MODELING OF CONCENTRATED LIQUID-SOLIDS FLOW IN PIPES DISPLAYING SHEAR-THINNING PHENOMENA

This paper describes our work in modeling concentrated liquid-solids flows in pipes. Based on our previous analyses, some concentrated liquid-solids suspension flows display shear-thinning rather than Newtonian phenomena. Therefore, we developed a new two-phase non-Newtonian power-law model that includes the effect of solids concentration on solids viscosity. With this new two-phase power-law solids-viscosity model, and with constitutive relationships for interfacial drag, virtual mass and shear lift forces, and solids partial-slip boundary conditions at the pipe walls, COMMIX-M is capable of analyzing concentrated three-dimensional liquid-solids flows.     

Modeling rheological behavior of bentonite suspensions as Casson and Robertson-Stiff fluids using Newtonian and true shear rates in Couette viscometry

The Casson model and the Robertson-Stiff model have been used to determine whether they can describe the rheology of aqueous bentonite suspensions. The assessment utilized a total of twelve sets of experimental viscometric data from literature and from this work. Equations have been presented which allowed the determination of the true shear rates experienced by the fluids within the gap of the rotational viscometer for both rheological models. Non-linear regression has been applied to determine the two rheological parameters for the Casson model and the three rheological parameters for the Robertson-Stiff model using true shear rates and Newtonian shear rates, which are used most often in the analysis of rheometric data. The results showed that both models describe well the experimental data of these bentonite suspensions with good statistical indicators. Furthermore, analysis showed that true shear rates are always higher than Newtonian shear rates for both models. The differences depend on the particular suspension and are larger at low shear rates while they become smaller at higher shear rates indicating that the fluid behavior approaches Newtonian behavior at higher shear rates. The shapes of the rheograms remained essentially unchanged indicating that the rheological parameters determined with the use of true shear rates are very similar to the rheological parameters determined with the use of Newtonian shear rates. This was further confirmed with the computation of the rheological parameters for both models and both approaches. For the Casson model differences in the yield value computed with true shear rates were at most at 7% while for the plastic viscosity at 3%. For the Robertson-Stiff model, differences of the order of 2 to 5% were observed for the K-values, of 7% for γ˙₀-values while no differences were observed for the n-values. These small differences, however, do not justify use of Newtonian shear rates when analytical solutions exist which allow use of true shear rates without any compromise.     

Suspension polymerisation of methyl methacrylate using sodium polymethacrylate as a suspending agent

Aqueous solutions of sodium polymethacrylate (PMA-Na) are used as suspending agents for the suspension polymerisation of methyl methacrylate. These aqueous polyelectrolyte solutions are viscous and they show a non-Newtonian shear thinning behaviour. The Sauter mean drop diameter decreases with increasing continuous-phase viscosity, but increases with increasing stirring speed. The maximum drop sizes follow the same trends. The Sauter mean diameter also decreases, initially, for increasing hold-up, reaches a minimum, and then increases with increasing hold-up. Taylor's theory of viscous break-up seems to be suitable to describe the breakage of the droplets.     

Effect of Impeller Spacing on the Flow Field of Yield-Pseudoplastic Fluids Generated by a Coaxial Mixing System Composed of Two Central Impellers and an Anchor

The three-dimensional flow field generated by a coaxial mixer composed of double Scaba impellers and an anchor in the mixing of the xanthan gum solution, a non-Newtonian yield-pseudoplastic fluid was investigated using the computational fluid dynamics (CFD) technique. The mixing time measurements were performed by a non-intrusive flow visualization technique called electrical resistance tomography (ERT). To evaluate the influence of the impeller spacing on the hydrodynamics of the double Scaba-anchor coaxial mixer, the upper impeller submergence was set to 0.140?m while the lower impeller clearance and the spacing between two central impellers were changed within a wide range. The experiments and simulations were conducted for both co-rotating and counter-rotating regimes at different impeller spacing. The analysis of the collected data with respect to the power number, flow number, mixing time, and pumping effectiveness proved that the co-rotating mode had superiority over the counter-rotating regime. Furthermore, the impact of the impeller spacing in the co-rotating mode was assessed with respect to the mixing time, power number, and mixing energy. The results demonstrated that a coaxial mixer with the impeller spacing of almost equal to the central impeller diameter (C₂?=?0.175?m) and the impeller clearance of C₃?=?0.185?m was the most efficient configuration compared to the other cases. Additionally, the influence of the impeller spacing on the flow pattern was assessed in terms of the radial velocity, tangential velocity, axial velocity, shear rate, and apparent viscosity profiles. When the impeller spacing (C₂) was varied, the merging flow and parallel flow patterns were observed.     

Numerical simulation of the impact of polymer rheology on polymer injectivity using a multilevel local grid refinement method

Polymer injectivity is an important factor for evaluating the project economics of chemical flood, which is highly related to the polymer viscosity. Because the flow rate varies rapidly near injectors and significantly changes the polymer viscosity due to the non-Newtonian rheological behavior, the polymer viscosity near the wellbore is difficult to estimate accurately with the practical gridblock size in reservoir simulation. To reduce the impact of polymer rheology upon chemical EOR simulations, we used an efficient multilevel local grid refinement (LGR) method that provides a higher resolution of the flows in the near-wellbore region. An efficient numerical scheme was proposed to accurately solve the pressure equation and concentration equations on the multilevel grid for both homogeneous and heterogeneous reservoir cases. The block list and connections of the multilevel grid are generated via an efficient and extensible algorithm. Field case simulation results indicate that the proposed LGR is consistent with the analytical injectivity model and achieves the closest results to the full grid refinement, which considerably improves the accuracy of solutions compared with the original grid. In addition, the method was validated by comparing it with the LGR module of CMG_STARS. Besides polymer injectivity calculations, the LGR method is applicable for other problems in need of near-wellbore treatment, such as fractures near wells.     

非牛顿流体微挤出过程动态建模与数值仿真

非牛顿流体微挤出量难以在线测量,对挤出量的高一致性要求在很大程度上依靠预测模型的精度来保证。针对工程中常用的一类幂率非牛顿流体,在分析其动态特性的基础上,建立了非牛顿流体微挤出时的流速、流量及微挤出量的物理预测模型,且模型中保留了驱动压力、时间等挤出过程主要影响因素的物理量,使得模型便于与控制算法集成。通过数值仿真,验证了模型的有效性。研究结果表明,所建模型对幂率非牛顿流体微挤出量的预测精度达到了1%以上,为非牛顿流体定量微挤出过程的精确控制提供了基础。     

Numerical investigation of heat transfer enhancement using carbon nanotube-based non-Newtonian nanofluids

In this study convective heat transfer of multi-wall carbon nanotube (MWCNT)-based nanofluids in a straight tube under constant wall heat flux condition is numerically investigated. To achieve this goal Navier–Stokes equations are solved using the finite volume technique with considering CNT-based nanofluids as non-Newtonian fluids of shear-thinning character using the non-Newtonian power law model. The objectives of this research are to provide detailed information of non-Newtonian behavior of CNT nanofluids, comparison of the numerical simulation predictions to the experimental measurements and investigation of non-Newtonian effects on the local heat transfer of the CNT nanofluid and compare the thermal performance of the CNT nanofluids and conventional fluids. As a result the heat transfer coefficient is dominated by the wall region due to non-Newtonian behavior of CNT nanofluid. The results reported in this paper illustrate that the numerical simulation can be one of the most powerful and beneficial tools for the CNT nanofluids optimization and performance analysis.     

Tomography measurements of gas holdup in rotating foam reactors with Newtonian, non-Newtonian and foaming liquids

Rotating solid foam reactors have already proven to show high mass transfer rates and to be a potential alternative to slurry reactors. The rotation of a foam block stirrer results in a high mass transfer and in the development of different reactor sections showing specific hydrodynamics and gas holdup distributions. In order to optimize the reactor system the hydrodynamics in a lab scale reactor are studied using γ-ray tomography, a powerful method to measure the gas holdup in three-phase reactors. The influence of liquid properties, such as viscosity and surface tension, and the rotational speed on the gas/liquid distribution in the different reactor sections is investigated. Especially the viscosity has a strong effect on the entrapment of gas bubbles in the foam block structure, while the surface tension is the dominant parameter in the outer reactor section. The influence of these parameters on the inset of foaming and the collapse of the gas/liquid dispersion is investigated. Conclusions on the mass transfer performance are drawn and recommendations for further optimizations of the reactor design and the operational conditions depending on the liquid properties are developed.     

An experimental investigation on the breakup of surfactant-laden non-Newtonian jets

The combined effect of polymers and soluble surfactants on the dynamics of jet breakup, and especially on satellite drop formation, was experimentally investigated. Xanthan gum and Carbopol^® 934 NF were dissolved in water with Sodium Dodecyl Sulfate as the surfactant. Controlled disturbances were imposed at the laminar jet interface using a piezoelectric vibrating nozzle with breakup dynamics recorded using a high-speed camera. Drop and ligament diameters were measured from the digital images. The focus of the work was investigating how bulk and interfacial properties of the prepared fluids influenced ligament and drop evolution. It was found that if the proper concentration of surfactant (close to the critical micelle concentration, CMC) was selected, and if the flow time scales were large enough, Marangoni interfacial stresses may lead to an increase in satellite drop size as previously reported for breakup simulations of shear-thinning jets covered with insoluble surfactant. It was also experimentally confirmed that the introduction of surfactant contributes to a delay in jet breakup.