Analysis of Flow Field Characteristics of Sand Removal Hydroyclone Applicable to Solid Fluidization Exploitation of Natural Gas Hydrate

Analysis of Flow Field Characteristics of Sand Removal Hydroyclone Applicable to Solid Fluidization Exploitation of Natural Gas Hydrate | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Analysis of Flow Field Characteristics of Sand Removal Hydroyclone Applicable to Solid Fluidization Exploitation of Natural Gas Hydrate Na Wei, Yi Qiao, Shuanshi Fan, Meng Cai, Haitao Li, Shouwei Zhou, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2980319/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract With the development of economy and society, the consumption of fossil energy is gradually increasing. In order to solve the current energy dilemma, NGH is considered as an ideal alternative energy. At the same time, the solid fluidization exploitation is an ideal exploit method for NGH at present. However, in the process of solid fluidization exploitation, sand and hydrate ore bodies enter the closed pipeline together, which will block the pipeline and increase the difficulty of exploitation. Therefore, the pre-separation of sand by hydrocyclone plays an important role in solid fluidization exploitation. In this study, the numerical simulation method was used to study the internal flow field characteristics of the hydrocyclone under different conditions, and the effects of different flow rate, different flow ratio, different sand content and different particle diameter on the phase distribution are investigated. The results show that: at the same axial position, the increase of flow rate and sand content makes the sand phase more distributed at the edge of the flow field, while the change of flow ratio has no significant effect on the distribution of sand phase. Under the same working conditions, the sand gradually migrates to the center of the flow field with the increase of the axial distance, while the particle diameter change has no significant effect on the sand distribution. By calculation, it is obtained that under the optimum working condition of the flow rate is 4.83m 3 /h, the flow ratio is 20%, the sand content is 20%, and sand particle diameter is 80µm, the maximum E s is 22.1% and the minimum is 86.1%. Finally, a comprehensive analysis of the hydrocyclone in this study shows that this type of hydrocyclone is applicable to rough pre-separation of sand in the process of solid fluidization exploitation of NGH, and can not fine separate complex mixture. Through the study of the internal flow field characteristics and phase distribution law of the hydrocyclone, this study provides a reference for the practical engineering application of sand phase pre-separation in the solid fluidization exploitation of NGH. Physical sciences/Energy science and technology Physical sciences/Engineering/Energy infrastructure Natural gas hydrate Cyclone separation Flow field characteristics Sand removal hydroyclone Solid fluidization exploitation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 13 Figure 14 1. Introduction With the development of economy and industry, the consumption of global fossil energy is gradually increasing. According to statistics, the total global energy consumption in 2018 was 14.301 billion tons of oil equivalent, of which oil accounted for 31%, coal accounted for 26%, and natural gas accounted for 23% [ 1 – 2 ]. A large amount of fossil energy consumption makes social development fall into a dilemma of serious shortage of resources and rapid deterioration of ecological environment [ 3 ]. Therefore, finding an alternative clean energy has become the key to solve the current energy dilemma. Natural gas hydrate (NGH) is widely known for its abundant energy reserves, wide distribution, clean combustion and high energy density [ 4 – 6 ]. Natural gas hydrate is an ice-like and combustible clathrate crystalline compound formed by water molecules and light hydrocarbon gas molecules under low temperature and high pressure environment, so natural gas hydrate is also called “Combustible ice” [ 7 ]. Under standard conditions, 1m 3 natural gas hydrate can release 164m 3 natural gas [ 8 – 9 ]. It is estimated that the current global natural gas hydrate reserves are about 2×10 16 m 3 , equivalent to 2×10 13 tons of oil equivalent, about 40 times that of conventional natural gas reserves, and the content of organic carbon is twice that of the world’s proven fossil fuels[ 10 – 12 ]. Natural gas hydrates are mainly distributed in seabed sediments below 300m and in land permafrost layer at 200-2000m [ 13 – 14 ]. Therefore, the reservoir-forming environment of low temperature and high pressure has become the main factor limiting the large-scale exploitation of gas hydrate. At present, the exploitation methods of natural gas hydrate mainly include depressurization method, thermal excitation method, chemical injection method and so on [ 15 – 18 ]. The depressurization method is to break the equilibrium pressure condition of the hydrate phase by lowering the reservoir pressure, so as to promote the decomposition of the hydrate [ 19 ]. The thermal excitation method is to promote the release of methane gas by injecting heat into the hydrate reservoir and breaking the temperature condition of hydrate phase equilibrium [ 20 ]. The chemical injection method is to inject natural gas hydrate inhibitors into hydrate reservoirs to decompose hydrates [ 21 ]. However, there are some disadvantages such as uncontrollable phase transition, high energy consumption, unstable gas production and high economic cost in the exploitation of natural gas hydrate by the above methods [ 22 – 23 ]. In order to solve the problems existing in the exploitation of natural gas hydrate at present, Zhou put forward the solid state fluidization exploitation method of natural gas hydrate [ 24 – 25 ]. The natural gas hydrate solid fluidization exploitation method is to use high-pressure jet or mechanical mining to break the solid hydrate ore body on the shallow surface of the seabed into fine particles, and then mix the broken hydrate ore body with seawater to form a hydrate slurry. The hydrate slurry is transported to the offshore platform through a closed pipeline for later separation treatment [ 26 – 27 ]. The solid fluidization exploitation method changes the uncontrollable decomposition of gas hydrate into continuous controllable decomposition, which realizes the in-situ exploitation of natural gas hydrate and avoids catastrophic production accidents caused by hydrate decomposition in the process of exploitation [ 28 – 29 ]. During the exploitation of natural gas hydrate by solid fluidization exploitation method, the hydrate slurry is transported from the seabed to the offshore platform in a closed pipeline [30]. With the change of temperature and pressure, the hydrate ore body gradually decomposes into three phases of gas, water and sand, and the flow changes from solid and liquid two-phase flow to gas, liquid and solid three-phase flow in the closed pipeline [ 31 ]. Therefore, the three-phase separation of gas, water and sand in the hydrate slurry is the key to realize the solid fluidization exploitation of natural gas hydrate. At present, the main methods used for separating hydrate slurry are gravity separation, chemical separation, and cyclone separation [ 32 – 34 ]. Among them, the cyclone separation method has attracted much attention because of its high efficiency, small size and high separation speed [35]. The hydrate slurry is injected into the hydrocyclone by the closed pipeline, and the mixture moves in a circle along the wall of the cyclone chamber. Due to the density difference of gas, water and sand, the centrifugal force difference is generated during the circular movement, thus the separation of different phases is realized. At present, many experts and scholars have carried out extensive research on the application of three-phase hydrocyclone in the exploitation of natural gas hydrate. Qiu et al. [ 36 ] analyzed the impact of reservoir sand production on the exploitation of natural gas hydrate and designed an underground hydrocyclone based on this. At the same time, the structural parameters of the hydrocyclone were optimized by numerical simulation method, and the separation efficiency of the optimized cyclone separator was evaluated. Fang et al. [37] studied the response relationship of sand particle diameter, sand volume fraction and natural gas volume fraction with the gas collection efficiency and sand removal efficiency of hydrocyclone based on the small hydrocyclone with classical structure, providing a basis for the practical application of hydrocyclone in the solid fluidization exploitation of hydrate. Wei et al. [ 38 ] optimized the structural parameters of the traditional three-phase hydrocyclone by using the computational fluid dynamics method, analyzed the effect of various structural parameters on the separation efficiency of hydrate slurry in the hydrocyclone, and obtained the optimum combination of structural parameters of the hydrocyclone. Lin [39] designed an axial annulus in situ hydrocyclone desander (AAIHD), and explored the applicability of this hydrocyclone in solid fluidization exploitation of hydrate. Chang et al. [ 40 ] proposed a hydrocyclone applicable to the exploitation of subsea natural gas hydrate. The effects of operational and structural parameters on the separation performance of the hydrocyclone were studied using a combination of numerical simulation and experiments, and the optimal ratio of structural parameters was obtained. However, so far, there are few studies on the internal flow field characteristics and phase distribution law of hydrocyclone used in the solid fluidization exploitation of natural gas hydrate. In this paper, based on the hydrocyclone proposed by Chang et al. [ 40 ], which is applicable to solid fluidization exploitation of natural gas hydrate, the numerical simulation method is used to study the flow field distribution characteristics and phase distribution law in the hydrocyclone under the condition of water and sand two-phase. In order to ensure the universality and accuracy of the research, combined with the actual engineering situation, the effects of different flow rates, different flow ratios, different sand volume fraction and different sand particle diameter on the internal flow field characteristics and phase distribution of the hydrocyclone were studied. The sand discharge efficiency and water discharge efficiency of the hydrocyclone were calculated under different conditions. It provides some guiding significance for the practical engineering application of the hydrocyclone in the solid fluidization exploitation of natural gas hydrate. 2. Method 2.1 Physical model In this paper, based on the hydrocyclone proposed by Chang [ 40 ], which is applicable to in-situ separation of sand phase in solid fluidization exploitation of natural gas hydrate, the flow field characteristics and the distribution of different phase in the hydrocyclone are analyzed and the separation efficiency of the hydrocyclone is calculated. The structure of the hydrocyclone applicable to the in-situ separation of sand phase in the solid fluidization exploitation of natural gas hydrate is shown in Fig. 1 . In the process of solid fluidization exploitation of natural gas hydrate, the shallow weakly cemented hydrate reservoir on the seafloor is broken into a hydrate ore body by mechanical crushing method or high pressure jet method, and then the hydrate orebody and sediment enter the closed pipeline with the sea water. Considering the narrow space in the actual natural gas hydrate mining project, an axial-flow hydrocyclone is used to initially separate the sand entering the pipeline at the exploitation site, and the separated sand is backfilled. As shown in Fig. 1 , the mixture of water and sediment enters the hydrocyclone from the inlet at an axial velocity, and after passing through the spiral flow path, part of the axial velocity of the mixture is transformed into a tangential velocity. At this time, the flow field inside the hydrocyclone become a swirling flow field. Due to the density difference between water and sand, a centrifugal force difference is generated in the swirling flow field. The density of the water phase is smaller than sand phase, and the centrifugal force generated in the circular motion is small, so the water phase is distributed at the axis of the hydrocyclone, and enters the separator pipe, ultimately discharged from the hydrocyclone through the water outlet. The density of the sand phase is relatively high, and centrifugal force generated in the circular motion is large, Therefore, the sand phase is distributed on the inner walls of the hydrocyclone, and finally discharged from the hydrocyclone through the sand outlet. Thus, the preliminary separation of sand phase in the process of solid fluidization exploitation of natural gas hydrate is completed. In this study, a three-dimensional model was used to study the flow field characteristics and the distribution law of different phase in the in-situ sand removal hydrocyclone for solid fluidization exploitation of natural gas hydrate. In the numerical simulation of the swirling flow field, the three-dimensional model can more objectively and comprehensively reflect the differences of different physical fields and different phase in different directions, which plays a significant role in improving the accuracy of numerical simulation of the flow field in the hydrocyclone [ 41 ]. The dimensions of the hydrocyclone as shown in Table 1 . Table 1 Dimensions of the hydrocyclone Structure Symbol Value(mm) Main diameter D 100 Separator Pipe diameter d 25 Sand Outlet diameter d so 35 Inlet length l i 100 Spiral Flow Path length l s 100 Water Outlet length l wo 100 Separator Pipe length l p 120 2.2 Mathematical model 2.2.1 Governing equation The fluid flow in a hydrocyclone can be regarded as a viscous incompressible fluid, which follows the basic governing equations as shown in Eq. ( 1 )-( 3 ) [42–43]: Continuity equation: $$\frac{\partial }{{\partial {x_j}}}\left( {\rho {u_j}} \right)=0$$ 1 Momentum conservation equation: $$\frac{\partial }{{\partial {x_j}}}\left( {\rho {u_i}{u_j}} \right)= - \frac{{\partial p}}{{\partial x}}+\frac{\partial }{{\partial {x_j}}}\left( {\mu \frac{{\partial {u_i}}}{{\partial {x_j}}}} \right)+\left( {\rho - {\rho _a}} \right){g_j}$$ 2 Energy conservation equation: $$\frac{\partial }{{\partial {x_j}}}\left( {\rho {u_j}T} \right)=\frac{1}{{{C_p}}}\frac{\partial }{{\partial {x_j}}}\left( {{k_t}\frac{{\partial T}}{{\partial {x_j}}}} \right)+\frac{{{C_{pv}} - {C_{pa}}}}{{{C_p}}}\left[ {\frac{\partial }{{\partial {x_j}}}\left( {\frac{{{\mu _t}}}{{{\sigma _c}}}} \right)\frac{{\partial \omega }}{{\partial {x_i}}}} \right]\frac{{\partial T}}{{\partial {x_j}}}$$ 3 2.2.2 Turbulence modeling In this study, the numerical simulation was performed via the commercial software Ansys’s Fluent 2020. Due to the fact that the internal flow field of the hydrocyclone is considered a strong vortex flow field, choosing the correct turbulence model has a significant impact on the accuracy of numerical simulation results. Among many turbulence models, the Reynolds Stress Model (RSM) takes into account continuity equation, momentum equation, transport equation and anisotropic turbulent shear equation at the same time, which is mainly applied to the numerical simulation of complex three-dimensional flow field considering Reynolds stress anisotropy. Therefore, the RSM is used to simulate the flow field in the hydrocyclone. The Reynolds stress model is based on the average Reynolds number theory, and the governing equations are shown in equations ( 4 )-( 10 ) [ 44 – 46 ]. Reynolds stress transport equation: $$\frac{\partial }{{\partial t}}\left( {\rho \overline {{{{u^{\prime}}_i}{{u^{\prime}}_j}}} } \right)+\frac{\partial }{{\partial {x_k}}}\left( {\rho {u_k}\overline {{{{u^{\prime}}_i}{{u^{\prime}}_j}}} } \right)={D_{T,ij}}+{P_{ij}}+{\varphi _{ij}} - {\varepsilon _{ij}}$$ 4 Turbulent kinetic energy diffusion term equation: $${D_{T,ij}}= - \frac{\partial }{{\partial {x_k}}}\left( {\rho \overline {{{{u^{\prime}}_i}{{u^{\prime}}_j}{{u^{\prime}}_k}}} +\overline {{p{{u^{\prime}}_j}}} {\delta _{jk}} - \mu \frac{\partial }{{\partial {x_k}}}\overline {{{{u^{\prime}}_i}{{u^{\prime}}_j}}} } \right)$$ 5 Molecular viscous diffusion term equation: $${D_{L,ij}}=\frac{\partial }{{\partial {x_k}}}\left[ {\mu \frac{\partial }{{\partial {x_k}}}\left( {\overline {{{{u^{\prime}}_i}{{u^{\prime}}_j}}} } \right)} \right]$$ 6 Shear stress equation: $${P_{ij}}=\rho \left( {\overline {{{{u^{\prime}}_i}{{u^{\prime}}_k}}} \frac{{\partial {u_j}}}{{\partial {x_k}}}+\overline {{{{u^{\prime}}_j}{{u^{\prime}}_k}}} \frac{{\partial {u_i}}}{{\partial {x_k}}}} \right)$$ 7 Buoyancy generation term equation: $${G_{ij}}= - \rho \beta \left( {{g_i}\overline {{{{u^{\prime}}_j}\theta }} +{g_j}\overline {{{{u^{\prime}}_i}\theta }} } \right)=\beta \frac{{{\mu _t}}}{{0.85}}\left( {{g_i}\frac{{\partial T}}{{\partial {x_j}}}+{g_j}\frac{{\partial T}}{{\partial xi}}} \right)$$ 8 Pressure strain term equation: $${{\Phi}_{ij}}= - 0.18\rho \frac{\varepsilon }{k}\left( {\overline {{{{u^{\prime}}_i}{{u^{\prime}}_j}}} - \frac{2}{3}k{\delta _{ij}}} \right) - 0.6\left( {{p_{ij}} - \frac{2}{3}p{\delta _{ij}}} \right)+f\left( {k,\varepsilon ,{n_x},d} \right)$$ 9 Viscous dissipative term equation: $${\varepsilon _{ij}}=2\mu \overline {{\frac{{\partial {{u^{\prime}}_i}}}{{\partial {x_k}}}\frac{{\partial {{u^{\prime}}_j}}}{{\partial {x_k}}}}}$$ 10 2.3 Numerical method and grid generation In this study, the Finite Volume Method (FVM) and the First-order Upwind scheme are used to solve the problem, and the governing equations are discretized based on the pressure solver. The Mixture model was selected to study the distribution law of the flow field in the hydrocyclone and the Semi-Implicit-Method for Pressure-Linked Equations (SIMPLE) algorithm was used to solve the problem iteratively. The SIMPLE algorithm is a numerical method mainly used to solve incompressible fluids. Its core is to use the “guess-correction” process to calculate the pressure field on the basis of staggered grids, so as to solve the momentum equation [ 47 ]. Combined with the actual natural gas hydrate exploitation project, considering the influence of gravity on the cyclone separation process, the acceleration of gravity was set to 9.81m/s 2 . Set the total number of calculation steps to 10000 steps, and save 1 data file every 1000 steps. In order to ensure the accuracy of numerical simulation, the convergence accuracy is set to 10 − 6 . The fluid domain model of the in-situ sand removal hydrocyclone for natural gas hydrate solid fluidization exploitation was meshed, and four level grids were divided. In order to ensure the accuracy of calculation and reduce the amount of calculation, the grid independence test was carried out. Because of the complexity of fluid migration characteristics and mechanical distribution in the swirl field, in order to improve the stability and accuracy of numerical simulation and avoid false diffusion in the discretization process, local grid refinement was carried out around the separator pipe. 2.4. Boundary conditions In this study, water was set as continuous phase and sand as discrete phase. The density of water is 998.2kg/m 3 , the viscosity is 0.001pa s, and the density of sand is 2700kg/m 3 . The boundary condition of the axial inlet of the hydrocyclone was set as the velocity inlet, and the incident velocity of the water phase and the sand phase is the same. Set the water outlet and the sand outlet as outflow. The wall of the hydrocyclone was set to wall, the wall roughness is 0, and there is no slip wall boundary. 2.5. Simulation scenarios In this study, the numerical simulation method was used to study the internal flow field characteristics and phase distribution law of hydrocyclone applicable to in-situ separation of sand phases in solid fluidized exploitation of natural gas hydrate. Based on the hydrocyclone model proposed by Chang et al. and combined with the actual operating conditions of solid fluidization exploitation of natural gas hydrates, the effects of flow rate, flow ratio, sand volume fraction and sand particle diameter on the flow field characteristics in the hydrocyclone were studied. Numerical simulation scenarios were shown in Table 2 . In 13 cases, Case1 was set as the basic case. Case1-4 studies the distribution law of sand phase and water phase and tangential velocity field in swirling flow field under different flow conditions. Case5-7 and Case1 study the distribution of sand and water phases in the swirl field under different flow ratio. Case8-10 and Case1 study the effect of inlet sand content change on tangential velocity field and sand volume fraction distribution. Case 11–13 and Case 1 study the distribution of tangential velocity field and sand phase in swirling flow field under different sand particle diameters. In order to ensure the objectivity and accuracy of the research results, the parameter changes of each factor were uniformly distributed. At the same time, in order to avoid the interaction of various factors, the control variable method was used to study the effects of different factors on the flow field characteristics. Table 2 Numerical simulation scenarios Scenario Flow rate(m 3 /h) Flow ratio(%) Sand Volume fraction(%) Sand particle diameter(µm) Case1 4.83 5 20 80 Case2 3.83 Case3 2.83 Case4 1.83 Case5 10 Case6 15 Case7 20 Case8 10 Case9 30 Case10 40 Case11 20 Case12 40 Case13 60 The water-sand two-phase mixture enters the device from the inlet of the hydrocyclone, and the mixture changes from axial motion to circular motion after passing through the spiral flow path. Due to the density difference between the water phase and the sand phase, the centrifugal force generated by the sand phase in the circular motion is large, so the sand migrates to the side wall of the hydrocyclone under the centrifugal force and is discharged from the device by the sand outlet, while the water phase is distributed in the axial center of the hydrocyclone and enters the water outlet through the separator pipe. Therefore, the flow field area between the spiral flow path and the separator pipe is the key area for water-sand separation. In order to more accurately study the variation characteristics and laws of the water-sand separation flow field area, three monitoring lines L MA , L MB , and L MC are set equidistantly in this analysis area. According to the structural parameters of the hydrocyclone, the distances from the three monitoring lines to the inlet are 121mm, 200mm, and 279mm, respectively. The analysis area and the location of the monitoring line were shown in Fig. 2 . In order to calculate the efficiency of sand discharge and water discharge in different cases. The dimensionless parameter E was defined as the efficiency evaluation value, which is expressed by the ratio of the mass flow rate at the outlet of each phase to the mass flow rate at the inlet. The calculation of sand discharge and water discharge efficiency of hydrocyclone were shown in Eq. ( 11 )-( 12 ). $${E_s}=\frac{{{m_{so}}}}{{{m_{si}}}}$$ 11 $${E_w}=\frac{{{m_{wi}}}}{{{m_{wo}}}}$$ 12 Finally, by analyzing the variation trend of velocity field, sand phase volume fraction and water phase volume fraction on the analysis area and monitoring lines, the influence of various factors on the internal flow field characteristics and distribution law of each phase of the hydrocyclone were obtained. In this study, in order to ensure the accuracy of the visibility of numerical simulation results, Ansys post-processing software was used to process the simulation results, and the ratio of icon size to model size is 1:1. 3. Result and discussion 3.1 Grid independence The Ansys’s pre-processing software Gambit was used to grid the fluid domain model of hydrocyclone which is applicable to sand removal in solid fluidization exploitation of natural gas hydrate, five levels of grids with 1821724, 2286356, 2799447, 3216424 and 3691497 cells were examined. The static pressure distribution on the monitoring line L MA under different grid levels was analyzed, as shown in Fig. 3 . The static pressure distribution curve with grid level of 1821724, 2286356, 2799447,3216424 was fitted by polynomial fitting, and the correlation coefficient R 2 is 0.993387. It is proved that under the four grid number levels, the grid number has little influence on the numerical simulation results. When the number of grids is 3691497, the static pressure on the monitoring line L MA changes greatly. In order to ensure the accuracy of numerical simulation and save calculation time, the fluid domain model of cyclone separator is divided into 2799447 grid elements, and the meshing results was shown in Fig. 4 . 3.2 Model validation In this study, Xu's experiments were used to verify the accuracy of numerical simulation and turbulence model [48]. In Xu's experimental research, the experimental platform was designed according to the actual working conditions, so this paper re-establish the numerical simulation calculation model based on Xu's experiment. The structural parameters of the hydrocyclone were shown in Table 3 , and other structural parameters are the same as those of the experimental device. In the experiment, the distribution law of pressure drop under the condition of inlet flow rate of 4.83m 3 /h and gas outlet flow ratio of 56%-64% was studied. Therefore, the same physical model and boundary conditions as the experimental device were establish, and the Mixture model and Reynolds stress model were used to carry out numerical simulation. The gas outlet pressure drop distribution obtained from numerical simulation and experiment under the condition of gas outlet flow ratio of 56%-64% was shown in Fig. 5 . It can be seen from Fig. 5 that due to the simplification of the real process in the numerical simulation process, the numerical simulation results are generally smaller than the experimental results. By polynomial fitting between the numerical simulation results and the experimental results, the fitting degree R 2 is 0.958, which proves the accuracy of the numerical simulation and the turbulence model. Table 3 Experimental device structure parameters Structure Swirl chamber length (mm) Main diameter (mm) Inverted cone height (mm) Drain hole height (mm) Inlet area (mm 2 ) Parameter 238 45 96 10 4*14 3.3 Flow field characteristics and phase distribution laws under different parameters In order to study the effects of different parameters on the flow field characteristics and phase distribution law and the separation efficiency of hydrocyclone, the numerical simulation method was used to study the influence of different flow rate, different flow ratio, different sand volume fraction and different sand particle diameter on the velocity field distribution and the sand phase and water phase distribution law. 3.3.1 Flow field characteristics and distribution rules under different flow rate The distribution of sand phase on monitoring line L MA , L MB , and L MC under different flow conditions were shown in Fig. 6 ( a )-Fig. 6 ( c ). It can be seen from Fig. 6 ( a ) that on the monitoring line L MA , the volume fraction of sand phase gradually increases in the radial position range of 0mm-±50mm. When the flow rate is 4.83m 3 /h, the sand volume fraction reaches a maximum of 19% at the radial position ± 50mm, and when the flow rate is 1.83m 3 /h, the sand volume fraction reaches a minimum of 10.5% at the radial position ± 50mm. As the flow rate increased from 1.83m 3 /h to 4.83m 3 /h, the sand volume fraction at the inner wall of the hydrocyclone increased by 8.5%. It is proved that as the flow rate increases, the tangential velocity in the flow field increases, and the sand phase migrates to the flow field edge more significantly in the process of separation. The distribution of sand volume fraction on monitoring line L MB under different flow conditions was shown in Fig. 6 ( b ). It can be seen from Fig. 6 ( b ) that on monitoring line L MB , the sand volume fraction at the inner wall of the hydrocyclone still increases with the increase of flow rate, but the sand volume fraction at the axis decreases with the increase of flow rate. As the axial distance increases from 121 mm to 200 mm from the inlet, the sand volume fraction at the radial position ± 50 mm in the flow field gradually increases. When the flow rate is 4.83m 3 /h, the sand volume fraction reaches a maximum of 21.2% at the edge of the flow field, and the sand volume fraction reaches a minimum of 6.7% at the axial center of the flow field. When the flow rate is 1.83m 3 /h, the sand volume fraction at the edge of the flow field is 16.3%, and the sand volume fraction at the axis of the flow field is 12.4%. The distribution of sand volume fraction on monitoring line L MC was shown in Fig. 6 ( c ). From Fig. 6 ( c ), it can be seen that under the flow rate conditions of 1.83m 3 /h-4.83m 3 /h, the sand volume fraction rapidly decreases at the axial position of 279mm and the radial position of ± 10mm, and all reach their minimum at the radial position of 0mm. The flow rate increased from 1.83m 3 /h to 4.83m 3 /h, and the sand volume fraction at the axis center of the flow field decreased from 13–9.2%. When the flow rate is in the range of 2.83m 3 /h-4.83m 3 /h, the sand volume fraction still shows an increasing trend at the radial position ± 50mm. Compared with the monitoring line L MB , the sand volume fraction at the edge of flow field increases by 1.8%, 1.8% and 1.5% respectively under the conditions of 2.83m 3 /h, 3.83m 3 /h and 4.83m 3 /h. However, when the flow rate is 1.83m 3 /h, the sand volume fraction at the edge of flow field decreases by 0.4%. It is proved that when the flow rate is in the range of 2.83m 3 /h-4.83m 3 /h, the tangential velocity in the flow field increases gradually from the axial position 121mm to 279mm. When the flow rate is 1.83m 3 /h, the tangential velocity decreases gradually within the 200mm-279mm range of the axial position of the flow field, and the separation effect on the sand phase is gradually decreased. The tangential velocity distribution on monitoring line under different flow conditions were shown in Fig. 7 ( a )-Fig. 7 ( c ). Figure 7 ( a ) shows the tangential velocity distribution on monitoring line L MA . It can be seen from Fig. 7 ( a ) that the tangential velocity on monitoring line L MA shows a symmetrical distribution characteristic and takes the radial position 0 mm as the axis of symmetry that first increases and then decreases from the radial position 0 mm to ± 50 mm. The reason why the tangential velocity decreases at the side wall is that the wall roughness was set to 0 and there was no slip during the numerical simulation. The maximum tangential velocity under the four flow conditions is greater than 0m/s, indicating that part of the axial velocity of the mixture changes into a tangential velocity after passing through the spiral flow path. When the flow rate is 4.83m 3 /h, the maximum tangential velocity is 1m/s, which appears at the radial position of ± 40mm. When the flow rate is 1.83m 3 /h, the maximum tangential velocity of 0.23m/s appears at the radial position of ± 30mm. It shows that with the increase of the flow rate, the axial velocity at the inlet increases, which leads to the increase of the tangential velocity of the fluid after passing through the spiral flow path. Figure 7 ( b ) shows the tangential velocity distribution on monitoring line L MB under the flow condition of 1.83m 3 /h-4.83m 3 /h. As the axial distance from the inlet increases from 121mm to 200mm, the maximum tangential velocity at the edge of flow field decreases under different flow conditions, but the tangential velocity gradually increases within the range of -20mm-20mm in the radial position. When the flow rate is 4.83m 3 /h, the tangential velocity reaches a maximum of 0.33m/s at the edge of flow field. Compared with the monitoring line L MA , the maximum tangential velocity decreases 0.67m/s. Similarly, when the traffic is 1.83m 3 /h and 3.83m 3 /h, the maximum tangential velocity decreases 0.35m/s and 0.01m/s, respectively. It is proved that as the axial distance increases, the tangential velocity in the swirling flow field decreases gradually, and the separation effect of the swirling flow gradually weakens. Figure 7 ( c ) shows the tangential velocity distribution on monitoring line L MC under different flow conditions. It can be seen from Fig. 7 ( c ) that the maximum value of the tangential velocity in the flow field under different flow conditions at the axial position of 279mm appears at the radial position of 10.8 mm. According to the local enlargement, the maximum tangential velocity of 1.83m 3 /h, 2.83m 3 /h, 3.83m 3 /h and 4.83m 3 /h at the radial position 108mm is 0.13m/s, 0.19m/s, 0.27m/s and 0.35m/s, respectively. The maximum tangential velocity still shows the distribution law that increase with the increase of flow rate. However, compared with the monitoring line L MA , the tangential velocity decreases by 0.65m/s, 0.34m/s and 0.1m/s respectively under the flow conditions of 1.83m 3 /h, 3.83m 3 /h and 4.83m 3 /h. When the flow rate is 2.83m 3 /h, the maximum tangential velocity remains unchanged. It shows that with the increase of the axial distance, the tangential flow produced by the spiral flow path gradually weakens, and the intensity of the swirl flow in the flow field gradually weakens. The water phase distribution in the swirling flow field under different flow conditions was shown in Fig. 8 ( a )-Fig. 8 ( b ). As shown in Fig. 8 ( a ), when the flow rate is in the range of 1.83m 3 /h-4.83m 3 /h, the water volume fraction on monitoring line L MA reaches 100% at the radial position of 0mm and the water volume fraction decreases gradually from the radial position of 0mm to ± 50 mm under each flow rate condition. Among them, when the flow rate is 3.83m 3 /h and 4.83m 3 /h, the water volume fraction is concentrated in the range of radial position ± 24mm, and the concentration of water phase is more significant with the increase of flow rate. At the radial position ± 50mm, the water volume fraction decreases with the increase of flow rate. When the flow rate increases from 1.83m 3 /h to 4.83m 3 /h, the water volume fraction at the edge of flow field decreases from 88.8–81.2%. It shows that the tangential velocity in the flow field increases with the increase of the flow rate. Since the density of the water phase is smaller than that of the sand phase, according to the principle of cyclone separation, the distribution of the water phase is closer to the center of the flow field. The water volume fraction distribution on monitoring line L MC under different flow rate conditions was shown in Fig. 8 ( b ). As can be seen from Fig. 8 ( b ), compared with the monitoring line L MA , the water phase distribution on monitoring line L MC is more concentrated to the center of the flow field, and the concentrated distribution range of the water phase does not change significantly under different flow conditions, all in the range of radial position ± 10mm. The water volume fraction at the radial position 0mm increases with the increase of the flow rate, the flow rate increases from 1.83m 3 /h to 4.83m 3 /h, and the water volume fraction at the center of the flow field is 86.9%, 88.1%, 89.2% and 90.3%, respectively. The water volume fraction at the radial position ± 50mm decreases with the increase of flow rate, the flow rate increases from 1.83m 3 /h to 4.83m 3 /h, and the water volume at the edge of flow field is 85.3%, 80.5%, 78.5% and 77%, respectively. It shows that at the axial distance of 279 mm from the inlet, the volume fraction of the water is significantly changed by the flow rate, but the distribution area of ​​the water phase is not affected by the flow rate. 3.3.2 Flow field characteristics and distribution rules under different flow ratio The distribution of sand volume fraction on monitoring lines L MA , L MB , and L MC under different flow ratio conditions was shown in Fig. 9 . It can be seen from Fig. 9 that at different monitoring lines, the sand volume fraction shows a gradually increasing distribution law in the radial position range of 0 mm to ± 50 mm. On monitoring line L MA , the sand volume fraction reaches a minimum of 0% at the axial center of the flow field and reaches a maximum of 18.8% at the edge of the flow field. On monitoring line L MC , the sand volume fraction reaches a minimum of 8.9% at the axial center of the flow field and reaches a maximum of 22.6% at the edge of the flow field. That is, within the axial range of 121mm-279mm from the inlet, the sand volume fraction at the axial center and edge of the flow field increases by 8.9% and 3.8%, respectively. However, on the same monitoring line, the flow ratio of the sand outlet increases from 5–20%, and there is no significant difference in the sand volume fraction. It shows that the flow ratio of the sand outlet has no significant effect on the separation of the sand phase. The distribution of sand volume fraction on monitoring lines L MA , L MB , and L MC under different sand outlet flow ratios was shown in Fig. 10 . It can be seen from Fig. 10 that the volume fraction distribution of water phase is complementary to that of sand phase. The increase of sand outlet flow ratio from 5–20% has no significant effect on the distribution of water volume fraction on the same monitoring line. In the axial area from L MA to L MC , the distribution of water volume fraction shows the distribution law of aggregation to the axial center. On the monitoring line L MA , the water phase volume fraction within the radial range of ± 9 mm is about 100%, which proves that the sand phase at the axial position of 121 mm of the flow field has been completely separated. On the monitoring line L MC , the water volume fraction at the radial position of 0 mm reaches a maximum of 90.3%. It shows that as the axial distance increases from 121mm to 279mm, the water volume fraction around the axis center of flow field decreases by 9.7%, which proves that as the axial distance increases, a small part of the water phase migrates to the side wall. 3.3.3 Flow field characteristics and distribution rules under different sand content The distribution of sand phase in the analysis area under different sand volume fraction was shown in Fig. 11 ( a )-Fig. 11 ( c ). Figure 11 ( a ) shows the s distribution of and volume fraction at the on monitoring line L MA . As can be seen from Fig. 11 ( a ), at the axial distance 121mm from the inlet, the sand content is in the range of 10–40%, and the sand distribution in the flow field shows a symmetrical distribution characteristic with the radial position 0mm as the symmetry axis. In the range of 0mm-±50mm in the radial position, the sand volume fraction increases gradually, indicating that the sand volume fraction gradually increases from the center to the edge of the flow field. The sand volume fraction at the center of the flow field is 0%, and the sand volume fraction at the edge of the flow field increases with the increase of sand content. When the sand content is 40%, the sand volume fraction at the edge of the flow field reaches a maximum of 38.8%, which is 29.5%, 20%, 10.1%higher than that under the conditions of sand content of 10%, 20%, 30%. The distribution of sand volume fraction on monitoring line L MB under different sand content conditions was shown in Fig. 11 ( b ). It can be seen from Fig. 11 ( b ) that on monitoring line L MB , the sand volume fraction in the swirling flow field under different sand content conditions still shows a distribution law that gradually increases from the center to the edge of flow field. However, there are significant differences in the sand volume fraction under different sand contents, and the sand volume fraction in the flow field increases with the increase of sand content. As the sand content increases from 10–40%, the sand volume fraction at the center of the swirling field increases from 2.9–20.1%, and the sand volume fraction at the edge of the swirling field increases from 10.7–41.5%. Compared with the monitoring line L MA , the sand volume fraction in the center and edge of the flow field are both increased. It shows that as the axial distance increases, the sand continues to move towards the side wall of the hydrocyclone under the action of the swirling flow, but the separation of sand is gradually weakened due to the gradual weakening of cyclone separation in the flow field. The distribution of sand volume fraction on monitoring line L MC under different sand content conditions was shown in Fig. 11 ( c ). It can be seen from Fig. 11 ( c ) that the sand volume fraction on monitoring line L MC forms a decrease area within the radial range of ± 12.5mm, and gradually stabilizes within the radial range of ± 12.5mm-±50mm. Among them, the sand volume fraction fluctuates in a small range due to the influence of the separator pipe at the radial position of ± 12.5mm. In the decrease area, the sand volume fraction at the center of the flow field increases with the increase of sand content. When the sand content is 10% and 40%, the sand volume fraction at the center of the flow field is 4.2% and 25.2% respectively. Compared with the sand volume at the inlet of the hydrocyclone, the sand volume fraction at the center of the flow field under the four sand content conditions decreased by 5.8%, 10.6%, 13.9%, and 14.8%, respectively. It is proved that with the increase of sand content, the amount of sand discharged from the water outlet is larger, but the proportion of sand discharged from the sand outlet is larger. 3.3.4 Flow field characteristics and distribution rules under different sand particle diameter Figure 12 shows the distribution of tangential velocity in the swirling flow field under different sand particle diameter. It can be seen from Fig. 12 that the maximum tangential velocity on monitoring line L MA is at the radial position of ± 36mm, and the maximum tangential velocity on monitoring line L MC at the radial position of ± 12.5mm. And the maximum tangential velocity on monitoring line L MA is significantly higher than that on monitoring line L MC . It shows that as the axial position increases from 121mm to 279mm from the hydrocyclone inlet, the tangential velocity generated by the spiral flow path gradually weakens in the axial and radial directions, and the swirl separation effect in the swirl field also gradually decreases as the tangential velocity decreases. According to Fig. 12 , the change of sand particle diameter does not have a significant effect on the tangential velocity at the same axial position in the flow field. From the local enlargement, it can be seen that the change of sand particle diameter has only a slight effect on the tangential velocity on monitoring line L MA . When the sand particle diameter is 20µm, the maximum tangential velocity is 1.21m/s, and when the sand particle diameter is 80µm, the minimum tangential velocity is 1.01m/s. As the sand particle diameter increases from 20 µm to 80 µm, the maximum tangential velocity decreases 0.2m/s. However, on monitoring line L MC , the maximum tangential velocity in the flow field under different particle diameters is 0.28m/s. It is proved that under the condition of strong swirling flow, the tangential velocity in the flow field decreases with the increase of sand particle diameter, but the change of sand particle diameter has little effect on the tangential velocity. The distribution of sand phase in the analysis area under different sand particle diameter was shown in Fig. 13 ( a )-Fig. 13 ( c ). Among them, Fig. 13 ( a ) shows the distribution of sand volume fraction on monitoring line L MA . It can be seen from Fig. 13 ( a ) that under the condition of different sand particle diameters, the sand volume fraction shows a distribution law that gradually increases from the center to the edge of the flow field. When the sand particle diameter is in the range of 20–80µm, the sand volume fraction in the swirling field decreases gradually with the increase of particle diameter on monitoring line L MA , but the sand volume fraction reaches about 20% at the edge of the flow field under different sand particle diameter conditions. At the radial position 0mm, when the sand particle diameter is 20µm and 80µm, the sand volume fraction reaches the maximum and the minimum is 16.9% and 0%, respectively. It is proved that in the process of cyclone separation, under the condition of the same flow rate and the same sand content, the larger the sand particle diameter is, the easier it is to separate. The distribution of sand volume fraction on monitoring line L MB under different particle diameter conditions was shown in Fig. 13 ( b ). As shown in Fig. 13 ( b ) that the sand volume fraction decreases with the increase of sand particle diameter in the flow field at the distance from the inlet 200mm of the hydrocyclone. Compared with the monitoring line L MA , the sand volume fraction at the radial position 0mm increases. However, the sand volume fraction is still roughly the same at about 20% at the edge of the flow field under different particle diameters. At this time, the sand volume fraction at the center of the flow field under the four particle diameters is 18.9%, 15.6%, 11.2% and 7%, respectively. Compared with the monitoring line L MA , which increases by 2%, 7.6%, 9.8% and 7%, respectively. Figure 13 ( c ) shows the distribution of sand volume fraction on monitoring line L MC under different sand particle diameter conditions. As can be seen from Fig. 13 ( c ), at the axial position 279mm, the sand volume fraction decreases rapidly in the radial range ± 12.5mm and reaches the minimum at 0mm. And the sand volume fraction at the axial center of the flow field is inversely proportional to the sand particle diameter. When the sand particle diameter is 80µm, the sand volume fraction reaches a minimum of 9.4% at the axial center of the flow field. At the same time, due to the effect of the separator pipe wall, there is a small fluctuation in the distribution of sand volume fraction at ± 12.5mm. The sand volume fraction near the inner wall of the hydrocyclone is different under the condition of different particle diameters, and the distribution law is positively correlated with the sand particle diameter. When the sand particle diameter is 80µm, the maximum sand volume fraction is 22.9%. When the sand particle diameter is 20µm, the sand volume fraction decreases slightly due to the effect of water phase migration in the range of radial position ± 12.5mm, but the overall stability is 20%. According to the analysis of the sand volume fraction distribution of from the L MA to L MC shows that there is a positive correlation between the degree of sand separation and sand particle diameter in the process of cyclone separation. In a certain range, the larger the sand particle diameter, the easier it is to achieve sand phase separation. 3.4 Efficiency calculation The sand discharge rate and water discharge rate were calculated according to the Eq. ( 11 )-( 12 ). The E s and E w calculations for Case1-Case13 are shown in Fig. 14 . From the distribution law of sand discharge efficiency curve and drainage efficiency curve in Fig. 14 , it can be seen that there is a negative correlation between sand discharge efficiency and drainage efficiency in hydrocyclone. Among them, the maximum E s is 22.1% of Case7, indicating that when the flow rate is 4.83m 3 /h, the sand outlet flow ratio is 20%, the sand content is 20%, and the sand particle diameter is 80µm, the sand phase separation efficiency of this hydrocyclone is the highest. The minimum E w is 86.1% of case6 and case7, it indicates that the water discharge efficiency is the same when the flow rate is 4.83m 3 /h, the sand volume fraction is 20%, the sand particle diameter is 80µm, and the sand outlet flow ratio is 15% and 20%, respectively. 4. Conclusion In this paper, based on the hydrocyclone proposed by Chang, which is applicable to the solid fluidization exploitation of natural gas hydrate, the numerical simulation method was used to study the internal flow field characteristics of this type of hydrocyclone under different working conditions and its applicability in the solid fluidization exploitation of natural gas hydrate. Based on the results and discussions above, the following conclusions were drawn: (1)The numerical simulation method was used to study the flow field characteristics and distribution law of the hydrocyclone which is applicable to the solid fluidization exploitation of natural gas hydrate under the conditions of different flow rate, different flow ratio, different sand content and different sand particle diameter. In the same axial position, when the flow rate is in the range of 1.83m 3 /h to 4.83m 3 /h and the sand content is in the range of 10–40%, the sand volume fraction decreases at the center of the flow field and increases at the edge of the flow field. When the sand particle diameter increases from 20µm to 80µm, the sand volume fraction decreases at the center of the flow field, but there is no obvious change at the edge of the flow field. When the flow ratio increases from 5–20%, there is no significant effect on the distribution of sand volume fraction in the flow field. Therefore, it is suggested that the initial sand removal efficiency of solid fluidization exploitation of natural gas hydrate should be improved by increasing the inlet flow rate in engineering practice. (2) When the axial position in the flow field increases from 121mm to 279mm from the inlet. When the flow rate, flow ratio and sand content are constant, the sand volume fraction increases gradually at the center of the flow field and decreases at the edge of the flow field. When the sand particle diameter is constant, the sand volume fraction has no significant change at the edge of the flow field. (3)The E s and E w of the hydrocyclone under different working conditions were calculated, and the results show that the maximum E s is 22.1% and the minimum E w is 86.1% when the flow rate is 4.83m 3 /h, the sand outlet flow ratio is 20%, the sand volume fraction is 20% the sand particle diameter is 80µm. The optimum working conditions for this type of hydrocyclone were obtained. It provides a reference for the practical engineering application of sand pre-separation in solid fluidization exploitation of natural gas hydrate. (4)The hydrocyclone studied in this paper has a low separation efficiency for water and sand phases, and is only applicable to rough pre-separation of sand phase in the process of solid fluidization exploitation of natural gas hydrate, and cannot perform fine separation for complex mixture. In the follow-up research and practical engineering application, the optimization of structural parameters should be further carried out to improve its separation efficiency. Declarations Funding The research is funded by National Key Research and Development Program (No. 2021YFC2800903), National Natural Science Foundation of China (No. U20B6005-05), 111 Project (No. D21025), Sichuan High-end Foreign Talent Introduction Project (No. SYZ202124) Acknowledgments This research was supported by the National Key Research and Development Program (No. 2021YFC2800903), National Natural Science Foundation of China (No. U20B6005-05), 111 Project (No. D21025) and Sichuan High-end Foreign Talent Introduction Project (No. SYZ202124) Author contribution NW: Resources, project administration, funding acquisition. YQ: Conceptualization, methodology, software, formal analysis, data curation, writing-original draft, writing-review and editing. SSF: Investigation. MC: Investigation. HTL: Project administration. SWZ: Investigation, visualization. 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Qiao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA00lEQVRIiWNgGAWjYDACZhBhAGYdOPDhB2la2BIPzuwhzT4e48McbESo4zvO/PAxT0Fd4naJnA+HGXgY5PnFDuDXInmYzdiYx+Bw4s4ZuRsOF1gwGM6cnYBfi8FhBjNpHoMDuRtuALXM4GFIMLhNUAv7N6CWOqCWnAeHediI0sIDsoUZpIWBOC2Sh3mKDecYHK7f2fPMABjIEoT9wnf++MYHb/7UGZuzJz/+8OGHjTy/NAEtDAcYGJh4GKCxycAgQUA5VAvjD4SWUTAKRsEoGAWYAACVM0bqZK8WaQAAAABJRU5ErkJggg==","orcid":"","institution":"State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation","correspondingAuthor":true,"prefix":"","firstName":"Yi","middleName":"","lastName":"Qiao","suffix":""},{"id":206409712,"identity":"943e430c-48ea-4b8e-80fc-455322d71454","order_by":2,"name":"Shuanshi Fan","email":"","orcid":"","institution":"State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation","correspondingAuthor":false,"prefix":"","firstName":"Shuanshi","middleName":"","lastName":"Fan","suffix":""},{"id":206409714,"identity":"3077fd13-5520-422a-80c3-c1e36dc079b3","order_by":3,"name":"Meng Cai","email":"","orcid":"","institution":"Daqing Oilfield of CNPC","correspondingAuthor":false,"prefix":"","firstName":"Meng","middleName":"","lastName":"Cai","suffix":""},{"id":206409716,"identity":"4b3b88ea-ea00-4331-b784-a7c504ee52bd","order_by":4,"name":"Haitao Li","email":"","orcid":"","institution":"State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation","correspondingAuthor":false,"prefix":"","firstName":"Haitao","middleName":"","lastName":"Li","suffix":""},{"id":206409718,"identity":"de11b7db-8965-4fff-985e-915645696fd2","order_by":5,"name":"Shouwei Zhou","email":"","orcid":"","institution":"State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation","correspondingAuthor":false,"prefix":"","firstName":"Shouwei","middleName":"","lastName":"Zhou","suffix":""},{"id":206409720,"identity":"5f1e5053-a3ab-4383-bda6-48935e6b9ed1","order_by":6,"name":"Jinzhou Zhao","email":"","orcid":"","institution":"State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation","correspondingAuthor":false,"prefix":"","firstName":"Jinzhou","middleName":"","lastName":"Zhao","suffix":""},{"id":206409723,"identity":"7eca5ba9-bf5d-4273-ae3c-ab76d8cf9a83","order_by":7,"name":"Liehui Zhang","email":"","orcid":"","institution":"State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation","correspondingAuthor":false,"prefix":"","firstName":"Liehui","middleName":"","lastName":"Zhang","suffix":""},{"id":206409725,"identity":"769ea4d7-a898-4340-882f-afd34e1920f1","order_by":8,"name":"Richard Coffin","email":"","orcid":"","institution":"Department of Physical and Environmental Science, Texas A\u0026M University","correspondingAuthor":false,"prefix":"","firstName":"Richard","middleName":"","lastName":"Coffin","suffix":""}],"badges":[],"createdAt":"2023-05-25 09:44:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2980319/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2980319/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":38105080,"identity":"3dc618d0-9d7b-4041-ac44-17817a19a7ea","added_by":"auto","created_at":"2023-06-06 14:56:46","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":154198,"visible":true,"origin":"","legend":"\u003cp\u003eThe Structure of hydrocyclone for in-situ sand removal\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-2980319/v1/a0a87229edfcf4ebf732dd08.png"},{"id":38103009,"identity":"0c81afbd-3b6a-464e-b590-0823dea139a3","added_by":"auto","created_at":"2023-06-06 14:40:46","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":86349,"visible":true,"origin":"","legend":"\u003cp\u003eAnalysis area and monitoring line position\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-2980319/v1/906a35da776113d9ad115684.png"},{"id":38106588,"identity":"2fda8479-40a0-4dec-af71-e03eb19dd32f","added_by":"auto","created_at":"2023-06-06 15:12:46","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":89101,"visible":true,"origin":"","legend":"\u003cp\u003eGrid independence verification\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-2980319/v1/9acee837358ea5779a0cbeeb.png"},{"id":38103010,"identity":"512e02db-97fd-4d0d-b1e7-8cb86bc6eb1c","added_by":"auto","created_at":"2023-06-06 14:40:46","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":388608,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of grid generation\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-2980319/v1/1ddb076c4906263c095c8288.png"},{"id":38104289,"identity":"d13f2714-455f-45b7-aeb2-95993593a6a1","added_by":"auto","created_at":"2023-06-06 14:48:46","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":88295,"visible":true,"origin":"","legend":"\u003cp\u003eSimulation reliability verification\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-2980319/v1/3a8b9c223b4001222b623909.png"},{"id":38104291,"identity":"d6258dd9-bffe-4618-a1e4-6916237490e2","added_by":"auto","created_at":"2023-06-06 14:48:46","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":389038,"visible":true,"origin":"","legend":"\u003cp\u003e(\u003cstrong\u003ea\u003c/strong\u003e) Distribution of sand phase on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e under different flow rate conditions\u003c/p\u003e\n\u003cp\u003e(\u003cstrong\u003eb\u003c/strong\u003e) Distribution of sand phase on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMB\u003c/sub\u003e under different flow rate conditions\u003c/p\u003e\n\u003cp\u003e(\u003cstrong\u003ec\u003c/strong\u003e) Distribution of sand phase on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e under different flow rate conditions\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-2980319/v1/7ad7fb581b48cde6a9c8959b.png"},{"id":38103021,"identity":"b3ac8100-da3e-4ff0-b920-17db5b2d341e","added_by":"auto","created_at":"2023-06-06 14:40:46","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":420227,"visible":true,"origin":"","legend":"\u003cp\u003e(\u003cstrong\u003ea\u003c/strong\u003e) Distribution of tangential velocity on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e under different flow rate conditions\u003c/p\u003e\n\u003cp\u003e(\u003cstrong\u003eb\u003c/strong\u003e) Distribution of tangential velocity on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMB\u003c/sub\u003e under different flow rate conditions\u003c/p\u003e\n\u003cp\u003e(\u003cstrong\u003ec\u003c/strong\u003e) Distribution of tangential velocity on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e under different flow rate conditions\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-2980319/v1/dfa33b6eec48e00ad14f3eed.png"},{"id":38105085,"identity":"a3ceb9f8-3b9d-43eb-9c3b-7d682843a8c4","added_by":"auto","created_at":"2023-06-06 14:56:46","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":379935,"visible":true,"origin":"","legend":"\u003cp\u003e(\u003cstrong\u003ea\u003c/strong\u003e) Water distribution on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e under different flow rate conditions\u003c/p\u003e\n\u003cp\u003e(\u003cstrong\u003eb\u003c/strong\u003e) Water distribution on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMB\u003c/sub\u003e under different flow rate conditions\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-2980319/v1/c42f450a0d4642421c47062b.png"},{"id":38103014,"identity":"33d56677-1698-4d0e-aba0-4030e0b70bbd","added_by":"auto","created_at":"2023-06-06 14:40:46","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":120893,"visible":true,"origin":"","legend":"\u003cp\u003eSand distribution on monitoring lines under different flow ratio conditions\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-2980319/v1/0a2278071b9227839e2ae2d6.png"},{"id":38106589,"identity":"9c7445c1-db5b-4908-9a19-5384f56ab811","added_by":"auto","created_at":"2023-06-06 15:12:46","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":128479,"visible":true,"origin":"","legend":"\u003cp\u003eWater distribution on monitoring lines under different flow ratio conditions\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-2980319/v1/f20ea7dc31e76c04c6686157.png"},{"id":38106033,"identity":"bf496ec4-0a8c-4ca3-a275-672b1099b85b","added_by":"auto","created_at":"2023-06-06 15:04:46","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":388677,"visible":true,"origin":"","legend":"\u003cp\u003e(\u003cstrong\u003ea\u003c/strong\u003e) Sand distribution on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e under different sand content conditions\u003c/p\u003e\n\u003cp\u003e(\u003cstrong\u003eb\u003c/strong\u003e) Sand distribution on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMB\u003c/sub\u003e under different sand content conditions\u003c/p\u003e\n\u003cp\u003e(\u003cstrong\u003ec\u003c/strong\u003e) Sand distribution on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e under different sand content conditions\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-2980319/v1/cdf46418864f44515144e35f.png"},{"id":38105082,"identity":"608dd3a8-6e60-4ae3-9da0-6c872f2c2a8c","added_by":"auto","created_at":"2023-06-06 14:56:46","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":360206,"visible":true,"origin":"","legend":"\u003cp\u003e(\u003cstrong\u003ea\u003c/strong\u003e) Sand distribution on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e under different sand particle diameter conditions\u003c/p\u003e\n\u003cp\u003e(\u003cstrong\u003eb\u003c/strong\u003e) Sand distribution on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMB\u003c/sub\u003e under different sand particle diameter conditions\u003c/p\u003e\n\u003cp\u003e(\u003cstrong\u003ec\u003c/strong\u003e) Sand distribution on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e under different sand particle diameter conditions\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-2980319/v1/f36680e654c9f5b6d2f7f225.png"},{"id":38106030,"identity":"7b3828fd-fa59-4af6-9b74-cd949301eabc","added_by":"auto","created_at":"2023-06-06 15:04:46","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":83520,"visible":true,"origin":"","legend":"\u003cp\u003eEfficiency calculation\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-2980319/v1/7dce32b6c36f087313ea3df4.png"},{"id":39558579,"identity":"ad8d6695-31ff-4692-8fd2-7989f405c947","added_by":"auto","created_at":"2023-07-05 08:59:49","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2555480,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2980319/v1/5d1c3d1a-0286-4a77-8439-b81652276ab3.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Analysis of Flow Field Characteristics of Sand Removal Hydroyclone Applicable to Solid Fluidization Exploitation of Natural Gas Hydrate","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eWith the development of economy and industry, the consumption of global fossil energy is gradually increasing. According to statistics, the total global energy consumption in 2018 was 14.301\u0026nbsp;billion tons of oil equivalent, of which oil accounted for 31%, coal accounted for 26%, and natural gas accounted for 23% [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. A large amount of fossil energy consumption makes social development fall into a dilemma of serious shortage of resources and rapid deterioration of ecological environment [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Therefore, finding an alternative clean energy has become the key to solve the current energy dilemma. Natural gas hydrate (NGH) is widely known for its abundant energy reserves, wide distribution, clean combustion and high energy density [\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Natural gas hydrate is an ice-like and combustible clathrate crystalline compound formed by water molecules and light hydrocarbon gas molecules under low temperature and high pressure environment, so natural gas hydrate is also called \u0026ldquo;Combustible ice\u0026rdquo; [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Under standard conditions, 1m\u003csup\u003e3\u003c/sup\u003e natural gas hydrate can release 164m\u003csup\u003e3\u003c/sup\u003e natural gas [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. It is estimated that the current global natural gas hydrate reserves are about 2\u0026times;10\u003csup\u003e16\u003c/sup\u003em\u003csup\u003e3\u003c/sup\u003e, equivalent to 2\u0026times;10\u003csup\u003e13\u003c/sup\u003e tons of oil equivalent, about 40 times that of conventional natural gas reserves, and the content of organic carbon is twice that of the world\u0026rsquo;s proven fossil fuels[\u003cspan additionalcitationids=\"CR11\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eNatural gas hydrates are mainly distributed in seabed sediments below 300m and in land permafrost layer at 200-2000m [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Therefore, the reservoir-forming environment of low temperature and high pressure has become the main factor limiting the large-scale exploitation of gas hydrate. At present, the exploitation methods of natural gas hydrate mainly include depressurization method, thermal excitation method, chemical injection method and so on [\u003cspan additionalcitationids=\"CR16 CR17\" citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. The depressurization method is to break the equilibrium pressure condition of the hydrate phase by lowering the reservoir pressure, so as to promote the decomposition of the hydrate [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. The thermal excitation method is to promote the release of methane gas by injecting heat into the hydrate reservoir and breaking the temperature condition of hydrate phase equilibrium [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. The chemical injection method is to inject natural gas hydrate inhibitors into hydrate reservoirs to decompose hydrates [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. However, there are some disadvantages such as uncontrollable phase transition, high energy consumption, unstable gas production and high economic cost in the exploitation of natural gas hydrate by the above methods [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn order to solve the problems existing in the exploitation of natural gas hydrate at present, Zhou put forward the solid state fluidization exploitation method of natural gas hydrate [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. The natural gas hydrate solid fluidization exploitation method is to use high-pressure jet or mechanical mining to break the solid hydrate ore body on the shallow surface of the seabed into fine particles, and then mix the broken hydrate ore body with seawater to form a hydrate slurry. The hydrate slurry is transported to the offshore platform through a closed pipeline for later separation treatment [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. The solid fluidization exploitation method changes the uncontrollable decomposition of gas hydrate into continuous controllable decomposition, which realizes the in-situ exploitation of natural gas hydrate and avoids catastrophic production accidents caused by hydrate decomposition in the process of exploitation [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eDuring the exploitation of natural gas hydrate by solid fluidization exploitation method, the hydrate slurry is transported from the seabed to the offshore platform in a closed pipeline [30]. With the change of temperature and pressure, the hydrate ore body gradually decomposes into three phases of gas, water and sand, and the flow changes from solid and liquid two-phase flow to gas, liquid and solid three-phase flow in the closed pipeline [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Therefore, the three-phase separation of gas, water and sand in the hydrate slurry is the key to realize the solid fluidization exploitation of natural gas hydrate. At present, the main methods used for separating hydrate slurry are gravity separation, chemical separation, and cyclone separation [\u003cspan additionalcitationids=\"CR33\" citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. Among them, the cyclone separation method has attracted much attention because of its high efficiency, small size and high separation speed [35]. The hydrate slurry is injected into the hydrocyclone by the closed pipeline, and the mixture moves in a circle along the wall of the cyclone chamber. Due to the density difference of gas, water and sand, the centrifugal force difference is generated during the circular movement, thus the separation of different phases is realized.\u003c/p\u003e \u003cp\u003eAt present, many experts and scholars have carried out extensive research on the application of three-phase hydrocyclone in the exploitation of natural gas hydrate. Qiu et al. [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] analyzed the impact of reservoir sand production on the exploitation of natural gas hydrate and designed an underground hydrocyclone based on this. At the same time, the structural parameters of the hydrocyclone were optimized by numerical simulation method, and the separation efficiency of the optimized cyclone separator was evaluated. Fang et al. [37] studied the response relationship of sand particle diameter, sand volume fraction and natural gas volume fraction with the gas collection efficiency and sand removal efficiency of hydrocyclone based on the small hydrocyclone with classical structure, providing a basis for the practical application of hydrocyclone in the solid fluidization exploitation of hydrate. Wei et al. [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e] optimized the structural parameters of the traditional three-phase hydrocyclone by using the computational fluid dynamics method, analyzed the effect of various structural parameters on the separation efficiency of hydrate slurry in the hydrocyclone, and obtained the optimum combination of structural parameters of the hydrocyclone. Lin [39] designed an axial annulus in situ hydrocyclone desander (AAIHD), and explored the applicability of this hydrocyclone in solid fluidization exploitation of hydrate. Chang et al. [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e40\u003c/span\u003e] proposed a hydrocyclone applicable to the exploitation of subsea natural gas hydrate. The effects of operational and structural parameters on the separation performance of the hydrocyclone were studied using a combination of numerical simulation and experiments, and the optimal ratio of structural parameters was obtained. However, so far, there are few studies on the internal flow field characteristics and phase distribution law of hydrocyclone used in the solid fluidization exploitation of natural gas hydrate.\u003c/p\u003e \u003cp\u003eIn this paper, based on the hydrocyclone proposed by Chang et al. [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e40\u003c/span\u003e], which is applicable to solid fluidization exploitation of natural gas hydrate, the numerical simulation method is used to study the flow field distribution characteristics and phase distribution law in the hydrocyclone under the condition of water and sand two-phase. In order to ensure the universality and accuracy of the research, combined with the actual engineering situation, the effects of different flow rates, different flow ratios, different sand volume fraction and different sand particle diameter on the internal flow field characteristics and phase distribution of the hydrocyclone were studied. The sand discharge efficiency and water discharge efficiency of the hydrocyclone were calculated under different conditions. It provides some guiding significance for the practical engineering application of the hydrocyclone in the solid fluidization exploitation of natural gas hydrate.\u003c/p\u003e"},{"header":"2. Method","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 \u003cem\u003ePhysical model\u003c/em\u003e\u003c/h2\u003e \u003cp\u003eIn this paper, based on the hydrocyclone proposed by Chang [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e40\u003c/span\u003e], which is applicable to in-situ separation of sand phase in solid fluidization exploitation of natural gas hydrate, the flow field characteristics and the distribution of different phase in the hydrocyclone are analyzed and the separation efficiency of the hydrocyclone is calculated. The structure of the hydrocyclone applicable to the in-situ separation of sand phase in the solid fluidization exploitation of natural gas hydrate is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the process of solid fluidization exploitation of natural gas hydrate, the shallow weakly cemented hydrate reservoir on the seafloor is broken into a hydrate ore body by mechanical crushing method or high pressure jet method, and then the hydrate orebody and sediment enter the closed pipeline with the sea water. Considering the narrow space in the actual natural gas hydrate mining project, an axial-flow hydrocyclone is used to initially separate the sand entering the pipeline at the exploitation site, and the separated sand is backfilled. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the mixture of water and sediment enters the hydrocyclone from the inlet at an axial velocity, and after passing through the spiral flow path, part of the axial velocity of the mixture is transformed into a tangential velocity. At this time, the flow field inside the hydrocyclone become a swirling flow field. Due to the density difference between water and sand, a centrifugal force difference is generated in the swirling flow field. The density of the water phase is smaller than sand phase, and the centrifugal force generated in the circular motion is small, so the water phase is distributed at the axis of the hydrocyclone, and enters the separator pipe, ultimately discharged from the hydrocyclone through the water outlet. The density of the sand phase is relatively high, and centrifugal force generated in the circular motion is large, Therefore, the sand phase is distributed on the inner walls of the hydrocyclone, and finally discharged from the hydrocyclone through the sand outlet. Thus, the preliminary separation of sand phase in the process of solid fluidization exploitation of natural gas hydrate is completed.\u003c/p\u003e \u003cp\u003eIn this study, a three-dimensional model was used to study the flow field characteristics and the distribution law of different phase in the in-situ sand removal hydrocyclone for solid fluidization exploitation of natural gas hydrate. In the numerical simulation of the swirling flow field, the three-dimensional model can more objectively and comprehensively reflect the differences of different physical fields and different phase in different directions, which plays a significant role in improving the accuracy of numerical simulation of the flow field in the hydrocyclone [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. The dimensions of the hydrocyclone as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDimensions of the hydrocyclone\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStructure\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSymbol\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eValue(mm)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMain diameter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSeparator Pipe diameter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003ed\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSand Outlet diameter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003ed\u003c/em\u003e\u003csub\u003eso\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInlet length\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003el\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Flow Path length\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003el\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWater Outlet length\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003el\u003c/em\u003e\u003csub\u003ewo\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSeparator Pipe length\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003el\u003c/em\u003e\u003csub\u003ep\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 \u003cem\u003eMathematical model\u003c/em\u003e\u003c/h2\u003e \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e \u003ch2\u003e2.2.1 Governing equation\u003c/h2\u003e \u003cp\u003eThe fluid flow in a hydrocyclone can be regarded as a viscous incompressible fluid, which follows the basic governing equations as shown in Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e)-(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) [42\u0026ndash;43]:\u003c/p\u003e \u003cp\u003eContinuity equation:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\frac{\\partial }{{\\partial {x_j}}}\\left( {\\rho {u_j}} \\right)=0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eMomentum conservation equation:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\frac{\\partial }{{\\partial {x_j}}}\\left( {\\rho {u_i}{u_j}} \\right)= - \\frac{{\\partial p}}{{\\partial x}}+\\frac{\\partial }{{\\partial {x_j}}}\\left( {\\mu \\frac{{\\partial {u_i}}}{{\\partial {x_j}}}} \\right)+\\left( {\\rho - {\\rho _a}} \\right){g_j}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eEnergy conservation equation:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\frac{\\partial }{{\\partial {x_j}}}\\left( {\\rho {u_j}T} \\right)=\\frac{1}{{{C_p}}}\\frac{\\partial }{{\\partial {x_j}}}\\left( {{k_t}\\frac{{\\partial T}}{{\\partial {x_j}}}} \\right)+\\frac{{{C_{pv}} - {C_{pa}}}}{{{C_p}}}\\left[ {\\frac{\\partial }{{\\partial {x_j}}}\\left( {\\frac{{{\\mu _t}}}{{{\\sigma _c}}}} \\right)\\frac{{\\partial \\omega }}{{\\partial {x_i}}}} \\right]\\frac{{\\partial T}}{{\\partial {x_j}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e2.2.2 Turbulence modeling\u003c/h2\u003e \u003cp\u003eIn this study, the numerical simulation was performed via the commercial software Ansys\u0026rsquo;s Fluent 2020. Due to the fact that the internal flow field of the hydrocyclone is considered a strong vortex flow field, choosing the correct turbulence model has a significant impact on the accuracy of numerical simulation results. Among many turbulence models, the Reynolds Stress Model (RSM) takes into account continuity equation, momentum equation, transport equation and anisotropic turbulent shear equation at the same time, which is mainly applied to the numerical simulation of complex three-dimensional flow field considering Reynolds stress anisotropy. Therefore, the RSM is used to simulate the flow field in the hydrocyclone.\u003c/p\u003e \u003cp\u003eThe Reynolds stress model is based on the average Reynolds number theory, and the governing equations are shown in equations (\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e)-(\u003cspan refid=\"Equ10\" class=\"InternalRef\"\u003e10\u003c/span\u003e) [\u003cspan additionalcitationids=\"CR45\" citationid=\"CR43\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e46\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eReynolds stress transport equation:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\frac{\\partial }{{\\partial t}}\\left( {\\rho \\overline {{{{u^{\\prime}}_i}{{u^{\\prime}}_j}}} } \\right)+\\frac{\\partial }{{\\partial {x_k}}}\\left( {\\rho {u_k}\\overline {{{{u^{\\prime}}_i}{{u^{\\prime}}_j}}} } \\right)={D_{T,ij}}+{P_{ij}}+{\\varphi _{ij}} - {\\varepsilon _{ij}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eTurbulent kinetic energy diffusion term equation:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$${D_{T,ij}}= - \\frac{\\partial }{{\\partial {x_k}}}\\left( {\\rho \\overline {{{{u^{\\prime}}_i}{{u^{\\prime}}_j}{{u^{\\prime}}_k}}} +\\overline {{p{{u^{\\prime}}_j}}} {\\delta _{jk}} - \\mu \\frac{\\partial }{{\\partial {x_k}}}\\overline {{{{u^{\\prime}}_i}{{u^{\\prime}}_j}}} } \\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eMolecular viscous diffusion term equation:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$${D_{L,ij}}=\\frac{\\partial }{{\\partial {x_k}}}\\left[ {\\mu \\frac{\\partial }{{\\partial {x_k}}}\\left( {\\overline {{{{u^{\\prime}}_i}{{u^{\\prime}}_j}}} } \\right)} \\right]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eShear stress equation:\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$${P_{ij}}=\\rho \\left( {\\overline {{{{u^{\\prime}}_i}{{u^{\\prime}}_k}}} \\frac{{\\partial {u_j}}}{{\\partial {x_k}}}+\\overline {{{{u^{\\prime}}_j}{{u^{\\prime}}_k}}} \\frac{{\\partial {u_i}}}{{\\partial {x_k}}}} \\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eBuoyancy generation term equation:\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$${G_{ij}}= - \\rho \\beta \\left( {{g_i}\\overline {{{{u^{\\prime}}_j}\\theta }} +{g_j}\\overline {{{{u^{\\prime}}_i}\\theta }} } \\right)=\\beta \\frac{{{\\mu _t}}}{{0.85}}\\left( {{g_i}\\frac{{\\partial T}}{{\\partial {x_j}}}+{g_j}\\frac{{\\partial T}}{{\\partial xi}}} \\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ePressure strain term equation:\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$${{\\Phi}_{ij}}= - 0.18\\rho \\frac{\\varepsilon }{k}\\left( {\\overline {{{{u^{\\prime}}_i}{{u^{\\prime}}_j}}} - \\frac{2}{3}k{\\delta _{ij}}} \\right) - 0.6\\left( {{p_{ij}} - \\frac{2}{3}p{\\delta _{ij}}} \\right)+f\\left( {k,\\varepsilon ,{n_x},d} \\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eViscous dissipative term equation:\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$${\\varepsilon _{ij}}=2\\mu \\overline {{\\frac{{\\partial {{u^{\\prime}}_i}}}{{\\partial {x_k}}}\\frac{{\\partial {{u^{\\prime}}_j}}}{{\\partial {x_k}}}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.3 \u003cem\u003eNumerical method and grid generation\u003c/em\u003e\u003c/h2\u003e \u003cp\u003eIn this study, the Finite Volume Method (FVM) and the First-order Upwind scheme are used to solve the problem, and the governing equations are discretized based on the pressure solver. The Mixture model was selected to study the distribution law of the flow field in the hydrocyclone and the Semi-Implicit-Method for Pressure-Linked Equations (SIMPLE) algorithm was used to solve the problem iteratively. The SIMPLE algorithm is a numerical method mainly used to solve incompressible fluids. Its core is to use the \u0026ldquo;guess-correction\u0026rdquo; process to calculate the pressure field on the basis of staggered grids, so as to solve the momentum equation [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]. Combined with the actual natural gas hydrate exploitation project, considering the influence of gravity on the cyclone separation process, the acceleration of gravity was set to 9.81m/s\u003csup\u003e2\u003c/sup\u003e. Set the total number of calculation steps to 10000 steps, and save 1 data file every 1000 steps. In order to ensure the accuracy of numerical simulation, the convergence accuracy is set to 10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe fluid domain model of the in-situ sand removal hydrocyclone for natural gas hydrate solid fluidization exploitation was meshed, and four level grids were divided. In order to ensure the accuracy of calculation and reduce the amount of calculation, the grid independence test was carried out. Because of the complexity of fluid migration characteristics and mechanical distribution in the swirl field, in order to improve the stability and accuracy of numerical simulation and avoid false diffusion in the discretization process, local grid refinement was carried out around the separator pipe.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.4. \u003cem\u003eBoundary conditions\u003c/em\u003e\u003c/h2\u003e \u003cp\u003eIn this study, water was set as continuous phase and sand as discrete phase. The density of water is 998.2kg/m\u003csup\u003e3\u003c/sup\u003e, the viscosity is 0.001pa s, and the density of sand is 2700kg/m\u003csup\u003e3\u003c/sup\u003e. The boundary condition of the axial inlet of the hydrocyclone was set as the velocity inlet, and the incident velocity of the water phase and the sand phase is the same. Set the water outlet and the sand outlet as outflow. The wall of the hydrocyclone was set to wall, the wall roughness is 0, and there is no slip wall boundary.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e2.5. \u003cem\u003eSimulation scenarios\u003c/em\u003e\u003c/h2\u003e \u003cp\u003eIn this study, the numerical simulation method was used to study the internal flow field characteristics and phase distribution law of hydrocyclone applicable to in-situ separation of sand phases in solid fluidized exploitation of natural gas hydrate. Based on the hydrocyclone model proposed by Chang et al. and combined with the actual operating conditions of solid fluidization exploitation of natural gas hydrates, the effects of flow rate, flow ratio, sand volume fraction and sand particle diameter on the flow field characteristics in the hydrocyclone were studied. Numerical simulation scenarios were shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. In 13 cases, Case1 was set as the basic case. Case1-4 studies the distribution law of sand phase and water phase and tangential velocity field in swirling flow field under different flow conditions. Case5-7 and Case1 study the distribution of sand and water phases in the swirl field under different flow ratio. Case8-10 and Case1 study the effect of inlet sand content change on tangential velocity field and sand volume fraction distribution. Case 11\u0026ndash;13 and Case 1 study the distribution of tangential velocity field and sand phase in swirling flow field under different sand particle diameters. In order to ensure the objectivity and accuracy of the research results, the parameter changes of each factor were uniformly distributed. At the same time, in order to avoid the interaction of various factors, the control variable method was used to study the effects of different factors on the flow field characteristics.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eNumerical simulation scenarios\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eScenario\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFlow rate(m\u003csup\u003e3\u003c/sup\u003e/h)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFlow ratio(%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSand Volume fraction(%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSand particle diameter(\u0026micro;m)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe water-sand two-phase mixture enters the device from the inlet of the hydrocyclone, and the mixture changes from axial motion to circular motion after passing through the spiral flow path. Due to the density difference between the water phase and the sand phase, the centrifugal force generated by the sand phase in the circular motion is large, so the sand migrates to the side wall of the hydrocyclone under the centrifugal force and is discharged from the device by the sand outlet, while the water phase is distributed in the axial center of the hydrocyclone and enters the water outlet through the separator pipe. Therefore, the flow field area between the spiral flow path and the separator pipe is the key area for water-sand separation. In order to more accurately study the variation characteristics and laws of the water-sand separation flow field area, three monitoring lines \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e, \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMB\u003c/sub\u003e, and \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e are set equidistantly in this analysis area. According to the structural parameters of the hydrocyclone, the distances from the three monitoring lines to the inlet are 121mm, 200mm, and 279mm, respectively. The analysis area and the location of the monitoring line were shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn order to calculate the efficiency of sand discharge and water discharge in different cases. The dimensionless parameter \u003cem\u003eE\u003c/em\u003e was defined as the efficiency evaluation value, which is expressed by the ratio of the mass flow rate at the outlet of each phase to the mass flow rate at the inlet. The calculation of sand discharge and water discharge efficiency of hydrocyclone were shown in Eq.\u0026nbsp;(\u003cspan refid=\"Equ11\" class=\"InternalRef\"\u003e11\u003c/span\u003e)-(\u003cspan refid=\"Equ12\" class=\"InternalRef\"\u003e12\u003c/span\u003e).\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$${E_s}=\\frac{{{m_{so}}}}{{{m_{si}}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ12\" name=\"EquationSource\"\u003e\n$${E_w}=\\frac{{{m_{wi}}}}{{{m_{wo}}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eFinally, by analyzing the variation trend of velocity field, sand phase volume fraction and water phase volume fraction on the analysis area and monitoring lines, the influence of various factors on the internal flow field characteristics and distribution law of each phase of the hydrocyclone were obtained. In this study, in order to ensure the accuracy of the visibility of numerical simulation results, Ansys post-processing software was used to process the simulation results, and the ratio of icon size to model size is 1:1.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Result and discussion","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.1 \u003cem\u003eGrid independence\u003c/em\u003e\u003c/h2\u003e \u003cp\u003eThe Ansys\u0026rsquo;s pre-processing software Gambit was used to grid the fluid domain model of hydrocyclone which is applicable to sand removal in solid fluidization exploitation of natural gas hydrate, five levels of grids with 1821724, 2286356, 2799447, 3216424 and 3691497 cells were examined. The static pressure distribution on the monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e under different grid levels was analyzed, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The static pressure distribution curve with grid level of 1821724, 2286356, 2799447,3216424 was fitted by polynomial fitting, and the correlation coefficient \u003cem\u003eR\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e is 0.993387. It is proved that under the four grid number levels, the grid number has little influence on the numerical simulation results. When the number of grids is 3691497, the static pressure on the monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e changes greatly. In order to ensure the accuracy of numerical simulation and save calculation time, the fluid domain model of cyclone separator is divided into 2799447 grid elements, and the meshing results was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.2 \u003cem\u003eModel validation\u003c/em\u003e\u003c/h2\u003e \u003cp\u003eIn this study, Xu's experiments were used to verify the accuracy of numerical simulation and turbulence model [48]. In Xu's experimental research, the experimental platform was designed according to the actual working conditions, so this paper re-establish the numerical simulation calculation model based on Xu's experiment. The structural parameters of the hydrocyclone were shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, and other structural parameters are the same as those of the experimental device. In the experiment, the distribution law of pressure drop under the condition of inlet flow rate of 4.83m\u003csup\u003e3\u003c/sup\u003e/h and gas outlet flow ratio of 56%-64% was studied. Therefore, the same physical model and boundary conditions as the experimental device were establish, and the Mixture model and Reynolds stress model were used to carry out numerical simulation. The gas outlet pressure drop distribution obtained from numerical simulation and experiment under the condition of gas outlet flow ratio of 56%-64% was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. It can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e that due to the simplification of the real process in the numerical simulation process, the numerical simulation results are generally smaller than the experimental results. By polynomial fitting between the numerical simulation results and the experimental results, the fitting degree \u003cem\u003eR\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e is 0.958, which proves the accuracy of the numerical simulation and the turbulence model.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExperimental device structure parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStructure\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSwirl chamber length\u003c/p\u003e \u003cp\u003e(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMain diameter\u003c/p\u003e \u003cp\u003e(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eInverted cone height\u003c/p\u003e \u003cp\u003e(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDrain hole height\u003c/p\u003e \u003cp\u003e(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eInlet area\u003c/p\u003e \u003cp\u003e(mm\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e238\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4*14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e3.3 \u003cem\u003eFlow field characteristics and phase distribution laws under different parameters\u003c/em\u003e\u003c/h2\u003e \u003cp\u003eIn order to study the effects of different parameters on the flow field characteristics and phase distribution law and the separation efficiency of hydrocyclone, the numerical simulation method was used to study the influence of different flow rate, different flow ratio, different sand volume fraction and different sand particle diameter on the velocity field distribution and the sand phase and water phase distribution law.\u003c/p\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003e3.3.1 Flow field characteristics and distribution rules under different flow rate\u003c/h2\u003e \u003cp\u003eThe distribution of sand phase on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e, \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMB\u003c/sub\u003e, and \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e under different flow conditions were shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e6\u003c/span\u003e(\u003cb\u003ea\u003c/b\u003e)-Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e6\u003c/span\u003e(\u003cb\u003ec\u003c/b\u003e). It can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e6\u003c/span\u003e(\u003cb\u003ea\u003c/b\u003e) that on the monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e, the volume fraction of sand phase gradually increases in the radial position range of 0mm-\u0026plusmn;50mm. When the flow rate is 4.83m\u003csup\u003e3\u003c/sup\u003e/h, the sand volume fraction reaches a maximum of 19% at the radial position\u0026thinsp;\u0026plusmn;\u0026thinsp;50mm, and when the flow rate is 1.83m\u003csup\u003e3\u003c/sup\u003e/h, the sand volume fraction reaches a minimum of 10.5% at the radial position\u0026thinsp;\u0026plusmn;\u0026thinsp;50mm. As the flow rate increased from 1.83m\u003csup\u003e3\u003c/sup\u003e/h to 4.83m\u003csup\u003e3\u003c/sup\u003e/h, the sand volume fraction at the inner wall of the hydrocyclone increased by 8.5%. It is proved that as the flow rate increases, the tangential velocity in the flow field increases, and the sand phase migrates to the flow field edge more significantly in the process of separation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe distribution of sand volume fraction on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMB\u003c/sub\u003e under different flow conditions was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e6\u003c/span\u003e (\u003cb\u003eb\u003c/b\u003e). It can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e6\u003c/span\u003e(\u003cb\u003eb\u003c/b\u003e) that on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMB\u003c/sub\u003e, the sand volume fraction at the inner wall of the hydrocyclone still increases with the increase of flow rate, but the sand volume fraction at the axis decreases with the increase of flow rate. As the axial distance increases from 121 mm to 200 mm from the inlet, the sand volume fraction at the radial position\u0026thinsp;\u0026plusmn;\u0026thinsp;50 mm in the flow field gradually increases. When the flow rate is 4.83m\u003csup\u003e3\u003c/sup\u003e/h, the sand volume fraction reaches a maximum of 21.2% at the edge of the flow field, and the sand volume fraction reaches a minimum of 6.7% at the axial center of the flow field. When the flow rate is 1.83m\u003csup\u003e3\u003c/sup\u003e/h, the sand volume fraction at the edge of the flow field is 16.3%, and the sand volume fraction at the axis of the flow field is 12.4%.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe distribution of sand volume fraction on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e6\u003c/span\u003e(\u003cb\u003ec\u003c/b\u003e). From Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e6\u003c/span\u003e(\u003cb\u003ec\u003c/b\u003e), it can be seen that under the flow rate conditions of 1.83m\u003csup\u003e3\u003c/sup\u003e/h-4.83m\u003csup\u003e3\u003c/sup\u003e/h, the sand volume fraction rapidly decreases at the axial position of 279mm and the radial position of \u0026plusmn;\u0026thinsp;10mm, and all reach their minimum at the radial position of 0mm. The flow rate increased from 1.83m\u003csup\u003e3\u003c/sup\u003e/h to 4.83m\u003csup\u003e3\u003c/sup\u003e/h, and the sand volume fraction at the axis center of the flow field decreased from 13\u0026ndash;9.2%. When the flow rate is in the range of 2.83m\u003csup\u003e3\u003c/sup\u003e/h-4.83m\u003csup\u003e3\u003c/sup\u003e/h, the sand volume fraction still shows an increasing trend at the radial position\u0026thinsp;\u0026plusmn;\u0026thinsp;50mm. Compared with the monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMB\u003c/sub\u003e, the sand volume fraction at the edge of flow field increases by 1.8%, 1.8% and 1.5% respectively under the conditions of 2.83m\u003csup\u003e3\u003c/sup\u003e/h, 3.83m\u003csup\u003e3\u003c/sup\u003e/h and 4.83m\u003csup\u003e3\u003c/sup\u003e/h. However, when the flow rate is 1.83m\u003csup\u003e3\u003c/sup\u003e/h, the sand volume fraction at the edge of flow field decreases by 0.4%. It is proved that when the flow rate is in the range of 2.83m\u003csup\u003e3\u003c/sup\u003e/h-4.83m\u003csup\u003e3\u003c/sup\u003e/h, the tangential velocity in the flow field increases gradually from the axial position 121mm to 279mm. When the flow rate is 1.83m\u003csup\u003e3\u003c/sup\u003e/h, the tangential velocity decreases gradually within the 200mm-279mm range of the axial position of the flow field, and the separation effect on the sand phase is gradually decreased.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe tangential velocity distribution on monitoring line under different flow conditions were shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e7\u003c/span\u003e(\u003cb\u003ea\u003c/b\u003e)-Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e7\u003c/span\u003e(\u003cb\u003ec\u003c/b\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e7\u003c/span\u003e(\u003cb\u003ea\u003c/b\u003e) shows the tangential velocity distribution on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e. It can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e7\u003c/span\u003e(\u003cb\u003ea\u003c/b\u003e) that the tangential velocity on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e shows a symmetrical distribution characteristic and takes the radial position 0 mm as the axis of symmetry that first increases and then decreases from the radial position 0 mm to \u0026plusmn;\u0026thinsp;50 mm. The reason why the tangential velocity decreases at the side wall is that the wall roughness was set to 0 and there was no slip during the numerical simulation. The maximum tangential velocity under the four flow conditions is greater than 0m/s, indicating that part of the axial velocity of the mixture changes into a tangential velocity after passing through the spiral flow path. When the flow rate is 4.83m\u003csup\u003e3\u003c/sup\u003e/h, the maximum tangential velocity is 1m/s, which appears at the radial position of \u0026plusmn;\u0026thinsp;40mm. When the flow rate is 1.83m\u003csup\u003e3\u003c/sup\u003e/h, the maximum tangential velocity of 0.23m/s appears at the radial position of \u0026plusmn;\u0026thinsp;30mm. It shows that with the increase of the flow rate, the axial velocity at the inlet increases, which leads to the increase of the tangential velocity of the fluid after passing through the spiral flow path.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e7\u003c/span\u003e(\u003cb\u003eb\u003c/b\u003e) shows the tangential velocity distribution on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMB\u003c/sub\u003e under the flow condition of 1.83m\u003csup\u003e3\u003c/sup\u003e/h-4.83m\u003csup\u003e3\u003c/sup\u003e/h. As the axial distance from the inlet increases from 121mm to 200mm, the maximum tangential velocity at the edge of flow field decreases under different flow conditions, but the tangential velocity gradually increases within the range of -20mm-20mm in the radial position. When the flow rate is 4.83m\u003csup\u003e3\u003c/sup\u003e/h, the tangential velocity reaches a maximum of 0.33m/s at the edge of flow field. Compared with the monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e, the maximum tangential velocity decreases 0.67m/s. Similarly, when the traffic is 1.83m\u003csup\u003e3\u003c/sup\u003e/h and 3.83m\u003csup\u003e3\u003c/sup\u003e/h, the maximum tangential velocity decreases 0.35m/s and 0.01m/s, respectively. It is proved that as the axial distance increases, the tangential velocity in the swirling flow field decreases gradually, and the separation effect of the swirling flow gradually weakens.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e7\u003c/span\u003e(\u003cb\u003ec\u003c/b\u003e) shows the tangential velocity distribution on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e under different flow conditions. It can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e7\u003c/span\u003e(\u003cb\u003ec\u003c/b\u003e) that the maximum value of the tangential velocity in the flow field under different flow conditions at the axial position of 279mm appears at the radial position of 10.8 mm. According to the local enlargement, the maximum tangential velocity of 1.83m\u003csup\u003e3\u003c/sup\u003e/h, 2.83m\u003csup\u003e3\u003c/sup\u003e/h, 3.83m\u003csup\u003e3\u003c/sup\u003e/h and 4.83m\u003csup\u003e3\u003c/sup\u003e/h at the radial position 108mm is 0.13m/s, 0.19m/s, 0.27m/s and 0.35m/s, respectively. The maximum tangential velocity still shows the distribution law that increase with the increase of flow rate. However, compared with the monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e, the tangential velocity decreases by 0.65m/s, 0.34m/s and 0.1m/s respectively under the flow conditions of 1.83m\u003csup\u003e3\u003c/sup\u003e/h, 3.83m\u003csup\u003e3\u003c/sup\u003e/h and 4.83m\u003csup\u003e3\u003c/sup\u003e/h. When the flow rate is 2.83m\u003csup\u003e3\u003c/sup\u003e/h, the maximum tangential velocity remains unchanged. It shows that with the increase of the axial distance, the tangential flow produced by the spiral flow path gradually weakens, and the intensity of the swirl flow in the flow field gradually weakens.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe water phase distribution in the swirling flow field under different flow conditions was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e8\u003c/span\u003e(\u003cb\u003ea\u003c/b\u003e)-Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e8\u003c/span\u003e(\u003cb\u003eb\u003c/b\u003e). As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e8\u003c/span\u003e(\u003cb\u003ea\u003c/b\u003e), when the flow rate is in the range of 1.83m\u003csup\u003e3\u003c/sup\u003e/h-4.83m\u003csup\u003e3\u003c/sup\u003e/h, the water volume fraction on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e reaches 100% at the radial position of 0mm and the water volume fraction decreases gradually from the radial position of 0mm to \u0026plusmn;\u0026thinsp;50 mm under each flow rate condition. Among them, when the flow rate is 3.83m\u003csup\u003e3\u003c/sup\u003e/h and 4.83m\u003csup\u003e3\u003c/sup\u003e/h, the water volume fraction is concentrated in the range of radial position\u0026thinsp;\u0026plusmn;\u0026thinsp;24mm, and the concentration of water phase is more significant with the increase of flow rate. At the radial position\u0026thinsp;\u0026plusmn;\u0026thinsp;50mm, the water volume fraction decreases with the increase of flow rate. When the flow rate increases from 1.83m\u003csup\u003e3\u003c/sup\u003e/h to 4.83m\u003csup\u003e3\u003c/sup\u003e/h, the water volume fraction at the edge of flow field decreases from 88.8\u0026ndash;81.2%. It shows that the tangential velocity in the flow field increases with the increase of the flow rate. Since the density of the water phase is smaller than that of the sand phase, according to the principle of cyclone separation, the distribution of the water phase is closer to the center of the flow field.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe water volume fraction distribution on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e under different flow rate conditions was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e8\u003c/span\u003e(\u003cb\u003eb\u003c/b\u003e). As can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e8\u003c/span\u003e(\u003cb\u003eb\u003c/b\u003e), compared with the monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e, the water phase distribution on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e is more concentrated to the center of the flow field, and the concentrated distribution range of the water phase does not change significantly under different flow conditions, all in the range of radial position\u0026thinsp;\u0026plusmn;\u0026thinsp;10mm. The water volume fraction at the radial position 0mm increases with the increase of the flow rate, the flow rate increases from 1.83m\u003csup\u003e3\u003c/sup\u003e/h to 4.83m\u003csup\u003e3\u003c/sup\u003e/h, and the water volume fraction at the center of the flow field is 86.9%, 88.1%, 89.2% and 90.3%, respectively. The water volume fraction at the radial position\u0026thinsp;\u0026plusmn;\u0026thinsp;50mm decreases with the increase of flow rate, the flow rate increases from 1.83m\u003csup\u003e3\u003c/sup\u003e/h to 4.83m\u003csup\u003e3\u003c/sup\u003e/h, and the water volume at the edge of flow field is 85.3%, 80.5%, 78.5% and 77%, respectively. It shows that at the axial distance of 279 mm from the inlet, the volume fraction of the water is significantly changed by the flow rate, but the distribution area of ​​the water phase is not affected by the flow rate.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e \u003ch2\u003e3.3.2 Flow field characteristics and distribution rules under different flow ratio\u003c/h2\u003e \u003cp\u003eThe distribution of sand volume fraction on monitoring lines \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e, \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMB\u003c/sub\u003e, and \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e under different flow ratio conditions was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e9\u003c/span\u003e. It can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e9\u003c/span\u003e that at different monitoring lines, the sand volume fraction shows a gradually increasing distribution law in the radial position range of 0 mm to \u0026plusmn;\u0026thinsp;50 mm. On monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e, the sand volume fraction reaches a minimum of 0% at the axial center of the flow field and reaches a maximum of 18.8% at the edge of the flow field. On monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e, the sand volume fraction reaches a minimum of 8.9% at the axial center of the flow field and reaches a maximum of 22.6% at the edge of the flow field. That is, within the axial range of 121mm-279mm from the inlet, the sand volume fraction at the axial center and edge of the flow field increases by 8.9% and 3.8%, respectively. However, on the same monitoring line, the flow ratio of the sand outlet increases from 5\u0026ndash;20%, and there is no significant difference in the sand volume fraction. It shows that the flow ratio of the sand outlet has no significant effect on the separation of the sand phase.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe distribution of sand volume fraction on monitoring lines \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e, \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMB\u003c/sub\u003e, and \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e under different sand outlet flow ratios was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e10\u003c/span\u003e. It can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e10\u003c/span\u003e that the volume fraction distribution of water phase is complementary to that of sand phase. The increase of sand outlet flow ratio from 5\u0026ndash;20% has no significant effect on the distribution of water volume fraction on the same monitoring line. In the axial area from \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e to \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e, the distribution of water volume fraction shows the distribution law of aggregation to the axial center. On the monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e, the water phase volume fraction within the radial range of \u0026plusmn;\u0026thinsp;9 mm is about 100%, which proves that the sand phase at the axial position of 121 mm of the flow field has been completely separated. On the monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e, the water volume fraction at the radial position of 0 mm reaches a maximum of 90.3%. It shows that as the axial distance increases from 121mm to 279mm, the water volume fraction around the axis center of flow field decreases by 9.7%, which proves that as the axial distance increases, a small part of the water phase migrates to the side wall.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003e3.3.3 Flow field characteristics and distribution rules under different sand content\u003c/h2\u003e \u003cp\u003eThe distribution of sand phase in the analysis area under different sand volume fraction was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e11\u003c/span\u003e(\u003cb\u003ea\u003c/b\u003e)-Fig.\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e11\u003c/span\u003e(\u003cb\u003ec\u003c/b\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e11\u003c/span\u003e(\u003cb\u003ea\u003c/b\u003e) shows the s distribution of and volume fraction at the on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e. As can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e11\u003c/span\u003e(\u003cb\u003ea\u003c/b\u003e), at the axial distance 121mm from the inlet, the sand content is in the range of 10\u0026ndash;40%, and the sand distribution in the flow field shows a symmetrical distribution characteristic with the radial position 0mm as the symmetry axis. In the range of 0mm-\u0026plusmn;50mm in the radial position, the sand volume fraction increases gradually, indicating that the sand volume fraction gradually increases from the center to the edge of the flow field. The sand volume fraction at the center of the flow field is 0%, and the sand volume fraction at the edge of the flow field increases with the increase of sand content. When the sand content is 40%, the sand volume fraction at the edge of the flow field reaches a maximum of 38.8%, which is 29.5%, 20%, 10.1%higher than that under the conditions of sand content of 10%, 20%, 30%.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe distribution of sand volume fraction on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMB\u003c/sub\u003e under different sand content conditions was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e11\u003c/span\u003e(\u003cb\u003eb\u003c/b\u003e). It can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e11\u003c/span\u003e(\u003cb\u003eb\u003c/b\u003e) that on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMB\u003c/sub\u003e, the sand volume fraction in the swirling flow field under different sand content conditions still shows a distribution law that gradually increases from the center to the edge of flow field. However, there are significant differences in the sand volume fraction under different sand contents, and the sand volume fraction in the flow field increases with the increase of sand content. As the sand content increases from 10\u0026ndash;40%, the sand volume fraction at the center of the swirling field increases from 2.9\u0026ndash;20.1%, and the sand volume fraction at the edge of the swirling field increases from 10.7\u0026ndash;41.5%. Compared with the monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e, the sand volume fraction in the center and edge of the flow field are both increased. It shows that as the axial distance increases, the sand continues to move towards the side wall of the hydrocyclone under the action of the swirling flow, but the separation of sand is gradually weakened due to the gradual weakening of cyclone separation in the flow field.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe distribution of sand volume fraction on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e under different sand content conditions was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e11\u003c/span\u003e(\u003cb\u003ec\u003c/b\u003e). It can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e11\u003c/span\u003e(\u003cb\u003ec\u003c/b\u003e) that the sand volume fraction on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e forms a decrease area within the radial range of \u0026plusmn;\u0026thinsp;12.5mm, and gradually stabilizes within the radial range of \u0026plusmn;\u0026thinsp;12.5mm-\u0026plusmn;50mm. Among them, the sand volume fraction fluctuates in a small range due to the influence of the separator pipe at the radial position of \u0026plusmn;\u0026thinsp;12.5mm. In the decrease area, the sand volume fraction at the center of the flow field increases with the increase of sand content. When the sand content is 10% and 40%, the sand volume fraction at the center of the flow field is 4.2% and 25.2% respectively. Compared with the sand volume at the inlet of the hydrocyclone, the sand volume fraction at the center of the flow field under the four sand content conditions decreased by 5.8%, 10.6%, 13.9%, and 14.8%, respectively. It is proved that with the increase of sand content, the amount of sand discharged from the water outlet is larger, but the proportion of sand discharged from the sand outlet is larger.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e3.3.4 Flow field characteristics and distribution rules under different sand particle diameter\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig19\" class=\"InternalRef\"\u003e12\u003c/span\u003e shows the distribution of tangential velocity in the swirling flow field under different sand particle diameter. It can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig19\" class=\"InternalRef\"\u003e12\u003c/span\u003e that the maximum tangential velocity on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e is at the radial position of \u0026plusmn;\u0026thinsp;36mm, and the maximum tangential velocity on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e at the radial position of \u0026plusmn;\u0026thinsp;12.5mm. And the maximum tangential velocity on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e is significantly higher than that on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e. It shows that as the axial position increases from 121mm to 279mm from the hydrocyclone inlet, the tangential velocity generated by the spiral flow path gradually weakens in the axial and radial directions, and the swirl separation effect in the swirl field also gradually decreases as the tangential velocity decreases. According to Fig.\u0026nbsp;\u003cspan refid=\"Fig19\" class=\"InternalRef\"\u003e12\u003c/span\u003e, the change of sand particle diameter does not have a significant effect on the tangential velocity at the same axial position in the flow field. From the local enlargement, it can be seen that the change of sand particle diameter has only a slight effect on the tangential velocity on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e. When the sand particle diameter is 20\u0026micro;m, the maximum tangential velocity is 1.21m/s, and when the sand particle diameter is 80\u0026micro;m, the minimum tangential velocity is 1.01m/s. As the sand particle diameter increases from 20 \u0026micro;m to 80 \u0026micro;m, the maximum tangential velocity decreases 0.2m/s. However, on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e, the maximum tangential velocity in the flow field under different particle diameters is 0.28m/s. It is proved that under the condition of strong swirling flow, the tangential velocity in the flow field decreases with the increase of sand particle diameter, but the change of sand particle diameter has little effect on the tangential velocity.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe distribution of sand phase in the analysis area under different sand particle diameter was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig22\" class=\"InternalRef\"\u003e13\u003c/span\u003e(\u003cb\u003ea\u003c/b\u003e)-Fig.\u0026nbsp;\u003cspan refid=\"Fig22\" class=\"InternalRef\"\u003e13\u003c/span\u003e(\u003cb\u003ec\u003c/b\u003e). Among them, Fig.\u0026nbsp;\u003cspan refid=\"Fig22\" class=\"InternalRef\"\u003e13\u003c/span\u003e(\u003cb\u003ea\u003c/b\u003e) shows the distribution of sand volume fraction on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e. It can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig22\" class=\"InternalRef\"\u003e13\u003c/span\u003e(\u003cb\u003ea\u003c/b\u003e) that under the condition of different sand particle diameters, the sand volume fraction shows a distribution law that gradually increases from the center to the edge of the flow field. When the sand particle diameter is in the range of 20\u0026ndash;80\u0026micro;m, the sand volume fraction in the swirling field decreases gradually with the increase of particle diameter on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e, but the sand volume fraction reaches about 20% at the edge of the flow field under different sand particle diameter conditions. At the radial position 0mm, when the sand particle diameter is 20\u0026micro;m and 80\u0026micro;m, the sand volume fraction reaches the maximum and the minimum is 16.9% and 0%, respectively. It is proved that in the process of cyclone separation, under the condition of the same flow rate and the same sand content, the larger the sand particle diameter is, the easier it is to separate.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe distribution of sand volume fraction on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMB\u003c/sub\u003e under different particle diameter conditions was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig22\" class=\"InternalRef\"\u003e13\u003c/span\u003e(\u003cb\u003eb\u003c/b\u003e). As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig22\" class=\"InternalRef\"\u003e13\u003c/span\u003e(\u003cb\u003eb\u003c/b\u003e) that the sand volume fraction decreases with the increase of sand particle diameter in the flow field at the distance from the inlet 200mm of the hydrocyclone. Compared with the monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e, the sand volume fraction at the radial position 0mm increases. However, the sand volume fraction is still roughly the same at about 20% at the edge of the flow field under different particle diameters. At this time, the sand volume fraction at the center of the flow field under the four particle diameters is 18.9%, 15.6%, 11.2% and 7%, respectively. Compared with the monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e, which increases by 2%, 7.6%, 9.8% and 7%, respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig22\" class=\"InternalRef\"\u003e13\u003c/span\u003e(\u003cb\u003ec\u003c/b\u003e) shows the distribution of sand volume fraction on monitoring line \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e under different sand particle diameter conditions. As can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig22\" class=\"InternalRef\"\u003e13\u003c/span\u003e(\u003cb\u003ec\u003c/b\u003e), at the axial position 279mm, the sand volume fraction decreases rapidly in the radial range\u0026thinsp;\u0026plusmn;\u0026thinsp;12.5mm and reaches the minimum at 0mm. And the sand volume fraction at the axial center of the flow field is inversely proportional to the sand particle diameter. When the sand particle diameter is 80\u0026micro;m, the sand volume fraction reaches a minimum of 9.4% at the axial center of the flow field. At the same time, due to the effect of the separator pipe wall, there is a small fluctuation in the distribution of sand volume fraction at \u0026plusmn;\u0026thinsp;12.5mm. The sand volume fraction near the inner wall of the hydrocyclone is different under the condition of different particle diameters, and the distribution law is positively correlated with the sand particle diameter. When the sand particle diameter is 80\u0026micro;m, the maximum sand volume fraction is 22.9%. When the sand particle diameter is 20\u0026micro;m, the sand volume fraction decreases slightly due to the effect of water phase migration in the range of radial position\u0026thinsp;\u0026plusmn;\u0026thinsp;12.5mm, but the overall stability is 20%. According to the analysis of the sand volume fraction distribution of from the \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMA\u003c/sub\u003e to \u003cem\u003eL\u003c/em\u003e\u003csub\u003eMC\u003c/sub\u003e shows that there is a positive correlation between the degree of sand separation and sand particle diameter in the process of cyclone separation. In a certain range, the larger the sand particle diameter, the easier it is to achieve sand phase separation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e3.4 \u003cem\u003eEfficiency calculation\u003c/em\u003e\u003c/h2\u003e \u003cp\u003eThe sand discharge rate and water discharge rate were calculated according to the Eq.\u0026nbsp;(\u003cspan refid=\"Equ11\" class=\"InternalRef\"\u003e11\u003c/span\u003e)-(\u003cspan refid=\"Equ12\" class=\"InternalRef\"\u003e12\u003c/span\u003e). The \u003cem\u003eE\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e and \u003cem\u003eE\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e calculations for Case1-Case13 are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig23\" class=\"InternalRef\"\u003e14\u003c/span\u003e. From the distribution law of sand discharge efficiency curve and drainage efficiency curve in Fig.\u0026nbsp;\u003cspan refid=\"Fig23\" class=\"InternalRef\"\u003e14\u003c/span\u003e, it can be seen that there is a negative correlation between sand discharge efficiency and drainage efficiency in hydrocyclone. Among them, the maximum \u003cem\u003eE\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e is 22.1% of Case7, indicating that when the flow rate is 4.83m\u003csup\u003e3\u003c/sup\u003e/h, the sand outlet flow ratio is 20%, the sand content is 20%, and the sand particle diameter is 80\u0026micro;m, the sand phase separation efficiency of this hydrocyclone is the highest. The minimum \u003cem\u003eE\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e is 86.1% of case6 and case7, it indicates that the water discharge efficiency is the same when the flow rate is 4.83m\u003csup\u003e3\u003c/sup\u003e/h, the sand volume fraction is 20%, the sand particle diameter is 80\u0026micro;m, and the sand outlet flow ratio is 15% and 20%, respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eIn this paper, based on the hydrocyclone proposed by Chang, which is applicable to the solid fluidization exploitation of natural gas hydrate, the numerical simulation method was used to study the internal flow field characteristics of this type of hydrocyclone under different working conditions and its applicability in the solid fluidization exploitation of natural gas hydrate. Based on the results and discussions above, the following conclusions were drawn:\u003c/p\u003e \u003cp\u003e(1)The numerical simulation method was used to study the flow field characteristics and distribution law of the hydrocyclone which is applicable to the solid fluidization exploitation of natural gas hydrate under the conditions of different flow rate, different flow ratio, different sand content and different sand particle diameter. In the same axial position, when the flow rate is in the range of 1.83m\u003csup\u003e3\u003c/sup\u003e/h to 4.83m\u003csup\u003e3\u003c/sup\u003e/h and the sand content is in the range of 10\u0026ndash;40%, the sand volume fraction decreases at the center of the flow field and increases at the edge of the flow field. When the sand particle diameter increases from 20\u0026micro;m to 80\u0026micro;m, the sand volume fraction decreases at the center of the flow field, but there is no obvious change at the edge of the flow field. When the flow ratio increases from 5\u0026ndash;20%, there is no significant effect on the distribution of sand volume fraction in the flow field. Therefore, it is suggested that the initial sand removal efficiency of solid fluidization exploitation of natural gas hydrate should be improved by increasing the inlet flow rate in engineering practice.\u003c/p\u003e \u003cp\u003e(2) When the axial position in the flow field increases from 121mm to 279mm from the inlet. When the flow rate, flow ratio and sand content are constant, the sand volume fraction increases gradually at the center of the flow field and decreases at the edge of the flow field. When the sand particle diameter is constant, the sand volume fraction has no significant change at the edge of the flow field.\u003c/p\u003e \u003cp\u003e(3)The \u003cem\u003eE\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e and \u003cem\u003eE\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e of the hydrocyclone under different working conditions were calculated, and the results show that the maximum \u003cem\u003eE\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e is 22.1% and the minimum \u003cem\u003eE\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e is 86.1% when the flow rate is 4.83m\u003csup\u003e3\u003c/sup\u003e/h, the sand outlet flow ratio is 20%, the sand volume fraction is 20% the sand particle diameter is 80\u0026micro;m. The optimum working conditions for this type of hydrocyclone were obtained. It provides a reference for the practical engineering application of sand pre-separation in solid fluidization exploitation of natural gas hydrate.\u003c/p\u003e \u003cp\u003e(4)The hydrocyclone studied in this paper has a low separation efficiency for water and sand phases, and is only applicable to rough pre-separation of sand phase in the process of solid fluidization exploitation of natural gas hydrate, and cannot perform fine separation for complex mixture. In the follow-up research and practical engineering application, the optimization of structural parameters should be further carried out to improve its separation efficiency.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding\u003c/h2\u003e\n\u003cp\u003eThe research is funded by National Key Research and Development Program (No. 2021YFC2800903), National Natural Science Foundation of China (No. U20B6005-05), 111 Project (No. D21025),\u0026nbsp;Sichuan High-end Foreign Talent Introduction Project (No. SYZ202124)\u003c/p\u003e\n\u003ch2\u003eAcknowledgments\u003c/h2\u003e\n\u003cp\u003eThis research was supported by the National Key Research and Development Program (No. 2021YFC2800903), National Natural Science Foundation of China (No. U20B6005-05), 111 Project (No. D21025) and Sichuan High-end Foreign Talent Introduction Project (No. SYZ202124)\u003c/p\u003e\n\u003ch2\u003eAuthor contribution\u003c/h2\u003e\n\u003cp\u003eNW: Resources, project administration, funding acquisition.\u003c/p\u003e\n\u003cp\u003eYQ: Conceptualization, methodology, software, formal analysis, data curation, writing-original draft, writing-review and editing.\u003c/p\u003e\n\u003cp\u003eSSF: Investigation.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eMC: Investigation.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eHTL: Project administration.\u003c/p\u003e\n\u003cp\u003eSWZ: Investigation, visualization.\u003c/p\u003e\n\u003cp\u003eJZZ: Project administration\u003c/p\u003e\n\u003cp\u003eLHZ: Project administration\u003c/p\u003e\n\u003cp\u003eRBC: Investigation, visualization\u003c/p\u003e\n\u003ch2\u003eCompeting interests\u003c/h2\u003e\n\u003cp\u003eThe author(s) declare no competing interests.\u003c/p\u003e\n\u003ch2\u003eData availability statement\u003c/h2\u003e\n\u003cp\u003eThe original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eLiang, L., Sun, J., Yue, M. 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DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.3901/JME.2017.08.175\u003c/span\u003e\u003cspan address=\"10.3901/JME.2017.08.175\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Natural gas hydrate, Cyclone separation, Flow field characteristics, Sand removal hydroyclone, Solid fluidization exploitation","lastPublishedDoi":"10.21203/rs.3.rs-2980319/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2980319/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWith the development of economy and society, the consumption of fossil energy is gradually increasing. In order to solve the current energy dilemma, NGH is considered as an ideal alternative energy. At the same time, the solid fluidization exploitation is an ideal exploit method for NGH at present. However, in the process of solid fluidization exploitation, sand and hydrate ore bodies enter the closed pipeline together, which will block the pipeline and increase the difficulty of exploitation. Therefore, the pre-separation of sand by hydrocyclone plays an important role in solid fluidization exploitation. In this study, the numerical simulation method was used to study the internal flow field characteristics of the hydrocyclone under different conditions, and the effects of different flow rate, different flow ratio, different sand content and different particle diameter on the phase distribution are investigated. The results show that: at the same axial position, the increase of flow rate and sand content makes the sand phase more distributed at the edge of the flow field, while the change of flow ratio has no significant effect on the distribution of sand phase. Under the same working conditions, the sand gradually migrates to the center of the flow field with the increase of the axial distance, while the particle diameter change has no significant effect on the sand distribution. By calculation, it is obtained that under the optimum working condition of the flow rate is 4.83m\u003csup\u003e3\u003c/sup\u003e/h, the flow ratio is 20%, the sand content is 20%, and sand particle diameter is 80\u0026micro;m, the maximum \u003cem\u003eE\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e is 22.1% and the minimum is 86.1%. Finally, a comprehensive analysis of the hydrocyclone in this study shows that this type of hydrocyclone is applicable to rough pre-separation of sand in the process of solid fluidization exploitation of NGH, and can not fine separate complex mixture. Through the study of the internal flow field characteristics and phase distribution law of the hydrocyclone, this study provides a reference for the practical engineering application of sand phase pre-separation in the solid fluidization exploitation of NGH.\u003c/p\u003e","manuscriptTitle":"Analysis of Flow Field Characteristics of Sand Removal Hydroyclone Applicable to Solid Fluidization Exploitation of Natural Gas Hydrate","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-06-06 14:40:40","doi":"10.21203/rs.3.rs-2980319/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"cb8ae9ca-67e5-468f-a8d7-6dcbb5ffc6bb","owner":[],"postedDate":"June 6th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":22067345,"name":"Physical sciences/Energy science and technology"},{"id":22067346,"name":"Physical sciences/Engineering/Energy infrastructure"}],"tags":[],"updatedAt":"2023-07-05T08:59:31+00:00","versionOfRecord":[],"versionCreatedAt":"2023-06-06 14:40:40","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2980319","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2980319","identity":"rs-2980319","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}