Catalytic CO 2hydration by immobilized and free human carbonic anhydrase II in a laminar flow microreactor –Model and simulations
Ion Iliuta,Maria Cornelia Iliuta,Faical Larachi ⇑
Department of Chemical Engineering,Laval University,Québec,Canada G1V 0A6
a r t i c l e i n f o Article history:
Received 2April 2012
Received in revised form 9November 2012Accepted 9January 2013
Available online 26January 2013Keywords:
Laminar flow microreactor CO 2hydration
Human carbonic anhydrase II Modeling Simulation
a b s t r a c t
Ex vivo applications of human carbonic anhydrase II (HCA II)for its potential in CO 2capture technologies are emerging owing to the formidably large hydration turnover number Nature endowed this enzyme with to catalyze aqueous hydration of CO 2near diffusion limits.In this work,we investigated the CO 2hydration process catalyzed by solution-phase or immobilized HCA II enzyme in a laminar flow microreactor with the purpose to simulate the reaction–transport of HCA II in microchannels.The effects of operating condi-tions as well as the contribution of carbonic anhydrase on the performances of the CO 2hydration process are presented.Numerical simulations indicate that in laminar flow microreactor with HCA II immobilized on the inner surface of the tube,interpreting the data as a one-dimensional plug flow results will lead to significant error.Therefore,coupling of transport
phenomena and surface enzymic reaction necessitates the use of a two-dimensional analysis.Simulations reveal that hydrodynamic and diffusional constraints do not permit reasonable utilization of the immobilized HCA II enzyme in a laminar flow microreactor,even if HCA II has a very high hydration turnover and the uncatalyzed bulk CO 2hydration is the dominant pro-cess.In the microreactor with solution-phase HCA II enzyme ‘‘plug flow’’is achieved under laminar flow conditions and the contribution of uncatalyzed CO 2hydration process is not considerable.
Ó2013Elsevier B.V.All rights reserved.
1.Introduction
The reversible hydration of carbon dioxide catalyzed by human carbonic anhydrase II (HCA II)in aqueous solutions has been exten-sively investigated,mainly from a biochemistry and catalytic standpoint [1–4].HCA II-catalyzed CO 2=HCO À3inter-conversion plays a significant role in a multitude of physiological processes such as pH homoeostasis,respiratory gas exchange,photosynthe-sis,ion transport,as well as it is a fairly important reaction for drug design [5]and has been thoroughly investigated and described in a number of reviews [6–9].
Emerging ex vivo applications of HCA II for its potential use in CO 2capture and sequestration technol
ogies have recently at-tracted the researchers’attention [10,11].The main incitement to this interest is the very high hydration turnover,k h %106s À1,and 2nd-order rate constant,k h =K CO 2%108M À1s À1,that Nature endowed this enzyme with to effectuate catalytic hydration of CO 2near the limits imposed by diffusion encounters in aqueous media [12].Unfortunately,application of free HCA II enzyme in solution-phase is not always suitable and optimal because of the large volume of enzyme required.Binding of HCA II enzyme on a solid support is an attractive modification of its application having several advantages,including easier separation of the reaction products without catalyst contamination,ability to recover and re-use the enzyme,increase of the enzyme stability and operational lifetime,continuous operation of enzymatic processes and flexibil-ity of the reactor design [13,14].However,attaching HCA II to a so-lid macrosurface may lead the enzyme to behave differently [14]because:(i)the immobilization may cause the enzyme molecules to adopt a different conformation;(ii)the immobilized enzyme ex-ists in an environment different from that when it is in solution-phase;(iii)there is a partitioning of substrate between the solution and support,with the result that the substrate concentration in the neighborhood of the enzyme may be significantly different from that in the bulk solution;and (iv)diffusional effects play a more important role with immobilized enzymes.
The present contribution focuses on the CO 2hydration process catalyzed by solution-phase or immobi
lized HCA II enzyme in a laminar flow microreactor –which allows strict control of reaction conditions in time.The objective lies on exploring the possibility to use this micro enzyme reactor system as a tool for further under-standing and development of CO 2hydration process with a view to elaborate a comprehensive theoretical framework of these sys-tems and to apply it for experimental data reduction.The behavior of CO 2hydration laminar flow microreactor with human carbonic anhydrase attached to the inner surface of the tube was explored using a detailed kinetic model developed for reversible CO 2hydra-tion catalyzed by solution-phase HCA II (pseudo random Quad
1383-5866/$-see front matter Ó2013Elsevier B.V.All rights reserved./10.1016/j.seppur.2013.01.006
⇑Corresponding author.
E-mail addresses:ion.iliuta@gch.ulaval.ca (I.Iliuta),maria.iliuta@gch.ulaval.ca (M.C.Iliuta),faical.larachi@gch.ulaval.ca (F.Larachi).
Quad Iso Ping Pong mechanism with one transitory complex[15]). Particular attention has been given to the following items:(i)util-ity of the numerical simulations for refining the reactor operating conditions when determining the catalyzed CO2hydration kinetics data in a laminarflow microreactor with immobili
zed human car-bonic anhydrase,(ii)numerical identification of conditions,if any, to approximate plugflow operation,and(iii)evaluation of the ef-fects of uncatalyzed CO2hydration and two-dimensionality of the flow on laminarflow microreactor performance.Finally,we reveal the difficulties that result in interpreting the data obtained when HCA II is immobilized on the microreactor wall.
2.Laminarflow microreactor model
The system considered consists of a circular tube with solution-phase HCA II enzyme or with HCA II enzyme uniformly attached on its inner surface.The microreactor is isothermal.The entireflow in the tube may be viewed as consisting of three sections[13]:the so-called hydrodynamic inlet section,the concentration inlet section, and the fully developed section.In the hydrodynamic inlet section the initiallyflat liquid velocity profile evolves toward a parabolic velocity profile which remains translationally invariant in the downstream direction.The hydrodynamic inlet section is esti-mated to be fairly short(less than1mm)compared to the total length of the tube(0.1m)and we may consider that the laminar flow with a parabolic velocity profile is developed from the en-trance of the tube.Owing to the enzymatic reaction in solution-phase or on the tube wall and the diffusion of substrate towards the wall,the initiallyflat concentration profile changes gradually and becomes fully established in the third region.Flat entrance velocity profile would tend to shorten residence time of liquid lay-ers nearby the w
all.In the presence of the chemical reaction,this leads to radial reactant concentration gradients which are larger than those with parabolic velocity profiles.Hence,‘‘all-through’’parabolic velocity profiles are expected to lead to lesser conver-sions thanflat entrance velocity profiles evolving towards para-bolic.However,it is reasonable to assume that our simulations lead to conservative estimation of CO2conversion in the presence of solution-phase HCA II enzyme or HCA II immobilized enzyme.
The pseudo random Quad Quad Iso Ping Pong mechanism with one transitory complex,which implies a possible competitive in-ter-molecular proton transfer step by the CO2=HCOÀ
3
pair with re-spect to external buffer(B),was used to describe the reversible hydration of carbon dioxide catalyzed by human carbonic anhy-drase II[15]:
CO2þZnOHÀðEÞ¢ZnHCOÀ
3
ðESÞð1Þ
H2OþZnHCOÀ
3ðESÞ¢HCOÀ
3
þZnH2OðE WÞð2Þ
E W¢H Eð3ÞBþZnH2OðH EÞ¢BHþþZnOHÀðEÞð4ÞHCOÀ
3
þZnH2OðH EÞ¢CO2þH2OþZnOHÀðEÞð5ÞThe mechanism of uncatalyzed hydration of CO2and dehydra-tion of H2CO3under the conditions used in enzymatic process was described in the following way[16]:
H2OþCO2¢k31
k13
HþþHCOÀ
3
ð6Þ
HþþHCOÀ
3
¢k12
k21
H2CO3ð7Þ
H2OþCO2¢k32
k23
H2CO3ð8Þ
2.1.Model for CO2hydration laminarflow microreactor with immobilized HCAII enzyme
The unsteady-state mass balance equations for a chemical species j in the liquid phase are formulated
taking into account that in laminarflow regime the transport in the lateral direction occurs as a result of molecular diffusion only and the transport in the longitudinal direction occurs by both advection and diffusion:
@C CO
2
@t
þ2m‘1À
r
R
2
@C
CO2
@z
¼D CO
2
@2C CO
2þD CO
2
1@
r
@C CO
2
ÀR uc
CO2
ðC jÞð9Þ
@C HCOÀ
3þ2m‘1À
r  2
@C
HCOÀ
3
¼D HCOÀ
3
@2C HCOÀ
3þD HCOÀ
3
1@
r
@C HCOÀ
3
þR uc
CO2
ðC jÞð10Þ
@C B
@t
þ2m‘1À
r
R
2
@C
B
@z
¼D B
@2C B
@z2
þD B
1
r
@
@r
r
@C B
@r
ð11Þ
@C BHþ
@t
þ2m‘1À
r
R
2
@C
BHþ
@z
¼D BHþ
@2C BHþ
@z2
þD BHþ
1
r
@
@r
r
@C BHþ
@r
ð12Þ
To complete the description of the system,the following initial and boundary conditions are written:
t¼0C jð0;z;rÞ¼C in
j
ð13Þ
z¼0C jðt;0;rÞ¼C in
j
ð14Þz¼L
@C j
@z
ðt;L;rÞ¼0ð15Þ
Nomenclature
a s specific surface area,m2=m3
reactor
C E0enzyme load,kmol=m3
reactor
C j concentration of species j in liquid phase,kmol/m3
D j molecular diffusion coefficient in liquid phase,m2/s L microreactor length,m
r radial position within microreactor,m
R microreactor radius
R j reaction rate,kmol/m3s t time,s
v‘liquid velocity,m/s z axial coordinate,m Subscripts/Superscripts
c catalyzed
in microreactor inlet uc uncatalyzed
62I.Iliuta et al./Separation and Purification Technology107(2013)61–69
r¼0@C j
@r
ðt;z;0Þ¼0ð16Þ
r¼RÀD j @C j
ðt;z;RÞa s¼R c
j
ðC j j
r¼R
Þð17Þ
The boundary condition selected for the outlet does not set any restrictions except that convection dominates transport out of the reactor.Thus this condition keeps the outlet boundary open with-out restrictions on the concentration.
2.2.Model for CO2hydration laminarflow microreactor with solution-phase HCAII enzyme
The unsteady-state mass balance equations for a chemical spe-cies j in the liquid phase are:
@C CO
2 @t þ2m‘1À
r
R
2
@C
CO2
@z
¼D CO
2
@2C CO
2
@z2
þD CO
2
1
r
@
@r
r
@C CO
2
@r
ÀR uc
CO2
ðC jÞÀR c
CO2
ðC jÞð18Þ
@C HCOÀ
3þ2m‘1Àr  2
@C
HCOÀ
3¼D HCOÀ
3@2C HCOÀ
3þD HCOÀ
3
1@
r
@C HCOÀ
3
þR uc
CO2ðC jÞþR c
CO2
ðC jÞð19Þ
@C B @t þ2m‘1À
r
R
2
@C
B
@z
¼D B
@2C B
@z2
þD B
1
r
@
@r
r
@C B
@r
ÀR c
CO2
ðC jÞð20Þ
@C BHþ@t þ2m‘1À
r
R
2
@C
BHþ
@z
¼D BHþ
@2C BHþ
@z2
þD BHþ
1
r
@
@r
r
@C BHþ
@r
þR c
CO2
ðC jÞð21Þ
The initial and boundary conditions are:
t¼0C jð0;z;rÞ¼C in
j
ð22Þ
z¼0C jðt;0;rÞ¼C in
j
ð23Þ
z¼L
@C j
@z
ðt;L;rÞ¼0ð24Þ
r¼0
@C j
ðt;z;0Þ¼0ð25Þ
r¼R
@C j
ðt;z;RÞ¼0ð26Þ
The boundary condition selected for r=R makes sure that no
materialflow through the reactor wall.
2.3.Uncatalyzed CO2hydration kinetics
The overall rate of uncatalyzed conversion of dissolved CO2to
bicarbonate developed by Ho and Sturtevant(1963)was used[16]:
R uc
CO2
¼k0
31
C CO
2
Àk0
13
C HþC HCOÀ
3
where k0
31
¼k31þk32;
k0
13
¼k13þk23=K H
2
CO3
ð27Þ
The rate constants at25°C are:k0
31
¼0:037sÀ1and
k0
13
¼5:5Â104m3=kmol s[16].
Table1
The rate constant aggregates,turnover,apparent Michaelis and inhibition constants [15].
Rate constant aggregates Turnover,apparent Michaelis and inhibition
constants
k3
k1
¼9:5Â10À3M k h¼1:1Â106sÀ1;k d¼9:4Â104sÀ1 K E
a1
k1þk5¼8:4Â106MÀ1sÀ1K CO2¼9:5mM
k1
kÀ1
¼1:11Â103MÀ1K B1¼5:2mM;K BHþ1¼0:23mM
K HCOÀ
3
¼22:2mM
K i HCOÀ
3;1
¼14:8mM;K i HCOÀ
3
;2
¼127:9mM;
K i HCOÀ
3;3
¼37:5mM;K i HCOÀ
3
;4
¼61:9mM;
K i HCOÀ
3;5
¼12:2mM
Table2
The equilibrium constants[15].
Equilibrium constant Value
CO2þH2O¢HCOÀ3þHþK
a1¼½HCOÀ3 ½Hþ
2
;mol=l p K a1=5.97
Proton-transfer group acid dissociation
H E¢EþHþK
E
¼½E ½Hþ
½H E
;mol=l p K E=7.1
Catalytic group acid dissociation
E W¢EþHþK
E ¼½E ½Hþ
½E W
;mol=l p K E%7.1
BþHþBHþK
a2¼½B ½Hþ
½BHþ
;mol=l
Buffer:
Na2HPO4p K a2=7.2 1,2-Dimethylimidazole(1,2-DMI)p K a2=8.2
I.Iliuta et al./Separation and Purification Technology107(2013)61–6963
2.4.Catalyzed CO2hydration kinetics
The pseudo random Quad Quad Iso Ping Pong mechanism with one transitory complex,which implies a possible competitive in-ter-molecular proton transfer step by the CO2=HCOÀ
3
pair with re-spect to external buffer,B,was used to describe the reversible hydration of carbon dioxide catalyzed by HCA II[15]:
In addition to enzyme isomerization,the model takes into ac-
count the intermolecular CO2=HCOÀ
3
-subtended proton transfer via
a½CO2 Á½HCOÀ
3
coupling,the CO2=HCOÀ
3
-subtended proton transfer
via½HCOÀ
3
2and½CO2 Á½HCOÀ
3
2couplings,and the enzyme-substrate
transitory complex via½CO2 Á½HCOÀ
3
Á½B coupling.The hydration and dehydration turnover rate constants,k h and k d,the apparent Michaelis constants,K CO
2
,K HCOÀ
3
,K B,Kþ
BH
,and the apparent bicarbon-ate inhibition constants,K i HCOÀ
3
;j
are defined as follows:
k h%
K a1
K E
k3
k1
K E
K a1
k1þk5
;k d%
K a1
K E
k3
k1
K E
K a1
k1þk5
1þk3
À1
ð29Þ
K CO
2
%
k3
k1
;K HCOÀ
3
%
2
1þk3
kÀ1
K a1
K E
k3
k1
;
K B¼K B1
K EþK a2
K E
;K BHþ¼K BHþ1
K EþK a2
K a2
ð30Þ
Table3
Laminarflow microreactor operating conditions.
Operating conditions Data
Channel diameter  2.0mm
Microreactor length0.1m
Active HCA II loading4:32Â10À7kmol=m3
reactor Microreactor temperature298K
Inlet CO2concentration0.017mol/l
Inlet superficial liquid velocity0.0025–0.0.005m/s
R c CO2¼
k h C CO
2
C BÀK a2
a1
C HCOÀ
3
C BHþ
1þC HCOÀ3
i HCOÀ
3
;
3
C E0
K B C CO
2
þK CO
2
C BþK B
2
K E
K a1
C HCOÀ
3
þ2K CO
2
K a2
K E
C BHþþC CO
2
C Bþ2K CO2
K HCOÀ
3
K a2
K E
C HCOÀ
3
C BHþþK B
K i HCOÀ
3
;1
C CO
2
reaction diffusionC HCOÀ
3
Â
1
K CO
2
K i HCOÀ
3
;2
C B C HCOÀ
3
þ1
2
K B
K i HCOÀ
3
;3
K E
K a1
C HCOÀ
3
2
þK B
K i HCOÀ
3
;1
K i HCOÀ
3
;4
C CO
2
C HCOÀ
3
2
þ1
K i HCOÀ
3
;5
C CO
2
C B C HCOÀ
3
ð28Þ
64I.Iliuta et al./Separation and Purification Technology107(2013)61–69
K i HCOÀ
3;1
%2
K a1
K E
k1
kÀ1
þ2
k1
k3
k5
K E
a1
k1þk5
!À1
;
K i HCOÀ
3;2
¼
K a1
E
K CO
2
;K i HCOÀ
3
;3
¼
K a1
E
k3
1
K E
K a1
k1þk5
5
ð31Þ
K i HCOÀ
3;4
¼
K2
i HCOÀ
3
;3
K i HCOÀ
3
;3
ÀK i HCOÀ
3
;1
;
K i HCOÀ
3;5
¼
1
2
1
K i HCOÀ
3
;1
À
1
K i HCOÀ
3
;3
!À1
ð32Þ
The rate constant aggregates with the inferred turnover and apparent Michaelis constant and inhibition constants are tabulated in Table1.The equilibrium constants are given in Table2.The ki-netic model was developed for reversible hydration of carbon diox-ide in the presence of solution-phase human car
bonic anhydrase II. However,the kinetic model is expected to be suitable under immo-bilization enzyme conditions taking into account the comparable CO2removal efficiency of the immobilized HCA II and the soluble counterpart for extended periods[17].
2.5.Method of solution
In order to solve the system of partial differential equations,we discretized in space and solved the resulting set of ordinary differential equations.The spatial discretization was performed using the standard cell-centeredfinite difference scheme.The GEAR integration method for stiff differential equations was em-ployed to integrate the time derivatives.The relative error toler-ance for the time integration process in the present simulations was set at10À6for each time step.
3.Results and discussion
The model was initially used to compare the performance of the laminarflow microreactor with solution-phase or immobilized HCA II enzyme under the same HCA II loading.Both catalyzed and uncat-alyzed CO2hydration processes were considered.Figs.1and2show typical CO2and HCOÀ
3
radial and axial steady-state concentration profiles obtained under the same operating conditions(Table3).Dif-fusional effects are more important with immobilized HCA II en-zyme(Fig.1a)and the result is a lower CO2conversion(Fig.2a). On the other side,with solution-phase HCA II enzyme,the species concentration is nearly uniform in the radial direction(Fig.1b) and this is close to the ideal‘‘plugflow’’conditions[18].Numerical simulations indicate that in laminarflow microreactor with the HCA II immobilized on the inner surface of the tube the coupling of transport phenomena and chemical reaction necessitates the use of two-dimensional analysis in processing the experimental data.
I.Iliuta et al./Separation and Purification Technology107(2013)61–6965

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