*3.1. Pressure Drop*

Plate pressure drop includes dry plate pressure drop and wet plate pressure drop, which are directly related to energy consumption in the operation process. A low pressure drop of the tray means that the fluid flowing through the tray loses less energy. Pressure

drop is an important indicator for evaluating the performance of the tray [33,34]. The pressure drop (Δ*P*) is calculated via Formula (1):

$$
\Delta P = P\_b - P\_t \tag{1}
$$

where *Pb* is the pressure at the bottom of the tray and *Pt* is the pressure at the top of the tray.

#### 3.1.1. Dry Plate Pressure Drop

The dry plate pressure drop refers to the energy loss caused by the gas passing through all of the components on the tray when there is no liquid flow, which reflects the influence of the tray structure on the performance [28]. Energy loss in dry pressure drop during TST operation is mainly caused by the gas passing through the plate holes and spray holes.

The change in dry plate pressure drop under different rolling amplitudes of the TST was experimentally analyzed under a rolling period of 8 s and F0 = 15. The experimental results are shown in Figure 6a. At times 0T, 0.5 T, and 1T, the tray was horizontal, and the dry plate pressure drop of the tray was similar to that in the static state. In addition, in a rolling period, the pressure drop at other times was larger than that in the static state. The pressure drop reached the maximum value in the first half-period and the second halfperiod at 0.25 T and 0.75 T. It can be seen from the figure that when the rolling amplitude was 0–4◦, the pressure drop changed little compared to that in the static state, and the maximum pressure drop increased by 20 Pa compared to that in the static state. When the rolling amplitude exceeded 4◦, the fluctuation degree of the pressure drop increased significantly. When the rolling amplitude was 7◦, the maximum pressure drop increased by 50 Pa. The reason for this is that, due to the influence of rolling, the gas coming out of the plate hole was no longer parallel to the spray tube. This gas directly impacted the inclined spray tube at an angle, making it more likely to form vortices and lose more energy, resulting in an increased pressure drop. With increasing rolling amplitude, the influence is more obvious. It can be seen that rolling had the adverse effect of increasing the TST dry plate pressure drop, but the effect was small when the rolling amplitude was within 4◦.

**Figure 6.** The dry plate pressure drop under rolling motion. (**a**) Different rolling amplitudes; (**b**) different rolling periods.

For rolling amplitudes of 4◦ and 7◦, the dry plate pressure drop under different rolling periods was analyzed. The experimental results are shown in Figure 6b. It can be seen that the curve trends of the dry plate pressure drop under different rolling periods were consistent, and the change was small across different rolling periods. When the periods were 8 s and 20 s, the maximum pressure drop difference was only 2%; the pressure drop can thus be considered to be unaffected by the rolling period.

#### 3.1.2. Wet Plate Pressure Drop

The wet plate pressure drop of the TST is different from that of other bubbling trays due to its special structure and gas–liquid flow mode. The wet plate pressure drop of the TST includes two parts: one is the energy loss of gas through the tray structure; the other is the energy lost when the gas contacts the liquid through the spray tube. The wet plate pressure drop of the tray is an important index to evaluate the hydraulic performance of a tower, and it represents the energy lost by the gas phase passing through the tray. According to these data, the tower structure can be improved, which is of great significance to the optimization of the tray structure [35].

Figure 7 shows the change in wet plate pressure drop under rolling motion when F0 = 8.74, VL = 2.2 m3/h, and T = 8 s. It can be seen from Figure 7a that when rolling occurred, the pressure drop fluctuated with the rolling and reached maximum fluctuation values in the first half-cycle and the second half-cycle at about 0.25 T and 0.75 T. When the rolling amplitude was not more than 4◦, the wet plate pressure drop fluctuated little compared to that in the static state, and when the rolling amplitude reached 4◦, the pressure drop at 0.25 T and 0.75 T changed by 2.3% and 2.7%, respectively, compared to that in the static state. After 4◦, the pressure drop fluctuated obviously with increased rolling amplitude. When the rolling amplitude reached 7◦, the pressure drops at 0.25 T and 0.75 T changed by 8.1% and 8.9%, respectively, compared to that in the static state. The reason for this is that the rolling motion causes a fluctuation in the clear liquid layer on the tray, and weeping may occur during this process, which leads to fluctuations in the pressure drop. At 0.25 T, the spray tube sloshes to the lowest position, and the pressure drop increases due to the increase in the liquid level around the spray tube. At 0.75 T, the spray tube sloshes to the highest position and the liquid level at the spray tube is the lowest, resulting in the lowest pressure drop. The larger the rolling amplitude, the greater the pressure drop fluctuation, and the more unstable the working state of the tray.

**Figure 7.** The wet plate pressure drop under rolling motion. (**a**) Different rolling amplitudes; (**b**) different rolling periods.

Figure 7b shows that the degree of pressure drop fluctuation under different periods differed little, and the difference between the maximum pressure drop and the minimum pressure drop at 0.25 T and 0.75 T was only about 1%.

We can see that the wet plate pressure drop under rolling conditions fluctuated with rolling, and the smaller the fluctuation, the stronger the ability to resist sloshing. A rolling amplitude within 4◦ had little effect on the wet plate pressure drop. When it reached 7◦, the fluctuation was controlled at 10%, indicating that the TST can still maintain a good pressure drop distribution under rolling conditions. Further, the change was small under different rolling periods, showing little effect due to the rolling period.

#### *3.2. Weeping*

When the rising gas velocity is low, the rising gas' power in the riser is not enough to support the liquid. The liquid directly drops from the riser, which is called weeping. Weeping will affect the plate's gas–liquid contact and reduce the tower plate's efficiency. At the same time, serious weeping will make the plate unable to accumulate fluid, resulting in abnormal operation [29,31]. It is generally considered that the weep rate should not exceed 10%. Therefore, the gas velocity at a weep rate of 10% is called the weep point gas velocity in the industry. The gas velocity at the weeping point is the lower limit of the normal operating range of the tray. The weep rate (*eL*) is calculated via Formula (2).

$$
\omega\_L = \frac{V\_W}{V\_L} \tag{2}
$$

In the formula, *VW* and *VL* are the volume flow rates of the weeping liquid and the feed liquid, respectively.

Figure 8 shows the weeping under rolling motion with different F0 at VL = 2.2 m3/h. It can be seen from Figure 8a that there was no weeping under the three conditions in the static state, and the weep rate increased with increased rolling amplitude. The growth rate was flat when F0 = 8.74 and F0 = 10.05, and the weep rate was still less than 1% when the rolling amplitude reached 7◦. The tray operated well. When F0 = 7.86, the weep rate increased significantly with increased rolling amplitude, and the weep rate reached 7% when the rolling amplitude reached 7◦, which is a significant change from the static state. It can be seen that the rolling motion had the adverse effect of increasing the weep rate. At low gas velocity, the rolling motion changes the height of the clear liquid layer and the distribution of the airflow, resulting in the local airflow kinetic energy being insufficient to support the liquid gravity, causing weeping. Moreover, when the rolling amplitude exceeded 4◦, the liquid level unevenness increased and the pressure drop fluctuated significantly, so the weep rate increased significantly compared to that from before.

**Figure 8.** Weeping under rolling motion. (**a**) Different rolling amplitudes; (**b**) different gas velocities; and (**c**) different rolling periods.

It can be seen from Figure 8b that with increased rolling amplitude, the weep rate increased, and the lower operating limit of the tower increased. In the static state, the weep rate reached 10% at F0 = 6.3. When the rolling amplitude was 4◦, the weep rate reached 10% at F0 = 6.75. Under a rolling amplitude of 7◦, the weep rate reached 10% when F0 = 7.7. We can see that the rolling motion reduced the normal operating range of the tower plate. When the rolling amplitude was 4◦, the lower operating limit of the tower increased by about 7.5% compared to that in the static state, having little effect on the tower. When the rolling amplitude was 7◦, the lower operating limit of the tower increased by about 22% compared to that in the static state. However, the weep rate can still be well controlled under the appropriate plate hole kinetic energy factor. Figure 8c shows that as the rolling period changed in the range of 8 s ~ 20 s, the differences between the weep rates of each period were small and could be ignored.

#### *3.3. Entrainment*

When the gas flow velocity is low, weeping occurs, making the tray unable to operate normally. Conversely, when the gas velocity is too large, some small droplets will be carried by the gas to the upper tray, which is called entrainment. Excessive entrainment will affect the efficiency of the tower [36]. In industrial production, remedial measures must be taken when entrainment reaches 5% [37]. Entrainment is calculated via Formula (3):

$$
\epsilon\_v = \frac{M\_e}{M\_G} \tag{3}
$$

where *Me* is the mass rate of the liquid lifted to the foam capture tray by the gas and *MG* is the mass rate of the gas.

In order to better study the entrainment of the tray, experimental analysis was carried out with different FT at VL = 2.2 m3/h. It can be seen from Figure 9a that with increasing rolling amplitude, the entrainment tended to decrease, and the larger the gas velocity, the more obvious the change trend. When FT = 1.16, the tray had no entrainment under the rolling condition as it was under the static state, and when FT = 2.42, the entrainment decreased slightly with increased rolling amplitude.

It can be seen from Figure 9b that the entrainment was positively correlated with FT and decreased with increased rolling amplitude. When FT = 2.42, the entrainment was reduced by about 5% compared to that in the static state when the rolling amplitude was 4◦, and it was reduced by 9% when the rolling amplitude was 7◦. The reason for this is that, due to the influence of rolling, in the process of gas–liquid injection, part of the gas is sprayed downward and part of the gas is sprayed upward. The gas and liquid sprayed obliquely downward will directly fall on the tray, and due to the effect of gravity, the liquid-carrying rate of this part of the gas is relatively higher. Rolling increases the collision between the droplets and the tower components so that some of the small droplets converge into large droplets after collision and fall directly. The higher the gas velocity, the greater the collision's severity. Therefore, rolling causes the entrainment to slightly decrease.

Figure 9c shows that when FT was low, the rolling period did not affect the entrainment. When FT was high, entrainment increased with increased period length. When the rolling amplitudes were 4◦ and 7◦ under the condition of FT = 2.42, the entrainment ratios in the 20 s period increased by 4.1% and 5.3%, respectively, compared to that in the 8 s period. The reason for this is that, with an increase in the rolling period length, the collision intensity between droplets decreases, which makes the entrainment rise.

**Figure 9.** Entrainment under rolling motion. (**a**) Different rolling amplitudes; (**b**) different gas velocities; and (**c**) different rolling periods.

#### *3.4. Liquid Level Unevenness*

When the tower is tilted due to rolling motion, the free liquid level on the plate will be different, and the liquid level at each position will change at any time with the rolling. In this paper, the degree of liquid level unevenness at a certain time is called the liquid level unevenness. The greater the liquid level unevenness is, the greater the pressure drop fluctuation of the tray is, and the easier it is to cause weeping and other adverse effects. Eight test points were taken on the tower wall in the experiment, as shown in Figure 10.

**Figure 10.** The locations of monitoring points.

In this experiment, the diameter of the tower and the frequency of rolling were small, so it can be considered that the free liquid level on the tower plate was still in the horizontal state and did not fluctuate during the rolling. The liquid layer on the tray had a clear free liquid level, which could be read directly. We reduced the observation error by measuring the liquid level under multiple periods and calculating the average value. After measuring the liquid level at the eight points, the liquid level unevenness was calculated according to Formula (4).

$$M\_f = \left[\frac{1}{n} \sum\_{i=1}^{n} \left(\frac{h\_i - \overline{h}}{\overline{h}}\right)^2\right]^{0.5} \tag{4}$$

In the formula, *n* represents the number of measuring points on the tower wall; hi represents the liquid level at point *i* on the tower wall, mm; and *h* represents the average liquid level height on the tray, mm.

Figure 11 shows the influence of different rolling amplitudes and rolling periods on the liquid level unevenness when F0 = 8.74 and VL = 2.2m3/h. Figure 11a shows that the liquid level unevenness under different rolling amplitudes fluctuated periodically with time, reaching upper and lower half-period maxima at around 0.25 T and 0.75 T. The fluctuation in amplitude of liquid level unevenness increased with increased rolling amplitude. Figure 11b shows that the trend of level unevenness on the tower plate was consistent under different rolling periods, and the difference between each period was small enough to be ignored. It can be seen that rolling motion had adverse effects on free surface fluctuation, but there was no sharp change in the free surface in the experiment, and the tray could still work normally.

**Figure 11.** Liquid level unevenness under rolling motion. (**a**) Different rolling amplitudes; (**b**) different rolling periods.

#### **4. Conclusions**

In this paper, a new type of total spray tray (TST) with gas–liquid countercurrent contact was proposed to solve the problem of poor resist sloshing ability in existing towers under offshore conditions. Its hydrodynamic performance was experimentally studied under rolling motion to evaluate the influence of offshore conditions on the TST. The following conclusions were obtained under the experimental conditions:

Rolling caused adverse effects such as hydrodynamic performance fluctuation of the tray. When the rolling amplitude did not exceed 4◦, the fluctuation was small. As the rolling amplitude exceeded 4◦, the influence of rolling on the TST gradually increased.

The dry plate pressure drop of the TST fluctuated with the rolling motion. When the rolling amplitude was 4◦, the dry plate pressure drop fluctuated by a maximum of 9% compared to that in the static state, and the fluctuation was 22% when the rolling amplitude was 7◦. The fluctuation amplitude of wet plate pressure drop increased with increased rolling amplitude. When the rolling amplitude was 4◦, the maximum fluctuation of wet plate pressure drop was 2.7% compared to that in the static state, and when the rolling amplitude was 7◦, the fluctuation was 8.9%.

Rolling induced weeping, reducing the normal range of the tray. When the rolling amplitude was 4◦, the lower limit of operation of the tray was 7.5% higher than that in the static state, which had little effect on the tower. At 7◦, the lower limit of operation of the tray was 22% higher than that in the static state. However, under the condition of an appropriate kinetic energy factor, the weep rate could still be well controlled within 10%.

Entrainment decreased slightly with an increase in the rolling amplitude, which shows that the rolling motion had little effect on the entrainment. The fluctuation in liquid level unevenness increased with increased rolling amplitude. However, there was no serious liquid level fluctuation at large amplitudes, and the tower could still operate stably.

The difference in the hydrodynamic performance of the TST in different periods was very small, so different rolling periods can be considered to have little effect on the performance of the tray.

At the same time, it can be seen that increasing the gas velocity within the appropriate range can reduce the adverse effects such as weeping caused by sloshing in practical applications.

**Author Contributions:** Conceptualization, methodology, J.T.; data curation, writing—original draft, software, G.Z.; validation, J.Y.; software, L.W.; writing—review and editing, F.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **Nomenclature**



#### **References**


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