Pressure Behavior for Spherical Flow in a Reservoir of Non-Newtonian Power-Law Fluids

The pressure variations during polymer flooding of oil reservoirs for oil recovery projects can be used to analyze the flow in the reservoir which is especially useful for the partially perforated reservoirs. This paper presents a relationship between the viscosity and the shear rate which is similar to forms developed for radial flow (Odeh, A. S., Yang, H. T. ([1979]). SPEJ. AIME (Jun.) 155). The power-law viscosity model is used to give the variation of the fluid viscosity with the spherical radius for a mathematical model of unsteady spherical flow for non-Newtonian fluids with wellbore storage and skin. An analytical solution for the wellbore pressure responses derived in Laplace space is used to analyze the behavior characteristics at early and later times to interpret the well-test parameters. The pressure variations are similar to those for a Newtonian fluid at the early times, but at later times, the variation of the viscosity with the power-law exponent is important, so the pressure response differs from that for a Newtonian fluid. The solution has significance for interpreting well test parameters for non-Newtonian spherical flow.     

Origin of the negative wake behind a bubble rising in non-Newtonian fluids

The present work aims at understanding the behavior of individual bubbles in non-Newtonian fluids. By means of a Particle Image Velocimetry (PIV) device, the complete flow field around either a single non-spherical bubble rising in polyacrylamide (PAAm) solutions or a solid sphere settling down in the same fluids shows for the first time the similar coexistence of three distinct zones: a central downward flow behind the bubble or the sphere (negative wake), a conical upward flow surrounding the negative wake zone, and an upward flow zone in front of the bubble or the sphere. This excludes then the possible influence of the interface deformation on the negative wake. A theoretical lattice Boltzmann scheme coupled to a sixth-order Maxwell model was developed for computing the complex flow field around a solid sphere. The good agreement with the experimental measurements provides evidence that the physical mechanism responsible for the negative wake in such fluids could be related to the fluid's viscoelastic properties.     

NUMERICAL STUDY ON QUASI- STEADY FLOW OF NONNEWTONIAN FLUID IN SUCK-ROD PUMP

This paper presents a numerical method for simulation of the flow and thecalculated results of the quasi-steady axisymmetrical flow field and pressure distribution on valveball with power-law model for Non-Newtonian fluid in suck-rod pump.We believe the methodcan provide a foundation for further research and improvement of the design of suck-rod pump.     

Free convection and mass transfer flow of non-newtonian fluid with thermal diffusion effect

An analytical study is performed to examine the thermal diffusion characteristics of free convection and mass transfer flow in a non-Newtonian fluid (Walters, 1962: liquid B') past a uniformly accelerated infinite vertical plate in the presence of thermal diffusion. The expression for the velocity field is obtained by the Laplace transform technique. The influence of the Soret number (a thermal diffusion parameter) on the velocity field is extensively discussed with the help of graphs.     

Estimation of rheological parameters using velocity measurements

In the present investigation, we develop a method for estimating rheological parameters of viscoelastic fluids using velocity measurement in a square straight channel. It is believed that a somewhat complicated patterns of secondary flows due to the non-zero second normal stress difference are more useful than the simple viscometric flows traditionally adopted in the determination of rheological parameters. The inverse problem of determining the rheological parameters from a set of velocity measurements is solved using a conjugate gradient method. When applied to a general constitutive equation encompassing the UCM model, the Oldroyd-B model and the PTT model, the present method is found to yield a reasonably accurate estimation of five rheological parameters simultaneously even with noisy velocity measurements.     

Bubble nucleation and growth in fluids

The nucleation and growth of CO₂ bubbles in non-Newtonian and Newtonian fluids that were initially supersaturated under different pressures are investigated in the present work. Quantitative information by means of two cameras reveals that at an immobile nucleation site the bubble grows rapidly followed by a linear increase in bubble diameter with time. After reaching a critical size, the bubble detaches from the stagnant site to rise in liquids with an exponential temporary increase for both the diameter and distance. A simple physical reasoning was proposed to qualitatively explain these observed phenomena. Recently, the growth rate and flow fields around a CO₂ micro-bubble were measured in a microdevice by a micro-Particle Image Velocimetry in water. This information at microscale gives new insight into the complex mechanism of bubble nucleation and growth in fluids and could help to develop a rigorous theoretical modelling and numerical simulation such as the Lattice Boltzmann approach.     

Shear rates investigation in a scraped surface heat exchanger

The electrodiffusion technique was performed in order to investigate the shear rate on a scraped surface heat exchanger. Microelectrodes were placed inside: the walls of the outer cylinder; the inlet and outlet bowls; the rotor and the blades. Highly viscous Newtonian fluid (Emkarox HV45 solutions) and non-Newtonian model fluid (aqueous solutions of CMC) were used. The electrodiffusion method allowed us to measure wall shear rates. Maximum shear rate was observed at the scraping surface and caused by blades scraping, high shear rate was also measured on the leading edge of the blades. In the other parts of the exchanger, shear rate remained low but the development of Taylor vortices completely modified the scraped surface heat exchangers behaviour inside the surface of the bowls. A dimensionless representation of the friction factor was established for the inner and outer wall surface of the exchanger.     

ESTIMATION OF EFFECTIVE SHEAR RATE FOR AERATED NON-NEWTONIAN LIQUIDS IN AIRLIFT BIOREACTOR”“

Effective shear rate is one of the indispensable parameters for the design of aerobic fermentors using a viscous non-Newtonian system. The estimation of effective shear rate in airlift loop bioreactors has been investigated with liquid circulation velocity. An empirical correlation of effective shear rate in airlift loop reactors is proposed.

γ_eπ= 3.26-3.51 ; 10²U_G + 1.48 10⁴U²_G

It is found that the effective shear rate is lower in airlift reactors than in bubble columns. This equation can be used for the cultivation of cells sensitive to shear stress.     

Gas/liquid dispersions with a SMX static mixer in the laminar regime

A Sulzer SMX mixer was used to disperse gas into viscous, Newtonian and non-Newtonian fluids. The investigation covered the effect of the dispersed phase volume fraction, the viscosity of the continuous phase, the mixer length and the power draw. The flow regime was kept laminar in all the experiments. The dispersion of gas was carried out with gas concentrations between 1% and 7% in volume. Using the “process viscosity” concept, it was possible to collapse all the measured sizes on a single master curve by using the energy consumption in the mixer as the common variable between the experiments. Comparison was made with a Kenics mixer. The SMX mixer was found to be better adapted to the dispersion task due to its internal structure.     

UCM流体的最小二乘有限元解法

提出了求解UCM流体的最小二乘有限元方法。将稳态不可压缩蠕动流的UCM本构方程,利用速度和应力的近似值进行线性化。建立由所有方程残量的L2范数加权和构造的目标泛函,将微分方程组的求解转化为目标泛函的极小化问题。利用目标泛函对应的欧拉-拉格朗日方程建立迭代格式,最后使用有限元方法求解迭代方程。