Computation of Global and Local Mass Transfer in Hollow Fiber Membrane Modules

Abstract

Computational fluid dynamics (CFD) provides a flexible tool for investigation of separation processes within membrane hollow fiber modules. By enabling a three-dimensional and time dependent description of the corresponding transport phenomena, very detailed information about mass transfer or geometrical influences can be provided. The high level of detail comes with high computational costs, especially since species transport simulations must discretize and resolve steep gradients in the concentration polarization layer at the membrane. In contrast, flow simulations are not required to resolve these gradients. Hence, there is a large gap in the scale and complexity of computationally feasible geometries when comparing flow and species transport simulations. A method, which tries to cover the mentioned gap, is presented in the present article. It allows upscaling of the findings of species transport simulations, conducted for reduced geometries, on the geometrical scales of flow simulations. Consequently, total transmembrane transport of complete modules can be numerically predicted. The upscaling method does not require any empirical correlation to incorporate geometrical characteristics but solely depends on results acquired by CFD flow simulations. In the scope of this research, the proposed method is explained, conducted, and validated. This is done by the example of CO2 removal in a prototype hollow fiber membrane oxygenator.

Suitable CO2 Solubility Models for Determination of the CO2 Removal Performance of Oxygenators

“…CO 2 concentration of ingoing sweep flow was assumed zero as medical O 2 was used as sweep fluid, Equation (18). Q CO2,sweep = Q sweep × ∆c CO2, with c CO2,inlet = 0 (medical O 2 ): Q sweep × c CO2,outlet (18) Sweep flow rate (Q sweep ) was measured using a high accuracy volumetric piston stroke meter (Defender 510, Bios DryCal). According to the manufacturer, the device has a measurement error of 1% of reading.…”

“…Utilizing Equation (18) and the measured average errors (sweep flow rate: 1.3%, CO 2 concentration: 1.7%) the total error of the sweep flow-based method (Q CO2,sweep,error ) can be estimated to 3% of predicted CO 2 removal (3% of reading): Q CO2,sweep + Q CO2,sweep,error = Q sweep × 1.013 × c CO2,outlet × 1.017 = Q CO2,sweep + Q CO2,sweep × 0.03 (19) In addition to the high accuracy of the measurement devices, the sweep flow-based method has the following principal advantages over the blood-based method:…”

“…The in vivo study results displayed in this study represent a secondary analysis of previously published data. This preceding publication investigated the prediction of the CO 2 removal rate of oxygenators using CFD simulations [ 18 ]. For validation of the CFD model, the CO 2 removal predicted by CFD was compared to the CO 2 removal predicted by the sweep flow-based method.…”

“… Scheme of the in vivo test setup with prototype oxygenator, blood pump, pressure sensors (PR), flow rate sensors (FR), BGA sample ports (BG) and CO 2 concentration sensor (QR)–by Lukitsch et al [ 18 ], (CC BY 4.0). …”

In silico simulation of the liquid phase pressure drop through cylindrical hollow‐fiber membrane oxygenators using a modified phenomenological model

“…In this regard, various approaches were already presented for modeling and quantifying this phenomenon. Introducing permeability, Darcy proposed a phenomenological definitive law for liquid pressure drop through porous media 25–27 . Afterward, Carman and Kozeny developed an equation to calculate permeability, using the equivalent hydraulic diameter, tortuosity, and porosity 28,29 .…”