Computational Analysis of Centrifugal Pump Delivering Solid-liquid Two-phase Flow during Startup Period

The transient behavior of centrifugal pumps during transient operating periods, such as startup and stopping, has drawn more and more attention recently because of urgent needs in engineering. Up to now, almost all the existing studies on this behavior are limited to using water as working fluid. The study on the transient behavior related to solid-liquid two-phase flow has not been seen yet. In order to explore the transient characteristics of a high specific-speed centrifugal pump during startup period delivering the pure water and solid-liquid two-phase flow, the transient flows inside the pump are numerically simulated using the dynamic mesh method. The variable rotational speed and flow rate with time obtained from experiment are best fitted as the function of time, and are written into computational fluid dynamics （CFD） code-FLUENT by using a user defined function. The predicted heads are compared with experimental results when pumping pure water. The results show that the difference in the transient performance during startup period is very obvious between water and solid-liquid two-phase flow during the later stage of startup process. Moreover, the time for the solid-liquid two-phase flow to achieve a stable condition is longer than that for water. The solid-liquid two-phase flow results in a higher impeller shaft power, a larger dynamic reaction force, a more violent fluctuation in pressure and a reduced stable pressure rise comparing with water. The research may be useful to tmderstanding on the transient behavior of a centrifugal pump under a solid-liquid two-phase flow during startup period.

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）.

Numerical Simulation and Analysis of Solid-liquid Two-phase Flow in Centrifugal Pump

The flow with solid-liquid two-phase media inside centrifugal pumps is very complicated and the relevant method for the hydraulic design is still immature so far. There exist two main problems in the operation of the two-phase flow pumps, i.e., low overall efficiency and severe abrasion. In this study, the three-dimensional, steady, incompressible, and turbulent solid-liquid two-phase flows in a low-specific-speed centrifugal pump are numerically simulated and analyzed by using a computational fluid dynamics （CFD） code based on the mixture model of the two-phase flow and the RNG k-~ two-equation turbulence model, in which the influences of rotation and curvature are fully taken into account. The coupling between impeller and volute is implemented by means of the frozen rotor method. The simulation results predicted indicate that the solid phase properties in two-phase flow, especially the concentration, the particle diameter and the density, have strong effects on the hydraulic performance of the pump. Both the pump head and the efficiency are reduced with increasing particle diameter or concentration. However, the effect of particle density on the performance is relatively minor. An obvious jet-wake flow structure is presented near the volute tongue and becomes more remarkable with increasing solid phase concentration. The suction side of the blade is subject to much more severe abrasion than the pressure side. The obtained results preliminarily reveal the characteristics of solid-liquid two-phase flow in the centrifugal pump, and are helpful for improvement and empirical correction in the hydraulic design of centrifugal pumps.

Numerical Study of Solid-Liquid Two-Phase Flow in StirredTanks with Rushton Impeller(Ⅱ) Prediction of Critical Impeller Speed

Three-dimensional solid-liquid flow is mathematically formulated by means of the 'two-fluid' approach and the two-phase k-ε-AP turbulence model. The turbulent fluctuation correlations appearing in the Reynolds time averaged governing equations are fully incorporated. The solid-liquid flow field and solid concentration distribution in baffled stirred tanks with a standard Rushton impeller are numerically simulated using an improved 'inner-outer'iterative procedure. The flow pattern is identified via the velocity vector plots and a recirculation loop with higher solid concentration is observed in the central vicinity beneath the impeller. Comparison of the simulation with experimental data on the mean velocities and the turbulence quantities of the solid phase is made and quite reasonable agreement is obtained except for the impeller swept volume. The counterpart of liquid phase is presented as well.The predicted solid concentration distribution for three experimental cases with the average solid concentration up to 20% is also found to agree reasonably with the experimental results published in the literature.

Numerical Study of Solid-Liquid Two-Phase Flow in Stirred Tanks with Rushton Impeller (Ⅰ) Formulation and Simulation of Flow Field

The critical impeller speed, N_(JS), for complete suspension of solidparticles in the agitated solid-liquid two-phase system in baffled stirred tanks with a standardRushton impeller is predicted using the computational procedure proposed in Part Ⅰ. Three differentnumerical criteria are tested for determining the critical solid suspension. The predicted N_(JS)is compared with those obtained from several empirical correlations. It is suggested the mostreasonable criterion for determining the complete suspension of solid particles is the positive signof simulated axial velocity of solid phase at the location where the solid particles are mostdifficult to be suspended.

IMPROVED SUBGRID SCALE MODEL FOR DENSE TURBULENT SOLID-LIQUID TWO-PHASE FLOWS

The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules.Assuming that the solid-phase velocity distributions obey the Maxwell equations,the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow,the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations.Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale(SGS)model,in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor,is proposed to model the two-phase governing equations by applying dimension analyses.Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls,the velocity and pressure fields,and the volumetric concentration are calculated.The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.

Numerical simulation and analysis of solid-liquid two-phase threedimensional unsteady flow in centrifugal slurry pump

Based on RNG k-ε turbulence model and sliding grid technique, solid-liquid two-phase three-dimensional(3-D) unsteady turbulence of full passage in slurry pump was simulated by means of Fluent software. The effects of unsteady flow characteristics on solid-liquid two-phase flow and pump performance were researched under design condition. The results show that clocking effect has a significant influence on the flow in pump, and the fluctuation of flow velocity and pressure is obvious, particularly near the volute tongue, at the position of small sections of volute and within diffuser. Clocking effect has a more influence on liquid-phase than on solid-phase, and the wake-jet structure of relative velocity of solid-phase is less obvious than liquid-phase near the volute tongue and the impeller passage outlet. The fluctuation of relative velocity of solid-phase flow is 7.6% smaller than liquid-phase flow at the impeller outlet on circular path. Head and radial forces of the impeller are 8.1% and 85.7% of fluctuation, respectively. The results provide a theoretical basis for further research for turbulence, improving efficient, reducing the hydraulic losses and wear. Finally, field tests were carried out to verify the operation and wear of slurry pump.

Estimation of solid concentration in solid-liquid two-phase flow in horizontal pipeline using inverse-problem approach

In this study,an inverse-problem method was applied to estimate the solid concentration in a solid-liquid two-phase flow.An algebraic slip mixture model was introduced to solve the forward problem of solid-liquid convective heat transfer.The time-average conservation equations of mass,momentum,energy,as well as the volume fraction equation were computed in a computational fluid dynamics(CFD)simulation.The solid concentration in the CFD model was controlled using an external program that included the inversion iteration,and an optimal estimation was performed via experimental measurements.Experiments using a fly-ash-water mixture and sand-water mixture with different solid concentrations in a horizontal pipeline were conducted to verify the accuracy of the inverse-problem method.The estimated results were rectified using a method based on the relationship between the estimated results and estimation error;consequently,the accuracy of the corrected inversion results improved significantly.After a verification through experiments,the inverse-problem method was concluded to be feasible for predicting the solid concentration,as the estimation error of the corrected results was within 7%for all experimental samples for a solid concentration of less than 50%.The inverse-problem method is expected to provide accurate predictions of the solid concentration in solid-liquid two-phase flow systems.

Evaluation of frictional pressure drop correlations for air-water and air-oil two-phase flow in pipeline-riser system

Accurate prediction of the frictional pressure drop is important for the design and operation of subsea oil and gas transporting system considering the length of the pipeline. The applicability of the correlations to pipeline-riser flow needs evaluation since the flow condition in pipeline-riser is quite different from the original data where they were derived from. In the present study, a comprehensive evaluation of 24prevailing correlation in predicting frictional pressure drop is carried out based on experimentally measured data of air-water and air-oil two-phase flows in pipeline-riser. Experiments are performed in a system having different configuration of pipeline-riser with the inclination of the downcomer varied from-2°to-5°to investigated the effect of the elbow on the frictional pressure drop in the riser. The inlet gas velocity ranges from 0.03 to 6.2 m/s, and liquid velocity varies from 0.02 to 1.3 m/s. A total of885 experimental data points including 782 on air-water flows and 103 on air-oil flows are obtained and used to access the prediction ability of the correlations. Comparison of the predicted results with the measured data indicate that a majority of the investigated correlations under-predict the pressure drop on severe slugging. The result of this study highlights the requirement of new method considering the effect of pipe layout on the frictional pressure drop.

Pressure transient characteristics of non-uniform conductivity fractured wells in viscoelasticity polymer flooding based on oil-water two-phase flow

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery.In contrast to water,polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening,polymer convection,diffusion,adsorption retention,inaccessible pore volume and reduced effective permeability.Meanwhile,the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution,formation damage,and proppant breakage.In this paper,we present an oil-water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior,and non-uniform fracture characteristics in fractured polymer flooding.The hydraulic fracture is firstly divided into two parts:high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section.A hybrid grid system,including perpendicular bisection(PEBI)and Cartesian grid,is applied to discrete the partial differential flow equations,and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution.The combination of polymer behavior characterizations and numerical flow simulations are applied,resulting in the calculation for the distribution of water saturation,polymer concentration and reservoir pressure.Compared with the polymer flooding well with uniform fracture conductivity,this non-uniform fracture conductivity model exhibits the larger pressure difference,and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section.The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately,and yields fracture half-lengths that better match engineering reality,enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity.The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology,as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.

Integrated numerical simulation of hydraulic fracturing and production in shale gas well considering gas-water two-phase flow

Based on the displacement discontinuity method and the discrete fracture unified pipe network model,a sequential iterative numerical method was used to build a fracturing-production integrated numerical model of shale gas well considering the two-phase flow of gas and water.The model accounts for the influence of natural fractures and matrix properties on the fracturing process and directly applies post-fracturing formation pressure and water saturation distribution to subsequent well shut-in and production simulation,allowing for a more accurate fracturing-production integrated simulation.The results show that the reservoir physical properties have great impacts on fracture propagation,and the reasonable prediction of formation pressure and reservoir fluid distribution after the fracturing is critical to accurately predict the gas and fluid production of the shale gas wells.Compared with the conventional method,the proposed model can more accurately simulate the water and gas production by considering the impact of fracturing on both matrix pressure and water saturation.The established model is applied to the integrated fracturing-production simulation of practical horizontal shale gas wells.The simulation results are in good agreement with the practical production data,thus verifying the accuracy of the model.

Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.

Numerical Simulation of Oil-Water Two-Phase Flow in Low Permeability Tight Reservoirs Based on Weighted Least Squares Meshless Method

In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.

Identifying the enhancement mechanism of Al/MoO_(3) reactive multilayered films on the ignition ability of semiconductor bridge using a one-dimensional gas-solid two-phase flow model

Energetic Semiconductor bridge(ESCB)based on reactive multilayered films(RMFs)has a promising application in the miniature and intelligence of initiator and pyrotechnics device.Understanding the ignition enhancement mechanism of RMFs on semiconductor bridge(SCB)during the ignition process is crucial for the engineering and practical application of advanced initiator and pyrotechnics devices.In this study,a one-dimensional(1D)gas-solid two-phase flow ignition model was established to study the ignition process of ESCB to charge particles based on the reactivity of Al/MoO_(3) RMFs.In order to fully consider the coupled exothermic between the RMFs and the SCB plasma during the ignition process,the heat release of chemical reaction in RMFs was used as an internal heat source in this model.It is found that the exothermal reaction in RMFs improved the ignition performance of SCB.In the process of plasma rapid condensation with heat release,the product of RMFs enhanced the heat transfer process between the gas phase and the solid charge particle,which accelerated the expansion of hot plasma,and heated the solid charge particle as well as gas phase region with low temperature.In addition,it made up for pressure loss in the gas phase.During the plasma dissipation process,the exothermal chemical reaction in RMFs acted as the main heating source to heat the charge particle,making the surface temperature of the charge particle,gas pressure,and gas temperature rise continuously.This result may yield significant advantages in providing a universal ignition model for miniaturized ignition devices.

Optimizing Two-Phase Flow Heat Transfer:DCS Hybrid Modeling and Automation in Coal-Fired Power Plant Boilers

In response to escalating challenges in energy conservation and emission reduction,this study delves into the complexities of heat transfer in two-phase flows and adjustments to combustion processes within coal-fired boilers.Utilizing a fusion of hybrid modeling and automation technologies,we develop soft measurement models for key combustion parameters,such as the net calorific value of coal,flue gas oxygen content,and fly ash carbon content,within theDistributedControl System(DCS).Validated with performance test data,thesemodels exhibit controlled root mean square error(RMSE)and maximum absolute error(MAXE)values,both within the range of 0.203.Integrated into their respective automatic control systems,thesemodels optimize two-phase flow heat transfer,finetune combustion conditions,and mitigate incomplete combustion.Furthermore,this paper conducts an in-depth exploration of the generationmechanismof nitrogen oxides(NOx)and low oxygen emission reduction technology in coal-fired boilers,demonstrating a substantial reduction in furnace exit NOx generation by 30%to 40%and the power supply coal consumption decreased by 1.62 g/(kW h).The research outcomes highlight the model’s rapid responsiveness,enabling prompt reflection of transient variations in various economic indicator parameters.This provides a more effective means for real-time monitoring of crucial variables in coal-fired boilers and facilitates timely combustion adjustments,underscoring notable achievements in boiler combustion.The research not only provides valuable and practical insights into the intricacies of two-phase flow heat transfer and heat exchange but also establishes a pioneering methodology for tackling industry challenges.

Numerical Solutions of the Classical and Modified Buckley-Leverett Equations Applied to Two-Phase Fluid Flow

Climate change is a reality. The burning of fossil fuels from oil, natural gas and coal is responsible for much of the pollution and the increase in the planet’s average temperature, which has raised discussions on the subject, given the emergencies related to climate. An energy transition to clean and renewable sources is necessary and urgent, but it will not be quick. In this sense, increasing the efficiency of oil extraction from existing sources is crucial, to avoid waste and the drilling of new wells. The purpose of this work was to add diffusive and dispersive terms to the Buckley-Leverett equation in order to incorporate extra phenomena in the temporal evolution between the water-oil and oil-water transitions in the pipeline. For this, the modified Buckley-Leverett equation was discretized via essentially weighted non-oscillatory schemes, coupled with a three-stage Runge-Kutta and a fourth-order centered finite difference methods. Then, computational simulations were performed and the results showed that new features emerge in the transitions, when compared to classical simulations. For instance, the dispersive term inhibits the diffusive term, adding oscillations, which indicates that the absorption of the fluid by the porous medium occurs in a non-homogeneous manner. Therefore, based on research such as this, decisions can be made regarding the replacement of the porous medium or the insertion of new components to delay the replacement.

NUMERICAL SIMULATION OF 3-D DENSE SOLID-LIQUID TWO-PHASE TURBULENT FLOW IN A NON-CLOGGING MUD PUMP

A mathematical model is set to evaluate the 3-D dense solid-liquid two-phaseturbulent flow in a non-clogging mud pump, the flow feature in the impeller channel is simulatedwith the tool of IPSA. Meanwhile, resort to TECPLOT as the post-processor, the simulation results isvisualized. The results show the main flow characteristics: There exists backflow and aberrantvelocities at inlet area and a relative velocity slip between two phases; A jet-wake flow pattern isdiscerned around the shroud-suction side area; The relative velocity vector of solid phase iscloser to the pressure surface than that of liquid phase and the trend is more obvious with theincrease of diameter; The kinetic energy of turbulence k and the dissipation rate e reach theirpeaks at the corner of pressure and suction surface. The simulation results show a good agreementwith the experimental flow features in the impeller channel, which prove the turbulent model used isvalid and provide a theoretical design basis to non-clogging pumps.

Mixed Model for Silt-Laden Solid-Liquid Two-Phase Flows

The kinetic theory of molecular gases was used to derive the governing equations for dense solid-liquid two-phase flows from a microscopic flow characteristics viewpoint by multiplying the Boltzmann equation for each phase by property parameters and integrating over the velocity space. The particle collision term was derived from microscopic terms by comparison with dilute two-phase flow but with consideration of the collisions between particles for dense two-phase flow conditions and by assuming that the particle-phase velocity distribution obeys the Maxwell equations. Appropriate terms from the dilute two-phase governing equations were combined with the dense particle collision term to develop the governing equations for dense solid-liquid turbulent flows. The SIMPLEC algorithm and a staggered grid system were used to solve the discretized two-phase governing equations with a Reynolds averaged turbulence model. Dense solid-liquid turbulent two-phase flows were simulated for flow in a duct. The simulation results agree well with experimental data.

Ultrasonic method for measuring water holdup of low velocity and high-water-cut oil-water two-phase flow

Oil reservoirs with low permeability and porosity that are in the middle and late exploitation periods in China＇s onshore oil fields are mostly in the high-water-cut production stage.This stage is associated with severely non-uniform local-velocity flow profiles and dispersed-phase concentration（of oil droplets） in oil-water two-phase flow,which makes it difficult to measure water holdup in oil wells.In this study,we use an ultrasonic method based on a transmission-type sensor in oil-water two-phase flow to measure water holdup in lowvelocity and high water-cut conditions.First,we optimize the excitation frequency of the ultrasonic sensor by calculating the sensitivity of the ultrasonic field using the finite element method for multiphysics coupling.Then we calculate the change trend of sound pressure level attenuation ratio with the increase in oil holdup to verify the feasibility of the employed diameter for the ultrasonic sensor.Based on the results,we then investigate the effects of oildroplet diameter and distribution on the ultrasonic field.To further understand the measurement characteristics of the ultrasonic sensor,we perform a flow loop test on vertical upward oilwater two-phase flow and measure the responses of the optimized ultrasonic sensor.The results show that the ultrasonic sensor yields poor resolution for a dispersed oil slug in water flow（D OS/W flow）,but the resolution is favorable for dispersed oil in water flow（D O/W flow） and very fine dispersed oil in water flow（VFD O/W flow）.This research demonstrates the potential application of a pulsed-transmission ultrasonic method for measuring the fraction of individual components in oil-water two-phase flow with a low mixture velocity and high water cut.

LARGE-EDDY SIMULATION OF TWO-PHASE REACTING FLOW IN MODEL COMBUSTOR

The gas-droplet two-phase reacting flow in a model combustor with the V-gutter flame holder is studied by an Eulerian-Lagrangian large-eddy simulation (LES) approach. The k-equation subgrid-scale model is used to simulate the subgrid eddy viscosity, and the eddy-break-up (EBU) combustion subgrid-scale model is used to determine the chemical reaction rate. A two-step turbulent combustion subgrid-scale model is employed for calculating carbon monoxide CO concentration, and the NO subgrid-scale pollutant formation model for the evaluation of the rate of NO formation. The heat flux model is applied to the prediction of radiant heat transfer. The gas phase is solved with the SIMPLE algorithm and a hybrid scheme in the staggered grid system. The liquid phase equations are solved in a Lagrangian frame in reference of the particle-source-in-cell (PSIC) algorithm. From simulation results, the exchange of mass, moment and energy between gas and particle fields for the reacting flow in the afterburner with a V-gutter flame holder can be obtained. By the comparison of experimental and simulation results, profile temperature and pollutant of the outlet are quite in agreement with experimental data. Results show that the LES approach for predicting the two-phase instantaneous reacting flow and pollutant emissions in the afterburner is feasible.