# An Assessment on Average Pressure Drop and Dust-Holding Capacity of Hollow-Fiber Membranes in Air Filtration

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Analysis on Average Pressure Drop of Air Filters

_{avg}is the average pressure drop and Q, T, H, m(t), and K, respectively, are the air flowrate, air temperature, air humidity, and dust amount loaded at a given time and a constant describing dust and/or filter type. The overall process is quite complex and is often simplified using various averaging models including the arithmetic model, which is a simple arithmetic average of initial (pressure drop of a new filter, Δp

_{i}) and final pressure drop (Δp

_{f}) as follows:

_{up}are instant time of filtration, filtration efficiency, and upstream particle concentration, respectively. Equation (6) can be used to estimate instant dust mass deposited on the surface of planar filter media. The parameter a expresses the distance of the loading curve intersection on the y-axis from zero, which can be approximated by initial pressure drop Δp

_{i}:

_{f}.

## 3. Materials and Methods

#### 3.1. Hollow-Fiber Membrane Bundles

#### 3.2. Experimental Setup

#### 3.3. Dust Supply Scheme

^{3}[9] were used to calculate the particle sedimentation velocity v

_{p}as follows:

_{c}, ρ

_{c}, ρ, g, and ξ are the particle diameter, particle density, fluid density, gravitational acceleration, and friction coefficient. Friction coefficient depends on the sedimentation profile which can be characterized by Reynolds number Re = d

_{p}v

_{p}ρ/µ. However, we can see that the sedimentation velocity we need to estimate is included in the Reynolds number formula. Therefore, the Archimedes number must be introduced to assess the character of sedimentation:

## 4. Results and Discussion

#### 4.1. Experimental Data

_{meas}), initial (Δp

_{i}) and final pressure drop (Δp

_{f}), the total amount of dust fed during the experiments (M), and experiment duration (t). We did experiments at a constant dust loading rate of 4 g/h with two different membranes (refer to Table 1) at different permeate velocity (a velocity of the air stream within the pipe at the downstream side of the membrane, refer to Figure 2, part 11—air intake/suction pipe). Based on the series of these experiments, we further chose to assess the P80 membrane at a constant permeate velocity of 20 cm/s but at three different dust loading rates (2, 4 and 6 g/h). This was done to compare the influence of dust concentration on the loading behavior of the P80 membrane in terms of average pressure drop calculated using different models. P80 at 20 cm/s was chosen to further evaluate due to an optimal loading behavior similar to the pressure drop/dust load trends observed in planar filters. The data obtained for this membrane was thus possible to approximate using the exponential curve fit, which is generally done in the ASHRAE dust-holding capacity test [21] and which was previously used in several studies [12,17]. We could then better compare among different average pressure drop models including the exponential, even though, for the other experimental configurations, the exponential curve did not fit well and polynomial dependence must have been used instead. However, both of these curve fits were used to approximate obtained data (no matter of fitting accuracy) and compared for each experiment configuration to better see the variations in the results obtained using different average pressure drop models.

_{meas}is the experimentally obtained dust-holding capacity, A is the membrane surface area, and t

_{f}is the final time of filtration.

^{2}), we can see better tightness of polynomial fit compared to the exponential. We can also compare the absolute terms, which in both models correspond to the values of membrane initial pressure drop. The absolute terms from both models are different by more than 200 Pa in some cases, so we can assume that different fitting after integrating the equation will provide quite different values of dust mass-averaged pressure drop.

#### 4.2. Average Pressure Drop

_{c-o}). The first three average pressure drops (arithmetic, geometric and integral) are calculated solely based on experimental values of initial pressure drop of the membrane (clean membrane at the beginning of the experiment) and final pressure drop after dust loading (membrane heavily loaded with dust at the end of the experiments). They do not include the influence of gradual dust accumulation in the filter, which, according to Montgomery et al. [17], can bring an error in the average pressure drop results and thus underestimate the power demand and supply when designing a filtration system [24]. In different experiments at a loading rate of 4 g/h (refer to Figure 5a), we can see the average pressure drop values decrease in order (model) polynomial–exponential–arithmetic–geometric–integral in all experiments, except P80 membrane at 20 cm/s. Excluding the P80 at 20 cm/s, this is quite different from previous work [12] aiming at a comparison of different filter media, namely a V-pack filter, box filter, bag filter, and panel filter. All these filter media had average pressure drop based on the exponential model comparable to that calculated using the integral model or slightly higher. Thus, the integral model was considered reliable to predict the average pressure drop of the tested filters.

#### 4.3. Dust-Holding Capacity

_{f}) or more generally time when the filter reaches the final pressure drop Δp

_{f}and related to unit membrane area (A):

_{i}

_{f}

_{pol}(DHC calculated from polynomial fit parameters), as follows:

_{T}ratio (a ratio of deposited dust to total dust fed in the filtration chamber), which increased with increasing flowrate (Figure 7a). However, it is also important to note that the experiments were conducted in a narrow flowrate range so further research is necessary, also due to the pressure drop effects along the fiber length, which can be significant. This is confirmed in Figure 7a where the cake pressure drop per gram of deposited dust is different even though it should be practically the same as the same mass of particles should cause the same pressure drop increase. The pressure drop fluctuations are caused by the significant effect of inner fiber diameter, which is described by the Hagen–Poiseuille equation [31].

_{T}ratio (Figure 7b) with increasing dust concentration is not in accordance with the results presented in Figure 6b. According to Figure 6b, the DHC/M

_{T}ratio (Figure 7b) should also increase. Thus, there is probably influence of the final dust load (which was due to experimental conditions different) or the increasing trend of DHC with dust load is only at an early stage of membrane dust fouling. This would mean that the trend in Figure 6b would be reversed if the experiments were further prolonged. However, this would be possible only in planar filter geometry. It is a problem with hollow fibers as the cake cannot be retained on the membrane surface and falls off. Hence, further work is necessary especially for filtration on a long-term basis and with concentrations common for general filtration applications. Here, we used extremely high dust concentrations to fasten the membrane fouling, which could also have an effect on DHC.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

a | a curve fitting parameter |

A | membrane surface area |

Ar | Archimedes number |

b | a curve fitting parameter |

B | a constant in relationship for pressure drop at filter exchange |

C_{up} | upstream particle concentration |

d_{p} | particle diameter |

D | discriminant |

DHC | dust-holding capacity |

DHC_{meas} | experimentally measured dust-holding capacity |

DHC_{exp} | dust-holding capacity from exponential fit |

DHC_{pol} | dust-holding capacity from polynomial fit |

DHC_{theor} | theoretical dust-holding capacity |

g | gravitational acceleration |

H | humidity |

K | constant describing dust and/or filter type |

m | dust accumulation in filter |

m_{HFM} | instantaneous mass of dust deposited on HFM |

m_{load} | dust loading rate |

m(t) | mass of dust on filter at a given time |

M | final dust loading |

M_{T} | total amount of dust dosed to the chamber |

∆p(m) | pressure drop as a function of dust load |

∆p(t) | pressure drop as a function of time |

∆p_{avg} | average pressure drop |

∆p_{c-o} | pressure drop at change out of the filter |

∆p_{f} | final pressure drop |

∆p_{i} | initial pressure drop |

Q | air flowrate |

Re | Reynolds number |

t | instant time of filtration |

t_{f} | final time of filtration |

T | temperature |

v | curve fitting parameter |

x | curve fitting parameter |

y | curve fitting parameter |

z | curve fitting parameter |

η | filtration efficiency |

µ | fluid viscosity |

ν_{p} | sedimentation velocity |

ξ | friction coefficient |

ρ | fluid density |

ρ_{p} | particle density |

## References

- Chen, J.; Brager, G.S.; Augenbroe, G.; Song, X. Impact of Outdoor Air Quality on the Natural Ventilation Usage of Commercial Buildings in the US. Appl. Energy
**2019**, 235, 673–684. [Google Scholar] [CrossRef] - Yu, B.F.; Hu, Z.B.; Liu, M.; Yang, H.L.; Kong, Q.X.; Liu, Y.H. Review of Research on Air-Conditioning Systems and Indoor Air Quality Control for Human Health. Int. J. Refrig.
**2009**, 32, 3–20. [Google Scholar] [CrossRef] - Bulejko, P. An Analysis on Energy Demands in Airborne Particulate Matter Filtration Using Hollow-Fiber Membranes. Energy Rep.
**2021**, 7, 2727–2736. [Google Scholar] [CrossRef] - Leung, W.W.-F.; Hau, C.W.-Y. A Model of Backpulse and Backblow Cleaning of Nanofiber Filter Loaded with Nano-Aerosols. Sep. Purif. Technol.
**2016**, 169, 171–178. [Google Scholar] [CrossRef] - Leung, W.W.-F.; Hau, C.W.Y. Skin Layer in Cyclic Loading-Cleaning of a Nanofiber Filter in Filtering Nano-Aerosols. Sep. Purif. Technol.
**2017**, 188, 367–378. [Google Scholar] [CrossRef] [PubMed] - Bulejko, P.; Krištof, O.; Dohnal, M.; Svěrák, T. Fine/Ultrafine Particle Air Filtration and Aerosol Loading of Hollow-Fiber Membranes: A Comparison of Mathematical Models for the Most Penetrating Particle Size and Dimensionless Permeability with Experimental Data. J. Membr. Sci.
**2019**, 592, 117393. [Google Scholar] [CrossRef] - Bulejko, P. Numerical Comparison of Prediction Models for Aerosol Filtration Efficiency Applied on a Hollow-Fiber Membrane Pore Structure. Nanomaterials
**2018**, 8, 447. [Google Scholar] [CrossRef] [Green Version] - Wang, L.-Y.; Yu, L.E.; Chung, T.-S. Effects of Relative Humidity, Particle Hygroscopicity, and Filter Hydrophilicity on Filtration Performance of Hollow Fiber Air Filters. J. Membr. Sci.
**2020**, 595, 117561. [Google Scholar] [CrossRef] - Bulejko, P.; Krištof, O.; Svěrák, T. Experimental and Modeling Study on Fouling of Hollow-Fiber Membranes by Fine Dust Aerosol Particles. J. Membr. Sci.
**2020**, 616, 118562. [Google Scholar] [CrossRef] - Bulejko, P.; Svěrák, T.; Dohnal, M.; Pospíšil, J. Aerosol Filtration Using Hollow-Fiber Membranes: Effect of Permeate Velocity and Dust Amount on Separation of Submicron TiO2 Particles. Powder Technol.
**2018**, 340, 344–353. [Google Scholar] [CrossRef] - Xu, H.; Jin, W.; Wang, F.; Li, C.; Wang, J.; Zhu, H.; Guo, Y. Preparation and Properties of PTFE Hollow Fiber Membranes for the Removal of Ultrafine Particles in PM2.5 with Repetitive Usage Capability. RSC Adv.
**2018**, 8, 38245–38258. [Google Scholar] [CrossRef] - Sun, C.; Woodman, D. Delivering Sustainability Promise to HVAC Air Filtration-Part I: Classification of Energy Efficiency for Air Filters. ASHRAE Trans.
**2009**, 115, 581–585. [Google Scholar] - Eurovent 4/21—2014: Calculation Method for the Energy Use Related to Air Filters in General Ventilation Systems—First Edition | Eurovent. Available online: https://eurovent.eu/?q=content/eurovent-421-2014-calculation-method-energy-use-related-air-filters-general-ventilation (accessed on 11 November 2020).
- Zhang, W.; Deng, S.; Wang, Y.; Lin, Z. Dust Loading Performance of the PTFE HEPA Media and Its Comparison with the Glass Fibre HEPA Media. Aerosol Air Qual. Res.
**2018**, 18, 1921–1931. [Google Scholar] [CrossRef] [Green Version] - Long, J.; Tang, M.; Sun, Z.; Liang, Y.; Hu, J. Dust Loading Performance of a Novel Submicro-Fiber Composite Filter Medium for Engine. Materials
**2018**, 11, 2038. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Sun, C. Delivering Sustainability Promise to HVAC Air Filtration: Part II: Life Cycle Sustainability of Air Filters. ASHRAE Trans.
**2010**, 116, 25–32. [Google Scholar] - Montgomery, J.F.; Green, S.I.; Rogak, S.N.; Bartlett, K. Predicting the Energy Use and Operation Cost of HVAC Air Filters. Energy Build.
**2012**, 47, 643–650. [Google Scholar] [CrossRef] - Zena Membranes s.r.O. Available online: www.zena-membranes.cz/ (accessed on 14 May 2021).
- Sverak, T.; Bulejko, P.; Ostrezi, J.; Kristof, O.; Kalivoda, J.; Kejik, P.; Mayerova, K.; Adamcik, M. Separation of Gaseous Air Pollutants Using Membrane Contactors. IOP Conf. Ser. Earth Environ. Sci.
**2017**, 92, 012061. [Google Scholar] [CrossRef] [Green Version] - Kůdelová, T.; Bartuli, E.; Strunga, A.; Hvožďa, J.; Dohnal, M. Fully Polymeric Distillation Unit Based on Polypropylene Hollow Fibers. Polymers
**2021**, 13, 1031. [Google Scholar] [CrossRef] [PubMed] - ASHRAE 52.2-2017. Method of Testing General Ventilation Air-Cleaning Devices for Removal Efficiency by Particle Size; (ANSI Approved); ASHRAE: Peachtree Corners, GA, USA, 2017. [Google Scholar]
- Bulejko, P.; Dohnal, M.; Pospíšil, J.; Svěrák, T. Air Filtration Performance of Symmetric Polypropylene Hollow-Fibre Membranes for Nanoparticle Removal. Sep. Purif. Technol.
**2018**, 197, 122–128. [Google Scholar] [CrossRef] - Zhang, X.; Liu, J.; Liu, X.; Liu, C. Performance Optimization of Airliner Cabin Air Filters. Build. Environ.
**2021**, 187, 107392. [Google Scholar] [CrossRef] - Banik, R.; Das, P.; Ray, S.; Biswas, A. Prediction of Electrical Energy Consumption Based on Machine Learning Technique. Electr. Eng.
**2020**. [Google Scholar] [CrossRef] - Maduna, L.; Patnaik, A. Textiles in Air Filtration. Text. Prog.
**2017**, 49, 173–247. [Google Scholar] [CrossRef] - Azimi, P.; Stephens, B. HVAC Filtration for Controlling Infectious Airborne Disease Transmission in Indoor Environments: Predicting Risk Reductions and Operational Costs. Build. Environ.
**2013**, 70, 150–160. [Google Scholar] [CrossRef] [PubMed] - Tian, X.; Ou, Q.; Liu, J.; Liang, Y.; Pui, D.Y.H. Influence of Pre-Stage Filter Selection and Face Velocity on the Loading Characteristics of a Two-Stage Filtration System. Sep. Purif. Technol.
**2019**, 224, 227–236. [Google Scholar] [CrossRef] - Walsh, D.C. Possibilities for the Design of Fibrous Filter Materials with Enhanced Dust Holding Capacity. J. Aerosol Sci.
**1998**, 29, S939–S940. [Google Scholar] [CrossRef] - Chang, D.-Q.; Tien, C.-Y.; Peng, C.-Y.; Tang, M.; Chen, S.-C. Development of Composite Filters with High Efficiency, Low Pressure Drop, and High Holding Capacity PM2.5 Filtration. Sep. Purif. Technol.
**2019**, 212, 699–708. [Google Scholar] [CrossRef] - Rebai, M.; Prat, M.; Meireles, M.; Schmitz, P.; Baclet, R. Clogging Modeling in Pleated Filters for Gas Filtration. Chem. Eng. Res. Des.
**2010**, 88, 476–486. [Google Scholar] [CrossRef] - Shao, P.; Huang, R.Y.M. An Analytical Approach to the Gas Pressure Drop in Hollow Fiber Membranes. J. Membr. Sci.
**2006**, 271, 69–76. [Google Scholar] [CrossRef] - Tang, M.; Chen, S.-C.; Chang, D.-Q.; Xie, X.; Sun, J.; Pui, D.Y.H. Filtration Efficiency and Loading Characteristics of PM2.5 through Composite Filter Media Consisting of Commercial HVAC Electret Media and Nanofiber Layer. Sep. Purif. Technol.
**2018**, 198, 137–145. [Google Scholar] [CrossRef]

**Figure 2.**A scheme of the experimental setup:

**1**—chamber,

**2**—hollow-fiber membrane bundle,

**3**—opening for dust dosing,

**4**—differential pressure sensor,

**5**—air velocity probe,

**6**—inverter,

**7**—blower,

**8**—laptop,

**9**—DAQ card,

**10**—laboratory power source,

**11**—air intake (downstream) pipe,

**12**—air return (exhaust) pipe.

**Figure 3.**SEM image of ASHRAE A2 dust used in filtration experiments at magnification 100× (

**a**) and 1000× (

**b**).

**Figure 4.**Dust loading curves fitted with different models: (

**a**) various membranes and velocities at a constant loading rate of 4 g/h with exponential fit (the minor x-axis in red is for P60, at 40 cm/s), (

**b**) the same fitted with 4th order polynomial (the minor x-axis in red is for P60, at 40 cm/s), (

**c**) P80 membrane at 20 cm/s at different loading rates with exponential fit, (

**d**) the same fitted with 4th order polynomial.

**Figure 5.**Average pressure drop of different membranes at different permeate velocities at a constant loading rate of 4 g/h (

**a**) and P80 membrane at 20 cm/s at different loading rates (

**b**).

**Figure 6.**Dust-holding capacity per cake pressure drop of different membranes at different permeate velocities at a constant loading rate of 4 g/h (

**a**) and P80 membrane at 20 cm/s at different loading rates (

**b**), DHC measured (DHC

_{meas}), DHC from exponential fit (DHC

_{exp}) and DHC from polynomial fit (DHC

_{pol}) are at the major axis, DHC theoretical (DHC

_{theor}) is at the minor axis.

**Figure 7.**Cake pressure drop increase per gram of dust deposited and a ratio of DHC to total mass of dust dosed (M) for different membranes at different permeate velocities at a constant loading rate of 4 g/h (

**a**) and P80 membrane at 20 cm/s at different loading rates (

**b**).

Hollow-Fiber Membrane | P60 | P80 |
---|---|---|

Fiber outer diameter (µm) | 300 | 620 |

Number of fibers | 1380 | 300 |

Active length (mm) | 730 | 730 |

Surface area (m^{2}) | 0.95 | 0.43 |

Initial pressure drop (Pa m^{−2}) | 1143 ± 13 | 307 ± 2 |

Experiment | DHC_{meas} (g) | Δp_{i} (Pa) | Δp_{f} (Pa) | M_{T} (g) | t_{f} (h) | |
---|---|---|---|---|---|---|

4 g/h | P60 (20 cm/s) | 16.2 | 1204 | 2072 | 180 | 45 |

P60 (40 cm/s) | 4.7 | 3239 | 5581 | 24 | 6 | |

P80 (20 cm/s) | 15.7 | 714 | 1453 | 192 | 48 | |

P80 (40 cm/s) | 21.4 | 1870 | 3789 | 140 | 35 | |

20 cm/s | P80 (2 g/h) | 9.0 | 717 | 1115 | 66 | 33 |

P80 (4 g/h) | 15.7 | 714 | 1453 | 192 | 48 | |

P80 (6 g/h) | 13.6 | 717 | 1318 | 180 | 30 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bulejko, P.; Krištof, O.; Dohnal, M.
An Assessment on Average Pressure Drop and Dust-Holding Capacity of Hollow-Fiber Membranes in Air Filtration. *Membranes* **2021**, *11*, 467.
https://doi.org/10.3390/membranes11070467

**AMA Style**

Bulejko P, Krištof O, Dohnal M.
An Assessment on Average Pressure Drop and Dust-Holding Capacity of Hollow-Fiber Membranes in Air Filtration. *Membranes*. 2021; 11(7):467.
https://doi.org/10.3390/membranes11070467

**Chicago/Turabian Style**

Bulejko, Pavel, Ondřej Krištof, and Miroslav Dohnal.
2021. "An Assessment on Average Pressure Drop and Dust-Holding Capacity of Hollow-Fiber Membranes in Air Filtration" *Membranes* 11, no. 7: 467.
https://doi.org/10.3390/membranes11070467