ORIG. RUSSIAN: EXTRACTION PROCESSES AND THEIR MATHEMATICAL DESCRIPTION

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP88-00904R000100100045-1
• Release Decision: RIPPUB
• Original Classification: U
• Document Page Count: 25
• Document Creation Date: December 22, 2016
• Document Release Date: August 12, 2009
• Sequence Number: 45
• Publication Date: May 1, 1964
• Content Type: STUDY

 Approved For Release 2009/08/17: CIA-RDP88-00904R000100100045-1
Third United Nations
International Conference
on the Peaceful Uses
of Atomic Energy
Confidential until official release during Conference
A/C 014F. 28/P/346
USSR
lay 15641
Uridinal: RUb31AN
EXTRACTION PROCESSES AND THEIR MATHEMATICAL DESCRIPTION
Rozen A.M. , Bezzubova A.I. , Elatomtsev B.V. Khorkhorina L. P. ,
Nemirovsky A.M. , Nikolotova Z.I., Phushlenkov M.F. , Reshetko Yu.V.
Shuvalov O.N., Teterin E.G., Vasiliev V.A., Yurkin V.G.
In the present paper which generalizes and develops papersl-15)
the quantitative regularities of the extraction chemistry and
engineering are studied and interpreted.
1.Extraction Equilibria
1.General. The extraction equilibrium regularities are discuss-
ed using the extraction of nranyl and other actinide nitrates by
neutral organophosphoric compounds(for general discussion see4) )as
an example.These systems show the elect rolyt e-nonelect rolyte equili-
brium when the chemical bond of an extractant with a compound being
recovered is necessary to overcome the electrostatic interaction in
an aqueous phase.However,the bond should be sufficiently weak to
permit stripping(the interaction energy < 1 kO cc1).Accordingly, to
mole
interpret the extraction power of solvents the theory of chemical
bond is required while due to the chemical interaction weakness when
describing the dependence of equilibria on the extraction conditions
it is necessary to consider the contribution of the Van.,der.,Waals
(up to 3kcal/mole)and especially electrostatic interactions to the
chemical potential in terms of the solution theoiy(the electrolyte
solution theory for the aqueous phase processes while the multi-
component nonelectrolyte one for the organic phase).
The extraction,not complicated by the hydrolysis or formation
of anionic complexes is described by:Men++nA-+qS+hH2O=MeAngS.hH2O
where A is an anion,S,an extractant.Accordingly, the distribution
coefficient for unhydrated solvates(A=N 0 )will be:
d=Y/a=g(N03)n~"n+1($)q t8'tc (1.1)
where K is a thermodynamic distribution constant;y and x,concentra-
tions of a compound in aqueous (a.p.)and organic (o.p. )phases ,the
round brackets denote concentrations, (+,tc, r
s are activity coeffici-
ents of ions in a.p.,of a solvate in o.p.and of an extractant,the dot
1
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!notes the concentration coefficients: (=1 at x=o or y=O;r=1 atN=1
S s
The terms of the equation define 'Kr an extractabillity; (NO3 )nr++1
processes in a.p.,salting out;Sq=the effect of dilution due to solva-
tion(in case of the extraction of several compounds it describes the
competition for a free extractant) q/ =die' is the effect of the dilu-
'~s ~c
ent peculiarity(weak interactions in o.p.).These effects are to be
discussed consecutively.
Extractability depends on the extraction power of the solvent
and -the forces retaining, a compound in a.p. According to4)5)
KN=exp (~ n- org)/RT=o++1 (0)acl/X(0)org`r++1 (0)an(1+KS) (1 .1 )
where e (0) is the value at a zero concentration, Ks ,the solvation
constant in o.p.The values of e(O)so far determined only for HC1 and
HNO3are very low(jt2=3.10'"5and 2.1x10_2,respectively)i.e.ions are
strongly bonded with waterx) Therefore for the effective extraction
a strong solvation is needed in o.p.
Extraction power of phosphine oxides is maximum and diminishes
on substitution of alkyl groups R by electrophylic ones(Ro,Ph,Cl)16,17
To obtain the quantitative regularities it is necessary to improve
the criteria of extractability and structure.The effective constant
K'=K~s/ =a 5
KdcC') and the elect ronegativity (EN) of roups,X,were assumed
to be such criteria ).To improve the EN scale18 the infrared spectra
of a number of organophosphoric compounds R1R2R3PO were investigated
and the following scales were obtained (fig.2a,b):
a) XF=4.0; E X=XRI+XRZ+xR3=6+0.024 (WpO?.1170) (1.2)
b )X=3.919X=6.6+0.021 (W "0-1170) (1-3)
Group
R OR Ph OPh CH2C1 CC13
Ph OPh CH2 1 CH2C1CH2 CC1
Scale BQ
X, Spectral
X eff.(from extraction)
18)
1.2
1.3
1.65
1.85
2.2
2.0 3.0
2.0 2.9
2.253.0
2.4
2.3
2.5
3.2 2.85
3.1 2.6
3.172.8
3.35
3.2
3.3
2.7
2.65
2.8
3.5 3.3
3.4 3.1
3.473.2
2.7
2.6
2.8
4.6
4.3
4.2
Lg K(the free energy)drops approximately linearly with the increase
of EN,the number of radicals,nORand wPOwhen alkyl radicals are sub-
stituted b ethereal ones (fig.1 ), (i.e.when the negative 0-charge
diminishes-): lg K=A-B E X ='? A1,-B1 nOR= A2-.B2 W PO (1.4)
x)Particularly for HC1,due to which it is more poorely extracted by
TBP(KHCl =2.10" ,KHNO =0.2),though the bond strength of both the
acids with TBP is clo;e.KS,HCl --7,KS,HNO = 10.
xx)The experiments were carried out usin CC14 for Which th 1.TheU,Pu
extraction isotherms were measured for the K calculation reliability,
a H was determined from the lgK temperature dependence.
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where constants A and B depend on the nature of the compounds extrac-
ted.A stronger extractability decrease when introducing phenyl or
chlormethyl radicals is approximately described (fig.1b)x)by eq(1.4).
with the help of effective (increased )EN, Xe f=Xa+ A Xef=Xa+/ueX;where
Xa is EN of the alkyl radical substituted, oX=X-Xa , /a=const ~ 2
(e.g.XC013-Xa=1 ,35;XCC13-Xa=2,6,,u ^1 ,9) .
The influence of the entropy or steric factors is one of the
reasons effecting a difference between Xe farad X as EN is responsible
only for the change of the binding energy but not for all the free
energy.In fact,the deviation from the general regularity is less for
AH as compared to \F(fig.2c,d),i.e. .-AH=A3-B3ZX=A4-B4 lv P0'
With the hydrocarbon chain elongation nc,EN is slightly decreas-
ed only for the first members of the series while the steric diffi-
culties are increased,which results in the weak maximum of K obser-
ved at nc=6-7(fig.1d, n0 Znc/3).To describe the effect of nci.e.the 0)
influence of the entropy-steric factors,the dependence lgK=p.vq(C/03j ,
determined for ethers,can be used as the EN change cannot explain the
constant decrease and C/0=2nc.As for the highly branched radicals the
effective hydrocarbon chain length may be 1 > nc,the general equation
of the extraction power is
-AFo/RT=lgK=A-B 2: Xe f-ql=A3-B3 Z .X - ql (1-5)
The similar dependencies are expected in extracting by amines
and acidic extractants(in this case B -,0);Xef.differing from X even
more owing to polymerization6).
Salting out Theory4~based on the electrolyte solution theory,
allows the effect of the salting out agent to be predicted,when the
effective diameter of the extracted ions, the hydration numbers of
ions and of the salting out agent are known.'JVhen computing it is
convenient to express the activity coefficients by Harned' a equation
and in case of a linear concentration dependence of ~ by Rozen's ono,t
19r( e9'salt=1g ~ (3:~ne10)+( Isalt (1.5)
For U02 and Pu0Z2nitrates lg j`( e,0)=_0,46+0.116 I,i.ec -S -0.116
r PuVI-
The approximate values of Harned's coefficients are :
Cation
H+
Na+
NH4
Mg++, Be++,Ca++
Al +++
for U(VI)
0
+0.06
0.08
0.033
0.054
for Pu(VI)
0
-
0.13
0.053
0.078
x a,b,c:I-(R0)33PO,II(R0)R PO IIIROR2PO,IVR PO( .0 ,oC );f .1bs
1. (RO 2PhO PO;27(C$ CI.CHO) P0,J, (R0~2PhP0,4-(RO)2C21 PORK-pienyll;
fig. 2 -. &;P-dihexyIphenylp o sphonate, DHCI,MP-dihexyl6hloromethyl-
phoaphonat e.
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- 4 -
Effect of Diluents. The solvate formation results in the
extraction dependence on the extractant concentration S(o(^Sq)
whichis not affected by the diluent nature; the latter determining
the value of the diluent = z
parameter dierslI c , The activity coeffi-
cients in multicomponent systems taking part in die may be express-
ed and interpreted by the properties of binary rystems with the
help of the solution theory. the activity coefficients in binary
systems diluent-TBP and di.luent-uranyl nitrate solvate,are approxi-
mately described by the equation with two constants: e8~`i = T 2 (B!2 z~i~rA
dlz =b(z - szr Vz/V1 , while the data on the three-component systems
by the equation with data on the binary systems x)at C=O.Acid and
water taken into account the expression die becomes most complicated
and contains 20 constants, describing all the possible binary inter-
actions ;accordingly die depends on the nature of the diluent and
the compound being extract ed(fig.3a,b)as well as on the acid concen-
tration (fig.3c )xx).The die values derived from the data on the acti-
vity coefficients of binary systems and from the extraction data are
in agreementxxx).The die values are similar for all the diluents
except CHC13,although the non-ideality sign in the TBP-diluent solu-
tion is different and ~Tvaries by 100 times.It is explained by the
similarity of the properties of TBP and solvate(with the higher non-
ideality in solvate systems)due to which the interactions TBP-diluent
and solvate-diluent affecting c/iL in an opposite way are partially
compensated,b31" 2b21.As compared to CC14,die is increased(fig.3a)
due to the predominance of the interaction with TBP(hexane)or with
solvate (C6H6) .The positive non-ideality of the TBP and solvate solu-
tions in saturated hydrocarbons shows that the interaction between
similar molecules is stronger than that between different ones,which
is typical of the Van-der-Waals forces.The strong negative non-idea-
x) t', y=(i-'!)Ctfz(Bjj 2+pi'8f2 ~'J3(1513-2t~IAf3)1 +fz73L(L 1 C)(I-2'f~)-523V2/v11; C,
is ternary constant nos of components: 1-diluent , 2,extractant,3,
solvate} ,the volume fraction;V,the molal volume.
xx)For the extraction of metal microamounts(y O)with diluted extrac-
tant(Y2-O)one obtains simple eqns,the form ofwhich depends on the
selected standard state of the solvate: diej -a pure solvate,
II-a diluted solution in dry TBP,III-a solution in TBP,containing
water and acid. E.g.lgdiel=2b21--b311g diell-2bl-b31+b332,i.e.the devia
tion from ideality is due to the extractant -diluent(b21),solvate-
diluent (b31 )and solvate-extractant (b )interactions.
xxx)For C61 ,C6H and CHC13from extra9tion dier/die cce = R/KCe 1,55 ;
2,35;0,O2,frgth y :~,55;2,42;0,013. (dielc ~"z(O)/ra(U) x 1).Nos of
curves in fig.4a,b,d:1,5 CC14 diluent ,2,6-C6H6;3,7hexane'4,8 CHC13.
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ity in the TBP.-CHC13 system results from the hydrogen bond formation
as evidenced by the spectroscopic data 21 t 14)and the high value of
the heat of mixi ng(fig.4d) .The main reason for the moderate negative
non-ideality in systems with CC14and C6H6(and in CHC13-solvate) is
an athermal effect,i.e.the solution entropy increase due to the
difference in sizes of the component molecules(fig.4a,b).However,the
negative non-ideality is not confined to the athermal effect as the
entalpy of mixing is neptive.Thus,in these systems the"molecular"
negative non-ideality(r= 3/tatherm.z1 )5 jietsx)which may be interpretQd
by the unstable compound formation .The uranyl nitrate solvate-
TBP system is also characterized by the negative non-ideality(b23 -
-0. 6)and a high value of the heat of mixing(h0. 5=_7?5mo e )which may
be interpreted by trisolvate U02(NO3)2.3TBP formation with Ks=1-2.
The interaction of diluents with solvates of Th and Pu(IV) nitrates
is similar to that with uranyl nitrate solvate;but for Th solvate,
the positive non-ideality is stronger in the systems with saturated
hydrocarbons which results in the formation of two organic phases.
The solutions of Th solvate in CC14 and in C6 H6 are close to athermal
ones (h0.5 5Ocal/mole)i.e.there is even a small molecular positive
non-ldeality.When substituting ethereal groups by alkyl ones(TBP-TOPO
series)the activity coefficients of CC 14,C2H4C12and CHC13 and.hence,
the extract ant -diluent interactions are markedly changed only for
TBPO1 5)(fig.4c).
The Extraction Isotherm Calculation. In case of the concurrent
distribution of U,Pu and HNO 3 macroamounts one obtains8) .
YU=fU S2; Ypu=fpuS2; YH=(fIH+2f2H) S (1 .6) xx
S=2So/(1+f1H +f211)(1+ 1+8F o); 0=S0/(1+Bu/2) (1.7)
where y and x are concn.of compounds in organic and aqueous phases,
S and So are free and initial extractant concentrations
1- 4 fU=kuxu N03 , f kpuxpuN03' f 1H-kIHxHNO3 0 f 2H=k2HxH NO3
N03=xH+2xU+4xp+ zixs 1 I ;13U=0, 00247 S0/(o , 747+O232S0) , BH=QU/2.
For TBP k~l{N ~7.1.10~ ? 4 (xU+xg/3+xp ,k =0,19,k -0 , O004. If the
1 A 2H
component concentrations are related to the solvent volumes, then
8H=aN=O; =5.95.10 0.625(xU+xH/3+xPu k1H_O.174: k2H=O.0002.
x) Probably, there is a weak acceptor-donor interaction between
Tr-electrons of benzene and uncompleted Cl 3d-orbitals with TBP.
xx)1gns.(1.6)are obtained by the combined solution of U,Pu and HNO
distribution egns (1 .1) . 3
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Extraction Cascades
Calculation of Cascades. If the apparatuses are not numerous
it is convenient to calculate graphically (fig .5a )the macrocomponent
distribution over the extractor stages by the method of successive
approximations 9) . The distribution of elements present in micro-
amounts is calculated analytically, fig. 6. The equations are obtained
by the combined solution of equations of equilibrium yi=oaixiand
material balance which for some i-stage is:
Li-1 xi-1 +Vi+1 Yi+i =Lixi+Viyi , (2.1)
where L and V are volumes of a.p.and o.p. The decontamination
factor Kd, in the extraction section at a in< 1 determined by the
extraction conditions at the first stage does not depend on the
cascade (column)length.Conversely, in the scrubbing section atoc'n'L
41,K d depends on the number of the stages;if cx '=const.
Kd casca1n1 ),1/(0(' n' )N
If a'n'>l,the scrubbing is not effevtive:
K d,scrub;- 1+1/a'n1+1(a 1 'n )(oc 2 n') + ... L2 (2.2)
e.g.for Ru at a'=0.2 and n'._10 we obtain Kscrub. 2.If the extrac-
tion is accompanied by a chemical reaction(the reduction stripping),
the element concentration in the solution at the i-stage which
would bekx10=x1.-1+n(yi+1'-yi)in the absence of the reaction,will be
Xi-xi e i i, ki,the rate constantx)t i the time of the contact.
Assuming yi= a ixi,we obtain the equation describing the process in
the cascade:
xi( (X i+ekiti)=xi-1+nyi+1=xii-1+ oci+ix1+1 (2.4)
If the reduction is effective(ekiti>10)so that the Pu(IV)concentra-
tion in a.p. at the i-stage inlet xi-,~ O,a simple relationship
between the concentration of the elements not reduced and the
initial one(yf+1 ) is obtained
y1=yN+1/A1A2..'AN' yi=yN+1/Ai+1Ai+2''' ~N' (2-5)
where Ai=l+ekit1/&i,effective stage reduction coefficient.
The above calculation method based on the stagewise contact pattern
describes the process in the column satisfactorily(fig.5c).If two
x) The value* of the rate constants may be estimat d from data22).
k=2000[Fe][Pu +] provided that Pu4+=Pu(IV)/(1+E2j
N0 )= Pu(IV)/(1+S),
where 3 .is constant of complexing with nitrate ions.It is interest-
ing to note that too low rate constants are obtained when using 8
found by the extraction methodic/:at Fe=0.04m/1 and xH=2m/i,S=360,
1/Kcalc.=4min.wri le 1/k 410sec. The extraction method overesti-
mates the 13-values. exp.
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actinide elements present in macroamounts and when a great number
of calculations are needed (the static characteristic determination)
EC should be used. We employed the programmes of direct (Ural I )and
stagewise (Minsk I) computing.In the latter case the equations of
equilibrium(1.7),of material balance(2.1 )and those of mixing are
used.The programme provides for the minimization of the deviation
of the calculated inlet concentrations from the fixed ones by
affecting the assumed values of the waste concentrations xN.Direct
computing lies in the combined solution of equations relating the
material concentrations to the value at all the cascade stages 15) .
The microcomponent concentrations are computed after the actinide
and acid determinations using an additional programme.
Static characteristics of the extractor processes are determi-
ned by a number of variables(L0,L' ,V0,xU,x0
R,S,etc.) their influence
may be approximately described as an action of one generalized
parameter? the degree of approximation to the limiting conditions
(the flow theoretically minimum one ratio)10)
=Y/Yp=V /V=1/(cK n)1 , (2.6)
(where y,yp are maximum operating and equilibrium U-concentrations
in o.p.,V and Vmin.are operating and minimum o.p.flows).It is seen
from the illustrative calculation of the Purex extraction-scrubbing
column(the impurity effect on the Zr and Pu microamount s was
neglected)(N=4;N'=1 ,L=76,5, L'=56,2, V=383, $=1.8m/1, xoo-0.95m/l,
( ( )'=2m/l,T =1.2m/1).The data on U8) HN07a) 3) 7b) 23)
o- , 3 , Fu , Z r and R:u were
used 10).The decontamination from Ru was estimated by the separate
distribution of tri- and dinitroso-nitrates RuT and RuD(o(t,,.=CR,am+C?a?
where C is a fraction of species in a.p aT)ata23) were recalculated
for U-solut ions (fig. 7g) ;it was assumed that C?=f(xHo)=0.025,and in
the scrubbing section CT=1,ot=(Y T.The flows L V and concentrations
xQ,T were varied.As it follows from figs .7,8 with the ? growth the
uranium zone is expanded,the accumulation of Pu and Ru increases
(the accumulation decrease at 2>99% results from the species losses
due to the insufficient stage number),the waste concentrations of U
and Pu and Kd from Zr and Rux)rise.Fig.8 also shows that the static
characteristics of the extractor are defined by the approximation
degree to the limiting conditions while the way of approximation
a sa Ta , is extracted completely and KRu=1/CT ~50 does not
depenront however the RuT accumulation is very large(fig.7e)and if
the reaction RuT-RuD in the presence of U is rapid enough,KRu
incr
h
eases wit
14 . 3 4 6
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is of little importance. This conclusion is also true of the
extraction stage number change.
Optimization of Conditions. A possible way of optimization
is a maintenance of the maximum R(high)at the permissible U,Pu
losses. Introduction of the optimization criterion is an alternative
method. Assuming the conditions providing for the maximum Kd with
the minimum loss of U and Pu and minimum Pu accumulation to be
optimum,a criterion is
opt.=KZrKPu/(x )r(q )s (2.7)
where m,n,r and s are coefficients characterizing the significance
of each factor when processing various fuels x).In many cases all
these factors are equal,m=n=r=s=1 (fig.9d,curve 1) .?then processing
natural U the Pu accumulation is of no importance, s=0 (curve2). If
the highly active material is processed the importance of the
decontamination increases and m=n=2 may be assumed(curve 3)The
range of the optimum conditions is? =0.90.0.99 ;the greater is the
importance attached to the decontamination,the higher is 7 opt. The
use of conditions close to limiting ones is possible only with a
sensitive systems of control(e.g.with that retaining the uranium
front location in the extractor).
Extraction Dynamics. If dy/dx-o(=const, Lhe nonstationary mass-
transfer eq:'Imay be solved either approxi.-iately by the similarity
method13'24)or exactly by the operational one24).At t>t0
xo-x(z,t) = (xo-xp)(1-a-t/to), (2.8)
where xp(z)=x(z,00)is the equilibrium concentration while the relaxa-
tion time t0(the time constant)is defined from the relationl3'24)
to=removed material/initial transport=M/j 0 (2.9)
where J=V yp(xo)=L xo n,M=Mo-Mp=Zgol(x0-x)+Qyol(yo-y); ? holdups.
More accurately t =(1-A)to,the correction ,l is estimated from the
accurate solution 94) .As in case of any separating cascades the
similiarity of the stationary and non-stationary concentration
distribution corresponds to eq.(2.8).The degree of approximation
x n ro uction of the coefficients of decontamination from Ru and
Zr as separate factors is useful owing to the different effect
of acidity,the scrubbing temperature, etc. on them.
4-(ny c3x -(T tn~ ax+(T +~ _-- c?zx _
yla at ~Xcy~tz -0, yP=ax
a) d Z x -_ X ax at
E=z/HTU;H=N; T,HTU time(=HTU holdup/flow) ;x,y,averaged x,y.
e.g. =C f xc/J/H~xo/e,I; xp=X~C[f#e)e~"' ~ t]/C(i+e,?''-ij ~xoe~z; ?=ocn?j.
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to equilibrium f =(xo-x)/(xo-xp)=1-a-t/to depends on time rather
than on the coordinate.Time of equilibrium setting in is(3.5)to,
which corresponds to T =0.95-0.99.The starting period curve found
experimentally for the columm of 200mm,H=2,8m,with Rashig's rings
of 25x25x4,5mm(x~o-35g/1,xx=0.5m/1,n=V/L=1,(x=1 )is close to the
exponent(fig.9a)while therelaxation time is close to that calculated
from eq. (2.9) .
L=230 1/hr ; Tc olumn 14 , 6min
NETS, rn 1
.11 0.95
to,min,calQ4
.35 4.8
to,min,exp.3
.3 4.8
When starting from a blank solution the expression for the
xoutlet is close to the exponent(2.8) (to=M/jo,M gol.g+2 yoi; jo=Lxo
with delay.In case of nonlinear extraction isotherms(uranyl nitrate
in wide ranges of ::o)ncentrations and acidities) the process equations )
were solved with the help of E.C.Simultaneously the dynamic charac-
teristics of the pulsed column of fd200mm,4,2m high with a packing
of 15xl 5xlmm were experimentally determined while starting up from
a"solution" (xoU=250g/l,xg=1 .55m/1, yH,1=yUo.-0.2g/l,To=0.8m/1,L=75e/hr,
V=315E/hr)and from an acid(x~0, x~? 2m/l )with I=700mm/min.The start-
ing period curves for uranyl nitrate are close to the exponents
(fig.9c,f)with the lag timeoi which increases with moving away from
the bottom of the column(it being the disturbance source,i.e.not
saturated o.p).By contrast, in starting up from an "acid"when the
concentration front moves down the column the timea'L=z/rWcis increas-
ed from the top to the bottom(fig.9e,f).Mp =19kg is removed, jo=27kg/
hr and eq 2.9 gives t =0.7hr>t exp ? 0.4hr.'en starting up from an
acid 1 =7kg, jo=17,5 and toalc.-o_0.4h.r(to~'0.3hr).
The results of the transition process computations are close
to the experimental data
Masstransfer
The Driving force (D. f.) 'With non'.linear extraction isotherms
the boundary concentrations xi and yi=aixi cannot be excluded by
a simple procedure from the expressions for the flux through the
,?dX;/dt +- 2yjdyj/dt =L (xc-i-XL) tV(yj?, -yi~ j 5ej , i-stage holdup.
L=3001/hr , Zc olumri 11 , 2min
Pulsation intensity, J=af, mm/min
0 x 8 4x108 0 4x54 4x108
0.65 1.11 0.905 0.565
5.6 3.3 3.7 4.35
5.6 2.6 3.2 4
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diffusion boundary layersx),the standard masstransfer equation
becomes incorrect.In case of the nonelectrolyte distribution the
task may be solved using the irreversible process thermodynamics
according to which the diffusion flux is proportional to the chemical
potential gradient: j=-Docddu/dz=B(a-a) ,where R=D0RT/y(?- (B/);(average
da/dz '2z-(a-a)/S. With the equilibrium condition ay=l ax one obtains the
general masstransfer equation with the D.f.expressed in terms of the
activities: ]=A (ay-ay)=Ax(ax-aX); 1/Ay=1/By+K/fix;a*=Kax; Ax =KAY;
;
An alternative useful method for the electrolyte extraction (when
it is difficult to average B)is the calculation of the boundary
concentrations.let yp=F(x) and x-xi=aX, ?hen yi=F(xi)=F(x_ox) and
the flux is j=Bx x=By y F[(x-ax)-yj Knowing F and B one can obtain
AX,Xi,yi and j(or directly j,substitutingAX by j/Bx) from this
equation.It is possible ,e.a.to expand F(X-iX)in a series on
,5x--J/13 x power.It gives ~Ky (yp-y) ,1/Ky 1/By+(y' + A ox. The correction
A~n(yp-Y)/(yp +BR/By) depends on By,therefore with (yp-y) D. f.
the resistances are not quite additive.
Masstransfer in a real apparatus is complicated by longitudial
diffusion,axial mixing(am) by the macroflows,and by transverse non-
vniformity(tn).All these effects may be approximately described by
a longitudinal diffusion with the effective coefficient De f=DT+Dam+Dtn
resulting in the HTU increase;
h=hk+Def. x/wx+Def.y/wy=hk+hD,x+hD,y -hk+h D,xax) (3.13)
where hk is HTU defined by the masstransfer coefficient;w the velocity
hk=S, hD=hT+ham+htn; hT=Dx/Wx, htt2Dtn,xx+Dtn,y/Wy.
The transverse non-.uniformity(inconsistency of the flow rates
over the column cross-section)is of a particular importance as it is
the principal reason of apparatus effectiveness lowering with a dia-
meter and height increase(h may be 5 and more times higher than hk).
The diffusion correction hD=D/w is large with low rates,therefore
the effectiveness of columns of a large diameter increases with the
flow rates(fig.11a,htn=h-hk; hk=NETS of column 25mm in dia.If Dy is
decreased with the increase of the hole numbers and DX drops with
sectioning and in the latter case Dy_Dx 1.5m2/hr,then curve 1 cores-
X) i =13 x x-xL )=By(yL -y),where B=D/c,t, ~)masstransfer coefficient;
S, dii fusion boundary layer thicness hence j=K(or~xby) ;1/K=1/q+ay/R, ;
xx) more accurately ;,A=-(j/P,)Yp"12N+(J/(JyP13! -... where yP~''=d nF(x)/dxn
xxx)more accurately hoy=hk.~hpxf-i+(an-1)h,~/h]+hpyEI +(?n-I)hpa./h]/[t-(an-i)hpy/hJ
3 4- b
-10-
D.f.is(atx-Y)>(yp_Y) 9
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ponds to Dy=5.5m2/hr, Dx=3.5,the o.p.t.n.is greater than i,n. a.p.).
The pattern peculiarity is an anisotropy,a large difference in the
diffusion coefficients in the longitudinal (Def )and transverse(DI =
=DT+Den)directions :Def.=Dl+Dtn D1 .As the tranverse non-uniformity
decreases with the mixing intensification one may expect11b)that
Dth=C1/Dm(where Dthi.e, Clis increased with the column diameter,C., -dcol
or exp do ) and Def.=DJ+C1/Dlm 11 )so that 1 )De f. and Dlshould come nearer
when turbulized. (This assumption is confirmed by fig.11 c) . 2 )Oppo-
site to the small columns,in large dia columns the pulsation may lower
Def. due to the transverse non-uniformity decrease (Dtri C1/(Do+C 2dPachi),U d
C1 is high).In fact.,for 500mm,dia column at W==7m/h without pulsation
Dx=2m2/h,with I=500mm//min D x lm2/h ,for 100mm column DX 0,5 and
0,85m /h, resp,(as DT=DT+cId~It is important that the transverse non-
uniformity is a hydraulic phenomenon therefore its study and elimina-
tion is possible using hydraulic scale-up without the experiments
with masstransferg.Constructive measures result from the theory based
on the channeling pattern24).
ht n=1X (n L//Lx) +ly o Ly/Ly
where AL/L is the flow fraction evading the masstransfer,l is the
by-pass length.These measures consist in the diminishing of L by
setting phase distributors and the decrease of Eby the apparatus
sectioning, providing for the transverse flow mixing;a good mixing is
obtained by means of "louver" rotary plates 28)'
The distribution of the dispersed phase in the packed column
700= in diameter was studied by hydraulic scale-up.With the pulsa-
tion intensity increase the feed cone section expands while the
number of feed sources required for the uniform distribution is
decreased(fig.12b).Flow density levelling off with pulsation was
also observed for the distributors of a hydraulic seal type(fig.12c,d)
The uniformity degree of the continuous phase motion may be controll-
ed by an impulse method13b);it being important to scale up the density
gradient that increases the by-.pass length and, correspondingly,HETS
in the uranium zone(fig.5c,also 28) ).
Mechanism of the extraction intensification is often associated
with the surface renewal,i.e.with the increase of the masstransfer
x)Thus,the effectiveness of 5m in dia di tillation plates with a
directed motion was increased by 50%24).
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coefficient.The analysis of the elemental components of the process
and of the experimental data on the sieve-plate and packed pulse
columns )showed that the effectiveness rise is due to the increase
of the phase contact surface,while the effective coefficient of mass-
transfer is even decreased ,K,~l,fig.15a.'( KF=ho/h;KR=do/d;KS2=S2/4? ,
Ks=S/So and Km=k/ko are coefficients of effectivity, dispersion holdup
surface and masstransfer variation index "o"denotes the value before
intensification; KP=KH K KM=Ks Km Ks). In the first approximation the
SG and k variations are secondary and are defined by the drop diameter
decreasex).Then the knowledge of the dependence 1)of the drop radius
on the intensification variable (revolutions n,pulsation intensity I)
and 2)of the terminal velocity and the masstransfer coefficient on
the drop diameter d is sufficient to advance a quantitative theory.
The dependences of d on the intensity of I/d-v1"1'5/G0'5type found
for various apparatuses 11j12) correspond to the theoretical ones 25 )
s
i.e.the drop size is determined from the general regularities of a
dispersion in a turbulent flow. The terminal dropvelocity dependence u
on its diameter is seen from fig. 14a(gene rallsed coordinatnes
Q-ulu/G, R=d/b4_Af16- ~dld,OX, SZCp (//U 2,dldminfT 'PG31 2Y~Qf~ _ S/R
dmax/dmtn=V). The flooding flow rate wf proportional to the terminal
drop velocity should be decreased when dispersed;the dependence of
w f on I sholld reproduce fig.14a in a mirror image which is really
observed(fig.15b,c),w f ~wf/[I+0,265 (clef)?] 12) x)
The increase of hold-up with the intensity may/ be described by
Pratt's eq.as the characteristic velocity (vo w f~U)depends on I ;hence,
the dependences of S2 on I and on the flow rates are similar and are
defined by the degree of approximation to the flooding conditions
q=w/wf11 .The masstransfer coefficient is somewhat decreased on
dispersioning which together with the longitudinal diffusion growth
accounts for the dependence of Km on I11 ) The effectivity increase of
packed-pulsed columns in two systems at I