Mass transfer of CO₂ gas pocket in horizontal pipe flow

Gas–liquid mass transfer occurs when the gas solubility in the liquid phase is lower than the saturation solubility, or when the partial pressure of the gaseous solute in the liquid phase is higher than that in the gas phase (Cheng et al. 2008). The bubble mass transfer phenomenon can be observed in nature like river reoxygenation and industrial processes (Shimizu et al. 2000). Recently, algae blooms caused by eutrophication have become increasingly serious, and the pH of raw water has risen sharply as a consequence (Liu et al. 2016). Injecting gaseous CO₂ into transportation pipelines has been proposed as a method of pH control for raw water in water supply engineering. Since this method is considered economical, environmentally friendly, safe, stable, and efficient in the removal of organic matter, it is receiving increasing attention. Although the mass transfer of small bubbles or bubble swarms moving in still/flowing fluid has been extensively studied, the understanding of the mass transfer from large gaseous CO₂ pockets to flowing water in a pipe with restricted space is relatively limited. Investigating the features of such mass transfer processes is crucial for both industrial applications and the development of bubble mass transfer theories.

It has been commonly recognized that the mass transfer between a bubble and its surrounding water is determined by the bubble–water interfacial area, bubble residence time, mass transfer coefficient, and concentration difference. The rate of mass transfer can be written as: ⁠, where M is the gas mass inside the bubble, t is time, K_L is the mass transfer coefficient, A is the bubble–water interfacial area, C is the dissolved gas concentration in water, and C_s is the liquid-phase equilibrium concentration under the local partial pressure of the gas. The calculation of K_L is one of the key issues in bubble mass transfer. Over the last hundred years, researchers have proposed different theories for K_L depending on how the solute is transferred from the gas phase to the liquid phase. The most recognized models are the two-film theory proposed by Whitman (1923), the percolation theory by Higbie (1935), and the surface renewal model by Danckwerts (1951). The three classical mass transfer theories have provided a clear interpretation of the mass transfer processes and laid a solid foundation for subsequent studies.

Based on the three classical mass transfer theories, there have been extensively modified models developed through experimental studies and numerical simulations. Kubaczka & Bandrowski (1991) improved the two-film theory by including the variation of mass transfer coefficient with temperature and concentration in the model. Ma & Yu (1998) proposed the three-film theory of gas–liquid mass transfer as an improvement of the two-film theory by considering three resistance films for gas–liquid mass transfer. Perlmutter (1961) adjusted the surface renewal model by considering the flow of fluid elements from the liquid bulk to the interface as a tandem process. Models developed by combining two or three of the classical models have also been reported. For example, Hanratty (1956) proposed the film-penetration theory which was a combination of the two-film theory and the penetration theory.

The process of bubble mass transfer is significantly influenced by the bubble characteristics and the properties of the surrounding fluid. Cai et al. (2012) reported that as the bubble equivalent diameter increased, the bubble agglomeration behavior decreased, leading to an increase in both the gas–liquid interface area and the gas–liquid mass transfer coefficient. Motarjemi & Jameson (1978) experimentally verified that a single CO₂ bubble with a diameter of 2–3 mm had the highest mass transfer efficiency, compared with the bubbles of other sizes. Also, the bubble shape affects the contact area between the fluid and the bubble, which in turn affects the mass transfer efficiency (Xie et al. 2022). In addition, the flow velocity, viscosity, and the degree of turbulence of the fluid can influence the bubble mass transfer efficiency (Shaw & Hanratty 1977; Stoodley et al. 1997; Song et al. 2017). The liquid-phase flow rate affects the thickness of the diffusion boundary layer on the membrane surface, which, in turn, affects the gas transfer efficiency (Wang et al. 2016). Yang et al. (2022) found that the mass transfer coefficient increased with the liquid flow rate through both experiments and numerical modeling.

However, most of the existing studies focus on the mass transfer of a single bubble or bubble swarms moving freely in a stationary or flowing water body (Nock et al. 2016; Li et al. 2020). The situation of bubble mass transfer in the pipe flow is more complex due to the different dynamic features of gas/water flow under the constraint of the pipe wall, which has hardly been studied. Also, many previous studies have analyzed the bubble mass transfer process by assuming that the surrounding dissolved gas concentration is zero, considering the large space of the ambient fluid. The knowledge on the mass transfer of large gas pockets in a constrained space is limited, where the surrounding dissolved gas concentration is not negligible. This study experimentally investigated the mass transfer of a large stagnant CO₂ gas pocket in a horizontal pipe with flowing water. In the experiments, gaseous CO₂ was injected into the horizontal pipe until a stagnant CO₂ gas pocket was formed. The pH variation in the pipe under different water flow rates and CO₂ injection rates was measured and analyzed. The corresponding CO₂ gas pocket volume change was also recorded. The mass transfer coefficients were then calculated for each experimental condition, and their variation with the CO₂ injection rate and the water flow rate was also investigated.

In the experiments, the CO₂ flow rate was measured by a rotameter (LZB-3WB6, manufactured by Nanjing Dahua, Inc.), and the water flow rate was recorded by a flow meter (Lux-dn15, manufactured by Baoji Huaqiang, Inc.). The changes in pH were measured by a pH meter (MIK-Ph160, manufactured by Hangzhou Asmik) placed 0.5 m away from the end of the pipe (see Figure 1). These measurements were taken at a frequency of 0.2 Hz. The real-time pH data (i.e., pH – t curves) were recorded by the Asmik software on the computer. The pressure in the pipe was measured by a pressure gauge, as shown in Figure 1. The appearance of the CO₂ gas pocket inside the pipe was recorded by five cameras (SONY HDR-CX405). These cameras, named Camera #1, #2, #3, #4, and #5, were placed at 0.5 m intervals along the pipe in the direction of water flow (see Figure 1). The dimensions of the gas pocket were then obtained from the camera video images. The temperature of water was measured by a contact thermocouple thermometer (KOMAX, manufactured by Hangzhou Komax, Inc.). The details of the installation of the instruments are presented in Figure 1.

Before the experiment, the desired water flow rate was first achieved by adjusting the valve, and the pipe was filled with water. The glass electrode was then inserted into the water and started to record the pH values. Following that, all the cameras were turned on, and the illumination device was opened. The start of the experiment was marked as the moment of starting the gaseous CO₂ injection, i.e., t = 0 s. The pH dropped first as CO₂ was continuously injected into the water, while it got steady after a certain period. The gas injection was then stopped, and a CO₂ gas pocket was formed in the pipe. Subsequently, the size of the CO₂ gas pocket kept decreasing due to the dissolution of gaseous CO₂ . The experiment ended once the CO₂ gas pocket disappeared. The change in the gas pocket volume and the variation of pH in water were recorded simultaneously. The experiments were conducted under nine different conditions, as listed in Table 1. The flow rate was 15.6–24.7 L/min, the corresponding pipeline flow velocity was 0.13–0.18 m/s, and the corresponding Re = 7.3 × 10³–1.01 × 10⁴. The initial pH of the raw water used in this experiment was around 8.2, and the water temperature was 25 °C.

The morphological characteristics of the CO₂ gas pocket recorded by Camera #1 at different time points, specifically t = 120 s, t = 240 s, and t = 420 s, are shown in Figure 3(b). The experimental condition is Case 2, with the water flow rate Q_w = 18.1 L/min, the CO₂ injection rate Q_a = 4 L/min, the duration of CO₂ injection Δt = 122 s (i.e., CO₂ injection stopped at t = 122 s), and the total injected CO₂ volume V_a = 8.14 L. From Figure 3(b), the volume of the gas pocket keeps decreasing since the CO₂ injection stops. Qualitatively, the gas pocket disappears from the field of view of Camera # 5 at t = 150 s and from the field of view of Camera # 4 at t = 210 s. It can only be observed in the field of view of Camera # 1 starting from t = 240 s.

Figure 6(a) shows the pH curve under different water flow rates but the same CO₂ flow rate and injection duration. Under the water flow rate Q_w = 24.7 L/min, the time for water pH goes back to the initial value (about 8.2), i.e., pH recovery time, is t = 380 s. When the water flow rate Q_w = 15.6 L/min, the pH recovery time is t = 500 s. The results show that the rate of pH decrease is almost the same in the lowering regime. At higher water flow rates, CO₂ reacts with water at a faster rate and the corresponding pH recovery time is shorter. Figure 6(b) shows the pH curve under different CO₂ injection rates but with the same CO₂ injection time and the water flow rate. According to the experimental results, a higher CO₂ injection rate leads to a faster reduction of water pH. After stopping the CO₂ injection, the water pH returns to its initial value within a similar duration in these cases, approximately t = 440 s. Figure 6(c) shows the pH change curve under the same CO₂ injection rate and the water flow rate but different injection durations. It is seen that the decrease in water pH is more significant as the injection duration increases. After stopping the CO₂ injection, there is a long plateau on the pH curve. Subsequently, the pH gradually rises to its initial value at around t = 600 s. In addition, a longer CO₂ injection duration results in a greater pH recovery rate.

From Figure 7, the variations of mass transfer coefficients under all the experimental conditions show similar patterns. The mass transfer coefficient first increases but then decreases after a certain period. The increase in the mass transfer coefficient can be due to the fact that at the beginning of the mass transfer, the resistance at the gas–liquid interface is low and the gas molecules can dissolve rapidly into the liquid phase (Mavroudi et al. 2006). As the mass transfer process continues, the concentration gradient at the gas–liquid interface is reduced, and the driving force for mass transfer is weakened, which leads to a decrease in the mass transfer rate. Comparing Cases 2 and 3, under the same water flow rate, the increase in the CO₂ injection rate, i.e., the increase in the ratio of the CO₂ flow rate to the water flow rate in the pipeline, results in the increase in the mass transfer efficiency. It is due to the enlarged gas–liquid contact area, as reported by Farajzadeh et al. (2007). Based on the results of Cases 4 and 5, with the same CO₂ flow rate and injection duration, the mass transfer coefficient increases with the water flow rate at the beginning of the mass transfer process. It is because an increase in the water flow rate leads to a higher degree of turbulence and promotes the mass transfer process. As the mass transfer process is close to the end, the water flow rate has little effect on the mass transfer coefficient. The reason is that when the volume of the CO₂ gas pocket is reduced to a certain level, the concentration of CO₂ in water is much lower compared to that at the beginning of the mass transfer. The mass transfer driving force is weakened, so the effect of the water flow rate on the mass transfer coefficient becomes less significant.

In this paper, the mass transfer process of a large CO₂ gas pocket in the pipe flow was investigated, which can occur during the pH adjustment process of raw water in water supply engineering, and is also a phenomenon having been hardly studied experimentally before. The changes in pH, the volume of the CO₂ gas pocket, and the mass transfer coefficients under different water–gas conditions were recorded and analyzed. According to the experimental results, the ratio of the gaseous CO₂ injection rate to the water flow rate, the volume of the gas pocket, and the dissolved CO₂ concentration in the pipe flow all have large influences on the mass transfer process.

More specially, the injection of gaseous CO₂ into the pipe flow could effectively adjust the pH. The gas pocket volume was reduced approximately exponentially under all the experimental conditions. The pH change process could be divided into three regimes, including the lowering regime, the steady regime, and the recovery regime. The mass transfer coefficient of the CO₂ gas pocket in the steady regime was larger than that in the recovery regime. The results also validated the close relationship between the mass transfer coefficients and the variation of CO₂ concentration in the pipe flow due to the large volume of the gas pocket, which is different from many studies neglecting the ambient CO₂ concentration for simplified calculation. The mass transfer coefficient increased with the increasing ratio of the CO₂ injection rate to the water flow rate. The outcomes of this paper can contribute to a better understanding of gas bubble mass transfer in pipe flows and are meaningful for practical applications.

The authors gratefully acknowledge financial support from the National Key R&D Program of China (Grant No. 2022YFC3202602), the Natural Science Foundation of Zhejiang Province (Grant No. LZJWZ23E090009), the National Natural Science Foundation of China (Grant No. 52300122).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.