Introduction

Filter elements are utilized in various applications including compressed air filtration, long-distance gas transport, sealed gas filtration, and metal cutting [1,2,3]. The filter media used in this paper are mainly used in natural gas transmission field applications where pressures range from 3 to 15 MPa. Effective removal of impurity droplets in the gas is crucial to avoid damage to downstream equipment, corrosion of transport pipelines, or risk to worker safety. Coalescence separation is an effective method for removing small droplets in gas, and the performance of this method relies heavily on the liquid distribution in the fibre filter media, which serves as the core of the filter.

On one hand, most of the current research on pressure drop, saturation, liquid distribution patterns, media filtration efficiency and others has been done at atmospheric pressure. Numerous studies have investigated the distribution pattern of liquid within the fibre filter media. Kasper [4,5,6] proposed a “jump-and-channel” pressure drop model for filter media performance at atmospheric pressure and used the light-curing method to obtain the transport pattern of liquid channels inside oleophobic filter media. Gervais et al. [7] investigated the motion pattern in pleated wave filters under different operating conditions using radiolabeled aerosols and combining single photon emission computed tomography (SPECT) and X-ray computed tomography. Saeedi [8] researched the effect of the face velocity and particle concentration on the efficiency and beta ratio was investigated used for natural gas filtration. The effects of changes in other parameters, such as wetting characteristics, surface tension, surface energy [9,10,11], droplet morphology [12,13,14] and the interaction between the droplets and fibres [15,16,17,18] on the performance of filter media, have also been widely studied.

On the other hand, the research at high pressure are rarely reported, the pressure at the natural gas field is basically over 3 MPa. Song [19] measured the water-SS304 contact angle at different pressure working conditions (up to 15 MPa). As pressure increases, nitrogen is more strongly adsorbed to the water surface, leading to a reduction in interfacial tension between water and nitrogen. Zhai [20] researched surface tension and viscosity of binary ionic liquid mixtures from high vacuum up to pressures of 10 MP, an increase in the pressure up to 10 MPa has a negligible influence on the viscosity, while it causes a distinct reduction in the surface tension compared to the value at 0.1 MPa. Innocentini et al. [21] focused on the permeability of filter media at the absolute pressure ranged from 93 to 693 kPa to obtain the applicable range of permeability coefficients used in the Forchheimer equation. Tanabe et al. [22] studied the performance of metal filters at the absolute pressures of 193, 293 and 693 kPa. Xu et al. [23] investigated the performance of air filters in the pressure range of 60–130 kPa. Chang et al. [24] measured the pressure drop and the permeability coefficient of natural gas filtration media at 0.1 and 11 MPa. However, this study focused on permeability of the filters. Recent studies have shown significant changes in the filtration performance of materials under high pressure. Liu et al. [25] evaluated the performance of four different sizes of filters after 410 days of field application for high-pressure natural gas and found that the pressure drop increased by 5.28 times, the filtration efficiency decreased, and the quality factor of the filter element decreased by 50.3% on average.

However, the pressures in the above research literature are not very high, the highest pressure reaches 0.7 MPa. In addition, the decline in the performance of the filter media under high pressure is directly related to the pressure drop of the material, the degree of saturation and the liquid distribution pattern. And the changes in these patterns are unclear and require further investigation.

Therefore, this study aims to investigate the impact of pressure changes on the performance of filtration materials. Specifically, the law of pressure drop, saturation, and liquid distribution pattern of filtration media under 1–5 MPa. By using the UV light-curing method to discover new experimental phenomena and analyze the results based on previous research and fundamental physical laws. The findings provide insight into the influence of pressure change on filtration system design and optimization under different pressure conditions.

Experimental Setup and Material Properties

Figure 1 shows the system for testing the performance of the filter media under high pressure with the specific equipment listed in Table 1. The experimental setup can be divided into three parts, the first part consists of a compressor, a buffer cylinder and a filter which can provide a clean gas source for the test. The second part consists of a gas–liquid buffer tank and two gas pipelines, pipeline 1 is a clean gas channel and pipeline 2 is an aerosol generating channel. The third part is the filter media test system, which consists of a filter media clamping device, a differential pressure transmitter, a pressure-reducing valve, a mass flow controller, a filter and a data acquisition system, which can test the differential pressure, saturation and filtration efficiency of filter media at different pressures.

Fig. 1
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Flowchart of experimental equipment

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Table 1 Instrumentation parameters
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A compressor (HP15-70, Ingersoll Rand) was used as the main gas source for the experiment. Pressure-reducing valves were used to adjust the pressure of the deeding gas. A differential pressure transmitter was used to monitor the pressure drop continuously at either end of the filter media. An air filter was installed at the inlet of the compressor for the pre-filtration of the gas. An oil mist filter and a 5A molecular sieve filter were installed at the inlet of the gas–liquid mixing tank to ensure the cleanliness of the inlet gas. After the clean gas enters the pipeline, valve 1 is opened while valve 2 is closed. At this stage, there is no aerosol generated in the pipeline. After the gas flow is stable, valve 2 is opened while valve 1 is closed. The aerosol is gradually captured on the filter media until a steady-state phase is reached and the test is completed.

To ensure experimental safety, the filter holder was made of 304 stainless steel with a maximum working pressure of 10 MPa. The main line of the setup is made up of standard 1-in. seamless steel pipe connections with a maximum working pressure of 25 MPa. The pressure-bearing of all instruments and equipment is not less than 10 MPa. The mixing tank is connected to two pipelines with pipelines 1 above and 2 below the liquid, equipped with many small openings at a diameter of 1.5 mm, to improve the gas–liquid mixing. By closing pipeline 1 while opening pipeline 2, an aerosol is generated by gas shear. The specific structure is shown in Fig. 1. Meanwhile, the upstream particle size distribution was measured by using German Palas as shown in Fig. 2, and the upstream particle size distribution remained consistent at different pressures.

Fig. 2
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Upstream particle size distribution

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Two types of glass fiber filter media, oleophilic (A) and oleophobic (B), were analyzed using two different aerosol particles specified in the international test standard. The two aerosols used were dioctyl sebacate (DEHS) and a non-volatile UV-curing agent (TB-6103B). The liquid distribution law of the filter media needs to be achieved with the help of light curing, and since DEHS cannot be cured by light curing, TB-6103B was chosen for the study of the liquid distribution law, which has physically close properties to DEHS liquids. To achieve effective UV curing, a special stainless-steel ring-shaped chamber was assembled with six 365 nm UV LEDs installed on the ring. The stainless-steel ring was fixed inside a clamping device to ensure a safe seal while maintaining the stability of the UV illumination. The wettability of the filter media surface was determined by measuring the contact angle using an Attension contact angle meter from BiolinScientific, Sweden. Each measurement was repeated three times. The thickness of the filter media was measured using a micrometer, and the grammage was obtained by weighing a circular disc (80 mm in diameter) of the clean filter media. The physical parameters of the liquid and filter media are listed in Tables 2 and 3.

Table 2 Physical properties of DEHS and TB-6103B liquid
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Table 3 Physical parameters of filter media A and B
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Experimental Results

In the experiment, loading rates and flow velocities were kept constant at 0.12 kg/h/m2 and 0.07 m/s, respectively. Gas pressures of 1, 2, 3, 4, and 5 MPa were selected at the same air velocity and loading rate. Six layers of media were used in the filter. The experimental temperature was kept at 22–25 °C. The efficiency and resistance of the filter media measured in this state can be used to evaluate the performance of the filter media. At the steady state, the media were UV-cured for 3 min to ensure the liquid is effectively cured in the filter media. During the curing, the constant flow was maintained. The cured filter media was dissected into layers to observe the liquid distribution. The internal liquid distribution was observed by a scanning electron microscope (SU8010, Hitachi, Japan). The weights of the filter media before and after the experiment were measured to obtain the amount of liquid held by the filter media and the saturation, S, of the filter media at the steady state. According to the ISO12500 standard, it is stipulated that when the pressure drop of the filter media changes less than 1% in 1 h, the filter media is considered to reach a stable state. When the filter media reaches the steady-state stage, indicated by the stable differential pressure, the UV-curing light is turned on for 3 min to fix the liquid distribution in the filter. Then, the filter media is removed for further analysis.

In this section, the TB6103-B was utilized to investigate the resistance and liquid distribution pattern of two different types of filter media under different pressures ranging from 1 to 5 MPa, while maintaining a constant filtration velocity of 0.07 m/s and a constant concentration of 100 mg/m2 for each experimental group with equal duration, the temperature was maintained constant at 25 °C. SEM images were collected to analyze the two UV-cured filter media. Notably, the UV light source was only able to penetrate the first and last layers of the filter media, as depicted in Fig. 3a. Therefore, only these layers were selected for observation, as the middle layers had relatively lower UV exposure, resulting in incomplete curing. To ensure accuracy in sampling, only samples collected from the center of the grids marked by the blue squares in Fig. 3b were analyzed. All images were captured at the same magnification to facilitate appropriate comparisons.

Fig. 3
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a Curing location, b sampling location

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Experimental Results on Oleophilic Filter Media A

Pressure Drop and Saturation of Oleophilic Filter Media A

The pressure drop and saturation results of filter media A are shown in Fig. 4a and b, respectively. The data in Figs. 4b and 8b were obtained using TB-6103B, which was not irradiated by UV light. If TB6103-B had been irradiated by UV light, the filter media would have been fixed, and it would not have been possible to distinguish the saturation accurately. At the same time, as shown in Fig. 1, ball valves and pressure-reducing valves were arranged before and after the filter. The upstream valve was closed when the pressure was reduced. The air velocity of the filter media surface was 0.07 m/s to avoid blowing out the liquid inside the filter material, as suggested by Wurster et al. [26]. The final pressure drop at different pressures remains around 9.2 kPa, but the higher the pressure, the longer it takes to reach the steady-state stage due to the increased fluid holding capacity at higher pressure. Which means that the total saturation of the filter media should gradually increase with increasing pressure at the same concentration and loading time, which is exactly in line with the results of Fig. 4b. When the pressure increases from 1 to 5 MPa, the saturation of oleophilic filter media A increases in each layer. Based on the results of saturation of the first layer of filter media at different pressures, it was found that the saturation of the first layer increased from 0.26 at 1 MPa to 0.34 at 5 MPa with an increase of about 30%, the largest growth rate. The saturation of the last layer increased from 0.35 to 0.39 with a growth rate of 11%, which is the smallest increase in saturation among the six layers of filter media.

Fig. 4
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Pressure drop (left graph) and saturation (right graph) of filter media A

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The pressure drop of filter media at different pressures ranging from 1 to 5 MPa has been thoroughly investigated. In specific, a distinction has been made between the magnitude of the channel pressure drop and the jump pressure drop, which represent two different mechanisms of pressure drop in filter media. As shown in Fig. 5, the change in channel pressure drop with pressure is relatively small and increases only slightly. This is due to the increase in pressure leads to an increase in gas density, resulting in an increase in flow resistance.

Fig. 5
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ΔPjump and ΔPchannel of filter media A

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On the other hand, the jump pressure drop gradually decreases as the pressure increases, as shown in Fig. 5. This phenomenon can be explained by the fact that the jump pressure drop is primarily due to formation of the liquid film [4], which are influenced by the pressure-induced changes in the fluid flow and particle deposition behavior. Moreover, our results suggest that the jump pressure drop is more sensitive to changes in pressure than the channel pressure drop. In addition, the change in the jump pressure drop means that the liquid distribution in the last layer of filter media has changed. Through the light-curing experiments, it was found that the liquid distribution pattern of the first and the last layers of the filter media A changed under different pressures, and the specific changes are shown in Sect. 3.1.2.

Microscopic Liquid Distribution of Oleophilic Filter Media A

The scanning electron microscopy (SEM) images presented in Fig. 6a1–c1 illustrate the surface morphology of the 1st layer of filter media A under different pressure conditions, whereas the corresponding images for the last layer can be observed in Fig. 6a2–c2. At a pressure of 1 MPa for the 1st layer, the liquid predominantly adheres to the fibers of the filter media. However, as the pressure is increased to 3 MPa, liquid bridges begin to form between the fibers, although they are unevenly distributed. With further increases in pressure up to 5 MPa, the liquid bridges coalesce and form a thin liquid film. For the last layer, at a pressure of 1 MPa, the majority of the filter media's surface is covered by a continuous liquid film, as indicated in Fig. 6a2. Subsequently, increasing the pressure to 3 MPa results in the thinning of the liquid film, while at 5 MPa, the liquid film entirely disappears, giving way to a multitude of liquid bridges throughout the surface of the filter media. Meanwhile, Fig. (d) shows the liquid distribution results of the last layer of Kampa [5] oleophilic filter media under one atmospheric pressure. By comparing the results with this paper, it was found that the liquid distribution pattern in the last layer of the lipophilic filter media is close to the results in this paper with a pressure at 1 MPa.

Fig. 6
figure 6

a1–c1 Liquid variation patterns on the surface of the first layer of filter media A, a2–c2 Liquid variation patterns on the surface of the last layer of filter media A, d Liquid distribution of the last layer of the oil-wet filter media in Kampa under one atmospheric pressure

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The changes in the liquid film of the last layer provide evidence for the reduction in jump pressure drop. However, it is well known that jump pressure drop decreases gradually with increasing pressure, and if the liquid film disappears completely, a significant change in jump pressure drop should occur. Surprisingly, this phenomenon was not observed in our study. Therefore, we conducted a detailed observation and analysis of the liquid distribution in the cross-section of the last layer of the filter media.

The liquid distribution on the outlet surface of the filter media is illustrated in Fig. 7a–c. At a pressure of 1 MPa, the liquid in the filter media is distributed in the form of a liquid film on the outlet surface. At 3 MPa, the liquid film is still visible on the outlet surface, but its overall thickness has decreased. When the pressure is further increased to 5 MPa, the liquid film disappears completely from the outlet surface. This phenomenon can be explained by the fact that, at high pressures, the liquid is forced to move from the surface of the filter media into the interior of the filter media. As a result, the jump pressure drop does not show a significant change but rather gradually decreases with increasing pressure. Furthermore, the absence of a significant change in the jump pressure drop is likely due to a multitude of liquid bridges that continue to facilitate the flow of liquid through the filter media even as the pressure increases.

Fig. 7
figure 7

a–c The variation of liquid distribution in the sixth cross-sectional layer of filter media A

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Experimental Results on the Oleophobic Filter Media B

Pressure Drop and Saturation of Oleophobic Filter Media B

Figure 8a illustrates the process pressure drop of filter media B under different pressures, indicating that the final pressure drop remains within a range of about 5.4 kPa at different pressures. In addition, as shown in Fig. 8b, the first layer of filter media B exhibits a gradually decreasing saturation range with increasing pressure, the saturation of the first layer of filter media decreased from 0.45 at 1 MPa to 0.35 at 5 MPa, a 22% decrease in saturation. It is confirmed by the results of photocuring in the Sect. 3.2.2. For the remaining five layers of filter material, the saturation level gradually increases with increasing pressure. The saturation of remaining five layers of filter media increased by more than 80% in saturation from 1 to 5 MPa. The overall saturation is still increasing, which is consistent with the pattern for the lipophilic filter media A, although the saturation decreases in the first layer of the media.

Fig. 8
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Pressure drop (left graph) and saturation (right graph) of filter media B

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Meanwhile, the channel pressure drop and jump pressure drop of filter media B has been analyzed, as shown in Fig. 9. It can be observed that, unlike the filter media A, the channel pressure drop of filter media B increases slowly with the increase of pressure. One thing to note is that there is a significant change in the increase of the channel pressure drop when the pressure reaches 5 MPa. This was found by comparing the last layer of filter media frontal photographs as shown in Fig. 10. At 5 MPa, the liquid channel of the last layer of filter media is larger and more wetted by the liquid, which is the reason for the obvious increase in the channel pressure drop. The jump pressure drop decreases slowly, which is a similar characteristic of both materials.

Fig. 9
figure 9

ΔPjump and ΔPchannel of filter media B

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Fig. 10
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Photos of the sixth layer of filter media B

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Microscopic Liquid Distribution of Oleophobic Filter Media B

The first layer of filter media B plays a crucial role in promoting the liquid enrichment during filtration. As the pressure increases, the degree of liquid coalescence on the first layer of filter media B decreases, which indirectly indicates the decrease in the saturation of the first layer. SEM images shown in Fig. 11 reveal that at a pressure of 1 MPa, the liquid film did not cover the top of the fibers but formed a layer between the fibers, resulting in many continuous beads distributed between the fibers with a smaller diameter. The formation of the liquid film is mainly due to the capillary force and gravity acting on the liquid. Once these smaller fibers are connected, a local layer of liquid film is formed, as shown in Fig. 11d. This phenomenon is also observed in other layers of filter media B, but with different degrees of droplet coalescence. However, by observing the results of Kampa [5] at one atmosphere, it can be found that the liquid enrichment in the first layer is higher at lower pressures, which is also consistent with the trend of pressure-induced changes in this paper.

Fig. 11
figure 11

a–c The variation law of liquid distribution on the surface of the 1st layer of oleophobic filter media B, d is the enlarged diagram of the red mark in a, e is the liquid distribution in the first layer of the oleophobic filter media in the Kampa’s paper

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Explanation of the Phenomenon of Liquid Distribution of Filter Media A and B

In the present study, the only variable considered is pressure. Based on the experiments, it was found that changes in pressure induce variations in the wetting properties between the liquid and filter media, known as the contact angle. According to the results of Bernardin [27], due to the incompressibility of pure liquids (such as water), the interactions between liquid molecules remain largely constant with variations in pressure. Therefore, they posit that pressure has minimal impact on the surface tension of gas–liquid interfaces, and contact angles are correspondingly insensitive to changes in pressure. It is well known that variations in the surface tension of gas–liquid interfaces can significantly alter the wettability of solid surfaces, whereas the surface tension of pure liquids is in principle unaffected by pressure [28]. However, Chow [29] and Yan [30] have observed that the surface tension of water in a range of incompatible gas environments, such as nitrogen, decreases with increasing pressure. To investigate changes in the surface tension of liquids in the present study, contact angles of DEHS on a hydrophobic filter medium B were measured at different pressures using the Theta high-pressure optical tensiometer, manufactured by Biolin Scientific AB, Finland. Nitrogen gas was used as the gas phase, the temperature was maintained constant at 25 °C. The measured contact angles are presented in Table 4. It can be found that with the gradual increase of pressure from 0.1 to 20 MPa, the surface tension of the DEHS decreases from 28.72 to 17.10 mN/m, and the contact angle between the droplet and the fibre decreases from 133.51° to 90.12°.

Table 4 Contact angle of DEHS on filter media B at different pressure (25 °C)
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Firstly, the filter face velocity, aerosol concentration, aerosol loading time, and temperature were kept constant. The pressure was varied from 1 to 5 MPa. Thermodynamics provides a more detailed explanation of the dissolution of gases in liquids as the pressure increases. Substances always move from high chemical potential to low chemical potential. The dependence of the chemical potential of the ith component on the state parameters is determined by the following equation [31]:

$${\text{d}}U_{i} = - S_{i} {\text{d}}T + V_{i} {\text{d}}p + \sum\limits_{k = 1}^{n - 1} {\frac{{\partial U_{i} }}{{\partial x_{k} }}} {\text{d}}x_{k} ,$$
(1)

where Si and Vi are the molecular entropy and volume of the ith component, respectively. T is the temperature, and p is the pressure. xk is the molar fraction of a kth component, and n is the total number of the components. The volume of a substance in the gaseous state exceeds that of the same substance in the liquid phase, resulting in a greater change in chemical potential between the two phases. At room temperature, substances with lower volatility are energetically favored to transfer from the gas phase to the liquid phase, leading to gas condensation and mixing with the liquid. As the pressure increases, the gas phase dissolves into the liquid phase, causing the phases to become more similar and leading to a reduction in surface tension at the gas–liquid interface.

On one hand, increasing pressure generally leads to an increase in gas density and resistance. However, in the context of porous media, reducing the contact angle in pore channels causes a decrease in droplet height (H1–H3) distribution and a smaller cross-sectional area of the pore channels between fibers, as shown in Fig. 12. These effects result in smoother gas flow channels with lower airflow resistance, which partially offsets the increase in resistance due to higher gas density. Consequently, under steady-state conditions, the pressure drop remains relatively constant across a range of different pressures.

Fig. 12
figure 12

Diagram of change in contact angle between droplet and fibre with increase in pressure

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On the other hand, the decrease in the contact angle leads to an increase in the three-phase contact line (L1–L3). Hence, the adhesion between the liquid and the filter media is enhanced, which strengthens the wettability of the filter.

In addition, the droplet morphology in filter medium B was found to be shell-shaped at 1 MPa, wrapped around the fibres with the smallest possible liquid–solid interface. When the pressure was increased to 5 MPa, the droplets still showed a shell shape, but the droplet–fibre interface was increased, as shown in Fig. 13, marked with red circles.

Fig. 13
figure 13

Distribution characteristics of liquid droplets on filter media B at 1 MPa and 5 MPa

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Based on the above analysis, combined with the results of Washburn [32] and Mullins [33], we obtained the capillary resistance for the glass fibre filter media:

$$P = \frac{2\gamma \cos \theta }{{ - 16.7\ln \left( {\frac{\alpha }{{r_{{\text{f}}} }}} \right) - 19.3}},$$
(2)

where α is the filling density of the filter material, rf is the fibre radius, γ is the surface tension of the liquid, and θ is the droplet contact angle. In this experiment, α/rf is constant, and γ decreases as the pressure increases. Meanwhile, the capillary force prevents the liquid from leaving filter media A and prevents the liquid from entering filter media B since the capillary resistance is in the opposite direction for oleophilic and oleophobic materials.

By integrating the data presented in Table 4, the capillary force of filter media B decreases from 0.20 mN at an initial pressure of 0.1 MPa to 0.13 mN when the pressure is increased to 5 MPa. Furthermore, as the pressure continues to increase up to 20 MPa, the capillary force is expected to 3.6 × 10–4 mN. Based on experimental results, it was observed that the jump pressure drop decreased slightly for both media. The exit capillary force of filter media A also decreases with increasing pressure. This decrease in pressure is due to the openings in the liquid film becoming larger as the entrance or exit pressures decrease. This phenomenon could also explain the breaking up of the film observed in the SEM pictures. Furthermore, an increase in adhesion of droplets in the channels with operating pressure requires a higher drag force to move them through and maintain a steady oil flow. This higher drag force is generated by a higher channel pressure drop, which in turn requires a higher level of saturation.

Conclusion

This paper shows that the gas density increases with the increase from 1 to 5 MPa, thus leading to a rise in airflow resistance. However, the solubility of the gas in the liquid increases with the increase in pressure, the surface tension of the DEHS decreases from 28.72 to 25.26 mN/m, and the contact angle between the droplet and the fibre decreases from 133.51° to 120.36° which causes a decrease in the surface tension of the liquid and the contact angle between the droplet and the fibre, resulting in a smoother gas flow channel with a lower resistance of airflow through the flow channel. As a result, the steady-state pressure drop is almost identical at different pressures.

With the increase in operating pressure, the adhesiveness of droplets in the channel increases, requiring higher resistance to move them and maintain stable oil flow, resulting in higher channel pressure drop and requiring higher saturation. Additionally, both types of media show a slight decrease in jump pressure drop as pressure increases, the capillary force of filter media B decreases from 0.20 mN at 0.1 MPa to 0.13 mN when the pressure is increased to 5 MPa which is due to the decrease in pressure being caused by the increase in opening of the liquid film with the decrease in inlet or outlet pressure. The influence of pressure cause changes in the liquid distribution, saturation of the filter media and the surface tension of a liquid. Therefore, further investigation of the changes in filtration performance of the filter media under high-pressure conditions is of great scientific significance and engineering value.