Numerical simulation of predicting and reducing solid particle erosion of solid-liquid two-phase flow in a choke

Chokes are one of the most important components of downhole flow-control equipment. The particle erosion mathematical model, which considers particle-particle interaction, was established and used to simulate solid particle movement as well as particle erosion characteristics of the solid-liquid two-phase flow in a choke. The corresponding erosion reduction approach by setting ribs on the inner wall of the choke was advanced. This mathematical model includes three parts： the flow field simulation of the continuous carrier fluid by an Eulerian approach, the particle interaction simulation using the discrete particle hard sphere model by a Lagrangian approach and calculation of erosion rate using semiempirical correlations. The results show that particles accumulated in a narrow region from inlet to outlet of the choke and the dominating factor affecting particle motion is the fluid drag force. As a result, the optimization of rib geometrical parameters indicates that good anti-erosion performance can be achieved by four ribs, each of them with a height （H） of 3 mm and a width （B） of 5 mm equaling the interval between ribs （L）.

K-ε-T MODEL OF DENSE LIQUID-SOLID TWO-PHASE TURBULENT FLOW AND ITS APPLICATION TO THE PIPE FLOW

To predict the characteristics of dense liquid-solid two-phase flow, K-Ε-T model is established, in which the turbulent flow of fluid phase was described with fluid turbulent kinetic energy Kf and its dissipation rate Εf, and the particles random motion was described with particle turbulent energy Kp and its dissipation rate Εp and pseudothermal temperature Tp. The governing equations were also derived. With K-Ε-T model, numerical study of dense liquid-solid two-phase turbulent up-flow in a pipe is performed. The calculated results are in good agreement with experimental data of Alajbegovic et al. (1994), and some flow features are captured.

Modeling of gas-solid flow in a CFB riser based on computational particle fluid dynamics

A three-dimensional model for gas-solid flow in a circulating fluidized bed（CFB） riser was developed based on computational particle fluid dynamics（CPFD）.The model was used to simulate the gas-solid flow behavior inside a circulating fluidized bed riser operating at various superficial gas velocities and solids mass fluxes in two fluidization regimes,a dilute phase transport（DPT） regime and a fast fluidization（FF） regime.The simulation results were evaluated based on comparison with experimental data of solids velocity and holdup,obtained from non-invasive automated radioactive particle tracking and gamma-ray tomography techniques,respectively.The agreement of the predicted solids velocity and holdup with experimental data validated the CPFD model for the CFB riser.The model predicted the main features of the gas-solid flows in the two regimes;the uniform dilute phase in the DPT regime,and the coexistence of the dilute phase in the upper region and the dense phase in the lower region in the FF regime.The clustering and solids back mixing in the FF regime were stronger than those in the DPT regime.

Numerical simulation of stratified turbulent two-phase flow in aquatic environment

The two fluid model of stratified turbulent two phase flow in aquatic environment is developed in this paper. The motion of each phase is described by a unified multi fluid model in an Eulerian coordinate system. The laws of turbulent transportation for each phase, and the restriction of each other between the two phases are completely simulated. The complex two phase turbulence with strong buoyancy effects is selected to examine numerically. The extensive experimental data obtained in stratified flow are used here. Comparison of the results of numerical simulation with the experimental data is conducted. It has shown that the results of numerical simulation are satisfactory.

Solid Particles Injection in Gas Turbulent Channel Flow

This paper represents a review of the recent researches that investigate the behavior of the gas turbulent flow laden with solid particles. The significant parameters that influence the interactions between the both phases, such as particle size, loading ratio and the gas velocity, have been extensively reviewed. Those parameters are presented in dimensionless numbers in which the applicability of studying its effect in terms of all circumstances of the gas turbulent channel flow at different condition is possible. The represented results show that the turbulence degree is proportional to the particle size. It was found that at the most flow conditions even at low mass ratio, the particle shape, density and size significantly alter the turbulence characteristics. However, the results demonstrate that the particle Reynolds number is a vital sign: the turbulence field becomes weaker if particle Reynolds number is lower than the critical limit and vies verse. The gas velocity has a strong effect on the particles settling along the channel flow and as a result, the pressure drop will be affected.

Size dependent flow behaviors of particles in hydrocyclone based on multiphase simulation

To investigate the flow behaviors of different size particles in hydrocyclone,a designed process was numerically simulated by the transient solver,where the quartz particles possessing a size distribution were injected into a 100 mm diameter hydrocyclone with the steady water field and air core inside.A lab experimental work has validated the chosen models in simulation by comparing the classification efficiency results.The simulated process shows that the 25 μm quartz particles,close to the cut size,need much more time than the finer and coarser particles to reach the steady flow rate on the outlets of hydrocyclone.For the particles in the inner swirl,with the quartz size increasing from 5 to 25 μm,the particles take more time to enter the vortex finder.The 25 μm quartz particles move outward in the radial direction when they go up to the vortex finder,which is contrary to the quartz particles of 5 μm and 15 μm as they are closely surrounding the air core.The studies reveal that the flow behaviors of particles inside the hydrocyclone depend on the particle size.

RESEARCH ON METHOD TO CALCULATE VELOCITIES OF SOLID PHASE AND LIQUID PHASE IN DEBRIS FLOW

Velocities of solid phase and liquid phase in debris flow are one key problem to research on impact and abrasion mechanism of banks and control structures under action of debris flow. Debris flow was simplified as two-phase liquid composed of solid phase with the same diameter particles and liquid phase with the same mechanical features. Assume debris flow was one-dimension two-phase liquid moving to one direction, then general equations of velocities of solid phase and liquid phase were founded in two-phase theory. Methods to calculate average pressures, volume forces and surface forces of debris flow control volume were established. Specially, surface forces were ascertained using Bingham＇s rheology equation of liquid phase and Bagnold＇s testing results about interaction between particles of solid phase. Proportional coefficient of velocities between liquid phase and solid phase was put forward, meanwhile, divergent coefficient between theoretical velocity and real velocity of solid phase was provided too. To state succinctly before, method to calculate velocities of solid phase and liquid phase was obtained through solution to general equations. The method is suitable for both viscous debris flow and thin debris flow. Additionally, velocities every phase can be identified through analyzing deposits in-situ after occurring of debris flow. It is obvious from engineering case the result in the method is consistent to that in real-time field observation.

ON EQUATION OF DISCRETE SOLID PARTICLES' MOTION IN ARBITRARY FLOW FIELD AND ITS PROPERTIES

The forces on rigid particles moving in relation to fluid having been studied and the equation of modifications of their expressions under different flow conditions discussed, a general form of equation for discrete particles' motion in arbitrary flow field is obtained. The mathematical features of the linear form of the equation are clarified and analytical solution of the linearized equation is gotten by means of Laplace transform. According to above theoretical results, the effects of particles' properties on its motion in several typical flow field are studied, with some meaningful conclusions being reached.

ON BASIC EQUATIONS OF TURBULENT SWIRLING GAS-SOLID FLOWS AND THEIR APPLICATION IN CYCLONES

The basic equations of turbulent gas-solid flows are derived by using the pseudo-fluid model of particle phase with a refined two-phase turbulence model.These equations are then applied to swirling gas-particle flows for analyzing the collection efficiency in cyclone separators.

Flux vector splitting solutions for coupling hydraulic transient of gas-liquid-solid three-phase flow in pipelines

The gas-liquid-solid three-phase mixed flow is the most general in multiphase mixed transportation. It is significant to exactly solve the coupling hydraulic transient problems of this type of multiphase mixed flow in pipelines. Presently, the method of characteristics is widely used to solve classical hydraulic transient problems. However, when it is used to solve coupling hydraulic transient problems, excessive interpolation errors may be introduced into the results due to unavoidable multiwave interpolated calculations. To deal with the problem, a finite difference scheme based on the Steger- Warming flux vector splitting is proposed. A flux vector splitting scheme is established for the coupling hydraulic transient model of gas-liquid-solid three-phase mixed flow in the pipelines. The flux subvectors are then discretized by the Lax-Wendroff central difference scheme and the Warming-Beam upwind difference scheme with second-order precision in both time and space. Under the Rankine-Hugoniot conditions and the corresponding boundary conditions, an effective solution to those points located at the boundaries is developed, which can avoid the problem beyond the calculation region directly induced by the second-order discrete technique. Numerical and experimental verifications indicate that the proposed scheme has several desirable advantages including high calculation precision, excellent shock wave capture capability without false numerical oscillation, low sensitivity to the Courant number, and good stability.

Heavy-organic particle deposition from petroleum fluid flow in oil wells and pipelines

Suspended asphaltenic heavy organic particles in petroleum fluids may stick to the inner walls of oil wells and pipelines. This is the major reason for fouling and arterial blockage in the petroleum industry. This report is devoted the study of the mechanism of migration of suspended heavy organic particles towards the walls in oil-producing wells and pipelines. In this report we present a detailed analytical model for the heavy organics suspended particle deposition coefficient corresponding to petroleum fluids flow production conditions in oil wells. We predict the rate of particle deposition during various turbulent flow regimes. The turbulent boundary layer theory and the concepts of mass transfer are utilized to model and calculate the particle deposition rates on the walls of flowing conduits. The developed model accounts for the eddy diffusivity, and Brownian diffusivity as well as for inertial effects. The analysis presented in this paper shows that rates of particle deposition （during petroleum fluid production） on the walls of the flowing channel due solely to diffusion effects are small. It is also shown that deposition rates decrease with increasing particle size. However, when the process is momentum controlled （large particle sizes） higher deposition rates are expected.

THE EFFECT OF PARTICLES ON FLUID TURBULENCE IN A TURBULENT BOUNDARY LAYER OVER A CYLINDER

The turbulent fluid and particle interaction in the turbulent boundary layer for cross how over a cylinder has been experimentally studied. A phase-Doppler anemometer was used to measure the mean and fluctuating velocities of both phases. Two size ranges of particles (30 mu m similar to 60 mu m and 80 mu m similar to 150 mu m) at certain concentrations were used for considering the effects of particle sizes on the mean velocity profiles and on the turbulent intensity levels. The measurements clearly demonstrated that the larger particles damped fluid turbulence. For the smaller particles, this damping effect was less noticeable. The measurements further showed a delay in the separation point for two phase turbulent cross how over a cylinder.

FLOW OF A TRAIN OF DEFORMABLE FLUID PARTICLES IN A TUBE

In the article, the boundary integral technique is used to salve the hydrodynamic movement. of a train of deformable fluid particles in a tube. When a fluid particle is: in a tube, the total normal stress difference is not constant any more; this force tends to distend and elongate the particle. We find that the difference between the velocity of a deformable fluid particle and a sphere (with the same radius) increases as the distance between the particles decreases, and that the increase in velocity with L'/a' is greater the capillary number, and this increase becomes less pronounced as radius' decreases.

RESEARCH ON THE EFFECT OF CYLINDER PARTICLES ON THE TURBULENT PROPERTIES IN PARTICULATE FLOWS

The fluid fluctuating velocity equations which include the term of cylinder particles were established. The turbulent intensity and Reynolds stress of fluid were obtained by averaging fluctuating velocity based on the solution of the fluctuating velocity equations. Above approach was used to solve the channel turbulent flows, and computational results were compared with the experimental ones for the case of single phase flow. The effects of volume fraction of particles, the ratio of particle length to diameter and the particle relaxation time on turbulent properties were illustrated by changing cylinder particle parameters. It is shown that particles play a restraining role to turbulent properties in the flows. The degree of restraint is directly proportional to the volume fraction of particle, the ratio of particle length to diameter and inversely proportional to particle relaxation time.

Mathematical Modelling of Particle Movement Ahead of the Solid-liquid Interface in Continuous Casting

Whether the particle will be trapped by the solid-liquid interface or not is dependent on its moving behavior ahead of the interface, so a mathematical model has been developed to investigate the movement of the particle ahead of the solid-liquid interface. Based on the theory for the boundary layer, the fluid velocity field near the solid-liquid interface was obtained, and the trajectories of particles were calculated by the equations of motion for particles. In this model, the drag force, the added mass force, the buoyance force, the gravitational force, the Saffman force and the Basset history force are considered. The results show that the behavior of the particle ahead of the solid-liquid interface is affected by the physical property of the particle and fluid flow. And in the continuous casting process, if it moves in the stream directed upward or downward near vertical solid-liquid interface or in the horizontal flow under the solid-liquid interface, the particle with the diameter from 5 um to 60um can reach the solid-liquid interface. But if it moves in horizontal flow above the solid-liquid interface, only the particle with the diameter from 5 um to 10 um can reach the solid-liquid interface.

Numerical Simulation of Gas-Solid Flow in Square Cyclone Separators with Downward Exit

Cyclone separators are widely used in industrial applications. The separation efficiency and pressure drop are the most important parameters to evaluate the performance of processing system. In the simulations,the flow behavior of gas and particles within a square cyclone separator is simulated by means of computational fluid dynamics. The RNG k- ε model and the Reynolds stress model( RSM) are used to model gas turbulence. The flow behavior is examined in the term of tangential velocity components,static pressure and pressure drop contour plots for flow field and solid volume fraction. The effects of the turbulence model and solid volume fraction on the square cyclone are discussed. The results indicate that the pressure drop increases with the increase of solid volume fraction,and increase with the increase of inlet velocities for two turbulence models, moreover,the simulations results are compared with pressure field. For all runs,the RSM model gives a higher pressure drop compared to the RNG k- ε model. The RSM model provides well the forced vortex and free vortex,and captures better the phenomena occurring during intense vortex flow in the presence of walls within cyclone separators.

Turbulent Modulation in Particulate Flow: A Review of Critical Variables

A review of the main mechanisms influencing turbulent modulation in the presence of spherical and non-spherical particles is presented. The review demonstrates the need for more numerical and experimental work with higher accuracy than obtained so far and the need to resolve the flow near the surface of particles with the aim to re-evaluate the quantitative effect of different parameters on turbulent modulation. The review reveals that non-spherical particles have more adverse effect on turbulence as compared to spherical ones, for the same ambient conditions.

EXPERIMENTAL INVESTIGATION OF INCEPTION CAVITATION IN LIQUIDSOLID TWO PHASE TURBULENT FLOW

The experimental investigation of inception cavitation of liquid-solid two phase turbulent flow has been carried out in a two dimensional hydraulic tunnel. The experimental result shows that the cavitation existing in the sediment laden flow is different from that in the clear water. We also found that the inception cavitation of sediment laden flow only has a weak relation with the shape of the experimental model in which the cavitation originated, yet it has direct relation with the density of sediment concentration in the flow and the diameter of the sediment particles and the distribution of particle sizes. The results given in the paper could be used for engineering designing and hydraulic machine making.

Transitional phenomenon of particle dispersion in gas-solid two-phase flows

Without using any turbulent model, direct numerical simulation of a three-dimensional gas-solid two-phase turbulent jet was performed by finite volume method. The effects on dispersion of particles with different Stokes numbers by the transitional behavior of turbulent structures were investigated. To produce high-resolution results and reduce the computation and storage, the fractional-step projection algorithm was used to solve the governing equations of gas phase fluid. The low-storage, three-order Runge-Kutta scheme was used for time integration. The governing equations of particles were solved in the Lagrangian framework. These numerical schemes were validated by the good agreement be-tween the statistical results of flow field and the related experimental data. In the study of particle dis-persion, it was found that the effects on particle dispersion by the spanwise vortex structures were prominent. The new behaviors of particle dispersion were also observed during the evolution of the flow field, i.e. the transitional phenomenon of particle dispersion occurs for the particles with small and intermediate Stokes numbers.

STUDIES OF SOLID－LIQUID TWO－PHASE TURBULENT FLOWS AND WEAR IN HYDRAULIC TURBOMACHINERY

The Lagrangian equation of motion for solid particles in an arbitrary flow field is derived. The linear differential equation form and the general solution of this equation are obtained. Motion of solid particles in dilute solid-liquid turbulent flows is numerically solved and analysed. The K-εtwo-equation turbulence model, the volume fraction turbulence model, the mixed Eulerian-Lagrangian turbulence model, and the dense mixture turbulence model as well as the erosive wear model are developed. Using these models, the turbulent flows and the erosive wear in some hydraulic turbomachinery ducts are numerically predicted. The numerical results show good agreement with the experiments.