Hollow Fiber Membrane Contactors for Post-Combustion Carbon Capture: A Review of Modeling Approaches

Abstract

Hollow fiber membrane contactors (HFMCs) can effectively separate CO2 from post-combustion flue gas by providing a high contact surface area between the flue gas and a liquid solvent. Accurate models of carbon capture HFMCs are necessary to understand the underlying transport processes and optimize HFMC designs. There are various methods for modeling HFMCs in 1D, 2D, or 3D. These methods include (but are not limited to): resistance-in-series, solution-diffusion, pore flow, Happel's free surface model, and porous media modeling. This review paper discusses the state-of-the-art methods for modeling carbon capture HFMCs in 1D, 2D, and 3D. State-of-the-art 1D, 2D, and 3D carbon capture HFMC models are then compared in depth, based on their underlying assumptions. Numerical methods are also discussed, along with modeling to scale up HFMCs from the lab scale to the commercial scale.

Keywords: carbon capture membrane modeling; hollow fiber membrane contactor modeling; post-combustion carbon capture.

Figure 1

Illustration of flow patterns of a gas-liquid HFMC for post-combustion carbon capture (PCC) (a) counter-current flow, (b) cross-flow, and (c) co-current flow.

Figure 2

Graphic of the one-dimensional modeling framework for a gas-liquid HFMC. The radial dimension is the one dimension of interest; variations in the axial and angular dimensions are not taken into account. Liquid solvent flows through the inside or ”tube-side” of the fiber, while flue gas flows outside or on the ”shell-side” of the fiber.

Figure 3

A resistance-in-series (RIS) illustration for CO${}_2$ crossing a membrane in a HFMC. There are mass transfer resistances associated with the gas phase, the membrane, and the liquid phase. Each resistance can be expressed as the inverse of the mass transfer coefficient for that phase. The layers included to accomplish this analysis are the gas, gas film, membrane, liquid film, and liquid.

Figure 4

A resistance-in-series illustration for CO${}_2$ crossing a membrane in a HFMC with partial membrane wetting, where both liquid and gas fill the membrane pores.

Figure 5

Graphical depiction of the solution-diffusion three-step process in a carbon capture HFMC for gas mixture of molecule A and B: 1. Molecule A sorption at the gas-membrane interface, 2. Molecule A diffusion through the membrane, and 3. Molecule A desorption at the solvent-membrane interface. The permeants are separated because of the differences in the solubilities and the variations in the diffusive rates of the different flue gas species in the membrane [92,93].

Figure 6

Graphical depiction of the pore flow model, where molecule A crosses the membrane due to a pressure difference. The illustration is not drawn to scale to emphasize the flow through permanent pores [70,94].

Figure 7

Graphic of the two-dimensional axisymmetrical modeling framework for a gas-liquid HFMC. The axial and radial dimensions are the dimensions of interest; variations in the angular dimension are not considered due to symmetry. In this graphic, solvent flows on the tube-side, while flue gas flows counter-flow on the shell-side.

Figure 8

Velocity profiles in a counter-flow, gas-liquid HFMC. The liquid flows on the tube-side, entering at $z=L$, and the gas enters the shell-side at $z=0$. This 2D-axisymmetric model resolves properties in a 2D cross-section (left), then revolves those results around the z-axis to form a 3D plot (right). These images were produced using COMSOL Multiphysics 5.5.${}^{\circledR }$).

Figure 9

Graphic of the three-dimensional modeling framework for a gas-liquid HFMC. Axial (z), radial (r), and tangential ($\theta$) variations are all resolved. In this graphic, solvent flows on the tube-side while flue gas flows on the shell-side.

Figure 10

The road map is separated based on three defining questions: (1) Is the modeler taking into account 1D model assumptions? (2) Does the modeler have access to the mass transfer coefficient values? (3) Does the modeler have computational or time constraints? Depending on those qualifications, 1D, 2D, or 3D models can be chosen. Each modeling approach previously described for 1D, 2D, and 3D models provide specific end goal phenomena to be described. These goals for 1D models shown here are solving for the equivalent circuit analysis (eq. circ. analysis), the wetting effects, and CO${}_2$ flux removal. Depending on the overall goal, the RIS, solution-diffusion or pore flow model could be used. For 2D axisymmetric/3D single fiber models, the end goal could consist of observing the absorption reaction rate, the wetting effects and overall velocity and CO${}_2$ concentration profiles. The mass, momentum and energy equations could be coupled to recover the velocity and concentration profiles in all three domains (tube, membrane, and shell domains). Finally, 3D models observe the overall bundle of the HFMC. If the final goal is to determine detailed fluid and concentration distributions within the bundle, the mass, momentum and energy equations should be used for more accurate results. However, if the overall goal is to observe the CO${}_2$ flux rate, the porous media approach should work just as well.

Figure 11

Graphic of a conventional CO${}_2$ capture process using HFMC modules in the absorber. The blue represents the absorption process, and the orange represents the stripped portion of the system.