Investigations of phase inversion and frictional pressure gradients in upward and downward oil–water flow in vertical pipes

The present study has attempted to investigate phase inversion and frictional pressure gradients during simultaneous vertical flow of oil and water two-phase through upward and downward pipes. The liquids selected were white oil (44 mPa s viscosity and 860 kg/m³ density) and water. The measurements were made for phase velocities varying from 0 to 1.24 m/s for water and from 0 to 1.87 m/s for oil, respectively. Experiments were carried either by keeping the mixture velocity constant and increasing the dispersed phase fraction or by keeping the continuous phase superficial velocity constant and increasing the dispersed phase superficial velocity. From the experimental results, it is shown that the frictional pressure gradient reaches to its lower value at the phase inversion point in this work. The points of phase inversion are always close to an input oil fraction of 0.8 for upward flow and of 0.75 for downward flow, respectively. A few models published in the literature are used to predict the phase inversion point and to compare the results with available experimental data. Suitable methods are suggested to predict the critical oil holdup at phase inversion based on the different viscosity ratio ranges. Furthermore, the frictional pressure gradient is analyzed with several suitable theoretical models according to the existing flow patterns. The analysis reveals that both the theoretical curves and the experimental data exhibit the same trend and the overall agreement of predicted values with experimental data is good, especially for a high oil fraction.     

水平管内油——水两相流动压降规律的实验研究

设计和建造了内径为26．1mm,长30m的水平不锈钢多相流实验环道,利用白油与水进行了油－水两相流流型和压降实验。本文针对各种流型,分析了油－水两相流动的压降规律和油－水混合液有效粘度,指出有效粘度法只适用于油－水分散流型的压降预测,对于分层流型式其它混合流型使用合适该种流型的压降预测模型来计算压降。研究结论对油田现场的油水混输管路的经济运行具有较大的指导意义。     

Direct numerical simulation of modulation of isotropic turbulence by poly‐dispersed particles

A direct numerical simulation technique based on two‐way coupling is presented to study a particle‐laden, decaying isotropic turbulent flow. Physical characteristics of turbulence modulation because of the mono‐dispersed (i.e., particles with single Stokes number) and poly‐dispersed particles (i.e., particles with more than one Stokes number) were investigated. A scale dependent effective viscosity that summarizes the aspects of the interaction between the velocity field and particles is defined in the study. Particles of Stokes number (St) 3.2,6.4 and 12.8 were used in performing the simulations. Poly‐dispersed particles were acquired by mixing particles of two different Stokes numbers at a time. As a whole, decay of turbulence because of the poly‐dispersed particles is observed to be larger than that of the decay of turbulence because of the mono‐dispersed particles. Simulations of poly‐dispersed particle indicate nonlinear characteristics in the modification of the temporal evolution of turbulence energy and dissipation. The scale dependent effective viscosity, which correlates with the energy spectrum plot, indicates that the decay of turbulence is mostly observed at the intermediate scales of turbulence. The effective viscosity for the simulations of the poly‐dispersed particles was calculated to be higher than that of the simulations of the mono‐dispersed particles. Copyright © 2011 John Wiley & Sons, Ltd.     

Friction factor improved correlations for laminar and turbulent gas–liquid flow in horizontal pipelines

We develop improved correlations for two-phase flow friction factor that consider the effect of the relative velocity of the phases, based on a database that includes 2560 gas–liquid flow experiments in horizontal pipes. The database includes a wide range of operational conditions and fluid properties for two-phase friction factor correlations. We classify the experiments by liquid holdup ranges to obtain composite analytical expressions for two-phase friction factor vs. the Reynolds number by fitting logistic dose curves to the experimental data with. We compute the liquid holdup values used to classify the experimental data using correlations proposed previously. The Reynolds number is based on the mixture velocity and the liquid kinematic viscosity. The Fanning friction factor for gas–liquid is defined in term of the mixture velocity and density. Additionally, we sort the experimental data by flow regime and obtain the two-phase friction factor improved correlations for dispersed bubble, slug, stratified and annular flow for different holdup ranges. We report error estimates for the predicted vs. measured friction factor together with standard deviation for each correlation. The accuracy of the correlations developed in this study is compared with that of other 21 correlations and models widely available in the specialized literature. Since different authors use different definitions for friction factors and Reynolds numbers, we present comparisons of the predicted pressure drop for each and every data point in the database. In most cases our correlations predict the pressure drop with much greater accuracy than those presented by previous authors.     

流动聚焦装置中液滴的形成:喉部尺寸的影响

在本文中,研究了液滴在一个流动聚焦微流体设备中的形成过程,分析了喉部长度和宽度以及连续相的流速和分散相的粘度对液滴尺寸的影响。在固定的分散相流速(Qd)下,连续相流速(Q_c)对于液滴尺寸有重要的影响。当Q_c0.7mL/h,液滴尺寸在喉部长度到达一个临界值之前先趋于增加,之后随着喉部尺寸的继续增加逐渐下降;当Q_c0.7mL/h,液滴尺寸随着喉部长度的增加而降低。而越大的喉部宽度会产生越大尺寸的液滴。在Q_c继续增长的过程中通常会出现从挤压模式到滴模式的转变,最终液滴尺寸呈现出随着Q_c的增加指数降低的特征。归因于流速控制破碎机制,低粘度分散相下,液滴尺寸随粘度的增加而增加。     

Shear Rate Determination from Pore-Scale Flow Fields

Aqueous solutions with polymer additives often used to improve the macroscopic sweep efficiency in oil recovery typically exhibit non-Newtonian rheology. In order to predict the Darcy-scale effective viscosity \(\mu _{\mathrm{eff}} \) required for practical applications often, semi-empirical correlations such as the Cannella or Blake–Kozeny correlation are employed. These correlations employ an empirical constant (“C-factor”) that varies over three orders of magnitude with explicit dependency on porosity, permeability, fluid rheology and other parameters. The exact reasons for this dependency are not very well understood. The semi-empirical correlations are derived under the assumption that the porous media can be approximated by a capillary bundle for which exact analytical solutions exist. The effective viscosity \(\mu _{\mathrm{eff}} (v_{\mathrm{Darcy}} )\) as a function of flow velocity is then approximated by a cross-sectional average of the local flow field resulting in a linear relationship between shear rate \(\gamma \) and flow velocity. Only with such a linear relationship, the effective viscosity can be expressed as a function of an average flow rate instead of an average shear rate. The local flow field, however, does in general not exhibit such a linear relationship. Particularly for capillary tubes, the velocity is maximum at the center, while the shear rate is maximum at the tube wall indicating that shear rate and flow velocity are rather anti-correlated. The local flow field for a sphere pack is somewhat more compatible with a linear relationship. However, as hydrodynamic flow simulations (using Newtonian fluids for simplicity) performed directly on pore-scale resolved digital images suggest, flow fields for sandstone rock fall between the two limiting cases of capillary tubes and sphere packs and do in general not exhibit a linear relationship between shear rate and flow velocity. This indicates that some of the shortcomings of the semi-empirical correlations originate from the approximation of the shear rate by a linear relationship with the flow velocity which is not very well compatible with flow fields from direct hydrodynamic calculations. The study also indicates that flow fields in 3D rock are not very well represented by capillary tubes.     

Composite power law holdup correlations in horizontal pipes

A wide range of experimental holdup data, from different sources, are analyzed based on a theoretical model proposed in this work to evaluate the holdup in horizontal pipes. 2276 gas–liquid flow experiments in horizontal pipelines with a wide range of operational conditions and fluid properties are included in the database. The experiments are classified by mixture Reynolds number ranges and composite analytical expressions for the relationship between the liquid holdup and no-slip liquid holdup vs. the gas–liquid volumetric flow rate are obtained by fitting the data with logistic dose curves. The Reynolds number appropriate to classify the experimental data for gas–liquid flows in horizontal pipes is based on the mixture velocity and the liquid kinematic viscosity. Composite power law holdup correlations for flows sorted by flow pattern are also obtained. Error estimates for the predicted vs. measured holdup correlations together with standard deviation for each correlation are presented. The accuracy of the correlations developed in this study is compared with the accuracy of 26 previous correlations and models in the literature. Our correlations predict the liquid holdup in horizontal pipes with much greater accuracy than those presented by previous authors.     

Large Eddy Simulations Using an Unstructured Grid Compressible Navier - Stokes Algorithm

Large Eddy Simulation (LES) of the decay of isotropic turbulence and of channel flow has been performed using an explicit second-order unstructured grid algorithm for tetrahedral cells. The algorithm solves for cell-averaged values using the finite volume form of the unsteady compressible Jittered Navier-Stokes equations. The inviscid fluxes are obtained from Godunov's exact Riemann solver. Reconstruction of the flow variables to the left and right sides of each face is performed using least squares or Frink's method. The viscous fluxes and heat transfer are obtained by application of Gauss' theorem. LES of the decay of nearly incompressible isotropic turbulence has been performed using two models for the SGS stresses: the Monotone Integrated Large Eddy Simulation (MILES) approach, wherein the inherent numerical dissipation models the sub-grid scale (SGS) dissipation, and the Smagorinsky SGS model. The results using the MILES approach with least squares reconstruction show good agreement with incompressible experimental data. The contribution of the Smagorinsky SGS model is negligible. LES of turbulent channel flow was performed at a Reynolds number (based on channel height and bulk velocity) of 5600 and Mach number of 0.5 (at which compressibility effects are minimal) using Smagorinsky's SGS model with van Driest damping. The results show good agreement with experimental data and direct numerical simulations for incompressible channel flow. The SGS eddy viscosity is less than 10% of the molecular viscosity, and therefore the LES is effectively MILES with molecular viscosity.     

Effects of fluid properties and pipe diameter on two-phase flow patterns in horizontal lines

Extensive new data have been obtained on the transitions between two-phase flow patterns during co-current gas liquid flow in horizontal lines. Fluid properties were varied in a systematic manner to determine the effects of liquid viscosity, liquid density, interfacial tension and gas density. Line sizes varied from 1.2 to 5 cm for most of the tests. Visual observations were supplemented by an analysis of pressure drop fluctuations and hence the present data are believed to be less subjective than most past observations.

The transition data from the present tests, as well as available literature data, were compared to the most frequently used transition line correlations. In almost all cases serious deficiencies were observed. Revised dimensionless correlations which fit present data, and those previously available, are presented.     

Assessment of effect of heat of internal friction on characteristics of structured flow of viscoplastic liquid in a round tube

A structured pressure flow of viscoplastic liquid in an infinite round tube is examined. Energy dissipation is given due consideration; it is assumed that the temperature dependences of the plastic viscosity and the ultimate shear stress are exponential. The solution obtained when the parameter characterizing the rate of production of heat of internal friction is assumed to be small indicates that energy dissipation has a sgnificant effect on the local flow characteristics and the hydraulic-resistance coefficient, for which an expression suitable for engineering calculations is given.     

The influence of flow-induced non-Newtonian fluid properties on turbulent drag reduction

Friction factors and velocity profiles in turbulent drag reduction can be compared to Newtonian fluid turbulence when the shear viscosity at the wall shear rate is used for the Reynolds number and the local shear viscosity is used for the non-dimensional wall distance. On this basis, an apparent maximum drag reduction asymptote is found which is independent of Reynolds number and type of drag reducing additive. However, no shear viscosity is able to account for the difference between the measured Reynolds stress and the Reynolds stress calculated from the mean velocity profile (the Reynolds stress deficit). If the appropriate local viscosity to use with the velocity fluctuation correlations includes an elongational component, the problem can be resolved. Taking the maximum drag reduction asymptote as a non-Newtonian flow, with this effective viscosity, leads to agreement with the concept of an asymptote only when the solvent viscosity is used in the non-dimensional wall distance.     

Flow pattern transitions in vertical and upwardly inclined lines

Additional data has been obtained on flow pattern transitions during cocurrent gas-liquid flow in vertical and upwardly inclined lines. These data, together with those previously available in the literature, have enabled the development of improved dimensionless correlations for flow pattern boundaries. The individual boundary lines bave been combined into simple overall flow pattern maps.     

Effect of a liquid dispersed phase on the wall flow structure in static mixer

The effect of a liquid dispersed on the wall flow structure in static mixer is analyzed by using an electrochemical method. Both laminar and turbulent flows have been investigated. The axial wall velocity gradient and turbulent intensity have been studied along the static mixer in both flow regimes and for different dispersed phase concentrations. The spectral analysis of the wall velocity gradient fluctuations was analyzed in the turbulent regime. For volume fraction higher than 5%, the effect of the dispersed liquid phase is very important for all the studied parameters. The turbulence associated to the dispersed phase leads to an increase of the energy dissipation in the static mixer and also to a modification of energy dissipation mechanism.     

Capillary flow behavior of bicomponent polymer blends

The flow behavior of bicomponent polymer blends of four types of polymers (polypropylene, polystyrene, high-density polyethylene and polymethyl-methacrylate) was examined using a capillary extrusion rheometer. The viscosity of the blend was generally less than the value calculated by the theoretical or empirical additivity rules proposed in previous reports, whereas the entrance pressure loss, which is considered to be an effect of elasticity, was larger than the estimated value. Thus the variation of the viscosity with blending ratio was inversely proportional to the variation in the elastic property. The cross-section of the material extruded in a roughly dispersed state showed an annularly stratified flow pattern in which the lower viscosity component polymer appeared to form the outer skin layer. However, the observation that the viscosity of the properly blended material at certain blending ratios was sometimes lower than that of either homopolymer could not be explained.     

Dynamic Network Model of Mobility Control in Emulsion Flow Through Porous Media

Modeling the flow of emulsion in porous media is extremely challenging due to the complex nature of the associated flows and multiscale phenomena. At the pore scale, the dispersed phase size can be of the same order of magnitude of the pore length scale and therefore effective viscosity models do not apply. A physically meaningful macroscopic flow model must incorporate the transport of the dispersed phase through the porous material and the changes on flow resistance due to drop deformation as it flows through pore throats. In this work, we present a dynamic capillary network model that uses experimentally determined pore-level constitutive relationships between flow rate and pressure drop in constricted capillaries to obtain representative transient macroscopic flow behavior emerging from microscopic emulsion flow at the pore level. A parametric analysis is conducted to study the effect of dispersed phase droplet size and capillary number on the flow response to both emulsion and alternating water/emulsion flooding in porous media. The results clearly show that emulsion flooding changes the continuous-phase mobility and consequently flow paths through the porous media, and how the intensity of mobility control can be tuned by the emulsion characteristics.     

Implementation of physical boundary conditions into computational domain in modelling of oscillatory bottom boundary layers

This paper discusses the importance of realistic implementation of the physical boundary conditions into computational domain for the simulation of the oscillatory turbulent boundary layer flow over smooth and rough flat beds. A mathematical model composed of the Reynolds averaged Navier–Stokes equation, turbulent kinetic energy (k) and dissipation rate of the turbulent kinetic energy (ε) has been developed. Control‐volume approach is used to discretize the governing equations to facilitate the numerical solution. Non‐slip condition is imposed on the bottom surface, and irrotational main flow properties are applied to the upper boundary. The turbulent kinetic energy is zero at the bottom, whereas the dissipation rate is approaching to a constant value, which is proportional to the kinematic viscosity times the second derivative of the turbulent kinetic energy. The output of the model is compared with the available experimental studies conducted in oscillatory tunnels and wave flume. It is observed that the irrotational flow assumption at the upper boundary is not realistic in case of water tunnels. Therefore, new upper boundary conditions are proposed for oscillatory tunnels. The data of wave flume show good agreement with the proposed numerical model. Additionally, several factors such as grid aspect ratio, staggered grid arrangement, time‐marching scheme and convergence criteria that are important to obtain a robust, realistic and stable code are discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

A procedure to determine the viscosity function from experimental data of capillary flow

The accurate calculation of the viscosity η as function of the shear rate &γdot; from capillary viscometry is still a matter of debate in the literature. In fact, this problem involves the inversion of an integral equation, which leads to multiple solutions due to the unavoidable noise present in the experimental data. The purpose of this work is to develop an efficient procedure to determine the viscosity function from experimental data of capillary flow without presenting the difficulties inherent in other methods discussed previously in the literature. The system identification procedure is used here to estimate the parameters of a viscosity model, which is appropriately selected for the fluid under study through preliminary calculations involving the apparent shear rate – shear stress data. Once the model is chosen by satisfying criteria for the fit goodness and its parameters are evaluated, a smooth and continuous function η(γdot;) is obtained in the range of experimental shear rates. The procedure proposed is also applicable to fluids in shear flow that present two Newtonian plateaus, as it is typically found in macromolecular dilute solutions. The mean value theorem of continuous functions is used to reduce significantly the computational time. Received: 15 November 1999 Accepted: 7 November 2000     

Bimodal model of slurry viscosity with application to coal-slurries. Part 1. Theory and experiment

The rheological behavior of stable slurries is shown to be characterized by a bimodal model that represents a slurry as made up of a coarse fraction and a colloidal size fine fraction. According to the model, the two fractions behave independently of each other, and the non-Newtonian behavior of the viscosity is solely caused by the colloidal fraction, while the coarse fraction increases the viscosity level through hydrodynamic interactions. Data from experiments run with colloidal coal particles of about 2–3 µm average size dispersed in water show the viscosity of these colloidal suspensions to exhibit a highly shearrate-dependent behavior and, in the high shear limit, to match very closely the viscosity of suspensions of uniform size rigid spheres although the coal volume fraction must be determined semi-empirically. Different amounts of coarse coal particles are added to the colloidal suspension and the viscosity of the truly bimodal slurries measured as a function of shear rate. In agreement with the bimodal model, the measured shear viscosities show the coarse fraction to behave independently of the colloidal fraction and its contribution to the viscosity rise to be independent of the shear rate. It is shown that the shear rate exerted on the colloidal fraction is higher than that applied by the viscometer as a result of hydrodynamic interactions between the coarse particles, and that it is this effective higher shear rate which is necessary to apply in the correlations. For determining the coal volume fraction a relatively simple and quite accurate measurement technique is developed for determining the density and void fraction of coarse porous particles; the technique directly relates volume fraction to mass fraction.     

Review of Experimental Data on Incompressible Turbulent Round Jets

This article reviews measurements for the canonical flow: incompressible turbulent round jets issuing into a large, ideally infinite, quiescent domain. The available far-field data on mean velocity, momentum-flux conservation, Reynolds stresses and triple fluctuation correlations are presented. The budget equations for turbulent kinetic energy and for the individual Reynolds stresses are shown, including different formulations for dissipation and pressure-velocity correlations. Evidence of the persistence of source conditions in the self-preserving far field is observed in several cases. This article analyses and compares several data sets, obtained at different levels of detail, against analytical constraints, discusses limitations and provides insights aided by reference to recent numerical work. It is hoped that this will prove useful in guiding future experiments and numerical test cases, where complete details of the jet configuration are required for validation and comparison.     

Improved artificial dissipation schemes for the Euler equations

The influence of artificial dissipation schemes on the accuracy and stability of the numerical solution of compressible flow is extensively examined. Using an implicit central difference factored scheme, an improved form of artificial dissipation is introduced which highly reduces the errors due to numerical viscosity. A function of the local Mach number is used to scale the amount of numerical damping added into the solution according to the character of the flow in several flow regimes. The resulting scheme is validated through several inviscid flow test cases.