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>
..., ..
I
Ir/
....,3
I~
'-, IJ
,....
I
60
" 0
!i ...
..
50
~
8.
! ....
40
0
'" ~
30
!i
20
10
0.1
0.2
0.3
qas phase mol fraction of S03
ne.
17
INTERFACE TEMPERATURE RISE AT THE JET SURFACE
218
Fig. 18. With reference to Fig. 14 the interference of the reaction kinetic parameters is not complicated by possible multiplicity of the heat and mass transf~ profiles, since an activiation energy of around 25.fkcal molcan only give rise to single solutions. . The exothermicity of the absorption process results in a rapid increase in the reaction speed along the jet. This is presented in terms of the half-lives of the reacting sulphur trioxide at the jet surface ~in Fig. 19. For the nominal 10% S03 in the gas phase, the half-life has become less than 10 mill~seconds at the end of the jet. The much greater surface temperature achieved in the 30% S03 case means that the half-life decreases along the jet surface from around 10 'milliseconds close to the jet nozzle to less than a microsecond on entry to the receiver. These experiments appear to establish that the absorption of S03 into DDB is significantly exothermic for gas compositions of 10% or greater, especially at long exposure times. Thus even for 10% SO, the bOiling point of DDB of 296°e is calculated to be ~chieved in an exposure time of 1.2 seconds_ The corresponding values for 3% and 30% are 12 seconds and 0.1 seconds respectively. These observations are relevant to operating practise for falling film sulphonation columns. The operation of bubbling sulphonators with surface exposure times of 10 milliseconds for typical bubble size ranges do not appear to be prone to interfacial temperatures in the region of 0 100 e above datum. However, the industrial sulphonation of linear alkyl benzenes presents an interesting problem of associated severe discolouration and the formation of malodourous compounds when sulphonation is carried out at high gas composition of SOq_ The productivity of sulphonators is limited by these fa~tors and the role of localised high temperatures in the absorption process has yet to be fully appreciated. In the longer term, improved fundamental understanding of exothermic gas absorption will lead to new and possibly novel concepts of sulphonator reactor design which will be capable of high productivity at high selectivity with reduced by-product formation.
219
120
100
0(,)
~..
'"
80
..~
30\ S03
,Q
t
60
(l.
!
40
~" ...
;:
20
POsition along jet cm
FIG. 18
TEMPERATURE PROFILE ALONG A JET
10- 1
10- 2
10- 3
;... ....
~ .:
10-4 30% SO) 10- 5
j
~
""
10-6
10- 7
position along jet cm
fIG. 19
REACTION HALF-LIFE OF S03 AT JET SURFACE
220
NOMENCLATURE
C
concentration in liquid phase
C*(o)
interfacial concentration at t absorption
C*(t)
interfacial concentration'after time t in penetration theory
C*
interfacial concentration in film theory
c
specific heat of liquid phase
p
=
D
liquid phase diffusion coefficient
d
diameter of laminar jet
E
absorption enhancement factor
ER
activation energy
H(t)
peripheral heat exposure time t
D. HR
heat of reaction
D. Hs
heat of solution
accumulation
on
0
or for physical
jet surface
hL
heat transfer coefficient
K
liquid phase thermal conductivity
kL
mass transfer coefficient
k(T)
reaction rate constant at temperature T
M
diffusion/reaction
M'
diffusion/reaction parameter evaluated at T*
n
ratio of D. HR/ D. Hs
n'
constant in hyperbolic solubility relationship
0
PA
evaluated at Tb
vapour pressure of pure absorbing gas radius of laminar jet
after
221
r(C, T) reaction
r~te
at C and T
T
temperature
T*(o)
interfacial absorption
T*(t)
interfacial temperature after time t theory
T*
interfacial temperature in film theory
t
exposure time
vet)
liquid phase velocity due to volume change
x
penetration
xA
mol fraction of absorbing gas in liquid phase
~
thickness of mass transfer film
x
thickness of heat transfer film
H
temperature at
t
=
0
or for physical in penetration
de~th
YA
mol fraction of absorbing gas in gas phase
ex
thermal diffusivity
p
liquid phase density
~tup
to
k'
3 - C10 H21 Cl
-4...c 30 possible chlorides k'4
4 - C H21 Cl _ _"';:)P>1 isomers 10 k'
5 - C H21 Cl _ _5....;:>~.... 10 Occasionally particular isomers have specially desirable properties, but their manufacture by gas-liquid reaction gives rise to considerable difficulty when such a massive variety of associated products is possible. Similar considerations apply to the hydrogenation unsaturated fatty acids (9), which can be represented by
of
227
,
/.
mono-unsaturated fatty acid ~
~H2
di-unsaturated
fatty acid
"".z
+ H2
? ~mono-unsaturated ~ fatty acid H2
saturated fatty acid
+ H2
as a typical example. These problems of liquid product selec.tivity typified by oxidation, chlorination and hydrogenation can be contrasted with those involving a requirement for selective absorption from a gas stream containing a number of soluble reactive gases. For example, in the scrubbing of gases produced from the incineration of pvc type plastic waste with low-grade high-sulphur fuel oil, it is desirable to selectively absorb the acid gases hydrogen chloride and sulphur dioxide whilst at the same time suppressing the absorption of carbon dioxide, which is necessarily present in large excess. All of these gas-liquid reaction problems are characterised by a considerable reaction complexity because of the abundance of possible reactions accompanying the necessary mass transfer and absorption processes. This reaction complexity is compounded by the complexities inherent in the mixing and contacting of the gases and liquids in some suitable reaction vessel. Fig. 1 portrays this schematically for a quite arbitrary contacting of gas and liquid. Complex reactions are then often accompanied by gas-liquid flow complexities and the overall difficulty is intensified by the fact that the classical gas-liquid reactor types packed colum..n plate column bubble column stirred vessel imply only a weak control over the gas-liquid flow processes and contacting pattern, with a good deal of uncertainty over the distribution of surface area and mass transfer potential.
228
•• gas feed
FEEDS eo
flow rates
and
::>
0-
....
compositioDs
REACTOR reaction kine tic. - number of reac tiODS - types of reactioDs reactor
flov rates
~
and compositions
Ero~ertie8
-
structure of liquid flow structure of gas flow contacting pattern distribution of interfacial area - mass tran. fer coefficien~
Fig. I.
PJIODUCTS
?•
r-
~
?.
GENERAL PJIOBLEM OF GAS-LIQUID REACTOR ANALYSIS AND
DESIGN
~
229
Thus from Fig. 1, the general problem can be stated thus. If the flow rates and composition of the gas and liquid flow streams are specified, the reaction kinetics are fully quantified and the gas-liquid contacting pattern is accurately definable, what will be the flow rates and composition of any product streams? Even leaving aside the fact that reaction kinetic information is scarce, and unders tanding of gas-liquid contacting is weak', the problem remalnlng is still significantly severe, since determining the overall performance of the reactor/contactor requires the resolution of the interactions of absorption, mass transfer and reaction. A general approach capable of handling reactions which are arbi trarily numerous and complex in character is a long term goal. What follows is merely a preliminary evaluation of the difficulties involved in doing this. ANALYSIS OF A BACKMIXED REACTOR FOR A SINGLE SIMPLE REACTION The strong interactions and coupling between the mass transfer and chemical reaction processes are the primary component in complicating the analysis of even a very simplified reactor. This can be illustrated with respect to some qualitative features of a simple single reaction in which a reagent 'A' is decomposed irreversibly in the liquid phase to a product P, such that A - P o The simplest possible reactor configuration is that in which both the liquid and gas phases are absolutely perfectly backmixed with uniform internal properties as indicated in Fig. 2. The perfect backmixing assumption incorporates a uniform specific surface area per unit volume of liquid a and a uniform mass transfer coefficient kLA for the purposes of simplicity, although the assumption of perfect backmixing does not restrictively require that kL~ and should be uniform, ~r that the associated gas bubbles or Liquid drops which create a should all be of the same size.
a
Qualitatively, four distinct regimes can be recognised concerning the interaction between the mass transfer and reaction of A as shown in Fig. 3, in which it is assumed that the film theory is an adequate basis for considering diffusion and reaction phenomena in a gas-liquid reactor. In regime I the reaction is so negligibly slow that the entire film and bulk liquid phase are saturated at the concentration CA*. As the reaction speed increases to regime II, the rate of consumption of A in the bulk liquid phase is balanced
230
off-gas
~
.'•• liquid produ2t
liquid feed
•• •
gas feed A BACKMIXED CAS-LIQUID REACTOR ELEMENT
Fig. 2
I
~a -~I
liquid film regime I
nO
buIlt liquid
reaction
regime 11
reaction only in bulk
cA•
........_ _ _ _---"_ _ _ CAb
significant reaction i n both film and buIlt
Fig. 3
reaction entirely iD the EU.
REACTION REGIMES IN AIISORPrIOH OF A SINGLE GAS
231
by the rate of transfer of A through the liquid film.
Negligible rate of reaction' in the film results in a linear concentration gradient. A further' increase in reaction speed results eventually in comparable amounts of reaction taking place in the film and bulk and this is characterised by a curved concentration profile as shown in regime Ill. Ultimately at very high reaction speed, virtually all the A is consumed within the film and this is characterised by a zero gradient at the film/bulk junction as shOwn in regime IV in Fig. 3. Danckwerts (1) has proposed characterising these regimes by means of inequalities given by (for 1st order reaction of A)
regime I
k1 T »
regime 11
DA ky'kL
regime III
[--~ DA a
regime IV
1 2
«
,
2.'
[
DA k1/kL
+
2
»
I
't
J
»
1
Regime IV is the so called fast reaction regime, and the criterion is derived on the basis that the volume of the bulk liquid phase is significantly greater than the film volume. Two difficulties arise in relation to the use of 'criteria of this type. Firstly, how can one handle the case of non-first-order reactions? Secondly, in respect of the problems arising when more than one reaction is present, it becomes necessary in quali tati vely establishing reactor performance to move beyond these simple qualitative discriminants in such a way that the proportion of film and bulk reaction are directly determined. It is possible for example when two reactions are present for one to take place largely in the film and the other predominantly in the bulk. In such circumstances direct calculation of performance needs to be initiated without prior assumptions on the role of filmwise and bulkwise reaction.
232
In recognition of some aspects of these difficulties, Kulkarni and Doraiswamy (10) have proposed the use of an effectiveness factor concept to characterise reactor behaviour (by analogy with similar definitions used in diffusion/reaction analysis in catalytic phenomena).' They proposed that an effectiveness factor be defined by Tt
=
rate of reaction evaluated at interfacial concentration overall rate of reaction in film and bulk.
For first order reaction, with 2 d CA
or with
MC 1)
(1 )
=
(2)
=
their results show that for only bulk reaction Tt
=
1 + MC 1)
(3)
S
and for significant reaction taking place in the film
Tt
=
1
(1 +/M(1) S tanh /M(1)
+ tanb{M ( 1) J" /M(1)
_
(4)
The effectiveness factor depends upon {M(1) (often called the Ha tta number) and the parameter S given by
s=
volume per unit area of bUlk/volume per unit area of film (5)
and this is an essential distinction between the gas-liquid reactor and the catalyst particle, since in the latter case there is no equivalent of reaction in the bulk. However, the use of the term effectiveness factor is somewhat misleading since Tt becomes very small when the reaction becomes fast. In this circumstance the absorption effectiveness is increased, and so an increasing absorption effectiveness is described by a decreasing effectiveness factor. The definition of effectiveness factor is also
rI !
233
inadequate since it does not directly distinguish the contributions of film and bulk reaction to the overall performance. This can be more satisfactorily achieved in the following way. The perfectly backmixed uniform property gas-liquid zone concept illustrated in Fig. 2 can be envisaged alternatively as shown in Fig. 4. The interaction of the processes of dissolution, mass transfer with reaction and the overall input and output flows of gas and liquid can be set out as follows. If G. is the molar feed rate of gas containing a dissolving and react\ng component I Af at a mol fraction y A"1 then the rate of absorption at the interface NAlx=o is given by NA \x=o
=
GiYAi
GoYAo
(6)
Moreover, if there is no net change in the throughput of inert gases then
For transport through the gas film Na/x=o
=
*) V kgA -a (P Ag - PA
(8)
and since the gas phase is fully backmixed, the outlet gas composition equals the bulk composition and therefore
(9)
= Also if the solubility of the Henry's law
*
pA
reacting component A obeys (10 )
=
Diffusion and simultaneous reaction of A through the liquid film is described by the differential equation 2 d CA
( 11)
=
if the reaction is simple first order. The solution of this equation is subject to the boundary conditions at each end of the liquid film x
=
0,
=
CA*
x
=
I ntermed i ate
PA
react ion in
IV'
V'
VI'
Intermediate
fa~t
fast
diffusion of A and with reaction
curved prof! le of A through film curved prof 11 e of B through fllm
reaction restricted to a zone adjacent to Interface
curved profile of A In film no grad I ent of B through film
reaction restricted to a zone within the film
curved profile of A In film curved profile of B In film
reaction at a plane within the film
11 near prof 11 e of A to react Ion plane linea r prof iI e of to react ion plane
CIIb
CAb
Cab
'A
P~-NV:
C IIb
CAb..o
VII'
Ins tantaneous
eBb
m I
VIII'
Ins tantaneous
FIG.8
surface react Ion
both film and bulk
linear profile of B to Interface
REACTION REGIMES WHEN GAS REAGENT 'A' REACTS WITH LIQUID REAGENT B
I
'Aa
"
I I
1
reaction conf! ned to film
ca•
:
~
250
under infinitely fast reaction conditions, the overall reaction rate is governed by the diffusion of A and B to the reaction plane. At this condition, the nature of the kinetics is irrelevant, and the enhancement factor has reached an ultimate asymptotic value. This is give~by'
(53)
+
and this condition can be expected to apply when
(54)
/ M(g)
As long ago as 1948 Van Krevelyn and Hoftizjer proposed that approximations based upon / M(m)- {
(55) tanh/ M(m) { ---:=----:-} would be asymptotically exact and moreover provided an excellent approximation (with maximum error of a few percent) in the intermediate range (17). Setting = ,; M(m) {
EAi E
EA
_ 1
}
(56)
Ai the procedure for determining the rate of absorption of A is to use ______ }
cosh M(m,n)
,.;....;;..c:..=.=..o..;;.;;..'--_ _
(57)
tanh/ M(rn, n)
Typical computations for EA based upon the assumption that GAb ~ 0 are shown in Fig. 9. The pseudo first order case with GBb constant through the film is the upper limit of behaviour. Eqn (57) is implicit in EA and contains the unknown bulk concentra tion CBb • The per formance of a backmixed reactor
251
1000
100
< 0
u
c
e
i
10
\
100
10
FIG. 9
ENlWICEMENT FACTORS FOR mth-nth ORDER REACTION B£l\iEEN
GAS PHASE REACTANT A AND LIQUID PHASE REACElIT B
~
"...
'"
ZOO
>
1 g,
""
.s::
100
300
400
500
reactor temperature OK FrG. 10
MULTIPLICITY OF OI'ERATING STATES FOR A GAS-LIQUID REACTOR PROCESSING A SUU'LE SING!.!:: REACTION [Re£(l8)]
1000
252
element is therefore determined by the stoichiometrica'lly balanced consumption of 'A' and 'B', where A is treated exactly as in the single reagent case and the liquid phase reagent 'B' should satisfy _ dC B } Q (C Bo - CBb ) = VL a ~ .iC= 6 + k VLb CAb CBb { 1
I
s ~F
A series of differential equations describes the evolution of liquid phase products with time in a semi-batch reactor with continuous feed of the gas. If the formations of the by-products E and F are second order in the reacting. gas A and all other reactions are first order, and moreover if A absorbs and reacts significantly only in the bulk liquid phase, so that film reaction is negligible and the 'slow' regime applies, then a series of ordinary differential equations describe the concentration trajectories of liquid phase products with time. These were:
=
(99)
=
(100 )
=
(101)
=
(102)
276
dCEb dt dC
Fb dt
=
=
2 k2 CAb
2 k4 CAb
(103)
CCb
C Rb
(104)
Since the decOJinpositions to by-products E and F are of a higher order in the dissolved gas A, in regions of any reactor where high dissolved gas concentrations occur, the rate of reaction to form by-products will be accelerated and the yield of desired product R will be reduced on two counts. Firstly because the precursor C will be diverted to E and secondly because the desired product R will be diverted to F. If the performance of a batch reactor is to be described by solving the differential equations for liquid phase components B, C, R, S, E and F, it is necessary to determine CAb by solving the material balance on A across the semi-batch reactor. The unsteady behaviour of dissolved gas concentration, assuming quasi-stationary behaviour of the gas-liquid phases, is then given by
1:
=
Cl
(I) dC1b
(105)
dt
where B + a. (I) A - + I for I = C, R, S, E and F. In this last relationship a. (I) is the number of mols of reacting gas A contained in a mol of B when converted into 1. The material balance on A across the gas phase requires that
=
277
and the treatment parallels that outlined for the single reaction with a quadratic in y , from which C * and CA can be found as the set of differentiff equations are A lntegrate8 through time. For the parameters shown in Table 3, results showing the mol fraction of desired intermediate R as a function of the conversion of B are presented in Fig. 20. As the gas input rate increases, the mols of R produced in the batch decline. The corresponding yield behaviour is shown in Fig. 21. In this way, the reaction rate constants k1 to k5 can be found by matching semi-batch product trajectories to experimental results. This kinetic information can then be utilised to evaluate various forms of reactor design, particularly for plant scale continuous flow reactors. In carrying out such calculations, it is unwise to make too many assumptions concerning the ideality of mixing achieved inside a reactor. This is especially the case for very large volume reactors used in large tonnage production. A series of idealised backmixed elements can be assembled into a stirred tank configuration as shown in Fig. 6 which is intended to allow for the mass transfer, absorption and reaction to be incorporated into reasonably realistic descriptions of the internal gas-liquid flow phenomena. The calculation of the overall performance of such a reactor, with backmixed zones assembled into loops, given only the input gas and liquid flow rates, involves the solution of large sets of algebraic equations. In the example given with five reactions, the solution of a single backmixed zone contains seven equations, with seven unknowns. . When constructed into two loops with four elements in each loop, the problem comprises fifty six simultaneous equations. These can nevertheless be solved for the case where mass transfer resistance is significant, but there is negligible reaction in the film Le. the slow reaction regime. Some results relating to the distribution of gas phase composition of A (for a feed mol fraction YA. = 0.21) for the final reactor in a train of three reactors are1presented in Fig. 22. Whilst. small scale reactors are almost.perfectly mixed, the calculations show that scaling up at equal tip speed gives progressively worse mixing quality as the scale increases. Plant scale in this example represents two orders of magnitude increase in linear length dimension. The regions of high reactant gas composition in the gas phase give rise to high dissolved concentration C b in the associated bulk phase, with a correponding higA rate of by-product formation locally. A poor yield is therefore obtained at the large scale when compared with small scale operation.
278
H
----------------------~--~----------
o·g 0:: 0·8
~ 0·7
9 w
>=
0·6
;;J. 0·5 z
~ 0·4
u
~ 0·3 u.
0·1 8
10
12
CONVERSION OF
B
14 %
FIG.21 EFFECT OF GAS FEED RATE ON YIELD OF R FOR SEMI-BATCH OPERATION
PLANT SCALE
FIG.22 EFFECT OF INCREASING SCALE FOR 3 REACTORS IN SERIES WITH GAS FED TO THE IMPELLER
279
It is important to appreciate this effect, since even in the slow reaction regime, as Fig. 5 has shown, bulk phase reaction can correspond to relatively large rate constants. In Fig. 5 bulk r~~ction takes place with a first order rate constant of up to 200 s. The rates of mixing processes close to the interface are sufficiently fast to give negligible depletion by reaction. However, in a reactor for which overall mixing processes are in the range of seconds, as in the example just described, macroscopic depletion of the reagent gas does take place. As the example showed, for complex reactions the consequences can be highly significant. Moreover, this effect has only been considered in respect of the slow reaction regime.' The problem of handling say five reactions with diffusion and reaction taking place in the mass transfer film has so far proved too difficult to resolve, though it is certainly worthy of continued effort. ABSORPTION OF TWO GASES REACTING TOGETHER IN THE LIQUID The case where two gases A1 and A2 dissolve in a liquid phase and react together is a case for which a large number of commercial examples exist (33). A general stoichiometry can be written
products
Some general qualitative features of such cases are presented in Fig. 23. If the liquid phase reaction is so fast as to be considered instantaneous, the transport of the least soluble gas to the interface through the gas film will be rate controlling. If Aj is the least soluble gas, profiles will be as in Fig. 23(a) as Pangarkar and Sharma (34) have shown. On the other hand, if the reaction is slower and the solubility of A2 is very much greater than for A , then A2 may be readily' absorbed 1 into the liquid phase giv1ng a large excess of A with correspondingly negligible consumption of A in the liqui~ film. A, might then be consumed by pseudo first or~r reaction in either tne slow, intermediate or fast reaction regimes.
280
P A2g
(a)
P A1g
C A2b
x=O
X"'O
CA
2
*
P A1g
(b)
PA g 2
FIG • .!3
C A1b
SIMPLIFIED CASES FOR ABSORPTION AND R.lW:TION OF TWO GASES REACTING TOGETHER [Ref(34)J
281
In some respects, however, these specific instances are no easier to resolve than the general case. This is because, as with our previous analyses of a single absorbing gas, the bulk phase boundary conditions can only be determined by a full evaluation of the interactions of film and bulk reactions with the overall gas phase transfer and material balance rela t.ionships • The use of profile approximations has been proposed by Sada et al (35), and recently, Zarzycki et al have proposed some analytical (36) and approximate (37) solutions to the enhancement factors which might assist in the solution of the general case. The extended case where A1 and A2 can react together and one of the gas phase reagents can react with a liquid phase reagent was aH30 considered by Pangarkar and Sharma (34) • Stoichiometrically this case can be represented by
k1 A1
+
A1
+
vA
VB
2
A2
B
k2
..
P
1
,..
A practical example of this is the absorption of COL and NH~ into alkanolamines, when it is desired to absorb one oT the species selectively. As far as selective absorption of A1 is concerned, this is bound to be greatest when A1 reacts instantaneously with Band there is a large excess of B. In this case the instantaneous reaction plane is close to the interface, so that the opportunity for AJ and A2 to react together is suppressed. From this point of view, co-current flow of gas and liquid would be most appropriate, since in this contacting mode A1 and B will deplete together and the possible reaction between A1 and A2 in the region between x = 0 and x = 0 will thereby be reduced to a minimum.
282
However, as might be expected from Fig. 8, the overall number of reaction regimes is formidably large and a general approach to the solution of the backmixed gas-liquid reactor element remains daunting. ABSORPTION OF TWO GASES ACCOMPANIED BY SEVERAL REACTIONS As the number of absorbing components and the number of liquid phase reactions increases the feasibility of a generalised approach seems to recede, and the nature and type of approximation and the strategy for incorporating them into a generalised approach can hardly be discerned. Each example become:s an individual case, and each individual case requires a depth and understanding of the specific complications which can only be realised by those with consid~rable experience and insight into the special features of the individual case. This can be illustrated by the work of Cornelisse et al (38) who have considered the selective absorption of H S into 2 secondary or primary amines in the presence of CO , Th1S is of 2 commercial importance in the selective scrubbing of a number of industrial gas streams. The reactions involved can be written (following previous notations)
C+ D
A1 + B
infinitely fast
k2
D E
= carbonate ion
A2 B
k3 A2 +
2B~
k4
C+ E
slower
HS 2
= = = = =
A1
k1
C
CO2 amine ammonium ion bisulphide ion
In this reaction scheme, the formation of bicarbonate is neglected. This is therefore an example of two gas phase reagents reacting with a liquid phase reagent with two reversible reactions incorporating four reactions overall, Reversible reactions are essential to such systems, since it is the reversibility that is the basis of regeneration and reuse of the absorbing liquor. In this example, not only are there four liquid phase reactions taking place, but also the consumption of A2 (identified with CO ) is described by a complex rate law given 2 by
283
(106 )
=
which adds phenomena.
fUrther
complexity
to
the
diffusion/reaction
The authors analysis (38) uses film theory on the gas-side and penetration theory on the liquid side. The penetration theory was adopted as offering a more realistic basis to describe the diffusion and reaction. The set of parabolic partial differential equations which describe this diffusion and reaction were solved in conjunction with the customary boundary conditions, plus a number of subsidiary relationships which ensure electrical neutrality and are compatible with the initial loadings of reagent amine. Equilibrium was assumed to be established in the bulk, but otherwise the fluxes were not jointed to the overall material balances on the gas and liquid phases. Even so, the computation appears quite formidable. In a very similar example, Cornelissen (39), examined the same selecti ve absorption problem using a tertiary amine for which case the reaction of CO 2 is slower. The overall scheme is k1
C+ D
infinitely fast
k2
A2 +
B + H2O
A2 +
B + OH -
k~ \il>"
k4 po
C+ F
slower
E + H2O
slower
In this instance there are now two parallel irreversible reactions consuming CO. Cornelissen assumed that Aj/B equilibrium is establisged instantaneously everywhere (in the film and the bulk), but the reaction speed of the A2 (carbon dioxide) is slower and whilst some reaction took place w~thin the film, significant amounts of reaction also occurred in the bulk.
284
The reaction of A2 was taken to be pseudo first order in the film. The curved concentration profiles within the mass transfer film were approximated by straight lines, such that at either end of zones within the film, the linearised concentration gradients exactly matched the gradients of the curved profile. This approach is equivalent to approximating reaction throughout a zone by the equivalent amount of reaction taking place at a properly positioned plane within the zone. The :replacement of the curved profiles by straight lines preserves unchanged the diffusion and reaction balances across the whole mass transfer film. By this ingenious method, the set of ordinary differential equations describing the complexities of diffusion and reaction becomes! replaced by a set of algebraic equations. Unlike the previous analysis (38), the boundary conditions were properly treated as dependent variables found by taking account of film and bulk reaction balanced with the input and output flows and mass transfer fluxes across a tray. The approach (39) involved perfect backmixing of the liquid, but with provision of the possibility of axial mixing in the gas phase being represented by staging of backmixed zones. In practise though, the authors claimed that a single gas zone was sufficiently accurate. For an individual tray in a tray column, the problem resolves to 27 non-linear algebraic equations in 27 unknowns. Solution of each tray has to be incorporated into a separate algorithm for the iterative tray-to-tray calculations. The performance of a O.11m valve tray column was successfully simulated, and the method has been adopted as a basis for the design of commercial scale absorbers up to 8.5m in diameter used ~or the selective. absorption of H S in the presence of CO " 2 2 The possibility of significant errors developing due to the use of approximating straight line profiles was not considered. However, the method offers a promising basis for avoiding the computational difficulties encountered when the diffusion/reaction equations are embedded into the overall mass transfer and flow material balances. A general adoption of the technique requires a framework for realistic replacement of the diffusion reaction equations given only the diffusion and reaction kinetic parameters. As with many of the cases described so far, there is still a great deal to be done before gas-liquid reactors can be designed or analysed from first principles using only physico-chemical data and knowledge of the input flow rates and compositions.
285
NOMENCLATURE
a
gas-liquid interfacial area
C~
interface concentration of component I
CIb
bulk concentration of component I
DI
diffusion coefficient of component I absorption enhancement factor for component I
E* I
absorption factor for absorption of I
EIi
asymptote of absorption enhancement factor for I
G i
total molar feed rate of gas
Go
total molar efflux rate of gas
HI
Henry's Law coefficient for solubility of I
k
reaction rate constant for ith reaction
i
kL
liquid mass transfer coefficient for I
K
equilibrium constant
KgI
overall mass transfer coefficient for I
kgI
gas phase mass transfer coefficient for I
M(m)
diffusion/reaction factor for (pseudo) mth order reaction
M(g)
diffusion/reaction factor for general reaction kinetics
Me (m)
diffusion/reaction
factor
for
reversible mth order
reaction M (m) n
diffusion/reaction factor for mth-nth order reaction
M(m,n)
diffusion/reaction factor modified according to Eqn (56)
286
NI
molar flux of I
PIg
partial pressure of I in bulk gas phase
Pt
partial pressure of I at gas-liquid interface
Q
volumetric flow rate of liquid phase
V L
volume of liquid phase
XI
conversion of component I
x
position in mass transfer film
Yli
inlet mol fraction of I in gas phase
Ylo
outlet mol fraction of I in gas phase
S
volume per unit area of bulk/volume per unit area of film
o
mass transfer film thickness
n
effectiveness factor for a gas-liquid reactor -
T
liquid phase residence time
~
instantaneous yield function
~
overall yield function
subscripts I
is a general subscript referring to components A, B, C, D, ••• etc
A
refers to gas-phase reactants, subscripted 1, 2, ••• for more than one gas-phase reagent
B
refers
to
liquid-phase
reactant,
subscripted
•••• for more than one liquid phase reagent P
usually refers to products of reaction
R
usually refers to a desired intermediate product.
1,
2
287
REFERENCES ( 1)
Danckwerts, P •V• , "Gas-Liquid Reac tions It, McGraw-Hill, (1970).
(2)
Juvekar, V.A., and Sharma, M.M., Tran.I.Chem.Engrs., 77, (1977).
( 3)
Barona, N., Hydrocarbon Processing,
(4)
Charpentier, (1978).
(5)
Shah, Y.T., and Sharma, M.M., Trans.I.Chem.Engrs, 54, 1, (1976).
(6)
Shah,· Y.T., lIGas-Liquid-Solid Reactor Design", McGrawHill, (1979).
( 7)
Spielman, M.,
J.C.,
A.C.S. Symposium Series, 72, 223,
...::..:..:~...:.=;;..;;;;;;..::.-;;;..;;::...:.,
( 8)
179, (1979).
lQ, 496·, (1964).
Sharma, S. , fl, 76, (1974).
and
Luss,
D. ,
and
Nagata,
S. ,
( 9)
Hashimoto, K., Teramoto, M., JI.Chem.Eng.Japan, ~, 150, (1971).
(10)
Kulkarni, B.D., and Doraiswamy, L.K., 501, (1975).
( 11)
Mavros, P.P., M.Sc. Manchester, (1978).
(12 )
Peterson, E.E., "Chemical Reaction Hall, (1965).
(13)
Danckwerts, P.V. and Kennedy, A.M., Trans.I.Chem.Engrs., 32, 549, (1954).
(14)
Steeman, J. W.M. Chem.Eng.Sci. ,
(15)
Carberry, J.J., Chem.Eng.Sci., 11, 675, (1962).
(16)
Nagel, 0., Hegner, B, and Kurten, H., Chem.lng.Tech., 50, 934, (1978).
Dissertation,
A.I.Ch~E.JI., ~,
University
of
Prentice-
Kaarsemaker, S., and Hoftijzer, P.J., 139 , (1961).
288
(17)
Van Krevelen, D.W., and Hoftijzer, P.J., Rec.Trav.Chim., 67, 563 (1948).
(18)
Hoffman, L.A., Sharma, £1.,318, (1975).
(19)
Sim, M.T., and Mann, R., Chem.Eng.Sci., )0, 1215, (1975).
(20)
Joosten, G.E.H., Maatman, H., Prins, W., and Stamhuis, E.J., Chem:Eng.Sci., 223, (1980).
(21)
Onda, K., Sada, Chem.Eng.Sci. ,
(22)
Hikita, H., and Asai, S., Kagaku 'Kogaku, 27, 823, (1963).
(23)
Onda, K., Sada, E., Kobayashi, T., Chem.Eng.Sci., 25, 1023, (1970).
and Fujine, M.,
(24)
Van de Vusse, J.G., Chem.Eng.Sci.,
631, (1966).
(25)
Hashimoto, K., Teramoto, M., Nagayasu, T, and Nagata, S., Jl.Chem.Eng.Japan, 1, 132, (1968).
(26)
Teramoto, M., Nagayasu, T., Ma tsui, T." Hashimoto, K., and Nagata, S., Jl.Chem.Eng.Japan, ~, 186, (1969).
(27)
Teramoto, M., Hashimoto, K., Jl.Chem.Eng.Japan, ~, 522, (1973).
(28)
Sharma, S., Hoffman, L.A. and Luss, D., A.I.Ch.E.Jl., 22, 324, (1976).
(29)
Schmi tz, R. A., and Amundson, N. R. , Chem. Eng. Sci., 1§., 265, (1963).
(30)
Ho, S-P., and Lee, S-T., Chem.Eng.Sci., 35, 1139, (1980).
(31)
Huang, D.T-J., Carberry, J.J., A.I.Ch.E.Jl., 26, 832, (1980).
(32)
Mann, R., Middleton, J.C., and Proc.2nd.Europ.Conf.Mixing, F3, (1977).
(33 )
Ramachandran, P.A., and Sharma, Trans.I.Chem.Engrs., 49, 253, (1971).
(34)
Pangarkar, V.G., and Sharma, M.M., Chem.Eng.Sci., 29,
S.~~
ahd Luss, D., A.I.Ch.E.Jl. ,
E., Kobayashi, 753, (1970).
T.,
and Fujine, M.,
and
Nagata,
and
Varma,
Parker,
S. ,
A. ,
I.B. ,
M.M. ,
289
2297, (1'974). (35)
Sada, E., Kumazawa, H., and Butt, M.A., Can.Jl.Chem.Eng., 54, 97, (1976).
(36)
Zarzycki,
Ledakowicz, S. , 36, 105, (1981) •
and
Starzak,
M.,
(37)
Zarzycki, R. , Ledakowicz, S. , Chem.Eng.Sci., 36, 113, (1981).
and
Starzak,
M. ,
(38)
Cornelisse, R., Beenackers, A.A.C.M., Van Beckum, F.P.H., and Van Swaaij, W.P.M., Chem.Eng.Sci., 1245, (1980).
(39)
Cornelissen, A.E.,
R. ,
Chem.En~.Sci.,
Trans.I.Chem.Engrs~
58, 243, (1980).
291
PROCESS DESIGN ASPECTS OF GAS ABSORBERS
Erdogan Alper Department of Chemical Engineering Ankara University, Besevler, Ankara, Turkey
1. INTRODUCTION Equipment which is used in contacting a gas with a reactive liquid can be gas absorber or a gas-liquid reactor. This terminology itself shows the interdisciplinary nature of the process which involves both chemical (i.e. reaction kinetics) and physical (molecular diffusion, fluid mechanics etc.) phenomena. Thus the subject does not fall entirely within the province of either the chemist or the conventional engineer. The classical literature on this area (Astarita (1), Danckwerts (2), Sherwood et al. (3) etc.) has mainly dealt with gas absorption, in which the reaction is ap~lied merely to enhance the rate of mass transfer. In such cases, there is also always a physical gas absorption process to refer to and the reactions are usually IIfast". On the other hand, many industrial reactions in organic chemistry such as oxidations and chlorinations (4), are relatively slow and the main emphasis is the conversion of the liquid phase product. Therefore, two approaches may be used to characterize the interaction of mass transfer and chemical reaction between components of a gas and a liquid, one expressing the enhancement effect of a relatively fast reaction on the physical mass transfer leading to the classical concept of the "enhancement factorll (1-3) and a second, a relatively new one, expressing of slowing down of the already slow reaction rate by mass transfer and leading to the lltil ization factorll (5,6). Consequently equipment may respectively be called a gas absorber or a gas-liquid reactor. Although, the treatment in this review has a general approach, the emphasis is on the enhancement of gas absorption rate; hence it deals with the process design aspects of gas absorbers in which relatively fast reactions are occuring.
292
The design of gas absorbers when only physical absorption is involved, is relatively a simple matter (provided that the necessary data are available) and need not be.described here. Apart from the hydrodynamical data such as flooding, only values of kGa and kLa under the prescribed conditions and the parameters of a proper tw07phase contactor model are required. The latter will be discussed in some detail in Section 3; in many cases even the simple generalised design procedures, such as those reviewed by Pavlica and Olson (7) are not necessary and ideal flow patterns for instance, plug flow - may be adequately used. On the other hand, in the presence of a reaction, the rational process design is usually a complicated matter. The main stages of the design procedure is as shown schematically in Figure 1. First, the specific design problem should be defined. This leads to a number of independent parameters, such as flowrates of each phase, the choice of equipment and its details (for instance, packing material) temperature and pressure. The choice of such pa rallleters for an -i ndi vua 1 task often i nvo 1ves very delicate economic balances and is, to a large extent, well beyond the scope of this review. Then a number of other parameters, such as mass transfer coefficients, gas-liquid interfacial 'area and liquid hold-up, depend on these independent parameters and should be known or estimated prior to any rational design approach. Such data are often available for some standard systems and conditions and the estimation for precribed conditions, often causes a major problem. The second stage, which involves the determination and the estimation of "process specific data such as solubilities and diffusivities, reaction kinetics and rate constants, is highly spec i fic and 'has to be obta ined for each system at the prescri bed conditions. Some of these data, such as relevant kinetics and the equilibrium constants etc., may in fact be measured but this is as laborious task. Even more difficult is the estimation of quantities which cannot be measured directly, particularly the solubility and diffusivity of the dissolved gas in a solution with which it reacts. The final stage of the design consists of both "microscopic scale (or local) modeling (or absorption-reaction model) and "macroscopic" scale (or integral) modeling (or two-phase contactor model) in order to compute the capacity of the equipment from first principles -for instance, in the case of a packed column, the required height). Under certain circumstances, it is possible to use laboratory models instead of theoretical modeling either at microscopic or both microscopic and macroscopic scales. By doing so, it is often possible tb avoid most or all of the Stage 2, which is of course highly specific and requires normally a laborious task. However, it may be p.ointed out that all the information involved in Stage 1, -with the exception of separate \
ll
,
ll
293
DEFINITION
OF
DESIGN
PROBLEM
(Throughputs, inlet and outlet Concentrations)
i REACTOR TYPE AND DETAILS (Distributors, packings)
ADJUSTABLE OPERATING PARAMETERS (Flowrates, P,T, mode of operation)
NONADJUSTABLE STAGE
1
( kL'
PARAMETERS
kG' a , v , r )
PROCESS SPECIFIC DATA (physicochemical data(solubilities diffusivities) ,
STAGE 2
ROUTE:
3
MICRO SCALE MODELING
Experimental
(ABSORPTION-REACTION MODELS) MACRO SCALE HODELING
Computation
Computation
(TWO-PHASE REACTOR MODELS) STAGE
3
Figure 1. reactor)
Main stages of gas absorber (gas-liquid design.
Experimental
294
values of kL and a rather than kLa all these data are also required for rational design of physical absorbers -, should be available no matter whether theoretital or laboratory models are used. In this review, theoretical modeling both at microscopic scales will only be very briefly ~iscussed and the main emph~sis will be given to the laboratory models and their use with special reference to packed columns. 2. MICROSCOPIC SCALE MODELING (ABSORPTION-REACTION MODELS) Microscopic modeling considers a small but statistically representative volume element of the absorber (or reactor), that is, a "point" in the equipment. Recently, Thoenes (8) grouped such ,considerations as "volume element modeling". It is necessary to make energy and component mass balances in the reactive liquid-phase (it is assumed that no reaction takes place in the gas phase). Fortunately for most systems, the isothermal approximation is often justified. Thus, the components mass balance yields: -7 dAi ( D. \7 - v 1\7A. = - t - + z. r· ( 1) , , ~ l' Solution of this equation requires not only various physlcochemical and reaction kinetics data, but also a detailed knowledge of the fluid mechanics near the interface which is however not available in any but artificially simplified agitated system (see, for instance, reference (9) for a detailed review of interphase mass transfer models and description of interfaces). However, the concentration gradient \7 Ai and the velocity vector ~ are approximately perpendicular to each other, hence the scalar product of them is always negligible. Furthermore, diffusion is usually unidimensional. Therefore Eqn (1) reduces to: 2
'dA. D. __1_ , ~X2
'CA.
= --'dt
+
z. r. "
(2 )
It is now justifiable to solve this equation using the b9undary conditions of the simplified physical absorption models (1,2). Solution of Eqn (2) then enables us to calculate the absorption rate at a particular "point" in the absorber. These results are usually expressed in terms of an enhancement factor, i.e. a factor by wh fch the rate of ab·sorpti on is increased by the chemical reaction. It is well known that this enhancement factor differs little in value whether film or the Higbie or Danckwerts surface renewal models are used as the basis of calculation. Figure (2) shows the typical representation of the effect of chemical reaction for a second order (r=k2A B) irreversible reaction. With the exception of Region IV, all regions are amenable to analytical solutions. In fact, the enhancement factor predic-
295
'*u
20
iI
10
I I
I I I I
5
"0:::
I5Z.
I
2
11
:y I
UJ
100
10
01
Figure 2.
Effect of second order
9I
reaction on absol:ption rate
I
mean Higbie contact flm€
I
I I
I
I I
1 : Surface
I
2 : Random velocity length 3 : Random length
I
9
3
fCl newa L
4 :. Long sLow fLow path
e
I
Contact
time
Figu1"e3. Different contact-time distributions compared at the SartE overall physical absorption rate corresponding to a rrean Higbie contact time of 0.1 s (11).
296
tions are identical for Regions I and III for all three models. In Region V, predictions based upon the three models are similar -indeed they are identical if the diffusivities are" equal. In Region 11, the maximum difference .is often much less than 5%. Finally, the the transition Region IV, no analytical solution is possible. However, numerical solutions indicate little dependency of the enhancement factor E on the chosen model (10). Further, in this regime, the effect of contact time distributions has been examined in some detail by many workers (11-14). For instance, for arbitra,rily chosen models, including those of Higbie and Danckwerts, Porter (11) derived the contact time distribution functions which are shown in Figure (3). These distribution funct;."ons (11-15) are based on considerations which bear some relation to possible flow mechanisms in packed columns and they all lead to numerically almost the same predictions (2). Similar types of conclusions may also be drawn for other kinetics such as (m,n) th order reactions (14); thus it appears that the effect of chemical reaction on the relative increase in the rate of mass transfer does not depend strongly on the theoretical models (thus the actual flow pattern near the interface). It means that it is not of crucial importance which sort of a theoretical model we use if we want to predict the effect of chemical reaction on gas absorption. Hence, for instance, explicit approximate equations which agree with predictions from one of the theoretical models may be used for design purposes (16). One of the earliest and the most accurate equation for second order irreversible reaction is (16,17): E
=
(1 +
VM)
Cl
=
\[Mi
(E
Cl
i
(1 - ex p( - 0 •65{M Cl
)
-1) + exp (0.68j{M' -O.45WCEi-1)
(
3 •a )
(3.b)
Recently other simple explicit equations were also proposed (18, 22) and the accuracy was tested by Wellek et al. (11). In general, the overall accuracy is reduced with simplicity and Wellek et al. recommend the following equation for general use: (E _1)-1.35 = (E
i
_1)-1.35
+
(E
1
_ 1)-1.35
(4.a)
where E1 = '{M / tanh {M
(4.b)
A second but more important conclusion in the above considerations is that it suggests that it does not matter much what sort of a laboratory model (as opposed to a theoretical model) we use if we want to experimentally simulate an absorber -provided it has the right value of kL' it is of no importance how it is generated. Further consideration of this aspect is given in
297
OPERATION
APPROXIMATE FLOW PATTERN Gas Phase Liquid Phase
EXAMPLES
Plug flow
Completely mixed
Gas sparged reactor
Completely backmixed
Completely backmixed
Mechanically agitated
Plug flow
Plug flow
Packed column,packed bubble column
Plug flow
Completely backmixed (?)
Bubble column
Completely backmixed
Plug flow
Spray column
Completely backmixed (?)
Each plate of a plate column Sectionalized bubble column
Semi-batch
Continuous, Cocurrent, Countercurrent
Continuous, Cocurrent, Countereurrent
(?)
Cross-flow Continuous, (stagewise) countercurrent, Cross-flow
Plug flow
Continuous, Cocurrent, Countercurrent, Cross flow
Miscellaneous (Not studied in sufficient (Wetted-wall column, detail ) venturiscrubber, turbulent bed contactor etc.
TABLE I. DIVERSE GAS ABSORBERS (GAS-LIQUID REACTORS)
298
Section 5. The above treatment assumes a known value of interfacial concentration of the dissolved gas" whJch, of course, depends 6n the gas phase resistance, if any. As i~ the case of liquid-side phenomena, the exact nature of processes on the gas-side is also not clearly known. However, the situation is simpler as there is usually no reaction to be considered and it is usual to employ the film model approach. The addition of resistances was studied by many workers (23-27) and mathematical investigations (25,26) showed that' it does not matter which liquid-side model one adopts. i
3. NACROSCOPIC SCALE MODELING (TWO-PHASE CONTACTOR r~ODELS) THe above treatment considered only the modeling of the local process. The design of an absorber/gas-liquid reactor requires also an examination of global issues. In the terminology of Thoenes (8) this covers both "partial and overall reactor" models. Table 1 shows some of the diverse gas absorbers/reactors. Each of the two phases of gas and liquid may be either in plug flow or completely backmixed as the two extreme cases of macromixing. In plug flow, longitudinal mixing is nonexistent; but due to complete radial mixing, all fluid elements within the system have identical residence time. In a completely mixed system, the residence time distribution of fluid follows an exponential decay, with the exit stream composition being identical to that within the system. It is a well known fact, that, in general, the flow of one or both of the phases may deviate considerably from the above extreme cases and the backmixing lies in between. These deviations may be the combined results a number of different phenomena; these may be nonuniform velocity profiles, short circuiting, bypassing and channeling, velocity fluctuations due to molecular and turbulent diffusion, effects of contactor shape and internals, backflow of fluids due t9 velocity differences between phases and recycling due to agitation. Hartland and Mecklenburgh (28) and Mecklenburgh (29) discussed in some detail, these so called nonideal flow patterns and unlike axial mixing phenomena such as channeling,recirculation, wall flow etc. cannot be considered as random processes~ Figure (4) shows possible transverse -that is, the dir€ction perpendicular to flow-nonuniformity of the velocity distribution in countercurrent absorbers (for example, a packed column) (30). Figure (5) shows nonuniform~ ties in plates of a plate-column absorber which employs crosscurrent flow (30). One of the most simple models is known as the "axial dispersion model". Here a one dimensional Fick1s law type> of diffusion equation is accepted and the constant of proportionanty is com-· monly termed the axial dispersion coefficient. In the model, complete mixing in the radial direction is assumed. Although the
(Cl)
~
(c) G
HMU GI PACKING HEIGHT N
( b)
Figure 4. Transverse nonunifonmity of the velocity distribution: (a) randan non-unifonnity, (b) considerable transverse non-unifonnity, (c) channeling.
Figure 5. Non-uniformity of plate Figure 6. Schematic representation of series operation with cross-current flow: (a) longitudinal non-unifor- of stirred tanks rncdel mity in gas flow, (b) transverse (cell rrodel) • non-unifonnity in liquid flow, (c) channeling (by passing) •
N \0 \0
300
assumption that all mlxlng processes follow Fick1s law type of diffusion equation is a gross oversimplification~ it is widely used as it involves only one parameter~ the dispersion coeffic~ent (E z ) expressed a~ the P~cle~ n~m~er (Pe=U~ IE z ) in dimenslonless form where U lS the lnterstltlal velocl€Y. In bubble or spray columns,L c could be either the diameter of the column or the diameter of the bubble. For packed columns, Lc is usually the characteristic diameter of the packing. Under this situation, Pe is often denoted as the Bodenstein number. The v~lue of the Pe (or Bodenstein) number denotes the degree of backmixing. For complete mixing Pe~O and for Pe~ the plug flow prevails. Sherwood et al. (3) have reviewed and outlined the use of the "axial dispe~sion model in two-phase contactor design. Another one parameter model is the series of stirred tank model (often referred to as the cell model)~ In this model, the equipment is represented by a series of perfectly mixed' stages (31-34) and the number of cell is a measure of the degree of backmixing. Considerable effort has also been devoted to many multiparameter models. One of the simplest is the "two zone model which is largely applied to packed columns (35). The underlying idea. for such a model is that only a fraction of liquid flows through the packing, while at each height there is a stagnant zone in which the liquid is well mixed and which exchanges mass with the flowing fraction. The general problem of backmixing in gas-liquid systems for both simple and complex models of gas-liquid reactors were recently reviewed by Shah, Stiegel and Sharma (36) and Ca 10 (37). ll
11
4. PROCESS DESIGN CALCULATIONS FOR GAS ABSORBERS Design procedures of contactors for simultaneous gas absorption with chemical reaction require all the data -such as floodin~ hold-up, kLa and kGa and axial dispersion coefficients whenever they are relevant-which are normally required for the design of physical gas absorbers too. Further to these data, separate values of kL and a are also required in order to estimate the enhancement factor using one of the absorption-reaction models. The quantities kGa and kLa can easily be me~sured but special care must be paid to the validity of the macroscopic model employed. The value of specific interfacial area (a) may, for example, be obtained by using so called chemical methods (38-41). Other required data~ such as liquid and/or gas hold-ups etc., present few difficulties. However all these data must be obtained from large scale equipment which are representative of industrial absorbers. The work is thus expensive and laborious but is worth doing once and for all to establish the essential characteristics of the absorber under consideration, without which no rational de-
301
sign as outlined in Figure (1) can be undertaken. In these re~ spects, special attention has to be devoted to non-aqueous solutions of industrial importanCe which have been studied ohly rarely (42-48). There is also a need for caution about the interpretation of such measurements as the precise fulfillment of the required conditioris is not usually eas~. For instance, chemical methods of measuring interfacial area (a) purport to measure the area which is effective under the chosen conditions. There is however good evidence that the effective interfacial area may well depend on the type of reaction proceeding in the liquid as illustrated for packed columns (49). . Finally, the theoretical predictions require data which are extremely specific -that is, Stage 2 of Figure 1. It is essential that such data should be known both quantitatively and accurately. Obtaining them is not only laborious, in addition some of them can only be estimated in any case. However, if all these data are available (i.e. Stage 1 and 2 of Figure 1), we can proceed and calculate the capacity by coupling microscopic and macroscopic scale models. For the former, anyone of the well known models is sufficient; particularly such explicit expressions as Eqns. (3) and (4) are most suitable for design purposes (16). For macroscopic scale modeling, it seems, in many cases, ideal flow patterns suffice (50). In any case, so far only the axial dispersion model (or the cell model) has been used for improvement and the experience shows that any model containing more than two parameters will not find extensive use for design purposes. Recently, Juvekar and Sharma (50) considered the reaction A+zb -t products (r=k mn Am Bn) and many cases of different conditions -but all assuming one of the two extreme cases of plug flow and/or complete mixing - and derived analytical equations which can readily be used for design purposes. Table 2 shows the cases examined by them and the underlying assumptions and the basis of derivations are outlined below. 4.1. Packed columns . Many workers (51-56) have considered the design of countercurrent ~acked columns. The equipment can effectively be used in co-current operation since there is no disadvantage due to driving force as in the case of physical absorbers (57). Figure 7 shows schematically such a column and Table 3 gives the simplifying assumptions of Juvekar and Sharma (50). A material balance of the solute over a differential height dh of the column can now be written as: -G I dy = a ( He ) P [y / ( 1+Y)] R S dh ( 5) o = ( L/z ) dB
302
~
CASE
.NO·
SATISFIED
1
, ,
kla
2
2
kl~» y
1ft
ft
,
»
.'
"3
"la ~ y "2 B
4
m
'lel a
6
.
1
lie
«:w
le
2
A-li
rf
k3 (A*)2
•
B
let. a (AfIIi-So ,
f,A""'-'S)n
, , 0
Ra, kmot/m1s
A-s ge
, ,
5
VM
kg:»
»,
a
V2DAk. AilS-
He "l \fflI
1
,.
e
at
8
0
2
.. S- V~ I5A~A~
9
,
2
aA·S·~
10
1
1
Ei»
2
kG
,
Ei "'>"> \[M »1
kGa A*" ~ le:! Er
~ '>"';>
kG+Hc~·
11
,
12
1
13
,
1
14
m
n
\f'M. ~
»He
Ej ~
""» Ice; ~
kl VM+l
He klVH
Ea »1 lea..
a
JtVf)A "2B +lct.2
a
1.';~kJ.B'j-+k2
~~+~MY+4M 2 Ei Et
\I'M?,>'
He
A·~
A' "skl Ei
Et
Iirc;+ He kl Et
2ABLE 2. Al:\IALYTICAL EXPRESSIONS' FOR THE RATE OF ABSORPTION OF A mm A SOL tn'ION CONTAINlG REAC'mNT B (Reaction is irreversible (m,n}th order; J2/(m+l) Dk [A*]m-l BO] n I E.= 1 +/[DB/o J [Bo/zA*l MA mn ~ ~ ~
-
303
where G is the molar flowrate of inerts, Y is the mole ratio of solute A to inert'gas, He js the Henryls law constant, P. is the total pressure, R is the specific absorption rate and S is the cross sectional area. Expressions for R can be obtained from microscopic modeling (that is, absorption-reaction models). 1
o
L, Si
( h
j H
':~"';"~":'-I " ... 0 ...... , . 8f' .. .
. .• .I . .......
'
GI Y":-d~ ..
" .,; .-
........-.' - - I ' "
I
-L dh
t-r---7-"-----I-
t
o
L, Bf
L I 8f
Figure 7 .. Schanatic representation Figure 80 Schematic representaof a packed-column absorber tion of a bubble column TABLE 3.ASSUMPTIONS FOR PACKED -coLUMN ABSORBER DESIGN(SO)
LPlug flow of both gas and liquid phases 2 .. Isothennal operation ( T = constant) 30 Constant total pressure in the column 4. Constant physical properties of the liquid S.Negligible gas-side resistance ;in sane cases it can however be accounted "for TABLE 4. ASSUMPTIOOS FOR BUBBLE COllJ1N DESIGN (50)
LPlug flow of gas and canpletely backmi.xed liquid 2.Linear pressure variation with height: P= P
T
3 .. Constant
(1 +'1' h) ~
where 'I'
,kG and a
=.l:... ( ~) PT
Oh
304
For instance, for the case 14 of Table 2, the integration yields: (6)
where Cl.
= - L ; S = kG a P S/G
I
(7)
zG Similar equations, 'often with more complicated terms, are also derived by Juvekar and Sharam (50) for cases 3,5,10',11,12 and 14 of Table 2 for both co-current and countercurrent operations as well as simplifications for lean gases. Juvekar and Sharma (50) have compared their analytical solutions with either the actual packing height or the results of numerical solutions of other workers for the limited cases where all the required information -that is, Stage 1 and 2 of Figure 1were available. These results indicate that the analytical solutions are sufficiently accurate for design purposes. 4.2. Bubble Column Contactors Figure 8 shows the pertinent details and the assumptions are given in Table 4. A material balance over a differential height gives:
~ dh
= R
a [S/G']
(8)
Inserting the expression for R for a particular case and integrating gives the desired total dispersion height. For instance, for case 5 of Table 2, we obtain: (9) H = -~ + }-[ 1+ ~ { (Yi-Yo)+ln(Y/Y o) }] 1/2 where \/ i O a H P S VDA k2 B S =-------G' and ~ is as defined in Table 4. Juvekar and Sharma (50) only compared their results with those of Mashelkar (58) but found good agreement. However, unlike packed column, it is exceedingly difficult to accept the ideal flow pattern of Table 4 for many bubble column applications. In-deed, the backmixing in the liquid phase is unavoidable and it usually reduces the contactor performance. Many authors (7,59-64) have employed the axial dispersion moqel for the liquid phase -in some cases the gas phase too. One of the most sophisticated design procedure was described by Deckwer (63,64) who showed that
305
1_ I
0
l ,8j
,..,-
.........
G' I 1 2
-::;:~igure
9. Schematic representation of a plate column absorber
-
~
tYn-1 t n-1
0
8 n- 1
'~ V"
~
8°n
in t
Y,,+1
t
~
t:I
8,,+1
n+1
N-1
N
J
.........
1
G', Yi T.P-BLE 5.ASSUMPTIONS FOR PACKED BUBBLE COLUMN DESiGN (50)
l.Pl'l.lg' flow'of both gas and liquid phases 2. ~sothelJUal operation ( T= constant) 3.Linear pressure variation with height 4.Constank ~1 kG and a TABLE 6.ASSUMPTIONS FOR PLATE-<x)LUMN
ABSORBER DESIGN(50)
l.Lean gas with respect to solute 2.Plug flow of gas and canpletely backmixed liquid on each plate 3. The solute concentration on a plate is the arithmetic mean of the concentration of inlet and outlet gases 3.Negligible pressure drop;or a linear variation of pressure' with plate number n: P=
( l+n6)
where
e
1
dP
PT
dn
= -(-)
306
axial variations in pressure and gas flowrate should be also accounted for. Even under isobaric conditions, the gas flow decreases owing to absorption which in turn leads to increased gas residence time; this higher conversions are obtained. Based on his analysis, Deckwer concluded simple isobaric, constant gas velocity models can be used without serious errors if the column operates at elevated pressures, say 20 atm, and if th~ gas shrinkage by absorption is small. He also pDinted out that in large diameter bubble columns (diameter> 0.5 m), gas phase dispersion may be very important. In a subsequent study, Deckwer applied his model ~uccessfully to the case of abiorption and reaction of isobutene in sulphuric acid. 4.3 . .Packed Bubble Columns By noting the observation (42) that the addition of packings in a bubble column considerably reduces the backmixing in the liqUid phase, Juvekar and Sharma (50) assumed plug-flow in both phases. Then, for short columns or columns operated at high pressures, the height can be obtained from the expressions for packed columns. Otherwise, a linear pressure variation with the height may be assumed and Juvekar and Sharma (50) presented analytical expressions for the cases 3,5,8,10,11 and 12 of Table 2 for both co-current and countercurrent operations. 4.4. Plate Column Absorbers Figure 9 shows the plate column schematically and Table 6 shows the s"impl ifying assumptions of Juvekar and Sharma (50). The material balance for the solute over the n th plate can be written as: ( 11)
where the absorption rate R is evaluated at the outlet concentration BR and at the arithmetic mean of solute concentrations in the gas at the inlet and exit of a plate. The material balance for the solute between the (n+1) th and n th plates gives: Yi- Yn+1 = (L/zG') [B~-B~1
(12)
If the specific form of the absorption rate equation is inserted into Eqn. (12), these two equations may be arranged to yield a relationship between BR-1 and Bg. Now it is possible to plot BR-1 against BR and the to construct McCabe-Thiele type steps, the actual number of plates required for the operation may then be found graphically (see, for example, (65)). Juvekar and Sharma (50) proposed, however, that the plot of BR-1 versus BR may be approximated to a straight line by a least square fit. Thus:
307
o
Bn-1
= m' B~n
( 13)
+ C
Here m' and C are obtained from the least square fitting~ The number of plates can now be obtained by the following Fenske type equation: 0 Bi ~C/(hm') ~C/(
1-ml) (14)
N
ln m' Under some circumstances it is also possible to use a modjfied Lewis method (50). This assumes a continuous function instead of a discrete realtion between Bg and n. Then if: 2
O
2
Bn/_dn _d_ _ _ ) «1 d dn
( 15)
The Taylor expansion yields: d Ba o Bn
= B0n- 1 +
n
(16)
The number of plates can then be found from the following equation: N
(-d B~/d n)
( 17)
The modified Lewis method can easily be employed once the relatio~ ship between Bg_ 1 and Bg is obtained provided that the condition in Eqn. (15) is satisfied. Juvekar and Sharma (50) listed expressions which were obtained from the modified Lewis method, for calculating the number of plates for cases 3,5,10,11 and 12 of Table 2. They compared the graphical results of Kawagoe et al. (65) for the case 12 of Table 2, and obtained excellent agreements both with a Fenske type equation and with the modified Lewis method. Juvekar and Sharma (50) also took into consideration the pressure ijariation along the column. However, the validity of these methods is far from beeing tested experimentally verified and in view of the great industrial importance of plate columns, experimental evidence in support of them is certainly required.
308
5. USE OF LABORATORY MODELS IN PROCESS DESIGN Computational design methods from first principles -that is, the Route 1 of Figure 1) require not only all the physical gas absorber data (such as kL a,kGa, ~ etc.) but also the process specific data of reaction kinetics, solubilities and diffusivities. Some of these data (i.e. Stage 2 of Figure 1) can only be estimated using methods which are generally speqking not very reliable. Therefore, Danckwerts and his coworkers (66-69) thought that it might be more statisfactory to build a laboratory model of the absorber, which simulates the essential features; and to make measurements on that rather than the computation from first principles. By "essential" features, it is not suggested to make a geometrically accurate model of the absorber, and to try to get complete dynamical similarity. This would, of course, be impossible, partly because of the large number of dimensionless groups involved and partly because important data, such as the kinetics and the rate of reaction, might be ignored (69). The model b~ilding of the Cambridge School was however based on the fact that the rate of absorption per unit interfacial area (R) depends only on the interfacial partial pressure of the gas, the liquid composition and the value of kL' the liquid-side mass transfer coefficient in the absence of reaction. It makes no difference how kL is generated -by turbulence promoted by stirring, by flow over a packing, or in other ways- equality of kL will give equality of specific rate of absorption. Equality of partial pressure at the interface will be assured by having the right bulk composition and value of kG' Another very important characteristic of the model is that it should have a definitely known contact area. It is convenient to describe two different types of model. The first one may be called a "point" model (67,69). Here only the absorption-reaction interaction (that is, microscopic scale phenomena) is simulated so that gas absorption rate per unit interface (R) may be measured for a variety of combinations of bulk gas and bulk liquid compositions. Then, these results are inserted into an appropriate two-phase contactor model (for example, those listed in Tables 3-6), to yield the required capacity. It is clear that the method eliminates theoretical modeling at the microscopic level and none of the quantitative process specific data (i.e. Stage 1 of Figure 1) is needed. However, some qualitative data are required as the model is applicable only to reactions which are fast enough to take place in the diffusion film near the interface so that there is no unreacted dissolved gas, and no reaction in the bulk of the liquid (inappropriate considerations of bulk reactions may ,result in vast design errors (70)). It is also confined to the case where a single gas is being absorbed. The reason for these limitations is mainly that, in these cases, there is a simple stoichiometric relationship
309
between the bulk composition of the gas and the bulk composition of the liquid at any poi~t (or level) in the abso~ber. The second method of modeling an absorber is to make what might be called an lIintegra or IIcomplete model (68,69). This would then consist of a laboratory scale absorber which simulates the industrial absorber with regards to microscopic as well as macroscopic modeling. The rules for such an lIintegral or IIcomplete modeling were first established by Alper and Danckwerts (68,69). It is interesting to note that, in this type of modeling, none of the process specific data are needed; thus the Stage 2 of Figure 1 is completely eliminated. Alper and Danckwerts (68, 69) have applied such modeling to packed columns and have shown that a special type of absorber could barely satisfy all the necessary cond-itions (see, Section 6.4). Recently, C~arpentier and his coworkers (71,72) tried to apply such a modeling to venturi scrubbers but coul d not sa ti sfy a 11 the necessary condi ti ons simultaneously. They were however able to simulate the absorber for some limiting cases, such as the case of only liquid phase resistance (71,72). 5.1. Laboratory Absorbers Laboratory absorbers for studying absorption into liquids may be divided into two groups. Some of them have effectively a quiescent liquid which comes into contact with gas for a desired time which can also be changed with relative ease. Strictly speaking these absorbers simulate the conditions which are foreseen by the Higbie model. Table 7 shows the main types and Danckwerts (2) discusses in some detail design characteristics and proper operation of many of these absorbers. These absorbers may also be used to obtain IIprocess specific datal! -such as, reaction kinetics, diffusivities etc. (2,73-75). The remaining laboratory absorbers (see Table 8) involve random or regular movements which tend to bring about mixing between liquid near the surface and in the bulk or replacement of one by the other, thus simulating agitated liquids. Here the essential feature is, in each case, a well defined and known inte~ face and relatively easy adjustment of the mass transfer coefficients kL and kG. Although, the use of all the types in Table 7 and 8 are advised repeatedly (71,72,76), it is our opinion that some have only a historical value. For instance, a conical wetted wall column (77) has no advantage over that of a cylindrical one, but it has the disadvantage that the end effect due to a rigid film at the liquid exit will be increased. For instance, the results from a disk column are difficult to reproduce (78) thus a string of spheres column may be preferred. Other types which have only historical value include the rotating drum and moving band absorbers ll
ll
ll
ll
310
TABLE 7, MAIN LAOORA'IORY ABSORBERS WITH AN EFFEcrIVE:LY QUIESCENT LIQUID (2).
APPARATUS
0:
2 d X* ....,* = 0 ---- dX * + DaX 2
( 1 2)
dz
with Danckwerts' boundary conditions: ""
1 dX* x*- -Bo d'z
1
at z = 0
o
at z
uL
where Bo Da
=
--Dax ll m uL
x*
1
(12b)
is the Bodenstein number,
= II m 'T
is the Darnk6hler number, the dimensionless cell mass concentration.in state, the dimensionless tower length, the length coordinate, the length of the tower, the flow velocity and the axial dispersion coefficient.
X/X o x/L
z x
=
( 12a)
L
u
Dax
The solutions of eq. (12) are given (1): for Ba I > 'Da or q > 0
[S~(l-Z) +2q cosh q~(l-Z)
2
f""I.*
X (z)
( 1 3)
(1 where q for Bo f'W
:x;z)
=
=
(1
+ 2q cosh
)1/2
-
4Da
4Da Bo
q =0
or
+ BO(1 - z) 2
exp
1 +
and for Bo 1
( 14)
420
'Xtz} where
Boz . bBo 2exp(-2-)\[s.l.n. -2-(1-z)+
bBo cos2-(1-z}] 2 bBo + 2b cos --2bBo ( 1-b ) sin -2-
( 1 5)
b = (4BaDa
Eg. (15) is only valid when Ba :and Da are related in such a way that , 4 2 _ _ Bo ,
11--------
'3
80 2 Bo (n),--~ Oa s..~ + -,-
..
(In)
80
Oa
0)
5
'2
10
Dd
(1) •
422
with X* = 1 for all z at 8 = 0
a x* 3z: =
1
X*- Bo
0
at z
o for
(18a) (18b)
8 ,. 0
and
ax* = rz
at z
0
x* = x/x o
where
XO
is the cell mass concentration at 8 = 0 -t
8
T
t
the dimensionless time and the real time measured from the moment of swi tching from ba-tch to continuous operation
The solution of eg. X
(18c)
1 for 8>' 0
(18) is given by (1): 00
Boz exp (-2-) l: A exp (- A 8) n=1 n n
* (8,z)
[~~-
sin(2 Il n Z )
+
( 19 )
cos(21l nZ)]
.n
where
an' n=1, 2, . .. are real roots of a tan 0.= B0 4
= - II
(20)
n
2 40. Bo + _ _ n _ Da 4 Bo
(21 )
n
8 a 2 __ n '[(BO) 2 + a 2 ] Bo 4 n BO + (BO) 2 + a 2
or acot
A
and A
Bo
~
4
4
(22)
n
The following particular cases should be considered: 1. If all eigen values an' n=1,2, •.. are positive for given Bo and Da washout will occur as 8 + 00 • The washout conditions follow from eg. (21): Da
2 4 0. 1 Bo <J3C) + Lt
(23)
423
where q, 1 is the smallest positive root satisfying eq. (20). This condition coincides with regions II and III in Fig. 1. In these'regions steady state solutions do not exist for sterile feed but they do for nonsterile feed. 2. If one or more of A n are negative, the cells will grow as6+ 00 -and attain a substrate or oxygen transfer limited growth state at the reactor exit. 3. If the smallest A n is zero the steady state solution is possible. However, this is an unstable steady state solution because any flow fluctuation will make the smallest A non-zero and the cells will either grow and reach the limited state or be wash"ed out. Steady state nonlimited growth can only be main~ tained in a tower reactor if growth is limited at the reactor exit. 1.1.3 Cell population growth in tower loop reactors. Air lift tower loop reactors are often used to carry out cultivation of microbial cells (2,3,4). In these reactors the medium is recirculated from the top of the tower to its bottom.
When assuming that (a) the tower can be described by a one-dimensional dispersion model, (b) the liquid residence time in the loop is negligible, and (c) the axial dependence of the local relative gas holdup is negligible, the following cell mass balance is obtained (5,6):
1 BO
(}2x R
-a
*
I
z2 -
1)x -;Pz
*
+ Da
R
X
*
(24)
Bo(1+ y) is the modified Bodenstein number
where
Da is the modified Damk6hler number 1+ y
uR u
y =
is the liquid recirculation ratio
t{u+u } R L X
X*
XO
X*
X
X0 VL/Q
is the dimensionless time,
for sterile feed for nonsterile feed.
I)
u = uR =
" Q Val
is the superficial liquid velocity, is the superficial liquid velocity due to recirculation,
424
•
V r. L V R
is the volumetric feed rate, is the volumetric flow rate in the loop, is the cross-sectional area of the tower anc is the time measured from the moment of switching from batch to continuous operatior
Q
t
Under steady state conditions eq. to (is):
(24) is reduced
o When are
----- are in the
feed, the boundary conditions
. . . *(0) dX dz
-* X (0) and
(25 )
-* (1) dX dz
( 26)
=0
Solution of eg. washout.
(27)
t"\J*
(25-27) results in X (z)
0, i.e.
When the feed contains some biomass the boundary conditions are:
,...;X(O) *
=
+
X*(1)
A>*
+ __ dX(O) BO
R
--crz-
(28)
and
(29) Eg. (25), subject to (28) and (29), were solved analytically (5,6). Again three cases can be distinguished: Bo r. For DaR < 4R, i.e. (A >0), the solution is given by
425
;v.
x*(z)
sinh
(S;R ';(1-z»+ A cosh (~. A(1-z»
• 2
where A = (1 _ 40a R ) 1/2 BO
Bo R exp(-r
z)
(30)
R
Since only positive X*s'are reasonable, the denominator in eq. (30) must always be positive. This leads to
x'
y < 1 -
with
x'= [
Xl
(31, a)
2 1 +A 2A
Ba
sinh
(2 A) + 2
BaR]
BaR
cash (--2-- A) exp(-~) (31 b)
i.e. A
II. For OaR
,...,*
X (z)
2
-I( HyJ]
0, the solution is given by
+ BOR (1-z) (2+
B~R )
-12
y exp
(+ )I
exp
BaR
(~3:»
The condition for positive cell mass is given by BaR
2 + -2y
--4- f l.e. A becomes imaginary, and the solution is glven by
426
=
~in( X~1-zl ).+2X,cos (x(1-z})
j(1+'lfJ1 (Boa-~ llSinX +-v xexp(~l+4Bxcosx 2
With: ,
B
and
exp([ z) = /
X=
(34 )
(35)
BO
R
-2- B
(36)
The requirement of positive cell mass concentration is fulfilled only, if 2 BO R BO R 40:. (37) -4- < Da R < -4- + BO 1 R The value of a 1 results from the condition that both numerator and denominator must be positive (5,6). In analogy to tower reactors without a loop (1.1.2) Fig. 3 shows the ranges of BOR and DaRt where
the different cases of the solution apply. It can be shown (5,6) that in case III an upper limit of DaR exists which leads to a cell mass concentration increase and to substrate or oxygen transfer limited growth at the reactor exit. This critical limit diminishes with increasing Y(Fig. 3). With an increasing recirculation ratio, y , one moves from region III via the limiting case II to region I. In region I, y can only be raised to Ymax' which is defined by eq. (31). In Fig. 4, Y max is plotted as a function of Da for various Bo. Onfor Da .t?; 1 is y max finite. At Bo = const, Y max increases with decreasing Da f as long as Bo is high enough
427
10 5.-------+--''1;:---+------+----1---#------1 "No reasonable
50-
/ lutlon '''explosion'')
y
o 0,5 0,5~-----L~F===~~~----+---._------~
2
0,1 L..-_'---..L-.L.£L,...L.L..L.U.._--'-----'--'-...................."'*-_-'--................ 0,5 10 50 5 0.1 Fia.3:Ranaes of physically correct solutions(S) (Case I: left from -' the liii.e - A,Case~II:eaual to the line A , Case III:riqht from the line A )
6
Ymax
5 4
3 CSTR
2
1,0 2,0 1,5 D.a Fig.4. Maximum recirculation ratio ¥Imax ,as a function . of Da with Bo as parameter(S)
428
In the CSTR, Y max
-+
00
•
In Fig. 5, the attain~ble dimensionless cell mass concentration at the exit,X*(1), is plotted as a functi< of ..::c. at Bo = 1 and Da as'a parame+:er. For low values of Da .x* (1) is hardly influenced by'Y • However, if the Da nufuber is slightly below the critical value of 1.17 (Fie 4), the recirculation ratio reveals a considerable in- ' f 1 uence on X*(1). At Da = 1.1 and Y ~ 2, for instance, X *( 1) is ten times as high as for Y = o. Under nonsteady state conditions and with cells in the feed, eq. (24) has to be solved with the boundary conditions:
* aX(1,e)
d x'to ,e)
.*
+ * X(O(6) = _1_ 1+y
Y X(1,e)
0
+
e> 0
(38)
e> 0
(38a
az
and the initial condition * X(z,e)
=
e~
0
(38b
0
The following closed solution was obtained (5,6):
*
B.O
X (z,9)
(z,
00)
R z) + exp (-z
00
~ Rx (z)
exp (Sk9 )
k=1 (39)
where
=
BOR OaR - -4- -
2 4ak' BOR
(39a)
429
1000
80 = 1 I I
IYma~2.328
x* (1 )
0.70 030
y
Fig. 5: Outlet biomass concentration in dependence of y for various Da- numbers (Bo ~ 1) (5) .
430
For the roots see (6) and for the solution technique see (5). The nonsteady-state behavior depends only on the terms of eq. (39): To attain a steady-state all these terms must disappear for e ~ 00 , i.e. values of SK must be negative. The condition for o follows from eg. (39a): 4a. 2 1
'+
BO
(40)
R
If this condition is fulfilled and 8 + 00 , eg. (39) reduces to the steady-state solution )(z,OO ): eg. 30, 32 or 34 depending on the value of A. Under nonsteady state conditions and with feed eq . .(24) has to be solved with the boundary conditions: x*(o,e)
a X*(l, az
y
x
*( 1 , e)
+
a X\.O,8) BO
R
(41 a)
a z e> 0
o
(41b)
and with the initial condition: X*(z,8) = 1
at
e =
(41 c)
0
e =
0 is the moment when the batch is switched to continuous operation.
The solution of eq. (24) and (41) is BO R , 00 x*(z,e) = exp(-2-'z;. L: 11«z) exp(SK 9 )
(42)
k=1
The RK(Z) values are given in ref. eg. (37)
(5,6). SK is given by
If SK~ 0, i.e. condition (40) is valid, X*(z,8) approaches zero for e + ~, which corresponds to washout. If only one SK> 0, the cell mass concentration increases as long as substrate or oxygen transfer limited growth is attained at the reactor exit. operation is only possible if one SK = 0, SK < 0, i. e.
431
(43) However,this solution is not stable and small deviations from the steady state lead: to either washout or expone~tial cell growth and limited growth.All solutions for tower loop reactors yield the corresponding solutions for tower reactors if y is set to zero. A comparison of stirred tank reactors (1.1.1) with tower reactors (1.1.2) and tower loop reactors (1.1.3) indicate that all of them behave similar if cell-free feed is used: at nonlimiting growth there is no stable state.
With cells containing feed stable steady states exist which differ from washout,and cell "explosion". The ranges of Bo and Da values which correspond to these states are similar in tower and tower loop reactors. However, application of a recycling process may increase the cell mass production considerably. 1.2
Substrate limited growth
Cell cultivation is usually carried out in the substrate limited growth range. 1.2.1 Substrate limited growth Several relationships have been pendence of the specific growth concentration. The most popular Monod (7):
in stirred tank reactors. recommended for the derate, 1-1, on the substrate is the relationship of (4 4 )
U = Urn
where KS is the saturation constant with regard to the substrate Two limiting cases can be distinguished:
(45)
for'S :»
the growth is of zeroth order with regard to the substrate (nonlimited growth) and for S«
KS
I
1-1
~
Urn
KS
S
(46)
432
growth is of first order with regard to the substrate (strong substrate limited growth) . In a batch reactor, eq. RX
=
dX dt
=
(47) holds true:
SX
(47
1-1m KS+S
The corresponding substrate and oxygen consumption rat! are: dS - dt
X _1_
( 48.
Yx/s
and dO -RO = - dt if no aeration is carried out. For the CSTR the following balance equations are valid: lI mS 1
(50)
1 + D(X o -X 1 )
'-K S X
s+ 1
(51)
dO dt
( 52)
where 0 * is at saturation. 1 kLa is volumetric mass transfer coefficient for 02 across the gas/liquid' interface. Under
conditions eq. d0
1
dt
=
0
(53) holds: ( 53)
This substrate limited cell growth in a steady-stc CSTR is called chemostat culture, if Xo = 0, because ii has a character (8,9), i.e. it is a
433
stable state 7 "...,;
I~X, exceeds below S, ~ccording
its steady state value X" S, drops to ego (51), this causes a reduction
of Xl to X, • N r..,J If X1 drops belo~ X1' Sl exceeds Sl and this causes an in.creas~ in X1 to Xl. With X0 :::: 0, eqs (50) and (53) yield:
....,
"'" 11l X1 - OX l
...v (1l1-D ) X,
=
(54)
0
Sl where II 1 :::: II m KS+S1 or
11 1
=
(55) (56)
0
Egs • (51) and (53) yield:
,
.-I
111 X1
-.J
o (So -S1)
Yx / s
When substituting ego
(56) into ego
(57) (55) we obtain (58 )
and eq. ,-J
X1
=
(56) into eq.
(57):
,...J
YX/ S (So-S1)
= Yx / s
[So-KSO/(}J m-D).J
(59 )
In Fig. 6, """"' X, is plotted as a function of D for two different So values. The cell production rate, RX 1 is given by N
Rx = OX 1
=
DY X/ S [3 0 -KSD/ ~ m-D) ]
( 60)
In Fig. 7, Rx is plotted as a function of D. It can be r~cognized that Rx passes a maximum. To evaluate the dilution rate, Dm' at which this maximum occurs ego (60) is differentiated with respect to D and the derivative is equated to zero. This results in (12):
434 """1 1-0 I I
--l..
X (sr=1·0 g/ll 0·5
0·4
~
::::::.
0>
,">
'c '1 f this increases 11 as well as X1 to X1' The steady-state is stable.
444
1.3.2 Oxygen transfer limited cell growth in tower reactors. If one assumes that the tower can be described by a one-dimensional dispersion model, the gas holdup variation along the tower i,s ~egligible and the longi tudinal dispersion coefficients 'in the liquid phase, DFt and in the gas phase, DG' are constant in the tower, the following steady state oxygen balance can be obtained (13,14) in the liquid phase:
o
( 81)
and in the gas phase: d
d XOG (x)
DG
P (x) d x
dx
d __ ]- [(p (x) XOG (x») dx
RG T EF - --E-
M02
G
_
,1(; (x)] -
*
,,-.J
kL{x) A(x) [OF (x) -OF (x)]
°
(82)
The Danckwerts boundary conditions are assumed; in the liquid ph as e ('V
d 0F(O) dx
AlE]
F [ -°F(O) - OF
u D
at x
F
=°
(81 a)
and N
d OF (L)
-a-x-
=
°
(81b)
at x
L
J
at x
°
( 82a)
at x
L
(82b)
and in the gas phase dS{'OG (0) dx
E
uG
rs-G
[.-vxOG(O)
rvE
- xOG'
and ""0./
d xOG (L) d x
°
445
where
,...;
x OG
is the mole fraction of 02 in the . gas phase, -./
"
is OF at the entrance, at x
-
"../
is x
°
at x = 0 OG are the gas and liquid holdup, respectively
The D.E. system (81) (82) can only be solved numerically.
,....,
"
~
°
-"'"
Since, in general, it is assumed that X, Sand are space dependent, the oxygen consumption rate also depends on x. Thus, for X and 'S similar balance equations are obtained.
1.3.3 Oxygen transfer limited cell growth in tower loop reactors. In addition to the assumptions in 1.3.2 i t can be assumed that the medium is completely free of a gas phase in the loop, furthermore,the longitudinal liquid dispersion coefficient in the loop can be neglected. These two assumptions hold true for tower reactors with an outer loop which has a considerably smaller cr0SSsectional area than the tower cross-sectional area (13, 14) •
The following D.E.'s are needed in addition to eq. (81) and (82): oxygen mass balance in the loop liquid:
d"OB (x*) ~
where index x
°
(83)
refers to the loop, is the longitudinal coordinate in the loop.
To solve eg. (83) the boundary condition at the lowwer end of the loop N
I'"
0B(O) = 0F(L) = O~
is used. In eq. the tower.
(84)
A
(84), OF is the exit concentration of
The solution of the oxygen balance is only possible if the conditions at the lower end of the tower are defined by
446 (85 )
By means of the C02 balance uG(x) can be calculate, in the tower (13,14). The substrate balance for a steadJ state in the tower is given by
2'" d S'F (x) DF
dx
2
(x)
d \u F
,..J
/'IJ
J'V
0
RSF(XF,SF,OF'x)
d x
(86 )
ar,l.d in the loop by
o
-~
d
(87)
x
with the boundary conditions I"W
u
dSF(O)
F [SF (0) DF
dX
~
-
("V
y
-{ 1-y } S ]
( 86a)
0
N
(L)
d d x (V
SB(O)
=
°
(86b)
SA F
( 87a)
The cell mass balance for a steady state in the tower is given by
DF
ctxF (x) d x
2
f'J
- uF
dX (x) F d x
N
N
"" + RXF{XF,SF,OF'x}
0
( 88)
and in the loop by ~
*
~(x )
+
-uB
rJ r- ,...., * RXB(~,SB/OB/x )
(89)
0
d x* Again boundary conditions link these two D.E.'s
o
( 88a)
447 f"'V
Cl X
F
(L)
=
Cl. x N
= XAF
~ (0)
(88b)
0
..
( 89a)
For sterile feed X = 0 . o For RXF ' RXB' RSF ' RsB , RaF and ROB the validity of the corresponding Monad kinetics "is a~surned, e.g. (90) and ( 91)
where 11 T is the specific death rate. These D.E. systems were numerically solved and the calculated data was fitted to the measured one. These measurements and simulations will be considered in the article flBiochemical Reactions and oxygen transfer into different fermentation broths fl by the author ~n th~s book.
2
PRODUC~
FORMATION
Different models were recommended for product formation. In general, a product can be linked with cell growth or not. In general, the product formation rate is given by dP dt
q
P
X
(92)
When the product is ~owth linked, the amount of product formed is directly proportional to the biomass formed: dP = Yp / x dX where Yp /
is the product yield referred to biomass formed. It follows that
x
(93)
448
(94) Thus the specific rate ofJprpduct formation is given by (95 )
When the product is non-growth~linked i t can be a complex function of ~. In the simplest case qp
=
k1
=
(96)
constant
Sometimes the product formation is partly growth linked and partly independent of a growth rate: qp
=
(97)
k1 + k2~
where k1
is the rate constant of the non-growth-linkec product formation, k 2 =Y p / X constant of the growth linked pr6duct formation.
In the following, eq. product formation. 2.1
(97) will be used to treat
Product Formation in the Stirred Tank Reactor.
The mass balance of the product for nonlimiting growth is given by (92 )
where Po and P1 are the product concentrations in the feed and in the reactor. With substrate and oxygen transport limited growth the following product balances hold true:
=
(k 1 + Yp /
~mS1
x
K +S X1 + D(P o -P 1 > S 1
(93)
and dP dt
(94)
449
under steady state dp = dt ~2
°
is'valid.
Product Formation in Tower Reactors
No general solutions of the product mass balance equation in tower reactors are known. However, one can draw some conclusions from the longitudinal cell, substrate and dissolved oxygen concentration profiles with regard to the longitudinal product concentration profile. When employing nonflocculating bacteria or yeasts or fungi without pellet formation in a laboratory bubble column only slight longitudinal cell mass concentration profiles can be expected (5). In non-substrate-limited growth and in laboratory bubble column reactors the longitudinal substrate concentrati-on is uniform (13). When substrate limited growth prevails longitudinal substrate concentration can be expected (13). Longitudinal dissolved oxygen concentration profiles always exist. They are most considerable at the end of the nonlimiting growth phase (15). In case of non-growth-linked product formation uniform product concentration should prevail. But also for growth linked product and in the presence of nonuniform longitudinal dissolved oxygen and/or substrate concentration profiles no or only slight longitudinal product concentrations can be expected. Hence in laboratory bubble column reactors, egs. (92), (93) and/or (94) can be used, where X1, 81 and 01 should be replaced by their mean values in the tower.
2.3
Product Formation in Tower Loop Reactors
In tower loop reactors with increasing liquid recycling the longitudinal concentraLion profiles become more and more uniform.Therefore the use of eqs.(92) 1 (93) and/or (94) is recomended. In the presence of flocculating cells or pellets a considerable longitudinal cell mass concentration profile usually prevails. This can cause very significant nonuniformity of dissolved oxygen concentration profiles. It is unlikely that under these conditions the longitudinal profile of product concentration is uniform in tower
450
loop reactors, especially in tower reactors without liquid recycling. B. CHARACTERIZATION OF FERMENTATION SYSTEMS The performance of bioreactors is considerably influenced by the medium properties. Therefore, knowledge of medium properties is necessary for the construction of bioreactors.
1.
MEDIUM PROPERTIES
Several properties influence the performance of bioreactors. Hm.,ever, in this lecture only a few selected ones should be considered. 1.1
Viscosity
Yeast and bacterium suspensions at concentrations which are used in bioreactors exhibit Newtopian properties. Reuss et al. (16) recommepd the following relatio ship for the dynamic viscosity, ii , of yeast (Saccharomyces cerevisiae and Candida utiLis) suspensions:
"s "0 where
(95 ) 1 - (h
s
E
.x
)
a
is the viscosity of the suspension, the viscosity of the supernatant, the volume fraction of the cells, the packing factor: hs = 0.0487 Fosm+ 1.59 and Pos m the osmotic pressure (bar = 10 5 Nm- 2 )
The rheology of highly viscous fermentation moulds of fungi cultivations was investigated by Metz et al. (17). However, these systems will not be considered here. 1.2
Coalescence Suppressing or Promoting Character.
The interfacial properties considerably influence the bubble coalescence process in liquids. At the same concentration and chain length, fatty acids have the strongest, alcohols intermediate, poly-
451
alcohols and ketones the slightest influence. The concentration, Ceo' at which coalescence suppression begins is inversely proportional to the number of carbon atoms, nC (18): C
eo
a \ nC
-1 5
(96)
•
Interfacial tension suppression, dO Idc, is also influenced by eeo (18): In
o
-(1.5 + 0.5 In eeo)
(97)
There is a definitive relationship between the coalescence suppressing effect of salt solutions, their ion strength and their position in the lyotropic (Hofmeister) series (19). At the same ion strength, the salt has a stronger effect which exhibits a greater tendency to flocculate proteins. Since no relationship is known for complex cultivation media the bubble coalescence behavior of media was experimentally determined by means of the volumetric mass transfer coefficients, kLa, which were measured in a standard bubble column reactor. These kLa values were compared,with the kLa values measured in the same equipment under the same operational conditions with water: (kLa)H O. The ratio, m: 2
m
(98)
was employed to characterise the cultivation medium for a fixed superficial gas velocity, wSG (20). In the presence of antifoam agents a modified relationship was used: m
(kLa)corr
(99)
(kLa)ref
where (k L a) corr = kL a - A (k L a) L1i(kLa) =: [kLa -
(kLa)ref] w =2cm s-1 SG
As a reference a nutrient salt solution with an antifoam agent was employed.
452
1.3
Foam Formation
Cultivations are often accompanied by foam formations due to the high foaming capacity of protein solutions. This capacity results from the stabilization of the gas liquid interface caused by the denaturation and strong adsorption of the surface proteins (21). Since mechanical foam breaking with its high input power requirements is expensive, antifoam agents are usually preferred in the fermentation industry. The presence of antifoam agents, however, deteriorates the efficiency of gas dispersion by increasing the bubble coalescence rate. The influence of salts (22) and alcohols (23) on the foaminess were investigated and simple relationship were found. The salt effect can be explained by the interaction between the water and the salt, i.e. by its influence on the water structure. The alcohol effect is due to the change of the water structure and the direct interaction between alcohols and proteins, where the direct interaction overcompensates the water structure effect. The influence of antifoam agents on foam formation seems to be a complex process. With increasinl antifoam concentration the foam formation is diminished step by step (24). 1.4
Cell Sedimentation and Flocculation
There is a significant disagreement among differen' research groups with regard to the cause of cell floccu· lation (25). The flocculation of yeast seems to be a genetic property. However, there is no flocculation during the nonlimited exponential growth phase. Ions, especially Ca ions r phosphates, the properties of cell membranes as well as the glycogen content of the cells, can influence the flocculation of yeasts during fermentation. Additives, which influence the water structure and protein solubility can alter the flocculation properties. Since the influence of different additives on cell sedimentation based on literature data is contradictory it is necessary to determine the cell sedimentation rate experimentally. For cells with low sedimentation rates batch runs were carried out and the displacements of the interfaces between layers of different cell concentrations along the column were determined optically.
453
For flocculating cells with high sedimentation rates continuous runs were used. The cell suspension was continuously fed into the sedimentation tank and, from the top, the clear liquid and, from the bottom, the concentrated cell suspension were continuosuly removed. cell mass enrichment was measured as a function of the mean cell residence time in this sedimentation tank (26). 2
PROPERTIES OF BIOLOGICAL TWO-PHASE SYSTEMS
Two-phase system properties can strongly influence cultivation conditions, especially if growth is oxygen transfer limited. To treat the oxygen transfer rate quantitatively it is necessary to determine the volumetric mass transfer coefficient, kLa, the dissolved oxygen concentration in rpe liquid bulk, OF' and at the gas liquid interface, OF' The specific interfacial area is influenced by the Sau-l.:er bubble diameter, d s ' and the relative gas holdup, € G' according to eq. (100):
d
s
(1-E ) G
,
( 100)
if the bubbles have a spherical shape, which holds true for small bubbles. The mass transfer coefficient, kL' is a complex function of several parameters such as d s ' interfacial properties and turbulence.
2.1 eq.
Relative Gas Holdup, EG The mean relative gas holdup, E G , is defined by (101) (101 )
where V VL
is the volume of the bubbling layer, the volume of the bubble-free layer.
In bubble column reactors the determination of EG is carried out by means of the height of the bubbling layer, H and bubble-free layer, HL' or of the corresponding hydrostatic pressures. The local relative gas holdup was measured by electrical conductivity probes (see 2.2).
454
2.2
Bubble Size Distributions
The Sauter bubble diameter, d s ' can be calculated from the bubble size distribution by eq. (102): N
3
l:
1 nidi N 2 l: n. d. 'I \ ~
where n
i
(102
~
is the frequency of the bubbles with the diameter die
The most bubble size distributions were measured with flash photography and semiautomatic evaluation of the photographs (27,29). Miniaturized electrical conductivity probes with two sensors and on-line computer evaluation are also popular (27,28,29). The measurements with these probes also yield the local gas holdup in tower reactors (27,29). 2.3
The Specific Interfacial Area
The specific interfacial area can be measured by means of chemical reaction (e.g. sulphite oxydation) if a model medium is used (e.g. 30). However, chemical methods cannot be employed for fermentations. Therefore they are usually calculated by means of eq. (100), if d and are available. Specific interfacial areas were determined during the cultivation of Candida boidinii (31), Hansenula polymorpha (32) and Escherichia coli (5) in tower loop reactors.
2.4
Volumetric Mass Transfer Coefficients
In reactors with uniform concentration of substrat cells and dissolved oxygen (reactors with lumped parameters), kLa can be calculated in batch operation by eq. (103): kLa
=
OTR
(1 O~
°f-01 and in continuous operation by eq.
(104):
~
I
I
455
I
I
9UR
- D(
° -° 1 ) 0
01* - 01
OTR
( 1 04)
0*-0 1 1
The oxygen transfer rate, OTR, can be calculated by the 02 balance of the gas phase by means of the gas compositions (02' C02' N2 ) at the gas reactor inlet and outlet. The oxygen utilization rate, OUR, can be calculated by eq. (105): OUR
=
fX/O
].l
(X 1 -X o )
(105 )
: The saturation concentration of dissolved oxygen, 01~ is calculated by means of the measured gas composition in the reactor and the measured solubility of 02 in the medium (33). The dissolved oxygen concentrations in the feed, 00' and reactor, 01' are measured by oxygen electrodes and calculated by the corresponding 02 solubility. In tower and tower loop reactors kLa was determined by fitting the calculated longitudinal dissolved oxygen profiles to the measured ones (13). Such data were evaluated during cultivation of Candida boidinii (31) and Hansenula polymorpha (13,15). Flow pattern and turbulence properties will not be discussed here, because they will be treated in the article of A. Llibbert in this book.
REFERENCES 1. Chen, M.S.K. AIChE J. 18 (1972) 849. 2. Seipenbusch, R. and H. Blenke. "The loop reactor for cultivating yeast on n-paraffin substrate". Adv. in Biochem.-Eng. 15 (1980). Ed. A. Fiechter, Springer VerI. p. 1 3. Cow, J.S., J.D. Littlehailes, S.R.L. Smith and R.B. WaIter. "Single Cell Protein" II. Eds. S.R. Tannenbaum, D.I.C. Wang, MIT Press(1975) 370 4. Faust, U. and W. Sittig. "Methanol as Carbon Source for Biomass Production in a Loop Reactor". Adv. in Biochem. Enq. 17 (1980) 63, ed. A. Fiechter, Springer Verlag
456
5. Adler, I. Dissertation, University Hanover 1980 6. Adler, I., W.-D. Deckwer and K. Schugerl. Part I. Chem. Eng. Sci. (in the press) 7. Monod, J. Recherches sur la Croissance des Cul~ tures Bacteriennes. 2nd edn t A9 42) Hermann Paris 8. Monod, J. Ann. Inst. Pasteur 79 (1950) 715 9. Novick, A. and L. Szilard. Science 112 (1950) 71~ 10. Todt, J., J. Lucke, K. Schuge~l and A. Renken. Chem. Eng. Sci. 32 (1977) 369 . 11. Chen, G.K.C., L.T. Fan, L.E.Erickson, Can. J. Chem. Eng. 56 (1972) 157 12. Pirt, S.J. "Principles of Microbe and Cell Cultivation ll • Blackwell Scientific Publ. Oxford 1975 , 13. Luttmann, R. Dissertation, University of Hanover 1980 14. Luttmann, R., M. Thoma, H. Buchholz and K. Schugerl. Computer and Chem. Eng. Part II (submitted) 15. Buchholz, H. Dissertation, University of Hanover 1979 16. Reuss, M. D. Josic, M. Popovic, W.K. Brown. European J. Appl. Microbiol. Biotechnol. 8 (1979) 167 17. Metz, B., N.W. Kossen and J.C. van Suijdam. "The Rheology of Mould Suspensions". Adv. in Biochem. Engng. Springer Verlag Vol. 11 (1979) 103. 18. Keitel, G. Dissertaion, University of Dortmund 1978 19. Zlokarnik, M. "Sorption Characteristics for GasLiquid Contacting in Mixing Vessels". Adv. in Biochem. E~. Springer Verlag. 7 (1978) 113. 20. Adler, I, J. Diekmann, W. Hartke, V. Hecht, F. Ro~n and K. Schugerl. European J. Appl. Microbiol. Biotechnol 10 (1980) 171 21. Cumper, C.W.N., A.E. Alexander~ Trans. Farad. SOl 49 (1950) 235 22. Bumbullis, W., K. Kalischewski and K. Schugerl. European J. Appl. Microbiol. Biotechnol. 7 (1979) 147 23. Bumbullis, W. and K. Schugerl. European J. Appl. Microbiol. Biotechnol. 8 (1979) 17 24. Muller, B. I V. Pfanz and K. Schugerl (in preparation) 25. Windish, W. Monatsschr. f. Brauerei 22 (1969) 69 26. Kuhlmann, W., A.Gebauer and I Schmidt. (In preparation) 27. Buchholz, R. and K. Schugerl. European J. Appl. Microbiol. Biotechnol. 6 (1979) 301 28. Buchholz, R. and K. Schugerl. European J. Appl. Microbiol. Biotechnol. 6 (1979) 315 29. Buchholz, R., W. Zakrzewski and K. Schugerl. Chem. Ing. Techn. 51 (1979) 568
457
30. Schumpe, A. and W.-D. Deckwer. Chem. Ing. Techn. 52 (1980)
468'
31. Schligerl, K., J. Llicke, J. Lehmann, and F. Wagner. Adv. in Biochem. Engng. 8 (1978) 63 32". Zakrzewski, W. Dissertation University of Hanover 1980
33. Deckwer, W.-D."Physical Transport Phenomena in Biological/Tower Reactors" (' Proceedings' of NATO' ABI on 1I~1ass transfer with chemi"ca"l re'action" "in: lrl"ult"in"has9 systems"" • !zmir ,Turkey, 1981)
459
PHYSICAL TRANSPORT PHENOMENA IN BIOLOGICAL TOWER REACTORS
W.-D. Deckwer Institut fur Technische Chemie Universitat Hannover (TH) D-3000 Hannover 1, FRG INTRODUCTION It is well known that the performance of biological processes may be influenced significantly by physical transport phenomena. In general, physical transport processes concern the transfer of mass, momentum and various kinds of energy. One can suspect that until now only few of the physical transport phenomena have been fully recognized and understood. The present paper will be mainly confined to mass transfer phenomena in a special type of biological process, i.e. aerobic fermentations. Various reactors have been developed to carry out aerobic fermentations. Among them the more popular are stirred aerated vessels, bubble columns (with external circulation of liquid) and various kinds of loop reactors. The present lecture will only deal with gas-in-liquid dispersions generated by various kinds of spargers and processed without mechanical tation at moderate liquid flow rates. In chemical reaction engineering such gas-liquid reactors are called bubble columns. and in biotechnology tower bioreactors. Applications of these reactors are found in waste water treatment (1-3) and aerobic fermentations (4,5). Recent examples concern the production of yeasts, i.e. Candida boidinii (6) and Hansenula polymorpha (7-9), the fermentat~on of Penicillium chrysogenum (10), and the production of animal cells (11).
460
A decisive mass transfer problem in the majority of , fermentations constitutes the transport of oxygen from the air phase to the locale of the reaction, i.e. the biomass phase which,in accordance with chemical engineering,willbe conveniently referred to as solid phase. The major reason that transfer may play an important role in processes is the limited oxygen capacity of the broth due to the low solubility of O2 , : The oxygen transfer typical three-phase biological system is shown in Fig. 1. The sit~ation is completely to the one encountered in catalytic reactors. It is generally accepted that before oxygen can be consumed by biomass particles several physical resistances have to be overcome, in principle. In terms of the simple film theory possible resistances may be - diffusion through the and the biomass particles brous or filamentous -
films around the bubble I flocculant, fi-
~ffective diffusion in with the consumption by reaction in the interior" of the biomass particles.
The latter phenomenon, i.e. effective diffusion and reaction in the biomass, may be or almost completely free of external influence. clear expositions are now available which treat the interaction of diffusion and reaction in analogy to catalysis by introducing the concept of effectiveness factors (12 -14). On the other hand, operational conditions and hydrodynamic flow behavior exert a on the transfer of oxygen through the around both the bubble and biomass particle. transresistances are characterized by coefficients and among others subject of this paper. 2
MODEL EQUATIONS OF FERMENTER
I there is no doubt that the and scaleup of chemical reactors should be based on mathematical models and computational optimization . This is certainly also true of biological reactors though are definitely more complex. The use of mathematical models requires to embed the microscopic of mass and reaction into the governing macro-
461
Biomass particle
qiffusion through stagnant , I liquid films
1\ I I
1
I I
Gas phase
~ Biomass /'
( pe Bets, fi bers. ~ filament)
~
I
~----c------~
/'
I :/ I Cs
I
i
Bulk liquid phase
1I I
r
Effective diffusion and reaction
::.-
~
/'" /'"
Fig. 1: Mass transfer resistances in biological reactor
COl)vective and
I
x+dx--,-~~------~____~v~_
~
~
Gas Liquid
Mass transfer / gas-liquid ./
x
T
+-~ /.
Biomass Diffusion and reaction (parallel)
~ "Mass transfer liquid -sol id ~
--~~~--~~T-----~~/~
/
High radial mixing
)..1 Sedimentation
Fig. 2: Schematic volume element of bioreactor
462
scopic balance equations of the fermenter. With the exception of stirred vessels/b~ological reactors usually have some degree of slenderness, i.e. the ratio L/d c >1, therefore the disper?ed plug flow model can be assumed to be a pertinent approach to describe fermenterse The differential equations of this model are obtained. in the usual way by balancing over a volume element under consideration of those phenomena which are thought to be of influence. In view of Fig. 2 the balance equations for ,oxygen are as follows: Gas phase
* -
d dx(
dC dC L L + kLa( dx ) - u L dx
*
cL )
o
(1)
-c L ) - k s a s (c L -c S )=0 (2 )
Biomass Ehase (external surface) (cL - c s ) - R(CS,cC,cB,Deff"") = 0
(3 )
Of course, the rate term R in the oxygen balance depends additionally on the local concentrations of the C source and the biomass (cC and cB)' and equivalent balances have to be formulated for both of them. In the case of biomass it may be necessary to take into account sedimentation, which gives the following balance equation:
+ R'
o
(4)
where R' is the generation term for biomass which needs no further specification for the present purpose. Us is the settling velocity of the biomass particles in the swarm. The above model equations, the structure of which is representative for distributed reactor models involve a series of parameters which characterize the physical transport phenomena. These are mixing (expressed by the dispersion coefficients EG1 EL' ES) and mass transfer properties (€ G, kLa, ksas). These physical or hydrodynamic transport parameters depend generally on physico-chemical ·properties (viscosity, surface tension),
463
geometrical sizes, the kind of gas distribution, the phase velocities and the flow regime. Due to the various influences the calculation or estimation of physical transport in nonagitated gas-in-liquid dispersions is often subject to serious unreliabilities, and their availability is an important problem in design and scaleup of fermenters. In the following, the utility of hydrodynamic parameters which characterize the physical phenomena will be reviewed in light of recent 3
GAS-LIQUID MASS TRANSFER
3.1
Gas Holdup
The fractional gas holdup EG is an important parameter to characterize gas-in-liquid dispersions. € depends mainly on the gas throughput, the sparger and on physico-chemical properties. If the column diameter is large compared to the bubble diameter, say larger by a factor of about 40, the column diameter has no significant effect. This is commonly valid if ~10 cm. The influence of the gas velocity on E G can conbe expressed by (5) At low gas velocities and if porous spargers are used flow prevails. Then the exponent n may vary from 0.7 to 1.2. In churn-turbulent (heterogeneous) flow, which occurs at higher gas velocities, and if and multinozzle spargers (do ~1 mm) are used,n is in the range of 0.4 to 0.7. . 3 presents data for water and aqueous systems including some from large-scale . The flow is and the exponent eq (5) is about 0.6. Akita and Yoshida (15), among others, proposed the following empirical correlation € ( 1 - EG)
0.2(
gd 2 c 0
P
L)
1/8
1/12
u
G
~gdc
(6)
The column diameter d c is only included to present the
464
Authors • d c . cm t 'foshida. Aklta(1965) 15.2 2 Mlyauchi. Shyu(19701 10 3 Alnta. 'foshida (1973, 15.2-60 , Deckwer et al (197l.\. 5 Ueyama. Miyauchl (1977) 6(; 6 Hlldta et al (1978) 10 7a BoHon et"al t 1978) 7,5
7b Bott on et al.(1978) Kataoka et aL11979)
0.02
25.48 550
e
4
6 8 10
20
40
60 80 100
200
---...... UG • cm/s
Fig. 3: Holdup vs. gas velocity (single & multiorifice spargers)
e
0.0°1.
•
to",_
Cl
0.2 ",.
-eo
l.ZOI.
G
0.4
"I.
fiI
1.4 "I.
~
Ji!J
~
0
-&
;t
~
c
5
2
1.8
20
10 aG. cm 54
Fig. '5: Gas holdup vs. gas velocity - CMC solutions
c.
o •
•o •
CO 2 /H 2 0 N2 0/H 2 0
.0 Cl
·0
•o
o
Cl
• o·
0.
200
o
o-~------
--
jrossl ing( 1938 I
..... ..... ..".
/Levieh(1962I
=-------
O~~~~I----~----~----~----~----~~ 1
3
10 5
7
_ _ _....... _ usd a
9
DL
• 6: Sherwood number vs. Peclet number
467
predictions of the model of Higbie (20) 1.13
I~ v¥
(7)
L
where the contact time e is calculated from the bubble rise 'velocity uB and the diameter dB" The Higbie model i.e. eg. (7), is in accorda~ce with the solution given by Boussinesq (21) for potential flow around a circulating sphere. If the bubbles are small the surface mobility is decreased and they behave as rigid spheres. Therefore, the values of small bubbles approach the limiting solution given by Levich (22) and FroBling (23). The Levich solution
Sh
=
0.997 Pe 1 / 3
is valid if Pe »1 and Re
(8 )
2.5 mm k S 1/2 L c
(10)
Thus, provided it is known whether the bubble diameter is greater or smaller than 2.5 mm the kL value can be calculated from physico-chemical properties alone. Hallensleben (19) has shown recently that liquidside mass transfer coefficients obtained from measurements with single bubbles apply with good accuracy to bubble swarms provided the bubbles do not interfere. This is the case if the gas-in-liquid dispersion is operated in the bubbly flow regime, i.e. at gas velocities less than about 5 cm/so Therefore the models and correlations for single bubbles can be utilized to
468
estimate kL values in bubble columns at low gas flow rates, at least. Empirical correlationsJ fO.r kL in bubble columns have been developed by Hughmark (25) and Akita and Yoshida (26). The equation given by Hughmark is often a good compromise, while, according to our experience, Akita's and Yoshida's correlation predicts a rather conservative estimate of k . L \
3.3
Bubble Diameter
Together with the fractional gas holdup the bubble diameter (volume-to-surface mean value) decisively determines the gas-liquid interfacial area which is given by (11 )
In addition, the discussion of kL for single bubbles has indicated the importance of the bubble diameter which essentially influences the constitution of the gas-liquid interface and the mean bubble rise velocity. Initial bubble size d s generated from single-orifice spargers can be calculated from the empirical equation d* s do
:0 )
1 .88 (
g
1/3
(12)
0
given by Akita and Yoshida (26). Here do is the orifice diameter and Uo the gas velocity in the orifice. The volume-to-surface mean bubble diameters d s in gas-inliquid dispersions can be calculated by a correlation developed by the same authors:
26 (
gd
2 c
a
3 PL ) -0.5 (_.) gd -0.12 u -0.12 c G ) (_ _ VL
Vgd
( 1 3)
c
Eg. (13) was established from experimental data with water, glycol (30 % and 100 %), methanol, and carbon tetrachloride in columns of 7.7, 15 and 30 cm diameter. Curiously, the correlation involves the column diameter giving d s a.d c -0.3 which is unexpected and probably due to the churn-turbulent flow.
469 Koide and coworkers (27) studied bubble sizes in coalescing media (water) and noncoalescing solutions of alcohols and electrolytes and proposed empirical correlations which involve modified Froude and Weber numbers. However, SchUgerl et al. (1' 6) have shown that the agreement is only sufficient for water and methanol solutions. Solutions of ethanol show large deviations which cannot be explained by surface tension veriation. Comprehensive data on mass transfer and bubble sizes in columns equipped with various gas spargers have been reported by SchUgerl et al. (16). These authors used liquid model media for simulating yeast fermentation, i.e. solutions of alcohols and glucose in the presence of salt mixtures typical in yeast fermentation. Due to the large variability of their findings, SchUgerl et al. (16) did not develop empirical correlations but discussed their results with respect to coalescence promoting and hindering properties of the liquid media and with respect to the bubble size stability diagram derived by Berghmans (28). For a given Bond number defined by
(14 )
Berghmans' analysis
We
a critical Weber number
(1 5 )
which devides regions of stable and unstable bubble sizes as shown in Fig. 7. The coalescence properties are mainly dependent on the added salts and the organic substances present. Let us first consider the effect of salts. If a bubble is generated, the concentrations of electrolyte at the interface and in the bulk liquid are equal at first. The ions have the tendency to move away from the interface, giving an enrichment of water there accompanied by an increase in surface tension. Since the transport of ions in the bulk liquid requires some time, the coalescence hindering action is only pronounced at short residence times of the bubbles. Therefore large effects of added electrolytes on d s (and hence on interfacial area a and volumetric mass transfer effects) can be observed in stirred vessels and multistage columns
470
. x Haberman.Morton (1953) O~ Schugerl. Lucke.Oels (19771 o Oe~kwer. Adler. ·Zaidi( 1978)
1,4 i-
Unst~ble
1.2 We
!egion
~-"'-C~~h.O'.ti,"1 ,\Of
1.0 r 0,8
Stable region
Berghmans (19731 -
\
0.61-
0.4
0.2
analy,i,
,~ 0
0
o
\
Oa.a with in;«'" no,,'. (Aqueous solutions of alcohols and electrolytes I ~
0,4
0.2
0,8
0.6
1.0
Bd
Fig. 7: Regions of stable and unstable bubble sizes
Spilrger
de.cm
L.
137 386
0
1.80
III
1522
v 2512 A
•
100
2791 4309
0
1.760 5496
~
7020
6
.15625 •
p/
.2L
t 19685 030862 ~ 31034 ~ 31455 III S0551
•
lA
~
16"~~.
•
10-1
10- 4
100
10 2
10 6
10' IIBr
E:
d~
vr
Fig. 14: Correlation of liquid-solid mass transfer coefficients
482
Calderbank and Moo-Young (24) for gas-liquid mass transfer from small rising bubbles. If the density difference between the particle and the fluid becomes nil the value approaches its lower li~it~ng value
(29) According to Calderbank and Jones (58) liquid-solid mas~ transfer depended only on physico-chemical properties did not consider\the influence of hydrodynamics, impeller speed, and geometry. other investigations (see, for instance, Boon-Long et al. (59»have shown that such parameters may not be negligible. ' In general, liquid-solid mass transfer coefficients are correlated by expressions like k d
s P
(30)
~ or
(31)
The slip velocity Us is usually difficult to estimate (60). Therefore, it is common practice now to compute the Reynolds number on the basis of Kolmogoroff's theory which gives Re
E d 4 c (--p-) P V3
(32)
Here the exponent p is dependent on the ratio of the particle size to the microscale of the eddies. In the case of tower bioreactors, the energy dissipation rate per uni t mass E can simply be calculated from
(33) While many studies on ks in the two-phase system liquid-solid were carried out only few have been reported for aerated suspensions in bubble columns (61,62). Most recently, liquid-solid mass transfer on suspended ionic resin beads was investigated by Sanger and Deckwer (63) in a bubble column. Aqueous solutions of polyethylene glycol (PEG) of various molecular weight were applied. With PEG solutions which show Newtonian flow behavior
483
the viscosities the diffusivities decreased only slightly (64). Owing to this behavior and the small density difference betw~en the resin beads and the liquid (i.e. 0.1 to 0.2 g/cm ) the results are thought to be particularly relevant to fermentations. Sanger and Deckwer (63) correlated their findings by Sh
=
1 3
2 + 0.545 Sc /
€ d 4
(
V~ )
0.264 (34)
14 shows that eq. (34) describes the measured data fairly well. The proposed correlation is also in reasonable agreement with the results reported by Sano et al. (62). The relative importance of mass transfer resistances at the liquid-biomass interface (i.e. 1/k s a s ) depends mainly on the size of the biomass particles. For instance, in yeast fermentations the particles are in the pm range (1-3 pm). One can show that for typical fermentation conditions (7) ksa~»kLa hence the oxygen transfer resistance is located completely at the gas-liquid interface. On the other hand, K6nig (10) carried out fermentations of Penicillium chrysogenum in bubble columns and found, under special conditions, biomass pellets of 0.3 to 2 mm diameter. Here oxygen mass transfer at the liquid-solid interface (and possibly pore diffusion) should be considered a major resistance since ksas«kLa.
5
MIXING
The global mixing effects in tower bioreactors can conveniently be described by the dispersion coefficients of both phases which are defined in analogy to Fick's law for diffusive transport. Dispersion in liquid phase has been the subject of many investigations which were recently reviewed by Shah et al. (65). In general, the liquid phase dispersion depends mainly on gas velocity and column diameter. The overall liquid flow rate, the kind of gas sparger, and also physico-chemical properties like viscosity and density do not significantly effect liquid phase dispersion. The majority of all the measured data in various bubble columns can be described empirically by a correlation given by Deckwer et al. (42)
484
1.4 - 0.3 ( 35) u G 2 Here EL is in cm /s, d in cn and u G in cm/so A dimensionless form of eq. (J5) under consideration of additional experimental data was recently proposed (66) 2.7
0.34
(36) or . pe
L
= 2 . 83
x Fr 0.34
(37)
Baird and Rice (67) have given a theoretical interpretation of in multiphase reactors on the basis of Kolmogoroff's theory of isotropic turbulence. Their results agree with eq. (3) only the of Fr being 1/3. The predictions of eq. (37) also with the empirical correlations proposed by Kato Nishiwaki (68) and Akita (69). Joshi and Sharma (70) have developed a circulation cell model for bubble columns. This model a circulation velocity U c which correlates well measured dispersion coefficients. The expression of Joshi and Sharma (70) is given by EL = 0.31 u e d c where u
c
( 38)
follows from
=
8
(39) [gd c (u G - EGu Boo 1/3 Eq. (38) also a good description of experimental results and shows approximately the same dependencies on u G and d c as eq. (35) and (36). U
c
1.31
An unusual dispersion behavior was observed by Konig et al.(71) who reported on measurements in bubble columns with porous and employing diluted soof alcohols as phase. The dependency of the gas velocity revealed steep changes and maximum values. The authors interpreted results as being affected by bubble size distribution, i.e. the Sauter diameter of the bubbles, which were measured simultaneously. Figure 15 shows as a function of d s . At very small diameters the entire liquid is attached to
485
2
4
3
---IIiJIIor'"
ds ,mm
Fig.15: EL- VS. d s in diluted alcohol solutions, porous sparger (Kcnig and coworkers, 1978)
1.2 cL
co
I,D
,IT·~: ~ ',~
0.8
pOlnl
Goi150 5Poi11g~f
0.2
0.1
0,2
0.3
0,4
-----
Fig. 16: Homogeneity vs. mixing time
2
ELt/L
0.5
486
the gas-liquid interface and carried upwards, which causes an underpressure and leads to violent eddies_ At medium values of d s (1 to 3 mm) bubbly' flow is assumed to prevail, which yields extremelY,Joyt values of EL- For larger bubbles the flow is churn-turbulent giving again high values of EL- The findings of Konig et al (71) indicate that the structure of the gas-in-liquid dispersion may play an important role in the mixing behavior. However, the interdependence appears rather complex and cannot yet be fully und~rstood. The influence of viscosity on EL was studied by Hikita and Kikukawa(73). Only a small effect was found, i. e. EL ctp-O. 12. Liquid phase dispersion coefficients in aerated non-Newtonian media were not yet measured directly. When matching experimental profiles of liquid phase oxygen concentrations with the predictions of the dispersion model, Schumpe et al. (18) obtained higher EL values than for low viscous media. However, these preliminary results need further clarification by direct measurements. In fermentation technology i t is the mixing time rather than the dispersion coefficient EL which is used to characterize the global mixing effects. The mixing time can be obtained from the transient solution of the dispersion model and is usually defined for 90 % homogeneity. In case a tracer is injected at the column top or bottom the solution of Ohki and Inoue (72) can be used. This solution is plotted for various values of 6 /L (dimensionless distance between injection and measuring point) in Fig. 16. For a desired homogeneity and a given value of 6 /L the value of a(c/c o '
o/L)
ELL
(40)
L2
can be read from the abscissa. Hence, by introducing the correlation for , i.e. eq. (36) the mixing time is given by a( .
(41)
In Fig.17, L is plotted vs~ the tower diameter for three different heights L. It is particularly the slenderness (L/d c ) which largely influences the mixing time.
487
1000
. UG ::
3 cm/s
c/co :: 0.9 oiL:: 0.9
L.cm 1000
500
200
20
50
300
100 d c ,cm
Fig. 17: Mixing time vs. tower diameter Owing to slight density differences between fermentation liquid and biomass the particles have the tendency to settle. Thus a biomass concentration profile along the tower may result. The pertinent model to account for biomass concentration profiles is the sedimentati.on-dispersion model (74,75). This model involves two parameters, namely, the solid dispersion coefficient ES and the mean settling velocity Us of the biomass particles in the swarm. Both parameters were determined by Kato et al. (75) in bubble columns for glass beads of 75 and 163)lffi diameter. The authors presented their results by empirical correlations for both ES and uS. Until other data for smaller density differences are available the application of the correlations of Kato and coworkers is recommended for biological systems also. It should be pointed out that the solid phase dispersion coefficient ES almost completely agrees with EL' i.e. the liquid phase dispersion coefficient. In contrast to liquid phase dispersion coefficients, data on gas phase dispersion are sparse, and, in general, the measurements reveal considerable scatter. Towell and Ackerman (76) proposed the following empirical equation for the gas phase dispersion coefficient
488
(42) This correlation includes also the data of other authors. Most recently, experimental data on gas phase dispersion have been reported by Mangartz and Pilhofer (79). On the basis of their findings with various liquids these authors conclude that the bubble rise velocity in the swarm (uG = u~/ E G) is a characteristic variable which mainly influences gas phase dispersion. Mangartz and Pilhofer (79) recommend the subsequent correlation: iEG = 5 x 1'0- 4
u~3
d 1.5 c
(43)
Though gas phase dispersion coefficients are high, and often considerably larger than those of the liquid phase the impact of gas phase dispersion on reactor performance was seldom taken into account (80), particularly, no experimental or numerical investigations have been reported for biological reactors though, owing to their usually large scale, gas phase dispersion may be of significant influence. 6
HEAT TRANSFER
Fermentation processes are accompanied by heat effects. Luong and Volesky (81) measured heat generation of 12 aerobic fermentation systems. They correlated the heat production with the oxygen uptake rate (OUR) and proposed 0.465 (MJ/mol O ) x OUR 2 where OUR is in mol 02/m3 h. One can estimate from this figure that heat generation in bioprocesses has the same order of magnitude as chemical reactions. For instance, in 3000 m3 fermenter of the Hoechst-Uhde SCP process the UOR is 10 kg 02/m3h giving a heat generation of 4.36x10 8 kJ/h. One has to consider that in case of bioprocesses the heat is deliberated in vessels which are larger by one or two orders of magnitude than conventional chemical reactors. In addition, the temperature level is low, therefore latent heats cannot be used. Owing to the low temperature difference between reaction and cooling media the heat transfer area must be large. Therefore the calculation of heat transfer coefficients is important for biological processes also.
489
Heat transfer coefficients in two-phase and threephase (i.e. slurry) column reactors were recently reviewed by Deckwer (82) and Deckwer et al.(83). The available data can be excellently described on the basis of a theoretical model which gives (82) h
(44)
pCpu G and in dimensionless numbers st
o . 1 ( R~
F r Pr 2 ) -1 / 4
(45 )
Eq. (45) is also in good agreement with the findings reported by Nishikawa, Kato and Hashimoto (84) for low and higher viscous Newtonian media. These authors also measured heat transfer coefficients in CMC solutions. By assuming that heat transfer data in aerated Newtonian and non-Newtonian fluids follow the same dependencies Nishikawa, Kato, and Hashimoto (84) have proposed valuable correlations for the average shear rate as a function of the gas velocity. With the shear rate known, the effective viscosity of non-Newtonian media in the tower reactor can be obtained from the shear stress vs. shear rate curve. In general, use of eq. (45) can be recommended for bubble column bioreactors. However, one should consider the possibility of slime formation and adherence of biomass part~cles at the heat transfer area which might reduce considerably heat transfer.
7
SUMMARY
From the lot of experimental data on physical transport parameters in aerated nonagitated tower bioreactors a number of correlations have been developed. These are thought to give rather reliable estimates for the dispersion parameters, the heat transfer coefficient and the liquid-solid mass transfer coefficients. Gas-liquid mass transfer data are particularly sensitive to the composition of the liquid media and the sparger design, i.e. the initial state of the gas-in-liquid dispersion. Correlations for kLa are based on data from water and aqueous solutions of simple composition. In simulated nutrition and fermentation media large variations in kLa can be observed which are not yet describable by correlations of broader applicability. However, some guidelines to esti-
490
mate the qualitative behavior have been proposed. Future investigations should place emphasis on measurements of physical transport parameters under "in situ" conditions, i.e. during fermentations. Under such circumstances only few data are available.
491
NOTATION specific gas-liquid interfacial area referred to dispersion volume specific gas-liquid interfacial area referred to liquid volume specific liquid-solid interfacial area referred to volume of nonaerated suspension constant in eq. (17) Bond number, eq. (14) or gd~Pl/O
a a' as b Bd c c
constant in eq. (16) concentration equilibrium solubility in liquid phase
c
heat capacity of gas-free liquid or suspension
P D Deff De
diffusivity effective diffusivity in biomass Deborah number, uBI ( Ads) mean bubble diameter
dB d c d
column diameter orifice diameter
0
diameter
d
P d s d s E Fr
Sauter (volume-to-surface) diameter initial Sauter diameter
G
dispersion coefficient / Froude number, u /(gd )1 2 or u~/(gdc) G c oxygen mass flow rate through interface
Ga
Galilei number,
g h k kL
gravitational acceleration heat transfer coefficient thermal conductivity gas-liquid mass transfer coefficient
gd~/V~
liquid-solid mass transfer coefficient tower length power of liquid jet
L P
L Pe
Pe
Peclet number, uBdB/D
L
L modified Peclet number, uGdC/EL
Pr
Prandtl number I V pc p Ik
q R, R'
gas throughput general rate terms
Ra
Raleigh number f
d~ll pg/( )lLDL)
492
Re Sc Sh
Reynolds number, usd p / V or eq. Schmidt number, VL/DL
(32)
Sherwood number, kLdB/PL:or k d /DL s P superficial gas velocity bubble rise velocity
Uo Us We X x Y
gas velocity in orifice slip or s,ettling velocity in particle swarm Weber number, eq. (15) power number, eq. (26) axial coordinate sorption number, eq. (25)
Greek
a.
y E E
A.
~ V
V
o 1:
constant shear rate fractional holdup energy dissipation rate, eq. (33) relaxation time dynamic viscosity kinematic viscosity effective (apparent) kinematic viscosity in non-Newtonian media surface tension mixing time
Indices B G L S
biomass or bubble gas liquid surface of solid
493
1. Bayer Turmbiologie (Bayer Tower Biology) (1978) Bayer Prospec'ts D 991-7127/89 7797 and E 589-777/68 619 2. Leistner, G.,' G. Muller, G. Sell and A. Bauer. Chem.-Ing.-Tech., 51 (1979) 288 3. Zlokarnik, M. Chem. Eng. Sci., 34 (1979) 1265 4. Smith, E.L. and R.N. Greenshields. Chem. Engnq. Janua~y 1974 (1974) 28 5! Schugerl, K. Chem.-Ing.-Tech. 49 (1977) 605 6. Schugerl, Ka, J. Lucke, J. Lehmann and F. Wagner. Adv. BiQchem. Eng. 8 (1978) 63 7. Buchholz, H. Dr. thesis, University of Hanover (FRG) ( 1 979 ) 8. Buchholz, H., R. Luttmann, W. Zakrzewski and K. Schugerl. Chem. Eng. Sci. 35 (1980) 111 9. Voigt, J. Dr. thesis, University of Hanover (FRG) (1980) 10. Konig, B. Dr. thesis, University o"f Hanover (FRG) (1980) 11. Katinger, H.W.D., W. Scheirer and E. Kroner (1979). Ger. Chem. Eng. 2 (1979) 31 12. Kobayashi, Ta, G. van Dedem and M. Moo-Young. Biotechn. Bioengng. 15 (1973) 27 13. Atkinson, B. "Biochemical Reactors;' chapter 4, (1974), Pion Ltd., London 14. Bailey, J.E. and DaF. Ollis. "Biochemical Engineering Fundamentals;' chapter 7, (1977), McGraw-Hill Co. New York 15. Akita, K. and F. Yoshida. Ind. Eng. Chem. Proc. Des. Dev. 1 2 ( 1 973) 76 16. Schugerl, K., J. Lucke and U. Oels. Adv. Biochem. @9:.., 7 (1977) 1 17. Schumpe, A. and W.-D. Deckwer. presented at Int. Syrup. on "Mass Transfer with Chemical Reaction in Twb-Phase Systems ll ACS meeting, March 29 - April 3, 1981, Atlanta, USA 18. Schumpe, A., K. Nguyen-tien and W.-D. Deckwer. Chem.-Ing.-Tech., submitted 19. Hallensleben, J. Dr. thesis, University of Hanover (FRG) (1980). Chem.-Ing.-Tech., to be published 20. Higbie, R. Trans. AIChE 31 (1935) 365 21. Boussinesq, J. J. Mathematiques, 6 e serie (1905) 285 22. Levich, V. G. "Physicochemical Hydrodynamics J' -Prentice Hall, Englewood Cliffs (1962) 23. Frossling, N. Beitr. Geophys. 32 (1938) 170 24. Calderbank, P.H. and M.B. Moo-Young. Chem. Eng. 16 (1961) 39 . Hughroark, G.A. Ind. Eng. Chem. Proc. Des. Dev. 6 (1967) 218
494
26. Akita, K. and F. Yoshida. Ind. Eng. Chem. Proc. Des. Dev. 1 3 (1974) 84 27. Koide, K., K. Kato, Y. Tanaka and H. Kubota. J. Chem. Eng. Japan 1 (1968) 51 • 28 (1973) 2005 28. Berghmans, J. • 8 ( 1 978) 1 33 29. Zlokarnik, M. --:;---:-;----:::..,~--:... Zaidi. Can. J. 30. Deckwer, W.-D., Chem. Eng. 56 (1978) 43 31. Voigt, J. and K. Schugerl. Chem. Eng. Sci. 34 (1979) 1221 32. Tsao, G.T. Abstracts of papers, Session 4, 5th Int. Ferm. Symp., Berlin (1976) (1977) 557 3~. Tsao, G.T. Biotechn. • Bioeng. 19 34. Yoshida, F. (1977) 561 35. Linek, V. and P. Benes. Biotechn. .LJ-'-'-' ..... .I..I.'-1. 19 (1977) 565 (1977) 1889 36. Merchuk, J.C. 37. Alper, E., Y. ~~~~~~~~~. Deckwer. Posterpaper 6th Int. Ferm. Symp., London, Ontario (1980) 38. Alper, E., M. Lohse and W.-D. Deckwer. Chem. Eng. Sci. 35 (1980) 2147 ---39. Tsao, G.T. Chem. Eng. Sci. 27 (1972) 1593 40. Kastanek, F. Collect. Czechoslov. Chem. Commun. 42 (1977) 2491 41. Hinze, J .0. '-r'urbulence "(1975), McGraw-Hill, New York 42. Deckwer, W.-D., R. Burckhart and G. Zoll. Chem . . Sci 29 (1974) 2177 --~3:-Deckwr~r, W.-D. and R. Burckhart. Abstract of Papers, Session 4, 5th Int. Ferm. Symp., Berlin (1976) 44. Deckwer, Wo-D., Jo Hallensleben and M. Popovic. . J Chem. . 58 (1980) 190 , M., C.G.J. Baker and M.A. ~ergoug o Sci 35 (1980) 1121 ---::=--r----;'"...::-.,-....::-.-,- Ho Takeuchi, K. Nakao, H. , T. Tadaki, T. Otake, T. Miyauchi, K. Washime, K. Watanabe and F. Yoshida. J. Chem.Eng. Japan 12 (1979) 105 47. Nakanoh, M. and F. Yoshida. lnd. . Proc. Des. Dev. 19 (1980) ------~----~-----48. Buchholz, H., R. Buchholz, J. Lucke and K. Schugerl. Chem. • Sci 33 (1978) 1061 49. , Hecht and K. Schugerl, Chem. Sci 35 (1 ) ---sO. Hecht, V., J. Voigt and K. Schugerl. Chem. Sci. 35 (1980) 1325 ---S1. Hikita, H., S. Asai, K. Tanigawa and K. Paper at CHlSA '78, Prague 1978 52. Nguyen-tien, ., Diplomarbeit, University of Hanover, 1981 0
495
53. Nagel, 0., H. Klirten and B. Hegner. Chem.-Inq.Tech. 45 ( 1 973) 91 3 . ~4. Nagel, 0., B. Hegner and H. Klirten. Chem.-Inq.Tech. 50 (1978) 934 ---S5. Zlokarnik, M. Korrespondenz Abwasser 27 (1980) 194 56. Kastanek, F., J. Kratochvil and M. Rylek. Collect. Czechoslov. Chem. Commun. 42 (1977) 3549 57. Jackson, M.L. and C.-C. Shen, AIChE-J. 24 (1978) 63 58. Calderbank, P.H. and S.J.R. Jones. Trans. Instn. Chem. Engrs. 39 (1961) 363 . 59. Boon-Long, S., C. Laguerie and J.P. Couderc. Chem. Eng. Sci. 33 (1978) 813 60. Satterfield, C.N. 'Mass Transfer in Heterogeneous catalysis" \1970). MIT Press, Cambridge (Mass.) 61. Kamawura, K. and T. Sasano. Kagaku Koqaku 29 (1965) 693 62. Sano, Y.N. Yamaguchi, and T. Adachi. J. Chem. Eng. Japan, 7 (1974) 255 63. Sanger, P. and W.-D. Deckwer. Chem. Eng. J. (1981i) to be published 64. Lohse, M., E. Alper, G. Quicker and W.-D. Deckwer. EFCE Publ. Sera 11 (1980) 116 65. Shah, Y.T., G.J. Stiegel and M.M. Sharma. AIChE-J. 24 (1978) 369 66. Shah, Y.T., and W.-D. Deckwer, in"Scaleup in the Chemical Process Industries"(1981), Ed. by R. Kabel and A. Bisio, J. Wiley & Sons, New York 67. Baird, M.H.I. and R.G. Rice. Chem. Eng. J. 9 (1975) 17 68. Kato, Y. and A. Nishiwaki. Int. Chem. Eng. 12 (1972) 182 69. Akita, K. Dr. thesis, Kyoto University (1973) 70. Joshi, J.B. and M.M. Sharma. Trans. Instn. Chem. Engrs. 57 {1979} 244 71. K6nig, B., R. Buchholz, J. Llicke and K. Schligerl. Ger. Chem. Eng. 1 ( 1 978) 1 99 72. Ohki, Y. and H. Inoue. Chem. Eng. Sci 25 (1970) 1 73. Hikita H. and H. Kukikawa. Chem. Bng. J. 8 (1974) 7 191 74. Cova, D.R. Ind. Eng. Chem. Proc. Des. Dev. 5 (1966) 21 75. Kato, Y., A. Nishiwaki, T. Fukuda and S. Tanaka. Chem. Eng. J. Japan 5 (1972) 112 76. Towell, G.D. and G.H. Ackerman. Proc. 2nd Int. Symp. Chem. React. Engng. (Amsterdam), B 3-1 (1972) 77. K6lbel, H., H. Langemann and J. Platz. DechemaMonogr. 49 (1964) 253
496 78. Carleton, A.J. t R.J. Flain, J. Rennie and F.H.H. Valentin. Chem. Eng. Sei. 22 (1.967) 1839 79. Mangartz, K.-H. and T. Pilhofer • .J1'erfahrensteehnik (Mainz) 14 (1980) 40 - 80. Deekwer, W. -D. Chem. Eng. Sei. 31 (1976) 309 81. Luong, J.H.T. and B. Volesky. Can. J. Chem. Eng. 58 (1980) 497 82. Deekwer, W.-D. Chem. Eng. Sei. 35' (1980) 1341 83. Deekwer, W.-D., Y. Louisi, A. Zaidi and M. Ralek. Ind. Eng. Chem. ,Proe. Des. Dev. 19 (1980) 198 84. Nlshikawa,M.,H.Kato and K.Hashimoto.lnd.Engng. 16 (1977) 1.
497
BIOCHEMICAL REACTIONS AND OXYGEN TRANSFER INTO DIFFERENT FERMENTATION BROTHS AND REACTORS
K. Schugerl Institut fur Technische Chemie Universitat Hannover Callinstr. 3, D-3000 Hannover 1 INTRODUCTION Few biochemical reaction systems are known which are thoroughly analysed. Since in the author's laboratory detailed investigations have been carried out in tower loop reactors, only these reactors will be considered here. Four different tower loop reactor types were used for the investigations: Two concurrent air lift tower loop systems (a single-stage and a ten-stage reactor) and two countercurrent tower loop systems (a singlestage and a three-stage reactor) . A stainless steel single-stage concurrent bubble coiumn air lift loop reactor, 15 cm in diameter, with a bubbling layer, 275 cm high, and a stainless steel porous plate were used for the cultivation of polymorpha (1) and (2) The same tower was also used as a ten-stage reactor. Nine perforated plates were installed, which separated the tower into 10 sections (Fig. 2). Each of the perforated plates had holes, 3 mm in diameter, and a relative free cross-sectional area of 6.5%. E. coli was cultivated in this reactor (2). A stainless steel, 254 cm countercurrent tower loop reactor, 20 cm in diameter, was operated in a single- or three-stage mode (3) (Fig. 3).
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20 exhaust gas cooler 21 cooling water
pressure reduction valve
22 waste water
gas flow meter
23 thermostat:1.zed water back flow
6
needle valve
24 induct:1.ve liqu:1.d flow meter
7
water vapor (121 'C)
25 alkali reservoir
8
sterile filter
26 ma.gnetic valve
9 valve 10 condensation collector
27 substrate reservoir 28 pressure gauge
11 thermostatized water inlet
29 heated exhAust gas tube sterile gas outlet
12 sampling valve 13 gas distributor
30 safety valve 31 exhaust gas
14 resistance thermometer 15 16 17 18
CO CO -analyzer (exhauat gas) 2 2 02 electrode 02 02-analyzer (exhauat gas) pH electrode or temperature measure and cODtrol compartmen t separa ting tray p U.qu:1.d pump overflow tube V induct1.ve flow meter
Flq.3 Schematical view of the three stage countercurrent tower loop' reactor (Reactor D )
501
At the bottom of the column a perforated plate aerator, 12.4 cm in diameter, and with holes, 0.5 mm in diameter, were installed. In the three-stage column separating were employed, which consisted of a perforated plate with a hole, 0.5 mm in diameter, and a free cross-sectional area of·0.34% and a 20 and/or 40 cm high overflow. Hansenula polymorpha was cultivated ih these reactors (3)·. All of these reactors were provided with pH- and temperature control, 13 oxygen electrodes along the concurrent columns and/or four oxygen electrodes along the countercurrent columns, a flow rate meter for recycling medium velocity, C02, 02' and ethanol concentration in exhaust gas and data loggers to store these data. Biomass, ethanol, and centrations, gas flow rate, and substrate were determined off-line. For seeding, composition of sub- and main cultures, see Ref. 2 and 3. 2
CONCURRENT SINGLE- AND TEN-STAGE TOWER LOOP REACTORS
The measurements of the local properties of twophase systems during cultivation indicate that radial profiles of are fairly uniform. Also, their longitudinal are fairly moderate, except in the neighborhood of the aerator (1, 4). The same holds true for the spacial variations of the local relative gas HV~UU~'~. At low superficial gas velocities the specific area, is fairly uniform also. At high gas (turbulent or heterogeneous the radial profile of a has a shape of an error function, with its maximum in the column center (5). The behavior of these parameters near the aerator depends on the aerator itself and on the medium character. If the diameter of the bubbles, d p , (at the aerator) is larger than the corresponding dynamic equilibrium bubble diameter, de, or if are equal, dS is constant in the aerator vicinity . Only if d~ «defdoes the bubble size increase with increasing d~stance from the aerator, x, due to coalescence until is attained. How quickly ~de is reached depends on the medium property. In systems a depends conon the longitudinal position, x~ a attains a constant value as soon as d&~de has been-established. Also, exhibits a strong dependency on x in these systems in the vicinity of the aerator, if d~~de. Since
502
in the investigated systems dp~de' the spacial dependency of kLa was to be considered by ( 1 a)
(1 b)
where kLa KST
E
is'the volumetric mass transfer coefficient at the gas entrance, x = 0, the "coalescence factor".
The simulations of longitudinal concentration profiles of dissolved oxygen indicate that all profiles could be fitted by assuming a constant validity range of eq. (1):0.= 0.1 L, where L = 276 cm. Thus, in these tower reactors the variation of kLa is only taken into account in the range x = 0 to x = 27.6 cm. In this range kLa diminishes exponentially with x according to eq. (1a) . In the range x = 27.6 to 276 cm, kLa is ~onstant and given by eq. (1b). This kLa is called kLaa. here: (2) The reduction of kLa E at the r~actor entrance to its spacial independent value, kLa a is characterized by the coalescence function, ' (3)
which is influenced considerably by the medium properties and operation conditions. In the following only the kLaa-values will be considered. Since the cultivations were carried out in the homogeneous or laminar flow range, the specific interfacial area, a, was also constant for 0.1 ~ z = ~~ 1 . Thus, the mass transfer coefficient, kL' was catculated by (4)
503
where a is the geometric specific which was calculated by eq. (5) :
interf~cial
area,
(5)
The Sauter bubble diameter, d s , and the local relative gas holdup, £G f were determined in three longitudinal positions in the tower. Since they were nearly identical, it was assumed that they were uniform in the range 0.1~ z~ 1. At first let us consider nonlimited and oxygenlimited growths. At the high medium recycling rates (1000 to 2000 I h- 1 ) the tower reactor exhibited CST~ behavior with regard to the cell mass, X, and substrate, S, concentrations. The longitudinal concentration profiles of dissolved oxygen were nonuniform and were described by a dispersion model (2, 6) with particular u·L Bo-numbers (Bo 0--) and space dependent kLa (6). ax The profiles were fairly uniform in nonlimited growth due to the low oxygen uptake rates (curves 1 to 5 in Fig. 4), and in the strongly oxygen-transfer-limited range due to the high oxygen uptake rate (curve 8) . At the beginning of oxygen transfer limitation (curve 7 in Fig. 4 and curves 1 to 3 in Fig. 5) the nonuniformity of the profiles is most significant. The dissolved oxygen was not recycled in the oxygentransfer-limited growth range, because it was consumed in the loop, as can be observed in the upper part of in which the dissolved oxygen saturation is plotas a function of the cultivation time, t, measured for Hansenula polymorpha on ethanol substrate at three different positions. At the end of the loop (z -0), no oxygen could be detected even at t 14 h, that is, "before the oxygen transfer limitation begins at t = 15 h (see the lower part of Fig. 6). By using the dispersion model, the dissolved oxygen concentration profiles were calculated and fitted to the measured ones, thus kLaE , kLa U and KST were identified. In Fig. 7 kLa U is shown as a function of the cultivation time for H. polymorpha and ethanol substrate (1). After inoculation kLa U drops to low values, then quickly increases at t~8 h, passes a maximum and diminishes at first rapidly and a£ter 14 h, gradually. In the specific interfacial area, ~,
504
1 T; 2.0h T= dOh T= 10.Oh "T:: 1 2 . 0 h , - i - - - - - - + - - - - - I - - - - - - - i S T= 13.0 h 6 T =".0 h 7 T=17.0h
2
3
!!JJl I
8 T =255 h
8~----+----~----+_---_;
0.25
0.50
0.75
1.00
z (-] ~: w!!~idunal
concentration profiles of dissolved oxygen, 1 ) ill Peactor A durill<J H. rx:>lyrroroha cultivation at different cultivation times,t.Substrate concentration: S = 5 g 1-1 ethanol.
r::x:x:
(mq
,.-------~------~------_r------~
o
t ... 11 h
... t::lt 19h • t :Ill 28h
°O~----~Q~.Z~----~O'~~~----~O~.~=-----~4~OO
zF~g. 5
:wn0itudinal concentration profiles of dissolved oxygen, cultivation at different cultivation times,t.Substrate concentration: 5 g/l ethanol (under strong oxyqen transfer limited grcwth).
rxx::
(:mq/l) ill Reactor A durin~ H.Pol~Jffi:Jrpha
505
fa
V
V
L
~ ~
~I"
,V/ /
~
1/
.J
1I/
/
.r
,(
,dMdrd cul'ur~ EIOH -conc~nll0'ion : 5 g/I
/ / //
a~,a l ;on :
r--
0.55 nm
r-
• EtOH .. utilization o X, b;omau -COlX .
VI- V
• 0., .OTR " Qco, ,COl product,on ra'~
1')/
5
I"
J'
",
.L
0.2
r-.
I V ~V V./ V/ .
10
15
t-
~
20
r--
I h
30
Ficj.6: H.polyrror)!ha cultivation m Reactor A employing substrate ethanol m extende culture oneration.Substrate concentration: 5 g/l kept constant by substrate feed.Aeration rate 0.55 VVffi. UpDer part of fiqure: relative saturation of dissolved oxygen as a function of the cultivation tirne.Longitudmal position of the 02 probes: - 11 z= -0 ( just below the aerator) • z= 0.90 ( at the aerator) A z= 0.90 (at the tower head) Lower part of figure: variation of the cultivation \.vith time III substrate untake rate (0,"/l.h) o (dry) cell InasS concentration, X (g/l ) A oxygen uptake rate ( g/l.h ) V CO production rate (g/l.h) 2
506
1800 ~;t....
h-1
f 1200 kia
1000
\
r I1
11,()()
,J
/
,:
\.
0 I--:,-..
~
0
~
800
5
10
15
20
~
b
30
h
t-
Fig.7:Volumetric mass transfer coefficient,~a,as a function of the cultivation time in Reactor A durinq the cultivation of H.nolvrrorpha on ethanol substrate,S= 5-'0"/LAeration rate:O.55vvm. 1600
0/
V
0
n
/0
1200
---
0~ '\
1000
V
I
0 200
to
20
h
.30
1-
Fin.8: Snecific interfacial area,a, as a function of the cultivaaion tfue,t, in Reactor A durin9 the cultivation of ·H.nolvrroroha on ethanol substrate , S= 5 g/l. Aeration rate : O. 55 vvm~'" .
507
calculated by eq. (5), is plotted as a function of t for the same run~ An initial drop, then a quick increase is common for kLa U and·~. However, k a U passes a maximum earlier and drops more rapidly, wkile a attains its maximum later and diminishes only slightly~ The mass transfer coefficient, kL' was calculated by eq. (4) (Fig. 9). For t ~ 4 h i t is constant, but soon after it gradually diminishes for t~15 h somewhat quicker, then slighter(1}. U The courses of kLa and ~ as a function of the cultivation time are rather different during cultivations on ethanol and glucose substrate (1). When using glucose, the dissolved oxygen concentration diminishes with increasing t as usual, but at 3.5 h it passes a minimum and gradually increases (upper part of Fig. 10). However, the deviation from exponential growth was not caused by growth limitation, because sufficient substrate and dissolved oxygen were present (Fig. 10 and upper part of Fig. 11). The reduction of the growth rate is accompanied by diminutions of the yield coefficients Yx/o and YX!S and the cell mass productivity (middle and lower parts of Fig. 11). Also, ethanol is produced (upper part of Fig. 11). 9bviously some kind of repression has occurred due to glucose. The longitudinal dissolved oxygen profiles are similar in this range to those measured in systems with ethanol substrate at the end of the exponential growth phase (Fig. 5 and Fig. 12). By fitting the calculated profiles to the measured ones, the corresponding kLaU-values were determined. shows that kLa U increases with t. The same holds ~ (Fig. 14). This is caused the increasing ethanol concentration. The kL-value is nearly constant (Fig. 15). A comparison of kLaa-values with ethanol and/or glucose substrate show that the former kLa a. is much higher (1400- 800 h- 1 ) than the latter (150~700 h- 1 ) (Fig. 7 and ll). With increasing alcohol concentration in the glucose system the kLa -values also approach 800 h- 1 . The same is true for the specific interfacial area, a, with ethanol (600-·1200 m- 1 ) (Fig. 8) and with glucose (200_1000 m....,1) (Fig. 14). kL-values are also higher in the ethanol (Fig. 9) than in the glucose (Fig. 15)system, but with increasing time and ethanol concentration they approach the same value. U The influence of ethanol concentration on kLa is a shown in Fig. 16. kLa increases with increasing ethanol concentration. Also, the operation mode influences U kLa U . In media with oxygen-tran3Port-limited growth kLa is the smallest. In Fig. 17 kLa is plotted as a function of the superficial gas velocity, W . In tower loop reacSG
508 0.06
cmls
~
\
"
:
~
\
~
0 ~
0
~~
--.......
0,01
5
15
10
20
30
h
t-
Fig.9:Mass transfer coefficient,kL,as a function of the cultivation tlllle,t,in Reactor A during the cUTtivation of H.polymorpha on ethanol substrate, S=5 g/l. Aeration rate:O.55 vvm.
'2
Fig. 11.Variation of yield ~ g/l1 coefflcients,yX/O and YX/S uo respiratory quotient,RQ, 8 ~ cell mass concentration, ~ X,cell productivity,Pr, 2,~/O and produced ethanol concentration as a function of cultivation time f t 1,6 in Reactor A during the l,WR.Q cultivation of H.polymor0, 8 pha at high glucose concentrations (S=9.2 12/0 g/l ).
- .
.
.
~
7 •
g/l
f g
8 (5
c:
0.8 .g
/'
... /
~
"-
'"
............ .YX/O "Yx/S
~ ~
0.2
~
"R.Q. ..P'
X
2;'
'/ ./
-Glucose (substra re) . o E thano/ (pro duced )
Cl)
fgll
V
1/ :/"'~~ 2
6
~
8 t-
~
gfhM
. t
0.8 h
12
0
Pr
509
~--
ill,o~~~~~~-+~~-r-*~--~~ (jVl
.~'O
~~
%~--~--~--~6--~8~--~h--~~~ t-
-""
!
1.0
20
/V
8
/
6
/ V
" V 2/ V V/ 1 fi ,81/
I
I I
L
~
//
/J
extended culture [glucose-cone.: a2 g/l :O,55vvm aeration III glucose utilization o X,biomass-conc.
V
o.I.~ I
"Gol,OTR .. Geol , CO2 production
,
Q,2
o
...0
~V
/
0,1
~
....,.. 1--'0
10
q6
/'
......
2
6
I
I
ratT
8
h
12
-
t---
Fig.lO : H.polyrnoroha cultivation in Reactor A ernployin~ 9lucose substrate in extended culture operation.Substrate concentration S = 902 g/l , constant substrate feed.Aeration rate: 0.55 VVffi.
part of the figure: dissolved oxygen concentration as a function of the cultivation tin1e.Lon('fitudinal position of the oxygen probes:
Upper
Z=
-0
Z= 0.09
z= 0.90
(just belc:r.v the aerator) (at the aerator) . (at the colUI!ll1 head) variation of the cultivation ,..,ith
<Jlucose uptake rate (g/l h ) (drv) cell mass concentration,X , (q /1 ) oxygen uptake rate (g/l.h); CO2 production rate (.
2 tm IV V
II
1
-
o
~
VI VII
vm
I
1)(
x
I
8.0 r----...,--...,--..,-...,---,---,:---r--r--,---,
t
::cc
o
~ o
\ \
\ \
20
\
n
I
,
\
ill
IV \V VI \
X
\ \
0,2
0,4
Z
...0,6
0,8
1,0
·fi ry.'19:. Longitudinal pro;Eiles of. cell mass concentration,X, substrate .concentration ,S, (uppe:- part) during the cultivation of E •'Coli in P.eactor B in batch and continuous operation
ox,
A S
(continuous)
upper
part
o IX)S at t :; 40 I!Ul1 (batch) A .ros at t =- 220 :m:in (continuous) lower part D OOS at t = 270 :m:in (continuous) A. ros at t :. 400-820 min (continuous) I-X are
the stages counted fran the bottan.
515
tors without,loop (measurements of Oels (7» kLa incre~ ses with WSG up to ~ cm s-1. In tower loop reactors kLa U increases with WSGr passes a maximum at about 3 cm- 1 , then diminishes (4). This is due to the increasing medium recycli~g rate, VR " In Fig. 18 kLa is shown as a function of VR during E. coli c~ltivation (2). The reduction of kLa with increasing VR is significant. This is mainly due to the reduction of EG' If the nonlimlted growth along the tower turns into substrate-limited growth, the longitudinal dissolved oxygen concentration profiles pass· a minimum at this position. These longitudinal profiles can only be simulated with a distrjbuted parameter model with regard to the substrate (4). In Fig. 19 the longitudinal cell mass, X, substrate r S, and relative oxygen, 0L/O*, concentrations are shown in the ten-stage concurrent tower loop reactor with E. coli (2). Whereas X and S are uniform in the tower, 0L/O* diminishes with Zr but remains higher than 0.5 at high liquid recycling rates and in batch operation. Thus, no oxygen transfer limitation occurs. In continuous cultivation 0L/O* drops to zero. With increasing cultivation time the numbers of stages increase, in which the oxygen supply of bacteria is not sufficient (Fig. 19). (The increase of 0L/O* in the 10th stage is caused by the mechanical foam destroyer at the top of the column, which also acts as an aerator). The inadequate oxygen transfer rate in the ten-stage tower is due to the formation of liquid-free layers below the perforated trays, which acted as very ineffective gas distributors, because of their large holes (3 mm in diameter) and free cross-sectional area (6.52%). In addition, the efficiency of the stage separating trays probably deteriorated because of foam formation below the trays. 3
COUNTERCURRENT SINGLE- AND THREE-STAGE TOWER LOOP REACTORS
In Fig. 20 the volumetric mass transfer coefficients are shown as a function of the cultivation time with H. polymorpha and ethanol substrate (3). In the threestage tower with a bubbling layer height of 40 cm considerably higher kLa-values can be attained than in the single-stage one with a bubbling layer of 160 cm height. However, whereas in the single-stage tower reactor the cultivation could be carried out without any difficultYr the multistage reactor could not be operated in absence of antifoam agents, since in this case the free volume
516
lOCXJ
F iq .20; Caonarison of the volurretric mass transfer coefficients ~als in Reactor C (single sta0'e tower loop) and Reactor C and- D (single- and three-staqe ta-rer loops) .
0.......: ..
- 0.25
-.....-.- ~ ~ ...
"-../
600
~
t 400
• -:
- 0,15
:
~
~
~
~ 200
..
~ .....
t
- £110 a
- 005
~
o single-stage 8
• three-stage (h::::
40 cm)
12
h
16
to single stage • multistage. H",I.OO mm no antifoam agent
20
Fig. 21 :Cell mass concentration X1 as a ftmction of the cultivation of H. palvrrnrpha in Reactor D (three-stage tcwer) in the absence of antifoarn agents employing substrate ethanol
I
li :lZOOI/h ~
16
j
A 3. stage (at the bottom)
/ )
I. V / /
o 1. sta0e (at the top) 2. stage
7 V
501
g//
12
•
#
10
X 8 6
I V / )
j
2 ~
f"
V
/
,/
........ ~
/
8
1. stage • 2. stage oil 3. stage
o
/ 12
t--
rL
16
~
h
multistage, H :lI.OOmm no on tifoam agent
517
between the bUbbling layer and the tray above the layer became filled by foam. By microflotation,the cells which were enriched in f6am, passed through the tray into the stage above. Here they were enriched in the foam again and so on. Through this microflotation effect, the cells were enriched in the upper stage; in the lower stages the qell concentration was diminished 'considerably (Fig. 21). It was not possible to reduce this cell segregation by increasing the liquid circulation rate, since the liquid transport capacity of the overflow was reduced considerably when foaming broth was present. To avoid this segregation antifoam agent WqS used. These runs with antifoam agent were carried out with two different bubbling layer heights: H = 20 and 40 cm in the three-stage tower. During the cultivations no foam formation was observed. Also, no differences were found in the cell mass concentrations of the three different stages. In Fig. 22 the volumetric mass transfer coefficients are plotted as functions of the cultivation time for the single-stage and the three-stage columns at H = 40 and 20 cm. The lowest kLa-values were found in the single~stage tower and the highest ones in the threestage tower with H 20 cm. The installation of trays improved the kLa-values. This improvement increased with diminishing bubbling layer height. 4
COMPARISON OF THE SYSTEMS
Because of the low liquid velocity, the difference in EG in the concurrent and the countercurrent tower reactors is slight. Therefore, they can be compared directly. In the concurrent single-stage tower reactor with a porous gas distributor (Reactor A) and the countercurrent one with a perforated plate gas distributor (Reactor C) are compared. One recognizes that OTR, kLa as well as the productivity, Pr, is much higher in Reactor A than in Reactor C due to the more efficient aerator. In Table 2 the single-stage and ten-stage tower loop reactors are compared. Because the stage-separating trays act as gas distributors and their efficiency is very low (3 mm hole-diameter and foam formation) f the single-stage tower with an efficient aerator yields a much higher productivity than the ten-stage tower. In Table 3 the single- and three-stage countercurrent tower reactors are compared in absence and pre-
518
400 0,100 h-I
0-
S-I
fj 200 0
0
:..., ..:oc
~
100
8
12
15
h
24 0
t ---single stage • multistage. H=400mm &. multi stag e, H = 200 mm antifoa m agen t: Desmophen o
Fier. 22 :Volurretric mass transfer coefficients I~a 's, as function of the cultivation t:irne, t, during the cilltivation of H.polymorpha in Reactors C and D employing substrate ethanol and Des:rrophen 3600 as antifoam aqent. o single stage • three-sta~e I h 40 cm A tree-sta0'9, h = 20 cm
=
519
Table 1: C01tI[.)arison of the perfo.rm:mce of Reactors A and C en:ploying H. palyrrorpha ·on ethanol substrate. Yx/ O _, ~a, 0l'R and Pr 0
.
In this case y opt
d~minishes
Da and K. (per Da< Dacrit and70r K> Kcrit
On the other hand f for Bo < Bo opt' "V opt
with increasing = 00 (CSTR)y
"I opt
= o.
528
3.2
Optimization with Regard to Cell Mass Productivity
It is obvious that maximum cell productivity can be attained if the cells are cultivated in the nonlimited growth range. However, when using cell-free feed, non~ limited growth systems are unstable (1). Furthermore, the substrate loss is considerable for nonlimited growth operations. Because of this, nonlimited.growth is an uneconomical operation. However, it is possible to maintain nonlimited growth at the entrance of a tower reactor and substrate limited growth at its exit and by that to achieve high productivity and substrate conversion in a stable steady state (2). In this case the reactor behavior can be described by the substrate limited rate equation. There is formal analogy between autocatalytic reactions and cell growth with substrate limitation. Bishoff has shown (4) that the maximum growth rate can be attained, if one uses a combination of a CSTR and a PFR. The size of the CSTR has to be chosen so that the growth rate has a maximum in it. The size of a CSTR can be graphically by plotting the inverse growth 1 as a function of the cell mass concentration, 1 and 2 show such plots where the dimensionless growth rate is
~"*
(4)
the growth rate according to Monod
'*
RX =~m
(5 )
and the dimensionless cell mass concentration
x
(6) -1
Figs. 1 and 2 show that RX passes a particular Cx which is called CXcrito For the CSTR is the optimum reactor. CXcrit is by (K+1)
-,J
K(K+1}~O.5
(7)
1~~\ I t~\~ 1IRx 10
•
F I\,""-
100 h
50 ~
0.15 0.30
/. 0.50
5
I I
I
1/JL
I \:\ t ~""
K .0.250
\
)10.125
= 0.5h-1 ---1lH = 0.3h-1 K= 0,050
-iJ.H
'1o ' (.-
, AA
., A.
, A~
I AA
, .A
(x---
Fi0.1:Reci~rocal related growth rate,p~l,as Fiq.2: Reciprocal related growth rate,R-l,as function of the dimensionless substrate a function of the dirrensionless .§yt;stra£e concentration,C ,at K = 0.125 for different concentration,C , at 1-1 0.5 h ( - - ) ~max.Caffibinatiofi of CSTR and PFR (3). and variable K,xas welJBX as ~ = 0.3 h- l and K = 0.05 (- - - -) (3).rnax
=
VI
N
1.0
530
i.e. for
Cx~0.5,
the CSTR is always the optimum reactor.
If a tower reactor with n'egligible longitudinal dispersion (PFR) is used,mi~ing can be controlled by employing medium recycling. There is an optimum recycling ratio, 'Yopt, at which RX reaches its maximum (3). If the dimensionless cell concentration is fixed at the exit of the reactor, CXF ' and a reactor' is used which yields the smallest necessary, volume, V R , and a mean residence time of the medium,~ or Da, i t turns out that there is a PFR'loop combination with 'Y opt at which Da has a minimum (Fig. 3), if CXF > CXFcrit where CXFcrit = (K+1) -
JK(K+1)
For CXF~ CXFcri t, 'Y opt = For CXF > CXFcri t
00
(CSTR)
g+-V
-y
( 1+ 'Y)
Da
where
T1
[
in
~ ++ 'Y
(8)
+ K in 11 + 'Y
]
(9 )
Cxo CXF 1-C
S
XO 1-CXF
'Y opt, to a considerable cell mass concentration, CXF' 'Y opt increases and 'Yopt also depends on K: ishes (3)
degree, depends on the exit CXF (Fig. 4). With d~creasing for CXF 6: CXFcri t, 'Y opt, = 00 with increasing K''Yopt dimin-
When using a tower reactor with longitudinal dispersion and medium recycling the relationships for substrate limitations (chapter 3.1) can be employed since the exit cell mass copcentration, CXF ' can also be written as YX/S (So-Se) Xo+YX/SS o
S -S o e - S - - = Us o
( 10)
Thus, reactor optimization with regard to Us (chapter 3.1) is also optimization with regard to C ' XF
6
5
On 4
Yopt =1.617
(S TR
3 2
0.001
0.005 0.01
0,05 0.1
0.5
5
10
50
100
500 1000
Y
Fiq 03: Da PFR with
number as a function of the :medium. recycling ratio for loon at K = 0 Sea = 0, = 0.95 (3).
VI
~
532
soo
100
K= 0.125 Vopt
::::0,75
(lCFcrit
1
O~.7
0,8
0.9
1.0
(xF---Fig. 4 : Optirmnn recycling ratio Yopt, as a function of the exit cell mass concentration'~ CXF' for PFR with loop at K 0.125, ~o 0.1 (3).
=
=
533
3.3
Optimization with Regard to the Oxygen Transfer and To maximize the oxygen conversion, U o OUR DOLO+OTR
( 11)
is the dissolved oxygen concentration in the medium at the medium entrance,
where
z=1 OUR
J
1 y-
r
kLa(OL - 0L) dz, the oxygen transfer rate,
z=O z=1 OTR
z=o
il.xdz, the oxygen utilization rate
X/O
.
*
growth must be oxygen transfer limited, at least at the medium exit. This leads to a problem similar to the one considered in chapter 3.1. However, the theoretical treatment of this system is more complex, since oxygen is transferred into the medium along the tower. This treatment is not considered here. In the oxygen transfer limited range, cell productivity is controlled by the OTR. In the CSTR, for maximum productivity, Prm , eq. (12) holds: Prm r-I YX!O kL a(o~ -
O~)
;
( 1 2)
since usually D(OLO - O~)«kLa(o~ - O~). Here, O~ is the critical dissolved oxygen concentration in the medium below which the cells cannot utilize oxygen and 0L is the saturation value of 0L" Because of the low oxygen solubility the maximum driving force (OL*- OE) is low. Yx/ O is determined by the microorganism and the substrate. Thus, Prm can usually be controlled by kLa. Since the variation range of kL is narrow the specific gas liquid interfacial area, ~, is the nain controlling parameter. ~ is given by: a
=
( 1 3)
if d S is small. Since EG is also a function of d S the Sauter bubble diameter, dS, is the primary variable.
534
d S is a function of the energy dissipation rate in the reactor and also depends on the medium properties with regard to bubble coalescence. It has been shown (5) that in coalescence suppressing media aerators with a spacially concentrated energy dissipation rate and in coalescence promoting media aerators with a spacially distributed energy dissipation rate give the highest OTR at the same specific power input, P!VR* However, in the same medium and with the same type of gas distributor the OTR also depends on the efficiency of the aerator. The higher the fraction of microeddies in the turbulencefthe higher the efficiency of the aerator. To minimize the specific power input the aerator efficiency has to be maximized. This holds true for primary dispersion. To minimize the specific power ~nput P/VR' the coalescence rate has to be minimized as well. Different strategies for minimizing the coalescence rate were considered in ref. 5. 4
PARTICULAR BIOREACTORS
Because of the wide variety of bioreactors it is difficult to classify them according to a physically acceptable system. They can be classified according to their construction or operation. However, here the power input mode is chosen as a decisive criterion. According to this criterion ,three different types of bioreactors can be distinguisned: 1. Power (Fig. 2. Power (Fig. 3. Power
input with mechanically agitated insertions 5, Table 1), input with a liquid pump in the outer loop 6, Table 2), input with gas compression (Fig. 7, Table 3)
Before the different reactors are briefly considered some general statements with regard to gas dispersion should be made. It is useful to distinguish between primary and secondary gas dispersing facilities. In a stirred tank, the gas is introduced into the ~edium through a simple tube, ring nozzle, etc. and dispersed only coarsely. The fine dispersion is carried out with a secondary gas dispersing facility (impeller). In a multistage tower reactor,the primary gas dispersion is usually carried out with a perforated plate or porous plate, the secondary gas dispersion facilities (stage separating trays) redisperse the large bubbles formed by coalescence from
535
TABLE 1 Bioreactors with power input due to mechanically agitated insertions (Fig. 5) (20) rotating impeller rotating impeller and loop (HID ~ 2) rotating impeller and loop (HID> 2) rotating self-aerator impeller rotating self-aerator impeller and loop rotating self-aerator impeller horizontal loop cascade reactors with rotating impellers cascade reactors with axially·oscillating mixing elements 1 .9 cascade reactors with pulsed l~quid 1 .10 rotating film reactor 1 . 11 rotating disc reactors 1 .12 rotating vane wheel reactors 1•1 1 .2 1 .3 1 .4 1 .5 1 .6 1 .7 1 .8
TABLE 2 Reactors with power input due to a liquid pump in the outer loop (Fig. 6) (20) 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9
plunging jet reactor jet loop reactor plunging channel reactor nozzle loop reactor multistage countercurrent tower reactor tubular loop reactor reactor with rotating injector counter current packed tower reactor concurrent down flow tower reactor
536 G
G
LR
LR
G
G 1.1
1.2
1.3
1.3
iiberfiillt
m;t .Uberlauf
LR
G
1.'
1.5
engine gas (air)
M
G
SB
LR
baffles draft tube
engine SZ foam destroyer G gas (air)
M
LR draft tube self-aerator impeller
1
G
G
G
~
t
I W
~@)
F G
M G
G
1.9
1.8
1.7
G
Pulsation
112
engine drum 1.10
Fig. 5: Bioreactors with power input due to mechanical insertions (20).
G
i
W
2M 1.11
537
TABLE 3 Reactors with power'input due to gas compression (Fig.7) ( 20)
3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9
Single-stage tower reactor single-stage air lift ,with a draft tube loop .single stage air lift with an outer loop single stage air lift with a partition wall concurrent down flow loop reactor (deep shaft reactor) concurrent multistage tower concurrent tower with static mixer tower loop with trays mUltistage tower loop with liquid pulsation and static mixer
TABLE 4 Sorption characteristics of aerators according to Z lokarnik (21) X ·1
Aerator single orifice 6.2 perforated plate ~ 6.4 (3 mm in hole diameter) 8.8 perforated plate (1 mm in.hole diameter) 14.0 porous plate submerge aerator of Frings* 9.5 static mixer (Kenics) 6.0
*'
'*
injector nozzle
*'
ejector (slot) nozzle
'* in '* * in
10.0 { 13.0 10.0 { 15.0
independent independent independent independent independent 1 • ~n}dependen t
~:g
H =7 m
2.0
bubble column bubble column and with sulphite solution
538 G
F
F
F 2.lI F
)( 2.5
2.3
1.6
2.8
f' liquid, G gas
Fig. 6: Bioreactors with power pump in the loop (20).
i~put
due to liquid
539
I I I
G
3.1
G
3.3
G
F 3,6
3.5 G
G 3,9
F :.1.7
3.8
F
liquid, G
gas
Fig. 7: Bioreactors with power input due to gas compression (20).
540
the small primary bubbles. In the latter case the degree of secondary gas dispersion is much lower than that of primary dispersion. It is useful to distinguish between coalescence suppressing and promoting media. In coalescence suppressing media the gas dispersion should be spacially concentrated (usually to the bottom of the :reactor). The high dispersion degree of the gas phase which is achieved in this range is largely preserved also if the bubbles arrive in ranges in which the dynamic equilibrium bubble sizes are much larger than the primary bubble sizes. The bubble diameter is mainly influenced by the primary dispersion degree and only slightly by the conditions which prevail in their actual surroundings. In contrast to this, in coalescence promoting media the gas dispersion should be uniformly distributed within the reactor since the actual bubble size is controlled by the dynamic equilibrium bubble size in their momentary surroundings. For the optimal strategy for the spacial distribution of the energy dissipation rate in the reactor, see' ref. 5. 4.1
Reactors with Power Input due to Mechanically
In the following, only the physical action of a turbine stirrer should be considered because i t is the most popular and best investigated stirrer type. The movement of the fluid in a stirred tank reactor enforced by a rotating impeller can be divided into primary and secondary flow patterns. The primary movement is the Lotational or tangential flow of the fluid. Most of the ~nergy transferred from the stirrer to the fluid is consumed by this movement. This controls the gas dispersion. However, it is of minor importance for the mixing process. The secondary movement consists of radial and axial components (Fig. 8). In mixing processes the secondary movement is the most important part of the flow pattern. Only a small fraction of the energy transferred to the fluid is contained in this secondary movement (6). Behind the upper and lower edges of the impeller gas is sucked into the wakes by the underpressure which prevails within them and dispersed by the high local shear stress. The bubbles formed in the wakes are collected in the core of the vortex. Bec,ause of the high bubble concentration in the vortex core, bubble coalescence is promoted here. The vortices lose their energy and thus their rotational speed with an increasing distance from the impeller due to internal friction. As a consequence, the
541
Fiq.8: Streamlines of secondary fluid movement(6)
Fiq.9: Bubble qeneration in vortex threads in the wake of a turbine stirrer (6).
542
underpressure reduces in the vortex core and the bubbles gradually become free. Their size depends on the local energy dissipation rate which prevails at this position, if a coalescence promoting medium is used. In the vicinity of the impeller blade pseudo-macroturbulence with a strong periodical character prevails which gradually transfers into true turbulence with an increasing d~s tance from the impeller (7). One can ass:ume that on the vortex surface free turbulence with microscales is formed which is very efficient with regard to gas dispersion. However, this free turbulence can hardly be used for gas dispersion since the bubbles are held together in the tube-like core of the vortex. At the position where the bubbles become free from this core, the free turbulence intensity has ~lready been reduced considerably. Hence, the energy dissipation in the vortex cannot be used very efficiently for gas dispersion. Only at longer distances from the impeller where the vortex has already been decomposed into small turbulent eddie~ can microturbulence be detected which is marked by a high energy dissipation rate, a nearly isotropic property and a high efficiency with regard to gas dispersion (8). Because of the high shear forces in the range of the impeller blades the size of the primary bubbles is much smaller than the size of the bubbles which are formed at the vortex end by microturbulence. Therefore the efficiency of the power input with regard to gas dispersion in stirred tank reactors is rather low. 4.2
Reactors with Power Input due to a Liquid Pump in
The utilization of the power input can be very different depending on the aerator type. Since gas dispersion with injector and/or ejector nozzles and plunging jets have recently been investigated fairly thoroughly, only these two gas dispersion organs will be considered. The mechanism of gas dispersion with ejector nozzles was investigated by Klirten and Maurer (9) and Hallensleben et al. (10). Through the internal nozzle a fast liquid jet is formed. From the buter annulus (nozzle) gas flows into the momentum exchange tube in which a large bubble is formed at first. The fast liquid jet pulsates and decomposes into fine droplets which hit the gas/liquid interface of the large bubble and destroy it. The small bubbles formed during this process are redispersed into much smaller bubbles in the momentum exchange tube due to the high dynamic pressure of the
543
turbulence which prevails in it. The mechanism of gas dispersion by means of plunging jets was investigated by Smith et al. (11), Burgess et al. (12) and Suicu et al. (13). By means of a nozzle a downcoming liquid jet is produced which hits the liquid pool surface and penetrates into it (2.1 in Fig. 6). The jet identity is preserved until a gas envelope of the jet exists. The disintegration of this envelope yields small bubbles of high density which move downwards in the liquid and in a transverse direction. Hence the bubble swarm forms a cone. This two-phase jet drags the surrounding liquid downwards due to its momentum exchange and mixes with it. Due to this the gradually decelerates. At the boundary of the two-phase jet and the surrounding liquid free turbulence develops. Its thickness increases in the direction of the flow. The final gas dispersion is again caused by turbulence. Large bubbles which are formed by coalescence from small bubbles rise and leave the pool. The small bubbles are dragged with the liquid and separated from it in a two-phase separator pump. The liquid is pumped to the top of the reactor and the loop is closed by forming the liquid jet by the nozzle. The properties of the liquid jet significantly influence gas dispersion (11). 4.3
Reactors with Power Input due to Gas Compression
Three ranges of gas dispersion can be distinguished: single bubble formation at low aeration rates, gas jet formation at intermediate aeration rates and dispersion in a turbulent field at high aeration rates. The range of single bubble formation was investigated most thoroughly (14). However, this range is not interesting in practice. The bubble formation in the second range is caused by the nonstable interface between the gas jet and the surrounding liquid. The bubble formation mechanism is analogous to the droplet formation from a liquid jet according to Rayleigh (15). Me'ister and Scheele developed a theory for this bubble formation (16). Hallensleben et al. (10) investigated this bubble formation experimentally and confirmed the theory of Meister and Scheele. If the aeration rate is increased the primary bubble size increases at first, then passes a maximum and diminishes. In the increasing size range, single bubble formation occurs, at the maximum, gas jet decomposition prevails and in the decreasing size range, a turbulence mechanism is responsible for bubble forma~
544
tion (10). The latter bubble formation mechanism prevails in industrial reactors. 4.4
Compa~ison
of the
Diffe~ent
Reactor
Typ~s
The considerations in 4.1 to 4.3 show that in the operation ranges which are important for the industry gas dispersion is always caused by turbulence, thus the comparison of different reactors with reqard to the oxytransfer based on the turbulence theory should possible . .Kolmogoroff (17) postulates that, at Reynolds numbers of turbulent motion, the local property of turbulent motion should have a universal character described by the following concepts. First., it is locally isotropic whether the large scale motions are isotropic or not. Second, the motion at the very small scales is chiefly governed by the viscous forces and the amount of energy which is passed down to them from the larger eddies. The large eddies tend to break down into smaller eddies due to inertial forces. These in turn break down into still smaller eddies and so on. At the same time, viscous forces dissipate these eddies into heat at very small scales. In the long series of cascading processes of reaching the smallest eddies, the turbulent motion adjusts itself to some definite state. The further down the scale, the less the motion is dependent on the large eddies. Furthermore, in line with Taylor's experimental findings, Kolmogoroff essentially postulates that practically all the dissipation of energy occurs at the smallest scales when Reynolds number of turbulent motion is sufficiently high (18). When assuming the validity of this theory, the microscale, 1, depends only on the power input, P/VR and the liquid porperties.
11 3/4 1
F
P 1/2 F
where~
(~) -1/4
VR
( 1 4)
F is the dynamic viscosity of the liquid and
P F the density of the liquid. If one assumes that the local structure of turbulence does not change in the presence of bubbles, relationship (15) holds true for the dynamic equilibrium (maximum stable) bubble size, de' which must be considerably larger than 1 (19).
545
"'C0.6
C ' 1 P
F
(~ ) -0.
4 ( 1 5)
'R
where"'C is the surface tension of the liquid 'Several relationships analogous to eq. (15) were developed (20). However, if de were only the function of"'C , p and p/VR,all of the aerators would result in the same de value,in the same medium and at the same specific power input, P/VR- This is obviously not the case. Of course 1 for coalescence s'uppressing media the deviation from this expectation could be caused by the difference between the actual bubble diameter, dS, and the dynamic equilibrium diameter, de- Therefore, in the following, coalescence promoting media are considered for which it can be assumed that dS~de holds true. Zlokarnik (21) _recommended for stirred tank reactors that instead of the volumetric mass transfer coefficient (16 ) a dimensionless group ( 1 7)
should be plotted as a function of a dimensionless group
x
R
1
g P
N ,)2/3 Hg F
( 1 8)
(instead of the specific power input P/VR)' In eqs. (16 to 18) G is the oxygen transferred into the medium per unit of time, ~ C = C;-O~ is the driving force for oxygen transfer, q the volumetric gas flow rate and y the kinematic viscosity of the liquid. He found simple relationships between Y2 and X for coalescence promoting systems:
(19)
546
For ejector-injector nozzles and static aerators the use of the following dimensionless groups was recommended (21 ) : G
liCqH ' In eq. (20)
wSG H
'y 2 1/3
y
3
= ~--(-) g
(20)
is the superficial gas velocity and the height of the aerated layer.
For perforated plates, single orifice,porous plates, aerators of and static mixers Y3 does not depend on X (Table 4). For injector and ejector nozzles Y3 increases with increasing X from Y3 = 7~10-5 at X = 2-10 4 to Y3 = 1.5.10- 4 at X = 5.10 5 (21) _ For the economy of the process the efficiency of the aerator is important. Some efficiencies, E = Gip, for different aerators at different aerated layer heights are given in Table 5. The injector nozzle attains its optimum effi-· ciency at H = 14 m~ E = 3.9 kg 02/kWh. Only the porous plate and the porous filter body exceed this value at lower liquid layer heights. subm~rse
The of different aerators differs considerably also in coalescence promoting media in which dS :: de can be set. What is the cause of difference? According to the theory of Kolmogoroff . (15), de should depend only on the liquid (in Tables 4 and 5, with one only water was used) and on P/VRo Thus, the Y3 values for the same P/VR should be the same. This is not the case. Since for all dispersion in the ranges which are important for the practice gas dispersion occurs due to turbulence mechanisms it is to be expected that there is a relationship between the turbulence properties and the efficiency of gas ion. It has already been pointed out that efficient gas dispersion is only pOSSible, if the microeddy size is smaller than de and if the percentage of microturbulence is high enough. Therefore the power spectrum of turbulence should influence the efficiency of gas dispersion. Fig. 10 shows one-dimensional power spectra in stirred tank reactors of different sizes according to van der Molen and van Maanen (22). As usual, the energy content of turbulent eddies was plotted as a function of the wave number, K, which is inversely proportional to the diameter Of the
547
TABLE 5
Efficiency of different aerators according to Zlokarnik (21)
tube s ti rrer turbine stirrer propeller plunging jet single orifice** perforated plate (3 mm in hole diameter) static mixer (Kenics) slot nozzle
*'
injector nozZla~* perforated plate ( 1 mm in hole diameter) porous plate submerse aerator of Frings
'*
* in *' * in
1 .4 2.0 to 2.8 0.8 to 1 • 1 0.88 3.32' 3.39
2 3 3 10 0.9 to 3.5 0.3
2.5 to 3.5 {3. ? 3.8 3.6 ):4
8.25
~4
~4
7
15 7
0.3 0.3 2 to 5
bubble column bubble column and with sulphite solution
VI
.j::..
00
10-
10J ,
'
sec
I D·9Dom'
10-3
/0'1
.,,\~\
,\
~(k)
10-' I
:.:: 1:)
g I.I..t
10- 5
..~,
/0.' 1
(i) @
10-6
([)
B.02cm/s 5. 35cmls WSG" 2. 67cmls
WSG" WSG=
. o
A
cm -1 3,0
30
300
11m
10 2
30000
}(---
~~__~_
One-dimensional power in stirred tank reactors with different tank diameters, D (23)
One-dimensional power in a tower reactor with perforated plate aerator 3 mm in hole diameter. 1 % methanol (23)
549
eddies. From this diagram the well-known phenomenon can be recognized that large eddies have a high energy content. With a diminishing eddy diameter, i.e. an increasing wave number, K, the energy content diminishes. The energy is mainly dissipated at very high wave numbers. The gas dispersion occurs exclusively at high wave numbers. While the energy cascades down from large eddies to microeddies, a considerable amount of energy is dissipated already_ In bubble columns with perforated or porous plates primary eddies are produced which are much smaller than in stirred tank reactors. Therefore, in bubble columns the low wave number range of the power spectrum is missing in which the energy is uselessly dissipated with regard to the gas dispersion. But also the same bubble column with the same medium yields different power spectra, if different aerators are used (Figs. 11 and 12). With a diminishing hole diameter of the perforated plate the power spectra are shifted to higher wave numbers. The re1ations can be illustrated even more clearly if the energy dissipation rate is plotted as a function of the wave number (Fig. 13). It can be noted that each energy dissipation spectrum exhibits a maximum. The shape of the spectra and the location of the maxima are different. Since gas dispersion occurs at high wave numbers it can be expected that the higher the wave number at which the maximum appears the higher is the efficiency of the aerator. When using a porous plate the maxima appear at higher wave numbers than for perforated plates (Fig. 13). With an increasing hole diameter and a free cross-sectional area of perforated plates the maximum is shifted to lower wave numbers. A comparison of the sequence: porous plate, perforated plate 0.5 mm, 1.0 mm and 3.0 mm in hole diameter (with regard to the position of the maximum of their energy dissipation spectra) with the sequence for their ef,ficiency shows a good agreement. It seems that when shifting the maximum of the energy dissipation spectrum to higher wave numbers by using different aerators an efficiency increase of the aerator can be expected. In addition, Fig. 13 shows that the increase in the aeration rate shifts the energy dissipation spectrum to higher energy dissipation rates but i t does not influence its shape or the position of its maximum. This is consistent with the observation that the efficiency of porous plates is independent of the aeration rate, i.e. of X '(Table 5). The same independence of the shape and the position of the maximum of the ener-
LIl LIl
o
(J)
lOO,
10-
1
.~ ~I
1
\ " 10-'
10° k/2lt-
8.02cm/s wSG" 5.35 cmls wSG'" 2.67cmls
WSO'"
~~--,
70 '
em· 1
10 2
1% methanol, wSL=1.8cmls, r-=Ocm porous plate 5J.l m perforated plate1mm wSG=2.57cmls ® perfora ted pIa te 3mm porous plate 5).Jm wSG=5.35cm/s
CD ®
100 k/2rr.--
cm-I
10 2
. 12: One-dimensional power spectra in a tower reactor with a porous plate aerator 5 pm in pore diameter. 1 % methanol (23)
Rb+>Cs+>Na+. Marcus et al. (61) have shown that crown ethers dissolved in solvents such as creosols, xylenols etc. can selectively extract KCI from brine containing Na, Mg and Ca chlorides. can also be used in conjunction with liquid membranes.
595
(b)
(a) l8-crown-6
(c) dicyclohexanol8-crown-6
dibenzo-18-crown-6
(dY
l5-crown-5
Cryptate[2.2.2] (Trade name Kryptofix222)
Figure 3. The structure of some of the simple Crown Ethers and Cryptates.
~O~HYdrOPhObiC~greasy)
(
,:
~O)
' . ... K't.'
0;0 ..... ' ...... '0
l....,..V
exter20r x-
r
weak anion-sol vent interactions
Figure 4. A simplistic view of the solubilization process.Solubilization of potassium salts in nonpolar and dipolar aprotic solvents.
596
However it must be stressed that the commercial explotation of crown ethers is not likely to be realised in immediate future due to their high costs. 5.2.2.Kinetics of Metal Extraction:Mass Transfer with reaction. Investigations on metal extraction kinetics were carried out on the assumption that the reaction was very slow and proper consideratiqns of mass transfel effects were often neglected.Thus,the information on relevant properties, such as contact area etc. were ofteI missing leading to contradictions.Recent studies {62,63)1 however, indicate reasonably clear that mass transfer play an important role and that there is interaction between mass transfer factors and chemical kinetics at least in the case of copper extraction with oximes. However,the process differs probably from the usual two-phase considered in the main part of this book~ is; in normal systems, the sparingly solur solute dissolves in a phase (usually aqueous) and reacts there with an already dissolved reactant, the products being also soluble in the :same phase.On the other hand, in metal systems, ions are insoluble in the organic and insolubility in water is one of the main selection criteria of complexing agents and the metal complex must also be insoluble in the aqueous phase. There is however still apparent controversy over the actual locale of the reaction, some workers (44,62) adopt the view of a interfacial reaction. Others, believe that the reaction takes place in a zone in the aqueous phase adjacent to the interface. This is, however/partly due to the different views of the interface as some appear to view it as a pseudo-crysalline boundary,while others consider it as a of finite thickness (64) . Considering the solubility of commercial extractants LIX63 and LIX65N (anti-form) in water are respectively 15.5 ppm and 1 ppm, Hanson and coworkers (67) postulated a reaction immediately adjacent to the interface but with a significant (and possit ly sometimes dominating) diffusional resistance, in a zone (likely to be of greater thickness) on the organic side of the interface. Kondo and coworkers (65,66) have studied the extraction of copper by benzylacetone and have found the customary interactions between mass transfer and reaction. Here, the partition constant is 7.24 x 10- 4 and the enhancement factors of as as 1000 were observed in a Lewis type stirred cell. Indeed, at low pH range of 4.5, experiments appear to fall into the regime of pseudo first order. At high pH of 7.5, the regime is close to that of an instantaneous reaction so that the process of
597
solvent extraction can be controlled by diffusion of metal ions and the agent to the reaction zone in the aqueous phase. Howev'er, often the process is extremely complicated great caution must be exercised in interpreting experimental results which in turn should be planned very carefully. Since the chemical reaction has usually a crucial role, together with mass transfer factors, the followings should also be carefully considered (45) (a) the difference in the reaction rate of possible stereospecific isomers (68), (b) nature of species (monomer, dimer etc.) (69), (c) role of impurities; synergism or inhibition (70), and (d) effect of diluents, including nature of specled, effect on interfacial area and interactions with extractants (71). 5.3.1. Reactions in organic phase. In the case of organic-aqueous phase'reactions, the locale of the reaction is often assumed to be in the aqueous phase. This is, of course, true for most of the liquid-liquid reactions. There are however cases where the reaction occurs entirely in the organic phase. Sharma (3,4) points out a number of examples. For 'instance, the rates of nitration of I-dodecene and l-octadecene under identical experimental conditions, are very similar even though the solubilities of them in aqueous phase are very different. This argument and some other related arguments indicate clearly that the reaction occurs in the organic phase (Gregory et al. (72». Another interesting example is polycondensation reactions to procedure polyesters and polyamides (73). Sharma (3,4) discusses also some aspects of interfacial polycondensationi here, for instance, the diacyl chloride, dissolved in a water immiscible organic solvent, may be contacted with hexamethylene diamine to procedum the polyamide, Nylon 66. Since diamine is very solubie in the organic phase and the reaction is very fast, the reaction occurs probably in organic phase, therefore acyl chloride cannot get an opportunity to get into aqueous phase where concurrent hydrolysis would have occured. Usually, a film of polymer is formed on the organic phase droplets disposed in water and thus droplets are encapsulated and interfacial area measurements can well be envisaged. 5.3.2. Phase transfer catalysis. This is an outstanding where the locale of the reaction is deliberately switched from aqueous to organic phase. The basic premise of phase transfer catalysis of two-phqse re-
598
action is that one can select a transfer agent that, used in catalytic quantities, can bring one of the reactants into the normal phase of the other reactant in such form that high reaction rates are observed (6,7(76) The most'common example, and the one for which a large amount of data is available, is simple cyanide displacement on alkyl chloride or bromides: (R-Cl)
org
+
(NaCN)
aq
~
(R-CN)
org
+ (NaCl)
aq
(1)
Simply heating and stirring of a two-phase mixture of l-chlorooctane with aqueous sodium cyanide leads to es~entially zero yield of l-cyanooctane. However, if a small amount of an appropriate quaternary ammonium salt is added, then very rapid formation of l-cyanooctane is observed. The general outline of the catalysis sequence is represented by Figure 5. Alternate of phase transfer catalysts for two-phase reactions involving salts are crown ethers, cryptates and dialkylpolyethylene oxides, which form reversible complexes with many cations. For example, crown ether 18-crown-6, also strongly reaction (1). In this case, the crown ether transfers the entire KCN molecule into the organic phase by complexation. In principle, diffusional resistance may be associated with the transfer of the reactant and the catalin Figure 5. Anion transfer by the catalyst into organic is considered to be an equilibrium process in two different ions in the aqueous phase associate with a quaternary cation in the organic phase: (QCl)
+ (CN-) (QCN) + (Cl-) (2) org aq org The rate determining step of the reaction is in the phase of the reaction mixture rather than in or at the interface or in the micel-
599
In thes~ studies (6,7,76), the intrinsically slow two-phase reactions have been studied. However, Sharma and coworkers (77) have recently studied the alkaline hydrolysis of a variety of formate esters, which are normally also fast, catalysed by PTC agents, such as cetyltrimethyl-, tricaprylmethyl-ammonium bromide etc. They have carried out experiments with this system in a fully baffled mechanically agitated contactors as well as in a constant area c~ll. The results are truly remarkable so that the presence of PTC results in an increase in the mass transfer rate ranging from 20 to over 200. It is interesting to note that much of the phase transfer catalysis has used a quaternary ammonium reagent (trade name Aliquat 336), which is also widely used in solvent extraction of metals. Recently, it has been suggested thaE PTC (as well as micellar catalysis) may play an important role in mixed reagents systems involving LIX63, DEHPA, Lauric acid, Aliquat 336 and HDDNS (78). Indeed, these authors (78) were able to offer an explanation for the catalytic effect of LIX63 on copper extraction by LIX6SN. It seems probable that metal extraction with mixture of chelating reagents and organic acid mixtures may well proceed via a phase transfer catalysis type mechanisms. Phase transfer catalysis may function not only through liquid-liquid systems, but also with liquidgas, liquid-solid, solid-gas and presumably solid-solid systems (6). Since the subject is actively pursued from many sides and since many of its potential fruits are far from being fully harvested, the industrial explotations have probably not yet been realised to any noticeable extent. 5.3.3. Micellar catalysis. A somewhat related phenomena to phase transfer catalysis occurs in Micellar Catalysis (79), which is however mechanistically and preparatively different. When good surfactants are added to a two-phase aqueous-organic system, normally mice11es are produced. These micelles usually take the form of small aggregations of 20-100 organic molecules dispersed in the aqueous phase r wherein the nonpolar parts of the surfactant and other nonpolar organic molecules occupy the internal hydrophobic volume of the micelle r while the highly polar groups, which are referred as heads, occupy the highly hydrophilic outer surface. Figure 6 illustrates the situation schematically. The micelles formed in aqueous surfactant solutions behave as a separate (pseudo phase) medium with unique
600
Figure 6. Hypothetical reaction schematic for quaternary ammonium surfactant-catalysed micelle reaction of alkyl chloride and aqueous sodium cyanide.
physical properties. The positively charged outer surface attracts and concentrates anions (e.g. cyanide) from the bulk aqueous solution into a counteranion layer near the surface of the micelle, strongly facilitating reaction of RCI in the micelle with CN- just at the micelle surface. The reverse case where a central core is hydrophilic, is in possible for reversed organic phase micelles. The kinetics and mechanisms of micelle-catalysed reactions have been intensively studied in recent years and they are much too complicated to be discusse.d here in detail (80,81). Micelles may also be considered as phase transfer agents of a sort which take the organic phase reagent into the aqueous phase for r€action. Many quaternary ammonium salts containingone or two large alkyl groups, such as cetyltrimethylammonium bromide, C16H33N (CH3)3Br, produce micelles as well as being phase transfer agents. Indeed, there are borderline cases where a particular quaternary ammonium salt may behave as both a surfactant and a phase transfer catalyst or as either one, depending on the particular reaction conditions. Starks (6) discusses further similarities and essent~al differences of the two phenomena. The most important difference is that whereas the rate of phase transfer catalysed reactions are directly
601
proportional ,to the catalyst concentration, the ratio of micelle-catalyseq reaction is low until the critical micelle concentration of surfactant is approached, then increases tremendously and reaches a maximum. Further increase in surfactant concentration has either no effect or decreases the rate slightly. It is also possible to inhibit an undesirable reaction in a two-phase system. Menger and Portney (82) and Bunton (83) have developed mathematical models on the basis of which -the catalysis and inhibition of reactions can be treated quantitatively. it has been suggested that many aspects of micellar and reverse micellar are relevant in commercially important extractants involving LIX63, DEHPA. Lauric acid, and Aliquat 336 (78). OsseoAsera and (78) were able to demonstrate that the potential for ' utilization of reversed micellar catalysis in liquid-liquid extraction systems depends primarily upon the ability of micelles to solubilize both extractant molecules and metal ions, and stabilize H2 0-extractant liquid exchange reactions. Reactions in micelle system are usually difficult for synthetic applications because of the problems in handling emulsions and the need for careful regulation of concentrations. However, there are many instances (e.g. emulsion polymerisation) where micelle systems are highly useful and are applied on a cQmmercial basis. 5.3.4. Dissociation Extraction. Dissociation extraction is a technique for the separation of mixtures of organic acids or bases, which depends upon differences both in the dissociation constants and the distribution coefficients of the components of the mixture, in a two-phase systems. It can be to closely related or isomeric compounds, which are difficult -if indeed possible- to separate by common methods of distillation, solvent extraction or fractional crystallization (84). Consider the case of a mixture of weak organic acids, m- and p-cresol witn dissociation constants of 9.8x10- 11 and 6.70x10- 11 respectively. If a mixture of these compounds, dissolved in a water immiscible organic solvent, such as toluene etc., is contacted with a stoichiometrically deficient amount of aqueous alkali, in relation to total acids, the stronger acid, having the large dissociation constant (mcresol) will preferentially react with the alkali. Thus, there will be an enrichment of in the organic
602
Figure 7. Dissociation extraction with a weak base.
octan-l-ol
~ H
;~
~~
'il
'l:j
0
l'J)
...,C,)
.~
{J
l'J)
m-cresol and I toluene
~ 8
Cl)
tl
:::l
'il
"""'i
l'J)
l'J) Q.)
C,)
:::l
0
Q.)
:::l
b1
~
FEED
m-cresol product
0
tI
b1
'il
m-cresol reflux
a
~ H
~ ~~ ~~
~~ tl~
p-cresol ana tolukne
~
8Cl) H
Cl
p-cresol product
p-cresol reflux Toluene
Figure 8. Flow diagram for the continuous separation of m- and p-cresols.
603
phase and the stronger acid will be in the aqueous phase as its dissociated salt. This process of dissociation extraction when carried out in a multistage extractor can lead to high purity components at the two ends. In the so called classical or conventional dissociation extraction process, m-cresol would be generated from its salt in the aqueous by treatment with strong mineral acid. Commercial applications of dissociation extraction have been considered for separation of organic acids and bases occuring in coal tar, particularly by m- and p-cresol (85), xylenols (86) and 2,6-lutidine, 3- and 4-picoline systems, separation of dichlorophenols, penicillin acids, benzoic acid derivatves r and close boiling amines, such as substituted aniline, heterocyclic amines, xylidines etc. The dissociation extraction efficiency is measured in terms of a separation factor, a, which is defined in an analogous manner to that of relative volatility in distillation: a-
(A] Ofg[Bl org
[A*J
(3 )
[B*] aq
where [A]org and [Blor are concentrations of A and B in the organic phase a~d [A*l and CB*1 are the equilibrium concentrations of A and B in the aqueous phase resepctivelYi A refers to the weaker of the two acids /bases. Anwar et al. (87) have developed the theory of dissociation extraction in a somewhat similar way to that of binary distillation. Recently, Wadekar and Sharma (88) have extended the theory to multicomponent and multifunctional systems. It is possible to directly predict the value of a in such systems provided that the data on dissociation constants and distribution coefficients are available. In the conventional dissociation extraction, the consumption of the extractant alkali or acid makes the process less attractive. To overcome this difficulty, Anwar et al. (84) have evolved a modified strategy where instead of strong acid/base, a weakly acidic/ basic extractant is used so that the reaction does not proceed to completion. Then the extract is contacted with a fresh solvent having a strong affinity for the undissociated organic component so that the reaction is reversed. The basic/acidic reagent is thereby and can be recycled (Figure 7). They have suggested both Na3P04 and monomethanolamine for sepa-
604
ration of m-cresol and p-cresol isomers. However, with weak reagents, in general, the reaction in the aqueous id incomplete, resulting in relatively low aqueous phase loadings and higher equipment and process costs. On the other hand, recently they were able to use a strong alkali, such as caustic soda, for the . separation of cresol isomers leading to higher aqueous phase loadings and separation factors, in cooperation with time an organic solvent with a very high affinity for the undissociated organic component, which is sufficiently'powerful to reverse the reaction despite the strong alkali. For the case of separation of cresol isomers, they used caustic soda and octan-l-ol and Figure 8 shows a flow diagram for a practical industrial separation process. No doubt similar processes could well be applied to other mixtures of acidic/ basic organic compounds. In some cases, it might also be possible to use a thermally regenrative extractant. For eKample, monomethylamine solution has been suggested for the separation of mixtures of p-chlorophenol/2,4-dichlorophenol. boiling the aqueous salt, monomethylamine is regenerated, and can thus be recycled. During recent years, Sharma and coworkers (88-90) have been able to find examples of dissociation extration which have distinct features and are truly remarkable. Firstly, they have illustrated that the use of a diluent may be avoided advantageously (89). This is particularly relevant for every sparingly water soluble organic acids/bases and, here, apart from the difference an ionisation constants, the relative solubilities of species (rather than the distribution coefficients) play an important role. Typical examples are mixtures of N-ethyl-o-toluidine and NN ' diethyl-o-toluidine where higher values of the separation factors are obtained without a solvent (4,89). The same process has been applied to sparingly water soluble acidic/basic solids and such a dissociative leaching has been illustrated for separation of 0- and p-chlorobenzoic acid mixtures (89). Secondly, they where able to recover and separate organic acids from dilute aqueous solutions by using modified dissociation extraction (90). For instance, they employed tri-noctylamine, clissolved in various water immiscible solvents, as an extractanti the acid-amine complex is soluble in organic solvents such as xylene. Very promising results were obtained for mixtures such as aceticacid/mono-chloroacetic acid, formic/oxalic acids etc.
605
(90). Of course, a similar strategy can be extended for the recovery and separation of aqueous solutions containing mixtures of basic compounds. The process is also intere"sting as it may conform to a situation where the reaction occurs in the organic . The work in this area so far involves only determination od separation factors from equilibrium considerations, and there is no published information on rates of mass transfer. However, the latter is likely to be an almost trivial exercise as the reactions involved are of a relatively simple type. 6. DISCUSSION AND CONCLUSIONS An examination of extraction with reaction processes reveals that it is an area which exploits chemistry to a greater extent than, for instance, other common separation processes. A variety of liquidliquid reactions are encountered in practice and some illustrative examples have been presented. Further challenging examples are frequently presented in many publications; such as the special section on Journal of Separation Science, Hydrometallurgy etc. as well as the more common journals, e.g. Chemistry and Industry etc. However, the real highlights are documented mainly at the tri-annual International Solvent Extraction Conferences; ISEC's, as well as many more specialised meetings; e.g. hydrometallurgy etc. Exami~ation of theoretical aspects indicates that although the conventional theories developed for gasliquid systems represents a very simplistic picture neglecting many important features of dispersion nomena, they can still be for design purposes. Indeed, in a number of cases of practical relevance, a simple analytical expression can be used for calcu~ lating the process design parameter in a manner which is practically the same as those of gas-liquid systems (20). However, this should,by no means/suffice and the continuation of fundamental studies on sion phenomena and the incorporation of them with mass transfer in reacting systems is not only essential for further scientific development of this area, but also extremely desirable as they will eventually lead to more design methods (10,91). In particular, new measuring techniques may well yield a better un~erstan ding of interaction of fluid dynamics, interfacial phenomena and mass transfer (92).
In terms of process development, metal extraction
606
has probably claimed much of the limelight over the last decade. This will probably continue to be so, particularly in solvent extraction of uranium as the expansion of nuclear power. g~neration in most industrialised countries offers inevitable. New processes, in terms of new chemical systems as well as new technique~ such as phase transfer catalysis, are likely to find interesting applications in coming years. Another relatively novel aspect which deserves full examination involves memqrane processes. This includes both membrane and liquid membrane processes. Recent state of the art reviews of both processes are already available; among others, Hafez (93) discusses the use of membranes in extraction and Halwachs and Schugerl (94) review liquid membranes. The latter is also discussed in this volume by Sawistowski (1). It seems, membrane processes lend themselves readily to processes such as metal extraction, waste water treatment and pharmaceutical and medical applications. Differential reactions, as in dissociation extraction, also appear to offer scope for more selective separations and the research which has been conducted during the 1970's could well come to fruition in the form of industrial processes during the next decades. Finally, it may be pointed out that relative increases in the cost of energy could well make liquidliquid extraction economically attractive for some separations in the general organic field.
607
REFERENCES 1. Sawistowski,H. "Physical aspects of liquidliquid extraction." (Proceesings of NATO ASI on "Ivlass transfer with chemical reaction in multiphase systems", Turkey, 1981). 2. Hartland,S. "Experience with liquid-liquid test systems in extraction.1! (Proceedings of NATO ASI on III>iass transfer with chemical reaction in multiphase systems", Turkey, 1981). 3. Sharma,M.M. "Extraction with reaction ll • Chapter 2a in Handbook of Extraction (To pe published, Wiley and
,
,
. Laddha,G.S. and T.E.Degaleesan. Transport Phenomena in Liquid Extraction (Tata Mc Graw Hill Co., New Dehl i, 1978). 6. Starks,C.M. and C.L.Liotta. Dehmlow,E.V. and S.S.Dehmlow. Phase Transfer Catalysis (Verlag Chemie, Weinheim, 1980). 8. Porter,K. and D.Roberts. .24 (1969) 695. 9. Grosjean,P.R.L. and H.Sawistowski. Chem.Engrs. 38 (1980) 60. 10. Tavlarides,L.L. and M.Stamatoudis. liThe analysis of interphase reactions and mass transfer in liquidliquid dispersions". Advances in Chemical Engng. Vol. 11 (Academic Press, London,1981). 11. Danckwerts,P.V. (Mc Graw Hill Co., New York, 19 12. Juvekar,V. and M.M.Sharma. ----',---:--=-" 55 (1972) 72. carnerrv,J.J. Chemical and Catalytic Reaction (Mc Graw Hill Co., New York, 1975). HQU~VU,C. Recent Advances in Liquid-Liquid Extraction (Pergamon Press, Oxford, 1971) . 429 ,E. "Process design aspects gas absorbers". (Proceedings of NATO ASI on "Mass transfer with chemical reaction in multiphase systems, Turkey, 1981) 16. Van Landeghem,H. Chem~E .Sci. 35 (1980) 1912 17. Sharma,M.M. and P.V.Danc werts. Brit 15 (1970) 522. ----------~~ 18. Sankholkar,D.S. and M.M.Sharma. Chem.Engng.Sci. 30 (1975) 729. 19. Laddha,S.S. and M.M.Sharma. 31 (1976) 843.
608
20. Vasudevan,T.V. and M.M.Sharma. "Some aspects of process design of liquid-liquid reactor." (Int. Symposium on "~1ass Transfer with Chemical Reaction in TwoPhase Systems ll , ACS-Meeti:qg, _Atlanta, 1981). 21. Sarkar,S., Mumford;C.J. and C.R.Philips. lnd. Engng.Chem.Proces.Des.Dev. 19 (1980) 665. 22. Nanda,A.K. and M.M.Sharma. Chem.Engng.Sci. 22 (1967) 769. 23. Sharma,R.C. and N.M.Sharma. J.Appl.Chem.Biotechnol. 19 (1969) 162 . 24. Sharma,R.C. and M.M.Sharma. Bull.Chem.Soc.Jap. 43 (1970) 43. 25. Albright,L.F. and C.Hanson (Editors). "Industriai and Laboratory Nitration". 22 (1975) . . Albright,L.F. and C.Hanson. "Loss Prevention ll (CEP Technical Manual) 3 (1969) 26. 27. Cox,P.R. and A.N.Strachan. Chem.Engng.Sci. 27 (1972) 457. 28. Chapman,J.W. and A.N.Strachan. J.Chem.Soc.Chem. Commun., (1974) 293. 29. Hanson,C. and H.A.M.lsmail. technol. 26 (1976) 111. 30. Komasawa,l., lonue,T. and T.Otake. Japan. 5 (1972) 34. ----3-1. Tiwari,R.K. and M.M.Sharma. Sci. 32 ( 19 77) 1253. 32. Richardson,J.A. and Rase,H.F. 17 (1978) 287. , .M. and P.Harriot. Ind .Chem.Proc.Des. Dev. 16 (1977) 282 . 46 . Dixon,J.K. and K.W.Saunders. Ind (1954) 652. 35. Bhave,R.R. and M.M.Sharrna. J.Chem.Tech.Biotechnolo 31 ( 1981) 93. ---36. Kothari,P.J. and M.M.Sharma. Chem. .Sci. 21 (1966) 391. 37. Harnisch,H. Pure Appl.Chem. 52 (1980) 809. 38. Carr,N.L. and Y.T.Shah. Can.JI.Chem.Engng. 57 (1979) 35. 39. Bailes,P.J., Hanson,C. and N.A.Hughes. Chern. Engng. 83 No:18 (1976) 86. -40. Fletcher,A.W. Chem.lnd. No:5 (1973) 414. 41. Lloyd,P.J. Solvent Extraction Chemistry. (Ed.D. Dyrssen, North-Holland, Amsterdam, 1967) p. 642. 42. Warner,B.F. Solvent Extraction Chemistry. (Ed.D. Dyrssen, North-Holland, Amsterdam) p. 635. 43. Chalan,M.J. Chem.lnd. (1967) 1590. 44. Sawistowski,H. "Aspects of metals extraction"
609
(Proceedings of NATO ASI on "Mass transfer with chemical reaction in mul1:;:iphase systems ll , Turkey, 1981). 45. Sharma,H.M. "Types of extractants and the chemistry of solvent extraction" (Unpublished work; Private communication, 1981) 46. Bautista,R.G. "Hydrometallurgy" in Advances in (Academic Press, New York, .M. 3 (1978) 111. 48. Freiser,H. extraction of metal chelates" (Proceedings of Int.Solvent Extraction Conf., ISEC'80, Belgium, 1980). 49. Mtihl,P. and K.Gloe. IIComparative studies on the metal extraction with different chelating extractants ll (Proceedings of Int.Solvent Extraction Conf., ISEC'80, Belgium, 1980). 50. Price,R. and J.Tumilty. "An interpretation of some aspects of solvent extraction as realted to the extraction of Copp~r using O-Hydroxyaryl Oximes" (Proceedings of Symposium on "Hydrometallurgy", Instn. Chem.E.Symp.Series No:42, 1975). 51. Van der Zeeuw. "Selective copper extractants of the 5-alkyl-2-Hydroxyphenyl Alkyl Ketone Oxime" (Proceedings of Symposium on "Hydrometallurgy", Instn. Chem.E.Symp.Series No: 42, 1975). 52. RitceYrG.M. CIM Transactions 74 (1973) 71. 53. Cox,~Jl. and W. Van Bronswijk. "Chemistry of extraction of copper, cobalt and nickel with substituted 8-sulphonamideoquinilines" of . Solvent Conf . "Kinetic aspects of the liquid-liquid extraction of germanium (IV) with the S-dodecenyl 8-hydroxyquinoline." (Proceedings of Int. Solvent Extraction Conf., ISEC'80, Belgium, 1980). 55. Guesnet,P., Sabot,J.L. and D.Bauer. "Kinetics of cobalt oxidation in solvent extraction by 8-quinolinol and KELEX 100" (Proceedings of Int.Solvent Extraction Belgium, 1980) ,541 (1960) i U.S.P. 2,969,275 (1961); U.S.P. 3,111,383 (1963) i U.S.P. 3,479,294 (1960); U. S . P. 3,493,349 ( 1 970) and U. S . P. 3, 741 ,731 ( 1 973) . 57. Su,Y.F. and D.Y.Yu. "Process development of boron recovery from ascharite" (Proceedings of Int. Solvent Extraction Conf., ISEC'80 1 Belgium, 1980). 58. M.J. "Modern science in winning minerals and metals" (Progress in Chemistry, 1967). 59. Dietrich,B. and J.M.Lehn. Acc.Chem.Res. 11 (1978) 49. 60. McDowell,W.J.,Kinard,v'l.P. and R.R.Shoun. "Sizeselective synergism by crown ethers in the extraction of alkali metals by di-( ) phosphoric acid"
610
(Proceedings of Int.Solvent Extraction Conf., ISEC ' 80, Belgium, 1980). 61. Marcus,Y., Asher,L.E., Hormadaly,J. and E.Pross. "Selective extraction of potassium chloride by crown ehters in substituted phenol' solvents ll 1 No:. (1975) 5. 62. Ajawin,L.A., Perez de Ortiz,S.E. and H.Sawistowski. "Kinetics of extraction of zinc: di(2-ethylhexyl) phosphoric acid in N-heptane ll • (Proceedings of Int. Solvent Extraction Conf., ISEC'80, Belgium, 1980). 63. R.J.Whewell, Hughes,A.M. and C.Hanson. "Aspects of the kinetics and mechanism of the extraction of copp,er with hydroxyoximes". vent Extraction Cont., ISEC' , 64. Krishna,R. "Interphase mass transfer models". (Proceedings of NATO ASI on lI.t-lul tiphase Chemical Reactors", Portugal, 1980) . . Kondo,K., Takahashi,S., Tsuneyuki,T. and F.Nakashio. J.Chem.Engng.Japan 11 (1978) 193. 66. Kondo,K., Tsuneyuki,T. and F.Nakashio. IISo l vent extraction kinetics of copper by benzoylacetone". (Proceedings of Solvent Extraction Conf., ISEC'80, Belgium, 1980). 67. Hanson,C., M.A.Hughes and R.J.Whewell. J.Appl. Chem.Biotechnol. 28 (1978) 435. 68. Van der Zeuw,A.J. and R.Kok. "Kinetics and mechanism of copper extraction with 5-alkyl-2-hydroxyphenyl alkyl ketoximes", of Extraction , Preston,J. and R.J.Whewell. J.lnorg.Nucl. 38 (1976) 2306. 70. Van der Zeuw,A.J. and R.Kok. IIIdeas and practice in the design of solvent extractant reagents ll • (Proceedings of the Inter.Solvent Extraction Conf., ISEC'77, Canada, 1977). 71. Dalton,R.F., Hauxwell,F. and J.A.Tumilty.Chem. and Industry 6 (March) (1976) 184. ----72. Gregory,D.P., .t-lartens,R.J., Stubbs,C.E. and J.D. Wagner. J.Appl.Chem.Biotechnol. 26 (1976) 623. 73. Morgan,P.W. Condensation Polymeres: By Interfacial and Solution Methods (Interscience Publishers, New York, 1965). 74. Dehmlow,E.V. Angew.Chem. 86 (1974) 187. 75. Dehmlow,E.V. Angew.Chem. 89 (1977) 521. 76. Weber,W.P. and G.W.Gokel. Phase Transfer Catalysis in Organic Synthesis (Springer Verlag, New York, 1977). 77. Lele,S.S., Bhave,R.R. and M.M.Sharma. Chem. Engng.Sci. 36 (1981) 955. ,-u"UU,u.u. ,
611
78. Osseo-Asare,K. and M.E.Keeney. "Phase transfer and micellar catalysis in hydrometallurgical liquidliquid extraction systems". (Proceedings of Int.Solvent Ectraction Conference, ISEC'80, Belgium, 1980). 79. Fendler,J.H. and E.J.Fendler. Catalysis in Micellar and Macromolecular Systems. (Academic Press, New York, 1975). 80. Fendler,E.J. and J.H.Fendler. Adv.Phys.Org.Chem. 8 (1970) 271. 81. Morawetz,H. 341. 82. Menger,F.M. Soc. 89 (1967) 4698. 83. Bunton,C.A. Catal.Rev.Sci.Eng. 20 (1979) 1. 84. Anwar,M.M .. Pratt,M.W.T. and Snaheen,M.Y. "Developments in Dissociation Extraction", (Proceedings of Int.Solvent Extraction Conf., ISEC'80, Belgium, 1980) . 85. Ellis,S.R.M. and J.D.Gibbon. The Less Common Means of separation: (Instn.Chem.Engrs., London, 1964). 86. Coleby,J. Recent Advances in Solvent Extraction (Pergamon Press, Ed.C.Hanson, London,1971). 87. Anwar,M ..M., Hanson,C. and M.W.T.Pratt. Trans. Instn.Chem.Engrs. 49 (1971) 95. 88. Wadekar,V.V. and Sharma,M.M. nolo 2 No: 1 (1981) 1. 89. Laddha,S.S. and M.M.Sharma. Biotechnolo 28 (1978) 69. 90. Jagirdar,G.C. and M.M.Sharma. Technol. 1 No:2 (1980) 40. ,K., Blaschke,H.G., Brunke,U. and R. Streicher. Interaction of fluid dynamics, interfacial phenomena and mass transfer in extraction processes". (CRC
=-------~----~~~~~~--~--------------------------
,
Villermaux,J. "Drop break-up and coalescence. Micromixing effects in liquid-liquid reactors". (Proceedings of NATO ASI on "Multiphase Chemical React:ors", portugal, 1980). 93. Hafez,M.M. "Membranes in extraction. A state of art review" (Proceedings of Int.Solvent Extraction Conf., ISEC'80, Belgium 1980). 94. Halwachs,W. and K.Schugerl. 50 No:10 (1978) 764.
613
PHYSICAL ASPECTS OF LIQUID-LIQUID EXTRACTION
H. Sawistowski Department of Chemical and Chemical Technology College of Science and Technology, London SW7 INTRODUCTION Liquid-liquid extraction is a process which relies on unequal distribution of components between two liquid phases. 1fuss transfer will therefore occur as a spontaneous process if the phases are not at equilibrium. The transferred components are referred to as solutes and the carrier as solvents. The splvents may be practically imrrdscible or partially miscible. Most of the fundamental work is being conducted on the transfer of a solute between two immiscible solvents and there is a number of such systems specially recommended for such tions by the European Federation of Chemical Engineerine (1). Partially miscible binary systems may also be used for this purpose as examples of mixtures with low interfacial tension. In practice, however, partially miscible Bulticomponent systems are often encountered, e-. g. in the removal of aromatics from lubricating oil. This represents an area which is not particularly well researched and documented. The process of liquid-liquid extraction is not very energy intensive. Consequently its application is on the in~rease although, on account of lack of proper understanding of the process, its is not yet fully utilized. A number 6f have therefore been selected here to highlight certain fundamentals of liquid-liquid extraction. Although, on pu~~ose, no attempt will be made to deal with extraction equipment, some references to it cannot be avoided.
614
The best equipment for a particular separation process is that in which the hydrodynamics matches best the process in question. The hydrodynamic behaviour is a function of throughput, that is of flow rates and phase ratios, and of column design. Thus, the problems will be differ~nt'in equipment with supported interfacial area, e.g. packed columns, from those encountered when the interfacial area is unsupported, as in sieve plate columns and stirred tanks. Conditions will also change if interfacial area is created by input of mechanical energy rather than by action of grav~ty. The factors which are directly affected by hydrodynamic conditions are: (a) (b) (c)
interfacial area, mass transfer coefficients, radial and axial mixing.
Of these, only the first two will be discussed here and discussion will be focussed on the following topics: (1)
(4) (5)
formation of dispersion as it occurs in spray columns and columns; behaviour and characterization of stirred dispersions; basic mass transfer phenomena including mass transfer to and from drops; mass-transfer induced interfacial convection; basic principles of the liquid membranes process.
1.
FO~1ATION
(2) (3)
OF DISPERSIONS
Liquid-liquid dispersions are frequently encountered in a number of industrial operations such as solvent extraction, directcontact heat transfer and heterogeneous chemical reactions. They are usually formed by the application of external energy to liquid/liquid systems and, depending on their behaviour on discontinuation of energy supply, they can be divided into stable dispersions or emulsions and unstable dispersions. Only the latter, in which the phases start separating as soon as the supply of external energy is stopped, are considered here and given the term "dispersions lt • The external force employed is either gravitational or mechanical and drops are formed either by forcing one liquid through nozzles, e.g. in a spray column, or by breaking it up in a high shear field, for instance by using an agitator in a baffled tank. The former will be used as an example of formation of a dispersion and discussed with reference to a single nozzle in a spray column.
615
(a)
Drop Formation
It is a well-known fact that when a drop is formed at a nozzle under pseudostatic conditions, its size is determined solely by the balance of interfacial tension and gravity or buoyancy forces. This forms the basis of,the drop-weight method of determination of surface and interfacial tension. Discrete drops continue to be forn~d with increasing velocity of the dispersed phase up to a critical velocity u .. The dispersion formed at each velocity is mono-disperse and J the drop diameter, d , can be obtained from a equation developed by Haywo¥th and Treybal (2) and based on the balance of forces. The critical velocity, also called the jetting velocity, is given by (3) (m/s)
(1)
where y is the interfacial tension, d the nozzle diameter and P d the density of the dispersed phase. Rbove this velocity no discrete drops will be formed at the nozzle, instead they will be produced by disintegration of jets.
A issuing from a nozzle will be subject to two types of hydrodynamic instabilities: symmetrical and sinuous, each characterized by a different time constant. Drops formed as a result of the fast growing symmetrical disturbance will detach along the axis of the nozzLe when. the amplitude of the disturbance becomes equal to the radi~s. However, drag resistance to the motion of such a drop is larger than to the motion of the jet. This results in lengthening of the and increase in its life time until the slow growing sinuous disturbance becomes effective. The of the jet begins to oscillate, drops are discharged in various directions and the jet starts to shorten. This phenomenon is referred to as "thrashing" and it begins when (4) u
n
= 2.83
-2
x 10
1
(y/d P )2 n c
(m/s)
(2)
where u is the nozzle and P the density of the continuous phRse. Between jetting and thra~hing the dispersion formed remains monodisperse with the drop volume equal to the volume of a liquid cylinder of diameter d and "length A, where A is the dominant wave length. The latt~r can be obtained by solving the characteristic equation due to Tomotika (5). Beyond the thrashing velocity the dispersion becoLles polydisperse and the standard deviation of drop size increases with increasing Reynolds number. This is particularly accentuated once the jet becomes turbulent.
616
60 50
40 ~ .......
30
H
20
10 0 0
1000
2000
3000
Re Fig. 1. Variation of dimensionless jet len~th with Reynolds number: • - chlorobenzene/water (y = 36.5 EN/m), 0 - chlorobenzene/water with propionic acid in phase equilibrium (y = 15 mN/m).
As seen from equations (1) and (2), a decrease in interfacial tension shifts the jetting and thrashing points towards lower nozzle velocities, i.e. lower Reynolds numbers. This has been confirmed experimentally (6) as shown in Fig. 1. Obviously, these phenomena are affected by the presence of mass transfer but this effect will be discussed at a later stage. (b)
Drop Ho tion
On account of throu~hput requirements drops in spray and sieve-plate columns are formed by jet break-up. In fact, sieve plates will not work satisfactorily unless jet formation occurs at all holes (7). Consequently, the dispersion is polydispersed unless the interfacial tension is low when a narrow size spectrum is obtained even under jettin~ conditions. A polydispersed swarm of drops is difficult to describe as drops of different size move with different velocities. Such a situation is favourable to enhance coalescence as drops pass each other or get caught in the wake of another drop. The direction of mass transfer, as explained later, is here of particular importance. Jet break-up for mass transfer into the drops produces smaller droplets than in the opposite direction of transfer and mass transfer will also oppose
617
coalescence. Hence, in this case, it is reasonable to assume that drops throughout the columns will be of formation size. The opposite will occur for ' mass transfer out of drops. Not only will drops produced by jet break-up be large but they will grow as the result of mass-transfer assisted coalescence until they reach a critical size. Any drop above the critical size will break up. A detailed description of such behaviour is outside the scope of this treatment which will be restricted to the behaviour of single drops.
A drop rises or falls through a liquid as the result of buoyancy or gravity forces opposed by frictional resistance to motion. The latter is characterized by a' drag coefficient, C , the knowledge of which makes it possible to calculate drop vePocity and hence the residence time of the drop in the column. Although the variation of drag coefficients with Reynolds number is well known for solid spheres, this is not the case for liquid drops, as shown by th~bottom line of Fig. 2. 1.4 1.2 ~
1.0
~
ru
.~
0 .~
0.8
~ ~
ru
0
u
0.6
~
ro
H Q
0.4 0.2 0 200
400
600
800
Re Fig. 2. Drag coefficient of nitrobenzene drops falling through water: e - pure p~ases, ~ - transfer of propionic acid into drops (CC = 0.375 kmol/m , CD = ~), 0 - transfer of acid out of drops (CC = 0, CD = 0.125 kmol/m The curve for solid spheres is dra~vn in for reference purposes.
618
Although small drops behave like rigid spheres, this similarity of behaviour does not extend beyond a Reyno1ds number of around 10. For larger drops internal circulation of the Hadamard-Rybczynski type sets in which reduces the drag coefficient to a value below that of a corresponding solid sphere. However, larger drops are also subject to deformation, the extent of which depends on the Weber number (8) dh/d
v
=
1.0 + 0.09/WeO. 95
(3)
. ' where We = du 2 p / y (d .1S the d1ameter 0f equ1valent sphere, subscripts h, v re~er to horizontal and vertical direction respectively, u is the relative drop velocity, y the interfacial tension and p the density of the continuous phase). Deformation becomes thereIore significant at We 1 and this will start counteracting the effect of internal circulation. According to Kintner (9) drop oscillation begins at We = 3. This overcomes the effect of internal circulation and with further increase of drop size the drag coefficient starts rising. The increase in drag coefficient becomes very pronounced since, on account of non-uniform vortex shedding, the drop ceases to move in a straight line and follows a zig-zag pattern. Finally, oscillation of drops is converted into a random change in shape and the 9roP disintegrates at around We = 12. It should be noted that relations CD = f(Re) ar~ reported (10) in which the drag coefficient does not drop below the value of a corresponding solid sphere. It can be assumed that in such cases the liquids were not free of impurities.
2.
BEHAVIOUR AND CHARACTERIZATION OF DISPERSIONS
(a)
Host of the work on characterization of dispersion is restricted to the determination of the Sauter mean drop diameter, d 32 , or the interfacial area per unit volume of dispersion, a, ana of the volumetric hold-up of the dispersed phase,~. These parameters are related by the equation: 6~/a
(4)
The problems encountered will be discussed with reference to a fully-baffled stirr~d tank operating under fully turbulent conditions, i.e. Re > 10. Under these conditions the Newton number, Ne, also called the power number, is constant so that the expression for power consumption P is p
const
(5)
619
where D is the imp~ller diameter and N the stirring speed (Hz). In such a tank the dispersion can be regarded as consisting of large eddies, generated
