- Email: [email protected]
Modeling of enzymatic conversion in the catalytic gel layer located on a membrane surface
DESALINATION ELSEVIER
Desalination 162 (2004) 327-334
i
i
Modeling of enzymatic conversion in the catalytic gel layer located on a membrane surface A. Noworyta, A. Trusek-Holownia* Institute of Chemical Engineering, Wroclaw University of Technology, Norwida 4/6, 50-373 Wroclaw, Poland Tel. +48 (71) 320-2653; Fax +48 (71) 328-1318; email." [email protected] Received 1 November 2003; accepted 14 November 2003
Abstract
Equations describing a multi-phase bioreactor with a catalytic membrane located on the boundary of phases, of which one is a substrate reservoir, were formulated. A model analysis of the process was carried out and the effect of main operating parameters of such a reactor, i.e., the catalytic layer thickness and the coefficients of diffusion mass transport in both phases, was determined. Two periods with different methods of supplying the catalytic layer can be distinguished in the process. There is also a characteristic thickness of the catalyst layer: when it is exceeded, the process duration is no longer shortened although full substrate conversion from the supply stream not always has a place. It is recommended to apply thin layers because then the catalyst activity is fully used. The analyses of the influence of mass transfer showed that substrate mass transfer in the water phase to the catalyst layer has a slight effect on the process rate when the intensification of its transfer in the organic phase might have a significant influence on the process rate. Keywords: Enzymatic gel layer; Catalytic membrane; Process modelling; Multi-phase reactor
1. I n t r o d u c t i o n
Due to broad substrate specificity, biocatalysts (enzymes, microorganism cells) are more often used for catalyzing the reactions aimed at the production o f desired compounds or degradation of environmental unfriendly substances [1-4]. *Corresponding author.
Due to high sensitivity to reaction media components, these applications are followed by numerous studies whose goal is to obtain preparations that will retain high catalytic activity for a relatively long time. There are different techniques o f catalyst stabilization, among them the stabilization o f protein molecule by way o f stiffening its structure due to immobilization.
Presented at the PERMEA 2003, Membrane Science and Technology Conference of Visegrad Countries (Czech Republic, Hungary, Poland andSlovakia), September ~11, 2003, Tatranskd Matliare, Slovakia. 0011-9164/04/$- See front matter © 2004 Elsevier B.V. All rights reserved PII: S0011-9164(04)00066-9
328
A. Noworyta, A. Trusek-Holownia / Desalination 162 (2004) 327-334
If a biocatalyst is immobilized on the surface or inside membrane pores, the membrane whose main task is the selective separation of the system components additionally assumes a catalytic character, and the catalytic reaction that takes place in the system can be related directly to the separation of reagents[5]. If the membrane is located on the boundary of two phases, it additionally plays the function of a phase contactor [6]. A particularly interesting case is the use of membranes for the separation of the organic phase from water; and depending on the hydrophobic-hydrophilic character of the membrane, its pores are filled with either the organic or water phase [7]. This type of a two-phase system is used, among other things, in the catalysis in the presence of hydrophobic reagents. In such a case, the organic phase is their reservoir from which they can be supplied in a controlled way to the reaction layer which, due to the biocatalyst properties, usually belongs to the water phase. Intensification of such processes should be directed towards a maximum use of the catalyst properties, particularly the increase of its stability and maximization of substrate concentration in the reaction zone. The study is dedicated to the modeling of a process that takes place in a multi-phase reactor with a bioeatalyst layer immobilized on the surface of a membrane that separates the organic phase from water.
2. Balance equations of a column reactor with a catalytic membrane
The considered system (Fig. 1), whose main element is a membrane module with a catalytic layer located on the membrane surface, in this case operates like a column reactor with a concurrent flow of phases on both sides of the membrane. The system can work either in a batch or continuous regime. Usually, because of the small value of the reacted substrate stream relative to the stream
Vl
T T V3
V~Co2
Vw, ew2
/
il
Va,
V2~ Cox
l
i'.-i
;i
? Vo, Col
....~
(1)
Vw, ewl
Fig. 1. Scheme of the system with the column reactor with catalytic membrane.
supplied to the column reactor, it is necessary to use circulation because a single flow of the substrate stream through the reactor does not ensure the required reaction degree. The following reaction was considered: S
enzyme
, P1 + P 2 +...
It was assumed that products being formed had no inhibiting effect on the reaction and were not characterized by a limited solubility in the reaction phase, so they did not affect the process. They were transported by diffusion to both phases, and concentrations of the reaction product in both phases corresponded to the interface equilibrium. Fig. 2 illustrates a differential element of the column bioreactor with a catalytic membrane. For concurrent plug flow, the mass balance of the substrate limiting the reaction is represented by the equations:
329
A. Noworyta, A. Trusek-Holownia / Desalination 162 (2004) 327-334 Vo, co (h+dh)
Vw, e,,,(h+dh)
leo
Z ~ i
/Co~/Cwi c,,(0)
ii[iii!i,i
" /
i
i
c~, (s)
/cw
dh 1"11
Fig. 3. Profile of concentrations in the reactor with a catalytic membrane.
T-
Vo, co(h)
The values of stream density nl, n 2 can be determined using the model of a catalytic membrane with a hydrophilic membrane (Fig. 3) [6]:
V,~, cw(h)
Fig. 2. Differential element of the column reactor with catalytic membrane.
CO
=
(3)
Vo,co (h)- Vo,Co(h +dh) (1)
(4)
-.1(~o, ~ ) , dA --0 1
kl
Vw*%(h)-Vw*%(h+dh)
(2)
+ .~ (~o,~ ) , ~ --o
* 13w*k 1 *[Co*eOsh(),*s ) - P *%] /'tl =
n2=
*
(~w+ P
+
--
P
+
-
1
-
~o ~
Assuming that the reaction is of the first order, the equation of stream density is obtained [8,9]:
Co*D *k, *k, *shah (k *s)
* k 1) * c o s h (~. * s) + (1) * k r + Dw * kl * P ) * s i l ~ ( ~ * s)
*Ow*kl * [co-P * % *eoshQ. *s)] - ~ w * c w * D * k , • sinh (~ *s) o: * (~lw +P * kl ) * Cosh (k * s) + (D * k~ + [~w* kl * P ) * sinh (~. *s)
P/r = r/1 - t'/2
(8)
(5)
VT-
X = ~D
(6)
(7) (10)
where e = D~/b--~,
(9)
Upon integration of Eqs. (1) and (2) for the initial
330
A. Noworyta, A. Trusek-Holownia / Desalination 162 (2004) 327-334
conditions (Fig. 1):
16 14 12 ,o
t-
O
Co(h = O) = %
(11) "6
% ( h = O ) =c.1
g
(12) "O
the values of limiting substrate concentrations in both phases at the outlet from the column reactor (Co2, c~2) are obtained. In the case of a continuous operation, streams V1and V3 are removed and streams V2and V4 with a properly selected composition are supplied to the system. In the general case (a continuous process), the mass balance of the limiting substrate in the reservoirs of both phases is given by the equations: I,',o *% (t +dr) - g,o ,eo(O =(go- V~)*Co2CO*dt
+ Vz *cox(t) dt
t~
2 0 6
2(t),dt
Vw,%(t)d t
(14)
The solution of Eqs. (1), (2), (6), (7), (13) and (14) allows us to determine the concentrations of both phases during the process duration. Due to non-linearity of Eqs. (6) and (7), in general it is not possible to obtain an analytical solution. Sottware using Turbo Pascal enabling a numerical solution was developed.
3. V e r i f i c a t i o n o f a r e a c t o r m o d e l
A model of the column bioreactor with a catalytic membrane shown in Fig. 1 was verified in the isooctane-polyamide membrane-water system. Due to the hydrophilic character of the membrane, its pores were filled by the water phase. The biocatalyst (lipase from Candida antarctica) was immobilized on the membrane
5
10
15
time [11]
Fig. 4. Comparison of experimental and model values of product concentration.
Table 1 Process parameters used for the verification and modeling of the process Parameter
(13)
, % (t + dt) - V=.,% (O =(gw- V3),c
+ V4 , c ~ ( t ) d t _
fi
8
6
Value Verification
Simulation
D
3.0x 10-12
3.0x 10-12
kr
o.lo
o.lo
P kI
1.74 2.9-5.1x10 -5
1.74 1 x10-7-1 x l 0 -4
13w s
5.1x10 -s 5.3-9.2x10 -7
1xl 0-1°-1 xl0 -4 1x10-Y-4x10 -5
c~(t = O)
0
o
c o(t = 0)
40
60
A H
0.014 0.10
0.014 0.10
surface by a chemical bond using glutaraldehyde. The amount of bound enzyme corresponded to the gel layer thickness equal to 5.3-9.2× 10 -7 m [10]. The enzyme catalyzed the reaction of hydrolysis of glycidyl butyrate, a compound whose separation coefficient in the tested system is equal to 1.74. Constants of the kinetic equation were determined in separate experiments [10]. By the low substrate concentration, the kinetics of the enzymatic reaction could be described by the first order according substrate kinetics:
A. Noworyta, A. Trusek-Holownia / Desalination 162 (2004) 327-334 =g • c
(15)
70-
g
=
In this case the constant is equal to 1.0 s-1 for the R-enantiomer and 0.49 s -1for the S-enantiomer of glycidyl butyrate. During the process, the amount of butyric acid [one of the reaction products whose whole mass was concentrated in the water phase (P<
4. Model analysis of the process
The subject of modeling was a batch process which can be more widely applied than the continuous one. It was assumed that at the beginning of the process the whole substrate mass was located in the organic phase in which, due to its hydrophobic properties, the substrate dissolves much better than in the water phase. When analysing typical concentrations in both phases for a broad range of parameters (Fig. 5), it was found that the process could be divided into two periods. In the first one, the phases are far from the extraction equilibrium state, the stream of substrate mass (nl) flowing to the catalytic layer is large, the substrate concentrations in the catalytic layer are high and so the stream of the reacted substrate is significant. Depending on the thickness and reactivity of the catalytic layer, part of the substrate mass (n2) is not reacted and
i
331
1
60-
.......................................................................
50'~
~I
40-
2O-
J~
0
i
0
3
'
,
i
6
9
12
15
18
time [hi Fig. 5. Substrate concentration in both phases in the batch process.
penetrates the water phase, thus increasing the substrate concentration. This period of the process is usually short. It is important that the concentration in the water phase, especially in the biocatalyst gel, does not exceed the saturation values since then it might cause substrate precipitation and disturb the catalytic membrane operation. After reaching the state close to interface equilibrium, the process slows down (it enters the second period). At the boundary of both periods, there is a maximum of the substrate concentration in the water phase. This implies a very interesting property of the system that consists of a change of the direction of substrate mass stream, n 2. In the second period of the process, the catalyst layer is supplied with a substrate from both surrounding phases. In a typical case, when the organic phase is a substrate reservoir, the value of stream n2 in the second period of the process duration is much lower than the value of stream H1 •
Fig. 6 shows schematically the substrate concentration in the catalyst layer and in the water layer in both periods considered (for the sake of figures clarity the scale was not kept). Parallel to the change of stream direction n2, the substrate concentration in the catalyst layer reveals a minimum. Its size and location depend on the thickness of the catalytic layer and size of streams nl
332
A. Noworyta, A. Trusek-Holownia / Desalination 162 (2004) 327-334
I lstperiod
t 2 n dperiod
I
-I -..-.
t
tim~
important for the process economy to determine this characteristic layer thickness. time
:i.!i!.::"
Fig. 6. Profile of substrate concentrationin both periods.
and n 2. The relation between streams n 1 and n z depends on the catalytic layer thickness and mass transfer coefficients on both sides of the gel. The main process parameters that can control the work of the analyzed reactor include kl, 13w and s. The effect of these parameters is shown below. 4.1. Thickness o f gel layer
The catalyst layer thickness is particularly important because, on one hand, its causes an increase of the amount of catalyst applied, which makes the reaction faster, and on the other hand, induces an increase of substrate mass transfer resistance in the gel layer. Fig. 7 illustrates the time necessary to obtain 90% conversion of the substrate present in the system depending on the gel layer thickness for various values of coefficient kv It was observed that there was a characteristic thickness of the catalyst layer (in the case considered this corresponds to the value s = 1× 10-5 m), above which a further increment of the catalyst amount does not shorten the process duration. Practically this values does not depend on coefficient ka. This follows from the fact that at this layer thickness the raw material contained in streams n~ and n2 reacts completely. A further increase of the layer thickness does not cause an increase of the process rate, which is controlled in this case by the diffusion rate of stream n~; it only changes the relation between streams n 1 and n 2. It is very
4. 2. Mass transfer coefficients
With a decrease of the catalyst layer thickness, a growth of the reaction time was observed. Starting from a certain value, this relation is very distinct. The role of coefficient k 1 is interesting. With its decrease, for a given layer thickness, the process duration is prolonged. This increase is very serious after exceeding a certain value (in the considered case kl < 2× 10-7 m s-~). A hypothetical reaction time was calculated for the case when no mass transport resistance occurred for the stream n 1 (kl~oo). As shown in Fig. 7 (continuous line), this hypothetical time does not differ much from the process time at high and medium values of kt(>5× 10-7 m s-l). This means that for these values o f k 1, the catalytic activity of the layer is used at maximum. A decrease of coefficient kl induces two reasons for which the process duration is increased: the stream of substrate supplied to the reaction layer by diffusion is decreased and the concentration gradient in the near-wall region increases, so the substrate concentration in the reaction layer is reduced. This means that the catalytic abilities of the gel layer are not fully used. The analyzed relations allow us to determine an optimum region of the reactor operation (marked area in Fig. 7). An increase of the catalyst layer is unjustified in many cases. Thin layers are recommended. Then the second period of the process appears very quickly and the catalytic layer is supplied from both phases; hence the catalyst activity is fully used. It is important that coefficient k~ be high enough. The situation is different when product purity is a priority. Then, in order not to allow the presence of the substrate in the water phase, the enzyme layer should be extended so as to reach full reaction of the substrate in it, i.e., to maintain the first period of the process all the time.
A. Noworyta, A. Trusek-Holownia /Desalination 162 (2004) 327-334 250
,.,,
200 150
',
50 \\
~
1
...... 2
.....
3
....... 4
"""'.
"-..
Y--.2.~=
Z : = ~-: = :'2: : . ~ =
it
0
0
0,5
1
1,5
2
thickness of gel layer [m*lff s]
Fig. 7. Time necessary to obtain 90% conversion of
substrate for various values of coefficient k~ (line 1: k~ = 5×10 -6 [m s-i]; 2: k 1 = lxl0 -6 [m s-~]; 3: k 1 = 5x10 -7 [m s-l]; 4: k 1 = lxl0 -6 [m s-l]). 7O 6O
"g 50 E
40 30 -t I
-9
-7
-5
l o g 1~.
Fig. 8. Effect of 13~on the process duration for various values of coefficient kl (line 1: k 1= 5x10 7 [m s-t]; 2: kl= lxl0 -6 [m s<]; 3: k~ = lxl0 5 [m s-~]).
catalytic membrane located at the boundary o f phases, it was found that: 1. Two periods with different methods o f supplying the catalytic layer can be distinguished in the process. In the first period, substrate is supplied to the layer only from its reservoir (organic phase), while in the second one from both phases that surround it. 2. There is a characteristic thickness o f the catalyst l a y e r - - when it is exceeded, the process duration is no longer shortened. It is recommended to apply thin layers because then the catalyst activity is fully used. 3. The process o f substrate mass transport by diffusion from its reservoir to the catalyst layer should be intensified, but there is some boundary value o f transfer coefficient kl, which when exceeded, does not cause an increase o f the process rate. 4. Transport ofsubstrate mass from the water phase to the catalyst layer has a slight effect on the process rate and there is no need to intensify it.
6. Fig. 8 illustrates the effect of~w on the process duration. A weak dependence o f the value of [3w on the process duration is observed. There is a possibility o f a weak maximum. The maximum is difficult to explain; it is probably a result o f the non-linearity o f the system of equations that describe the column reactor with a catalytic membrane. In the considered range of changes, a slight shortening o f the process duration can be observed with a decrease o f the value o f [3~. Hence, contrary to the phase which is the substrate reservoir, there is no need to maximize the mass transport conditions in this phase. 5.
Conclusions
As a result o f model analysis o f the process that takes place in a multi-phase reactor with a
333
Symbols
A 13
--
C
D h
---
F/]
--
n2
--
P
--
F S
--
--
Membrane surface, m 2 Mass transfer coefficient, m s -1 Substrate concentration, mol m -3 Diffusion coefficient, m 2 s -1 Current length o f column reactor, m Mass transfer coefficient to catalysts gel, m s -~ Reaction rate constant, s < Stream density o f converted substrate, mol m-2s -I Stream density o f entering substrate mass, mol m-'-s -~ Stream density o f nonconverted substrate mass, mol m-Zs -~ Partition coefficient Reaction rate, reel m-3s < Thickness o f gel layer, m
334 t V
A. Noworyta, A. Trusek-Holownia / Desalination 162 (2004) 327-334 ---
---
x
--
Time, s Flux, m 3 s -1 V o l u m e o f organic phase tank, m 3 V o l u m e o f water phase tank, m 3 Current thickness o f gel layer, m
[5]
Subscripts o w m 1,2
-----
[4]
Organic phase Water phase Membrane Cross section o f column reactor
[6]
[7] Acknowledgements
The support o f the Polish State Committee for Scientific Research (project P B Z / K B N / 1 4 / T 0 9 / 99/0 la) is gratefully acknowledged.
References
[1] M.G. Bramucci and V. Nagarajan, Industrial wastewater bioreactors: sources of novel microoganisms for biotechnology, TIBTECH, 18 (2000) 501-505. [2] Y.-Y. Linko, M. Lams~i,X. Wu, E. Uosukainen and 5. Sepp~ila, Biodegradable products by lipase biocatalysis, J. Biotechnol., 66 (1998) 41- 50. [3] K.K.B. Lee° L.H. Poppenborg and D.C. Stuckey, Terpene ester production in a solvent phase using a
[8]
[9]
[10]
[ 11]
reverse micelle-encapsulated lipase, Enzyme Mierob. Technol., 23 (1998) 253-260. Y. Shimada, Y. Watanabe, A. Sugihana and Y. Tominaga, Enzymatic alcoholysis for biodiesel fuel production and application of the reaction to oil processing, J. Mol. Catal. B: Enzymatic, 17 (2002) 133-142. L. Giomo and E. Drioli, Bioeatalytic membrane reactors: applications and perspectives, TIBTECH, 18 (2000) 339-349. A. Tmsek-Holownia, Membrane contactors, in: A. Noworyta and A. Trusek-Holownia, eds., Membrane Separations, Argi, Wroclaw, Poland, 2001, pp. 215-235. A. Trusek-Holownia and A. Noworyta, Catalytic membrane preparation for enzymatic hydrolysis reactions carried out in the membrane phase contaetor, Desalination, 144 (2002) 427-432. A. Trusek-Holownia and A. Noworyta, A mathematical model for enzymatic reaction carried out on the catalytic membrane, J. Membr. Sci., submitted for publication. A. Noworyta and A. Koziol, Model of catalytic membrane for the reaction carried out in biphase system, Inz. Apar. Chem., 3s (2002) 110-111. A. Trusek-Holownia, Process ofesters hydrolysis in enzyme layer immobilized on polymeric membrane, Conference materials of First International Symposium on Process Intensification and Miniaturisation, Newcastle, 2003. A. Trusek-Holownia and A. Noworyta, Mass transfer in the membrane contactor with a gel enzyme layer, Desalination, 162 (2004) 335-342.
Desalination 162 (2004) 327-334
i
i
Modeling of enzymatic conversion in the catalytic gel layer located on a membrane surface A. Noworyta, A. Trusek-Holownia* Institute of Chemical Engineering, Wroclaw University of Technology, Norwida 4/6, 50-373 Wroclaw, Poland Tel. +48 (71) 320-2653; Fax +48 (71) 328-1318; email." [email protected] Received 1 November 2003; accepted 14 November 2003
Abstract
Equations describing a multi-phase bioreactor with a catalytic membrane located on the boundary of phases, of which one is a substrate reservoir, were formulated. A model analysis of the process was carried out and the effect of main operating parameters of such a reactor, i.e., the catalytic layer thickness and the coefficients of diffusion mass transport in both phases, was determined. Two periods with different methods of supplying the catalytic layer can be distinguished in the process. There is also a characteristic thickness of the catalyst layer: when it is exceeded, the process duration is no longer shortened although full substrate conversion from the supply stream not always has a place. It is recommended to apply thin layers because then the catalyst activity is fully used. The analyses of the influence of mass transfer showed that substrate mass transfer in the water phase to the catalyst layer has a slight effect on the process rate when the intensification of its transfer in the organic phase might have a significant influence on the process rate. Keywords: Enzymatic gel layer; Catalytic membrane; Process modelling; Multi-phase reactor
1. I n t r o d u c t i o n
Due to broad substrate specificity, biocatalysts (enzymes, microorganism cells) are more often used for catalyzing the reactions aimed at the production o f desired compounds or degradation of environmental unfriendly substances [1-4]. *Corresponding author.
Due to high sensitivity to reaction media components, these applications are followed by numerous studies whose goal is to obtain preparations that will retain high catalytic activity for a relatively long time. There are different techniques o f catalyst stabilization, among them the stabilization o f protein molecule by way o f stiffening its structure due to immobilization.
Presented at the PERMEA 2003, Membrane Science and Technology Conference of Visegrad Countries (Czech Republic, Hungary, Poland andSlovakia), September ~11, 2003, Tatranskd Matliare, Slovakia. 0011-9164/04/$- See front matter © 2004 Elsevier B.V. All rights reserved PII: S0011-9164(04)00066-9
328
A. Noworyta, A. Trusek-Holownia / Desalination 162 (2004) 327-334
If a biocatalyst is immobilized on the surface or inside membrane pores, the membrane whose main task is the selective separation of the system components additionally assumes a catalytic character, and the catalytic reaction that takes place in the system can be related directly to the separation of reagents[5]. If the membrane is located on the boundary of two phases, it additionally plays the function of a phase contactor [6]. A particularly interesting case is the use of membranes for the separation of the organic phase from water; and depending on the hydrophobic-hydrophilic character of the membrane, its pores are filled with either the organic or water phase [7]. This type of a two-phase system is used, among other things, in the catalysis in the presence of hydrophobic reagents. In such a case, the organic phase is their reservoir from which they can be supplied in a controlled way to the reaction layer which, due to the biocatalyst properties, usually belongs to the water phase. Intensification of such processes should be directed towards a maximum use of the catalyst properties, particularly the increase of its stability and maximization of substrate concentration in the reaction zone. The study is dedicated to the modeling of a process that takes place in a multi-phase reactor with a bioeatalyst layer immobilized on the surface of a membrane that separates the organic phase from water.
2. Balance equations of a column reactor with a catalytic membrane
The considered system (Fig. 1), whose main element is a membrane module with a catalytic layer located on the membrane surface, in this case operates like a column reactor with a concurrent flow of phases on both sides of the membrane. The system can work either in a batch or continuous regime. Usually, because of the small value of the reacted substrate stream relative to the stream
Vl
T T V3
V~Co2
Vw, ew2
/
il
Va,
V2~ Cox
l
i'.-i
;i
? Vo, Col
....~
(1)
Vw, ewl
Fig. 1. Scheme of the system with the column reactor with catalytic membrane.
supplied to the column reactor, it is necessary to use circulation because a single flow of the substrate stream through the reactor does not ensure the required reaction degree. The following reaction was considered: S
enzyme
, P1 + P 2 +...
It was assumed that products being formed had no inhibiting effect on the reaction and were not characterized by a limited solubility in the reaction phase, so they did not affect the process. They were transported by diffusion to both phases, and concentrations of the reaction product in both phases corresponded to the interface equilibrium. Fig. 2 illustrates a differential element of the column bioreactor with a catalytic membrane. For concurrent plug flow, the mass balance of the substrate limiting the reaction is represented by the equations:
329
A. Noworyta, A. Trusek-Holownia / Desalination 162 (2004) 327-334 Vo, co (h+dh)
Vw, e,,,(h+dh)
leo
Z ~ i
/Co~/Cwi c,,(0)
ii[iii!i,i
" /
i
i
c~, (s)
/cw
dh 1"11
Fig. 3. Profile of concentrations in the reactor with a catalytic membrane.
T-
Vo, co(h)
The values of stream density nl, n 2 can be determined using the model of a catalytic membrane with a hydrophilic membrane (Fig. 3) [6]:
V,~, cw(h)
Fig. 2. Differential element of the column reactor with catalytic membrane.
CO
=
(3)
Vo,co (h)- Vo,Co(h +dh) (1)
(4)
-.1(~o, ~ ) , dA --0 1
kl
Vw*%(h)-Vw*%(h+dh)
(2)
+ .~ (~o,~ ) , ~ --o
* 13w*k 1 *[Co*eOsh(),*s ) - P *%] /'tl =
n2=
*
(~w+ P
+
--
P
+
-
1
-
~o ~
Assuming that the reaction is of the first order, the equation of stream density is obtained [8,9]:
Co*D *k, *k, *shah (k *s)
* k 1) * c o s h (~. * s) + (1) * k r + Dw * kl * P ) * s i l ~ ( ~ * s)
*Ow*kl * [co-P * % *eoshQ. *s)] - ~ w * c w * D * k , • sinh (~ *s) o: * (~lw +P * kl ) * Cosh (k * s) + (D * k~ + [~w* kl * P ) * sinh (~. *s)
P/r = r/1 - t'/2
(8)
(5)
VT-
X = ~D
(6)
(7) (10)
where e = D~/b--~,
(9)
Upon integration of Eqs. (1) and (2) for the initial
330
A. Noworyta, A. Trusek-Holownia / Desalination 162 (2004) 327-334
conditions (Fig. 1):
16 14 12 ,o
t-
O
Co(h = O) = %
(11) "6
% ( h = O ) =c.1
g
(12) "O
the values of limiting substrate concentrations in both phases at the outlet from the column reactor (Co2, c~2) are obtained. In the case of a continuous operation, streams V1and V3 are removed and streams V2and V4 with a properly selected composition are supplied to the system. In the general case (a continuous process), the mass balance of the limiting substrate in the reservoirs of both phases is given by the equations: I,',o *% (t +dr) - g,o ,eo(O =(go- V~)*Co2CO*dt
+ Vz *cox(t) dt
t~
2 0 6
2(t),dt
Vw,%(t)d t
(14)
The solution of Eqs. (1), (2), (6), (7), (13) and (14) allows us to determine the concentrations of both phases during the process duration. Due to non-linearity of Eqs. (6) and (7), in general it is not possible to obtain an analytical solution. Sottware using Turbo Pascal enabling a numerical solution was developed.
3. V e r i f i c a t i o n o f a r e a c t o r m o d e l
A model of the column bioreactor with a catalytic membrane shown in Fig. 1 was verified in the isooctane-polyamide membrane-water system. Due to the hydrophilic character of the membrane, its pores were filled by the water phase. The biocatalyst (lipase from Candida antarctica) was immobilized on the membrane
5
10
15
time [11]
Fig. 4. Comparison of experimental and model values of product concentration.
Table 1 Process parameters used for the verification and modeling of the process Parameter
(13)
, % (t + dt) - V=.,% (O =(gw- V3),c
+ V4 , c ~ ( t ) d t _
fi
8
6
Value Verification
Simulation
D
3.0x 10-12
3.0x 10-12
kr
o.lo
o.lo
P kI
1.74 2.9-5.1x10 -5
1.74 1 x10-7-1 x l 0 -4
13w s
5.1x10 -s 5.3-9.2x10 -7
1xl 0-1°-1 xl0 -4 1x10-Y-4x10 -5
c~(t = O)
0
o
c o(t = 0)
40
60
A H
0.014 0.10
0.014 0.10
surface by a chemical bond using glutaraldehyde. The amount of bound enzyme corresponded to the gel layer thickness equal to 5.3-9.2× 10 -7 m [10]. The enzyme catalyzed the reaction of hydrolysis of glycidyl butyrate, a compound whose separation coefficient in the tested system is equal to 1.74. Constants of the kinetic equation were determined in separate experiments [10]. By the low substrate concentration, the kinetics of the enzymatic reaction could be described by the first order according substrate kinetics:
A. Noworyta, A. Trusek-Holownia / Desalination 162 (2004) 327-334 =g • c
(15)
70-
g
=
In this case the constant is equal to 1.0 s-1 for the R-enantiomer and 0.49 s -1for the S-enantiomer of glycidyl butyrate. During the process, the amount of butyric acid [one of the reaction products whose whole mass was concentrated in the water phase (P<
4. Model analysis of the process
The subject of modeling was a batch process which can be more widely applied than the continuous one. It was assumed that at the beginning of the process the whole substrate mass was located in the organic phase in which, due to its hydrophobic properties, the substrate dissolves much better than in the water phase. When analysing typical concentrations in both phases for a broad range of parameters (Fig. 5), it was found that the process could be divided into two periods. In the first one, the phases are far from the extraction equilibrium state, the stream of substrate mass (nl) flowing to the catalytic layer is large, the substrate concentrations in the catalytic layer are high and so the stream of the reacted substrate is significant. Depending on the thickness and reactivity of the catalytic layer, part of the substrate mass (n2) is not reacted and
i
331
1
60-
.......................................................................
50'~
~I
40-
2O-
J~
0
i
0
3
'
,
i
6
9
12
15
18
time [hi Fig. 5. Substrate concentration in both phases in the batch process.
penetrates the water phase, thus increasing the substrate concentration. This period of the process is usually short. It is important that the concentration in the water phase, especially in the biocatalyst gel, does not exceed the saturation values since then it might cause substrate precipitation and disturb the catalytic membrane operation. After reaching the state close to interface equilibrium, the process slows down (it enters the second period). At the boundary of both periods, there is a maximum of the substrate concentration in the water phase. This implies a very interesting property of the system that consists of a change of the direction of substrate mass stream, n 2. In the second period of the process, the catalyst layer is supplied with a substrate from both surrounding phases. In a typical case, when the organic phase is a substrate reservoir, the value of stream n2 in the second period of the process duration is much lower than the value of stream H1 •
Fig. 6 shows schematically the substrate concentration in the catalyst layer and in the water layer in both periods considered (for the sake of figures clarity the scale was not kept). Parallel to the change of stream direction n2, the substrate concentration in the catalyst layer reveals a minimum. Its size and location depend on the thickness of the catalytic layer and size of streams nl
332
A. Noworyta, A. Trusek-Holownia / Desalination 162 (2004) 327-334
I lstperiod
t 2 n dperiod
I
-I -..-.
t
tim~
important for the process economy to determine this characteristic layer thickness. time
:i.!i!.::"
Fig. 6. Profile of substrate concentrationin both periods.
and n 2. The relation between streams n 1 and n z depends on the catalytic layer thickness and mass transfer coefficients on both sides of the gel. The main process parameters that can control the work of the analyzed reactor include kl, 13w and s. The effect of these parameters is shown below. 4.1. Thickness o f gel layer
The catalyst layer thickness is particularly important because, on one hand, its causes an increase of the amount of catalyst applied, which makes the reaction faster, and on the other hand, induces an increase of substrate mass transfer resistance in the gel layer. Fig. 7 illustrates the time necessary to obtain 90% conversion of the substrate present in the system depending on the gel layer thickness for various values of coefficient kv It was observed that there was a characteristic thickness of the catalyst layer (in the case considered this corresponds to the value s = 1× 10-5 m), above which a further increment of the catalyst amount does not shorten the process duration. Practically this values does not depend on coefficient ka. This follows from the fact that at this layer thickness the raw material contained in streams n~ and n2 reacts completely. A further increase of the layer thickness does not cause an increase of the process rate, which is controlled in this case by the diffusion rate of stream n~; it only changes the relation between streams n 1 and n 2. It is very
4. 2. Mass transfer coefficients
With a decrease of the catalyst layer thickness, a growth of the reaction time was observed. Starting from a certain value, this relation is very distinct. The role of coefficient k 1 is interesting. With its decrease, for a given layer thickness, the process duration is prolonged. This increase is very serious after exceeding a certain value (in the considered case kl < 2× 10-7 m s-~). A hypothetical reaction time was calculated for the case when no mass transport resistance occurred for the stream n 1 (kl~oo). As shown in Fig. 7 (continuous line), this hypothetical time does not differ much from the process time at high and medium values of kt(>5× 10-7 m s-l). This means that for these values o f k 1, the catalytic activity of the layer is used at maximum. A decrease of coefficient kl induces two reasons for which the process duration is increased: the stream of substrate supplied to the reaction layer by diffusion is decreased and the concentration gradient in the near-wall region increases, so the substrate concentration in the reaction layer is reduced. This means that the catalytic abilities of the gel layer are not fully used. The analyzed relations allow us to determine an optimum region of the reactor operation (marked area in Fig. 7). An increase of the catalyst layer is unjustified in many cases. Thin layers are recommended. Then the second period of the process appears very quickly and the catalytic layer is supplied from both phases; hence the catalyst activity is fully used. It is important that coefficient k~ be high enough. The situation is different when product purity is a priority. Then, in order not to allow the presence of the substrate in the water phase, the enzyme layer should be extended so as to reach full reaction of the substrate in it, i.e., to maintain the first period of the process all the time.
A. Noworyta, A. Trusek-Holownia /Desalination 162 (2004) 327-334 250
,.,,
200 150
',
50 \\
~
1
...... 2
.....
3
....... 4
"""'.
"-..
Y--.2.~=
Z : = ~-: = :'2: : . ~ =
it
0
0
0,5
1
1,5
2
thickness of gel layer [m*lff s]
Fig. 7. Time necessary to obtain 90% conversion of
substrate for various values of coefficient k~ (line 1: k~ = 5×10 -6 [m s-i]; 2: k 1 = lxl0 -6 [m s-~]; 3: k 1 = 5x10 -7 [m s-l]; 4: k 1 = lxl0 -6 [m s-l]). 7O 6O
"g 50 E
40 30 -t I
-9
-7
-5
l o g 1~.
Fig. 8. Effect of 13~on the process duration for various values of coefficient kl (line 1: k 1= 5x10 7 [m s-t]; 2: kl= lxl0 -6 [m s<]; 3: k~ = lxl0 5 [m s-~]).
catalytic membrane located at the boundary o f phases, it was found that: 1. Two periods with different methods o f supplying the catalytic layer can be distinguished in the process. In the first period, substrate is supplied to the layer only from its reservoir (organic phase), while in the second one from both phases that surround it. 2. There is a characteristic thickness o f the catalyst l a y e r - - when it is exceeded, the process duration is no longer shortened. It is recommended to apply thin layers because then the catalyst activity is fully used. 3. The process o f substrate mass transport by diffusion from its reservoir to the catalyst layer should be intensified, but there is some boundary value o f transfer coefficient kl, which when exceeded, does not cause an increase o f the process rate. 4. Transport ofsubstrate mass from the water phase to the catalyst layer has a slight effect on the process rate and there is no need to intensify it.
6. Fig. 8 illustrates the effect of~w on the process duration. A weak dependence o f the value of [3w on the process duration is observed. There is a possibility o f a weak maximum. The maximum is difficult to explain; it is probably a result o f the non-linearity o f the system of equations that describe the column reactor with a catalytic membrane. In the considered range of changes, a slight shortening o f the process duration can be observed with a decrease o f the value o f [3~. Hence, contrary to the phase which is the substrate reservoir, there is no need to maximize the mass transport conditions in this phase. 5.
Conclusions
As a result o f model analysis o f the process that takes place in a multi-phase reactor with a
333
Symbols
A 13
--
C
D h
---
F/]
--
n2
--
P
--
F S
--
--
Membrane surface, m 2 Mass transfer coefficient, m s -1 Substrate concentration, mol m -3 Diffusion coefficient, m 2 s -1 Current length o f column reactor, m Mass transfer coefficient to catalysts gel, m s -~ Reaction rate constant, s < Stream density o f converted substrate, mol m-2s -I Stream density o f entering substrate mass, mol m-'-s -~ Stream density o f nonconverted substrate mass, mol m-Zs -~ Partition coefficient Reaction rate, reel m-3s < Thickness o f gel layer, m
334 t V
A. Noworyta, A. Trusek-Holownia / Desalination 162 (2004) 327-334 ---
---
x
--
Time, s Flux, m 3 s -1 V o l u m e o f organic phase tank, m 3 V o l u m e o f water phase tank, m 3 Current thickness o f gel layer, m
[5]
Subscripts o w m 1,2
-----
[4]
Organic phase Water phase Membrane Cross section o f column reactor
[6]
[7] Acknowledgements
The support o f the Polish State Committee for Scientific Research (project P B Z / K B N / 1 4 / T 0 9 / 99/0 la) is gratefully acknowledged.
References
[1] M.G. Bramucci and V. Nagarajan, Industrial wastewater bioreactors: sources of novel microoganisms for biotechnology, TIBTECH, 18 (2000) 501-505. [2] Y.-Y. Linko, M. Lams~i,X. Wu, E. Uosukainen and 5. Sepp~ila, Biodegradable products by lipase biocatalysis, J. Biotechnol., 66 (1998) 41- 50. [3] K.K.B. Lee° L.H. Poppenborg and D.C. Stuckey, Terpene ester production in a solvent phase using a
[8]
[9]
[10]
[ 11]
reverse micelle-encapsulated lipase, Enzyme Mierob. Technol., 23 (1998) 253-260. Y. Shimada, Y. Watanabe, A. Sugihana and Y. Tominaga, Enzymatic alcoholysis for biodiesel fuel production and application of the reaction to oil processing, J. Mol. Catal. B: Enzymatic, 17 (2002) 133-142. L. Giomo and E. Drioli, Bioeatalytic membrane reactors: applications and perspectives, TIBTECH, 18 (2000) 339-349. A. Tmsek-Holownia, Membrane contactors, in: A. Noworyta and A. Trusek-Holownia, eds., Membrane Separations, Argi, Wroclaw, Poland, 2001, pp. 215-235. A. Trusek-Holownia and A. Noworyta, Catalytic membrane preparation for enzymatic hydrolysis reactions carried out in the membrane phase contaetor, Desalination, 144 (2002) 427-432. A. Trusek-Holownia and A. Noworyta, A mathematical model for enzymatic reaction carried out on the catalytic membrane, J. Membr. Sci., submitted for publication. A. Noworyta and A. Koziol, Model of catalytic membrane for the reaction carried out in biphase system, Inz. Apar. Chem., 3s (2002) 110-111. A. Trusek-Holownia, Process ofesters hydrolysis in enzyme layer immobilized on polymeric membrane, Conference materials of First International Symposium on Process Intensification and Miniaturisation, Newcastle, 2003. A. Trusek-Holownia and A. Noworyta, Mass transfer in the membrane contactor with a gel enzyme layer, Desalination, 162 (2004) 335-342.