Title Supersonic Condensation and Separation Characteristics of CO₂-Rich Natural Gas under Different Pressures

Nomenclature

1  Introduction

In recent years, with the optimization and upgrading of world's energy structure, natural gas has become more and more critical in the economic fields. More and more countries have proposed accelerating the pace of structural adjustments, increasing the proportion of natural gas consumption and expanding the natural gas consumption market [1–3]. Besides hydrocarbons, natural gas from wellheads often contains excessive CO2 (carbon dioxide) and other non-hydrocarbon gases. The presence of CO2 will reduce the natural gas calorific value and pipeline transportation capacity, and at the same time, it will cause severe corrosion of facilities and pipelines. Moreover, CO2 can form dry ice and block the pipeline at low temperatures. Thus, CO2 removal during natural gas processing is one of the key processes [4]. Currently, CO2 removal methods commonly used in the industry mainly contain chemical absorption, pressure swing adsorption, physical adsorption, and membrane separation. These methods have achieved CO2 removal to a certain extent. Still, at the same time, there are some problems such as high energy consumption, low removal efficiency, high investment cost, and large loss of hydrocarbon gas [5–7].

Supersonic separation technology is an emerging natural gas treatment technology which combines expansion refrigeration with swirling separation. In a separator, the swirling motion is generated by a swirl generation device. Natural gas expands to supersonic velocities in the Laval nozzle, resulting in low pressure and temperature. The nucleation and condensation of impure gases occur, and the impure gas begins to change into droplets. Then the liquid droplets are centrifuged onto the walls and removed from the gas mixtures. Compared with traditional processes, it has many advantages, such as being a compact structure, energy-saving, and environmentally protective innocation, of which is, widely used in natural gas dehydration [8,9] and liquefaction today [10,11].

Relevant scholars have carried out a lot of research work on the above technologies. Jassim et al. [12,13] adopted CFD technology to simulate the flow of high-pressure natural gas in Laval nozzles. They analyzed the effects of swirl strength, nozzle structure, and real gas effects on the flow characteristics. Malyshkina [14,15] used the Eulerian two-dimensional model to study the fluid flow characteristics in the supersonic separator, discussed the effects of aerodynamic shock waves on the supersonic flow field, and analyzed the influence of Mach number on the volume and composition of natural gas condensate and stress recovery ability. Ma et al. [16] developed a cone-core supersonic swirling separation device and set up an experimental platform to conduct performance tests with water and ethanol vapor as the medium. Lun et al. [17] conducted a numerical simulation study on the nonequilibrium condensation phase change law of water vapor during supersonic flow. Shooshtari et al. [18] established a two-component condensation theoretical model based on the mass transfer rate and applied the model to the simulation calculation of supersonic condensation of water vapor. Wen et al. [19] conducted field tests using a new type of natural gas supersonic dehydration device. The results show that the energy loss can be minimized through an overall optimization design. It can also reduce the power consumption of the refrigeration compressor by 50%–70% compared with the low-temperature process of propane refrigeration under the condition of the same condensate yield. Bian et al. [20,21] proposed a theoretical model for the supersonic condensation of natural gas mixtures; the condensation process of the methane-ethane mixture can be divided into four main stages in Bian’s model. This model reveals the supersonic condensation process of the mixture from a microcosmic point of view, laying a foundation for the study of the condensation of multi-component alkane mixtures. In addition, the influence of swirl on the supersonic condensation and liquefaction characteristics of natural gas was systematically studied [22].

As a supplement and improvement to the traditional natural gas purification process, Bian et al. [23,24] put forward applying the supersonic separation technology to the field of CO2 removal in the first place. However, up to now, the complex problems of condensation and cyclone separation in the process of supersonic CO2 removal are still well understood. In this paper, the condensation efficiency and removal efficiency of CO2 in supersonic separators under different pressure conditions were studied, which is of great significance to improving and developing the natural gas purification process and reduce the cost of gas field development.

2  Structure Design of the Nozzle and Supersonic Separator

Laval nozzle is the key part of realizing CO2 condensation in supersonic separator. In order to obtain a more uniform flow field, the convergent section adopts the Vitosinski curve [25,26], and the parameters are selected as follows: r0 = 40 mm, rcr = 5 mm, and l1 = 140 mm; the convergent section curve satisfies the following equation:

m=mcr=kR(2k+1)k+1k−1p∗T∗Aq(Ma)(1)

For the divergent section of the nozzle, so as to predigest the design process and realize expansion and rectification at the same time, considering the characteristics of each linear comprehensively, the straight-line method is adopted to take the shape of a cone. And the line type of the divergent section satisfies the equation [27]:

r2=l2tan⁡φ2+rcr(2)

In order to ensure that the airflow is evenly accelerated to the sonic speed and to prevent the sudden change of the flow area from causing instability of the airflow, a continuous and gradual curve connection is used at the nozzle throat to get a smooth transition.

The structure and location of the cyclone should meet the separation requirements, as well as coordinates with other units in the separator. The design method in the reference adopts a rotating vane structure; the thickness and the length of the vane are 0.5 and 10 mm, respectively, and the rotation angle is 90 degrees, the swirl vane is set at the rear of the divergent rectification section, 350 mm from the inlet. The lengths of each section are shown in Fig. 1.

Figure 1: Structure diagram of the supersonic separator

3  Mathematical Model

3.1 Governing Equation

Based on the component transport equation of two-component fluid, the governing equations are established respectively. The gas-phase flow governing equations include mass equations, momentum equations, and energy equations. In contrast, the liquid-phase equation consists of the conservation equation for the droplet number and the relation between the parameters related to nucleating flow [28,29].

The gas-phase governing equations:

∂ρv∂t+∂∂xj(ρvuj)=Sm(3)

∂∂t(ρvui)+∂∂xj(ρvujui)=−∂pv∂xi+∂∂xj[μ(∂uj∂xi+∂ui∂xj−23δij∂uj∂xj)]+∂∂xj(−ρvu′iu′j¯)+Su(4)

∂∂t(ρvE)+∂∂xj(ρvujE+ujpv)=∂∂xj(keff∂T∂xj+uiτeff)+Sh(5)

Sm=−mv(6)

Su=−mvu(7)

Sh=−mv(h−hlv)(8)

The liquid-phase governing equations:

∂∂t(ρvE)+∂∂xj(ρvujY)=SY(9)

∂∂t(ρvN)+∂∂xj(ρvujN)=J(10)

rd=(3Y4πρlN)13(11)

3.2 Calculation Equation of Nucleation and Droplet Growth

The condensation of CO2 gas mainly contains two processes: nucleation and droplet growth. The calculation formula of the nucleation process adopts the ICCT model. This model revised the free energy calculation formula based on previous studies. The expression form of the ICCT model has been listed in the references [30,31].

After the nucleation process is finished, the droplets begin to grow continuously. The heat transfer coefficient of a droplet in steam is in connection with the size of the droplet and the relative velocity of the droplet in the steam molecule. The growth model of droplets proposed by Gyarmathy is used to calculate the droplet growth rate [32,33].

3.3 Equations of Droplet Discrete Phase Motion

The discrete phase motion equation of a CO2 droplet is as follows:

mlduldt=mlg−ρggVl+F(12)

Due to the high velocity of the droplet in the swirling process, its centrifugal force far outweighs its own gravity, so the gravity term is ignored in the numerical simulation. Meanwhile, because the gas density is much less than the droplet density, the buoyancy of the droplet is ignored. The simplified discrete phase motion equation is as follows:

mlduldt=F(13)

F=FD+FO(14)

The expression of FD is as follows [34]:

FD=18μgρldl2CDRe24(ug−ul)(15)

The other forces FO mainly consider the effects of FT and FS. The expressions of these two forces are as follows [35]:

FT=−DT1mT∇T(16)

FS=2Kkν1/2ρdijρpdp(dlkdkl)1/4(ug−ul)(17)

where, Kk = 2.584.

3.4 Meshing and Boundary Conditions

The ANSYS FLUENT 16.0 software is adopted to simulate the CO2 supersonic condensation and separation processes. The Laval nozzle (two-dimensional) and the supersonic separator (three-dimensional) have meshed separately, and the boundary layer mesh is encrypted. In terms of the supersonic conditions, the inlet boundary and outlet conditions are set to be inlet pressure boundary and outlet pressure boundary, respectively. The time step is 10-6 in the numerical simulation. The convergence criterion is 10-6 for the energy equation and 10-3 for all other equations [36].

The grid independence was verified based on the above numerical calculation method. The grid numbers of the Laval nozzle and the supersonic separator were determined to be 15,410 and 281,095, respectively.

4  Results and Discussion

4.1 Condensation Efficiency of CO2 in Laval Nozzle under Different Pressures

So as to study the CO2 condensation in Laval nozzle under different pressure conditions, Tin = 273.15 K and M = 0.2 were kept unchanged. The pin was set to be 6, 7, 8, and 9 MPa, respectively. The effects of inlet pressure on condensation parameters were analyzed. The variation law of condensation parameters (nucleation rate and droplet radius) under different pressure conditions was obtained by numerical simulation.

As shown in Fig. 2, it shows that when Tin is 273.15 K and M is 20%, as the pin increases, the CO2 condensation position moves forward. When pin is 6 MPa, The condensation start position is at x = 143.27 mm, and when pin increases to 9 MPa, the position where the condensation occurs moves forward to x = 139.59 mm, because the reason is when pin increases, the partial pressure of CO2 steam also increases, the greater the degree of supersaturation, the greater the degree of expansion, and spontaneous condensation is possible to occur under the same temperature. After analyzing the variation of nucleation rate and droplet radius (Figs. 2 and 3), it can be concluded that as pin increases, the maximum CO2 nucleation rate gradually decreases, and the CO2 droplet radius gradually increases. This is because the higher the inlet pressure, the sooner the condensation occurs, the higher the temperature when condensation occurs, and the smaller the nucleation rate.

Figure 2: Nucleation rate distribution in the nozzle

Figure 3: Droplet radius distribution in the nozzle

So as to study the effects of pin on liquefaction efficiency and droplet radius, the liquefaction efficiency at the outlet of the nozzle (the ratio of the liquid mass to CO2 mass at the inlet) and droplet radius were calculated under different pressures; the results can be seen in Fig. 4.

Figure 4: The effects of pin on the liquefaction efficiency and droplet radius of nozzle outlet

As shown in Fig. 4 under the same other conditions, the CO2 liquefaction efficiency at the nozzle outlet increases with the increase of pin. As pin increases from 6 to 9 MPa, the CO2 liquefaction efficiency at the Laval nozzle outlet increases from 56.90% to 79.97%, and the outlet droplet radius increases from 0.39 to 0.72 μm. When pin is smaller than 8 MPa, the increasing pin has particularly obvious effects on improving the liquefaction efficiency.

4.2 Effects of Inlet Pressure on Separation Efficiency

After the droplets are formed, the removal of CO2 is realized only if the separator wall captures them to form a liquid film and flow to the collector or collected directly by the sump. Therefore, in addition to the liquefaction efficiency, the separation efficiency is also an important index to evaluate if the separator structure is reasonable. During the separation process, part of the liquefied CO2 droplets enters the collecting tank (assumed as mtrap). In contrast, the remaining part flows out of the dry gas outlet without separation and is re-gasified (assumed as mescape). The separation efficiency η is defined as mtrap/mtotal.

Fig. 5 shows the separation efficiency under different pin conditions. It can be seen that the separation efficiency increases with the growth of the inlet pressure. When pin = 6 MPa, the separation efficiency of the supersonic separator is only 54.92%, while pin increases to 9 MPa, the supersonic separator's separation efficiency reaches 68.18%. This is because when pin is smaller, the diameter of the CO2 droplet and the centrifugal force is smaller. Most of the droplets are not captured by the wall due to the inertial effects caused by the axial velocity and are discharged with the gas. When the diameter of the CO2 droplet increases, the influence of centrifugal force is more apparent, and the droplet is more likely to be thrown to the wall and captured by the separator.

Figure 5: The effects of pin on the separation efficiency

4.3 Effects of Inlet Pressure on CO2 Removal Efficiency

The removal efficiency of CO2 in the supersonic separation process is determined by both nozzle condensation efficiency and swirl separation efficiency. Therefore, it is necessary to evaluate the removal efficiency of the supersonic separator by comprehensively considering the two. η′ is defined as Y/Yin multiplied by η.

According to the liquefaction efficiency and the separation efficiency under different inlet pressure conditions obtained in the above sections, the removal efficiency of the supersonic separator under corresponding conditions is calculated, and the results are shown in Fig. 6.

Figure 6: The effects of pin on the removal efficiency

As shown in Fig. 6, the inlet pressure affects the removal efficiency obviously, and the removal efficiency increases with the growth of the pin. When pin = 6 MPa, the CO2 removal efficiency is 31.25%, and when pin increases to 9 MPa, the CO2 removal efficiency can be as high as 54.52%. The effects of inlet pressures on the removal efficiency of supersonic separator are mainly reflected in two aspects: one is that pin affects the liquefaction efficiency of CO2 gas; The other is that the droplet size is different when CO2 gas condenses under different pin conditions, which means that the separation efficiency of droplet after passing through the swirl vane will be different. The combined effects of the two aspects lead to significant differences in the removal efficiency of CO2 gas under different pressure conditions.

5  Conclusions

In this paper, the supersonic condensation and swirling separation models were established. The supersonic condensation and separation characteristics of CO2-rich natural gas under different pressures were studied. The following conclusions can be drawn:

With the increase of inlet pressure, the position of condensation moves towards the nozzle inlet, the maximum nucleation rate decreases, and the droplet radius and liquid phase mass fraction increase. The CO2 liquefaction efficiency of the nozzle outlet increases with the growth of inlet pressure. The inlet pressure obviously affects the removal efficiency of the supersonic separator, and the removal efficiency increases with the growth of the inlet pressure.

The influence of inlet pressure on the removal efficiency of the supersonic separator is mainly reflected in two aspects: the inlet pressure affects the liquefaction efficiency of CO2 gas. The other is that the droplet size is different when CO2 gas condenses under different inlet pressure conditions, which means that the separation efficiency of the droplet after passing through the swirl vane will be different.

In the following research, the experimental research of supersonic condensation and separation characteristics of CO2 under different inlet pressure conditions can be carried out to verify the numerical simulation models and results to lay a foundation for the field application of the supersonic separation technology.

Funding Statement: This work was supported by the Research Project of Technical Inspection Center of Sinopec Shengli Oilfield Company “Research of Energy Flow Optimization Analysis and Application Technology of Oilfield Production System” and the Natural Science Foundation of Shandong Province (Grant No. ZR2021QE030).

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.