Cavern formation in pulp suspensions using side-entering axial-flow impellers

Pulp fibre suspensions display non-Newtonian rheology, including a yield stress. In mixing operations, this creates regions of active motion around the impellers with the cavern size affecting the quality of mixing attained. Due to the opacity of the suspensions, two non-invasive techniques were evaluated for determining cavern dimensions: electrical resistance tomography (ERT) and ultrasonic Doppler velocimetry (UDV), with ERT chosen for most tests due to the speed of data acquisition. Cavern volume as a function of impeller speed is reported for a range of mixing conditions (hardwood and softwood pulp, suspension mass concentrations from one to five percent, two impeller offsets from the wall, and three suspension height-to-chest diameter ratios). A scaled version of a commercial axial flow impeller was used in a standard side-entering configuration. Measured cavern diameters were compared against model predictions available in the literature. The discrepancy between experimental data and model predictions were significant and were attributed to interaction between the developing cavern and the vessel walls. An alternative model was developed for predicting cavern volume taking this interaction into account.     

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.     

The effect of the macroscopic local inertial term on the non-Newtonian fluid flow in channels filled with porous medium

The transient hydrodynamics behavior of the non-Newtonian fluid flow in horizontal parallel-plate channels filled with porous medium is investigated numerically. The role of the macroscopic local inertial term in the porous domain momentum equation is studied. It is found that the macroscopic local inertial term has insignificant effect on the channel hydrodynamics behavior for all non-Newtonian fluids having power law index less than 0.5 and over the entire range of Darcy and Forchheimer numbers. However, the macroscopic local inertial term has significant effect when the power law index is greater than 1 over a wide range of Darcy and Forchheimer numbers especially for relatively high values of Darcy and low values of Forchheimer numbers. It is found that the effect of the macroscopic local inertial term is very sensitive to the Forchheimer number at high values of Darcy numbers and power law index. Also, there is an upper limit for n beyond which changing the power law index has insignificant effect on the local inertial term.     

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.     

An Analysis of Oil Well Testing for Non-Newtonian Fluid in a Fracture-Dominated Reservoir

A mathematical model based on a composite geometry was developed for a non-Newtonian power-law fluid in a fracture-dominated reservoir. An analytic solution in Laplace space for this reservoir model was used to determine the type-curves for various composite parameters. The dynamic behavior of the bottom hole pressure at early and later stages was also analyzed. Therefore, the model can be used to analyze the fluid flow and fractures in some polymer-flooding reservoirs.     

Viscous dissipation effect on entropy generation for non-Newtonian fluids in microchannels

An analytical study on the viscous dissipation effect on entropy generation in fully developed forced convection for single phase non-Newtonian fluid flow in circular microchannels is reported. In the first-law analysis, closed form solutions of the temperature distributions in the radial direction for the models with and without viscous dissipation term in the energy equation are obtained. In the second-law analysis, the two models are compared by analyzing their relative deviations in dimensionless entropy generation and Bejan number for different Brinkman number and power-law index. The findings show that under certain conditions the viscous dissipation effect on entropy generation in microchannels is significant and should not be neglected.     

Application of power addition as modelling technique for flow processes: Two case studies

In many of the continuum processes typically found in chemical engineering, the functional dependency of the dependent variable is only known for large and small values of the independent variable. Exact solutions in the transitional regime are often obscure for various reasons (e.g. narrow band within which the transition from one regime to the other occurs, inadequate knowledge of the physics in this area, etc.). An established method for the matching of limiting solutions is reviewed and subsequently applied. The method regards the known solutions as asymptotes and proposes addition to a power of such asymptotes. It yields a single, adjustable correlating equation that is applicable over the entire domain. This procedure circumvents the introduction of ad hoc curve fitting measures for the different regions and subsequent, unwanted discontinuities in piece-wise fitted correlative equations for the dependent variables. Experimental data of two diverse processes, namely flow in a straight-through diaphragm valve and the fluidisation of a packed bed, are analysed as case studies. Empirical results are investigated for possible asymptotic bounds whereafter power addition is applied to the functional dependencies. The outcome is compared to those of the empirical models and the results discussed. The procedure is revealed to be highly useful in the summarising and interpretation of experimental data in an elegant and simplistic manner. It may also, in general, aid the setup of experimental apparatus for investigation of continuum processes.     

COOLING AND SOLIDIFICATION IN THE PRESENCE OF RECIPROCATING NON-NEWTONIAN SHEAR FLOW: THE LIVE FEED INJECTION MOULDING PROCESS

The cooling and solidification of a non-Newtonian material in the presence of reciprocating flow is analysed. Finite difference solutions are obtained for a transient I-space-dimensional model of a shear thinning material with temperature dependent properties, contained between plane parallel surfaces to which it looses heat by conduction in the presence of periodically reversing flow. This situation is relevant to live feed injection moulding - an advanced technology for thermoplastics processing - in which alternating direction shear is imposed on melt in the mould cavity during the holding and packing stages. Interest centres on the effects of flow on cooling and solidification and the development of frozen-in strains, which have important implications for the control of material alignment and mechanical properties of mouldings. The governing dimensionless parameters are identified and their influence investigated in a series of numerical simulations, where the parameters range over the following values: Pearson number 0.5-5.0; Brinkman number 0.001-1.0; Stefan number 0.1 - 1.0; Power Law Index 0.2-1.0; dimensionless flow reversal time 0.01-1.0. Two operating modes are considered: (1) fixed applied pressure gradient, with a falling flow rate; (2) flow rate initially fixed, followed by a falling flow rate period at a fixed limiting pressure gradient. In mode 1 operation viscous heating does not significantly influence cooling rates, but in mode 2, for high Brinkman numbers, a dynamic equilibrium temperature field can be attained. Complex profiles of frozen-in material strain through the thickness of the moulding are predicted. In mode 1 operation the magnitude of the principle stretch rises to a peak close to the mould walls, and falls in a series of oscillations to unity (zero deformation) on the centre plane. High values of the Pearson number or low values of the Power Law Index damp these oscillations. In mode 2 operation sharply alternating regions of high and low strain are obtained indicating a structure with alternating layers of high and low material orientation.     

Mixed convection in the heated semi-circular lid-driven cavity for nonNewtonian power-law fluids: Effect of presence and shape of the block

The present work delineates the hydrodynamics and thermal characteristics due to mixed convection in the liddriven semi-circular cavity affected by the presence of the adiabatic block at its geometric center for twodimensional, steady-state, laminar and for non-Newtonian power-law fluids. The semi-circular cavity has a diameter of D. The horizontal wall/lid is sliding with a uniform horizontal velocity(u = U) and is subjugated to the ambient thermal condition; while the curved surface is subjugated to a higher isothermal temperature.The convective characteristics inside the system is explored for the broad range of Richardson number(0.1 ≤Ri ≤ 10), Prandtl number(1 ≤ Pr ≤ 100) and non-Newtonian power-law index(0.5 ≤ n ≤ 1.5) at a constant Grashof number of 10~4. Apart from this, the effect of shape(cross-section) of the inserted block, i.e., circular, square and triangular on heat transfer characteristics has also been explored. It is observed that the shear thickening fluids display better cooling characteristics. Besides, the cavity with immersed triangular block shows better heat transfer results than the circular and square blocks. The deviations observed in the flow and heat transfer characteristics in the cavity by inserting an adiabatic block as compared with cavity without block have been ascertained by calculating normalized Nusselt number(Nu~N). The presence of the block was found to have a diminishing effect on the heat transfer due to convection in the cavity. In the end, the results of the study are summarized in the form of a predictive correlation exhibiting the functional dependence of average Nusselt number with Prandtl number, power-law index, and Richardson number.     

高凝油流体特性研究

通过气相色谱分析了大庆油田某区块高凝油油样的组成,按照相应方法测量了油样的密度,凝固点,析蜡点和反常点,平均分子量等。使用HAKKE-RS150流变仪测量了剪切应力随剪切速率的变化和粘度随温度的变化,根据以上结果对高凝油油样的流变模式进行了分析研究。实验结果表明,含碳量最高值出现在C22附近;温度是影响高凝油的粘度的重要因素,其粘度与温度的关系曲线出现两个拐点;当温度较低时,此时高凝油受到剪切其粘度会大幅降低;当温度低于反常点时,3组油样均呈现出非牛顿流体的特性,具体表现为剪切变稀性,可以在井筒中的合适深度安装加热装置和剪切装置,从而降低高凝油粘度使其保持良好流动性。