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A countercurrent adsorptive reactor for acidifying bioconversions
ChemicalEngineeringScience, Vol. 51, No. 10, pp. 2315-2325, 1996
Pergamon
Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0009-2509/96 $15.00 + 0.00
S0009-2509(96)00088-7
A COUNTERCURRENT ADSORPTIVE REACTOR FOR A C I D I F Y I N G B I O C O N V E R S I O N S L.A.M. V A N DER W I E L E N , P.J. DIEPEN, J. H O U W E R S and K.Ch.A.M. L U Y B E N Department of Biochemical Engineering Delft University of Technolog? Julianalaan 67 2628 BC Delft, "[he Netherlands
Abstract - A :ountercurrent adsorptive reactor, based on the segregation tendenc~ of dense sorbcnt particles through a liquid fluidized bed of light biocatalyst particles, is described lor the acidil~'ing production of the key pharmaceuti,,', intermediate ~Aminopenicillanicacid from Penicillin G Mass transfer limited release of hydroxide l?om an ion exchange resin xsith simultaneous separation of the product by ion exchange, enabled axial control of the pH and product inhibition fhe complexityolthc countcrcurrent Trickle How Reactor requires a mathematical model, incorporating the efli~ctsof h3drodynamics, heterogeneous biocatalysis and multicomponent ion exchange. Such a mode[ is presented and the parameters in the Three Phase -liquid, biocatalyst, sorbent- Model were determined from independentexperiments. Model predictionsgave an adequate descriptionof experimentalreactor pcrfi)rmancc Using this model, the sensitivityof key parameters in the model, such as sorbent to liquid feed ratio and ion exchange ~electivit~,and reactor optimization are readily studied INTRODUCTION Simuhaneous product formation and recovery in a reactor-separator has been shown to be beneficial tbr systems with common thermodynamic and kinetic limitations. Integrated reaction-separation is in particular promising for instable biotechnological products in pH-sensitive biocatalytic systems (Hoist and Mattiasson, 1991; Freeman e t a / . , 1993). Various authors have reported adsorption and ion exchange to be convenient for integrated product separation (Kuczynski, 1986: Davison and Scott, 1992: Van der Wielen et al., 1990, 1993a). Integrated reaction-separation can be favorable Ibr the enzymatic deacylation of benzylpenicillin (Pen G) giving the target product 6-aminopenicillanic acid (6-APA) and phenylacetic acid (PhAc) as the acid by-product. PhAc-liberation decreases the reaction rate directly via inhibition and indirectly via pH-decrease. Furthermore, both reactant (Pen G) and desired product (6APA) decompose upon pH-deerease. In a previous paper, we described two alternative processes for continuously removing the unwanted phenylacetic acid and to control the pH during the reaction. Both approaches were based on fluidized bed systems of immobilized penicillin acylase with countercurrent adsorption using OH--charged resin particles (Van der Wielen e t a / . 1995al. The stoichiometric scheme for the enzymatic catalysis reads:
PenG
--~ 6 - A P A -
+ Ph,.tc
(11
+ H
and for the ion exchange reaction:
PhAc-
+ H + + resin-OH-
--~ r e s i n - P h A c
+ H~O
I2)
Alternatively, OH- can be replaced by HPO4-. The reactor exploits the segregation tendency of relatively dense sorbent particles in a fluidized bed of lighter biocatalyst particles to realize either a semi-continuous Pulzed Flow or a fully continuous countercurrent Trickle Flow of adsorbent (Van der Wielen et al., 1993a). A modified Extraction Factor based on the capacity ratio of the countercurrent sorbent and liquid flow has been demonstrated to be a convenient parameter for short-cut reactor design (Van der Wielen et al., 1995a). Preliminary studies favored the continuous Trickle Flow mode of operation. The Trickle Flow mode is shown schematically in Figure 1. The reactor allows for continuous operation as well as retention o f l h e light immobilized biocatalyst in a controlled manner. By selecting an anion exchange resin which is charged with OH--ions and which is selective for the inhibiting phenylacetic acid, some advantageous effects can be realized simultaneously: (i) the pH can be controlled along the reactor by the diffusion controlled release of the hydroxide ions, (ii) further downstream processing can be facilitated when both reaction products are separated in the reactor, (iii) the plug flow behavior of the reactor is favorable in case of product inhibition and (iv) the product inhibition can be reduced by removing the inhibiting species. 2315
2316
L.A.M. VANDERWIELENet aL
Sub-models
sorption Simple criteria such as the modified Extraction Factor '".." ,-all phac allow for a preliminary selection of operating I l / " l "~_, Pen G conditions. However, an accurate design of the Trickle Flow Reactor (Figure l) requires a detailed description of the hydrodynamics and the simultaneous reactionsorption phenomena, including the mass transfer effects between and within each of the three phases. We have ~~~i,,,,, - ~ Pen G developed a hydrodynamic model and tested it experimentally for the sedimentation velocities of heavy (or large) particles in fluidized bed systems of others particles (Van der Wielen et al., 1995bc). Multi".o~. reaction Three Phase Model ej • component ion exchange equilibria of the reactants have been investigated experimentally and a Figure ! Schematicrepresentationof the countercurrentTrickleFlow multicomponent ion exchange model, requiring binary Reactor and of the Three Phase Model. data only, has been developed (Van der Wielen et al., 1995d). In addition, a reaction-diffusion model has been developed to describe the kinetics of the heterogeneous biocatalyst over a wide range of reactant concentrations and pH~values (Van der Wielen et al., 1993b). Aim o f the paper
Relevant aspects of these models are integrated in a transient Three Phase Model for the Trickle Flow Reactor for the penicillin G deacylation. The model was verified using experimental results from integrated penicillin G conversion experiments in a laboratory scale reactor. Some characteristics of this new reactor are investigated. The model is also capable of simulating transient behavior, in particular start-up and close-down of the reactor as well as sensitivity of reactor performance to key parameters. This will be subject of a future publication.
D E V E L O P M E N T O F THE T H R E E PHASE M O D E L
We have chosen to derive a model to predict transient and steady state behavior of the countercurrent adsorptive Trickle Flow Reactor. This option is selected, instead of developing a steady state model, for two main reasons. The first reason is obvious: a model capable of predicting both transient and stationary behavior is more widely applicable than the corresponding steady state counterpart. The second reason is less obvious. The non-linearity of the resulting equations might, depending on the relevant parameter space, result in multiple solutions for the steady state situations (Dodds et al., 1973). This work is restricted to the simulation of start-up conditions and the computation of the corresponding steady state. The occurence of multiple solutions might slow down the convergence of the algorithm. However, identifying multiple solutions is a troublesome task and is not the aim of the present paper.
Continuity equations The following simplifying assumptions are made in the Three Phase (biocatalyst-liquid-sorbent) Model for the continuous countercurrent adsorptive Trickle Flow Reactor for enzymatic reactions: 1. 2. 3. 4. 5. 6. 7.
The reactor is in a hydrodynamic steady state with respect to hold-ups and fluxes of solids and liquid. The hold-ups of the biocatalyst, sorbent and liquid phase are uniform throughout the reactor. Isothermal operation of the reactor. Negligible radial gradients in the composition of any of the compounds. Deviations from plug flow behavior of liquid and sorbent flows are lumped in an axial dispersion coefficient for each phase separately. The biocatalyst activity can be described with a composition dependent effectiveness factor. The multicomponent ion exchange can be described by a constant selectivity model and a linear driving force model, lumping external and intraparticle mass transport.
Deviations of plug flow behavior are typically caused by velocity gradients in the reactor, by non-uniform liquid and solids distribution and by possible aggregation of the particles. Although deviations from plug flow behavior for the liquid flow and the countercurrent sorbent flow will be small (Van der Wielen et al. 1993b), we have incorporated them in the model by means of a single axial dispersion coefficient for each phase, to determine the sensitivity of the reactor to mixing phenomena. Therefore, an one-dimensional, axially dispersed plug flow model is used for the reactants in the fluid and sorbent phase. The axial coordinate z is positive in the upward direction.
A countercurrent adsorptive reactor
2317
The instationary continuity equation for the liquid phase concentration of reactant j reads:
e
~C /,-~
c~ C
' = e~E~__ .
- e~.u
/ . Oz 2
OC
l
, ~
- aa4 a -
g
n R 0¢) R ...... /
- 6,1R/I}
(3)
J,A is the molar flux of speciesj towards or from the sorbent particles (A), a A is the interfacial area of the sorbent, Rff ~ and R,a~ are the reactions in the biocatalyst particles (R) and the buffer reaction in the bulk of the solution (L) respectively. Qj is the average concentration of component j on the sorbent. The reaction in the biocatalyst is calculated at bulk conditions and is corrected with the overall effectiveness factor riov. The liquid phase has a hold-up eL, a linear velocity u t and an axial dispersion coefficient E L. The accumulation of species j at the adsorbent is described with the following equation:
e4°Q~ = e4EA__~Fz,(32QJ+ e4uC?QJ+a.~j,. ~
(4)
The linear driving force approach for the flux is usually convenient at lower concentrations and low sorbent loading when linear isotherm-conditions are approximately satisfied (Ruthven, 1984). This gives the following flux relation aAJ,, ~ = e J % ( Q , "
(5)
- Q,)
Q[ is the concentration of speciesj at the sorbent material at equilibrium with the liquid phase. The overall mass transfer constant kjA lumps the effects of external and internal mass transfer resistances of a homogeneous, geltype sorbent particle. A possible estimation for these quantities is given in a later section.
Boundary conditions The boundary conditions for this reactor are taken as closed at inlet and outlet of the system in the well-known Danckwerts form. For the liquid inlet-sorbent outlet of the reactor (z=0), this yields "
dCi = u1" (C
dQ~
-~- eL'-c,.) -_~_
= 0
(6)
and for the liquid outlet-sorbent inlet at the top of the reactor (z=L), one obtains
dQi = - u 4 dz
dC
E'7 (Qi - Qj/.); T
= 0
(7)
where QjF is the loading of component j at the regenerated ion exchange resin.
Dimensionless equations The large difference in time constants of the (instantaneous) buffer reaction in the liquid phase and the finite rate deacylation reaction in the biocatalyst introduces substantial stiffness in the set of partial differential equations. Therefore, we have eliminated the buffer reaction from the equations by pairwise adding of the continuity equations for HzPO4/HPO4 = and HPO4-/H* and by introducing the time derivative of expression for the buffer equilibrium. Substitution of the dimensionless variables z (= x L) and t (= ~L/u O, the set of equations (3-7) gives a~
O'r
_
0C___2 - CtASt~(Qj" - Q,) - %~Dal/n,,,r,
1 O2Cj
Pel.
OX 2
(8)
~X
and
OQ! c3"r
-
1
O:Qj
Pe A
Ox 2
, ~2
~o u~
j + stj(Q,"
- Q)
(9)
2318
L.A.M. VANDERWIELENetal.
with CtR=eR/eL,CtA=eA/eL, B=UA/UL, Sti=kjAL/u L and D a l = L k / u L. The boundary conditions are formulated accordingly for the bottom of the reactor :
c,
d____z'=PeI(cj-Cw) ; dQ) ~.~ =0
(10)
dx
and the top of the reactor
dQj
dCg
= - P e A ( Q j - Q;I.-) ; ~
=0
(11)
Because boundary conditions are specified at the bottom and the top of the reactor in the form of equations 10 and 11, the Three Phase Model is a two-point boundary value problem. Note that the model presented by Kiel et al. (1992) has an identical structure as the model presented here. N u m e r i c a l solution o f the Three P h a s e M o d e l
The set of coupled, non-linear partial differential equations has been solved with the 'method of lines' as described in earlier work (Van der Wielen et al., 1993a). This involves the space-discretization of the 2*NC partial differential equations into a system of 2*NC*(NP+I) ordinary differential equations for a grid of (NP+I) points. The latter are integrated in time using a common integration algorithm for ordinary differential equations such as the fourth order R.unge-Kutta algorithm. The first order differentials are approximated at x=iAx with an upwind difference scheme according to : a j 8y(iAx) = a i &
yi
-
yi-I
ifai<0;
=a i
yi*l
Ax
-Y Ax
i
ifai>0
(12)
and the second order differentials are approximated by central differences 0 2 y ( i A x ) = yi.t _ 2 y i Ox 2 Ax 2
+
yi-I
(13)
with i = 0,1 ..... NP. Initial values for the simulation of transient situations are given by the appropriate concentration values at the start of the simulation. The steady state solution of the system of equations is provided by convergence from a given, arbitrary initial situation to the steady state solution. To test for the possible occurrence of multiple steady states, we have used various initial conditions, which should give the same steady state solution. It should be noted that convergence to the steady state solution might -of course- be accelerated when initial profiles are provided which are relatively similar to the final numerical result. These initial profiles could be provided by solution of simplified forms of the Three Phase Model. The incorporation of the Danckwerts boundary conditions in the numerical algorithm requires some extra care. The grid points at the boundaries have to satisfy both the boundary conditions and the differential mass balance equations, The central difference approximation for the second order term requires a virtual point at the first and last positions of the grid, which are located outside the grid (i= -1 at x=0 and i=NP+I at x=l). These virtual points are eliminated from the scheme by substitution of the finite difference approximation of the boundary condition. The boundary condition for the liquid phase mass balance of component j at the bottom of the reactor than becomes: C/ - Cj-' 2Ax
= PeL(C/o _ C/.)
(14)
The resulting ordinary differential equation for the liquid phase concentrations reads:
ac/
c'"j - 2 c / + c / - '
cj'-q'-'
=
&
Per Ax 2
_ %Sti(Qj"
_ Q/) _ %¢Dalirl,,vr /
(15)
Ax
Disturbances in the liquid phase concentrations propagate from bottom to top at a maximum rate which equals the interstitial fluid velocity, whereas disturbances in the sorbent loading propagate from top to bottom at the solids velocity. This has of course impact on the numerical stability of the simulation of the dynamic behavior. The maximum ratio of time step and spatial mesh size for stable numerical solution can be estimated from the Courant
A countercurrent adsorptive reactor
2319
criterium. For disturbances in the liquid phase, the Courant criterium should be based on the interstitial liquid phase velocity whereas for disturbances in the solid phase, the Courant criterium should be based on the solids velocity. In the framework of equations 8 and 9, this corresponds to: A't < 1 iffl -< 1
and
A'~ <. 1 iffl > 1 ax /3
Ax
(16)
This is valid for high enough Pe-numbers (Pe>100). Because the axial dispersion is superimposed on the propagation velocity of the convective wave and 'information' is travelling at a higher rate than the convective wave, a larger amount of time steps i,; required.
ENZYMATIC DEACYLATION OF PENICILLIN (; The equilibrium conversion as well as the kinetics of the penicillin G deacylation are strong functions of pH, particularly at lower pH values (pH<7). In Figure 2, the pH-dependencies of the apparent equilibrium constant and maximum reaction rate are shown. Deviations from the thermodynamically ideal situation are mainly caused by the ionic strength of the solution and are relatively small (Tewari and Goldberg, 1988). The pH in the Fluidized Adsorptive Trickle Flow reactor may vary over the reactor length. Therefore, we have used the following, pHdependent expression for the reaction equilibrium which is valid in the relevant pH-interval (5.5
= K.,I = K"Pf'
Cl'e,,~,
-('ft
(17)
e,I
The catalytic mechanism of the penicillin amidase is described with a pseudo-uni-bi ping-pong model (Warburton et al., 1973). The reaclion rate is very dependent on pH, apparently due to an imidazole dissociation of a histidine amino acid in the active site with a pKaE of approximately 6.8 (Van der Widen et al., 1993b). As only the "neutral' fraction of the enzyme (bE°) is catalytically active, we have slightly modified the rate model by incorporating the effect ofpH on the reaction rate. The resulting relation which seems to be valid for a wide range of concentrations of reactants and pH (pH 5.5-8.5), reads :
K~41 [ c A - ~ -- R , = Fl;° kt¢
(1 + - -
c.,
K,,,A
I
Ix"/ ] % )( c~, + ~ 1 +__) K v
with /:," = _ _ 1
Kij
1 +
(18)
(7H K j
The indices correspond to PenG (A), 6-aminopenicillanic acid (P), phenylacetic acid (Q) and enzyme (E). The kinetic constants used in this work are summarized in Table 1. Note that the extent of conversion declines drastically, both in absolute magnitude and in rate when the pH is lowered to about pH 5-6 due to the combination of the pHdependencies of the reaction equilibrium and the reaction rate of the enzyme. Acidification o f the B i o c a t a l y s t ' s lnterior a n d Effectiveness Factor C a l c u l a t i o n
For the non-linear reaction kinetics of the deacylation, the relation between the effectiveness factor and the bulk concentrations of reactants and buffers is not straightforward (Van der Wieien et al., 1993b) but in principle depends on each of the species. Transport of the protons generated by the reaction in the biocatalyst particle is restricted by electrostatical coupling to the fluxes of the charged, bulky biomolecules. This causes a substantial lowering of the effectiveness factor due to internal acidification of the biocatalyst, which occurs already at very, low substrate concentrations. The buffer transports the liberated protons from the biocatalyst's interior towards the bulk of the liquid and thereby controls the pH in the biocatal~st's interior. Description of this phenomenon requires a mathematical effort, which is beyond the scope of the current paper but which is provided in a separate paper (Van der Wielen et al., 1993b). For a given biocatalyst, the relation between effectiveness factor and buffer concentration can be approximated with an proportionality with the active fraction of the buffer species (base form for acidifying reactions). We have used this approximate relation to reduce CPU-time.
L. A. M. VANDERWIELEN et al.
2320
Table 1 Kinetic parameters of the penicillin deacylation reaction at 310 K, determinedin batch experiments Keq
1.153 10.8
kR
- 10-3 *)
KmA K,O
1.257 10 .3 0.1828 3.555 10 .3
KaE
1.585 10.7
Kip
l~nol m-3 s-I kmol m 3 kmol m -3 kmol m -3
at 50 mol/m 3 phosphate buffer, pH 8; * exact value depending on enzyme loading.
O 5
6
7
8
9
pld It should be noted that the effectiveness factor results from the transient reaction-diffusion process and therefore may also depend on reactor history. For reactor start-up, this will result in an apparent decrease in the overall effectiveness factor due to mass transfer limited accumulation of the reactants in the biocatalyst particle. In a later section, we will discuss the computation of the effectiveness factor in the context of this model. The steady state transport of reactants and buffers in the biocatalyst particle is equimolar co-diffusion of the penicillin G and HPO 4 anions in the matrix and counterdiffusion of6-aminopenicillanate, phenylacetate and the H2PO 4"anions. Because the counterion (K ÷) of these anions is chemically inert, its steady state flux remains zero. The diffusion coefficients of the species are rather similar and the transport during the heterogeneous bioconversion is described with a single, effective diffusivity ensuring electroneutrality. Figure 2 Fractions of the maximumrate (v), equilibriumconversion
(o) and PenG stability([]) as a functionofpH at 310 K
Constraints
During our experiments, hardly any enzyme deactivation was observed when operated at normal conditions (310 K, pH 5.5-8.5). Therefore, the impact of enzyme deactivation on reactor performance is not explicitly incorporated in the model. However, the stability of B-lactam components is a strong function of pH. Benedict (1949) and Dennen (1967) have investigated the kinetics of the hydrolysis of PenG and 6-APA respectively. Both hydrolysis reactions follow first order kinetics with pH dependent rate constants. The optimum pH with respect to the stability of penicillin G is about pH 6 (Benedict, 1945). The interior of the OH--charged resin corresponds to a solution of about pH=13. Contact of the fl-lactam molecules with this harsh environment leads to rapid degradation and should be minimized. The short liquid and solids residence time in the Trickle Flow reactor helps in this respect, which gives a kinetic advantage to the fastest or most highly charged components such as the phenylacetate ion. This may improve the selectivity of the ion exchange towards phenylacetate and decrease the unwanted fl-lactam sorption. Ion E x c h a n g e Equilibria a n d Kinetics
We have measured ion exchange equilibria of the reactants (X) relative to OH- and CI- in binary batch experiments (Jansen et al, 1996; Van der Wielen et al, 1995c). The measured selectivities of anions X" relative to OH- are shown in Figure 3 as a function of the ionic fraction of X- in the liquid phase. The selectivities decrease with increasing ionic fraction, which is partially due to steric effects. This behavior is well known for bulky sorbates and can be modeled satisfactory with the Myers and Byington isotherm (Myers and Byington, 1986). The equilibrium composition in multicomponent mixtures is calculated as follows: Q/
=
SLrxJ
(19)
100
in 10
~A\o ooo o "~
o PhAc
A Ai
6 APA
-%:Z° 0.0
0.5
1.O X
k Figure 3 Ion exchange selectivities of the reactants relative to OH. Pen G (.), 6-APA (A) and PhAc (0). with j and r indicating the species of choice and the reference species respectively. Unfortunately, the selectivity at low ionic fractions favors the relatively hydrophobic Pen G, but the selectivity reverses at higher ionic
A countercurrentadsorptive reactor
2321
fractions to the more polar PhAc due to steric effects. Countercurrent contact in combination with the kinetic advantage increases the operational selectivity towards PhAc, but a further decrease of the pore size would be favorable. For the estimation of the overall mass transfer coefficient, a modified Glueckauf equation is used (Ruthven, 1984).
k:-"-~
6k:A + 66-'DA,,,/:]
For external mass transfer towards and from the biocatalyst and the resin, the correlation given by Tournie et al. (1979) for monocomponent fluidized beds was used. The fluxes towards and from the ion exchange resin are described in this way as long as the OH-content of the resin is not exhausted. Because electroneutrality applies, the flux of OH-ions from the resin to the liquid phase has to balance the combined fluxes of the adsorbing electrolytes. Therefore, the flux of OH-ions is computed from the fluxes of the adsorbing species as follows:
J,m = ~ z,J,
(21)
t
with i is PenG-, 6-APA-, PhAc-, HPO4= and H2PO4- respectively. The liberated OH--ions react instantaneously with the protons in the liquid phase and re-establishe the equilibrium. In the numerical model, the flux of hydroxide is modeled as a W-consumption term. The diffusion coefficients of all species are similar, which is a good assumption in ionic systems (Helfferich, 1962; Van der Wielen et al., 1993b). Equation 21 assures electroneutrality.
Hydrodynamics Crucial parameters in the model of the Trickle Flow reactor are the hold-up eA and linear velocity uAof the sorbent phase. Elsewhere, we have described a hydrodynamic model for the falling velocity of dense (sorbent) particles through a fluidized bed of lighter (biocatalyst) particles supported by a perforated plate (Van der Wielen et al., 1995b). The flow rate of the dense phase is governed by the transport through the holes in the perforated plate, which is at flooding conditions. The computation of the flow rate of dense solids requires information on the fluidization characteristics of the dense solids in the form of the Richardson and Zaki (1954) exponent n2, the terminal velocity ut2 and the liquid approach velocity ULhof the holes. The latter equals the superficial liquid velocity ULoin the column corrected for the free area fraction of the perforated plate ~ ) . In our experimental set-up, the ratio of hole diameter to diameter of the dense particle was rather low (<20) and the holes had a conical shape which causes turbulences. The actual terminal velocity in the hole of the plate was usually some 20% lower than that of a free falling particle without the wall effects. Corrections of the terminal velocity from infinite conditions to those of the hole of the plate by incorporation of the wall effect was usually sufficient. Experimentally obtained values at raining conditions in the hole of the dense phase provided the best description of the sorbent flux as a function of liquid velocity. See Figure 4 for the experimental and predicted sorbent fluxes for a free area percentage of the plate of 20.4%. The steady state flow rate of the dense phase through the Table 2 Propertiesof the biocatalystand the ion exchangeresin. hole equals the flow rate of the dense phase through the fluidized bed section. The hold-ups of the biocatalyst and Particle Reimmobilized Sorbent the sorbent, eR and e~ respectively can be obtained by Biocatalyst IRA 400 iterative solution of the multicomponent form of the hydrodynamic model. In practical situations, when the d [mm] 3.5 0.6 densities of biocatalyst and sorbent deviate not too much u, [mm/s] 18.9 25.3 (50-100 kg m3) and at relatively low solids flux, the u: [mm/s] 24.3 3 I. 1 hold-up of the sorbent is rather low (<2-5%). The bulk n [-] 2.53 4.28 density of the binary solids system is mainly determined p [kg/m 3] 1013 1065 by the fluidized bed of the lighter species. Then, the velocity of the dense particles can be computed explicitly *) raining velocity in hole of the perforated plate from a simplified form of the hydrodynamic model for a single particle falling in a fluidized bed of the lighter species. The corresponding hold-up of dense phase is then computed from the preset flux dA divided by the velocity of a single dense sorption particle. For high sorbent flow, the hold-up of the sorbent and thereby its influence on bulk density are not negligible. Then the complete model should be used.
2322
L.A.M. VANDEa WmLENet al.
EXPERIMENTAL SET-UP AND PROCEDURES
3 E
Materials In this work, we have used commercial Pen G and Pen G acylase catalyst (SeparaserM), donated by Gist-brocades NV. The biocatalyst was supplied in immobilized form, with a small diameter. As the catalyst was designed for other operating conditions than used in the Trickle Flow reactor, it was re-immobilized in a gelatin/alginate matrix using the resonance nozzle technique described by Hulst et al. (1985). Prior to reimmobilization, the original biocatalyst particles were disrupted to ensure homogeneous distribution throughout the new immobilization matrix. This procedure resulted in particles with the required low density and millimeter range diameter. The loss of enzyme activity during this procedure was about 20%. The ion exchange resin was a commercial grade strong basic anion exchange resin IRA 400 with a polystyrene backbone with a mesh size 20-50. The physical properties, including fluidization characteristics of the biocatalyst and sorbent particles are given in Table 2.
¢ -6
2
-× ~-
1
-~ ~
O O liquid
10
20
flux
~rn h o l e
30 mm/s]
Figure 4 Experimental and simulated sorbent fluxes as function of the superficial liquid velocity for free area fraction fh~0.204.
Laboratory scale reactor We have used the glass laboratory scale reactor set-up as described earlier (Van der Wielen et aL, 1990-5a). The main body of the reactor consisted of two jacketed, 0.88 m long sections with an internal diameter of 0.0354 m. The system was equiped with a pulseless rotary gear pump which was controlled by a PC coupled ADI- 1030. The reactor was modified to enable operation as a Trickle Flow reactor and some modifications for the usage offl-lactam antibiotics were made. The Trickle Flow mode results in high flow rates of the sorbent. For this situation, the lowdiameter piping at the bottom of the reactor showed to be a bottleneck in the solids removal. Therefore the bottom part of the reactor was replaced by a two-way perspex Y-valve with a teflon central part with a larger bore (2 cm). However, this was not enough to prevent plugging of the lower part of the reactor at higher sorbent flow rates. However, by connecting a 'closed' circuit with two removable, water filled vessels for the collection of the sorbent, a bubble trap and a second, pulseless rotary gear pump to the bottom of the reactor, it was possible to remove the sorbent particles at a high rate. This is shown in Figure 5.
At three locations along the reactor, pH-sensors were installed. Their signal and that of the magneto-inductive flow meter at the substrate feed flow were monitored via on-line data-acquisition. At three locations along the reactor, peristaltic pumps were installed to automatically draw samples from the reactor. Each PCcontrolled pump could draw samples from two sample ports simultaneously. One plate was mounted in the reactor provided with a central hole of the conical shape as decribed by Van der Wielen et al. (1995a). The sorbent was supplied from the top of the reactor from a glass vessel similar to the biocatalyst feed with a computer controlled peristaltic pump.
exit
11t
'--[~
feed
i
PC Laboratory scale Trickle Flow Reactor: reactor ~, pH-monitoring2'3, pulse mechanism4, sorbent supply 5, rotary gear pump 6, automatic sampling system 7, sorbent collection s, bubble trap 9.
U
,
O
m
_?
Figure 5 Laboratory scale Trickle Flow Reactor.
Operation of the Trickle Flow Reactor The first step in the start-ui~ of the reactor is to feed the reactor with the buffer solution at a flow rate well above the raining velocity of the biocatalyst particles through the hole in the perforated plate. Then adsorbent is supplied at a somewhat higher rate than the final set point. Because the sorbent flux is above the flooding condition, the resin accumulates in a 2-5 cm thick layer just above the plate. This prevents raining of the lighter biocatalyst and in general improves stability of the operation. The liquid flow rate can be decreased below the raining velocity of the
A countercurrent adsorptive reactor
2323
biocatalyst and the sorbent flow is adjusted accordingly. Analysis of the samples drawn from the reactor was performed by reversed phase HPLC and by capillary zone electrophoresis (CZE) on a Waters Quanta 4000 Capillary Electrophoresis System with a 50 cm, non-coated silica capillary. Table 3 Conditions for the experimental runs Run
resin
Pen G in feed mol m -3
1. 1-3 II. 1-3 I11.1-3 IV. 1-3 V. 1-3
OHOHOH HPO 4HPO4 =
32.1/52.2/49.1 49.1/49.4/52.01 47.3/38.8/38.9 45.6/47.2/44.6 45.1/36.4/37.4
¢t, L/h
qb,,/~bL
22.3/12.5/13.5 23.0/15.2/15.2 23.0/15.3/15/3 24.0/24.0/11.3 24.0/11.1/21.5
-/0.136/0.126 -/0.11/0.11 40.11/0.11 -/-/0.15 -/0.07/0.06
RESULTS
Operation without sorbent Figure 6 shows experimental axial profiles for the conversion of a 50 mol m50 11 3 penicillin G solution (pH 8, 310 K) in an aqueous buffer of 50 mol m 3 40 10 Pen G potassium phosphate without resin flow. The Dal-number and the catalyst hold-up were sufficiently high to ensure full 30 9 C pH conversion when the pH could be mol m3 maintained at pH 8. However, the pH 6-APA,PhAc 20 B decrease of the pH has a two-fold effecton the reaction rate, irrespective the 10 7 buffering effect of the phosphate. Firstly, it causes a decrease in the reaction rate i I 0 6 due to a shift in the reaction equilibrium. 0.5 1.0 z 0.0 1.5 Secondly, it decreases the activity of the m biocatalyst. Now, the reactor is not operated as an adsorptive Trickle Flow Figure 6 Experimental (markers) and simulated liquid composition profiles Icurves) at system. The conversion is computed with ¢^=0 (Run I1.1). Pen G ('), 6-APA (A) and PhAc (~). the Three Phase Model, setting the fluxes to and from the sorbent to zero. Model predictions and experimental data, using the data from Table 1-3, coincide within experimental error (< 5%).
~
Table 4 Base case data for the laboratory scale reactor Operation as countercurrent adsorptive Trickle Flow Reactor By starting the resin flow, the system pe A 50 c~R 0.11 qo, 0.5 was operated as a countercurrent pe L 50 c~.x 0.03 qbA/¢t 0.11 adsorptive Trickle Flow Reactor for the same feed conditions. In Figure Pen G 6-APA PhAc HPO 4 H2PO 4- H + 0H7, the effect of the countercurrent resin flow on the liquid composition Dal 45.7 45.7 45.7 45.7 profiles is demonstrated for S),oH 5.8" 6.2 12.4 8 7.3 1 experiment 1II.2 (d~A/~L=0.11). The St 7.3 9,8 9.8 13.6 13.6 13.6 pH was maintained at the set-point in the lower section of the reactor, but ~. average value in Myers and Byington model, variance increases sharply towards the top of parameter Wpe,g,OH_=14.7, skewness p=0.5 the reactor. The PenG-profile shows the gradual decrease along the reactor due to bioconversion and nonselective sorption. The reaction products show the typical parabolic profile due to product generation in the bottom section and countercurrent ion exchange in the top section of the reactor. The composition profiles have also been
2324
L.A.M. VANDERWIELENet al.
simulated with the Three Phase Model (curves) using the data from Tables 1-4, and provide a fair description of reactor performance. 60 11
5O
c 40
10
10
"~
G
9p H
~
0 0.0
7
0.2
0.4
0.6
0.8
6 1.0
x
Figure 7 Experimentaland simulatedliquidcompositionprofilefor ~A/~t=0.11 (Run 111.2).Pen G (.), 6-APA(A), PhAc(o) and pH (i). Location o f the p H shock The simulation with the Three Phase Model 11 shows a 'shock' profile of the pH, which is characteristic for countercurrent, adsorptive lO reactors (Rhee et al, 1989). The location of the pH shock corresponds to the near-complete 9 removal of the base form of the buffer (mono hydrogen phosphate ion) by ion exchange. The 8 diffuseness of the shock layer can be attributed to the axial dispersion in the system. In the top 7 section above the shock, the rate of the 0.05 acidifying bioconversion can not compensate I l I I 6 for the hydroxide release of the resin and the o.o 0.2 0.4 0.6 0 8 1.O pH increases to high values. This phenomenon x is unwanted because of rapid degradation of 13lactams in strongly basic environment. Hence, Figure 8 Calculated effect of varying ratio of resin and liquid flow ~^/~L at the shock position of the pH for parameters from Table I-3 (pH set-point: the Trickle Flow Reactor should be designed dotted line). such that the shock either does not occur or is located as close as possible to the liquid exit of the reactor. The position of the shock can be influenced by varying the resin-to-liquid ratio ~ A / ~ L . This is demonstrated in Figure 8 for various eA/¢V
CONCLUSIONS The Three Phase Model predicts the experimentally determined performance of the countercurrent adsorptive Trickle Flow Reactor adequately. It should be emphasized that the parameters in the model are obtained from independent equilibrium and rate experiments for biocatalysis, ion exchange and hydrodynamics and that model calulations are purely predictive and not fitted. Improvements can be made by incorporating more detailed modelling of, in particular, the heterogeneous biocatalysis and the multicomponent ion exchange process. This will further increase the complexity of the model and the computational effort. Hence, for optimization studies and parameter sensitivity analysis, the Three Phase Model presented in this work could be used as a starting point. In the top of the reactor, a drastic increase in pH may occur when the hydroxide flux exceeds the rate of the acidifying bioconversion. This increase has the form of a (diffuse) shock. Proper fine-tuning of the ratio of the sorbent to liquid flow rate for a specific sorbent shifts the shock towards the liquid exit, thereby reducing possible degradation of reactants and biocatalyst. Using the model, other process alternatives such as the use of ion exchange resins which are charged with monohydrogen phosphate could be investigated straightforwardly, provided that ion exchange parameters are known. An ideal sorbent should not adsorb Pen G and 6-APA, but take-up PhAc selectively. Hence, the relatively low selectivity of the ion exchange resin that was used in this study resulted in substantial and undesired adsorption of reactant Pen G. Using the model, the minimum requirements of a suitable sorbent can now be quantified. This is the the subject of current research.
A countercurrent adsorptive reactor
2325
ACKNOWLEDGMENTS Gist-brocades N.V. is acknowledged for the supply of penicillin G and penicillin acylase (SeparaseTM) and the Netherlands Organization for Scientific Research (NWO) for the financial support. Analytical support by C. Ras (HPLC) and H. Corstjens (CZE) is gratefully acknowledged.
NOTATION m:/m 3 a interfacial area kmol/m 3 C concentration d diameter m D diffusion coefficient m:/s E axial dispersion coefficient m:/s Ji free area fraction FE° active biocatalyst fraction ,J molar fluxes mol/mZs k overall mass transfer coefficient 1/s liquid phase mass transfer coefficient m/s kL L reactor length m Richardson and Zaki index n number of components NC ~) average resin phase concentration mol/m s F normalized reaction rate, eqn. (8) reaction rate mol/m3s R selectivity S l time s temperature K T linear, terminal velocity m/s /t, Ut X,2 (dimensionless) axial coordinate
Greek cq; 13
P
dummy variables, defined as eq=e/ee; uA/uc hold-up density kg/m 3
Dimensionless Damkohler(1) number Lk/u L Galileo number d3p2/~tL 2 density number (ps-pL)/PL Peclet number ULL/E Schmidt number WpD Sherwood number kd/D Stanton number k~AL/uL
Dal Ga My Pe Se Sh Stj
REFERENCES Benedict, R.G., Schmidt, W.H., Coghill, D. and Oleson, A.P., 1945, J. Bacteriol. 49, 85-95. Dennen, D.W., 1967, Y. Pharm. Sci. 56, 1273. Dodds, R., Hudson, P.I., Kershenbaum, I. and Streat, M., 1973, Chem. Engng Sci., 28, 1233-1248. Freeman, A., Woodley, J.M., and Lilly, M.D., 1993, BiG~Technology 11, 1007-1012 Helfferich, F. Ion exchange. McGraw-Hill Book Company, New York, 1962. Holst, O., and Mattiassson, B., 1991, Extractive Bioconversions, M. Dekker, New York Hulst, A.C., Tramper, J., Van 't Riet, K., Westerbeek, J.M.M., 1985, Biotechnol. Bioengng 27, 870-876 Jansen, M.L., Van der Wielen, L.A.M. and Luyben, K.Ch.A.M., 1996, accepted lnternat Conf Ion Exhange Development and Applications, Cambridge, 14-19 July Kiet, J.H.A., Prins, W. and Van Swaaij, W.PM., 1992, Chem. Engng. Sci. 47(17/18), 4271-4286. Kuczynski, M., Oyevaar, M.H., Pieters, R.T. and Westerterp, K.R., 1987, Chem. Engng. Sci. ,12(8), 1887-1898. Myers, A.L. and Byington, S., 1986, in Rodrigues, A.E. Ion Exchange. Science and Technology. NATO ASI Series Appl. Sci. E 107. 119-145 Rhee, H.-K, Aris, R. and Amundson, N.R., 1989, First Order Partial Differential Equations 11 Prentice-Hall, USA Tewari, Y.B., and Goldberg, R.N., 1988, Biophys. Chem. 29, 245-252. Tourni6, P., Laguerie, C. and Couderc, J.P., 1979, Chem. Engng. Sci. 34, 1247-1255. Warburton, P. Dunnill and M.D. Lilly, 1973, Biotechnol. Bioeng. 13, 25 Wielen, UAM. van der, Potters, J.J.M., Straathof, A.J.J. and Luyben, K.Ch.AM., 1990, Chem. Engng. Sci., 45(8), 2397-2404. Wielen, L.A.M van der, Straathof, A.J.J. and Luyben, K.Ch.A.M., 1993a, In M.P.C. ~eijnen and A.A.H. Drinkenburg Precision Process Technology, Kluwer Acad. Publ., 353-379, 493-502 Wielen, L.A.M. van der, Diepen, P.J., Straathof, A.J.J. and Luyben, K.Ch.AM., 1995a, Ann. N.Y. Acad. Sci., 750, 482-490 Wielen, L.A.M. van der, Dam, M.H.H. van, and Luyben, K.Ch.AM., 1995b, accepted Chem. Engng Sci. Wielen, UA.M. van der, Lankveld, M.J.A, and Luyben, K.Ch.A.M., 1995c, acceptedJ. Chem. Eng. Data
Pergamon
Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0009-2509/96 $15.00 + 0.00
S0009-2509(96)00088-7
A COUNTERCURRENT ADSORPTIVE REACTOR FOR A C I D I F Y I N G B I O C O N V E R S I O N S L.A.M. V A N DER W I E L E N , P.J. DIEPEN, J. H O U W E R S and K.Ch.A.M. L U Y B E N Department of Biochemical Engineering Delft University of Technolog? Julianalaan 67 2628 BC Delft, "[he Netherlands
Abstract - A :ountercurrent adsorptive reactor, based on the segregation tendenc~ of dense sorbcnt particles through a liquid fluidized bed of light biocatalyst particles, is described lor the acidil~'ing production of the key pharmaceuti,,', intermediate ~Aminopenicillanicacid from Penicillin G Mass transfer limited release of hydroxide l?om an ion exchange resin xsith simultaneous separation of the product by ion exchange, enabled axial control of the pH and product inhibition fhe complexityolthc countcrcurrent Trickle How Reactor requires a mathematical model, incorporating the efli~ctsof h3drodynamics, heterogeneous biocatalysis and multicomponent ion exchange. Such a mode[ is presented and the parameters in the Three Phase -liquid, biocatalyst, sorbent- Model were determined from independentexperiments. Model predictionsgave an adequate descriptionof experimentalreactor pcrfi)rmancc Using this model, the sensitivityof key parameters in the model, such as sorbent to liquid feed ratio and ion exchange ~electivit~,and reactor optimization are readily studied INTRODUCTION Simuhaneous product formation and recovery in a reactor-separator has been shown to be beneficial tbr systems with common thermodynamic and kinetic limitations. Integrated reaction-separation is in particular promising for instable biotechnological products in pH-sensitive biocatalytic systems (Hoist and Mattiasson, 1991; Freeman e t a / . , 1993). Various authors have reported adsorption and ion exchange to be convenient for integrated product separation (Kuczynski, 1986: Davison and Scott, 1992: Van der Wielen et al., 1990, 1993a). Integrated reaction-separation can be favorable Ibr the enzymatic deacylation of benzylpenicillin (Pen G) giving the target product 6-aminopenicillanic acid (6-APA) and phenylacetic acid (PhAc) as the acid by-product. PhAc-liberation decreases the reaction rate directly via inhibition and indirectly via pH-decrease. Furthermore, both reactant (Pen G) and desired product (6APA) decompose upon pH-deerease. In a previous paper, we described two alternative processes for continuously removing the unwanted phenylacetic acid and to control the pH during the reaction. Both approaches were based on fluidized bed systems of immobilized penicillin acylase with countercurrent adsorption using OH--charged resin particles (Van der Wielen e t a / . 1995al. The stoichiometric scheme for the enzymatic catalysis reads:
PenG
--~ 6 - A P A -
+ Ph,.tc
(11
+ H
and for the ion exchange reaction:
PhAc-
+ H + + resin-OH-
--~ r e s i n - P h A c
+ H~O
I2)
Alternatively, OH- can be replaced by HPO4-. The reactor exploits the segregation tendency of relatively dense sorbent particles in a fluidized bed of lighter biocatalyst particles to realize either a semi-continuous Pulzed Flow or a fully continuous countercurrent Trickle Flow of adsorbent (Van der Wielen et al., 1993a). A modified Extraction Factor based on the capacity ratio of the countercurrent sorbent and liquid flow has been demonstrated to be a convenient parameter for short-cut reactor design (Van der Wielen et al., 1995a). Preliminary studies favored the continuous Trickle Flow mode of operation. The Trickle Flow mode is shown schematically in Figure 1. The reactor allows for continuous operation as well as retention o f l h e light immobilized biocatalyst in a controlled manner. By selecting an anion exchange resin which is charged with OH--ions and which is selective for the inhibiting phenylacetic acid, some advantageous effects can be realized simultaneously: (i) the pH can be controlled along the reactor by the diffusion controlled release of the hydroxide ions, (ii) further downstream processing can be facilitated when both reaction products are separated in the reactor, (iii) the plug flow behavior of the reactor is favorable in case of product inhibition and (iv) the product inhibition can be reduced by removing the inhibiting species. 2315
2316
L.A.M. VANDERWIELENet aL
Sub-models
sorption Simple criteria such as the modified Extraction Factor '".." ,-all phac allow for a preliminary selection of operating I l / " l "~_, Pen G conditions. However, an accurate design of the Trickle Flow Reactor (Figure l) requires a detailed description of the hydrodynamics and the simultaneous reactionsorption phenomena, including the mass transfer effects between and within each of the three phases. We have ~~~i,,,,, - ~ Pen G developed a hydrodynamic model and tested it experimentally for the sedimentation velocities of heavy (or large) particles in fluidized bed systems of others particles (Van der Wielen et al., 1995bc). Multi".o~. reaction Three Phase Model ej • component ion exchange equilibria of the reactants have been investigated experimentally and a Figure ! Schematicrepresentationof the countercurrentTrickleFlow multicomponent ion exchange model, requiring binary Reactor and of the Three Phase Model. data only, has been developed (Van der Wielen et al., 1995d). In addition, a reaction-diffusion model has been developed to describe the kinetics of the heterogeneous biocatalyst over a wide range of reactant concentrations and pH~values (Van der Wielen et al., 1993b). Aim o f the paper
Relevant aspects of these models are integrated in a transient Three Phase Model for the Trickle Flow Reactor for the penicillin G deacylation. The model was verified using experimental results from integrated penicillin G conversion experiments in a laboratory scale reactor. Some characteristics of this new reactor are investigated. The model is also capable of simulating transient behavior, in particular start-up and close-down of the reactor as well as sensitivity of reactor performance to key parameters. This will be subject of a future publication.
D E V E L O P M E N T O F THE T H R E E PHASE M O D E L
We have chosen to derive a model to predict transient and steady state behavior of the countercurrent adsorptive Trickle Flow Reactor. This option is selected, instead of developing a steady state model, for two main reasons. The first reason is obvious: a model capable of predicting both transient and stationary behavior is more widely applicable than the corresponding steady state counterpart. The second reason is less obvious. The non-linearity of the resulting equations might, depending on the relevant parameter space, result in multiple solutions for the steady state situations (Dodds et al., 1973). This work is restricted to the simulation of start-up conditions and the computation of the corresponding steady state. The occurence of multiple solutions might slow down the convergence of the algorithm. However, identifying multiple solutions is a troublesome task and is not the aim of the present paper.
Continuity equations The following simplifying assumptions are made in the Three Phase (biocatalyst-liquid-sorbent) Model for the continuous countercurrent adsorptive Trickle Flow Reactor for enzymatic reactions: 1. 2. 3. 4. 5. 6. 7.
The reactor is in a hydrodynamic steady state with respect to hold-ups and fluxes of solids and liquid. The hold-ups of the biocatalyst, sorbent and liquid phase are uniform throughout the reactor. Isothermal operation of the reactor. Negligible radial gradients in the composition of any of the compounds. Deviations from plug flow behavior of liquid and sorbent flows are lumped in an axial dispersion coefficient for each phase separately. The biocatalyst activity can be described with a composition dependent effectiveness factor. The multicomponent ion exchange can be described by a constant selectivity model and a linear driving force model, lumping external and intraparticle mass transport.
Deviations of plug flow behavior are typically caused by velocity gradients in the reactor, by non-uniform liquid and solids distribution and by possible aggregation of the particles. Although deviations from plug flow behavior for the liquid flow and the countercurrent sorbent flow will be small (Van der Wielen et al. 1993b), we have incorporated them in the model by means of a single axial dispersion coefficient for each phase, to determine the sensitivity of the reactor to mixing phenomena. Therefore, an one-dimensional, axially dispersed plug flow model is used for the reactants in the fluid and sorbent phase. The axial coordinate z is positive in the upward direction.
A countercurrent adsorptive reactor
2317
The instationary continuity equation for the liquid phase concentration of reactant j reads:
e
~C /,-~
c~ C
' = e~E~__ .
- e~.u
/ . Oz 2
OC
l
, ~
- aa4 a -
g
n R 0¢) R ...... /
- 6,1R/I}
(3)
J,A is the molar flux of speciesj towards or from the sorbent particles (A), a A is the interfacial area of the sorbent, Rff ~ and R,a~ are the reactions in the biocatalyst particles (R) and the buffer reaction in the bulk of the solution (L) respectively. Qj is the average concentration of component j on the sorbent. The reaction in the biocatalyst is calculated at bulk conditions and is corrected with the overall effectiveness factor riov. The liquid phase has a hold-up eL, a linear velocity u t and an axial dispersion coefficient E L. The accumulation of species j at the adsorbent is described with the following equation:
e4°Q~ = e4EA__~Fz,(32QJ+ e4uC?QJ+a.~j,. ~
(4)
The linear driving force approach for the flux is usually convenient at lower concentrations and low sorbent loading when linear isotherm-conditions are approximately satisfied (Ruthven, 1984). This gives the following flux relation aAJ,, ~ = e J % ( Q , "
(5)
- Q,)
Q[ is the concentration of speciesj at the sorbent material at equilibrium with the liquid phase. The overall mass transfer constant kjA lumps the effects of external and internal mass transfer resistances of a homogeneous, geltype sorbent particle. A possible estimation for these quantities is given in a later section.
Boundary conditions The boundary conditions for this reactor are taken as closed at inlet and outlet of the system in the well-known Danckwerts form. For the liquid inlet-sorbent outlet of the reactor (z=0), this yields "
dCi = u1" (C
dQ~
-~- eL'-c,.) -_~_
= 0
(6)
and for the liquid outlet-sorbent inlet at the top of the reactor (z=L), one obtains
dQi = - u 4 dz
dC
E'7 (Qi - Qj/.); T
= 0
(7)
where QjF is the loading of component j at the regenerated ion exchange resin.
Dimensionless equations The large difference in time constants of the (instantaneous) buffer reaction in the liquid phase and the finite rate deacylation reaction in the biocatalyst introduces substantial stiffness in the set of partial differential equations. Therefore, we have eliminated the buffer reaction from the equations by pairwise adding of the continuity equations for HzPO4/HPO4 = and HPO4-/H* and by introducing the time derivative of expression for the buffer equilibrium. Substitution of the dimensionless variables z (= x L) and t (= ~L/u O, the set of equations (3-7) gives a~
O'r
_
0C___2 - CtASt~(Qj" - Q,) - %~Dal/n,,,r,
1 O2Cj
Pel.
OX 2
(8)
~X
and
OQ! c3"r
-
1
O:Qj
Pe A
Ox 2
, ~2
~o u~
j + stj(Q,"
- Q)
(9)
2318
L.A.M. VANDERWIELENetal.
with CtR=eR/eL,CtA=eA/eL, B=UA/UL, Sti=kjAL/u L and D a l = L k / u L. The boundary conditions are formulated accordingly for the bottom of the reactor :
c,
d____z'=PeI(cj-Cw) ; dQ) ~.~ =0
(10)
dx
and the top of the reactor
dQj
dCg
= - P e A ( Q j - Q;I.-) ; ~
=0
(11)
Because boundary conditions are specified at the bottom and the top of the reactor in the form of equations 10 and 11, the Three Phase Model is a two-point boundary value problem. Note that the model presented by Kiel et al. (1992) has an identical structure as the model presented here. N u m e r i c a l solution o f the Three P h a s e M o d e l
The set of coupled, non-linear partial differential equations has been solved with the 'method of lines' as described in earlier work (Van der Wielen et al., 1993a). This involves the space-discretization of the 2*NC partial differential equations into a system of 2*NC*(NP+I) ordinary differential equations for a grid of (NP+I) points. The latter are integrated in time using a common integration algorithm for ordinary differential equations such as the fourth order R.unge-Kutta algorithm. The first order differentials are approximated at x=iAx with an upwind difference scheme according to : a j 8y(iAx) = a i &
yi
-
yi-I
ifai<0;
=a i
yi*l
Ax
-Y Ax
i
ifai>0
(12)
and the second order differentials are approximated by central differences 0 2 y ( i A x ) = yi.t _ 2 y i Ox 2 Ax 2
+
yi-I
(13)
with i = 0,1 ..... NP. Initial values for the simulation of transient situations are given by the appropriate concentration values at the start of the simulation. The steady state solution of the system of equations is provided by convergence from a given, arbitrary initial situation to the steady state solution. To test for the possible occurrence of multiple steady states, we have used various initial conditions, which should give the same steady state solution. It should be noted that convergence to the steady state solution might -of course- be accelerated when initial profiles are provided which are relatively similar to the final numerical result. These initial profiles could be provided by solution of simplified forms of the Three Phase Model. The incorporation of the Danckwerts boundary conditions in the numerical algorithm requires some extra care. The grid points at the boundaries have to satisfy both the boundary conditions and the differential mass balance equations, The central difference approximation for the second order term requires a virtual point at the first and last positions of the grid, which are located outside the grid (i= -1 at x=0 and i=NP+I at x=l). These virtual points are eliminated from the scheme by substitution of the finite difference approximation of the boundary condition. The boundary condition for the liquid phase mass balance of component j at the bottom of the reactor than becomes: C/ - Cj-' 2Ax
= PeL(C/o _ C/.)
(14)
The resulting ordinary differential equation for the liquid phase concentrations reads:
ac/
c'"j - 2 c / + c / - '
cj'-q'-'
=
&
Per Ax 2
_ %Sti(Qj"
_ Q/) _ %¢Dalirl,,vr /
(15)
Ax
Disturbances in the liquid phase concentrations propagate from bottom to top at a maximum rate which equals the interstitial fluid velocity, whereas disturbances in the sorbent loading propagate from top to bottom at the solids velocity. This has of course impact on the numerical stability of the simulation of the dynamic behavior. The maximum ratio of time step and spatial mesh size for stable numerical solution can be estimated from the Courant
A countercurrent adsorptive reactor
2319
criterium. For disturbances in the liquid phase, the Courant criterium should be based on the interstitial liquid phase velocity whereas for disturbances in the solid phase, the Courant criterium should be based on the solids velocity. In the framework of equations 8 and 9, this corresponds to: A't < 1 iffl -< 1
and
A'~ <. 1 iffl > 1 ax /3
Ax
(16)
This is valid for high enough Pe-numbers (Pe>100). Because the axial dispersion is superimposed on the propagation velocity of the convective wave and 'information' is travelling at a higher rate than the convective wave, a larger amount of time steps i,; required.
ENZYMATIC DEACYLATION OF PENICILLIN (; The equilibrium conversion as well as the kinetics of the penicillin G deacylation are strong functions of pH, particularly at lower pH values (pH<7). In Figure 2, the pH-dependencies of the apparent equilibrium constant and maximum reaction rate are shown. Deviations from the thermodynamically ideal situation are mainly caused by the ionic strength of the solution and are relatively small (Tewari and Goldberg, 1988). The pH in the Fluidized Adsorptive Trickle Flow reactor may vary over the reactor length. Therefore, we have used the following, pHdependent expression for the reaction equilibrium which is valid in the relevant pH-interval (5.5
= K.,I = K"Pf'
Cl'e,,~,
-('ft
(17)
e,I
The catalytic mechanism of the penicillin amidase is described with a pseudo-uni-bi ping-pong model (Warburton et al., 1973). The reaclion rate is very dependent on pH, apparently due to an imidazole dissociation of a histidine amino acid in the active site with a pKaE of approximately 6.8 (Van der Widen et al., 1993b). As only the "neutral' fraction of the enzyme (bE°) is catalytically active, we have slightly modified the rate model by incorporating the effect ofpH on the reaction rate. The resulting relation which seems to be valid for a wide range of concentrations of reactants and pH (pH 5.5-8.5), reads :
K~41 [ c A - ~ -- R , = Fl;° kt¢
(1 + - -
c.,
K,,,A
I
Ix"/ ] % )( c~, + ~ 1 +__) K v
with /:," = _ _ 1
Kij
1 +
(18)
(7H K j
The indices correspond to PenG (A), 6-aminopenicillanic acid (P), phenylacetic acid (Q) and enzyme (E). The kinetic constants used in this work are summarized in Table 1. Note that the extent of conversion declines drastically, both in absolute magnitude and in rate when the pH is lowered to about pH 5-6 due to the combination of the pHdependencies of the reaction equilibrium and the reaction rate of the enzyme. Acidification o f the B i o c a t a l y s t ' s lnterior a n d Effectiveness Factor C a l c u l a t i o n
For the non-linear reaction kinetics of the deacylation, the relation between the effectiveness factor and the bulk concentrations of reactants and buffers is not straightforward (Van der Wieien et al., 1993b) but in principle depends on each of the species. Transport of the protons generated by the reaction in the biocatalyst particle is restricted by electrostatical coupling to the fluxes of the charged, bulky biomolecules. This causes a substantial lowering of the effectiveness factor due to internal acidification of the biocatalyst, which occurs already at very, low substrate concentrations. The buffer transports the liberated protons from the biocatalyst's interior towards the bulk of the liquid and thereby controls the pH in the biocatal~st's interior. Description of this phenomenon requires a mathematical effort, which is beyond the scope of the current paper but which is provided in a separate paper (Van der Wielen et al., 1993b). For a given biocatalyst, the relation between effectiveness factor and buffer concentration can be approximated with an proportionality with the active fraction of the buffer species (base form for acidifying reactions). We have used this approximate relation to reduce CPU-time.
L. A. M. VANDERWIELEN et al.
2320
Table 1 Kinetic parameters of the penicillin deacylation reaction at 310 K, determinedin batch experiments Keq
1.153 10.8
kR
- 10-3 *)
KmA K,O
1.257 10 .3 0.1828 3.555 10 .3
KaE
1.585 10.7
Kip
l~nol m-3 s-I kmol m 3 kmol m -3 kmol m -3
at 50 mol/m 3 phosphate buffer, pH 8; * exact value depending on enzyme loading.
O 5
6
7
8
9
pld It should be noted that the effectiveness factor results from the transient reaction-diffusion process and therefore may also depend on reactor history. For reactor start-up, this will result in an apparent decrease in the overall effectiveness factor due to mass transfer limited accumulation of the reactants in the biocatalyst particle. In a later section, we will discuss the computation of the effectiveness factor in the context of this model. The steady state transport of reactants and buffers in the biocatalyst particle is equimolar co-diffusion of the penicillin G and HPO 4 anions in the matrix and counterdiffusion of6-aminopenicillanate, phenylacetate and the H2PO 4"anions. Because the counterion (K ÷) of these anions is chemically inert, its steady state flux remains zero. The diffusion coefficients of the species are rather similar and the transport during the heterogeneous bioconversion is described with a single, effective diffusivity ensuring electroneutrality. Figure 2 Fractions of the maximumrate (v), equilibriumconversion
(o) and PenG stability([]) as a functionofpH at 310 K
Constraints
During our experiments, hardly any enzyme deactivation was observed when operated at normal conditions (310 K, pH 5.5-8.5). Therefore, the impact of enzyme deactivation on reactor performance is not explicitly incorporated in the model. However, the stability of B-lactam components is a strong function of pH. Benedict (1949) and Dennen (1967) have investigated the kinetics of the hydrolysis of PenG and 6-APA respectively. Both hydrolysis reactions follow first order kinetics with pH dependent rate constants. The optimum pH with respect to the stability of penicillin G is about pH 6 (Benedict, 1945). The interior of the OH--charged resin corresponds to a solution of about pH=13. Contact of the fl-lactam molecules with this harsh environment leads to rapid degradation and should be minimized. The short liquid and solids residence time in the Trickle Flow reactor helps in this respect, which gives a kinetic advantage to the fastest or most highly charged components such as the phenylacetate ion. This may improve the selectivity of the ion exchange towards phenylacetate and decrease the unwanted fl-lactam sorption. Ion E x c h a n g e Equilibria a n d Kinetics
We have measured ion exchange equilibria of the reactants (X) relative to OH- and CI- in binary batch experiments (Jansen et al, 1996; Van der Wielen et al, 1995c). The measured selectivities of anions X" relative to OH- are shown in Figure 3 as a function of the ionic fraction of X- in the liquid phase. The selectivities decrease with increasing ionic fraction, which is partially due to steric effects. This behavior is well known for bulky sorbates and can be modeled satisfactory with the Myers and Byington isotherm (Myers and Byington, 1986). The equilibrium composition in multicomponent mixtures is calculated as follows: Q/
=
SLrxJ
(19)
100
in 10
~A\o ooo o "~
o PhAc
A Ai
6 APA
-%:Z° 0.0
0.5
1.O X
k Figure 3 Ion exchange selectivities of the reactants relative to OH. Pen G (.), 6-APA (A) and PhAc (0). with j and r indicating the species of choice and the reference species respectively. Unfortunately, the selectivity at low ionic fractions favors the relatively hydrophobic Pen G, but the selectivity reverses at higher ionic
A countercurrentadsorptive reactor
2321
fractions to the more polar PhAc due to steric effects. Countercurrent contact in combination with the kinetic advantage increases the operational selectivity towards PhAc, but a further decrease of the pore size would be favorable. For the estimation of the overall mass transfer coefficient, a modified Glueckauf equation is used (Ruthven, 1984).
k:-"-~
6k:A + 66-'DA,,,/:]
For external mass transfer towards and from the biocatalyst and the resin, the correlation given by Tournie et al. (1979) for monocomponent fluidized beds was used. The fluxes towards and from the ion exchange resin are described in this way as long as the OH-content of the resin is not exhausted. Because electroneutrality applies, the flux of OH-ions from the resin to the liquid phase has to balance the combined fluxes of the adsorbing electrolytes. Therefore, the flux of OH-ions is computed from the fluxes of the adsorbing species as follows:
J,m = ~ z,J,
(21)
t
with i is PenG-, 6-APA-, PhAc-, HPO4= and H2PO4- respectively. The liberated OH--ions react instantaneously with the protons in the liquid phase and re-establishe the equilibrium. In the numerical model, the flux of hydroxide is modeled as a W-consumption term. The diffusion coefficients of all species are similar, which is a good assumption in ionic systems (Helfferich, 1962; Van der Wielen et al., 1993b). Equation 21 assures electroneutrality.
Hydrodynamics Crucial parameters in the model of the Trickle Flow reactor are the hold-up eA and linear velocity uAof the sorbent phase. Elsewhere, we have described a hydrodynamic model for the falling velocity of dense (sorbent) particles through a fluidized bed of lighter (biocatalyst) particles supported by a perforated plate (Van der Wielen et al., 1995b). The flow rate of the dense phase is governed by the transport through the holes in the perforated plate, which is at flooding conditions. The computation of the flow rate of dense solids requires information on the fluidization characteristics of the dense solids in the form of the Richardson and Zaki (1954) exponent n2, the terminal velocity ut2 and the liquid approach velocity ULhof the holes. The latter equals the superficial liquid velocity ULoin the column corrected for the free area fraction of the perforated plate ~ ) . In our experimental set-up, the ratio of hole diameter to diameter of the dense particle was rather low (<20) and the holes had a conical shape which causes turbulences. The actual terminal velocity in the hole of the plate was usually some 20% lower than that of a free falling particle without the wall effects. Corrections of the terminal velocity from infinite conditions to those of the hole of the plate by incorporation of the wall effect was usually sufficient. Experimentally obtained values at raining conditions in the hole of the dense phase provided the best description of the sorbent flux as a function of liquid velocity. See Figure 4 for the experimental and predicted sorbent fluxes for a free area percentage of the plate of 20.4%. The steady state flow rate of the dense phase through the Table 2 Propertiesof the biocatalystand the ion exchangeresin. hole equals the flow rate of the dense phase through the fluidized bed section. The hold-ups of the biocatalyst and Particle Reimmobilized Sorbent the sorbent, eR and e~ respectively can be obtained by Biocatalyst IRA 400 iterative solution of the multicomponent form of the hydrodynamic model. In practical situations, when the d [mm] 3.5 0.6 densities of biocatalyst and sorbent deviate not too much u, [mm/s] 18.9 25.3 (50-100 kg m3) and at relatively low solids flux, the u: [mm/s] 24.3 3 I. 1 hold-up of the sorbent is rather low (<2-5%). The bulk n [-] 2.53 4.28 density of the binary solids system is mainly determined p [kg/m 3] 1013 1065 by the fluidized bed of the lighter species. Then, the velocity of the dense particles can be computed explicitly *) raining velocity in hole of the perforated plate from a simplified form of the hydrodynamic model for a single particle falling in a fluidized bed of the lighter species. The corresponding hold-up of dense phase is then computed from the preset flux dA divided by the velocity of a single dense sorption particle. For high sorbent flow, the hold-up of the sorbent and thereby its influence on bulk density are not negligible. Then the complete model should be used.
2322
L.A.M. VANDEa WmLENet al.
EXPERIMENTAL SET-UP AND PROCEDURES
3 E
Materials In this work, we have used commercial Pen G and Pen G acylase catalyst (SeparaserM), donated by Gist-brocades NV. The biocatalyst was supplied in immobilized form, with a small diameter. As the catalyst was designed for other operating conditions than used in the Trickle Flow reactor, it was re-immobilized in a gelatin/alginate matrix using the resonance nozzle technique described by Hulst et al. (1985). Prior to reimmobilization, the original biocatalyst particles were disrupted to ensure homogeneous distribution throughout the new immobilization matrix. This procedure resulted in particles with the required low density and millimeter range diameter. The loss of enzyme activity during this procedure was about 20%. The ion exchange resin was a commercial grade strong basic anion exchange resin IRA 400 with a polystyrene backbone with a mesh size 20-50. The physical properties, including fluidization characteristics of the biocatalyst and sorbent particles are given in Table 2.
¢ -6
2
-× ~-
1
-~ ~
O O liquid
10
20
flux
~rn h o l e
30 mm/s]
Figure 4 Experimental and simulated sorbent fluxes as function of the superficial liquid velocity for free area fraction fh~0.204.
Laboratory scale reactor We have used the glass laboratory scale reactor set-up as described earlier (Van der Wielen et aL, 1990-5a). The main body of the reactor consisted of two jacketed, 0.88 m long sections with an internal diameter of 0.0354 m. The system was equiped with a pulseless rotary gear pump which was controlled by a PC coupled ADI- 1030. The reactor was modified to enable operation as a Trickle Flow reactor and some modifications for the usage offl-lactam antibiotics were made. The Trickle Flow mode results in high flow rates of the sorbent. For this situation, the lowdiameter piping at the bottom of the reactor showed to be a bottleneck in the solids removal. Therefore the bottom part of the reactor was replaced by a two-way perspex Y-valve with a teflon central part with a larger bore (2 cm). However, this was not enough to prevent plugging of the lower part of the reactor at higher sorbent flow rates. However, by connecting a 'closed' circuit with two removable, water filled vessels for the collection of the sorbent, a bubble trap and a second, pulseless rotary gear pump to the bottom of the reactor, it was possible to remove the sorbent particles at a high rate. This is shown in Figure 5.
At three locations along the reactor, pH-sensors were installed. Their signal and that of the magneto-inductive flow meter at the substrate feed flow were monitored via on-line data-acquisition. At three locations along the reactor, peristaltic pumps were installed to automatically draw samples from the reactor. Each PCcontrolled pump could draw samples from two sample ports simultaneously. One plate was mounted in the reactor provided with a central hole of the conical shape as decribed by Van der Wielen et al. (1995a). The sorbent was supplied from the top of the reactor from a glass vessel similar to the biocatalyst feed with a computer controlled peristaltic pump.
exit
11t
'--[~
feed
i
PC Laboratory scale Trickle Flow Reactor: reactor ~, pH-monitoring2'3, pulse mechanism4, sorbent supply 5, rotary gear pump 6, automatic sampling system 7, sorbent collection s, bubble trap 9.
U
,
O
m
_?
Figure 5 Laboratory scale Trickle Flow Reactor.
Operation of the Trickle Flow Reactor The first step in the start-ui~ of the reactor is to feed the reactor with the buffer solution at a flow rate well above the raining velocity of the biocatalyst particles through the hole in the perforated plate. Then adsorbent is supplied at a somewhat higher rate than the final set point. Because the sorbent flux is above the flooding condition, the resin accumulates in a 2-5 cm thick layer just above the plate. This prevents raining of the lighter biocatalyst and in general improves stability of the operation. The liquid flow rate can be decreased below the raining velocity of the
A countercurrent adsorptive reactor
2323
biocatalyst and the sorbent flow is adjusted accordingly. Analysis of the samples drawn from the reactor was performed by reversed phase HPLC and by capillary zone electrophoresis (CZE) on a Waters Quanta 4000 Capillary Electrophoresis System with a 50 cm, non-coated silica capillary. Table 3 Conditions for the experimental runs Run
resin
Pen G in feed mol m -3
1. 1-3 II. 1-3 I11.1-3 IV. 1-3 V. 1-3
OHOHOH HPO 4HPO4 =
32.1/52.2/49.1 49.1/49.4/52.01 47.3/38.8/38.9 45.6/47.2/44.6 45.1/36.4/37.4
¢t, L/h
qb,,/~bL
22.3/12.5/13.5 23.0/15.2/15.2 23.0/15.3/15/3 24.0/24.0/11.3 24.0/11.1/21.5
-/0.136/0.126 -/0.11/0.11 40.11/0.11 -/-/0.15 -/0.07/0.06
RESULTS
Operation without sorbent Figure 6 shows experimental axial profiles for the conversion of a 50 mol m50 11 3 penicillin G solution (pH 8, 310 K) in an aqueous buffer of 50 mol m 3 40 10 Pen G potassium phosphate without resin flow. The Dal-number and the catalyst hold-up were sufficiently high to ensure full 30 9 C pH conversion when the pH could be mol m3 maintained at pH 8. However, the pH 6-APA,PhAc 20 B decrease of the pH has a two-fold effecton the reaction rate, irrespective the 10 7 buffering effect of the phosphate. Firstly, it causes a decrease in the reaction rate i I 0 6 due to a shift in the reaction equilibrium. 0.5 1.0 z 0.0 1.5 Secondly, it decreases the activity of the m biocatalyst. Now, the reactor is not operated as an adsorptive Trickle Flow Figure 6 Experimental (markers) and simulated liquid composition profiles Icurves) at system. The conversion is computed with ¢^=0 (Run I1.1). Pen G ('), 6-APA (A) and PhAc (~). the Three Phase Model, setting the fluxes to and from the sorbent to zero. Model predictions and experimental data, using the data from Table 1-3, coincide within experimental error (< 5%).
~
Table 4 Base case data for the laboratory scale reactor Operation as countercurrent adsorptive Trickle Flow Reactor By starting the resin flow, the system pe A 50 c~R 0.11 qo, 0.5 was operated as a countercurrent pe L 50 c~.x 0.03 qbA/¢t 0.11 adsorptive Trickle Flow Reactor for the same feed conditions. In Figure Pen G 6-APA PhAc HPO 4 H2PO 4- H + 0H7, the effect of the countercurrent resin flow on the liquid composition Dal 45.7 45.7 45.7 45.7 profiles is demonstrated for S),oH 5.8" 6.2 12.4 8 7.3 1 experiment 1II.2 (d~A/~L=0.11). The St 7.3 9,8 9.8 13.6 13.6 13.6 pH was maintained at the set-point in the lower section of the reactor, but ~. average value in Myers and Byington model, variance increases sharply towards the top of parameter Wpe,g,OH_=14.7, skewness p=0.5 the reactor. The PenG-profile shows the gradual decrease along the reactor due to bioconversion and nonselective sorption. The reaction products show the typical parabolic profile due to product generation in the bottom section and countercurrent ion exchange in the top section of the reactor. The composition profiles have also been
2324
L.A.M. VANDERWIELENet al.
simulated with the Three Phase Model (curves) using the data from Tables 1-4, and provide a fair description of reactor performance. 60 11
5O
c 40
10
10
"~
G
9p H
~
0 0.0
7
0.2
0.4
0.6
0.8
6 1.0
x
Figure 7 Experimentaland simulatedliquidcompositionprofilefor ~A/~t=0.11 (Run 111.2).Pen G (.), 6-APA(A), PhAc(o) and pH (i). Location o f the p H shock The simulation with the Three Phase Model 11 shows a 'shock' profile of the pH, which is characteristic for countercurrent, adsorptive lO reactors (Rhee et al, 1989). The location of the pH shock corresponds to the near-complete 9 removal of the base form of the buffer (mono hydrogen phosphate ion) by ion exchange. The 8 diffuseness of the shock layer can be attributed to the axial dispersion in the system. In the top 7 section above the shock, the rate of the 0.05 acidifying bioconversion can not compensate I l I I 6 for the hydroxide release of the resin and the o.o 0.2 0.4 0.6 0 8 1.O pH increases to high values. This phenomenon x is unwanted because of rapid degradation of 13lactams in strongly basic environment. Hence, Figure 8 Calculated effect of varying ratio of resin and liquid flow ~^/~L at the shock position of the pH for parameters from Table I-3 (pH set-point: the Trickle Flow Reactor should be designed dotted line). such that the shock either does not occur or is located as close as possible to the liquid exit of the reactor. The position of the shock can be influenced by varying the resin-to-liquid ratio ~ A / ~ L . This is demonstrated in Figure 8 for various eA/¢V
CONCLUSIONS The Three Phase Model predicts the experimentally determined performance of the countercurrent adsorptive Trickle Flow Reactor adequately. It should be emphasized that the parameters in the model are obtained from independent equilibrium and rate experiments for biocatalysis, ion exchange and hydrodynamics and that model calulations are purely predictive and not fitted. Improvements can be made by incorporating more detailed modelling of, in particular, the heterogeneous biocatalysis and the multicomponent ion exchange process. This will further increase the complexity of the model and the computational effort. Hence, for optimization studies and parameter sensitivity analysis, the Three Phase Model presented in this work could be used as a starting point. In the top of the reactor, a drastic increase in pH may occur when the hydroxide flux exceeds the rate of the acidifying bioconversion. This increase has the form of a (diffuse) shock. Proper fine-tuning of the ratio of the sorbent to liquid flow rate for a specific sorbent shifts the shock towards the liquid exit, thereby reducing possible degradation of reactants and biocatalyst. Using the model, other process alternatives such as the use of ion exchange resins which are charged with monohydrogen phosphate could be investigated straightforwardly, provided that ion exchange parameters are known. An ideal sorbent should not adsorb Pen G and 6-APA, but take-up PhAc selectively. Hence, the relatively low selectivity of the ion exchange resin that was used in this study resulted in substantial and undesired adsorption of reactant Pen G. Using the model, the minimum requirements of a suitable sorbent can now be quantified. This is the the subject of current research.
A countercurrent adsorptive reactor
2325
ACKNOWLEDGMENTS Gist-brocades N.V. is acknowledged for the supply of penicillin G and penicillin acylase (SeparaseTM) and the Netherlands Organization for Scientific Research (NWO) for the financial support. Analytical support by C. Ras (HPLC) and H. Corstjens (CZE) is gratefully acknowledged.
NOTATION m:/m 3 a interfacial area kmol/m 3 C concentration d diameter m D diffusion coefficient m:/s E axial dispersion coefficient m:/s Ji free area fraction FE° active biocatalyst fraction ,J molar fluxes mol/mZs k overall mass transfer coefficient 1/s liquid phase mass transfer coefficient m/s kL L reactor length m Richardson and Zaki index n number of components NC ~) average resin phase concentration mol/m s F normalized reaction rate, eqn. (8) reaction rate mol/m3s R selectivity S l time s temperature K T linear, terminal velocity m/s /t, Ut X,2 (dimensionless) axial coordinate
Greek cq; 13
P
dummy variables, defined as eq=e/ee; uA/uc hold-up density kg/m 3
Dimensionless Damkohler(1) number Lk/u L Galileo number d3p2/~tL 2 density number (ps-pL)/PL Peclet number ULL/E Schmidt number WpD Sherwood number kd/D Stanton number k~AL/uL
Dal Ga My Pe Se Sh Stj
REFERENCES Benedict, R.G., Schmidt, W.H., Coghill, D. and Oleson, A.P., 1945, J. Bacteriol. 49, 85-95. Dennen, D.W., 1967, Y. Pharm. Sci. 56, 1273. Dodds, R., Hudson, P.I., Kershenbaum, I. and Streat, M., 1973, Chem. Engng Sci., 28, 1233-1248. Freeman, A., Woodley, J.M., and Lilly, M.D., 1993, BiG~Technology 11, 1007-1012 Helfferich, F. Ion exchange. McGraw-Hill Book Company, New York, 1962. Holst, O., and Mattiassson, B., 1991, Extractive Bioconversions, M. Dekker, New York Hulst, A.C., Tramper, J., Van 't Riet, K., Westerbeek, J.M.M., 1985, Biotechnol. Bioengng 27, 870-876 Jansen, M.L., Van der Wielen, L.A.M. and Luyben, K.Ch.A.M., 1996, accepted lnternat Conf Ion Exhange Development and Applications, Cambridge, 14-19 July Kiet, J.H.A., Prins, W. and Van Swaaij, W.PM., 1992, Chem. Engng. Sci. 47(17/18), 4271-4286. Kuczynski, M., Oyevaar, M.H., Pieters, R.T. and Westerterp, K.R., 1987, Chem. Engng. Sci. ,12(8), 1887-1898. Myers, A.L. and Byington, S., 1986, in Rodrigues, A.E. Ion Exchange. Science and Technology. NATO ASI Series Appl. Sci. E 107. 119-145 Rhee, H.-K, Aris, R. and Amundson, N.R., 1989, First Order Partial Differential Equations 11 Prentice-Hall, USA Tewari, Y.B., and Goldberg, R.N., 1988, Biophys. Chem. 29, 245-252. Tourni6, P., Laguerie, C. and Couderc, J.P., 1979, Chem. Engng. Sci. 34, 1247-1255. Warburton, P. Dunnill and M.D. Lilly, 1973, Biotechnol. Bioeng. 13, 25 Wielen, UAM. van der, Potters, J.J.M., Straathof, A.J.J. and Luyben, K.Ch.AM., 1990, Chem. Engng. Sci., 45(8), 2397-2404. Wielen, L.A.M van der, Straathof, A.J.J. and Luyben, K.Ch.A.M., 1993a, In M.P.C. ~eijnen and A.A.H. Drinkenburg Precision Process Technology, Kluwer Acad. Publ., 353-379, 493-502 Wielen, L.A.M. van der, Diepen, P.J., Straathof, A.J.J. and Luyben, K.Ch.AM., 1995a, Ann. N.Y. Acad. Sci., 750, 482-490 Wielen, L.A.M. van der, Dam, M.H.H. van, and Luyben, K.Ch.AM., 1995b, accepted Chem. Engng Sci. Wielen, UA.M. van der, Lankveld, M.J.A, and Luyben, K.Ch.A.M., 1995c, acceptedJ. Chem. Eng. Data