Effect of sand diameter on the performance of annular jet pumps

For the current problem of low efficiency of the annular jet pump in transporting particles, the effects of different sand diameters on the flow field, pressure and efficiency inside the annular jet pump are analysed, in order to improve the structure of the annular jet pump to adapt to the transport of solid particles. The results show that when the flow rate is relatively small, due to the small flow rate of the suction mixture, it can not meet the suction capacity of the primary flow, which causes reflux in the suction chamber or throat; with the increase of the flow rate ratio, the transport capacity of the annular jet pump for the sand shows a parabolic growth, so to maintain the efficient transport capacity, the flow rate ratio should be selected between 0.4-0.7; the efficiency of sand transport of the annular jet pump is much higher than that of the centre jet pump, and it is much higher than that of the centre jet pump. Annular jet pump compared to the centre of the pump transport sand efficiency appeared the opposite phenomenon.

1. Introduction D. Thomson of England in the mid-nineteenth century first used jet pumps to conduct experiments on pumping water and air, marking the introduction of jet pumps [1].The types of jet pumps have also been diversified to include centre-type, multi-nozzle type [2], and annular-air type, which enable the pumping efficiency to be improved, and can also meet the needs of different conditions [3].The centre type jet pump has its primary flow passing through the suction port located at the centre of the pump's shaft, while the annular jet pump has its primary flow ejected from its annular bumper nozzle near the wall.Multi-nozzle jet type jet pumps are further divided into centre multi-nozzle and ring multi-nozzle.China has abundant coalbed methane resources, most of which are stored in the central and western regions, and the exploitation of coalbed methane is of great significance in pulling the economic development of the central and western regions [4].As a high-quality energy source, CBM can improve the energy structure of China, fundamentally prevent coal mine gas accidents, effectively mitigate the greenhouse effect, and pull the development of related industries.Reasonable, economic and efficient exploitation of CBM has become a common concern nowadays.Jet pump discharge technology has been applied to oil well pumping in the 1960s, and after decades of development and improvement, it has become an important part of the oil and gas extraction process.Based on its special advantages, jet pump can be widely used in oil and gas fields with complex well structure, high temperature, high gas-liquid ratio, sand and corrosion, and other complex mining conditions, but also can be applied to the special operation of oil and gas wells.Compared with the traditional centre jet pump, the annular jet pump places the primary flow nozzle around the inlet pipe of the suctioned fluid, thus making the suction channel an unobstructed channel, which is especially suitable for conveying mixed fluids containing particles [6].
Although domestic and foreign scholars have carried out more detailed studies on annular jet pumps experimentally and theoretically, including the performance and internal flow mechanism of annular jet pumps, etc., and optimised the structure of annular jet pumps in terms of the mixing chamber angle, area ratio, throat length as well as diffusion tube angle and profile to improve its efficiency [7,8], Kuzuhara et al. theoretically investigated the effects of different structure and Kuzuhara et al. theoretically investigated the effects of different structures and parameters on the performance of annular jet pumps [9].Japanese scholars Shimizu et al. studied different jet ejection methods of annular jet pumps, and compared the effects of spinning and spinless working jets on the performance of annular jet pumps, and the results showed that spinning jets can increase the efficiency of the pump within a certain range, but the efficiency of the pump will decrease in other working conditions, and also studied the cavitation phenomenon of annular jet pumps [10].In order to reduce the generation of cavitation, Wang et al [11] improved the conical suction chamber to a streamlined suction chamber.A comparison of the numerical simulation results shows that the streamlined inhalation chamber structure is more efficient than the conical inhalation chamber, and the cavitation performance is more excellent.Wang et al [12] further designed the inhalation chamber, throat, and diffusion chamber as a curve with a uniform transition between parts A and B. The simulation results show that the streamlined annular structure is more efficient than the conical inhalation chamber, and the cavitation performance is more excellent.Simulation results show that the streamlined annular jet pump has a larger high-efficiency zone and exhibits better cavitation performance.Choi et al [13] designed a J-shaped groove installed inside the annular jet pump in order to improve the cavitation of the annular jet pump, and the simulation results show that the pressure inside the annular jet pump increases and improves the cavitation performance of the pump.Shrestha et al [14] improved the cavitation performance of the annular jet pump by changing the angle of the diffusion chamber and the depth of the J-shaped groove.Shrestha et al [14] designed a J-shaped groove to improve the cavitation performance by changing the angle of the diffusion chamber and the depth of the J-shaped groove.Shrestha et al [14] improved the suction performance of an annular jet pump model by varying the diffusion chamber angle and J-groove depth, and the results showed that the installation of J-grooves with suitable diffusion chamber angles could effectively improve the suction performance and thus suppress cavitation in the pump.A. Morrall et al. [15] completed a comparison of numerical simulations using two alternative models of Reynolds-averaged N-S, concluding that at the highest vortex levels, the Reynolds stress model yields higher performance predictions.Xiong [16] et al. analyzed the structure of the nozzle and obtained an optimization method for the nozzle design through computational analysis.Wang et al [17] improved the conical suction chamber to a streamlined suction chamber, and the simulation results showed that the streamlined annular jet pump has a larger high efficiency zone and exhibits better cavitation performance.
There are but few studies on sand transport using annular jet pumps [18], which is a promising hydraulic transport tool that is particularly suitable for the application of solid particles linking the bottom of coalbed methane (CBM) wells returned to the bottom of CBM wells during the drainage and extraction of CBM.Since the suction channel of the annular jet pump is in the middle, located on the same axis as the throat, this facilitates the transport of solid particles such as fish, potatoes, onions, and carrots [19].Since sand particles in the suction liquid are the main factor affecting the performance of the jet pump, the pump with the best performance among 25 pumps with different structures used in Shimizu's test [20] is chosen as the prototype for numerical simulation in this paper, and the RNG k-ε turbulence model combined with the Mixture multiphase flow model is used to study the effects of different sand particle characteristics on the internal flow field and performance of the annular jet pump, and to analyse how to improve its performance and optimise the structure and operating parameters of the jet pump for returning solid particles.The results of the study provide theoretical guidance for the annular jet pumps used in sand transport.

Prototype pump construction
Jet pump is fluid mechanical and mixing reaction device that uses the turbulent diffusion of a jet to transfer energy and mass [21].An annular jet pump is mainly composed of an annular nozzle, an inhalation nozzle, an inhalation chamber, a throat and a diffusion tube [22] (Figure 1).In the figure, Ds0 is the diameter of the suctioned channel, Dt is the diameter of the throat, and D0 is the diameter of the outlet.Ps is the pressure of the sucked fluid, Pp is the primary flow pressure, and Pd is the pressure of the outlet mixed fluid.The primary flow is ejected from the nozzle at high speed and coils the sucked fluid.The two fluids mix and exchange momentum in the throat, which increases the kinetic energy of the transported fluid and finally discharges it after converting most of the kinetic energy into pressure energy through the diffusion tube.Compared with the centre jet pump, the nozzle of the annular jet pump is located around the inlet pipe of the sucked fluid, thus forming a straight channel in the centre of the pump body, which is especially suitable for conveying mixed fluids containing particles.The performance parameters of the annular jet pump are flow ratio M=Qs/Qp, pressure ratio N=(Pd-Ps)/(Pp-Pd), and efficiency η=MN, where: Q, P are the volumetric flow rate and the total pressure; the subscripts d, o, s denote the position of the pump outlet, the nozzle inlet and the suction chamber inlet, respectively.Long Xinping took the pump with the best performance among the 25 pumps of different structures used in the Shimizu test as an improved prototype and used the experimental design method combined with numerical simulation to obtain the optimal size combination of the pump's performance (Table 1).In this paper, this optimal pump will be used as a prototype to study the effect of particle diameter size on the transport efficiency of annular jet pumps.

Numerical simulation
The flow inside the annular jet pump is set to be a constant incompressible flow and the flow field distribution has axisymmetric characteristics, so the choice of a two-dimensional axisymmetric surface for the computational region can satisfy the requirements of the study [23].The inlet length of the computational domain is set to 1 Ds0 and the outlet pipe length is set to 3 D0 to ensure the stability of convergence.
The controlling equations are the Reynolds-averaged N-S equation and the mass conservation equation; the RNG k-epsilon turbulence model and the Mixture multiphase flow model are used; the standard wall function is used to deal with the wall stresses; the medium of the jet pump is water, and mass inlet for both working inlet and suction inlet, and the velocity of the primary flow is given and kept constant, and the flow ratio is achieved by changing the flow rate of the suctioned flow rate change; the pressure boundary condition is used at the outlet; the SIMPLE algorithm is used to solve the velocity and pressure coupling; and the QUICK format is used to reduce the effect of pseudo-dissipation.In this paper, sand diameters of 0.05mm,0.1mm,0.2mmand 0.3mm were selected and these sand sizes were in accordance with the actual transportation situation [24].The mass flow rate of the sand is 15% of the suctioned mixed fluid.The simulation method of this paper has been verified in the comparison of the data obtained by Long Xinping and Ping et al [25] using Shimuzu experiments.The maximum efficiency obtained from the simulation of the prototype pump in this paper is closer to the results obtained by Long Xinping et al [25], so the simulation method in this paper is practicable.

Performance of the pump
In order to study the transport capacity of the annular jet pump for sand at different flow ratios, the flow rate of the suctioned fluid is varied.The sand is sucked into the annular jet pump through the sucked fluid channel, and the flow rate and velocity of the sucked fluid have an important influence on the sand transport of different diameters, by analysing the influence on the efficiency of the annular jet pump when the flow rate ratio is varied.The efficiency of the annular jet pump is the ratio of output energy to input energy, reflecting the ability of the annular jet pump to transfer energy.From the efficiency performance graph Figure 2, it can be seen that as the flow ratio increases, the flow rate of the sucked fluid increases, then the flow rate of the sucked fluid is also faster, so the efficiency of the annular jet pump to carry sand increases rapidly.When the flow ratio M is more than 0.4 and less than the efficiency reaches a large value.Since there are no studies on annular jet pumps for transporting sand and gravel, and the efficiency of center jet pumps fluctuates from 20% to 26% at flow ratios greater than 0.4 and less than 0.7 [26].In this paper, the efficiency of annular jet pump is obtained than 25% for different sand diameters.
When the flow ratio continues to increase the efficiency begins to decline.As the particle size increases, the efficiency increases, when the particle size D is 0.3mm is significantly greater than the efficiency of 0.2mm.The efficiency when the suctioned fluid does not contain sand is higher than the efficiency when it contains different particle sizes.
From Table 2, it is concluded that the flow ratio at which the maximum efficiency of the annular jet pump occurs when pumping sand varies, and the maximum efficiency when the suctioned fluid is not mixed with sand reaches 29.1% when the flow ratio M is taken as 0.6.When the minimum particle size D is taken as 0.05, its maximum efficiency is 25.9%, when the flow ratio M is 25.9%.

Analysis of internal flow mechanisms
Figure 3 shows that the high turbulence intensity of the annular jet pump at different flow ratios, the high turbulence intensity region is mainly concentrated in the suction chamber where the primary flow and the suctioned mixture are mixed, and the region near the wall.And the high turbulence intensity region exists inside the suction chamber and in the front part of the throat at small flow ratio (M≤0.2) conditions.With the increase of flow ratio, the potential flow core of both working and sucked fluids increases, and this smaller turbulence intensity region also increases, but with the increase of turbulence intensity area, the maximum turbulence intensity starts to decrease.Observation of Figure 4 pressure cloud and combined with the velocity cloud Figure 5 can be concluded: the fluid through the pipe with the increase in the cross-section of the diffusion tube, the velocity is gradually reduced, kinetic energy is converted into pressure energy, the increase in the pressure region began to expand.With the increase of the flow ratio, the region of larger flow velocity in the throat begins to shift to the axis, which is conducive to reducing the friction loss of the wall.Along with the increase of the flow ratio, the pressure inside the suction chamber of the annular jet pump begins to rise, and the larger value of the pressure begins to transfer to the throat, and the overall value of the pressure from the inlet of the throat to the inlet of the diffusion tube increases, which makes the pressure in the centre of the shaft increase significantly.With the full development of the flow, the primary flow and the secondary flow mixed with the radial velocity gradient decrease from the diffusion tube after the spray.As can be seen from Figure 6, the primary flow from the annular nozzle sprayed along the wall began to expand the extension of the high-speed primary flow injection into the suction chamber resulting in a sudden pressure drop, the formation of the pressure is much smaller than the secondary flow pressure, forcing the suction of the secondary flow into the suction chamber and mixing.The two fluids are mixed at the end of the annular jet pump throat or in front of the diffuser and finally discharged from the outlet pipe.In the figure, as the flow ratio increases, the high-speed flow region begins to approach the center of the axis and maintains high-speed flow in a larger area of the throat.
The reflux zone has disappeared at a flow ratio of 0.3, while the reflux zone of the suctioned fluid without sand doping disappears at a flow ratio of 0.4.This is related to the build-up of sand in the suction chamber, which affects the flow in the reflux zone, which in turn makes the reflux zone disappear earlier with the increase of the flow ratio.When there is no reflux, the high-velocity flow core of the sucked fluid can extend even to the diffuser inlet position.The velocity in the area from the annular nozzle inlet to the throat increases due to the gradual completion of the fusion of the suctioned fluid with the primary flow, and then gradually begins to decrease as the acceleration is less than the counterpressure gradient.As can be seen from Figure 7, the return area inside the suction chamber is larger under the condition of small flow ratio (M≤0.2), which results in the accumulation of sand in the front part of the return area, so the flow ratio of the annular jet pump used for pumping sand should be selected as a larger value (M＞0.2).This can avoid the situation of low pumping efficiency due to the reflux area.Combined with Figures 8 and 9, it can be seen that the primary flow is sprayed from the nozzle to generate negative pressure, and the solid-liquid two-phase mixture with a certain concentration is sucked into the suction channel located in the centre, and the primary flow begins to be mixed.At the beginning stage, the primary flow and the mixture are in convection because the velocity of the primary flow is large and the flow rate of the absorbed mixture is basically zero.When entering the throat, the sucked mixture and the primary flow are further mixed, the sand spreads in the axial direction, and the concentration of solid particles near the wall starts to decrease, while the concentration of solid particles in the axial direction gradually increases.Figure 8 shows that the volume fraction occupied by the sand increases with the increase of the sand particle size, which is one reason for the increase in the efficiency of the annular jet pump in pumping the sand with the increase of the particle size.

Conclusion
The effects of different sand diameters on the flow field, pressure and efficiency inside the annular jet pump are analysed based on the RNG k-ε turbulence model combined with the Mixture multiphase flow model, in order to improve the structure of the annular jet pump to adapt to the transport of solid particles.We came to the following conclusions： (1) When the flow rate is relatively small (M ≤ 0.2), due to the small flow rate of the suctioned mixture, it is not able to meet the coiling suction capacity of the primary flow, which causes the generation of reflux in the suction chamber or throat; (2) As the flow rate ratio increases, the transport capacity of the annular jet pump for sand shows a parabolic increase, so to maintain efficient transport capacity, the flow rate ratio should be selected between 0.4-0.7; (3) The opposite phenomenon occurs in the efficiency of the annular jet pump compared to the centre jet pump in transporting sand, where the efficiency of transporting sand within a certain range of sand diameters increases as the particle size increases;

Figure 2 .
Figure 2. The efficiency of annular jet pump at different particle sizes.

3 .
Turbulent kinetic energy cloud for different flow ratios with D=0.3.

Figure 8 . 8 Figure 9 .
Figure 8. Volume fraction clouds of sands with different grain sizes for M=0.2.

Table 1
Prototype pump dimensions.

Table 2
Maximum efficiency and its corresponding flow ratio.