catalytic co2 hydration by immobilized and free human carbonic anhydrase ii in a laminar flow...

Separation and Purification Technology 107 (2013) 61–69

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Separation and Purification Technology

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Catalytic CO2 hydration by immobilized and free human carbonic anhydrase IIin 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 2 April 2012Received in revised form 9 November 2012Accepted 9 January 2013Available online 26 January 2013

Keywords:Laminar flow microreactorCO2 hydrationHuman carbonic anhydrase IIModelingSimulation

1383-5866/$ - see front matter � 2013 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.seppur.2013.01.006

⇑ Corresponding author.E-mail addresses: [email protected] (I. Iliut

(M.C. Iliuta), [email protected] (F. Larachi).

a b s t r a c t

Ex vivo applications of human carbonic anhydrase II (HCA II) for its potential in CO2 capture technologies areemerging owing to the formidably large hydration turnover number Nature endowed this enzyme with tocatalyze aqueous hydration of CO2 near diffusion limits. In this work, we investigated the CO2 hydrationprocess catalyzed by solution-phase or immobilized HCA II enzyme in a laminar flow microreactor withthe 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 CO2 hydration processare presented. Numerical simulations indicate that in laminar flow microreactor with HCA II immobilizedon the inner surface of the tube, interpreting the data as a one-dimensional plug flow results will lead tosignificant error. Therefore, coupling of transport phenomena and surface enzymic reaction necessitatesthe use of a two-dimensional analysis. Simulations reveal that hydrodynamic and diffusional constraintsdo not permit reasonable utilization of the immobilized HCA II enzyme in a laminar flow microreactor, evenif HCA II has a very high hydration turnover and the uncatalyzed bulk CO2 hydration is the dominant pro-cess. In the microreactor with solution-phase HCA II enzyme ‘‘plug flow’’ is achieved under laminar flowconditions and the contribution of uncatalyzed CO2 hydration process is not considerable.

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1. Introduction

The reversible hydration of carbon dioxide catalyzed by humancarbonic anhydrase II (HCA II) in aqueous solutions has been exten-sively investigated, mainly from a biochemistry and catalyticstandpoint [1–4]. HCA II-catalyzed CO2=HCO�3 inter-conversionplays a significant role in a multitude of physiological processessuch as pH homoeostasis, respiratory gas exchange, photosynthe-sis, ion transport, as well as it is a fairly important reaction for drugdesign [5] and has been thoroughly investigated and described in anumber of reviews [6–9].

Emerging ex vivo applications of HCA II for its potential use inCO2 capture and sequestration technologies have recently at-tracted the researchers’ attention [10,11]. The main incitement tothis interest is the very high hydration turnover, kh � 106 s�1,and 2nd-order rate constant, kh=KCO2 � 108 M�1 s�1, that Natureendowed this enzyme with to effectuate catalytic hydration ofCO2 near the limits imposed by diffusion encounters in aqueousmedia [12]. Unfortunately, application of free HCA II enzyme insolution-phase is not always suitable and optimal because of thelarge volume of enzyme required. Binding of HCA II enzyme on asolid support is an attractive modification of its application having

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several advantages, including easier separation of the reactionproducts without catalyst contamination, ability to recover and re-use the enzyme, increase of the enzyme stability and operationallifetime, 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 moleculesto 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 solutionand support, with the result that the substrate concentration in theneighborhood of the enzyme may be significantly different fromthat in the bulk solution; and (iv) diffusional effects play a moreimportant role with immobilized enzymes.

The present contribution focuses on the CO2 hydration processcatalyzed by solution-phase or immobilized HCA II enzyme in alaminar flow microreactor – which allows strict control of reactionconditions in time. The objective lies on exploring the possibility touse this micro enzyme reactor system as a tool for further under-standing and development of CO2 hydration process with a viewto elaborate a comprehensive theoretical framework of these sys-tems and to apply it for experimental data reduction. The behaviorof CO2 hydration laminar flow microreactor with human carbonicanhydrase attached to the inner surface of the tube was exploredusing a detailed kinetic model developed for reversible CO2 hydra-tion catalyzed by solution-phase HCA II (pseudo random Quad

http://dx.doi.org/10.1016/j.seppur.2013.01.006

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http://dx.doi.org/10.1016/j.seppur.2013.01.006

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Nomenclature

as specific surface area, m2=m3reactor

CE0 enzyme load, kmol=m3reactor

Cj concentration of species j in liquid phase, kmol/m3

Dj molecular diffusion coefficient in liquid phase, m2/sL microreactor length, mr radial position within microreactor, mR microreactor radiusRj reaction rate, kmol/m3 s

t time, sv‘ liquid velocity, m/sz axial coordinate, m

Subscripts/Superscriptsc catalyzedin microreactor inletuc uncatalyzed

62 I. Iliuta et al. / Separation and Purification Technology 107 (2013) 61–69

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 operatingconditions when determining the catalyzed CO2 hydration kineticsdata in a laminar flow microreactor with immobilized human car-bonic anhydrase, (ii) numerical identification of conditions, if any,to approximate plug flow operation, and (iii) evaluation of the ef-fects of uncatalyzed CO2 hydration and two-dimensionality of theflow on laminar flow microreactor performance. Finally, we revealthe difficulties that result in interpreting the data obtained whenHCA II is immobilized on the microreactor wall.

2. Laminar flow microreactor model

The system considered consists of a circular tube with solution-phase HCA II enzyme or with HCA II enzyme uniformly attached onits inner surface. The microreactor is isothermal. The entire flow inthe 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 sectionthe initially flat liquid velocity profile evolves toward a parabolicvelocity profile which remains translationally invariant in thedownstream direction. The hydrodynamic inlet section is esti-mated to be fairly short (less than 1 mm) compared to the totallength of the tube (0.1 m) and we may consider that the laminarflow 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 towardsthe wall, the initially flat concentration profile changes graduallyand becomes fully established in the third region. Flat entrancevelocity profile would tend to shorten residence time of liquid lay-ers nearby the wall. In the presence of the chemical reaction, thisleads to radial reactant concentration gradients which are largerthan those with parabolic velocity profiles. Hence, ‘‘all-through’’parabolic velocity profiles are expected to lead to lesser conver-sions than flat entrance velocity profiles evolving towards para-bolic. However, it is reasonable to assume that our simulationslead to conservative estimation of CO2 conversion in the presenceof solution-phase HCA II enzyme or HCA II immobilized enzyme.

The pseudo random Quad Quad Iso Ping Pong mechanism withone transitory complex, which implies a possible competitive in-ter-molecular proton transfer step by the CO2=HCO�3 pair with re-spect to external buffer (B), was used to describe the reversiblehydration of carbon dioxide catalyzed by human carbonic anhy-drase II [15]:

CO2 þ ZnOH�ðEÞ ¢ ZnHCO�3 ðESÞ ð1Þ

H2Oþ ZnHCO�3 ðESÞ ¢ HCO�3 þ ZnH2OðEWÞ ð2Þ

EW ¢ HE ð3Þ

Bþ ZnH2OðHEÞ ¢ BHþ þ ZnOH�ðEÞ ð4Þ

HCO�3 þ ZnH2OðHEÞ ¢ CO2 þH2Oþ ZnOH�ðEÞ ð5Þ

The mechanism of uncatalyzed hydration of CO2 and dehydra-tion of H2CO3 under the conditions used in enzymatic processwas described in the following way [16]:

H2Oþ CO2 ¢k31

k13

Hþ þHCO�3 ð6Þ

Hþ þHCO�3 ¢k12

k21

H2CO3 ð7Þ

H2Oþ CO2 ¢k32

k23

H2CO3 ð8Þ

2.1. Model for CO2 hydration laminar flow microreactor withimmobilized HCAII enzyme

The unsteady-state mass balance equations for a chemicalspecies j in the liquid phase are formulated taking into accountthat in laminar flow regime the transport in the lateral directionoccurs as a result of molecular diffusion only and the transportin the longitudinal direction occurs by both advection anddiffusion:

@CCO2

@tþ 2m‘ 1� r

R

� �2� �

@CCO2

@z

¼ DCO2

@2CCO2

@z2 þ DCO2

1r@

@rr@CCO2

@r

� �� Ruc

CO2ðCjÞ ð9Þ

@CHCO�3

@tþ 2m‘ 1� r

R

� �2� �

@CHCO�3

@z

¼ DHCO�3

@2CHCO�3

@z2 þ DHCO�3

1r@

@rr@CHCO�3

@r

� �� þ Ruc

CO2ðCjÞ ð10Þ

@CB

@tþ 2m‘ 1� r

R

� �2� �

@CB

@z¼ DB

@2CB

@z2 þ DB1r@

@rr@CB

@r

� �� ð11Þ

@CBHþ

@tþ 2m‘ 1� r

R

� �2� �

@CBHþ

@z¼ DBHþ

@2CBHþ

@z2

þ DBHþ1r@

@rr@CBHþ

@r

� �� ð12Þ

To complete the description of the system, the following initialand boundary conditions are written:

t ¼ 0 Cjð0; z; rÞ ¼ Cinj ð13Þ

z ¼ 0 Cjðt;0; rÞ ¼ Cinj ð14Þ

z ¼ L@Cj

@zðt; L; rÞ ¼ 0 ð15Þ

Table 1The rate constant aggregates, turnover, apparent Michaelis and inhibition constants[15].

Rate constant aggregates Turnover, apparent Michaelis and inhibitionconstants

k3k1¼ 9:5� 10�3 M kh ¼ 1:1� 106 s�1; kd ¼ 9:4� 104 s�1

KEKa1

k1 þ k5 ¼ 8:4� 106 M�1 s�1 KCO2 ¼ 9:5 mM

k1k�1¼ 1:11� 103 M�1 KB1 ¼ 5:2 mM; KBHþ1 ¼ 0:23 mM

KHCO�3 ¼ 22:2 mMKiHCO�3 ;1 ¼ 14:8 mM; KiHCO�3 ;2 ¼ 127:9 mM;KiHCO�3 ;3 ¼ 37:5 mM; KiHCO�3 ;4 ¼ 61:9 mM;KiHCO�3 ;5 ¼ 12:2 mM

Table 2The equilibrium constants [15].

Equilibrium constant Value

CO2 þ H2O ¢ HCO�3 þ Hþ Ka1 ¼ ½HCO�3 �½Hþ�

½CO2 � ;mol=l pKa1 = 5.97

Proton-transfer group acid dissociation

HE ¢ Eþ Hþ KE ¼ ½E�½Hþ�

½H E� ;mol=l pKE = 7.1

Catalytic group acid dissociationEW ¢ Eþ Hþ KE ¼ ½E�½H

þ�½EW � ;mol=l pKE � 7.1

Bþ HþBHþ Ka2 ¼ ½B�½Hþ�

½BHþ� ;mol=l

Buffer:Na2HPO4 pKa2 = 7.21,2-Dimethylimidazole (1,2-DMI) pKa2 = 8.2

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

r, m

Stea

dy-s

tate

con

cent

ratio

n, m

ol/l

CO2

HCO3

(a)

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

r, m

Stea

dy-s

tate

con

cent

ratio

n, m

ol/l

CO2

HCO3

(b)

Fig. 1. Steady-state radial concentration profiles at z = L (catalyzed + uncatalyzedhydration): (a) immobilized HCA II; and (b) solution-phase HCA II. Feed conditions:vs‘ = 0.005 m/s, Cin

B ¼ 0:015 mol=l (Na2HPO4), CinBH ¼ 0:01 mol=l (NaH2PO4).

I. Iliuta et al. / Separation and Purification Technology 107 (2013) 61–69 63

r ¼ 0@Cj

@rðt; z;0Þ ¼ 0 ð16Þ

r ¼ R � Dj@Cj

@rðt; z;RÞas ¼ Rc

j ðCjjr¼RÞ ð17Þ

The boundary condition selected for the outlet does not set anyrestrictions except that convection dominates transport out of thereactor. Thus this condition keeps the outlet boundary open with-out restrictions on the concentration.

2.2. Model for CO2 hydration laminar flow microreactor with solution-phase HCAII enzyme

The unsteady-state mass balance equations for a chemical spe-cies j in the liquid phase are:

@CCO2

@tþ 2m‘ 1� r

R

� �2� �

@CCO2

@z¼ DCO2

@2CCO2

@z2 þ DCO2

1r@

@rr@CCO2

@r

� �� Ruc

CO2ðCjÞ � Rc

CO2ðCjÞ ð18Þ

@CHCO�3

@tþ 2m‘ 1� r

R

� �2� �

@CHCO�3

@z¼ DHCO�3

@2CHCO�3

@z2 þ DHCO�3

1r@

@rr@CHCO�3

@r

� �� þ Ruc

CO2ðCjÞ þ Rc

CO2ðCjÞ ð19Þ

@CB

@tþ 2m‘ 1� r

R

� �2� �

@CB

@z¼ DB

@2CB

@z2 þ DB1r@

@rr@CB

@r

� �� Rc

CO2ðCjÞ ð20Þ

@CBHþ

@tþ 2m‘ 1� r

R

� �2� �

@CBHþ

@z¼ DBHþ

@2CBHþ

@z2 þ DBHþ1r@

@rr@CBHþ

@r

� �� þ Rc

CO2ðCjÞ ð21Þ

The initial and boundary conditions are:

t ¼ 0 Cjð0; z; rÞ ¼ Cinj ð22Þ

z ¼ 0 Cjðt;0; rÞ ¼ Cinj ð23Þ

z ¼ L@Cj

@zðt; L; rÞ ¼ 0 ð24Þ

r ¼ 0@Cj

@rðt; z;0Þ ¼ 0 ð25Þ

r ¼ R@Cj

@rðt; z;RÞ ¼ 0 ð26Þ

The boundary condition selected for r = R makes sure that nomaterial flow through the reactor wall.

2.3. Uncatalyzed CO2 hydration kinetics

The overall rate of uncatalyzed conversion of dissolved CO2 tobicarbonate developed by Ho and Sturtevant (1963) was used [16]:

RucCO2¼ k031CCO2 � k013CHþCHCO�3 where k031 ¼ k31 þ k32;

k013 ¼ k13 þ k23=KH2CO3 ð27Þ

The rate constants at 25 �C are: k031 ¼ 0:037 s�1 andk013 ¼ 5:5� 104 m3=kmol s [16].

0

0.003

0.006

0.009

0.012

0.015

0.018

0 0.02 0.04 0.06 0.08 0.1z, m

Rad

ial a

vera

ge c

once

ntra

tion,

mol

/l

CO2

HCO3

(a)

CO2 conversion=0.473

0

0.003

0.006

0.009

0.012

0.015

0.018

0 0.02 0.04 0.06 0.08 0.1

z, m

Rad

ial a

vera

ge c

once

ntra

tion,

mol

/l

CO2

HCO3

(b)

CO2 conversion=0.76

Fig. 2. Steady-state axial concentration profiles (catalyzed + uncatalyzed hydra-tion): (a) immobilized HCA II; and (b) solution-phase HCA II. Feed conditions:vs‘ = 0.005 m/s, Cin


Table 3Laminar flow microreactor operating conditions.

Operating conditions Data

Channel diameter 2.0 mmMicroreactor length 0.1 mActive HCA II loading 4:32� 10�7 kmol=m3

reactor

Microreactor temperature 298 KInlet CO2 concentration 0.017 mol/lInlet superficial liquid velocity 0.0025–0.0.005 m/s

0

0.004

0.008

0.012

0.016

0.02

0.024

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

r, m

Stea

dy-s

tate

con

cent

ratio

n, m

ol/l

Catalyzed + uncatalyzed hydration

Catalyzed hydration

(a)

HCO3- concentration

CO2 concentration

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

r, m

Stea

dy-s

tate

con

cent

ratio

n, m

ol/l


Catalyzed hydration

(b)

CO2 concentration

HCO3- concentration

Fig. 3. Steady-state radial concentration profiles at z = L: (a) immobilized HCA II;and (b) solution-phase HCA II. Feed conditions: vs‘ = 0.005 m/s, Cin

B ¼ 0:015 mol=l(Na2HPO4), Cin

BH ¼ 0:01 mol=l (NaH2PO4).


2.4. Catalyzed CO2 hydration kinetics

The pseudo random Quad Quad Iso Ping Pong mechanism withone transitory complex, which implies a possible competitive in-ter-molecular proton transfer step by the CO2=HCO�3 pair with re-spect to external buffer, B, was used to describe the reversiblehydration of carbon dioxide catalyzed by HCA II [15]:

RcCO2¼

kh CCO2 CB � Ka2Ka1

CHCO�3 CBHþ

� �1þ

CHCO�3

KiHCO�3;3

�

KBCCO2 þ KCO2 CB þ KB2

KEKa1

CHCO�3 þ 2KCO2Ka2KE

CBHþ þ CCO2 CB þ 2KCO2

KHCO�3

� 1KCO2

KiHCO�3;2

CBCHCO�3 þ12

KBKiHCO�

3;3

KEKa1

CHCO�3

� �2þ KB

KiHCO�3;1KiHCO�

3;4

CCO2 CHCO�3

�

In addition to enzyme isomerization, the model takes into ac-count the intermolecular CO2=HCO�3 -subtended proton transfer viaa ½CO2� � ½HCO�3 � coupling, the CO2=HCO�3 -subtended proton transfervia ½HCO�3 �

2 and ½CO2� � ½HCO�3 �2 couplings, and the enzyme-substrate

transitory complex via ½CO2� � ½HCO�3 � � ½B� coupling. The hydrationand dehydration turnover rate constants, kh and kd, the apparentMichaelis constants, KCO2 , KHCO�3 , KB, KþBH, and the apparent bicarbon-ate inhibition constants, KiHCO�3 ;j are defined as follows:

kh �Ka1

KE

k3

k1

KE

Ka1k1 þ k5

� �; kd �

Ka1

KE

k3

k1

KEKa1

k1 þ k5

1þ k3k�1

ð29Þ

KCO2 �k3

k1; KHCO�3 �

21þ k3

k�1

Ka1

KE

k3

k1;

KB ¼ KB1KE þ Ka2

KE; KBHþ ¼ KBHþ1

KE þ Ka2

Ka2ð30Þ

�CE0

Ka2KE

CHCO�3 CBHþ þ KBKiHCO�

3;1

CCO2 CHCO�3

�2þ 1

KiHCO�3;5

CCO2 CBCHCO�3

ð28Þ

0

0.004

0.008

0.012

0.016

0.02

0 0.02 0.04 0.06 0.08 0.1

z, m

Rad

ial a

vera

ge c

once

ntra

tion,

mol

/l


Catalyzed hydration

(a)

HCO3- concentration

CO2 concentration



0

0.003

0.006

0.009

0.012

0.015

0.018

0 0.02 0.04 0.06 0.08 0.1

z, m

Rad

ial a

vera

ge c

once

ntra

tion,

mol

/l


Catalyzed hydration

(b)

CO2 concentration

HCO3- concentration

CO2 conversion=0.76


Fig. 4. Steady-state axial concentration profiles: (a) immobilized HCA II; and (b)solution-phase HCA II. Feed conditions: vs‘ = 0.005 m/s, Cin

B ¼ 0:015 mol=l (Na2-

HPO4), CinBH ¼ 0:01 mol=l (NaH2PO4).

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

r, m

Ste

ady-

stat

e co

nce

ntr

atio

n, m

ol/l

Model diffusion coefficients

Model diffusion coefficients*10

(a)

CO2 concentration

HCO3- concentration

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

r, m

Ste

ady-

stat

e co

nce

ntr

atio

n, m

ol/l



B concentration

BH concentration

(b)

Fig. 5. Steady-state radial concentration profiles at z = L in laminar flow microre-actor with immobilized HCA II enzyme – influence of diffusion coefficients. Feedconditions: vs‘ = 0.005 m/s, Cin

B ¼ 0:015 mol=l (Na2HPO4), CinBH ¼ 0:01 mol=l

(NaH2PO4).


KiHCO�3 ;1 � 2Ka1

KE

k1

k�1þ 2

k1

k3

k5KEKa1

k1 þ k5

!�1

;

KiHCO�3 ;2 ¼Ka1

KEKCO2 ; KiHCO�3 ;3 ¼

Ka1

KE

k3

k1

KEKa1

k1 þ k5

k5ð31Þ

KiHCO�3 ;4 ¼K2

iHCO�3 ;3

KiHCO�3 ;3 � KiHCO�3 ;1;

KiHCO�3 ;5 ¼12

1KiHCO�3 ;1

� 1KiHCO�3 ;3

!�1

ð32Þ

The rate constant aggregates with the inferred turnover andapparent Michaelis constant and inhibition constants are tabulatedin Table 1. The equilibrium constants are given in Table 2. The ki-netic model was developed for reversible hydration of carbon diox-ide in the presence of solution-phase human carbonic anhydrase II.However, the kinetic model is expected to be suitable under immo-bilization enzyme conditions taking into account the comparableCO2 removal efficiency of the immobilized HCA II and the solublecounterpart for extended periods [17].

2.5. Method of solution

In order to solve the system of partial differential equations, wediscretized in space and solved the resulting set of ordinary

differential equations. The spatial discretization was performedusing the standard cell-centered finite difference scheme. TheGEAR 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 simulationswas set at 10�6 for each time step.

3. Results and discussion

The model was initially used to compare the performance of thelaminar flow microreactor with solution-phase or immobilized HCAII enzyme under the same HCA II loading. Both catalyzed and uncat-alyzed CO2 hydration processes were considered. Figs. 1 and 2 showtypical CO2 and HCO�3 radial and axial steady-state concentrationprofiles obtained under the same operating conditions (Table 3). Dif-fusional effects are more important with immobilized HCA II en-zyme (Fig. 1a) and the result is a lower CO2 conversion (Fig. 2a).On the other side, with solution-phase HCA II enzyme, the speciesconcentration is nearly uniform in the radial direction (Fig. 1b)and this is close to the ideal ‘‘plug flow’’ conditions [18]. Numericalsimulations indicate that in laminar flow microreactor with the HCAII immobilized on the inner surface of the tube the coupling oftransport phenomena and chemical reaction necessitates the useof two-dimensional analysis in processing the experimental data.

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 10 20 30 40 50Time, s

Rad

ial a

vera

ge c

once

ntra

tion

at z

/L=1

, mol

/l



(a)HCO3- concentration

CO2 concentration



0.006

0.008

0.010

0.012

0.014

0.016

0.019

0 10 20 30 40 50Time, s

Rad

ial a

vera

ge c

once

ntra

tion

at z

/L=1

, mol

/l


Model diffusion coeficients*10

BH concentration

B concentration

(b)

Fig. 6. Unsteady-state concentration profiles in laminar flow microreactor withimmobilized HCA II enzyme – influence of diffusion coefficients. Feed conditions:vs‘ = 0.005 m/s, Cin


0

0.004

0.008

0.012

0.016

0.02

0 0.02 0.04 0.06 0.08 0.1z, m

Rad

ial a

vera

ge c

once

ntra

tion,

mol

/l

Liquid velocity=0.005 m/s


HCO3- concentration

CO2 concentration



(a)

0

0.003

0.006

0.009

0.012

0.015

0.018

0 0.02 0.04 0.06 0.08 0.1z, m

Rad

ial a

vera

ge c

once

ntra

tion,

mol

/l



CO2 concentration

HCO3- concentration

CO2 conversion=0.74


(b)

Fig. 7. Steady-state axial concentration profiles in laminar flow microreactor withimmobilized HCA II enzyme – effect of liquid velocity: (a) catalyzed CO2 hydration;and (b) catalyzed + uncatalyzed CO2 hydration. Feed conditions: Cin

B ¼ 0:015 mol=l(Na2HPO4), Cin

BH ¼ 0:01 mol=l (NaH2PO4).


Interpreting the data as one-dimensional plug flow results will leadto significant error.

It is of interest to investigate the behavior of CO2 hydration pro-cess by forcing artificially silencing of the uncatalyzed conversionof dissolved CO2 to bicarbonate (Figs. 3 and 4). As expected, withsolution-phase HCA II enzyme the contribution of uncatalyzedCO2 hydration is reduced and the overall reaction rate is dominatedby the enzymatic process (Fig. 4b). On the other side, the uncata-lyzed CO2 hydration is the prevailing process when HCA II enzymeis immobilized on the inner surface of the tube. Due to consider-able diffusional limitations (Fig. 3a), a relatively small amount ofHCO�3 is produced by catalyzed CO2 hydration process (Fig. 4a).Therefore, the hydrodynamic and diffusional constraints in laminarflow microreactors do not permit a reasonable utilization of HCA IIenzyme immobilized on the inner surface of the tube. It is antici-pated that such behavior will generate difficulties in interpretingexperimental data obtained with immobilized HCA II enzymes. Un-der these conditions, the microreactor configuration must be se-lected accurately to exploit the absorption potential of HCA IIenzyme (e.g., enhanced mixing to disrupt adjacent laminar fluidstreams by adding internals in the microchannel).

In laminar flow microreactors, an important parameter whichdictates mixing in the radial direction is the molecular diffusioncoefficient. The influence of the diffusion coefficients on the CO2

hydration process under immobilized HCA II enzyme conditionsis illustrated in Figs. 5 and 6 where both catalyzed and uncatalyzed

CO2 hydration processes were considered. It is evident that an in-crease in the molecular diffusion coefficient (a 10-fold increasewith respect to estimated values with Frank et al. [19] and Wil-ke-Chang (Reid et al. [20]) correlations) leads to higher mass trans-fer fluxes transported between the liquid and the catalytic solidsurface (Fig. 5) and the result is a higher CO2 conversion (Fig. 6a).Theoretically, as the molecular diffusion coefficient continues toincrease, the mixing in the radial direction will become faster aswell as the flux of CO2 toward the walls will be promoted. The highdegree of mixing in the radial direction will lead to a more uniformdistribution of mass across the cross section and a higher CO2

conversion.Figs. 7 and 8 show CO2 and HCO�3 axial and radial steady-state

concentration profiles obtained for two values of liquid velocityin the laminar flow microreactor with immobilized HCA II enzyme.Two cases were simulated: (i) catalyzed CO2 hydration process wasconsidered only, and (ii) both catalyzed and uncatalyzed CO2

hydration processes were considered. As expected, CO2 conversionincreases with the decrease of liquid velocity due to higher resi-dence time (Fig. 7). At lower liquid velocity, diffusional limitationcontinues to be considerable (Fig. 8a) and the uncatalyzed CO2

hydration becomes more important (Figs. 7 and 8b). The perfor-mance of the laminar flow microreactor with solution-phase HCAII enzyme increases slowly (not shown) with the decrease of liquidvelocity.

0

0.004

0.008

0.012

0.016

0.02

0.024

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

r, m

Stea

dy-s

tate

con

cent

ratio

n, m

ol/l


Liquid velocity=0.0025m/s

(a)

HCO3- concentration

CO2 concentration

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

r, m

Stea

dy-s

tate

con

cent

ratio

n, m

ol/l



CO2 concentration

HCO3- concentration

(b)

Fig. 8. Steady-state radial concentration profiles at z = L in laminar flow microre-actor with immobilized HCA II enzyme – effect of liquid velocity: (a) catalyzed CO2

hydration; and (b) catalyzed + uncatalyzed CO2 hydration. Feed conditions:Cin


0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0 0.02 0.04 0.06 0.08 0.1

z, m

Rad

ial a

vera

ge c

once

ntra

tion,

mol

/l

Inlet buffer concentration=0.015 mol/l


(a)

HCO3- concentration

CO2 concentration


CO2 conversion=0.19

0

0.004

0.008

0.012

0.016

0.02

0.024

0.028

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

r, m

Stea

dy-s

tate

con

cent

ratio

n, m

ol/l



B concentration

BH concentration

(b)

Fig. 9. Steady-state axial (a) and radial concentration profiles at z = L (b) in laminarflow microreactor with immobilized HCA II enzyme – effect of buffer concentration(only catalyzed CO2 hydration was considered). Feed conditions: vs‘ = 0.005 m/s, (a)Cin

B ¼ 0:015 mol=l, CinBH ¼ 0:01 mol=l; and (b) Cin

B ¼ 0:025 mol=l, CinBH ¼ 0:0 mol=l.


Figs. 9 and 10 show the effect of the inlet buffer (Na2HPO4) con-centration on the axial and radial steady-state concentration pro-files without uncatalyzed CO2 hydration in the laminar flowmicroreactor with solution-phase or immobilized HCA II, underthe same HCA II loading. Buffers in solution participate as pro-ton-transfer agents in the catalyzed CO2 hydration process. Lowbuffer concentration displaces the hydration into a regime wherethe inter-molecular proton transfer is rate determining and CO2

hydration rate is small. On the contrary, sufficiently high bufferconcentrations ensures that inter-molecular proton transfer isnot rate limiting and CO2 hydration rate is large. This behavior ex-plains the raise of CO2 conversion with the increase of inlet bufferconcentration (Figs. 9 and 10a). The enhancement is less importantwith immobilized HCA II enzyme because of the lower mass trans-fer fluxes of buffer transported between the liquid and the immo-bilized HCA II enzyme due to the diffusional limitation (Fig. 9b).Fig. 10b shows, once more, that the solution-phase HCA II enzymesystem is a non-diffusion limited system and ‘‘concentration’’ plugflow is achieved in laminar flow.

Fig. 11 shows the influence of the type of buffer (characterizedby the equilibrium constant Ka2) on the radial steady-state concen-tration profiles in the laminar flow microreactor with immobilizedHCA II enzyme. Both catalyzed and uncatalyzed CO2 hydrationprocesses were considered. The buffers used in simulations are:Na2HPO4 and 1,2-dimethylimidazole. CO2 conversion increases

with the decrease of equilibrium constant Ka2 due to the higherCO2 hydration driving force. The raise is less important with immo-bilized HCA II enzyme due to diffusional limitation (Fig. 11).

In the laminar flow microreactor with immobilized HCA II en-zyme – a diffusion limited system as mention above – the cata-lyzed CO2 hydration process is largely dictated by the diffusivefluxes between the liquid and the immobilized HCA II enzyme.Therefore, the system is not very sensitive to the increase of cata-lyzed CO2 hydration kinetic parameters. A 10-fold increase in thereactor HCA II loading and hydration turnover does not have a sig-nificant effect on the CO2 hydration process. So, because of diffu-sion limitations, the laminar flow microreactor with immobilizedHCA II enzyme on the internal surface is not suitable for kineticstudies, unless a method to enhance fluid mixing is employed.On the contrary, in laminar flow microreactor with solution-phaseHCA II enzyme, non-diffusion limited system, the catalyzed CO2

hydration process is largely dictated by the kinetics. A 10-fold in-crease in molecular diffusion coefficients values does not have asignificant effect on the CO2 hydration process.

4. Conclusion

The behavior of CO2 absorption enhanced by the enzyme car-bonic anhydrase in a laminar flow microreactor was studied with

0

0.003

0.006

0.009

0.012

0.015

0.018

0 0.02 0.04 0.06 0.08 0.1

z, m

Rad

ial a

vera

ge c

once

ntra

tion,

mol

/l


Inlet buffer concentration=0.025 mol/l CO2 concentration

HCO3- concentration

CO2 conversion=0.703CO2 conversion=0.912

(a)

0

0.005

0.01

0.015

0.02

0.025

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

r, m

Stea

dy-s

tate

con

cent

ratio

n, m

ol/l



(b)

B concentration

BH concentration

Fig. 10. Steady-state axial (a) and radial concentration profiles at z = L (b) inlaminar flow microreactor with solution-phase HCA II enzyme – effect of bufferconcentration (only catalyzed CO2 hydration was considered). Feed conditions:vs‘ = 0.005 m/s, (a) Cin

B ¼ 0:015 mol=l, CinBH ¼ 0:01 mol=l; and (b) Cin

B ¼ 0:025 mol=l,Cin

BH ¼ 0:0 mol=l.

0

0.005

0.01

0.015

0.02

0.025

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

r, m

Stea

dy-s

tate

con

cent

ratio

n, m

ol/l

buffer - Na2HPO4

buffer - 1,2-Dimethylimidazole

(a)

CO2 concentration

HCO3- concentration



0

0.005

0.01

0.015

0.02

0.025

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

r, m

Stea

dy-s

tate

con

cent

ratio

n, m

ol/l

buffer - Na2HPO4

buffer - 1,2-Dimethylimidazole

B concentration

BH concentration

(b)

Fig. 11. Steady-state radial concentration profiles at z = L in laminar flow microre-actor with immobilized HCA II enzyme – effect of the type of the buffer(catalyzed + uncatalyzed hydration). Feed conditions: vs‘ = 0.005 m/s,Cin

B ¼ 0:015 mol=l, CinBH ¼ 0:01 mol=l.


the purpose to understand the mechanism of HCA II enzyme reac-tions in a microchannel for further development of this process.The effects of operating conditions as well as the contribution ofcarbonic anhydrase on the performances of CO2 hydration are pre-sented. Numerical simulations indicate that in laminar flow mic-roreactor with the HCA II immobilized on the inner surface of thetube the coupling of transport phenomena and chemical reactionnecessitates the use of a two-dimensional analysis for data inter-pretation as a one-dimensional plug flow description will lead tosignificant error. The laminar flow microreactor with immobilizedHCA II enzyme is a diffusion limited system and hydrodynamic anddiffusional constraints do not permit a reasonable utilization of theimmobilized HCA II enzyme even if HCA II has a very high hydra-tion turnover (a better mixing is necessary to disrupt adjacent lam-inar fluid streams). The uncatalyzed CO2 hydration is the dominantprocess and this behavior will generate difficulties in interpretingthe experimental data. Because of diffusion limitations, the laminarflow microreactor with immobilized HCA II enzyme on the internalsurface is not suitable for kinetic studies, unless a method to en-hance fluid mixing is employed. In the microreactor with solu-tion-phase HCA II enzyme – a non-diffusion limited system,‘‘concentration plug flow’’ is achieved under laminar flow condi-tions, the enzymatic contribution to the overall reaction rate islarge and therefore the contribution of uncatalyzed CO2 hydrationprocess is not considerable.

Any future modeling studies of mixing in capillaries equippedwith internals to enhance mass transfer must benchmark or com-pare the enzymatic performance results with the present emptycapillary case. A branch which can take advantage of present find-ing is the design of reliable ‘‘kinetic study’’ devices more appropri-ate for immobilized enzymes. Our present contribution is on theright direction to help elucidating diffusion–reaction couplingsfor high-turnover enzymes.

References

[1] S.H. Koenig, R.D. Brown, H2CO3 as substrate for carbonic anhydrase in thedehydration of HCO�3 , Proc. Nat. Acad. Sci. 69 (1972) 2422–2425.

[2] D.N. Silverman, S. Lindskog, The catalytic mechanism of carbonic anhydrase:implications of a rate-limiting protolysis of water, Acc. Chem. Res. 21 (1988)30–36.

[3] S. Lindskog, Structure and mechanism of carbonic anhydrase, Pharmacol. Ther.74 (1997) 1–20.

[4] D.N. Silverman, R. McKenna, Solvent-mediated proton transfer in catalysis bycarbonic anhydrase, Acc. Chem. Res. 40 (2007) 669–675.

[5] V.M. Krishnamurthy, G.K. Kaufman, A.R. Urbach, I. Gitlin, K.L. Gudiksen, D.B.Weibel, G.M. Whitesides, Carbonic anhydrase as a model for biophysical andphysical–organic studies of proteins and protein–ligand binding, Chem. Rev.108 (2008) 946–1051.

[6] Y. Pocker, S. Sarkanen, Carbonic anhydrase: structure, catalytic versatility, andinhibition, Adv. Enzymol. 47 (1978) 149–274.

[7] S. Lindskog, Carbonic anhydrase, Adv. Inorg. Biochem. 4 (1982) 115–170.


[8] I. Bertini, C. Luchinat, A. Scozzafav, Carbonic anhydrase: an insight into the zincbinding site and into the active cavity through metal substitution, Struct. Bond.48 (1982) 45–92.

[9] D.N. Silverman, S.H. Vincent, Proton transfer in the catalytic mechanism ofcarbonic anhydrase, CRC Crit. Rev. Biochem. 14 (1983) 207–255.

[10] O. Lacroix, F. Larachi, Scrubber designs for enzyme-mediated capture of CO2,Recent Pat. Chem. Eng. 1 (2008) 93–105.

[11] I. Iliuta, F. Larachi, New scrubber concept for catalytic CO2 hydration byimmobilized carbonic anhydrase II & in situ inhibitor removal in three-phasemonolith slurry reactor, Sep. Purif. Technol. 86 (2012) 199–214.

[12] M.G. Snider, B.S. Temple, R. Wolfenden, The path to the transition state inenzyme reactions: a survey of catalytic efficiencies, J. Phys. Org. Chem. 17(2004) 586–591.

[13] T. Kobayashi, K. Laidler, Theory of the kinetics of reactions catalyzed byenzymes attached to the interior surfaces of tubes, Biotechnol. Bioeng. 16(1974) 99–118.

[14] K.J. Laidler, P.S. Bunting, The kinetics of immobilized enzyme systems,Methods Enzymol. 64 (1980) 227–248.

[15] F. Larachi, Kinetic model for the reversible hydration of carbon dioxidecatalyzed by human carbonic anhydrase II, Ind. Eng. Chem. Res. 49 (2010)9095–9104.

[16] C. Ho, J.M. Sturtevant, The kinetics of the hydration of carbon dioxide at 25�, J.Biol. Chem. 238 (1963) 3499–3501.

[17] S. Bhattacharya, M. Schiavone, S. Chakrabarti, S.K. Bhattacharya, CO2 hydration byimmobilized carbonic anhydrase, Biotechnol. Appl. Biochem. 38 (2003) 111–117.

[18] J.C. Lee, A.A. Yetter, F.L. Dryer, A.G. Tomboulides, S.A. Orszag, Simulation andanalysis of laminar flow reactors, Combust. Sci. Technol. IS9 (2000) 199–212.

[19] M.J.W. Frank, J.A.M. Kuipers, W.P.M. Swaaij, Diffusion coefficients andviscosities of CO2 + H2O, CO2 + CH3OH, NH3 + H2O, and NH3 + CH3OH liquidmixtures, J. Chem. Eng. Data 41 (1996) 297–302.

[20] R.C. Reid, J.M. Prausnitz, B.E. Poling, The Properties of Gases and Liquids, fourthed., McGraw Hill, New York, 1987.

catalytic co2 hydration by immobilized and free human carbonic anhydrase ii in a laminar flow...

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