Numerical Investigation of Micro-Scale Mass Transfer in Stretched and Compressed Kelvin-Cell Packings for Shipboard Carbon Capture

Abstract

For shipboard CCUS facilities, the integration of chemical absorption columns is constrained by a limited vertical envelope, which motivates packings with axially stretched or compressed Kelvin cells to support compact layout and flow control. This study employs computational fluid dynamics to investigate microscale flow and mass transfer characteristics in Kelvin cells. A comparison among the regular Kelvin cell (RKC), the vertically elongated Kelvin cell (VEKC), and the vertically compressed Kelvin cell (VCKC) indicates that axial stretching and compression modify internal flow distributions and gas–liquid mass transfer during CO₂ absorption. The liquid distribution transitions from a film along the struts with localized accumulation at the nodes in RKC to a continuous columnar stream in VEKC, and then to a stable hollow cylindrical liquid film promoted by lateral redistribution in VCKC. VCKC promotes a stable and expanded liquid film, whereas VEKC tends to induce columnar flow. Reducing the cell size and porosity improves mass transfer efficiency, and the liquid load governs mass transfer flux. These findings provide theoretical guidance for the design and optimization of compact packings for process intensification in shipboard carbon-capture applications.

1. Introduction

Stringent international regulations and emission reduction mandates compel the shipping industry to mitigate greenhouse gas emissions [1,2]. The International Maritime Organization (IMO) established a decarbonization strategy that drives the industry to accelerate the exploration of alternative fuels and onboard carbon capture technologies [3]. Post-combustion carbon capture serves as a primary pathway for near-term maritime carbon neutrality due to high compatibility with existing ship power systems [4,5]. Amine-based chemical absorption processes offer high capture efficiency and operational maturity, and they remain the dominant technological route in land-based post-combustion carbon capture systems [6]. However, marine applications impose severe spatial and weight constraints that prevent the implementation of traditional tall, land-based absorption columns. Consequently, the development of compact gas–liquid mass transfer internals has become a critical bottleneck for onboard carbon capture systems (OCCS) [7,8].

The packing geometry in an absorption column governs overall mass transfer performance. Corrugated plate packings such as the Mellapak series are widely used in industrial practice [9]. Their regular flow channels limit transverse mixing and intensify wall flow, which yields non-uniform liquid distribution and mass transfer dead zones in compact packed columns [10]. Full-scale testing of large packed columns is costly, and so numerical studies often replace complex periodic structures with representative elementary units (REU) for modeling and design optimization [11]. Although corrugated plates remain common in industrial structured packings, geometric constraints still restrict three-dimensional mixing and sustain liquid maldistribution with associated dead zones. These limitations are more pronounced in marine applications with strict space and load constraints, where compact column designs require higher volumetric mass transfer efficiency [12]. Studies of mass transfer mechanisms in packings remain central to the development of improved internal structures in absorption columns [13].

Recent advances in additive manufacturing enable the fabrication of porous media featuring complex configurations and fine microstructures [14]. Periodic open cellular structures (POCS) emerge as a research focal point due to their ability to replicate natural porous material configurations while offering the potential for structural lightweighting, functional customization, and multiphysics performance regulation [15,16]. Distinct from traditional packings, the fully interconnected three-dimensional frameworks of POCS provide high specific surface area and porosity, which enhances fluid turbulence and interphase contact [17,18]. Compared to randomly packed ceramic foams or particles, POCS reduce flow resistance while maintaining excellent heat and mass transfer performance [19,20]. Previous studies have verified the potential of POCS to maintain high liquid holdup and uniform liquid distributions, making them promising packing candidates for compact gas–liquid reactors [21,22].

Driven by increased computational capabilities, research efforts have shifted from macroscopic experimental measurements toward micro-scale simulations to elucidate fundamental transport mechanisms within POCS and understand coupling effects between geometric features, flow fields, and mass transfer processes [23,24]. The level-set method has been widely used in tracking pore-scale gas–liquid interface morphologies due to its ability to handle topological changes accurately [25], though resolving the mass transfer process limits overall accuracy [26]. Meanwhile, interfacial mass transfer models such as continuous species transfer (CST) quantitatively describe material exchange across phase boundaries [27]. Literature reports apply the CST method to analyze film flow and reactive absorption processes within traditional structured packings [28], verifying the reliability of numerical models in predicting key indicators such as mass transfer efficiency [29]. REU-based numerical simulations of POCS reveal pore-scale flow and mass transfer mechanisms while providing quantitative evaluations of macroscopic performance [30].

Among various POCS configurations, the Kelvin cell serves as a widely adopted standard theoretical model due to its capacity to replicate the structural features of open-cell foams [31]. Previous studies focus primarily on thermohydraulic performance in single-phase flows, confirming a superior heat transfer to pressure drop balance compared to traditional porous media. Furthermore, quantitative comparisons elucidate the differences in single-phase flow performance among various structural configurations, providing a fundamental basis for packing selection [32]. These collective efforts confirm the feasibility of Kelvin cells as efficient mass transfer packings and indicate that geometric configurations govern fluid behavior [16].

Despite the proven potential of Kelvin cells, most studies remain limited to isotropic standard cells and focus primarily on static porosity alongside performance metrics of equal-volume configurations [33]. In practical engineering and additive manufacturing processes, constraints from manufacturing techniques, assembly preloads, or specific marine cabin dimensions frequently force packing units into non-standard axially stretched or compressed morphologies [34]. This axial stretching or compression alters their initial porosity, specific surface area, and channel tortuosity. Furthermore, the confined spaces and continuous mechanical vibrations of marine environments impose strict requirements on stable fluid distribution within onboard absorption columns [35]. Limited vertical space in the engine casing and funnel casing constrains shipboard absorption columns and motivates packings with axially stretched or compressed unit cells, since solvent-based shipboard capture often requires tall packed sections that are difficult to accommodate onboard [8,36]. Additive manufacturing facilitates the proactive design of anisotropic Kelvin cells featuring axial elongation or compression. Modifying the geometric configuration accommodates confined space and provides an opportunity to structurally regulate two-phase gas–liquid flow distribution by altering pore channel tortuosity [37]. Although previous studies derive scalar relationships for permeability, pressure drop, and equivalent mass transfer area at the micro scale, parametric investigations regarding the coupled effects of axial stretching and compression on flow and mass transfer remain scarce [30].

Investigating the intrinsic impacts of axial stretching and compression on mass transfer efficiency holds significant importance for developing customized marine packings. This work employs micro-scale numerical simulations to investigate the mass transfer and flow characteristics of regular Kelvin cells (RKC), vertically elongated Kelvin cells (VEKC), and vertically compressed Kelvin cells (VCKC) during CO₂ absorption. The analysis quantifies how porosity, cell size, and liquid load affect liquid distribution, liquid holdup, mass transfer efficiency, and mass transfer flux across the three Kelvin cell variants.

2. Theoretical Model

All numerical simulations were performed using COMSOL Multiphysics (version 6.3) [38] based on the finite-element method (FEM). The two-phase flow field was solved using a level-set formulation coupled with the incompressible Navier–Stokes equations, and the CO₂ transport and absorption reaction were modeled by coupling the species convection–diffusion equation with the interfacial mass transfer model. The coupled fields were discretized using linear Lagrange elements with consistent stabilization enabled in COMSOL. The resulting linear systems were solved using the MUMPS sparse direct solver, with a relative tolerance of 1 × 10⁻³ adopted as the convergence criterion.

2.1. Two-Phase Flow Model

The two-phase flow model adopts an interface-capturing one-fluid formulation combined with a conservative level-set method and solves a unified set of governing equations over the computational domain to describe the flow, mass transfer, and chemical reactions of the gas and liquid phases [39]. This formulation differs from the volume-averaged Euler–Euler two-fluid models discussed in classical monographs [40,41]. The model treats both gas and liquid phases as incompressible Newtonian fluids under isothermal conditions, neglecting temperature variations and surfactant effects while maintaining a constant surface tension coefficient. A unified set of Navier–Stokes equations, comprising the continuity and momentum equations, governs the flow of the gas and liquid phases. The formulation represents both phases through the level-set variable φ, with phase-fraction-weighted properties and the volumetric surface tension force accounting for phase dependence and interfacial coupling.

$${\displaystyle \frac{\partial \rho }{\partial t}}+\nabla \cdot \left(\rho \mathit{u}\right)=0$$

(1)

$$\rho \left({\displaystyle \frac{\partial \mathit{u}}{\partial t}}+\mathit{u}\cdot \nabla \mathit{u}\right)=\nabla \cdot \left[-p\mathbf{I}+\mu \left(\nabla \mathit{u}+{(\nabla \mathit{u})}^T\right)\right]+{\mathit{F}}_{\mathrm{st}}+\rho \mathit{g}$$

(2)

Here u represents the velocity vector and ρ denotes the fluid density. The total stress tensor −pI + μ(∇u + (∇u)^T) incorporates the hydrostatic pressure p, the identity tensor I, and the dynamic viscosity μ. The source term F_st in the momentum equation represents the volumetric force induced by surface tension, and g denotes gravitational acceleration. Phase fractions determine the weighted calculations for density ρ and viscosity μ. The level-set method tracks the dynamic evolution of the gas–liquid interface according to the following transport equation [25]:

$${\displaystyle \frac{\partial \varphi }{\partial t}}+\mathit{u}\cdot \nabla \varphi =\gamma \nabla \cdot (\xi \nabla \varphi -\varphi (1-\varphi ){\displaystyle \frac{\nabla \varphi }{|\nabla \varphi |}})$$

(3)

The variable φ indicates the volume fraction transition region from 0 to 1 near the two-phase interface. The zero contour of φ defines the gas–liquid interface position, where γ serves as the interface reinitialization parameter (m/s) and ξ controls the interface transition zone thickness (m).

2.2. Mass Transfer and Reaction Model

The convection–diffusion equation describes the CO₂ mass transport within the system:

$${\displaystyle \frac{\partial C}{\partial t}}+\nabla \cdot \mathit{J}+\mathit{u}\cdot \nabla C=R_i$$

(4)

Here C represents the molar concentration (mol/m³), u denotes the velocity vector (m/s), and R_i acts as the chemical reaction source term (mol/(m³·s)). J indicates the mass flux induced by molecular diffusion (mol/(m²·s)). This flux couples with the mass balance equation for boundary conditions and flux calculations according to the following expression.

$${\mathit{J}}_i=-D\nabla C_i$$

(5)

Here D denotes the diffusion coefficient (m²/s), J_i represents the mass flux of a specific phase, and C_i indicates the molar concentration of the substance in a specific phase excluding the solvent (mol/m³). The continuous species transfer (CST) model, weighted by phase volume fractions [42], integrates the species concentration equations across both phases to describe the concentration distribution throughout the entire computational domain using a single equation. Mass transport at the gas–liquid interface satisfies flux continuity across the boundary and Henry’s law for dissolution equilibrium. The concentration ratio between the gas and liquid phases at the interface equals the Henry’s law constant, which dictates the equilibrium interfacial species concentration [43]. These two conditions constitute the boundary conditions for interfacial mass transfer.

$$J_{\mathrm{L},j}=J_{\mathrm{G},j}$$

(6)

$$C_{\mathrm{L},j}{H}_e=C_{\mathrm{G},j}$$

(7)

Here He represents the Henry’s law constant. When He differs from 1, the concentration field is discontinuous at the interface. The CST model assumes mass diffusion conservation at the phase interface and combines the two-phase variables into a unified global variable via phase volume fraction weighting to construct a single-fluid model [44]. The CST model introduces effective physical parameters weighted by the gas–liquid volume fraction φ. First, the model defines the average diffusion coefficient D_a as follows:

$$D_{\mathrm{a}}=\varphi D_L+(1-\varphi )D_{\mathrm{G}}$$

(8)

Here D_L and D_G denote the molecular diffusion coefficients of the solute in the liquid and gas phases, respectively. The model employs an effective diffusion coefficient D_h based on a harmonic mean to ensure continuous interfacial flux and suppress spurious fluxes.

$$D_{\mathrm{h}}={\displaystyle \frac{D_{\mathrm{L}}{D}_{\mathrm{G}}}{\varphi D_{\mathrm{G}}+(1-\varphi )D_{\mathrm{L}}}}$$

(9)

The convection–diffusion equation near the interface takes the following form:

$${\displaystyle \frac{\partial C}{\partial t}}+\nabla \cdot (\mathit{U}C)=\nabla \cdot (D_a\nabla C+\mathit{\Phi })$$

(10)

Here C represents the pseudo-concentration variable solved across the entire field, U denotes the mixture phase velocity vector, and Φ signifies the additional flux term introduced to address the concentration jump described by Henry’s law at the phase interface, expressed as follows:

$$\mathit{\Phi }=-D_h{\displaystyle \frac{C(1-H_{\mathrm{e}})}{\varphi +H_{\mathrm{e}}(1-\varphi )}}\nabla \varphi$$

(11)

The CST model describes the gas–liquid interfacial mass transfer without explicitly tracking the phase interface, which simplifies the numerical simulation. When the computational grid resides in a pure phase region or the Henry’s law constant equals 1, the Φ value reaches zero and the global concentration distribution remains continuous. An unequal Henry’s law constant yields a concentration discontinuity at the gas–liquid interface. By introducing the Φ term, the CST model creates a micro-scale diffusion transition zone at the phase interface to facilitate a smooth concentration transition and avoid numerical discontinuities [44]. The chemical absorption of CO₂ into MEA solutions functions as a second-order irreversible fast reaction governed by the reaction kinetics expressed as follows [45]:

$$C{O}_2+MEA+H_{2}O=MEACO{O}^{-}+H_3{O}^{+}$$

(12)

The reaction rate constant k_f constitutes the source term R_i in Equation (4), and the Arrhenius equation calculates k_f [46].

$$k_{\mathrm{f}}=A{e}^{-{\displaystyle \frac{E_{\mathrm{a}}}{RT}}}$$

(13)

Here A represents the pre-exponential factor, E_a denotes the activation energy (J/mol), R stands for the ideal gas constant (8.314 J/(mol·K)), and T denotes the reaction temperature. Unless otherwise stated, temperature T was fixed at 298 K (25°C) throughout the present study under an isothermal assumption. This setting allows the effects of micro-scale geometric configuration on flow behavior and liquid-film evolution to be isolated. Nevertheless, temperature affects CO₂ absorption in MEA systems. For example, Ye et al. [47] reported improved absorption performance when the operating temperature increased from 25 to 45 °C in microchannel reactors. Studies of MEA-based packed columns have also shown that the overall mass transfer performance of structured packings depends on liquid temperature in addition to other operating and design parameters [48,49]. Therefore, the optimization results reported here should be interpreted as valid under the specified isothermal condition of 298 K and under otherwise identical boundary conditions. A rigorous evaluation of temperature effects would require coupling the energy equation with temperature-dependent kinetics, transport properties, and thermodynamic parameters, which will be considered in future work.

3. Conceptual Model

This study selects the Kelvin cell as the fundamental geometric model. To investigate the impact of axial shape variation on mass transfer performance, this work constructs three Kelvin cell variants, including the regular Kelvin cell (RKC), the vertically elongated Kelvin cell (VEKC), and the vertically compressed Kelvin cell (VCKC). For the baseline comparison, the three Kelvin cells were designed with the same unit-cell volume. In the parametric study, cell size and porosity were varied to investigate their effects on gas–liquid two-phase flow and mass transfer performance.

Figure 1 illustrates the geometric configurations of the three Kelvin cell variants. For these configurations, we examine how cell size V_total and porosity ε affect flow and mass transfer. The following equation defines the cell size V_total:

$${\mathrm{V}}_{\mathrm{total}}=d_x\times d_y\times d_z$$

(14)

Here d_x, d_y, and d_z denote the lengths of the Kelvin cell along three orthogonal directions. The following equation defines the porosity:

$$\epsilon ={\displaystyle \frac{V_{\mathrm{fluid}}}{V_{\mathrm{total}}}}={\displaystyle \frac{V_{\mathrm{fluid}}}{V_{\mathrm{fluid}}+V_{\mathrm{solid}}}}=1-{\displaystyle \frac{V_{\mathrm{solid}}}{V_{\mathrm{total}}}}$$

(15)

Here V_fluid represents the fluid domain volume, V_solid indicates the solid volume of the Kelvin cell, and V_total denotes the total cell size. The calculation for the specific surface area S_v proceeds as follows:

$$S_v={\displaystyle \frac{S_{\mathrm{total}}}{V_{\mathrm{total}}}}$$

(16)

Here S_total represents the total enclosed surface area of the Kelvin cell, including the outer surface and the inner surface areas of internal pores and channels.

Table 1. Parameter ranges of geometric models for numerical simulations.

Cell Type	Cell Size dx × dy × dz (mm × mm × mm)	Porosity (ε)	Characteristic Diameter dc (mm)	Specific Surface Area Sv (m−1)
RKC	30 × 30 × 30	0.70 to 0.95	2.8 to 7.52	82.75 to 130.46
	10 × 10 × 10	0.85	1.67	378.5
	40 × 40 × 40	0.85	6.66	84.78
	80 × 80 × 80	0.85	13.31	42.35
VEKC	45 × 24.50 × 24.50	0.70 to 0.95	2.35 to 7.2	86.15 to 138.50
	15 × 8.160 × 8.160	0.85	1.6	419.48
	60 × 32.66 × 32.66	0.85	6.39	89.14
	120 × 63.32 × 63.32	0.85	9.71	37.71
VCKC	15 × 42.43 × 42.43	0.70 to 0.95	2.52 to 7.52	91.28 to 147.35
	5 × 14.14 × 14.14	0.85	1.67	408.03
	20 × 56.56 × 56.56	0.85	6.1	94.57
	40 × 113.14 × 113.14	0.85	12.21	47.31

details the specific geometric parameters for all simulation cases.

All numerical simulations utilize a representative elementary unit (REU) to balance computational accuracy and resource consumption [50]. The REU incorporates the basic geometric features of structured packings and captures the periodic characteristics of the structure. All configurations are compared on a constant total REU volume basis, so that the simulations correspond to the same macroscopic packing volume. The axial dimension d_z varies with axial stretching or compression and is not constrained to be identical across geometries. Under this volume constraint, variations in porosity and characteristic size isolate their intrinsic effects on two-phase flow and mass transfer.

Figure 2 illustrates the boundary conditions of the computational domain. To represent the fully developed local flow in a periodically repeating packing array, the computational domain applies symmetry boundary conditions on the front and back faces and periodic boundary conditions on the left and right faces. The representative elementary unit corresponds to a local Kelvin cell at a given bed depth within a continuous packed bed. The top boundary is an internal cut plane rather than a macroscopic liquid distributor surface.

Accordingly, the liquid inflow is not imposed uniformly over the entire top plane. Instead, the aqueous MEA solution enters the computational domain only through the inlet patch Ain on the top boundary. The liquid inlet patch conforms to the strut footprint at the cut plane and mimics the incoming strut-attached liquid from the upstream cell. On A_in, a downward inlet velocity boundary is prescribed for the liquid phase as u_in. The inlet velocity u_in is determined from volumetric-flow conservation using the liquid load Q_s, defined as the superficial volumetric flux referenced to as the REU top-projected area A_ref:

$$u_{\mathrm{in}}={\displaystyle \frac{Q_s}{3600}}\left({\displaystyle \frac{A_{\mathrm{ref}}}{A_{\mathit{in}}}}\right)$$

(17)

Here, A_ref is the projected area of the REU on the inlet plane, A_in is the total area of the liquid inlet patch, and 3600 converts hours to seconds. For each case, A_in is obtained from the geometry and u_in is adjusted accordingly to maintain the specified liquid load Q_s. At A_in, the inlet liquid is specified as an aqueous MEA solution without dissolved CO₂ [50]. All solid strut surfaces are treated as no-slip walls.

The remaining part of the top boundary is treated as an open boundary for the gas phase with a fixed relative pressure and fixed bulk gas composition (20% CO₂ and 80% N₂) to provide a near-constant gas environment during absorption. The reaction temperature is set to 298 K.

To simulate the constant supply of gas-phase CO₂ in localized regions, the open boundary maintains the initial gas composition and imposes the corresponding bulk CO₂ concentration onto the gas region to achieve near-constant gas conditions near the boundary. This approach assumes the CO₂ partial pressure in the local cell neighborhood exhibits negligible variation within the studied time scale. External gas convection and diffusion provide constant compensation for the consumed CO₂, directing focus to the two-phase gas–liquid mass transfer process. The investigated system entails a chemical absorption process where CO₂ crosses the gas–liquid interface into the liquid phase to undergo a rapid reaction with MEA, and liquid film resistance governs the mass transfer characteristics. Addressing the typical operational range of industrial MEA-based CO₂ capture, the liquid load Q_s ranges from 10 to 100 m³/(m²·h).

Table 2. Thermodynamic properties of the gas–liquid absorption process.

Dynamics Viscosity μ (Pa·s)	Density ρ (kg/m3)	Surface Tension σ (mN/m)	Henry’s Law Constant He (kPa·m3/mol)	Activation Energy Ea (kJ/mol)	Diffusion Coefficient (m2/s)
1.745 × 10−3 [51]	1004.5 [51]	68.45 [52]	3.11 [53]	41 [46]	2.29 × 10−9 [54]

lists the relevant thermodynamic parameters.

The present single-cell REU model is intended to represent local transport behavior within the interior of a packed bed. In shipboard CCUS systems, the total packing height often extends over several meters, whereas the present simulation resolves only one repeating unit. The periodic boundary conditions applied in the repeating directions are used to approximate the local flow and mass transfer environment in a periodically repeated packing array under the assumption of uniform phase distribution. As a result, the model represents the internal region of a deep packed bed rather than the full column. Column-scale effects, such as inlet distributor non-uniformity, global liquid maldistribution, and wall channeling, are not included. The REU model is therefore used to isolate intrinsic geometric effects and to extract volume-normalized mass transfer metrics, including the interfacial-area-averaged CO₂ flux. These cell-scale quantities could be used as physically grounded inputs for macroscopic packed-column models, such as rate-based or HTU-NTU models, to predict overall capture performance and estimate the required packed-bed height.

In the REU-scale simulations, a laminar formulation was adopted for both phases, and no turbulence model was employed. This choice follows common micro-scale and meso-scale CFD practices for structured packings and packing-like periodic geometries at the representative unit scale [55,56]. To support this flow-regime assumption, the liquid-phase Reynolds number was evaluated over the investigated operating conditions. Using the liquid properties in Table 2 and liquid loads of 10 to 100 m³/(m²·h), the resulting flow conditions are compatible with stable thin-film transport and do not indicate turbulence-dominated behavior at the REU scale. This behavior is consistent with a laminar treatment under the conditions examined in this work.

4. Results and Discussion

4.1. Model Validation

This study verifies the applicability of the developed mass transfer model for interfacial mass transfer and diffusion-controlled processes. The results demonstrate that, despite introducing a micro-scale diffusion transition zone to treat the phase boundary, the model accurately captures the gas–liquid interfacial concentration jump inherent in the physical process [57]. A one-dimensional steady-state pure diffusion model serves as validation (see Figure 3), featuring 5 mm lengths for both the gas and liquid regions. The pure diffusion nature of the simulation requires a zero-velocity field within the computational domain.

Table 3. Boundary conditions for the one-dimensional pure diffusion mass transfer problem.

Boundary Name	Phase Volume Fraction φ	Pressure p (Pa)	Concentration C (mol/m3)
Liquid phase (L)	Fixed value 1	Gradient 0	Fixed value 0
Gas phase (G)	Fixed value 0	Gradient 0	Fixed value 1

details the specific boundary conditions regarding the phase volume fractions and concentration parameters.

Neglecting convective mass transfer in the one-dimensional steady-state pure diffusion simulation yields a zero global velocity and simplifies the governing equation to the following form.

$${\displaystyle \frac{\partial \left(D\nabla C\right)}{\partial y}}=0$$

(18)

Incorporating relevant geometric scales and boundary parameters specifies the governing equation for typical local liquid film flow characteristics. The derivation assumes a uniform liquid film thickness e and sets the initial concentrations at the gas boundary y = 2e and liquid boundary y = 0 to C_G⁰ and C_L⁰, respectively. Applying Henry’s law and the interfacial flux continuity condition yields the following steady-state analytical solution.

Liquid phase concentration distribution (0 ≤ y ≤ e):

$$C_L={\displaystyle \frac{C_G^0-H_{\mathrm{e}}{C}_L^0}{H_{\mathrm{e}}+\frac{D_L}{D_G}}}{\displaystyle \frac{y}{e}}+C_L^0$$

(19)

Gas phase concentration distribution (e ≤ y ≤ 2e):

$$C_G={\displaystyle \frac{C_G^0-H_{\mathrm{e}}{C}_L^0}{1+H_{\mathrm{e}}\frac{D_G}{D_L}}}{\displaystyle \frac{y-2e}{e}}+C_G^0$$

(20)

The calculations evaluate the mass transfer model under three Henry’s law constant conditions including He = 0.1, 1, and 10. The analysis compares the numerical solution at the 20 s steady state with the analytical solution. Figure 3 presents the comparison between the numerical and analytical CO₂ concentrations across the section to verify the model accuracy in steady-state mass transfer problems. The results indicate excellent agreement between the numerically simulated concentration distribution and the theoretical analytical solution. Both profiles exhibit distinct concentration discontinuities at the phase interface to match theoretical expectations. The precise capture of the concentration distribution during liquid film mass transfer verifies the reliability of the model [44].

Evaluating the accuracy of the developed two-phase flow model for gravity-driven hydrodynamics requires establishing a standard two-dimensional vertical falling film benchmark model, as shown in Figure 4. This benchmark eliminates geometric interference from complex three-dimensional porous structures and compares the numerical results against the classical Nusselt laminar falling film analytical solution under simplified physical fields. This comparison establishes the hydrodynamic foundation for subsequent multiphase flow simulations within complex Kelvin cells [58]. Assuming fully developed flow for a gravity-driven laminar liquid film flowing along a vertical wall, the Nusselt analytical solution yields the following theoretical film thickness δ [29].

$$\delta ={\left({\displaystyle \frac{3\mu \Gamma }{\rho g\sin \theta }}\right)}^{1/3}$$

(21)

Here δ represents the theoretical liquid film thickness, μ denotes the liquid dynamic viscosity, Γ indicates the mass flow rate per unit width, ρ stands for the liquid density, g is the gravitational acceleration, and θ represents the wall inclination angle (set to 90° in this validation model). Meanwhile, the velocity distribution u(y) along the wall normal direction (y-direction) within the liquid film takes the following form [29]:

$$u(y)={\displaystyle \frac{\rho g\sin \theta }{2\mu }}(2\delta y-y^2)$$

(22)

In the numerical model setup, setting the computational domain length to L = 30δ ensures the fluid reaches a fully developed state. To simulate an ideal infinitely long flat plate flow field and eliminate inlet and outlet effects, the model applies periodic boundary conditions in the flow direction alongside a no-slip boundary condition at the wall and a free-slip condition at the outer gas boundary. To accelerate numerical convergence and ensure computational stability, Equations (21) and (22) initialize the flow field in the liquid region. Furthermore, a local grid refinement strategy ensures sufficient computational node density within the two-phase transition region to achieve precise capture of the velocity distribution across the gas and liquid phases.

Figure 5 presents the velocity distribution validation results. The results indicate excellent agreement between the numerical internal velocity profile of the liquid film and the Nusselt theoretical parabola. In the bulk liquid region, the numerical solution reproduces the theoretical flow characteristics with a relative deviation contained within 10%. Although wall curvature influences the internal flow within the Kelvin cell, the local flow behavior follows fundamental physical principles, and the liquid film evolution trend matches gravity-driven theory [58]. This result verifies the accuracy of the developed level-set two-phase flow model in solving the momentum conservation equation and demonstrates its capability to capture the hydrodynamic characteristics of falling film flow [59].

4.2. Grid Independence Verification

Addressing structural scale diversity and local gradient features, the finite element method utilizes unstructured tetrahedral grids to discretize the computational domain to balance geometric accuracy and computational stability. Because wall confinement strongly influences gas–liquid flow, and interfacial mass transfer governs overall performance, the grid-generation strategy prioritizes high resolution in these key physical regions. Deploying multi-layer prismatic boundary layer grids near solid walls and strut surfaces resolves velocity and concentration gradient features in near-wall regions. Simultaneous refinement of the overall computational domain enhances the numerical resolution of the gas–liquid distribution.

To ensure the reliability of numerical results and reduce grid scale effects, this study conducts a systematic grid independence analysis on the regular Kelvin cell. The test proceeds under a liquid load of 40 m³/(m²·h) with the boundary conditions outlined in Section 3 to verify the stability of the grid scheme in predicting mass transfer and flow. The grid independence analysis constructs five grid schemes with progressively increasing resolution, reducing the maximum cell size from 2.0 mm to 1.2 mm to cover discretization levels ranging from coarse to high precision. All schemes employ a boundary-layer grid near the solid wall to ensure consistent resolution of wall flow and mass transfer features. The total number of grid cells within the computational domain increases from approximately 550,000 to 2,100,000 to form a representative micro-scale grid system.

Steady-state numerical calculations for the five grids under identical conditions evaluate the sensitivity of key physical quantities to grid density, analyzing the liquid holdup reflecting the liquid volume fraction and the mass transfer efficiency, reflecting the overall cell mass transfer capability. Comparing the variation trends of liquid holdup and mass transfer efficiency with grid refinement provides a basis for selecting an appropriate grid scale for subsequent calculations.

Table 4. Grid independence test results for the regular Kelvin cell (RKC) under a liquid load of 40 m³/(m²·h).

Grid Scheme	Maximum Cell Size (mm)	Total Grid Cells (Approx.)	Liquid Holdup (%)	Mass Transfer Efficiency (%)
1 (Coarse)	2.0	550,000	18.21	29.71
2	1.8	820,000	19.21	31.21
3	1.5	1,250,000	19.81	32.24
4 (Fine)	1.3	1,680,000	20.11	32.71
5 (Finest)	1.2	2,100,000	20.23	32.94

presents the grid independence test results.

Table 4 indicates that both liquid holdup and mass transfer efficiency exhibit stable convergence behavior as grid resolution increases. Further refinement of the grid scheme from the fine level to the highest resolution constrains the relative change in liquid holdup to within 0.60% and the relative change in mass transfer efficiency to only 0.70%, demonstrating that the primary evaluation metrics remain insensitive to grid scale. When the total number of grid cells within the computational domain reaches approximately 1,680,000, the numerical results achieve independence from grid density and satisfy the grid independence criteria. Because continued grid refinement increases computational costs with marginal improvements in result accuracy, this study selects the grid scheme with approximately 1,680,000 cells as the final computational standard, and applies this strategy to subsequent numerical simulations across all conditions.

4.3. Effect of Axial Stretching and Compression on Flow Distributions

To examine how axial stretching and compression alter flow distributions, we compared the liquid volume fraction and velocity fields in three Kelvin cell variants and quantified the effects of axial stretching and compression on flow characteristics and liquid phase distribution. Figure 6 shows the liquid volume fraction distributions for RKC, VEKC, and VCKC at a liquid load of 10 m³/(m²·h) and a cell size of 2.7 × 10⁴ mm³. For clarity, we visualize the liquid distribution using representative cross-sectional slices through the unit-cell center and we annotate the corresponding S_IA value for each configuration. The specific interfacial area denotes the area available for gas–liquid mass transfer per unit liquid volume. We define the specific interfacial area as the gas–liquid contact area per unit liquid volume:

$$S_{IA}={\displaystyle \frac{A_{\mathrm{m}}}{V_{\mathrm{L}}}}$$

(23)

Here S_IA denotes the specific interfacial area, A_m denotes the gas–liquid contact area, and V_L denotes the liquid volume. The three Kelvin cell variants exhibit distinct internal liquid flow regimes. In the RKC, S_IA equals 294.8 m⁻¹, and the liquid forms a film along the struts with localized accumulation at the nodes. Droplets are retained at nodes due to geometric obstruction, while the strut surfaces remain wetted. In the cross-sectional view, this regime manifests as a strut-attached film with pronounced local thickening near the node junctions. In the VEKC, elongated struts increase the relative importance of gravity, driving the liquid toward the central axis and forming a continuous columnar stream. In the cross-section, the liquid concentrates into a filled core near the central axis, whereas the peripheral openings exhibit less liquid volume, indicating limited lateral spreading. This transition increases S_IA to 375.2 m⁻¹. However, this structure limits lateral spreading, leaves peripheral struts unwetted, and reduces the area available for mass transfer. By contrast, the axially compressed VCKC strengthens surface tension forces and horizontal capillary driving forces due to its flattened geometry, which promotes lateral redistribution of the liquid against gravity. This mechanism promotes a stable hollow cylindrical liquid film within the pore space between struts, which appears as an annular film surrounding a gas core in the cross-section. This configuration yields the highest S_IA at 422.5 m⁻¹. The results indicate that the VCKC geometry favors lateral film coverage and sustained gas–liquid contact.

Figure 7 shows flow characteristics in the different unit-cell geometries. The arrows indicate the local flow direction. In the standard RKC unit, node-induced obstruction limits the local velocity, and streamlines follow the strut surfaces. At the junctions, velocity decreases and streamlines diverge, which reduces flow continuity and limits renewal of the gas–liquid interface. In the VEKC unit, elongated struts form a low-resistance vertical pathway and promote a high-velocity columnar stream along the central axis. This increases the axial velocity but limits lateral spreading, which weakens near-wall convection. By contrast, the axially compressed VCKC unit forces lateral deflection of streamlines due to its flattened geometry and drives horizontal transport during wetting of the struts. This mechanism promotes a more uniform distribution within the pore space and increases gas–liquid mass transfer, indicating geometric advantages of VCKC for increasing residence time and strengthening micro-scale mixing.

4.4. Response of Liquid Holdup to Axial Shape Variation and Porosity

Porosity is a key geometric parameter that governs hydrodynamics and mass transfer in POCS structures and affects gas–liquid mass transfer behavior in Kelvin cells with different geometries. To quantify the influence of axial stretching and compression on mass transfer, we use liquid holdup to characterize the extent of liquid retention within a unit cell. Liquid holdup is defined as the liquid volume fraction within the Kelvin cell:

$$h_{\mathrm{L}}={\displaystyle \frac{V_{\mathrm{L}}}{V_{\mathrm{total}}}}$$

(24)

where h_L denotes the liquid holdup. Figure 8 shows the variation in liquid holdup in RKC, VEKC, and VCKC as a function of porosity. As porosity increases from 0.75 to 0.95, liquid holdup decreases, which is consistent with larger pores reducing capillary confinement and increasing gravitational drainage. VEKC shows the strongest sensitivity to porosity, with a pronounced decrease in liquid holdup as porosity increases. At a porosity of 0.75, the longitudinal channel in VEKC supports capillary retention, giving a liquid holdup of about 29%. At a porosity of 0.95, the larger size of the flow channel reduces capillary retention and promotes drainage, leading to a lower liquid holdup. By contrast, RKC shows limited variation in liquid holdup over porosities of 0.75 to 0.95, remaining near 23%. This behavior is consistent with the isotropic RKC geometry, which promotes the redistribution and local trapping of liquid. VCKC shows lower liquid holdup across all porosities, consistent with strut orientation that promotes lateral spreading and reduces local retention.

4.5. Effect of Porosity on Mass Transfer

To elucidate how axial shape variation regulates microscale gas–liquid mass transfer mechanisms, we define a dimensionless intensity index for local mass transfer and evaluate the spatial distribution of mass transfer driving force in unit cells among the three Kelvin cell variants. Gas–liquid absorption involves the interphase transport of the solute driven by concentration gradients. In the CST model, the interface is represented as a continuous transition region, and the liquid film thickness varies strongly in the flow field. The concentration field alone could not clearly identify regions with high mass transfer activity, and so we use the proposed index to identify zones with elevated local driving force. The dimensionless index I_MT represents the intensity of local mass transfer flux:

$$I_{MT}=\lg \left({\displaystyle \frac{D_h\left|{\nabla }^{2}C\right|}{D_L\cdot \frac{C_{\mathrm{ref}}}{L_{\mathrm{char}}}}}\right)$$

(25)

Here the numerator represents the local instantaneous diffusive flux, and the denominator provides a characteristic reference flux. L_char is the characteristic length of the Kelvin cell, and C_ref is the maximum concentration of CO₂ in the liquid phase.

Figure 9 shows the spatial distribution of I_MT at porosities of 0.7 and 0.95. At a porosity of 0.7, the denser solid framework imposes stronger geometric constraints on flow pathways and reduces the channel size. In both longitudinal and transverse sections, high-value regions form continuous annular or mesh-like connected distributions, indicating broader and more uniform coverage of interfacial zones with elevated mass transfer intensity. This trend may arise because the framework suppresses the formation of thick liquid columns and favors film coverage on strut surfaces, which reduces liquid-side diffusion resistance and increases I_MT.

At a porosity of 0.95, the void space within the Kelvin cell increases, and high-value regions preferentially concentrate along strut surfaces or near the outer perimeter. In contrast, a low-value core develops within the unit cell, especially near the center, and extends across the cell. At a porosity of 0.95, this low-value region is more pronounced in the longitudinal section of RKC, suggesting transport limitations in regions farther from the interface within a thick liquid layer. Overall, increasing porosity shifts high-intensity interfacial regions from broad connected coverage to localization along the struts, and is accompanied by mass transfer limitations in the central region.

To quantitatively compare CO₂ absorption performance among the different unit-cell configurations, mass transfer efficiency and mass transfer flux were selected as the primary evaluation metrics [60]. For cross-configuration comparison, both metrics are interpreted on a constant total REU volume basis so that all simulations correspond to the same macroscopic packing volume. Mass transfer efficiency reflects the overall extent of CO₂ removal achieved within the cell, whereas the area-averaged mass transfer flux represents the mean transfer rate across the gas–liquid interface. Together, these two metrics help identify the mechanisms responsible for mass transfer enhancement.

CO₂ mass transfer efficiency η is defined as follows:

$$\eta ={\displaystyle \frac{C_{C{O}_2,in}-C_{C{O}_2,out}}{C_{C{O}_2,in}}}\times 100\%$$

(26)

Because η is defined for a single REU, it is sensitive to the local axial contact path associated with each geometry. Therefore, together with η, we use the interfacial-area-averaged CO₂ mass transfer flux J_CO2 and its volumetric form as the primary metrics for cross-configuration comparison under equal packing volume. This treatment emphasizes the intrinsic interphase transfer rate rather than geometric differences in the axial extent of a single REU.

CO₂ mass transfer flux J_CO2 is defined as follows:

$${\mathit{J}}_{C{O}_2}={\displaystyle \frac{1}{A_m}}{\displaystyle {\int }_{A_m}{N}_{C{O}_2,n}}dA$$

(27)

N_CO2,n is the normal molar flux across the gas–liquid interface, and dA is a differential interfacial area element. Figure 10 shows how mass transfer efficiency η and mass transfer flux J_CO2 vary with porosity at low, intermediate, and high liquid loads. As shown in Figure 10a, the isotropic RKC unit exhibits a pronounced nonmonotonic response at higher liquid loads. The efficiency peaks at a porosity of about 0.8. This increase, followed by a decrease, suggests competing effects between interfacial area and hydrodynamic state. A moderate increase in porosity improves flow distribution and suppresses the formation of mass transfer limited zones, which increases the surface renewal rate. At higher porosity, the framework provides fewer attachment sites, which limits mass transfer performance. By contrast, VCKC and VEKC show a monotonic decrease in efficiency with increasing porosity over the tested range. This trend indicates that in axially stretched or compressed geometries, the reduction in gas–liquid contact area governs mass transfer performance.

Figure 10b shows that mass transfer flux decreases monotonically with increasing porosity. At high liquid load, VCKC exhibits the highest baseline flux and the steepest decline. This result indicates that maintaining a higher specific interfacial area by reducing porosity increases the volumetric mass transfer rate.

4.6. Effect of Cell Size on Mass Transfer

V_total governs the macroscopic packing density and sets the gas–liquid contact area and characteristic length scales, which influence gas–liquid mass transfer. Figure 11 shows the distributions of I_MT in RKC, VEKC, and VCKC at cell sizes of 2.7 × 10⁴ mm³ and 5.12 × 10⁵ mm³. At V_total = 2.7 × 10⁴ mm³, longitudinal sections show a continuous low-value region in RKC and VEKC, while high-value regions remain concentrated near the struts, leading to strong spatial variability. In transverse sections, all Kelvin cell variants form a near-strut annulus with intermediate to high values, indicating that mass transfer is dominated by regions adjacent to the framework.

When the cell size increases to 5.12 × 10⁵ mm³, the low-value regions in the longitudinal sections of RKC and VEKC weaken, and high-value regions become more continuous. The index field becomes smoother along the primary flow direction. In transverse sections, the high-value annulus in VEKC and VCKC contracts, and low-to-intermediate values occupy a larger area, indicating weaker lateral redistribution and reduced interface renewal. Under the larger-size condition, VEKC shows the strongest reduction in high-value regions. VCKC retains relatively continuous intermediate-to-high values, with a smaller reduction. Overall, increasing cell size alters the index distribution in a direction-dependent manner. In longitudinal sections, low-value regions shrink and the field becomes smoother. In transverse sections, the coverage of high values decreases and low-to-intermediate values expand.

Mass transfer performance was evaluated as a function of cell size at liquid loads of 10, 40, and 70 m³/(m²·h). As shown in Figure 12a, all three unit-cell configurations exhibit a pronounced scale effect. When the cell size increases from 10 mm to 30–40 mm, the mass transfer efficiency decreases and reaches a local minimum. When the cell size is further increased to 80 mm, efficiency partially recovers, yielding a nonmonotonic trend. This recovery may be associated with stronger gravity-driven film instabilities in larger cells, which promote film rupture and surface renewal and partially compensate for the loss of the gas–liquid contact area. The three Kelvin cell variants also differ in their sensitivity to cell size. The standard RKC shows the largest recovery in efficiency at larger sizes, whereas VCKC exhibits a weaker dependence on cell size, indicating that the compressed geometry helps mitigate performance loss during scale-up.

Figure 12b shows the mass transfer flux of RKC, VEKC, and VCKC as a function of cell size. Mass transfer flux decreases with increasing cell size. This trend is consistent with the scale dependence observed for mass transfer efficiency, but differences among configurations are more pronounced. Within the tested range, reducing cell size increases mass transfer flux for all configurations. The highest flux occurs when a smaller characteristic length is combined with axial compression. A smaller cell size increases the geometric specific surface area, and axial compression promotes lateral spreading and wetting coverage, thereby increasing the effective gas–liquid contact area and raising the flux.

At a size of 80 mm, flux decreases for all configurations because gas–liquid contact area decreases with increasing characteristic length. Even at larger sizes, VCKC maintains a higher flux than the other configurations, indicating that its geometric orientation continues to regulate flow redistribution under scale-up. By contrast, VEKC promotes channelized columnar flow, which confines high-flux regions and reduces the benefit of decreasing size. Therefore, for maximizing volumetric throughput, smaller VCKC packings provide higher mass transfer flux.

4.7. Effect of Liquid Load on Mass Transfer

Liquid load is a key operating parameter in absorption columns and influences liquid velocity, liquid holdup, and interfacial hydrodynamics. To assess how different unit-cell configurations respond to operating conditions, mass transfer performance was examined over a range of liquid loads. We systematically examined mass transfer performance over a range of liquid loads at d_z = 30 mm and ε = 0.85.

Figure 13 shows the distributions of I_MT at different liquid loads. At a liquid load of 10 m³/(m²·h), the index field in all three Kelvin cell variants is organized as a near-strut annulus, but low-value regions are more pronounced, reducing the area occupied by intermediate and high values. This pattern suggests limited lateral liquid spreading on the strut surfaces at low load. Locally thicker liquid layers or confined flow paths persist and expand the low-index regions. When the liquid load increases to 25 m³/(m²·h), intermediate and high values become more continuous, the field becomes smoother, and the low-value regions contract, indicating a larger effective wetted area at higher flow rates.

The response to increasing liquid load differs among the geometries. In VEKC, a continuous low-value region persists near the center of the longitudinal section at both liquid loads, while higher values remain concentrated in the surrounding region. This pattern indicates a persistent mass-transfer-limited zone that is not eliminated by increasing liquid load. In VCKC, the annular region of intermediate-to-high values in the transverse section becomes both stronger and wider at higher load, although a low-value core still remains at the center. Overall, increasing the liquid load enhances the index magnitude and broadens the area occupied by intermediate and high values, but the extent to which the central limited zone is alleviated depends on the geometry.

Figure 14a shows the variation in mass transfer efficiency with liquid load for the three Kelvin cell variants. Mass transfer efficiency increases monotonically with liquid load for all three variants. This trend reflects the increase in effective wetted area at higher liquid flow rates and stronger interfacial renewal and disturbance, which reduces liquid-side mass transfer resistance and increases overall performance. Among the geometries, VCKC gives the highest efficiency, followed by RKC, and then VEKC. These results indicate that VCKC promotes gas–liquid contact and interfacial renewal.

As shown in Figure 14b, the response of mass transfer flux to liquid load highlights differences in the mean interfacial flux among the geometries. Mass transfer flux increases with liquid load for all three variants. For VCKC, flux increases approximately linearly and the slope exceeds those of RKC and VEKC. This behavior indicates that VCKC converts added liquid flow into interfacial renewal and mass transfer more efficiently. By contrast, RKC and VEKC show lower flux and a weaker increase with liquid load. These results support VCKC for high-throughput operation, whereas RKC and VEKC serve as baseline geometries for comparison.

4.8. Identification of Key Factors Under Multi-Parameter Coupling

The preceding sections examined the effects of porosity, cell size, and liquid load on mass transfer performance. However, geometric parameters and operating conditions are coupled, and optimization of a single factor is constrained by the others. To quantify the relative contributions of each factor to mass transfer efficiency and mass transfer flux and to identify favorable parameter combinations, we compared overall performance across a multi-parameter design space.

Figure 15 shows mass transfer efficiency as a function of liquid load and porosity for the three Kelvin cell variants. For the isotropic RKC unit, efficiency varies nonmonotonically with porosity. High efficiency occurs near a porosity of about 0.8 at higher liquid loads and forms a local maximum. This distribution indicates that RKC performance reflects both geometric constraints and flow states. At higher porosity, efficiency decreases. At lower porosity, efficiency does not increase further. These results suggest that a porosity near 0.8 provides a favorable balance between gas–liquid contact and flow distribution. In contrast to RKC, efficiency in VEKC and VCKC increases with decreasing porosity and increasing liquid load. The maximum efficiency occurs at low porosity and high liquid load. This trend is consistent with increased wetted area and enhanced interfacial renewal at higher flow rates.

For VEKC, the contours vary more strongly along the porosity axis, indicating that porosity exerts a stronger influence on efficiency. At intermediate to high porosity, the gain from increasing liquid load is limited. At low porosity, increasing liquid load raises efficiency. Under high liquid load, VCKC exhibits a broader high-efficiency region. It also maintains higher efficiency at intermediate porosity, which indicates lower sensitivity to increasing porosity. This behavior is consistent with a geometry that promotes lateral liquid transport and redistribution. Stronger lateral transport in the liquid phase increases liquid-side mass transfer. Lower porosity and higher structural compactness have been reported to increase effective interfacial area and overall mass transfer in structured packings. This observation is consistent with the expansion of the high-efficiency region for VEKC and VCKC at low porosity.

Figure 16 shows mass transfer flux as a function of liquid load and porosity for the three Kelvin cell variants. Comparison of the flux contours indicates that mass transfer flux depends strongly on liquid load for all three variants. Flux increases monotonically with liquid load and is approximately linear over the tested range. This behavior is consistent with increased wetted area and enhanced interfacial renewal at higher liquid load, which increases the overall mass transfer rate. Porosity also influences flux. The tilted contours indicate that, at a fixed liquid load, reducing porosity increases flux and provides a consistent gain across the full load range.

Across the parameter space, VCKC maintains the highest flux among the three Kelvin cell variants. The high-flux region is most pronounced at low porosity and high liquid load. For example, within the tested range, the peak flux of VCKC is about 0.46 mol/(m²·h), which exceeds RKC and VEKC, and is about 3.5 times that of VEKC. This difference indicates that axial compression increases the effective interfacial area per unit volume and raises the attainable flux. Therefore, within the present conditions, combining low-porosity VCKC with higher liquid load yields higher flux when maximizing flux per cross-sectional area, while design constraints such as pressure drop and flooding should also be considered.

5. Conclusions

Onboard carbon capture systems face strict spatial constraints, making compact and adaptable packing designs a necessity. Kelvin cells with axially stretched or compressed geometries are potential candidates to fit these limited envelopes, but their effective application relies on clarifying the influence of axial shape variation on flow and mass transfer. To achieve this, it is essential to investigate the micro-scale mechanisms that govern their performance, which are often difficult to capture in macroscopic experiments. This study uses computational fluid dynamics with a level-set approach and a continuous species transfer model to examine gas–liquid two-phase flow and CO₂ mass transfer in the regular Kelvin cell (RKC), the vertically elongated Kelvin cell (VEKC), and the vertically compressed Kelvin cell (VCKC). Based on the simulation results, the following conclusions were drawn:

• Axial stretching or compression of the Kelvin cell alters gas–liquid phase distribution and affects mass transfer. In VCKC, horizontally oriented struts promote lateral spreading and sustain a more continuous liquid film, which increases the effective gas–liquid contact area and enhances interfacial renewal. In RKC, liquid flows along the struts with localized film accumulation, giving a mixed flow regime.
• RKC shows a nonmonotonic dependence of mass transfer efficiency on porosity with an optimal range. VEKC and VCKC show lower efficiency as porosity increases. These results indicate that higher efficiency in the axially stretched or compressed geometries requires lower porosity. Reducing cell size increases mass transfer efficiency, with a stronger sensitivity in RKC. As cell size increases, VCKC shows a smaller loss in efficiency and maintains higher mass transfer flux over the tested size range. Mass transfer flux increases with liquid load, and the increase is strongest for VCKC.
• Mass transfer performance depends on the coupled effects of porosity and liquid load. For RKC, the high-efficiency region is confined to a narrow parameter window near a porosity of about 0.8. By contrast, VCKC achieves higher flux at low porosity combined with high liquid load. It also maintains higher and more stable efficiency over a wider porosity range. These results indicate that VCKC offers advantages in high-throughput capability and robustness to operating conditions, which supports multi-parameter optimization of compact internals for shipboard carbon capture.
• VCKC provides the most favorable balance among the three Kelvin cell variants for engineering applications. Although its mass transfer efficiency is lower than that of RKC at smaller sizes, VCKC maintains a higher peak interfacial flux under the tested conditions and shows a stronger response to changes in liquid load. From a volume-constrained perspective, the higher flux together with sustained wetting coverage indicates a higher transfer rate per unit packing volume. Axial compression promotes lateral liquid spreading and sustains a more continuous interface, which may reduce the sensitivity of wetting coverage to liquid redistribution induced by ship motion. Therefore, VCKC is a candidate geometry for marine packing design, and its mass transfer performance increases with increasing liquid load.

Overall, the results demonstrate that using axially stretched or compressed Kelvin-cell geometries provides a feasible approach to control fluid flow and mass transfer within packings and provides a basis for the customized design of compact, high-efficiency marine packings for shipboard CCUS facilities.

This study was conducted under isothermal conditions at 298 K to establish a consistent computational baseline with identical boundary conditions and material properties for all geometries. This framework enables a clearer identification of the influence of geometric configuration on interfacial mass transfer performance and improves the consistency and reproducibility of the comparison. However, CO₂ absorption into MEA is an exothermic process, and local temperature rises may occur near the gas–liquid interface. Such temperature variations can affect reaction kinetics, gas–liquid equilibrium relationships, and key transport properties, including viscosity, density, and the diffusion coefficient. They may also induce interfacial flow and mixing through surface tension gradients under certain conditions. In future work, the present level-set-CST pore-scale framework will be extended by coupling the energy equation and the heat release associated with the absorption reaction. The extended model will incorporate temperature-dependent kinetics, equilibrium relationships, transport properties, and surface tension, so that the influence of non-isothermal effects can be quantified more rigorously. This extension will provide a stronger basis for thermal management and structural optimization under realistic engineering conditions.