Numerical Simulation Of Non-Newtonian-particles Two-phase Flow In The Liquid-solid Fluidized Beds

Liquid-solid two-phase flow has been widely used in petrochemical and other fields,such as liquid-solid fluidization process in the liquid-solid fluidized bed,drilling fluids carrying cuttings,erosion in oil pipelines,and fracturing processes,etc.As one of the main applications of fluidization technology,a liquid-solid fluidized bed is usually used for oilfield-produced liquid and sewage treatment in ground engineering.The ubiquitous fluids in the petroleum industry are the non-Newtonian fluids,since the shear stress of non-Newtonian fluids is not linear with its shear rate,and their rheological properties are mainly characterized by yield stress,consistency coefficient and flow behavior index.However,in the calculation model of liquid-solid two-phase flow,the nonlinear properties of non-Newtonian fluids are usually ignored.Spherical particles are usually used for the solid phase,and the influence of liquid filmwrapped particles on liquid-solid flow characteristics is always neglected.Therefore,to improve the accuracy of the numerical simulation results,three aspects are mainly studied in this paper when studying the flow process of the liquid-solid system.First,the properties of the liquid phase,considering the influences of power-law fluids and HB fluids’ rheology;Second,the properties of particles,considering the effects of liquid film and sphericity;Finally,the change of liquid-solid interphase interactions caused by particles properties and liquid phase properties.As an interphase force between liquid and solid,the appropriate drag model will directly affect the simulation results’ accuracy.Therefore,two non-Newtonian liquid-solid drag models(named Model I and Model II)considering the influence of rheological parameters are proposed in this paper,based on the rheological characteristics of power-law fluids and HB fluids,and the resistance characteristics between liquid and solid phase.The influence of viscosity term and inertia term on the pressure drop of the liquid-solid system are considered,respectively.Among them,Model I is a modified drag model considering the tortuosity of channels and the pore-throat ratio,and Model II is a blending drag model combining the drag coefficients of high particle concentration and low particle concentration.Using the two-fluid model,combined with the kinetic theory of granular flow(KTGF),the flow behaviors of liquid and solid in fluidized beds are numerically simulated according to the experimental parameters of Lali et al firstly.Compared with the prediction results obtained by the power-law liquid-solid drag models and the traditional drag models,the results show that the predicted voidage obtained by the power-law liquid-solid drag models are in good agreement with the measured values of Lali et al.,and the relative error is between 0.75% and 2.96%.In addition,compared with Bartosik’s experimental parameters,the Herschel-Bulkley liquid-solid drag models and traditional drag models are used to simulate the Herschel-Bulkley fluid-particle two-phase flow in horizontal tubes,and the predicted pressure drop gradients are compared with the experimental data.The results show that the relative error of the Herschel-Bulkley liquid-solid drag models are low,ranging from 7.18% to 8.63%,which proves the validity of the non-Newtonian drag models.The flow characteristics of particles in the beds using Model I and Model II are compared.Then,the influences of different parameters such as rheological parameters of non-Newtonian fluids,inlet superficial velocity of liquid and particle restitution coefficient on particles’ flow behaviors in the fluidized bed are analyzed.In the liquid-solid flow process,the particles are covered by liquid film.In this paper,the influence of liquid film on the collision properties of particles is characterized by the change of restitution coefficient.A dynamic normal restitution coefficient model considering the thickness of liquid film for wet particles is proposed.Based on the Euler-Euler two-fluid model,combined with the non-Newtonian liquid-solid drag models and the dynamic normal restitution coefficient model,the flow behaviors of dry and wet particles in the power-law liquid-solid fluidized bed are numerically simulated,and the differences between them are also compared.In the simulation process,considering the effect of liquid film,the results are closer to the experimental values,and the relative error of the predicted voidage is reduced by 0.78% to1.72%.The calculated relative error of the predicted pressure drop gradient is reduced by 1.25%to 2.05%,which indicates the necessity of considering the liquid film covering of the particles surface.Meanwhile,the effects of rheological parameters,particle size and density on the flow characteristics of dry and wet particles in the fluidized bed are compared,the results show that the liquid film thickness increases obviously with the increase of rheological parameters,particle size and particle density.The normal restitution coefficient of wet particles decreases with the increase of consistency coefficient and flow behavior index,and increases with the rise of particle size and density.In addition,it can be found that the energy dissipation of wet particles is significantly higher than that of dry particles.The shape of the particles will affect the stress between the particles and the interaction between the liquid and solid phases.Therefore,the sphericity of particles is introduced into the power-law liquid-solid drag models,the dynamic restitution coefficient model and stress equations of solid phase.The non-spherical particles with power-law fluids drag models and the non-spherical dynamic restitution coefficient model for wet particles are established.The flow behaviors of power-law fluids and non-spherical particles in fluidized beds are simulated by using the two-fluid model,the simulation results show that the predicted porosities of the new models are more consistent with the experimental porosities measured by Maiti et al.,and the relative errors are between 0.81% and 2.36%.The effect of sphericity on the flow characteristics of particles is studied,the results show that as the sphericity increases,the normal restitution coefficient,thickness of liquid film,granular pressure and viscosity will get higher,and the drag coefficient,bed pressure drop and granular temperature will be lower.Then the influences of initial particle concentration and boundary wall conditions on particle movement are studied,the results demonstrate that the bed height,granular temperature,drag coefficient and bed pressure drop are positively correlated with the initial particle concentration.With the increase of specularity coefficient or the decrease of particle-wall collision restitution coefficient,the expansion height of the bed decreases slightly,and the axial velocity of particles also decreases.The drag coefficient decreases with the increase of the specularity coefficient and the granular temperature increases with the increase of the particle-wall restitution coefficient.