Experimental study on the optimum number of layers of fiber mats for gas-liquid coalescer

The coalescer is widely used in deep gas dehydration due to its high efficiency. Most manufacturers make the filter by enwinding multiple layers of fiber mats to obtain high efficiency, which leads to high-pressure losses in practical applications. Obtaining the number of layers of fiber mats is based on engineering practice and experiences, which needs more data support and theoretical basis. 1-10 layers of hydrophilic fiber mat samples were made, and experiments were carried out at filter face velocities of 0.14m/s to 0.35m/s and liquid loading rate of 1.25g/min to 5g/min. In addition, the concept of collision probability based on fiber porosity is invoked. A model between efficiency and porosity is developed to obtain the optimal solution for the number of layers. The results show that the saturation is monotonically decreasing, while the pressure drop linearly increases as velocity increases. The optimum number of fiber mat layers decreases from 5 to 3 as the filter face velocity increases. The efficiency model based on the fiber porosity agrees with the experimental efficiency values, which provides theoretical support for calculating the optimal number of fiber mat layers.


Introduction
As a widely used equipment for deep gas-liquid separation, the coalescer is utilized in various fields such as chemical [1], medicine [2], and petroleum [3].Researchers have conducted extensive studies on the structural parameters that affect its separation performance, including pore size gradient, thickness, fiber diameter, and filler density.The coalescer's filter element is a multilayer winding structure of thin glass fiber mats layered around a metal skeleton.Resin adhesive seals and covers the components to complete the assembly.Obtaining the number of layers of fiber mats is based on engineering practice and experiences, and the actual number of layers of filter media used is much higher than the optimal value.High-pressure loss due to excessive material usage, which conflicts with national carbon peaking policies and carbon neutrality goals [4].
There are limited studies on the optimal number of filter layers.D. Kampa [5,6] conducted experiments on lipophilic and oleophobic fiber mats with 1-10 layers of 0.5mm thickness and proposed a jump and channel model by observing fiber saturation.However, the analysis did not include corresponding efficiencies and the optimal number of layers.Li [7] investigated the influence of filter thickness on coalescence performance and found that a thicker filter resulted in improved interception efficiency of small droplets, leading to higher cumulative efficiency.Chang [8][9][10] performed experiments on glass fiber mats with 4-10 layers of 0.4 mm thickness.However, their study 2 centered on the effect of adding a drainage layer structure on coalescer performance, liquid channeling, saturation, and other indexes, without mentioning the origin of the glass fiber mat quantity.It was not explicitly stated that Mullins et al. [11][12][13][14][15] utilized an optimal number of layers when employing a four-layer glass fiber filtration medium.
To determine the optimal number of glass fiber layers and establish a mathematical model between porosity and separation efficiency, experiments were conducted using 1-10 layers of filter media at filter face velocities (0.14, 0.21, 0.28, 0.35 m/s) and liquid loading rates (1.25, 2.50, 3.75, 5.00 g/min).The optimal number of layers was determined through repeated experimentation and comparing performance indicators such as efficiency, pressure drop, and quality factor.Furthermore, the collision probability was incorporated into the efficiency model to establish a mathematical relationship between porosity and efficiency.

Fiber and liquid materials
The glass fiber mats were obtained from Jiangsu Zeyusen Carbon Fiber Technology Co.During the wet forming process, an adhesive was applied to the surface of the alkali glass fiber, causing a modification in the fiber's hydrophilic properties.Following image processing techniques described in literature [8], the contact angle between the fiber mats and droplets was measured to be 130.75°, thereby confirming the hydrophobic nature of the fiber mats.Using a digital caliper, the thickness of the mats was measured to be 0.50±0.02mm.SEM images of the fibers were subjected to postprocessing, which allowed for the determination of an average fiber diameter of 10 ± 0.5 μm.Additionally, a specific gravity flask was designed and assembled using method described in literature [16,17] to achieve a porosity of 0.95 ± 0.01.In order to prevent any external interference from inorganic salt ions on experiment, deionized water was utilized, as has been reported in literature [18].

Experimental instruments
The experiment was conducted using the coalescence separation testing platform.Figure 1 presents the flow chart for the experiment.The gas in turn enters the coalescence filter through the gas pre-filter, the gas mass flow controller with PID control, and the wall flow separator.The gas flow controller, GRYLLS RS485-RTU, is obtained from Shengqi Technology (Beijing) Co.The pressure transmitter, HDSSWILL HCCY100-71-R-B-B-T-XY, is obtained from Qingdao Huacheng Measurement and Control Equipment Co.The ultrasonic nebulizer creates tiny droplets by converting electrical energy into mechanical energy through a diaphragm.A single ultrasonic nebulizer can produce tiny droplets at a 2.5g/min rate.The droplet size was repeatedly measured using an OMEC DP-02 spray laser particle size analyzer, revealing a roughly lognormal size distribution, with a median size value of 4.60 μm and a geometric standard deviation of 8.13.Additionally, intermittent water supply from a timing device ensures that the liquid level is within the atomizer's operating range.Installing a check valve downstream of the pump prevents gas from flowing backward into the water circuit.The wall flow, where liquid flows along the pipe wall before reaching the filter, is crucial for liquid aerosols.A wall flow separator was installed upstream of the partition by slotting the existing pipe and attaching a large-diameter round pipe to address this issue.An annular gap was created between two pipes of different diameters to pre-separate the wall flow.The coalescer filter is made of PMMA and features an 80mm high and 30mm wide channel for aerosols to pass through.Its left-right split structure includes a 50×100 mm filter media clamped in the airflow channel.The metal support was not used to prevent the effect of liquid accumulation on the surface of the support structure on separation efficiency.Trapezoidal grooves were machined on the lower surface of the inlet and outlet portions of the filter to improve water discharge and calculate separation efficiency.
During the experiment, pressure drops were continuously recorded at 5-second intervals using a pressure transmitter.Liquid discharged from the windward and backside sides of the filter was collected through a pipe in a wide-mouth bottle at the bottom of the filter.The liquid accumulation was then recorded using an electronic balance to evaluate filter efficiency.All experiments were conducted using a specific combination of filter layers and aerosol concentrations under defined and stable conditions.Each experiment began with freshly made dry filter media until the pressure drop did not fluctuate by more than 2% over four hours.The media was then dismantled and weighed to study filter media saturation.A steady state was reached after approximately 5 to 36 hours, as indicated by a horizontal pressure drop curve based on the loading rate and the number of filter layers.

Filter material preparation
During the experiment, it was discovered that when the filter media was clamped using a frame structure the liquid collected did not completely move in the airflow direction due to the capillary phenomenon.This phenomenon causes the accumulated liquid do not entirely move along the airflow direction, resulting in some liquid flowing out in the normal airflow direction between the layers of filter media.It is the reason why the efficiency and pressure drop values are lower than the actual values.To compensate for this flaw, a new type of filter media preparation method is proposed.The filter media adopts a plate structure (with a net size of 50mm × 100mm) consisting of multiple layers of thin wet-molded glass fiber mat, with an 30mm × 80mm effective separation area.Firstly, large rolls of glass fiber media were cut into 50mm × 100mm rectangles (Figure 2 (a)), and a 30mm × 80mm area was marked in the center using a marker pen with a homemade mold (Figure 2 (b)).Next, adhesive was applied to the 10mm area at the edge (Figure 2 (c)).The layers were stacked according to different numbers of layers in the experimental protocol.Then, the bonded filter media were placed in a homemade jig to secure them tightly (Figure 2 The flow chart of filter material preparation.Finally, the U-shaped sealing strip was installed by cutting the glued filter media into 46mm × 96mm sizes.Specific rubber glue was used to affix the strip around the filter media.During the installation of the four corners of the sealing strip, it was found that cutting the ends at a 45-degree angle (Figure 2(e)-(f)) worked best.The seal of the filter was ensured by sanding it after the glue had dried.The effective filtration area of the glass fiber filter was sealed with adhesive tape and nonwoven fabrics.The filter material was smoothed by placing it on the surface of 400-grit and 800-grit sandpaper before the filter preparation process was completed (Figure 2(g)-(h)).The transport of aerosols and liquids during the experiment can weaken the water-soluble binder in the filter media [19].To address this issue, the pressure drop curve was recorded for each newly made filter media.Each group of experiments was repeated three times using the newly-made filter media to ensure experimental reproducibility.

The effect of the number of layers on the properties of filter materials
Forty combinations of full experiments, each with three replicates, resulted in a total of 120 runs.These experiments were conducted at filter face velocities ranging from 0.14 to 0.35 m/s, with the number of layers ranging from 1 to 10.As depicted in figure 3, the dry pressure drop (a) and wet pressure drop (b) curves were measured for each layer and surface velocity.Figure 5(a) shows that the wet pressure drop increases as the liquid loading rate increases.This phenomenon was analyzed from an energy perspective, where the gas pressure loss across the porous medium remains constant.An increasing liquid loading rate signifies that more liquid is passing through the porous medium within the same unit of time.The energy requirement that gas through the porous medium remains constant, while the liquid necessitates additional energy to through.The energy consumption is represented by the pressure drop, which increases in unity with the liquid loading rate.The efficiency improvement in figure 5(b) results from a rise in the amount of atomized liquid, which leads to an increase in the concentration of large size droplets.

Determine the optimal number of filter layers
The filtration performance of the coalescer is mainly determined by the pressure drop and efficiency, and pressure drop is used to characterize the energy loss of the airflow through the filter media.The filtration efficiency shows the performance in intercepting micro-droplets.From the experimental data in Section 3.1, it is evident that as the number of layers increases, the separation efficiency increases while pressure drop also increases, meaning that the two indexes interact to some extent and oppose each other.Therefore, the researchers evaluated the separation performance by introducing a parameter quality factor γ [1] that considers pressure drop and separation efficiency.
where η is the separation efficiency (%); ΔPwet is the wet pressure drop (Pa).
Figure 6 shows the quality factor curves of 1-10 layers of filter media at filter face velocities of 0.14, 0.21, 0.28, and 0.35 m/s.The Figure 6 shows that the quality factor under different flow rates showed a trend of first increasing, then decreasing, and then gradually leveling off.The quality factor reaches its highest point for filter face velocity of 0.14 m/s when the number of filter media layers is 5, and the optimal number of layers for a filter face velocity of 0.21, 0.28, 0.35 m/s is 4, 3, 3 layers, respectively.As the filter face velocity increases, the value of the optimal layer gradually decreases.When the number of layers exceeds 8, the quality factor fluctuates above and below 0.01, and the efficiency of each layer is more than 93.62% when the number of layers exceeds 5.The data shows that the efficiency of this type of filter media reaches its optimal processing capacity when the number of layers exceeds 5.According to the literature [21], the maximum processing capacity of the filter media is determined by the tensile strength of the fibers and the fatigue limit.The optimal number of layers is determined by multiplying the experimental optimum by a safety factor that is more significant than one.Table 2 shows the percentage increase in pressure drops exceed the optimal number of layers, representing the filter media's pressure drop loss over the multilayer fibers compared to the optimal number of layers.To improve the process of determining the number of filter layers, an efficiency model based on particle collision probability in a circulating fluidized bed is established.The model explores the relationship between porosity and the efficiency of filter media.During the establishment of collision probability, the following assumptions were made: (1) The process of droplet impact on the fiber surface is only considered, and the collision between droplets is not considered.
(2) The droplet size change in the pipe and the gravity settling chamber before the droplet impact is not taken into account.The droplet particle size distribution is assumed to be unchanged during the movement from the coalescer's inlet to the fiber's front surface.
(3) The number of micro-droplets is large relative to the collision probability, and it is assumed that the probability of collision occurs obeys a Poisson distribution [22]; (4) The fibers intercept the droplets once the droplets move to the collision area.The modeling process is based on the particle collision process in the gas-solid system.The Figure 7 shows the fiber surface of control body unit C, blue spherical for the tracked tiny droplets.Assuming that the control body unit contains N different particle sizes (particle size distribution in line with the normal distribution) of the tiny droplets, then the probability of collision of droplets with the fiber was calculated for the equation ( 2). Figure 7(a) illustrates the transformation process of a fiber into a control body cell, with tiny droplets moving towards the fiber with velocity V.

Collision area with any fibre in the control body
Control body cross-sectional area p = (2) The schematic of the collision probability model.In Figure 7 (b), the grey area represents the fibers and the blue area represents the area within the control body where fiber-droplet collisions occur.The collision probability p is the ratio of the sum of the blue collision area and the grey fiber projection area to the total area of the control body.The distance between the blue boundary and the fiber surface is the droplet's radius, and the probability is that the theoretical value of the single-layer glass fiber intercepts tiny droplets.An OMEC laser particle size analyzer DP-2 measured the droplet size distribution, which gave a median of 4.60 ± 0.12 μm.Therefore, the effective collision diameter per fiber is the fiber diameter plus 4.60 μm.
According to Frising [23], the effective collision area of a clean filter media is assumed to be ：A=(df+ dliq) LT, where LT=4Z Ω αf/(πdf 2 ), and Ω is the area of the filter media.
The distribution of fibers is shown in Figure 7(b).Only the collision area of the fibers on the windward side is effective at intersections.The number of contact intersections Nc can be calculated by the model proposed by Meyer [24] and Zhu [25]: ( ) The effective collision area formula is changed to the following equation ( 4): ( ) Where ( ) ( ) , substituting this equation into the collision probability equation yields the filter media collision probability model as follows: ( ) ( ) The probability of collision of the filter media is the separation efficiency of the filter media, and the model ignores the effect of the number or thickness of the fiber layers.According to Azarafza's conclusions [26], the layers in a filter element behave more like individual filters than a monolithic entity, even in tightly packed "sandwich" media, with each layer having a characteristic liquid saturation profile repeated throughout the media.Each layer was treated as a separate filter element.The efficiency of each layer was solved separately using the iterative method from Frising [23], and a comparison between the experimental and theoretical values of the model is shown in Figure 8.The monotonic increase in separation efficiency with increasing filter face velocity is shown in figure 8, which is due to the increase in droplets separated by the inertial interception of fibers and the direct collision mechanism with an increasing velocity.Theoretical values predicted by the model are consistently lower than experimental values at four velocities when there are no more than five layers, as the model only considers median droplet size and fiber diameter.Table 3 shows the errors between the experimental and modeled values of separation efficiency.From the data in the table 3, the average errors are 8.16%, 7.68%, 10.58%, and 11.38% at four velocities.The error is more significant in the region with less than five layers, which requires further optimization.

Theory of liquid film interception of microdroplets
At the initial stage of coalescence experiment, we found that some aerosols escaped from the outlet of the coalescer (figure 9).The phenomenon is more intuitive in figure 6 in the literature [27], which shows that the concentration of downstream particles decreases exponentially and stabilizes with the increase of the jump pressure drop at the initial stage.In section 3.2, the efficiency of a single-layer glass fiber filter with a porosity of 0.95 can reach more than 60%, which is 24.10% higher than the 40.4% obtained from the ratio of collision areas.The difference indicated that the effective collision area of the fibers removed from the interception process plays a decisive role in the interception process, and other factors are also involved.In the literature of Mullins [12][13][14]28] and Mead-hunter [29][30][31], we found that the liquid film wrapped around the fibers during the interception process also increases the effective interception area.

Figure 9.
The aerosol escape at the beginning of filtration with 6 layers of filter media.D. Kampa [5] proposed that when experiments were carried out with wettable and non-wettable media, the saturation of the first layer reached its maximum value.In contrast, the subsequent layers remained dry because the first layer was first exposed to the aerosol and carried out the interception process, as demonstrated by Bitten [21] and Mead-Hunter [29].Unlike wettable filter, where droplets are intercepted on the filter fibers, non-wettable filters form tiny droplets on the windward side of the filter media, which gradually coalesce to form a liquid bridge and eventually a film on the front surface of the filter.This causes a significant increase in the initial pressure drop of non-wettable filter media.Under pressure, the liquid penetrates the first layer of filter media through areas of greater porosity, and this process is repeated for the subsequent layers.
To verify this phenomenon, we repeated D. Kampa's experiment using deionized water and thin glass fiber mats, using a 6-layer filter media at the optimum number of layers obtained in section 3.2.The liquid distribution versus saturation curves are shown in figure 10.Compared to D. Kampa's conclusion [5], the liquid distribution in the direction normal to the airflow of the non-wetted filter media after the experiment was not uniformly distributed.Instead, the liquids were distributed in the lower half of the filter media, indicating the effect of gravity on the interstices of the filter layers.The liquids were redistributed from layer to layer under the effect of gravity.The results of Azarafza [26] show that in the absence of clamping structures, such as circular perforated plates or diamond mesh, on both sides of the filter media, the gap between layers after applying the airflow will be much larger than 200 μm, and the liquid will complete the redistribution process inside this gap.This phenomenon contributes to an increase in the diameter of liquid passages and a reduction in pressure drop by significantly reducing the number of passages.However, this optimization is done at the cost of shortening the filter media's lifespan, which is not desirable in actual operation.Additionally, we found that the filter media becomes dry except for the liquid channel area when the number of layers is ≥3.This indicates that the previous layers' fibers have already intercepted the tiny droplets.Therefore, the non-wettable filter media can intercept the droplets during the coalescence process due to the existence of a liquid film formed on the surface of the fibers, transforming the fiber collision in section 3.2 into a process of interception between the liquid film and the tiny droplets.It is that liquid film has the same physical properties as droplets, and the influence of the fiber contact angle on droplet interception is weakened in a steady state, so the assumption that the droplets are intercepted after contacting the liquid film on the surface of the fiber can be ultimately confirmed.Figure 11 shows that the theoretical values of the model are more significant than the experimental values at four flow rates, as the model only considers theoretical values when the droplet size and fiber diameter are median.When the velocity is small, the inertial separation of droplets in the fiber weakens, and tiny droplets are more likely to escape, decreasing the experimental values.Furthermore, the efficiency values were obtained by the differential gravity method, which has a sizeable human error, and some droplets were not collected inside the coalescence or on the pipeline's wall, leading to low experimental values.Table 4 shows the errors between the experimental and modeled efficiencies, which are 8.75%, 7.14%, 4.89%, and 5.34% at the four velocities.Compared to the model in section 3.2, the error size is acceptable, and the model has good consistency.

Conclusion
In this paper, tests were conducted on 1-10 layers of single glass fiber mats at filter face velocities of 0.14, 0.21, 0.28, 0.35 m/s with liquid loading rates of 1.25, 2.50, 3.75, 5.00 g/min using full experiments, and the following conclusions were obtained: (1) Through a series of experiments varying in velocity, number of layers, and liquid loading rate, the results show that both dry pressure drop and wet pressure drop are monotonically increasing with the number of layers and surface velocity.The saturation has little relationship with the number of layers but decreases with the increase of air velocity, and wet pressure drop is also monotonically increasing with the liquid loading rate.
(2) The optimal number of layers under the filter face velocity of 0.14, 0.21, 0.28, and 0.35 m/s is determined to be 5, 4, 3, and 3 by comparing the quality factor.Then, the porosity and separation efficiency model is established by incorporating the collision probability.To explain the phenomenon of aerosol escape in the early stage of coalescence, the theory of liquid film interception of microdroplets was proposed.Based on the theory, efficiency optimized model of the single hydrophobic filter material has been proposed.However, this model may not apply to sandwich-type filter materials with multiple porosities and composite materials of varying types.There is no denying that the model provided data to support selecting the optimal number of layers of the filter media.

Figure 1 .
Figure 1.The flow chart of coalescence separation experiment platform.The wall flow, where liquid flows along the pipe wall before reaching the filter, is crucial for liquid aerosols.A wall flow separator was installed upstream of the partition by slotting the existing pipe and attaching a large-diameter round pipe to address this issue.An annular gap was created between two pipes of different diameters to pre-separate the wall flow.The coalescer filter is made of PMMA and features an 80mm high and 30mm wide channel for aerosols to pass through.Its left-right split structure includes a 50×100 mm filter media clamped in the airflow channel.The metal support was not used to prevent the effect of liquid accumulation on the surface of the support structure on separation efficiency.Trapezoidal grooves were machined on the lower surface of the inlet and outlet portions of the filter to improve water discharge and calculate separation efficiency.During the experiment, pressure drops were continuously recorded at 5-second intervals using a pressure transmitter.Liquid discharged from the windward and backside sides of the filter was collected through a pipe in a wide-mouth bottle at the bottom of the filter.The liquid accumulation was then recorded using an electronic balance to evaluate filter efficiency.All experiments were conducted using a specific combination of filter layers and aerosol concentrations under defined and stable conditions.Each experiment began with freshly made dry filter media until the pressure drop did not fluctuate by more than 2% over four hours.The media was then dismantled and weighed to study filter media saturation.A steady state was reached after approximately 5 to 36 hours, as indicated by a horizontal pressure drop curve based on the loading rate and the number of filter layers.

Figure 3 .
Figure 3.The dry pressure drop (a) and wet pressure drop (b) curves for layers 1-10 at filter face velocities of 0.14, 0.21, 0.28, and 0.35 m/s.

Figure. 3 Figure 4 .
Figure. 3 illustrates a linear single-increasing trend in the dry and wet pressure drops with an increase in the number of layers.The experimental data fit the Davies equation [20] perfectly, in which the pressure drop is a function of the filter face velocity and the number of layers.The slope of the dotted line in figure.3 explains the filter face velocity term in Davies' equation.The gradient enhances as the filter face velocity increases.Figure.4 (a) depicts the efficiency curves of 1-10 layers, which correspond to four velocities.As the pressure decreases at a plutonic function of the number of layers, the efficiency fluctuates around 95% when the number of layers exceeds 5, indicating that this is the maximum separable efficiency of this type of filter media.Efficiency increases with the rise in the filter face velocity of the filter media, leading to an increase in the probability of droplet interception by collision and inertial interception in the droplet interception mechanism of the filter media.Additionally, the inertial interception of droplets by wall flow at structural mutation increases efficiency with filter face velocity.

Figure 4 (Figure 5 .
Figure 4.The efficiency (a) and saturation (b) at the filter face velocities of 0.14, 0.21, 0.28 and 0.35 m/s for layers 1-10 filter media.Figure4(b) demonstrates a decrease in saturation as the surface velocity of the filter material increases, while exhibit none specific trend with the number of layers.The filter face velocity was at 0.21 m/s, considering various factors to evaluate the impact of liquid loading rate on coalescence performance.The liquid loading rate was altered by adjusting the number of atomizers.Figure5displays the variation curves of wet pressure drop and efficiency of 1-5 layers of filter media at liquid loading rates of 1.25, 2.50, 3.75, and 5.00 g/min under a surface gas velocity of 0.21 m/s.

Figure 6 .
Figure 6.The quality factor curves for 1-10 layers of filter media at filter face velocities of 0.14, 0.21, 0.28 and 0.35 m/s.

Figure 8 .
Figure 8.The comparison between separation efficiency and model.

Figure 10 .
Figure 10.The liquid distribution diagram and corresponding saturation curve for each layer of 6layer filter.In summary, the effective projected area in the empirical equation in section 3.2 needs to be increased by the thickness of the liquid film dfilm, and the model is changed to the following equation:

(
mass on the surface of the corresponding layer of filter media (Kg).Figure11shows the comparison between the optimized model (blue dotted line) and the experimental values.

Figure 11 .
Figure 11.The comparison between separation efficiency and optimized model.

Table 1
displays the physical properties of this deionized water.

Table 1 .
The physical parameters of deionized water at 20℃

Table 2 .
The pressure drop percentage increases as the number of layers exceeds the optimum value

Table 3 .
Error table between experimental values and model values