(380ak) Modeling and Scaling-up of Membrane Modules Leveraging Dimensional Analysis.

The efficiency of membrane modules depends on a set of interconnected design variables [1], [2]. As they scale up from lab experiments to industrial operations, accurately predicting separation performance at larger scales presents computational challenges, especially with complex high-fidelity models like Computational Fluid Dynamics (CFD) simulations [3]. As module size increases, so does the number of elements in the CFD model, leading to large computational overhead.

To tackle this issue, we employ dimensional analysis (DA), a proven method for designing full-scale processes by leveraging lab experiments and simulations across various scales or process conditions [3], [4]. DA generates dimensionless numbers from dimensional variables and simplified correlations, offering insights into the impact of design variables across the different scales [5]. These correlations serve as predictive tools, particularly useful when experimental or computational resources are limited. Additionally, DA reduces the complexity of the governing equations by pinpointing key dimensionless variables related to the physics involved [6]. This reduction in variables translates to significant efficiency gains, especially in design of experiments.

In this work, we focus on the CO₂-N₂ separation in membrane modules, which is a pertinent carbon capture application, and we develop correlations using experimental data and validated CFD simulations [7], [8]. Our findings suggest that dimensionless feed flow yields the strongest correlations to predict the separation performance.

The dimensionless feed flow (DF^feed) is defined as the ratio between the total input molar flowrate and the product of the feed pressure, the membrane area, and the permeance of the relevant component. In this way, this dimensionless number condenses relevant information about the input flowrate, the membrane size (area), and the membrane permeance. Notably, DF^feed has a relevant physical meaning for the separation process in membrane modules. Assuming ideal gas behavior, we found that the dimensionless feed flow is the ratio between the time scale of the fluid to penetrate through the membrane and the time for the fluid to exit the feed side. Therefore, a large value for DF^feed results in relatively low residence time in the membrane module and low recoveries of the relevant component. On the contrary, small values of DF^feed mean that the mass transfer through the membrane requires relatively low times, so the recovery of the relevant component is significantly large.

We apply the dimensional analysis to a carbon capture process using high-flux plate-and-frame membrane modules. To this end, we develop a Computational fluid dynamics (CFD) model for the membrane modules [1]. The input flow rate consists of a binary mixture of CO₂ and N₂ in 30/70 % ratio. The inlet flow rate enters the feed side of the module, where mass transfer through the membrane and to the permeate side takes place. As outcomes of the process, two streams are obtained, the retentate stream (outlet from the feed side) and the permeate stream (outlet from the permeate side), which is rich in CO₂ concentration.

In this approach, the CFD model provides valuable insights into the process performance under designs and operating conditions not covered in the set of experimental data. In this sense, we profit from CFD simulations to evaluate the separation performance considering different dimensions of the membrane module, input flowrate, and CO₂ permeance factors.

Using the experimental data and CFD simulations, we look for different correlations between the dimensionless numbers, which were previously identified. This overall strategy is shown in Fig. 1. We use the data to quantify the accuracy of the correlations and to make decisions on the most appropriate dimensionless numbers to describe the separation process using this membrane module.

As a result, we obtain that the stage cut could be expressed as a function of the dimensionless feed flow (DF^feed). Our observation reveals a decrease in the stage cut as the DF^feed increases. This trend is attributed to the fact that higher flow rates in a given membrane module result in a relatively low fraction of permeation flow. Furthermore, we find that the dimensionless feed flow alone (DF^feed) adequately describes the stage cut in the membrane separation process across different input flow rates, membrane scales, and CO₂ permeances. A power trendline yields an R² correlation coefficient exceeding 0.99, indicating the accuracy of the approach. Overall, we conclude that this methodology holds promise for various gas separations across different membrane modules beyond our case study.

References

[1] C. Dosso, L. Zhu, V. A. Kusuma, D. Hopkinson, L. T. Biegler, and G. Panagakos, “CFD Modeling of High-Flux Plate-and-Frame Membrane Modules for Post-Combustion Carbon Capture,” in AIChE Annual Meeting, 2023.

[2] J. R. Rivero, L. R. Nemetz, M. M. Da Conceicao, G. Lipscomb, and K. Hornbostel, “Modeling gas separation in flat sheet membrane modules: Impact of flow channel size variation,” Carbon Capture Sci. Technol., vol. 6, p. 100093, Mar. 2023.

[3] H. Khafajah, M. I. Hassan Ali, N. Thomas, I. Janajreh, and H. A. Arafat, “Utilizing Buckingham Pi theorem and multiple regression analysis in scaling up direct contact membrane distillation processes,” Desalination, vol. 528, p. 115606, 2022.

[4] G. Astarita, “Dimensional analysis, scaling, and orders of magnitude,” Chem. Eng. Sci., vol. 52, no. 24, pp. 4681–4698, 1997.

[5] B. Gu, C. S. Adjiman, and X. Y. Xu, “Correlations for Concentration Polarization and Pressure Drop in Spacer-Filled RO Membrane Modules Based on CFD Simulations,” Membranes, vol. 11, no. 5. 2021.

[6] T. Misic, M. Najdanovic-Lukic, and L. Nesic, “Dimensional analysis in physics and the Buckingham theorem,” Eur. J. Phys., vol. 31, no. 4, p. 893, 2010.

[7] L. Zhu, V. Kusuma, and D. Hopkinson, “Highly Permeable Thin-Film Composite Membranes of Rubbery Polymer Blends for CO2 Capture,” 2022.

[8] M. Pasichnyk et al., “Membrane technology for challenging separations: Removal of CO2, SO2 and NOx from flue and waste gases,” Sep. Purif. Technol., vol. 323, p. 124436, 2023.