# Theoretical modeling of enzyme-enhanced CO mass transfer in carbonate solutions using hollow fiber membrane contactors: A numerical approach

Mohamed Nadir Khelifi, Ouacil Saouli, Zineb Boutamine, Lokmane Abdelouahed

Abdelouahed

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Mohamed Nadir Khelifi, Ouacil Saouli, Zineb Boutamine, Lokmane Abdelouahed. Theoretical modeling of enzyme-enhanced CO mass transfer in carbonate solutions using hollow fiber membrane contactors: A numerical approach. Journal of engineering research = Mağallaṭ al-abḥāṭ al-handasiyyaṭ, 2025, 10.1016/j.jer.2025.08.020. hal-05328670

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# Theoretical modeling of enzyme-enhanced CO₂ mass transfer in carbonate solutions using hollow fiber membrane contactors: A numerical approach

Mohamed nadir Khelifi<sup>a,†</sup>, Ouacil Saouli<sup>a,†</sup>, Zineb Boutamine<sup>a</sup>, Lokmane Abdelouahed<sup>b,*</sup>

## ARTICLE INFO

**Keywords:**

Absorption

Carbonic anhydrase

CO₂

Carbonate solution

SspCA enzyme

Hollow fiber membrane contactors

## ABSTRACT

Carbon dioxide (CO₂) is one of the major contributors to climate change, whose atmospheric concentration has recently increased significantly due to immense burning of fossil fuels. This study deals with simulating the 2D of enzyme SspCA-CO₂ (Sulfurihydrogenibium sp. carbonic anhydrase) capture process by using carbonate solution (Na₂CO₃-NaHCO₃) as a chemical solvent in a counter-current membrane contactor with and without SspCA. A parametric analysis is also conducted to evaluate the effects of various parameters on the CO₂ capture process, including enzyme concentration, gas flow rate of CO₂, liquid flow rate and porosity of membrane. The results indicate that the CO₂ capture efficiency using 0.5 M of carbonate solution (0.5 Na₂CO₃-NaHCO₃) increases by 16 % with 5 mg/L of SspCA. Increasing the gas flow rate of CO₂ from 10 mL/min to 40 mL/min reduces CO₂ removal by 25 %. Increasing the liquid flow rate of 0.5 M (Na₂CO₃-NaHCO₃) from 10 mL/min to 40 mL/min with 5 mg/L SspCA improves CO₂ removal by 16 %. Additionally, increasing porosity leads to increased CO₂ removal and flux. This unique technique work seeks to examine the effects of HFMC and enzyme SspCA on CO₂ removal. This novel approach work aims to investigate the effect of HFMC and enzyme for seeing the effect of those in term of CO₂ removal (Separation) and CO₂ flux.

## Introduction

Carbon dioxide (CO₂) is widely recognized as one of the major drivers of global climate change. Its atmospheric concentration has increased sharply in recent years, mainly due to the widespread combustion of fossil fuels. Growing CO₂ emissions have raised increasing interest in efficient CO₂ capture technologies [1]. In recent decades, a multitude of techniques for CO₂ capture has been developed, with chemical absorption in packed or tray columns remaining the most extensively utilized conventional method [2]. Traditional absorber towers have a number of disadvantages associated with them, including channeling, foaming, flooding, aeration, and high operational and capital costs [3]. Comparative studies on the performance of CO₂ capture by conventional amine absorption techniques (packed or bubble columns) versus membrane gas absorption have identified several advantages of membrane systems, including a high surface-to-volume ratio, flexible operation, modularity, compact design, and linear scalability [4,5]. Membrane contactor absorption has emerged as an innovative

alternative, offering numerous advantages such as prevention of interphase dispersion, a high specific surface area, and a compact design [6]. In porous membrane contactors, CO₂ absorption occurs as the gas diffuses from the shell side through the membrane pores to contact the liquid phase inside the fibers. While industrial application of membranes for gas separation began in the 1980s, research on this topic can be traced back more than 150 years [7,8]. Extensive works were conducted to develop membrane contactor systems and improve mass transfer rates of membranes [9,10]. Membrane gas absorption has recently attracted much attention as one of the promising technologies for CO₂ capture because of its superior mass transfer efficiency [11].

Membrane contactors address these issues by facilitating CO₂ absorption within the membrane, where the gas phase interacts with the liquid phase on opposite sides of the membrane. The membrane serves as a barrier, preventing interphase mixing while enhancing mass transfer through increased membrane length [12]. Moreover, the membrane processes are considered environmentally friendly because they reduce the solvent loss to the atmosphere and can independently

<footnote><sup>a</sup> Laboratoire de Génie des Procédés pour le Développement Durable et les Produits de Santé (LGPPDPS), Département Génie des Procédés, Ecole Nationale Polytechnique de Constantine, Algeria</footnote>

<footnote><sup>b</sup> INSA Rouen Normandie, Univ Rouen Normandie, Normandie Univ, LSPC UR 4704, Rouen F-76000, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: nadir.khelifi@doctorant1.enp-constantine.dz (M. Khelifi), saouli_ouacil2000@yahoo.fr (O. Saouli), zaineb.boutamine@enp-constantine.dz (Z. Boutamine), lokmane.abdelouahed@insa-rouen.fr (L. Abdelouahed).</footnote>
control the liquid and gas flow rate [13]. But there are still many challenges, such as the wetting of membranes. The selection of an appropriate absorbent for membrane gas absorption depends on its surface tension and compatibility with the membrane material. Low surface tension absorbents can wet the membrane pores, leading to reduced performance. Alkanolamine solvents, such as MEA, are commonly used for CO₂ capture due to their rapid reaction rate with CO₂. However, they are associated with high regeneration energy demands and evaporative losses [14,15]. To overcome these drawbacks, other absorbents have been tried, one of which is aqueous carbonate solution. carbonate solution is inexpensive, noncorrosive, and its regeneration for CO₂ capture consumes less energy compared to MEA [16]. However, it also presents a smaller reaction rate with CO₂, especially at low temperature and low partial pressure [17]. A feasible way to improve the performance of carbonate solution is to add reaction promoters in it [18]. Carbonic anhydrase is an extremely effective catalyst discovered in 1933 from red blood cells, which catalyzes the reversible conversion of CO₂ to HCO₃⁻ [19]. These enzymes belong to a wide group of zinc metallo-proteins. They are part of three genetically distinct isoform families and are found in almost all living organisms, such as bacteria, plants, algae, and animals [20,21]. Of all the isoforms, human CA II, which is predominantly present in red blood cells, is the most well-characterized enzyme with the highest catalytic turnover rate [22].

In this work, we investigated CO₂ capture using a carbonate solvent, with a focus on evaluating the effect of a thermostable enzyme, SspCA (Sulfurihydrogenibium sp. carbonic anhydrase), to enhance the process of CO₂ capture. SspCA was selected for its unique properties, including high-temperature stability and exceptional catalytic efficiency [23,24]. This innovative approach aims to integrate thermostable enzyme SspCA into HFMC systems. To the best of our knowledge, very few studies have explored the use of SspCA in membrane contactor. Our work will contribute to the literature by assessing the efficiency of SspCA for CO₂ capture.

## Model development and governing equation

Fig. 1 illustrates a schematic of a single hollow fiber membrane, showing the directions of liquid and gas fluxes. It includes a cross-sectional view depicting the fiber's radius used in this study.

## Characteristics of PVDF hollow fiber membrane modules and considered specifications of the fluids used

The present work constitutes a numerical investigation of CO₂ capture, the aim of which is to observe and study the effect of enzymes utilizing membrane contactors. In this case, the specific parameters employed in the present work are enumerated in Table 1.

The following summarizes the key assumptions made in the development of the numerical model to simplify mass transfer calculations:

* Steady-state and constant properties of a hydrodynamic flow are considered: we assume that the gas and liquid velocity profiles are fully developed within the hollow fibers.

* Isothermal contactor.

* Only CO₂ is transferred through the membrane and into the tube side.

* The pseudo first order Michaelis-Menten kinetics is taken into account as the enzymatic reaction rate.

* The enzyme's deactivation constant is considered negligible for the purposes of this study.

A parabolic velocity profile is assumed for mass transfer modelling, and ideal gas behavior, along with the application of physical solubility according to Henry's law at the gas-liquid interface, minimizes the need for complex state equations. The uniform distribution of membrane pores ensures a consistent CO₂ flux throughout the process.

<caption>**Table 1**</caption>

Characteristics of PVDF hollow fiber membrane module and fluid specification used in this work [25].

<table><thead><tr><td>Parameters</td><td>Value</td><td>Unit</td></tr></thead><tbody><tr><td>Materiel</td><td>PVFD</td><td>-</td></tr><tr><td>Fiber length</td><td>0.210</td><td>m</td></tr><tr><td>Number of fibers</td><td>11</td><td>-</td></tr><tr><td>Membrane inner diameter (R₁)</td><td>2.1 × 10⁻⁴</td><td>m</td></tr><tr><td>Membrane outer diameter (R₂)</td><td>5.5 × 10⁻⁴</td><td>m</td></tr><tr><td>Module inner diameter (R₃)</td><td>0.004</td><td>m</td></tr><tr><td>Membrane thickness (δ)</td><td>3.4 × 10⁻⁴</td><td>m</td></tr><tr><td>Porosity (ε)</td><td>0.4585</td><td>-</td></tr><tr><td>Tortuosity (η)</td><td>5.14</td><td>-</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>Fig. 1. Depict a schematic diagram of HFMC related to a CO₂ absorption process.</figcaption></figure>
<table><caption>**Table 2**
Mass transfer equations boundary conditions.</caption><thead><tr><th>Position</th><th>Shell</th><th>Membrane</th><th>Tube</th></tr></thead><tbody><tr><td>z = 0</td><td>C<sub>CO₂</sub> = C₀</td><td>Insulated</td><td>Convective flux</td></tr><tr><td>z = L</td><td>Cₖₐₐ₃ = 0</td><td>Insulated</td><td>Cₖₐₐ₃ = 0</td></tr><tr><td>R₀</td><td>Convective flux</td><td>—</td><td>Axial symmetry</td></tr><tr><td>R₁</td><td>—</td><td>Cₐₐ₂ = Cₐₐ₂₇ₐ₃ / m' ∂Cₐₐ₂₇ₐ₃ / ∂r = 0 (Non wetted)</td><td>Cₐₐ₂ = Cₐₐ₂₇ₐ₃ × m'</td></tr><tr><td>R₂</td><td>Cₐₐ₂ = Cₐₐ₂₇ₐ₃</td><td>Cₐₐ₂ = Cₐₐ₂₇ₐ₃</td><td>—</td></tr><tr><td>R₃</td><td>Insulated</td><td>—</td><td>—</td></tr></tbody></table>

### Shell side's governing equation

The steady-state mass transfer equation in the shell side in cylindrical coordinates is then derived as [26]

$$D_{CO_2,S} \left[ \frac{\partial^2 C_{CO_2,S}}{\partial r^2} + \frac{1}{r} \frac{\partial C_{CO_2,S}}{\partial r} + \frac{\partial^2 C_{CO_2,S}}{\partial z^2} \right] = V_{z,S} \frac{\partial C_{CO_2,S}}{\partial z} \quad (1)$$

In the shell side, only the continuity equation of CO₂ needs to be solved, and no chemical reaction occurs in the shell side. Where $D_{CO₂,S}$ is diffusion coefficient of CO₂ in the shell side. $V_{z,S}$ denotes the velocity in the axial coordinate the Navier-Stokes equation is used to characterize the shell side velocity. For laminar flow, the Navier-Stokes equation applies [27]

$$\rho(V_{z,S} \cdot \nabla) \cdot V_{z,S} = - \nabla \cdot \left[ -p \cdot I + \mu \cdot (\nabla V_{z,S} + (\nabla V_{z,S})^T) \right] \quad (2)$$

Where $p$ is the pressure in the shell compartment of contactor, the symbol $V_{z,S}$ denotes the velocity in the axial coordinate, $I$ is the identity tensor, The density $\rho$ and the viscosity $\mu$ of the fluid is assumed to be constant in the whole shell.

$$\nabla \cdot V_{z,S} = 0 \quad (3)$$

The $R_3$ in the shell side part of the membrane contactor can be estimated by the development of the fluid around the fiber [27]. The area of the free void can be predicted by Happel's free surface model [28]

$$R_3 = \left( \frac{1}{1 - \emptyset} \right)^{1/2} R_2 \quad (4)$$

Where $R_3$ is the shell radius of gas around the fiber, $R_2$ is inner membrane radius (membrane thickness) $\emptyset$ is the volume fraction of the vacuum in the module. It can be calculated as follows:

$$1 - \emptyset = \frac{nR_2^2}{R_2^2} \quad (5)$$

Where $n$ is the number of fibers and $R$ is the module inner radius.

### Membrane side's governing equation

The steady state continuity equation for the transport of CO₂ inside membrane with cylindric coordinates, taken as that of diffusion (no wetted pores), can be written as [26,29]

$$D_{CO_2,M} \left[ \frac{\partial^2 C_{CO_2,M}}{\partial r^2} + \frac{1}{r} \frac{\partial C_{CO_2,M}}{\partial r} + \frac{\partial^2 C_{CO_2,M}}{\partial z^2} \right] = 0 \quad (6)$$

In this instance, it is hypothesised that the fibres are filled with the gas phase, a theory that is supported by the use of a hydrophobic polymer as the membrane, which is known to play a role in the operational control of the fibres.

The diffusivity of CO₂ in the membrane pores and tortuosity factor $\tau$ are calculated as [30]

$$D_{CO_2,M} = \varepsilon \frac{D_{CO_2,S}}{\tau} \quad (7)$$

$$\tau = \frac{(2 - \varepsilon)^2}{\varepsilon} \quad (8)$$

### Tube side's governing equation

On the tube side, the transmission continuity equation is as follows [26]:

#### For CO₂ (in the tube side)

$$D_{CO_2,T} \left[ \frac{\partial^2 C_{CO_2,T}}{\partial r^2} + \frac{1}{r} \frac{\partial C_{CO_2,T}}{\partial r} + \frac{\partial^2 C_{CO_2,T}}{\partial z^2} \right] = V_{z,T} \frac{\partial C_{CO_2,T}}{\partial z} - R_{CO_2-OH} + R_{CA} \quad (9)$$

$$R_{CA} = k_e [E] [CO_{2,T}] \quad (10)$$

Where $R_{CA}$ is the reaction rate of CA with CO₂, $k_e$ is the first order Michaelis-Menten kinetic, Table 4 presents several studies that experimentally determine the $k_e$ of the enzyme, which is specific to each enzyme. As the flow is considered as laminar, the liquid non-compressible and the regime in a steady-state the distribution of the velocity in the tube is determined using Eq. (12) and Eq (13).

$$V_{z,T} = 2\bar{V}_T \left[ 1 - \left( \frac{r}{R_1} \right)^2 \right] \quad (12)$$

$$\bar{V}_T = \frac{Q_l}{n\pi(R_1)^2} \quad (13)$$

Where $\bar{V}_T$ is the average velocity. $Q_l$ is the liquid flow rate, $r$ is the radius of module, $R_1$ is the outer membrane radius (tube side), $V_{z,T}$ is the velocity profile.

### Kinetics of CO₂ in carbonate solution and SspCA enzyme

The global reactions between CO₂ and alkaline solution [36] are presented as follows:

$$CO_3^{2-} + CO_2 + H_2O \leftrightarrow 2HCO_3 \quad (R1)$$

The above reaction is evidently made up of a sequence of elementary steps. The carbonate

ion first reacts with water to generate hydroxyl ions, which then react with CO₂ as follows [37]

$$H_2O + CO_3^{2-} \leftrightarrow OH^- + HCO_3 \quad (R2)$$

<table><caption>**Table 3**
Condition parameters and physical constant used [31,32].</caption><thead><tr><th>Parameters</th><th>Value</th><th>Unit</th></tr></thead><tbody><tr><td>D<sub>CO₂,S</sub></td><td>1.39 × 10<sup>-5</sup></td><td>m²/s</td></tr><tr><td>D<sub>CO₂,M</sub></td><td>D<sub>CO₂,S</sub> * (ε/η)</td><td>m²/s</td></tr><tr><td>D<sub>CO₂,T</sub></td><td>1.8 × 10<sup>-9</sup></td><td>m²/s</td></tr><tr><td>Physical solubility constant (m') (calculated)</td><td>0.66</td><td>-</td></tr></tbody></table>
<table><caption>**Table 4**
Carbonic Anhydrase kinetic constants.</caption><thead><tr><th>CA</th><th>family</th><th>k<sub>Cat</sub> (s<sup>-1</sup>)</th><th>k<sub>m</sub>(mM)</th><th>k<sub>Cat</sub>/k<sub>m</sub>(M<sup>-1</sup>×s<sup>-1</sup>)</th><th>References</th></tr></thead><tbody><tr><td>SspCA<br>(used<br>in this<br>work)</td><td>α</td><td>-</td><td>-</td><td>9.16 × 10<sup>8</sup></td><td>[33]</td></tr><tr><td>TaCA</td><td>α</td><td>1.6 × 10<sup>6</sup></td><td>9.9</td><td>1.6 × 10<sup>8</sup></td><td>[34]</td></tr><tr><td>CcaA274</td><td>β</td><td>3.34 × 10<sup>3</sup></td><td>2.8</td><td>1.19 × 10<sup>6</sup></td><td>[35]</td></tr></tbody></table>

$$CO_2 + OH^- \leftrightarrow HCO_3^- \qquad (R3)$$

$$H_2O \leftrightarrow OH^- + H^+ \qquad (R4)$$

In literature, for the catalysed reaction of CO₂ hydration, a mechanism for CA has been proposed by Lindskog [38]. Above pH 7 the dominant reaction mechanism of carbonic anhydrase with carbon dioxide can be described with as [39]:

$$CO_2 + EZnOH^- \leftrightarrow EZnOH-CO_2 \leftrightarrow EZnHCO_3^- \qquad (R5)$$

$$EZnHCO_3^- + H_2O \leftrightarrow EZnH_2O + HCO_3^- \qquad (R6)$$

Since Reaction 2 is an instantaneous reaction, Reaction 3 is the limiting reaction. So, the rate equation of CO₂ with hydroxyl ion (Reaction 3) expresses as Eq. (14).

$$r_{(CO_2-OH^-)} = (k_w + k_{OH^-} - [OH^-])[CO_2] \qquad (14)$$

Where $r_{(CO_2)}$ is the rate of reaction, $k_{OH^-}$ is the second order rate constant, and $[CO_2]$ and $[OH^-]$ are the concentrations of free CO₂ and base in the liquid phase.

The second order rate constant of reaction of CO₂ with OH⁻ and constant of water can be found from Eq. 15 and Eq 16 [40] [41].

$$\log k_{OH^-} = 13.635 - \frac{2895}{T} \qquad (15)$$

$$\log k_w = 329.85 - 110.541 \log(T) - \frac{17265.4}{T} \qquad (16)$$

Models to assess the main physicochemical constants are reported as the ratio of; (i) The diffusivity of CO₂ in water $D_{CO_20}$ at 25°C was $1.88 \times 10^{-9}$ (m²/s) [42] to (ii) The diffusivity of carbon dioxide in the carbonate/bicarbonate solution (buffer):

$$\frac{D_{CO_2,T}}{D_{CO_{2,0}}} = 1 - (C1[CO_3^2] + C2[HCO_3] + C3[OH^-]) \qquad (17)$$

Where C1, C2, and C3 are constant and equal to $2.61 \times 10^{-4}$ (m³/mol), $1.40 \times 10^{-4}$ (m³/mol), and $1.29 \times 10^{-4}$ (m³/mol), respectively. The distribution (physical solubility) of CO₂ in pure water ($m_0$) and in electrolyte solutions ($m'$) at atmospheric pressure were calculated according to Eqs. (16), (17).

The distribution coefficient of CO₂ in pure water was taken from V. Y. Dindore [31].

$$m_{0,CO_2} = 3.59 \times 10^{-7} RTe \left(\frac{2044}{T}\right) \qquad (18)$$

The distribution coefficient for CO₂ in aqueous carbonate solution were determined using Eq. (17)[43].

$h_G$ is the constant of CO₂ gas solubility. In this work, $h_{G,0}$ is reported in the literature (Table 5) as $hCO_2$, under the same conditions, specifically at 298 K and Ci is the molar concentration of each spice of carbonate solution.

$$\log(m_0/m') = \sum (h_{i+} + h_G)C_i \qquad (19)$$

<table><caption>**Table 5**
Constants $h_{i+}$, $h_G$ [43].</caption><thead><tr><th>Constant</th><th>Value</th></tr></thead><tbody><tr><td>hNa<sup>+</sup></td><td>0.1143</td></tr><tr><td>hCO<sub>2</sub></td><td>-0.0172</td></tr><tr><td>hHCO<sub>3</sub><sup>-</sup></td><td>0.0967</td></tr><tr><td>hCO<sub>3</sub><sup>-2</sup></td><td>0.1423</td></tr></tbody></table>

$$h_G = h_{G,0} - 0.338 \times 10^{-3}(T - 298.15) \qquad (20)$$

## Numerical solutions

A set of governing partial differential equations of CO₂ mass transfer from gas phase (Shell side) passing through hollow fibers contactor using carbonate solution with SspCA in liquid phase (Tube side) with appropriate boundary conditions (as listed in Table 2) were solved based on finite elements method (FEM) by COMSOL Multiphysics software (Version 5.0), which can divide different domains in the hollow fiber membrane contactor into small dimension units to obtain the simulated results of important parameters such as CO₂ concentration profiles at each point of the domains. Overview of CO₂ gas capture using HFMC mentioned in Table 6.

The Specifications of membrane and the related physical and chemical parameters are listed in Table 1 and Table 3, respectively. An internal numerical solver of COMSOL, PARDISO, is employed to achieve self-adaptive meshing and error control were employed to minimize the calculations errors.

### Mesh refinement and domain setup

Fig. 2 shows the design and domain configuration and the segment of the three parts of domain fiber contactor Shell (in the left), Membrane (in the middle) and Tube (in the right). The mesh used in this work contains approximately 10 million domains, with a minimum element size on the order of $1.8 \times 10^{-6}$ (m) and a maximum element size on the order of $0.5 \times 10^{-4}$ (m). The size of all domains, along with the distribution of free triangular and boundary layer elements, has been carefully considered to ensure accurate representation of the geometry.

The CO₂ removal and absorption flux can be calculated using the following equation:

$$CO_2\text{Removal} = 100 \times \left(1 - \frac{C_{\text{outlet}}}{C_{\text{inlet}}}\right) \qquad (16)$$

$$J_{CO_2} \left( \frac{mol}{m^2 \times s} \right) = \left( \frac{Q \times C_{\text{inlet}} - Q \times C_{\text{outlet}}}{S} \right) \qquad (17)$$

## Results and discussion

This study presents the results of a 2D simulation using COMSOL V5.0 to analyse CO₂ capture with a carbonate solvent enhanced by carbonic anhydrase in a hollow fibre membrane contactor operating in counter-current mode. The objective is to evaluate the impact of operational parameters as liquid and gas flow rates, enzyme concentration, and membrane porosity — on mass transfer performance. The model examines CO₂ concentration profiles in both axial and radial directions, as well as variations in non-wetted membrane pores, providing valuable insights for process intensification.

### SspCA enzyme concentration effect on absorbed flux and CO₂ removal

Fig. 3 presents the effect of concentration of SspCA on CO₂ absorption flux and removal efficiency. An increase in CO₂ absorption flux and CO₂ removal is observed from $0.895 \times 10^{-4}$ to $2.11 \times 10^{-4}$ mol/ (m².s).
<table><caption>**Table 6**

Overview of recent advancements in CO₂ gas capture using hollow fiber membrane.</caption><thead><tr><th>Membrane</th><th>Porosity (%)</th><th>Absorbent Solution</th><th>Gas Mixture</th><th>Absorption Flux (mol/m²·s)</th><th>Ref.</th></tr></thead><tbody><tr><td>Polyvinylidene fluoride (PVDF)</td><td>46</td><td>Nanofluid of MDEA + CNT</td><td>CO₂/N₂ (20/80)</td><td>1.14 × 10<sup>-3</sup></td><td>[25]</td></tr><tr><td>PP (3 M Liqui-Cel™)</td><td>–</td><td>Potassium glycinate amino acid salt</td><td>CO₂/N₂ (10/90)</td><td>2.27 × 10<sup>-4</sup></td><td>[44]</td></tr><tr><td>Mixed matrix PVDF + silica nanoparticles</td><td>39</td><td>Soybean-based solvent</td><td>CO₂/N₂ (12/88)</td><td>1.8 × 10<sup>-4</sup></td><td>[45]</td></tr><tr><td>Superhydrophobic PEEK</td><td>–</td><td>Activated K₂CO₃</td><td>CO₂/N₂ (13/87)</td><td>2.5 × 10<sup>-3</sup></td><td>[46]</td></tr><tr><td>Mixed matrix PVDF + hydrophobic SiO₂</td><td>79</td><td>Water</td><td>Pure CO₂</td><td>3.24 × 10<sup>-3</sup></td><td>[47]</td></tr><tr><td><strong>Polyvinylidene fluoride (PVDF)</strong></td><td><strong>45.85</strong></td><td><strong>Carbonate solution + SspCA</strong></td><td><strong>CO₂/N₂<br>(20/80)</strong></td><td><strong>1.38 × 10<sup>-4</sup></strong></td><td><strong>This work</strong></td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Segments of the mesh used. The three domains from left to right are the tube side, membrane, and shell side, respectively.</figcaption></figure>

and 28.97–68.41 % respectively, when SspCA concentration increases from 0 mg/L to 30 mg/L. Assume that the pseudo first order is still present at more than 15 mg/L.

According to Russo, M. E et al. [33], the kinetic constant considering the interval used for SspCA experience ranges from 2 mg/L to 15 mg/L. Fig. 3 shows that with 5 mg/L of SspCA the efficiency of CO₂ removal intensifies by average 16 % [48]. The use of SspCA enzyme has a notable impact by accelerating the CO₂ hydration reaction, which significantly increasing the effectiveness of the capture process in the interval between 0 and 30 mg/L. Beyond this concentration (30 mg/L), the efficiency is reaching a stable value, showing minimal additional improvement. SspCA enzyme improves mass transfer by maintaining a high concentration gradient, which implies a reduction in transfer resistance in the carbonate solution. This allows for faster and more efficient CO₂ capture, explaining the improved performance observed in the Fig. 3.

### Gas flow rate effect on CO₂ removal

Fig. 4 illustrates the relationship between gas flow rate of CO₂ and removal efficiency for 0.5 M Carbonate solution (Na₂CO₃-NaHCO₃), pure and with the SspCA (5 mg/L). Increasing the gas flow rate of CO₂ from 10 mL/min to 40 mL/min reduces CO₂ removal from 28.97 % to 13.39 %, whereas with 5 mg/L of SspCA increasing the gas flow rate of CO₂ from 10 mL/min to 40 mL/min reduces CO₂ removal from 44.84 % to 18.88 %. An increase in gas flow rate of CO₂ reduces the contact time between CO₂ and the absorbing liquid, which decreases the capture efficiency (which limits CO₂ transfer).

The absorption of CO₂ is often limited by the mass transfer between the gas phase and the absorbing liquid. We think that SspCA enzyme reduces this limitation by maintaining a high concentration gradient between the dissolved CO₂ and the reaction products (bicarbonates), which promotes the continuous absorption of CO₂. The improvement of the chemical reaction rate allows for the absorption of more CO₂ for the same amount of carbonate solution, which increases the overall
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** CO₂ removal and CO₂ flux as function of SspCA enzyme concentration, Q₁ = 10 mL/min, Qg = 10 mL/min, 0.5 M (Na₂CO₃/NaHCO₃), n = 11, L = 0.21 cm, ε = 0.4585.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** CO₂ removal as function of gas flow rate of CO₂, CCO₂ = 5.6 mol/m³, Q₁ = 20 mL/min, SspCA = 5 mg/L, n = 11, L= 0.21 cm, ε = 0.4585.</figcaption></figure>

efficiency of the process.

Liquid flow rate effect on CO₂ removal

Fig. 5 shows the impact of liquid flow rate on CO₂ flux and CO₂ removal efficiency with and without enzyme in 0.5 M Carbonate solution (Na₂CO₃·NaHCO₃). The results show that as the liquid flow rate increases from 10 to 40 mL/min CO₂ absorption flux increases from 0.895 × 10⁻⁴ to 1.83 × 10⁻⁴ mol/ (m²·s) and CO₂ removal increases from 28.97 % to 59.74 % without addition of SspCA enzyme. With 5 mg/L of SspCA enzyme it founds that CO₂ absorption flux increases from 1.38 × 10⁻⁴ to 1.97 × 10⁻⁴ mol/ (m²·s) and CO₂ removal increases from 44.84 % to 64.04 %. This enhancement due to SspCA which lowers the mass transfer resistance by speeding up the process that turns CO₂ into bicarbonate [49,50]. This explains the overall performance gain by enabling more effective CO₂ absorption in the solution. In this case, the enhancement is more noticeable at high flow rates, indicating that the enzyme enhances absorption even more at high liquid renewal rates. Here in Fig. 5, the growth is nearly linear, in contrast to the first instance

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** CO₂ removal and CO₂ flux absorbed as function of liquid flow rate, Qg = 10 mL/min, SspCA = 5 mg/L, 0.5 M (Na₂CO₃/NaHCO₃), n = 11, L= 0.21 cm, ε = 0.4585, T = 298 K.</figcaption></figure>

when a minor saturation appeared around 30–40 mL/min, indicating that the system can still be optimized before reaching a limit. All this improved the gas-liquid contact caused by the increased flow velocity facilitates the transmission of CO₂

Porosity of membrane effect on CO₂ removal and flux absorbed

Fig. 6. represent CO₂ removal and CO₂ flux absorbed as function of porosity. Fig. 6 shows as porosity increases from 0.2 to 0.8, the CO₂ removal increases from 42.94 % to 48.72 % the absorption flux increases from 1.32 to 1.5 mol/ (m²·s). This suggests that the increased porosity makes it easier for CO₂ to permeate through the membrane. The performance of membranes and porosity are directly correlated in term of mass transfer coefficient, increasing in porosity make the mass transfer coefficient of membrane increase. This implies that CO₂ is collected more effectively by membranes that are more porous. Better diffusion of CO₂ through the membrane is made possible by higher porosity, which lowers mass transfer resistance [51].

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** CO₂ removal and CO₂ flux absorbed as function of porosity, Qg = 10 mL/min, Q₁ = 10 mL/min, SspCA = 5 mg/L, 0.5(NaCO₃-NHCO₃), n = 11, L= 0.21 cm, T = 298 K.</figcaption></figure>
Conclusions

In a nutshell, robust and reliable mechanistic model and simulation methodology was implemented to study the effects of enzyme SspCA concentration, gas flow rate of CO₂, liquid flow rate and porosity, on CO₂ absorption flux absorbed and CO₂ removal in carbonate solution, using membrane process to study the performance of the hollow fibre membrane contactor is examined in terms of CO₂ absorption flux absorbed and CO₂ removal (separation). The 2D simulation using COMSOL demonstrated the effectiveness of a hollow fibre membrane contactor for CO₂ capture with carbonate solvents, highlighting the benefits of enzyme enhancement and acceleration. The gas flow rate of CO₂ has a significant effect on the CO₂ removal efficiency. When the gas flow rate of CO₂ increases from 10 mL/min to 40 mL/min, the removal efficiency decreases by 25 % and 15 % both with and without the enzyme SspCA, increasing in the liquid flow rate from 10 to 40 mL/min increases the CO₂ flux and CO₂ removal both with and without enzyme SspCA which enhances the removal by average 16 %. while porosity increase, the mass transfer coefficient increases which decrease the resistance in membrane's side that give higher CO₂ removal. Enzyme SspCA consistently increases CO₂ removal efficiency. These results underline the potential of enzyme-enhanced carbonate solvents in advancing sustainable CO₂ capture technologies, particularly in membrane systems.

Abbreviations

The following abbreviations are used in this manuscript:

<table><tr><td>C</td><td>Concentration (mol/m³)</td></tr><tr><td>CA</td><td>Carbonic Anhydrase</td></tr><tr><td>C₀</td><td>CO₂ concentration at inlet (mol/m³)</td></tr><tr><td>CO₂</td><td>Carbon dioxide</td></tr><tr><td>C<sub>CO₂</sub>, S</td><td>CO₂ concentration in the shell side (mol/m³)</td></tr><tr><td>C<sub>CO₂</sub>, M</td><td>CO₂ concentration in the membrane side (mol/m³)</td></tr><tr><td>C<sub>CO₂</sub>, T</td><td>CO₂ concentration in the tube side (mol/m³)</td></tr><tr><td>D<sub>CO₂</sub>, S</td><td>Diffusion constant of CO₂ in the shell side (m²/s)</td></tr><tr><td>D<sub>CO₂</sub>, M</td><td>Diffusion constant of CO₂ in the membrane side (m²/s)</td></tr><tr><td>D<sub>CO₂</sub>, T</td><td>Diffusion constant of CO₂ in tube side (m²/s)</td></tr><tr><td>HFMC</td><td>Hollow fiber membrane contactor</td></tr><tr><td>k<sub>OH⁻</sub></td><td>Specific reaction rate constant of amine m³/(kmol·s)</td></tr><tr><td>k<sub>Cat</sub></td><td>Turnover Number (1/s)</td></tr><tr><td>k<sub>m</sub></td><td>Michaelis Constant (M)</td></tr><tr><td>L</td><td>Length of the fiber (m)</td></tr><tr><td>m'</td><td>Physical solubility</td></tr><tr><td>n</td><td>Number of fibers</td></tr><tr><td>Q<sub>l</sub></td><td>Liquid flow rate (m³/s)</td></tr><tr><td>Q<sub>g</sub></td><td>Gas flow rate of CO₂ (m³/s)</td></tr><tr><td>R</td><td>Module radius (m)</td></tr><tr><td>R<sub>l</sub></td><td>Outer membrane radius (m)</td></tr><tr><td>R<sub>2</sub></td><td>Inner membrane radius (m)</td></tr><tr><td>R<sub>3</sub></td><td>Shell radius (m)</td></tr><tr><td>SspCA</td><td>Sulfurihydrogenibium sp. Carbonic anhydrase</td></tr><tr><td>V̄</td><td>Average velocity (m/s)</td></tr><tr><td>V<sub>z</sub></td><td>Velocity in the module (m/s)</td></tr><tr><td>V<sub>z</sub>-S</td><td>Velocity in the shell side (m/s)</td></tr><tr><td>V<sub>z</sub>-T</td><td>Velocity in the tube side (m/s)</td></tr><tr><td>Z</td><td>Axial distance (m)</td></tr><tr><td>Ø</td><td>Module volume fraction</td></tr><tr><td>δ</td><td>Thickness</td></tr><tr><td>ε</td><td>Porosity</td></tr><tr><td>μ</td><td>Viscosity (Pa·s)</td></tr><tr><td>ρ</td><td>Density (kg/m³)</td></tr><tr><td>τ</td><td>Tortuosity factor</td></tr></table>

CRediT authorship contribution statement

**Abdelouahed Lokmane:** Visualization, Validation, Resources, Methodology, Investigation.
**Ouacil Saouli:** Supervision, Methodology, Conceptualization.
**Boutamine Zineb:** Supervision, Resources, Methodology, Investigation.
**Mohamed nadir Khelifi:** Validation, Resources, Methodology, Investigation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Lokmane Abdelouahed reports was provided by INSA Group. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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