Computational Fluid Dynamics Modeling of Sweep Gas Flow Rate-Dependent Carbon Dioxide Removal in Oxygenators

Abstract

Computational fluid dynamics (CFD) models have been widely used to evaluate the hydrodynamic and gas exchange performances of oxygenators, which are crucial in supporting patients with lung diseases or failure. However, while CFD models have been effective in analyzing oxygen transfer, they have not adequately addressed the experimentally demonstrated effects of varying sweep gas flow rates on CO₂ removal. This is a critical gap, as sweep gas flow directly influences the CO₂ transfer efficiency in oxygenators. To fill this gap, we extend our previously developed 1D mathematical model into a 3D computational framework to predict both blood pressure drops and the rates of oxygen and CO₂ transfers in oxygenators. The comparison between our model predictions and experimental data validates the model’s capability in capturing the overall trends in CO₂ transfer/removal rates under different sweep gas flow rates. The results also demonstrated that our model can predict CO₂ removal more accurately, particularly in scenarios where adjusting the sweep gas flow rate is essential for optimizing the oxygenator performance.

1. Introduction

Lung disease continues to be a leading cause of death globally, affecting millions each year and resulting in significant annual mortality [1]. Blood oxygenators or artificial lungs are commonly used to support patients with lung disease or failure [2,3,4]. In the past two decades, significant research has focused on developing highly efficient, compact artificial lungs for both short-term and long-term support or as a bridge to transplantation [2,5,6,7]. The core component of modern blood oxygenators is the microporous hollow fiber membrane (HFM), which facilitates the gas exchange between blood and gas. These HFMs consist of hundreds or thousands of small hollow fibers. In most configurations, blood flows around the outside of the fibers, while sweep gas (typically pure oxygen) flows inside the fiber lumens. Due to the concentration gradients of oxygen (O₂) and carbon dioxide (CO₂) between the blood and the sweep gas, O₂ diffuses from the fiber wall into the blood while CO₂ diffuses from the blood into the fiber lumen. The performance of an HFM bundle is influenced by various factors, including the fiber material, the surface area of the fibers in contact with the blood and the contact time.

Computational fluid dynamics (CFD)-based models have been widely developed and implemented to analyze gas transfer in HFM bundles within oxygenators, enabling virtual prototyping that may reduce design costs. It also provides detailed insight into hemodynamic performance, unfavorable flow characteristics, regions with high shear stresses and shear-induced blood damage in most blood-contacting medical devices [8,9,10,11]. In CFD modeling, the HFM bundle is typically simplified as a homogeneous porous medium to numerically solve for the blood flow and gas transfer within the fiber bundles. Over the past decades, HFM bundles with various configurations have been extensively studied for their gas transfer performance using CFD methods. For example, Hormes et al. [12] modified a CFD model to predict both oxygen and carbon dioxide transfers in a custom-designed micromembrane oxygenator with a highly reproducible fiber arrangement and bundle geometry; Asiltürk et al. [13] evaluated the maximum gas transfer performance of microfluidic artificial lungs with fiber bundles arranged in varying column-to-row aspect ratios; Wu et al. [7,14] studied the gas transfer performances of flat and cylindrical oxygenators for both pediatric and adult applications; Barbian et al. [15] investigated the gas transfer of the oxygenator fiber membrane with triply periodic minimal surfaces; Focke et al. [16] studied the influence of the membrane fiber arrangement on gas exchange; Li et al. [17] examined the effects of clinical modalities and oxygenator configurations on oxygen transfer efficiency; and Tang et al. [18], from a different perspective, used a CFD model to study the influence of pulsatile blood flow on oxygen transport in oxygenators. Among these studies, most focused solely on oxygen transfer, and only a few considered both oxygen and carbon dioxide exchange. However, none accounted for the effect of the sweep gas flow rate on carbon dioxide removal—despite this phenomenon being reported in both experimental [2] and clinical studies [19].

Although the sweep gas flow rate—or its ratio to the blood flow rate—has been shown to have no impact on oxygen transfer, it does influence carbon dioxide removal [2,20]. To account for this effect, several 1D mathematical models [3,21] and a 2D simulation tool [20] have been developed. However, to the best knowledge of the authors, there is no reported 3D CFD model considering this effect when modeling carbon dioxide removal in oxygenators. Therefore, there is a need for a validated CFD model that includes this effect to enable a more accurate prediction of carbon dioxide removal.

This study aims to address this gap by extending a previously developed mathematical model into a 3D CFD framework that integrates the blood pressure drop across the device, oxygen transport and carbon dioxide removal while accounting for the sweep gas effect. The specific aims include the following:

• Develop a theoretical model that incorporates the blood pressure drop and gas transfer influenced by sweep gas flow rates;
• Implement the theoretical model into a CFD framework and validate it by comparing model predictions with experimental data;
• Apply the validated CFD model to investigate carbon dioxide removal in oxygenators under varying sweep gas flow rates.

2. Materials and Methods

2.1. Theory Formulation

2.1.1. Transfer of Oxygen

This study adopts the oxygen transfer model presented in [14], and a brief overview of its key components is provided here. Readers are referred to [14] for a detailed derivation. The model originated from the consideration of a mass balance law where the oxygen change within a blood control volume is contributed by oxygen diffusion in blood, oxygen convection due to blood flow, oxygen delivery from the gas phase and the exchange between the hemoglobin-bound and free (dissolved) oxygen in blood. The partial pressure of oxygen (${\mathrm{P}}_{{\mathrm{O}}_2}$) in blood can be considered as the measure of the concentration of mass species (${\mathrm{O}}_2$), and its spatial change under a steady-state condition is governed by

$$\mathbf{v}\cdot \mathsf{\alpha }\nabla {\mathrm{P}}_{{\mathrm{O}}_2}=\mathsf{\alpha }{\mathrm{D}}_{\mathrm{e}\mathrm{f}\mathrm{f}}\cdot {\nabla }^2{\mathrm{P}}_{{\mathrm{O}}_2}+{\displaystyle \frac{{\mathrm{k}}_{\mathrm{p}}\mathrm{A}({\mathrm{P}}_{{\mathrm{O}}_2}^{\mathrm{g}}-{\mathrm{P}}_{{\mathrm{O}}_2})}{1+\mathsf{\lambda }\left({\mathrm{P}}_{{\mathrm{O}}_2}\right)}}$$

(1)

where $\mathbf{v}$ is the blood flow velocity, and $\mathsf{\alpha }$ is O₂ solubility in blood. ${\mathrm{D}}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ is the effective diffusivity of O₂ proposed initially by Vaslef et al. [22] to account for the O₂ attached to the hemoglobin in blood and it has the following expression

$${\mathrm{D}}_{\mathrm{e}\mathrm{f}\mathrm{f}}={\displaystyle \frac{\mathsf{\alpha }\mathrm{D}}{\mathsf{\alpha }+{\mathrm{C}}_{\mathrm{h}}{\mathrm{S}}^{\mathrm{\prime }}\left({\mathrm{P}}_{{\mathrm{O}}_2}\right)}}$$

(2)

where ${\mathrm{C}}_{\mathrm{h}}$ is the concentration of hemoglobin in blood. $\mathrm{D}$ is the O₂ diffusivity in the region of hollow fiber membrane which is modeled as a continuum porous medium, and it is defined as $\mathrm{D}=\mathsf{\epsilon }{\mathrm{D}}_{\mathrm{b}}$ where $\mathsf{\epsilon }$ is the porosity of the membrane and ${\mathrm{D}}_{\mathrm{b}}$ is the O₂ diffusivity in blood. ${\mathrm{S}}^{\mathrm{\prime }}\left({\mathrm{P}}_{{\mathrm{O}}_2}\right)$ is the slope of the oxygen association curve reflecting the relationship between hemoglobin-bound O₂ saturation and O₂ partial pressure, which can be described using Hill equation [23]:

$${\mathrm{S}}^{\mathrm{\prime }}\left({\mathrm{P}}_{{\mathrm{O}}_2}\right)={\displaystyle \frac{\mathrm{n}({\mathrm{P}}_{50}{)}^{\mathrm{n}}{\mathrm{P}}_{{\mathrm{O}}_2}^{\mathrm{n}-1}}{{\left({\mathrm{P}}_{50}^{\mathrm{n}}+{\mathrm{P}}_{{\mathrm{O}}_2}^{\mathrm{n}}\right)}^2}}$$

(3)

where P₅₀ is the oxygen partial pressure corresponding to the 50% O₂–hemoglobin saturation at the oxygen association curve and n is an empirical constant. The values of P₅₀ and n can be determined by fitting Equation (3) to the experimentally measured data from specific blood samples. In Equation (1), $\mathrm{A}$ is the hollow fiber membrane surface area used in oxygenators, and ${\mathrm{P}}_{{\mathrm{O}}_2}^{\mathrm{g}}$ is partial pressure of O₂ in the sweep gas flowing through fiber lumens. ${\mathrm{P}}_{{\mathrm{O}}_2}^{\mathrm{g}}$ is assumed to remain constant along the longitudinal axis of the fiber lumen. ${\mathrm{k}}_{\mathrm{p}}$ is the shell-side mass transport coefficient governing the speed of O₂ transferring from the gas phase to blood phase through the hollow fiber membrane wall. The equation of ${\mathrm{k}}_{\mathrm{p}}$ is given by Hewitt et al. [24].

$${\mathrm{k}}_{\mathrm{p}}=\mathrm{a}\mathsf{\alpha }{\mathrm{d}}_{\mathrm{h}}^{-1}{\mathrm{D}}^{2/3}{\mathsf{\nu }}^{1/3}\mathrm{R}{\mathrm{e}}^{\mathrm{b}}$$

(4)

where $\mathrm{a}$ and $\mathrm{b}$ are two empirical constants, and $\mathsf{\nu }$ is the dynamic viscosity of the blood. $\mathrm{R}\mathrm{e}$ is the Reynolds number defined as $\mathrm{R}\mathrm{e}={\mathrm{V}}_{\mathrm{i}}{\mathrm{d}}_{\mathrm{h}}/\mathrm{v}$ where ${\mathrm{V}}_{\mathrm{i}}$ is the interstitial velocity magnitude of the blood volume in the region of hollow fiber membrane. Depending on the porosity of fiber bundle, the effective fiber diameter ${\mathrm{d}}_{\mathrm{h}}$ can be either ${\mathrm{d}}_{\mathrm{h}}=\mathrm{d}$ when $\mathsf{\epsilon }>0.5$ or ${\mathrm{d}}_{\mathrm{h}}=\mathsf{\epsilon }\mathrm{d}/(1-\mathsf{\epsilon })$ when $\mathsf{\epsilon }\le 0.5$. $\mathrm{d}$ is the diameter of a single fiber as the basic unit of the hollow fiber membrane.

2.1.2. Carbon Dioxide Removal

Carbon dioxide is transported from tissues to the lungs in three primary ways: it dissolves directly in plasma, binds to hemoglobin and forms bicarbonate ions in plasma. The majority of carbon dioxide in the blood is carried as bicarbonate. The CO₂ removal model is adapted from [21,25], and its 1D mathematical forms were also presented in our previous works [3]. Here, we extend this model for 3D fluid dynamics simulation. The effective diffusivity (${\overline{\mathrm{D}}}_{\mathrm{e}\mathrm{f}\mathrm{f}}$) of CO₂ in blood has a similar form to O₂ case but with more mechanisms in it, as described by

$${\overline{D}}_{\mathrm{e}\mathrm{f}\mathrm{f}}={\displaystyle \frac{D_{{\mathrm{C}\mathrm{O}}_2}+\frac{D_{{\mathrm{H}\mathrm{C}\mathrm{O}}_3}}{{\alpha }_{{\mathrm{C}\mathrm{O}}_2}}{\lambda }_{{\mathrm{C}\mathrm{O}}_2}}{1+\frac{1}{{\alpha }_{{\mathrm{C}\mathrm{O}}_2}}{\lambda }_{{\mathrm{C}\mathrm{O}}_2}}}$$

(5)

where $D_{{\mathrm{C}\mathrm{O}}_2}$ and $D_{{\mathrm{H}\mathrm{C}\mathrm{O}}_3}$ are the diffusivities of dissolved carbon dioxide and bicarbonate ions in blood, respectively. ${\alpha }_{{\mathrm{C}\mathrm{O}}_2}$ represents carbon dioxide solubility in blood. ${\lambda }_{{\mathrm{C}\mathrm{O}}_2}$ is the change in bicarbonate ion concentration with respect to the change in carbon dioxide partial pressure, which can be approximated by the slope of the carbon dioxide dissociation curve (carbon dioxide concentration versus carbon dioxide partial pressure) due to the large amount (90%) of bicarbonate ion relative to the total carbon dioxide. On a pressure range of 20–50 mmHg, the slope (${\lambda }_{{\mathrm{C}\mathrm{O}}_2}$) of the carbon dioxide dissociation curve can be fitted by using the following equation

$${\lambda }_{{\mathrm{C}\mathrm{O}}_2}=qt{P}_{{\mathrm{C}\mathrm{O}}_2}^{t-1}$$

(6)

where $P_{{\mathrm{C}\mathrm{O}}_2}$ is the CO₂ partial pressure, and $q$ and $t$ are two empirical constants. The mass transfer coefficient $k_{{\mathrm{C}\mathrm{O}}_2}$ for CO₂ in blood is adapted from [25]

$$\begin{array}{c}{k}_{{\mathrm{C}\mathrm{O}}_2}=c{\alpha }_{{\mathrm{C}\mathrm{O}}_2}{d}_{\mathrm{h}}^{d-1}{{\mathrm{V}}_{\mathrm{i}}}^d{\left(D_{{\mathrm{C}\mathrm{O}}_2}+{\displaystyle \frac{D_{{\mathrm{H}\mathrm{C}\mathrm{O}}_3}}{{\alpha }_{{\mathrm{C}\mathrm{O}}_2}}}{\lambda }_{{\mathrm{C}\mathrm{O}}_2}\right)}^{2/3}\\ {\left(1+{\displaystyle \frac{1}{{\alpha }_{{\mathrm{C}\mathrm{O}}_2}}}{\lambda }_{{\mathrm{C}\mathrm{O}}_2}\right)}^{1/3}{\nu }^{1/3-d}\end{array}$$

(7)

where c and d are two empirical constants.

2.1.3. Effects of Sweep Gas Rate

It was shown from [20] that the sweep gas flow rate has few effects on O₂ exchange in oxygenators. Therefore, in this study, we only consider the sweep gas flow rate effect on CO₂ removal. Previous works [21,26] have reported that adjusting the sweep gas flow rate will affect the concentration gradient of CO₂ in membrane oxygenator. More specifically, a higher sweep gas flow rate decreases CO₂ buildup along the sweep gas pathway [27]. As a result, the partial pressure ($P_{{\mathrm{C}\mathrm{O}}_2}$) of CO₂ in the sweep gas will not be constant along the gas pathway. In our previous work [3], the distribution of $P_{{\mathrm{C}\mathrm{O}}_2}$ along the long axis of the fiber lumen was derived to have the following form as

$${\overline{\mathrm{P}}}_{{\mathrm{C}\mathrm{O}}_2}^{\mathrm{g}}={\displaystyle \frac{{\mathrm{P}}_{\mathrm{a}\mathrm{t}}{\mathrm{D}}_{{\mathrm{C}\mathrm{O}}_2}{\mathrm{P}}_{{\mathrm{C}\mathrm{O}}_2}}{{\mathrm{Q}}_{\mathrm{g}}+{\mathrm{P}}_{\mathrm{a}\mathrm{t}}{\mathrm{D}}_{{\mathrm{C}\mathrm{O}}_2}}}+\mathrm{C}{\mathrm{e}}^{-{\displaystyle \frac{\left({\mathrm{Q}}_{\mathrm{g}}+{\mathrm{P}}_{\mathrm{a}\mathrm{t}}{\mathrm{D}}_{{\mathrm{C}\mathrm{O}}_2}\right)}{{\mathrm{Q}}_{\mathrm{g}}\mathrm{H}}}\mathrm{y}}$$

(8)

where ${\mathrm{P}}_{\mathrm{a}\mathrm{t}}$ and ${\mathrm{Q}}_{\mathrm{g}}$ are the atmospheric pressure and sweep gas flow rate, respectively. $\mathrm{H}$ is the length of the individual fiber, assuming axis y is along the long axis of the individual fiber and $\mathrm{y}$ denotes the location of any point at the fiber. $\mathrm{C}$ is an arbitrary constant and it can be determined using the boundary condition of pure oxygen sweep gas at the inlet (${\overline{\mathrm{P}}}_{{\mathrm{C}\mathrm{O}}_2}^{\mathrm{g}}=0$ at $\mathrm{y}=0$). An updated Equation (8) can be then obtained as

$${\overline{\mathrm{P}}}_{{\mathrm{C}\mathrm{O}}_2}^{\mathrm{g}}={\displaystyle \frac{{\mathrm{P}}_{\mathrm{a}\mathrm{t}}{\mathrm{D}}_{{\mathrm{C}\mathrm{O}}_2}{\mathrm{P}}_{{\mathrm{C}\mathrm{O}}_2}}{{\mathrm{Q}}_{\mathrm{g}}+{\mathrm{P}}_{\mathrm{a}\mathrm{t}}{\mathrm{D}}_{{\mathrm{C}\mathrm{O}}_2}}}-{\displaystyle \frac{{\mathrm{P}}_{\mathrm{a}\mathrm{t}}{\mathrm{D}}_{{\mathrm{C}\mathrm{O}}_2}{\mathrm{P}}_{{\mathrm{C}\mathrm{O}}_2}}{{\mathrm{Q}}_{\mathrm{g}}+{\mathrm{P}}_{\mathrm{a}\mathrm{t}}{\mathrm{D}}_{{\mathrm{C}\mathrm{O}}_2}}}{\mathrm{e}}^{-{\displaystyle \frac{({\mathrm{Q}}_{\mathrm{g}}+{\mathrm{P}}_{\mathrm{a}\mathrm{t}}{\mathrm{D}}_{{\mathrm{C}\mathrm{O}}_2})}{{\mathrm{Q}}_{\mathrm{g}}\mathrm{H}}}\mathrm{y}}$$

(9)

In the 3D computational modeling of gas exchange, we use the average value of ${\overline{\mathrm{P}}}_{{\mathrm{C}\mathrm{O}}_2}^{\mathrm{g}}$ over the fiber length as

$$P_{{\mathrm{C}\mathrm{O}}_2}^{\mathrm{f}}={\displaystyle \frac{\delta }{H}}{\int }_0^H {\overline{P}}_{{\mathrm{C}\mathrm{O}}_{2}s}^{\mathrm{f}}dy={\displaystyle \frac{P_{\mathrm{a}\mathrm{t}}{\overline{D}}_{{\mathrm{C}\mathrm{O}}_2}{P}_{{\mathrm{C}\mathrm{O}}_2}}{Q_{\mathrm{g}}+P_{\mathrm{a}\mathrm{t}}{\overline{D}}_{{\mathrm{C}\mathrm{O}}_2}}}\left[1+{\displaystyle \frac{e^{-\frac{\left(Q_{\mathrm{g}}+P_{\mathrm{a}\mathrm{t}}{\overline{D}}_{{\mathrm{C}\mathrm{O}}_2}\right)}{Q_{\mathrm{g}}}}-1}{1+P_{\mathrm{a}\mathrm{t}}{\overline{D}}_{{\mathrm{C}\mathrm{O}}_2}/Q_{\mathrm{g}}}}\right]$$

(10)

where $\delta$ is a scaling factor that amplifies or reduces the effect of the sweep gas rate on the CO₂ partial pressure in fiber lumens. This scaling parameter is motivated by [14], in which the authors suggested modifying or adding parameters to capture the effects of fiber type, fiber coating, fiber arrangement and other factors on gas transfer. We assume these factors also influence how the sweep gas rate affects the CO₂ partial pressure within the fiber lumens. The scaling parameter is important because it allows us to adjust the model—e.g., by assigning a different value when a different fiber type is used—to reflect these effects.

2.1.4. Blood Flow and Pressure Drop

The blood motion passing through the hollow fiber bundle (or membrane) is governed by the standard Navier–Stokes equation [28]. To theoretically describe the blood pressure drop across hollow fibers, the whole fiber bundle (or membrane) is considered as a continuum porous medium, and the classical Ergun equation is adopted. This equation assumes that the total energy or pressure losses for the fluid flowing through porous media can be attributed to the sum of viscous/permeability loss and kinetic/inertial loss (due to the flow separation and streamline direction change behind each fiber), and it has a 1D expression form as

$${\displaystyle \frac{dP}{dx}}={\displaystyle \frac{150\mathsf{\nu }{\left(1-\mathsf{\epsilon }\right)}^2 }{d^2{\mathsf{\epsilon }}^3}}{\mathrm{V}}_{\mathrm{S}}+{\displaystyle \frac{1.75\rho \left(1-\mathsf{\epsilon }\right)}{d{\mathsf{\epsilon }}^3}}{\mathrm{V}}_{\mathrm{S}}^2$$

(11)

where $P$ is the blood pressure, and ${\displaystyle \frac{dP}{dx}}$ represents its change along a specific direction. ${\mathrm{V}}_{\mathrm{S}}$ and $\rho$ are the superficial velocity and mass density of the blood, respectively.

2.2. Simulation Setup

2.2.1. Model Implementation

The theoretical models described in the last section were implemented into commercial computational fluid dynamics (CFD) package (Fluent 2023 R2, ANSYS, Inc, Canosburg, PA) for 3D device simulations. Specifically, for O₂ and CO₂ transfer models, we wrote C++ codes to implement them via user-defined functions (UDFs). To validate the developed models discussed in Section 2.1, we reconstructed a 3D oxygenator geometry (its detailed dimension is shown in Figure 1) from [2] based on the provided dimension and also due to the available experimental data of the O₂ and CO₂ transfer rates corresponding to that device. As shown in Figure 2, this device features two cylindrical fiber bundles and the computational fluid domain for it included the inlet, outlet, two flow chambers containing two cylindrical fiber beds and one fluid domain connecting the two chambers. It should be noted that because the detailed dimension of the volute (inlet part) of the device in the reference [2] was not given, we made an estimation of its size when reconstructing the 3D model. However, because the gas transfer performances of the device are primarily determined by the fiber bundles, we hypothesize that the small difference in the volute sizes will not have a significant effect on the simulation results. This assumption is supported by simulation results from our previous work, which showed that significant changes in gas transfer (e.g., oxygen transfer) occurred only within the fiber bundle region [7]. More details of the device we modeled are described in [2].

As for the boundary condition, constant mass flow rate and zero pressure were specified at the oxygenator inlet and outlet, respectively. Using UDFs, constant O₂ and CO₂ partial pressures of 45 mmHg were also applied at the device inlet. The walls of the device were assumed to be rigid and no-slip. The blood used for model demonstration was considered as an incompressible Newtonian fluid with the density of 1050 kg/m³ and viscosity of 0.0035 kg/m∙s [14]. The Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) pressure–velocity coupling scheme with second order accuracy was used to solve all fluid governing equations. The Menter’s Shear Stress Transport (SST) k–ω model was used to model the fluid turbulence in the device. The fiber bundle (blood, fiber walls and gas phase) was modeled as one lumped continuum (porous medium) in our simulation, and the hydrodynamic behaviors (e.g., pressure drop) of the fluid flowing across the fiber bundle were modeled using Ergun equation given in Equation (11). Experimentally measured pressure difference between the device inlet and outlet with blood was used to verify this estimation.

We used a two-step simulation procedure, which can be summarized as follows: The Ansys-Fluent setup was first used to solve the steady-state Navier–Stokes equations with a k–ω turbulence model to obtain the velocity and turbulence fields across the entire domain, including the porous media region. Once the flow field solution converged, we proceeded to solve the mass transport equations using UDFs implemented only within the porous region. The UDFs included source terms to model oxygen and carbon dioxide exchange across the membrane and used the previously computed steady-state velocity and turbulence fields as inputs—without re-solving the flow equations. This sequential approach effectively captures the influence of flow dynamics on gas transfer, while maintaining transport models that are governed primarily by molecular and facilitated diffusion, which is appropriate given the low turbulence (turbulent mixing is negligible) within the membrane domain [29].

2.2.2. Mesh Sensitivity Study

The mesh sensitivity verification is shown in Figure 3. Because this numerical study is focused on the carbon dioxide (CO₂) removal performance of the oxygenator, the CO₂ transfer rate of the oxygenator (constant CO₂ partial pressure of 45 mmHg at the device inlet) was computed for various mesh sizes. The results indicated that when the mesh element count is below 3 million, the predicted CO₂ transfer rate shows significant variations, resulting in low accuracy and consistency. However, for mesh sizes exceeding 5~7 million elements, the variations become minimal and stabilize. Therefore, to balance accuracy and computational efficiency and also to be consistent with the number of meshes used in [2], a mesh size of around 7 million linear-order elements was chosen for the subsequent calculations. We adopted a multistep meshing process for the entire geometry to ensure high mesh quality. The volute, outer fiber bundle, inner fiber bundle, inner fluid domain, outlet and inlet of the oxygenator (these different regions are labeled in Figure 1) were meshed sequentially using a combination of linear hybrid elements: 4-node tetrahedral (Tet4), 6-node wedge (Wed6) and 5-node pyramid (Pyr5) elements. The maximum mesh aspect ratio and skewness were 23.6 and 0.9, respectively, while the minimum orthogonal quality was 0.1. To better resolve velocity gradients near the fluid–wall interfaces, 5-layer inflation meshes were applied during the meshing process (Figure 2b). Figure 4 shows the turbulence intensity and flow velocity contours of the oxygenator, meshed with 7 million elements and simulated at a blood flow rate of 6 L/min.

2.2.3. Model Validation

To verify the prediction reliability of the CFD model developed in this study for simulating hydrodynamic and gas transfer performances of oxygenators, experimental data from Han et al. [2] regarding the blood pressure drop, O₂ transfer rate and CO₂ transfer rate at different blood flow rates were used for comparison. Particularly, we will demonstrate the model’s capability of predicting sweep gas rate-dependent CO₂ removal/transfer performances of the 3D oxygenator device, which was not reported in previous modeling works. The O₂ transfer rate (${\dot{\mathrm{m}}}_{\mathrm{O}2}$) of the device is calculated based on the O₂ partial pressure and saturation at the inlet and outlet of the device as [30]

$${\dot{\mathrm{m}}}_{\mathrm{o}2}=\left[13.4\times {\mathrm{C}}_{\mathrm{h}}\times \left({\mathrm{S}}_{\mathrm{o}2}^{\mathrm{o}\mathrm{u}\mathrm{t}}-{\mathrm{S}}_{\mathrm{o}2}^{\mathrm{i}\mathrm{n}}\right)+\mathsf{\alpha }\times {10}^3\times \left({\mathrm{P}}_{\mathrm{o}2}^{\mathrm{o}\mathrm{u}\mathrm{t}}-{\mathrm{P}}_{\mathrm{o}2}^{\mathrm{i}\mathrm{n}}\right)\right]{\mathrm{Q}}_{\mathrm{b}}$$

(12)

where ${\mathrm{C}}_{\mathrm{h}}$ is the hemoglobin concentration; ${\mathrm{S}}_{\mathrm{o}2}^{\mathrm{o}\mathrm{u}\mathrm{t}}$ and ${\mathrm{S}}_{\mathrm{o}2}^{\mathrm{i}\mathrm{n}}$ are the O₂ saturation at the outlet and inlet of the device, respectively; ${\mathrm{P}}_{\mathrm{o}2}^{\mathrm{o}\mathrm{u}\mathrm{t}}$ and ${\mathrm{P}}_{\mathrm{o}2}^{\mathrm{i}\mathrm{n}}$, respectively, represent the O₂ partial pressure predicted at the device outlet and inlet; and ${\mathrm{Q}}_{\mathrm{b}}$ is the volumetric blood flow rate. The detailed values of these parameters can be found in [14]. The CO₂ transfer rate (${\dot{\mathrm{m}}}_{\mathrm{C}\mathrm{O}2}$) is calculated based on the CO₂ concentrations at the device inlet (${\mathrm{C}}_{\mathrm{C}\mathrm{O}2}^{\mathrm{i}\mathrm{n}}$) and outlet (${\mathrm{C}}_{\mathrm{C}\mathrm{O}2}^{\mathrm{o}\mathrm{u}\mathrm{t}}$) as [2]:

$${\dot{\mathrm{m}}}_{\mathrm{C}\mathrm{O}2}=\left({\mathrm{C}}_{\mathrm{C}\mathrm{O}2}^{\mathrm{o}\mathrm{u}\mathrm{t}}-{\mathrm{C}}_{\mathrm{C}\mathrm{O}2}^{\mathrm{i}\mathrm{n}}\right){\mathrm{Q}}_{\mathrm{b}}$$

(13)

Figure 5 shows the model-predicted blood pressure drop across the oxygenator running at different blood flow rates. The simulation results agree very well with the experimental measurement even when the device geometry was not perfectly reconstructed, which also demonstrates that the classical Ergun equation (Equation(11)) is a good candidate to be used to model the fluid pressure drop across porous medium. Figure 6 shows the model-predicted oxygen (O₂) transfer rate of the device at different blood flow rates, which agree well with the experimental data. Figure 7 shows the model-predicted carbon dioxide (CO₂) removal rate of the device at different blood flow rates. While the model overestimated the absolute CO₂ transfer rates, it accurately captures the overall trend of CO2 transfer rate changes, meaning it can be used to conduct comparative studies. Figure 8 shows the predicted CO₂ transfer rates of the oxygenator at different sweep gas flow rates, which clearly demonstrate the model’s capability of predicting the sweep gas rate-dependent CO₂ transfer. The model did not capture absolute values of the experimentally measured CO₂ transfer rate, but it captures the overall trend of the CO₂ transfer rate changes when $\delta =10$ was used in the simulation. A scaling factor of 1 was chosen to represent the baseline case without accounting for any scaling effects from factors such as fiber type, coating or arrangement. We also tested values between 1 and 10 and found that a factor of 10 produces a noticeable difference compared to 1. Therefore, we selected 1 and 10 as representative values for comparison. As shown in Equation (10), the scaling factor effectively modulates the CO₂ partial pressure in the fiber lumens. A higher scaling factor results in a greater CO₂ partial pressure gradient across the fiber–blood interface, thereby increasing the CO₂ transfer rate. Figure 8 also shows that the scaling factor $\delta$ did amplify or reduce the effect of the sweep gas rate on the CO₂ transfer rate. While the model-predicted the sweep gas rate effect when the scaling factor was not used ($\delta =1$), this precited effect was relatively weak compared to the case when $\delta =10$ was used. Therefore, in the subsequent section of simulation analyses, we presented all the simulation results with $\delta =10$. The discrepancy between the simulation results and experimental data in Figure 8 may be attributed to the calculation of CO₂ partial pressure in the fiber lumens. Although Equation (10) accounts for the effect of sweep gas rate, it uses an average CO₂ partial pressure along the fiber length, despite it being non-uniform. A more accurate prediction could be achieved through mesoscale simulations that incorporate the spatial variation in CO₂ partial pressure directly. However, such models are computationally too expensive for simulating the entire device. Because this study is mainly focused on the CO₂ transfer/removal performances of the oxygenator, we only present CO₂-related simulation results.

3. Analysis of Simulation Results

3.1. CO₂ Patial Pressure Under Different Sweep Gas Rate

Figure 9 shows the CFD-simulated CO₂ partial pressure (P_CO2) distribution within the oxygenator at different sweep gas flow rates of 3 L/min, 6 L/min, 9 L/min and 12 L/min. Specifically, the sweep gas rate is related to the volumetric flow rates of air provided in the outer fiber bundle, while the flow rates of oxygen provided in the inner fiber bundle remained as a constant rate of 3 L/min [2]. The P_CO2 was set to have the same value of 45 mmHg at the device inlet but varied at the device outlet due to different sweep gas flow rates used. From Figure 9, the P_CO2 decreases when the blood flows from the device inlet to outlet, meaning that the oxygenator is functioning well and has successfully removed the CO₂ from the blood entering the device. A uniform P_CO2 gradient can also be found in the region of the inner fiber bundle, meaning that the device provides a stable CO₂ removal. In addition, it can also be found that the P_CO2 at the device outlet decreases from 38.4 mmHg to 36 mmHg, 35.2 mmHg and 34.8 mmHg when the sweep gas flow rate increases from 3 L/min to 6 L/min, 9 L/min and 12 L/min, which demonstrates that increasing the sweep gas flow rate can allow the oxygenator to remove more CO₂. This simulation finding is consistent with experimental and clinical measurements [2,19].

3.2. CO₂ Concentration Under Different Sweep Gas Rate

Figure 9 also shows the simulated CO₂ concentration distribution within the oxygenator at different sweep gas flow rates. The relationship between the CO₂ concentration and CO₂ partial pressure (P_CO2) can be represented by an exponential function [3], where the CO₂ concentration is increasing exponentially as the P_CO2 increases. Similarly to Figure 8, Figure 9 also shows that the CO₂ concentration decreases when the blood flows from the device inlet to outlet, meaning the oxygenator is functioning well and has successfully removed the CO₂ from the blood entering the device. A uniform CO₂ concentration gradient can also be found in the region of the inner fiber bundle, meaning the device provides a stable CO₂ removal. In addition, it can also be found that the CO₂ concentration at the device outlet decreases from 0.491 mL/mL to 0.480 mL/mL, 0.476 mL/mL and 0.474 mL/mL when the sweep gas flow rate increases from 3~L/min to 6~L/min, 9~L/min and 12~L/min. Considering that the CO₂ concentration is increasing exponentially as P_CO2 increases, the finding from Figure 9 can also demonstrate that increasing sweep gas flow rates can allow the oxygenator to remove more CO₂. Both the CO₂ concentration and P_CO2 can be used to indicate whether the oxygenator removes more or less CO₂.

3.3. Fiber Lumen CO₂ Patial Pressure Under Different Sweep Gas Rate

In order to show what is happening inside the fiber lumens that leads to the sweep gas flow rate-dependent phenomena shown in Figure 9, we directly used Equation (10) to calculate the CO₂ partial pressure within fiber lumens ($P_{{\mathrm{C}\mathrm{O}}_2}^{\mathrm{f}}$) vs. the sweep gas flow rate ($Q_{\mathrm{g}}$), and the calculation result is shown in Figure 10. The $P_{{\mathrm{C}\mathrm{O}}_2}^{\mathrm{f}}$ were normalized by dividing them by their maximum value. As the sweep gas flow rate increased, the CO₂ partial pressure within fiber lumens decreased, creating a larger P_CO2 gradient across the fiber–blood interface, which sped up the CO₂ removal rate and reduced more CO₂, as demonstrated in Figure 8.

4. Conclusions

In this study, we enhanced a previously developed mathematical model by implementing it within a three-dimensional CFD framework to predict both the blood pressure drop and gas exchange performance of oxygenators under clinically relevant flow conditions. A significant advancement of the current work is the explicit incorporation of the sweep gas flow rate as a significant factor in carbon dioxide (CO₂) removal, based on experimentally validated dependencies. Unlike prior models that often assume a constant CO₂ pressure in fiber lumens and neglect the sweep gas effect, our extended model integrates the variable of the sweep gas rate into the simulation, allowing for a more accurate representation of CO₂ exchange dynamics.

CFD predictions of CO₂ removal rates across a range of sweep gas flow rates were compared with experimental measurements, demonstrating the model’s ability to capture the correct trend and response behavior. This agreement supports the model’s utility as a predictive tool for evaluating the oxygenator performance, particularly in scenarios where sweep gas modulation is clinically necessary or operationally desirable. The inclusion of sweep gas effects not only enhances the model’s predictive accuracy but also improves its potential for use in design optimization, control strategies and individualized device tuning.

Nevertheless, the further refinement of the functional form used in Equation (10) is needed to improve the quantitative match between simulated and experimental values. Future work will focus on developing a more accurate representation of the localized CO₂ partial pressure distribution within the fiber lumens, possibly through the coupling with mesoscale or multiscale models, to further improve predictive fidelity.