SterliTECH Tip: Key Equations for Crossflow and Forward Osmosis Systems
Membrane processes are widely used for various separation applications across a diverse range of industries. Understanding key performance parameters is crucial in the development, operation and optimization of membrane filtration processes. This article serves as a quick guide for most commonly used equations in Crossflow Filtration (Microfiltration, Ultrafiltration, Nanofiltration, and Reverse Osmosis) and Forward Osmosis applications. The following equations serve as essential tools while developing and testing membrane processes using Sterlitech products including HP4750, Benchtop Systems, Skids, cells, and kits.
Permeate Flux
Permeate flux is the rate at which permeate passes through the membrane per unit area. It is typically measured in liters per square meter per hour (LMH). The permeate flux is commonly called Water flux when water is the base solution in the feed stream. To calculate the permeate flux (J), divide the permeate volume by membrane unit area (A) and time (t). The following equation can be used for Crossflow Filtration and Dead-end cells applications [1].
J: Permeate flux (LMH)
Vp: Permeate volume (L)
A: Membrane active area (m2)
t: Time taken to collect the volume (hours)
In the case of Forward osmosis and Membrane Distilation, it is difficult to directly measure the permeate volume. Therefore, it is recommended to measure the difference in volume of the draw solution tank over a predetermined time [2]. To calculate the permeate flux (JFO), divide the difference in draw solution volume over a predefined time by unit area (A) and time (t).
JFO: Permeate flux in forward osmosis (LMH)
V DS (i): Initial draw solution volume (L)
V DS (t): Draw solution volume after time (L)
A: Membrane active area (m2)
t: Time taken to collect the volume (hours)
Recovery Rate
Recovery rate is the percentage of the feedwater that is converted into permeate as it passes through the membrane pores. The recovery rate depends on the flow rate of feed solution and permeate [3]. However, in the case of lab scale Sterlitech products it is more practical to use the change in volumes of feed and permeate over a time period. To calculate the recovery rate (R%), divide the permeate volume (Vp) by the feed volume (Vf) as shown in the following equation. This equation is valid for Cross Filtration and Forward Osmosis. In Forward Osmosis, the permeate volume is determined based on the change of draw solution volume.
R%: Recovery rate
Vf: Feed volume (L)
Vp: Permeate volume (L)
Rejection Rate
Rejection rate is the percentage of contaminants concentration removed from system feedwater by the membrane. The rejection rate (Rs) can be calculated based on the feed concentration (Cf) and permeate concentration (Cp). The following equation can be used for Crossflow Filtration and Dead-end cells applications [4].
RS: Rejection rate of membrane
Cf: Concentration of targeted contaminant in feed (ppm)
Cp: Concentration of targeted contaminant in permeate (ppm)
In the case of Forward osmosis, the rejection rate (RS (FO)) can be calculated based on the change of concentration of the draw solution over time considering the dilution effect. The following equation can be used for Forward Osmosis application [5].
RS (FO): Rejection rate of Forward Osmosis membrane
CDS (t): Concentration of targeted contaminant in draw solution after time (ppm)
VDS (t): Volume of draw solution after time (L)
CDS (i): Initial concentration of targeted contaminant in draw solution (ppm)
VDS (i): Initial Volume of draw solution (L)
CFS (i): Initial concentration of targeted contaminant in feed solution (ppm)
VFS (i): Initial Volume of feed solution (L)
Reverse Solute Flux
Reverse solute flux (RSF) is one of the main challenges in forward osmosis process and defined as the reverse diffusion of salts from the draw solution to the feed solution. It is typically measured in grams per square meter per hour (GMH). RSF is calculated based on the change of concentration of the feed solution taken into consideration the feed solution concentering effect. The following equation can be used for forward osmosis application [5].
RSF: Reverse solute flux (g/m2/h)
CFS (t): Concentration of feed solution after time (ppm)
VFS (t): Volume of feed solution after time (L)
CFS (i): Initial concentration of feed solution (ppm)
VFS (i): Initial Volume of feed solution (L)
A: Membrane active area (m2)
t: Time taken to collect the volume (hours)
Membrane filtration processes offer highly efficient solutions for various industrial and environmental applications, particularly in water treatment and separation technologies. To ensure a proper optimization and design of the process, it is crucial to consider various parameters including permeate flux, recovery rate, rejection rate, and reverse solute flux. This article provides essential equations and insights that serve as a quick guide for those developing and testing membrane processes, enabling them to achieve optimal results.
Refences
[1] J. Zhang, S. Huang, H. Guo, A. G. Fane, and C. Y. Tang, “Effects of Crossflow Filtration cell configuration on membrane separation performance and fouling behaviour,” Desalination, vol. 525, p. 115505, Mar. 2022, doi: 10.1016/j.desal.2021.115505.
[2] Y. Zhou, Y. Shi, D. Cai, W. Yan, Y. Zhou, and C. Gao, “Support-free interfacial polymerized polyamide membrane on a macroporous substrate to reduce internal concentration polarization and increase water flux in forward osmosis,” Journal of Membrane Science, vol. 689, p. 122165, Jan. 2024, doi: 10.1016/j.memsci.2023.122165.
[3] L. F. Greenlee, D. F. Lawler, B. D. Freeman, B. Marrot, and P. Moulin, “Reverse osmosis desalination: Water sources, technology, and today’s challenges,” Water Research, vol. 43, no. 9, pp. 2317–2348, May 2009, doi: 10.1016/j.watres.2009.03.010.
[4] A. Safulko et al., “Rejection of perfluoroalkyl acids by nanofiltration and reverse osmosis in a high-recovery closed-circuit membrane filtration system,” Separation and Purification Technology, vol. 326, p. 124867, Dec. 2023, doi: 10.1016/j.seppur.2023.124867.
[5] E. Mendoza, G. Blandin, M. Castaño-Trias, L. L. Alonso, J. Comas, and G. Buttiglieri, “Rejection of organic micropollutants from greywater with forward osmosis: A matter of time,” Journal of Environmental Chemical Engineering, vol. 11, no. 5, p. 110931, Oct. 2023, doi: 10.1016/j.jece.2023.110931.
