I
I
Figure 15. Comparison of calculated concentration profiles and experimental ones by Bohnt and Niesmak. flow pattern from the perfect mixing assumption should be carefully examined. (2) Rotary Agitation. Figure 14 shows the model parameters Pep and Per for rotary agitation as a function of the impeller speed. For rotary agitation, the experimental data are still insufficient to draw a definite conclusion. Suffice it to say a t this stage that the Peclet number Pef approaches 0 at an impeller speed of about 20 revolutions per second or more in the present experimental conditions, while the parameter ratio Pef/Pepis approximately proportional to the impeller speed as the speed increases. The steady state solids concentration profiles in the mixing tank with propeller agitation (Bohnt and Niesmak, 1979) are compared in Figure 15 with those calculated by the sedimentation-disperion model described here. Note that the pattern of concentration profiles is somewhat different from that in our experiment (Figure 8). This may be attributed to the difference in the direction of impeller rotation. Figure 16 shows the effect of the operating variables and solids properties on the model parameters Pet or Pep(Pep/Pef)as a function of [(nd/u,)(d,/d)]or (ndp/uJ.A comparison of Figures 14 and 16 indicates that the ratio of the model parameters is approximately proportional to the impeller speed. It is also found that the Peclet number Pef is remarkably dependent on the direction of the liquid flow discharged by the impeller. At this stage, it is not sure whether the correlating equations of the model parameters presented here are applicable to larger scale slurry reactors. However, the scale-up problem in terms of the solids behavior in the slurry reactors will be included in our future work.
valid only when the dimensionless group defined by eq 21 is more than 5 or the amplitude to liquid depth ratio is larger than 0.3. For rotary agitation, on the other hand, the ratio of model parameters is approximately proportional to the impeller speed in high-speed agitation. The theoretical analysis indicates that both the dynamic and steady-state characteristics of the slurry reactor may be influenced appreciably by its solids flow pattern.
Acknowledgment The numerical calculations in this work were carried out by using special TSS service, Computer Center, University of Osaka Prefecture. Thanks are also extended to Mr. H. Tokuda, who helped in the experimental work.
Nomenclature
Conclusion
A = amplitude of disk vibration, cm = projected area of solid particles, cm2 solids concentration, g/cm3 or wt % Co = inlet solids concentration, g/cm3 or w t % C, = reactant concentration in the liquid phase, mol/cm3 C, = inlet reactant concentration in the liquid phase, m01/cm3 CN = number concentration of solids, l/cm3-slurry Cv = volume concentration of solids, cm3/cm3-slurry Cw = weight concentration of solids, wt % di = inside diameter of the tank, cm d = impeller diameter, cm d32 = volume-surface mean diameter of the solids, cm dd = vibrating disk diameter, cm d = particle diameter, cm I& = liquid phase dispersion coefficient, cm2/s E p = solids phase dispersion coefficient, cmz/s f = frequency of disk vibration, Hz f ( d p )= particle size distribution function H = liquid depth in the tank, cm h = height of sampling probe, cm hi = impeller height, cm I = intensity of illumination, cd k = mass transfer coefficient, cm/s 1 = path length of light beam, cm n = impeller speed, l / s Pep = Peclet number for solids phase (= u H / E ) Pef = Peclet number for solids phase (= ufH/lf) PeL = Peclet number for liquid phase (= uH/&)
Dynamic and steady-state solids flow characteristics in slurry tanks with both rotary agitation and vibratory agitation have been interpreted quite well by the sedimentation-dispersion model which takes into consideration the solids falling velocity. A correlating method for the model parameters has been also provided. For vibratory agitation, the perfect mixing assumption of the solids phase was
= liquid flow rate, cm3/s Qup = upward flow rate caused by disk vibration, cm3/s R, = reaction term defined by eq 3, mol/cm3 s S = cross sectional area of the light beam, cm2 t = time, s u = superficial velocity of liquid phase, cm/s u' = superficial upward velocity of liquid phase in eq 21, cm/s
2=
Q = ufu QL
Ind. Eng. Chem. Fundam. 1982, 21, 220-227
220
uf = falling velocity of the solids, cm/s
u, = free settling velocity of the solids, cm/s X = dimensionless solids concentration Y = dimensionless reactant concentration 2 = height, cm Greek Letters = dimensionless impeller height (= hilt0 E = dimensionless height (= Z/t0 K = extinction coefficient pp = density of the solids, g/cm3 T = dimensionless time defined by t / ( H / u ) (0, = reaction parameter
p
x
= dimensionless parameter defined by eq 21
+ = function of 2 A / H shown in Figure 13
Blass, E.; Cornelius, W. Int. J. Muhiphase Flow, 1977, 3 , 459. Bohnet, M.; Niesmak, 0. Chem. Ing. Tech. 1979, 51, 314. Fan, L. T.; Tojo, K.: Chang. C. C. I d . Eng. Chem. Process Des. D e v . 1979, 78, 333. Kafarov, V. V.; Braginskii, L. N.; Begachev, V. I.; Verkhorubov, B. A.; Gurevich, M. A.; Rybkina, I. S. Teor. Osn. Khim. Tekhnol. 1971, 5, 287. Nagata, S. "Mixing, Principles and Applications": Kodansha: Tokyo, 1975; Chapter 6. Parlushenko, I. S.;Kosin, N. M.; Matveev, S.F. Zh. Prikl. Khim. 1957, 30, 1160. Takeba, K.; Shlral, Y.; Kimoto, R. Paper presented at the 10th General Symposium of the Soclety of Chemical Engineers, Hamamatsu, Japan, 1971. Tojo, K.; Miyanami, K.; Yano, T. Powder Techno/. 1975, 12, 239. Tojo, K.; Miyanami, K.; Mitsui, H. Chem. Eng. Sci. 1981, 36, 279. Tojo, K.; Miyanami, K. 2nd World Congress of Chemical Engineering, Mixing Session I , Montreal, Canada, Oct 4-9, 1981. Zundlevlch, Yu, V. Theor. Found. Chem. Eng. (USSR) 1977, 17, 466. Zwietering, T. N. Chem. Eng. Sci. 1958, 8. 244.
Received for reuiezo July 1, 1980 Revised manuscript received January 25, 1982 Accepted April 21, 1982
Literature Cited Argo. W. 6.; Cova, D. R. I d . Eng. Chem. Process Des. D e v . 1965, 4 , 352. Azzopardi, B. J. Int. J. Heat Mass Transfer 1979, 22, 1245.
Catalytic Effect of LIX63 on Copper Extraction in the LIX63/LIX65N System Toshlnorl Kojlma and Terukatsu Mlyauchl' Department of Chemical Englneering, University of Tokyo, 7-3-1, Hongo, Bunkyoku, Tokyo, 113, Japan
Copper can be extracted from aqueous sulfuric acid solution into hydrocarbon solvent using organic chelating compounds, such as LIX65N. Afterwards the extracted copper is stripped using a high concentration of sulfuric acid solution. The effects of adding LIX63 to the LIX65N-Dispersol-copper system are studied theoretically and experimentally. No differences in extraction equilibrium are found between the LIX65N and the LIX65N LIX63 systems. However, extraction kinetics are enhanced by the addition of LIX63. At higher concentrations of LIX63, the extraction and stripping rates are proportional to the onahalf power of the concentration of the active component of LIX63 in the aqueous phase. This trend is explained theoretically and quantitatively.
+
Introduction LIX reagents (General Mills Chemicals, Inc.), especially LIX64N, are used to extract copper from sulfuric acid leaching solutions in the copper mineral industry. LIX64N is a mixture of LIN65N, &hydroxy oxime and a small amount of LIX63, a-hydroxy oxime (Atwood et al., 1975). The structures of the active components of LIX65N and LIX63 are shown in Figure 1. Flett et al. (1973) found that the addition of LIX63 enhanced the rate of extraction of copper without affecting the equilibrium distribution. Their rate equation is
r = k(W+)CR(Cg)1/2/(H+) (1) where (M2+)and (H+)are, respectively, concentrations of copper and hydrogen ion in the aqueous phase and CRand CB are, respectively, concentrations of LIX65N and LIX63 in the organic phase. Flett et al. (1973) proposed an interfacial reaction model to correlate their results. It is described as follows. Let the active component of LIX65N be designated as HR and LIX63 as HB. HR + HR,d (2) M2+ + HR,d F= MR+ + H+ (3) *Address correspondence to this author at Department of Industrial Chemistry, Science University of Tokyo, Kagurazaka, Shinjuku-ku, Tokyo, 162, Japan. 0196-43 1318211 0 2 1-0220$0 1.2510
MR+ + HB,d + MRB,d MRB,d
+ HR +
+ H+ +
(4)
(5) where the overbars and the subscripts "ad" denote species in the organic phase and interfacially adsorbed species, respectively. Reaction 4 was assumed to be rate controlling and to be first order with respect to copper, LIX65N and LIX63 concentration, and pH. However, experimental data indicated a one-half-order dependence for LIX63, this being attributed to the dimerization of LIX63, in the organic phase (Flett, 1977). Their experimental results are shown in Tables I and I1 and the effect of LIX63 concentration on extraction rate is shown in Figure 2. They did not perform an experiment at CB = 0 at the same conditions as in Figure 2; however, this result can be estimated using an apparent reaction order for LIX65N of -1.0 (Tables I and 11). The result is also shown in Figure E
2
m,
2.
Atwood et al. (1975) studied the extraction rate of copper in the LIX65N-LM63-xylene-copper-nitric acid system, using a single-drop method and obtained the following rate equation. r = k(M2+)(CgCR)1/2
(6)
Whewell et aI. (1975), also using a single-drop method, found that the extraction rate of copper for the LIX64NEscaid lWcopper-sulfuric acid system was a function of (M2+)/(H+).Later, Whewell et al. (1976) found that the 0 1982 American
Chemical Society
