Fluid Phase Velocity Research Articles

Transient Coupled Borehole/Formation Fluid-Flow Model for Interpretation of Oil/Water Production Logs

Summary Interpretation of two-phase production logs (PLs) traditionally constructs borehole fluid-flow models decoupled from the physics of reservoir rocks. However, quantifying formation dynamic petrophysical properties from PLs requires simultaneous modeling of both borehole and formation fluid-flow phenomena. This paper develops a novel transient borehole/formation fluid-flow model that allows quantification of the effect of formation petrophysical properties on measurements acquired with production-logging tools (PLTs). We invoke a 1D, isothermal, two-fluid formulation to simulate borehole fluid-phase velocity, pressure, volume fraction, and density in oil/water-flow systems. The developed borehole fluid-flow model implements oil-dominant and water-dominant bubbly flow regimes with the inversion point taking place approximately when the oil volume fraction is equal to 0.5. Droplet diameter is dynamically modified to simulate interfacial drag effects, and to effectively account for variations of slip velocity in the borehole. Subsequently, a new successive iterative method interfaces the borehole and formation fluid-flow models by introducing appropriate source terms into the borehole fluid-phase mass-conservation equations. The novel iterative coupling method integrated with the developed borehole fluid-flow model allows dynamic modification of reservoir boundary conditions to accurately simulate transient behavior of borehole crossflow taking place across differentially depleted rock formations. In the case of rapid variations of near-borehole properties, frequent borehole/formation communication inevitably increases the computational time required for fluid-flow simulation. Despite this limitation, in a two-layer reservoir model penetrated by a vertical borehole, the coupling method accurately quantifies a 14% increase of volume-averaged oil-phase relative permeability of the low-pressure layer caused by through-the-borehole cross-communication of differentially depleted layers. Sensitivity analyses indicate that the alteration of near-borehole petrophysical properties primarily depends on formation average pressure, fluid-phase density contrast, and borehole-deviation angle. A practical application of the new coupled fluid-flow model is numerical simulation of borehole production measurements to estimate formation average pressure from two-phase selective-inflow-performance (SIP) analysis. This study suggests that incorporating static (shut-in) PL passes into the SIP analysis could result in misleading estimation of formation average pressure.

Suspension model for blood flow through a catheterized arterial stenosis with peripheral layer of plasma free from cells

The present article describes the blood flow in a catheterized artery with radially symmetric and axially asymmetric stenosis. To understand the effects of red cell concentration, plasma layer thickness and catheter size simultaneously, blood is considered by a two-layered model comprising a core region of suspension of all the erythrocytes (particles) supposed to be a particle-fluid mixture and a peripheral zone of cell-free plasma. The analytical expressions for flow features, such as fluid phase and particle phase velocities, flow rate, wall shear stress and resistive force are obtained. It is witnessed that the presence of the catheter causes a substantial increase in the frictional forces on the walls of arterial stenosis and catheter, shear stress and flow resistance, in addition to that, have occurred due to the presence of red cells concentration (volume fraction density of the particles) and the absence of peripheral plasma layer near the wall of the stenosed artery. The introduction of an axially asymmetric nature of stenosis and plasma layer thickness causes significant reduction in flow resistance. One can notice that the two-phase fluid (suspension model) is more profound to the thickness of peripheral plasma layer and catheter than the single-phase fluid.

Slip effects and endoscopy analysis on blood flow of particle-fluid suspension induced by peristaltic wave

This study describes the endoscopy and slip effects on blood flow of particulate fluid suspension induced by peristaltic wave through a non-uniform annulus. An approximation of long wavelength and low Reynolds is used to model the governing equation of continuity and momentum equation for fluid phase and particulate phase. The influence of all the pertinent parameters has been obtained such as slip parameter (β), Jeffrey fluid parameter (λ1), particle volume fraction (C) and volume flow rate Q(z,t), velocity constant (v0) and the inner radius (ϵ) against pressure gradient, pressure rise, friction forces, velocity of fluid phase and particulate phase (uf,up). Numerical results are carried out for pressure rise and friction forces on the inner and outer tube.

Conducting dusty fluid flow through a constriction in a porous medium

<p><span lang="EN-IN">The flow of an unsteady incompressible electrically conducting fluid with uniform distribution of dust particles in a constricted channel has been studied. The medium is assumed to be porous in nature. The governing equations of motion are treated analytically and the expressions are obtained by using variable separable and Laplace transform techniques. The influence of the dust particles on the velocity distributions of the fluid are investigated for various cases and the results are illustrated by varying parameters like Hartmann number, deposition thickness on the walls of the cylinder and the permeability of the porous medium on the velocity of dust and fluid phase.</span></p>

On fluid-structure interactions of a cloaked submerged spherical shell

Backscattering from a cloaked submerged spherical shell is analyzed in the low, mid, and high frequency regimes. Complex poles of the scattered pressure amplitudes using Cauchy residue theory are evaluated in an effort to explain dominant features of the scattered pressure and how they are affected by the introduction of a cloak. The methodology used is similar to that performed by Sammelmann and Hackman in a series of papers written on scattering from an uncloaked spherical shell in the early 1990s. In general, it is found that cloaking has the effect of diminishing the amplitude and shifting tonal backscatter responses. Extreme changes of normal and tangential fluid phase velocities at the fluid-solid interface when cloaking is employed leads to elimination of the “mid-frequency enhancement” near the coincidence frequency for even modestly effective cloaks, while reduction of the “high-frequency enhancement” resulting from the “thickness quasi-resonance” near the cutoff frequency of the symmetric (SB 2) mode require more effective cloaking, but can be practically eliminated by employing a cloak that creates tangential acoustic velocities in excess of the SB 2 mode phase speed near cutoff.

Fluid-structure effects of cloaking a submerged spherical shell

Backscattering from a cloaked submerged spherical shell is analyzed in the low, mid, and high frequency regimes. Complex poles of the scattered pressure amplitudes using Cauchy residue theory are evaluated in an effort to explain dominant features of the scattered pressure and how they are affected by the introduction of a cloak. The methodology used is similar to that performed by Sammelmann and Hackman [J. Acoust. Soc. Am. 85, 114-124 (1989); J. Acoust. Soc. Am. 89, 2096-2103 (1991); J. Acoust. Soc. Am. 90, 2705-2717 (1991)] in a series of papers written on scattering from an uncloaked spherical shell. In general, it is found that cloaking has the effect of diminishing the amplitude and shifting tonal backscatter responses. Extreme changes of normal and tangential fluid phase velocities at the fluid-solid interface when cloaking is employed leads to elimination of the "mid-frequency enhancement" near the coincidence frequency for even modestly effective cloaks, while reduction of the "high-frequency enhancement" resulting from the "thickness quasi-resonance" near the cut-off frequency of the symmetric (S2(B)) mode requires more effective cloaking, but can be practically eliminated by employing a cloak that creates tangential acoustic velocities in excess of the S2(B) mode phase speed near cutoff.

HOMOTOPY SIMULATION OF TWO-PHASE THERMO-HEMODYNAMIC FILTRATION IN A HIGH PERMEABILITY BLOOD PURIFICATION DEVICE

A two-phase thermo-hydrodynamic model is presented for transport in the vertical chamber of a porous media blood filtration device. A non-Darcy drag force formulation was employed. The Marble–Drew fluid–particle suspension model was used to simulate the plasma phase and the suspension (erythrocyte) particle phase. The non-dimensional transport equations were solved using a semi-computational procedure known as the homotopy analysis method (HAM). With the judicious use of the auxiliary parameter ℏ, HAM affords a powerful mechanism to adjust and control the convergence region of solution series. This method provides an efficient approximate analytical solution with high accuracy, minimal calculation and avoidance of physically unrealistic assumptions. Detailed computations are presented for the effects of Grashof number (Gr), momentum inverse Stokes number (Skm), Darcy number (Da), Forchheimer number (Fs), particle loading parameter (PL), buoyancy parameter (B) and temperature inverse Stokes number (SkT) on the dimensionless fluid phase velocity (U), dimensionless particle phase velocity (Up), dimensionless fluid phase temperature (Φ) and the dimensionless temperature of particle phase (Φp). A Prandtl number of 25 was used to simulate blood at room temperature. Excellent correlation was obtained between the HAM and numerical shooting quadrature solutions. The results indicated that there is a strong decrease in fluid phase velocities with increasing Darcian (first order) drag and second-order Forchheimer drag, and a weaker reduction in particle phase velocity field. Applications of the study include porous media bio-filtration devices and dialysis simulations.

Keller Box and Smoothed Particle Hydrodynamic Numerical Simulation of Two-Phase Transport in Blood Purification Auto-Transfusion Dialysis Hybrid Device with Stokes and Darcy Number Effects

A computational simulation of laminar natural convection fully-developed multi-phase suspension in a porous medium channel is presented. The Darcy model is employed for the porous material which is valid for low velocity, viscous-dominated flows. The Drew-Marble fluid-particle suspension model is employed to simulate both particulate (red blood cell) and fluid (plasma) phases. The transformed two-point nonlinear boundary value problem is shown to be controlled by a number of key dimensionless thermo-physical parameters, namely the Darcy number (Da), momentum inverse Stokes number (Skm), particle loading parameter (pL), inverse thermal Stokes number (SkT), particle-phase wall slip parameter (W) and buoyancy parameter (B). Detailed numerical solutions are presented with an optimized Keller Box implicit finite difference Method (KBM) for the influence of these parameters on the fluid-phase velocity (U) and particle-phase velocity (Up). Validation is also included using the Smoothed Particle Hydrodynamic (SPH) Lagrangian method and excellent correlation achieved. Increasing Darcy number is observed to significantly accelerate the fluid-phase flow and less dramatically enhance particle-phase velocity field. Magnitudes of fluid phase velocity are also elevated with both increasing viscosity ratio and particle-phase wall slip parameter. Increasing buoyancy effect depresses particle phase velocity. An increase in particle loading parameter is also observed to suppress both fluid and particle phase velocities. No tangible change in fluid or particle phase temperatures is computed with increasing Darcy number. The study is relevant to dialysis devices exploiting thermal and porous media filtration features. Keywords: Biotechnology, blood flow, Prandtl number, two-phase suspension, Stokes number, particle phase velocity, Keller box finite difference algorithm, Smoothed particle hydrodynamics (SPH), Thermo-haemotological processing, autotransfusion medicine, biothermal devices. Read more →

Slip velocity of large neutrally buoyant particles in turbulent flows

We discuss possible definitions for a stochastic slip velocity that describes the relative motion between large particles and a turbulent flow. This definition is necessary because the slip velocity used in the standard drag model fails when particle size falls within the inertial subrange of ambient turbulence. We propose two definitions, selected in part due to their simplicity: they do not require filtration of the fluid phase velocity field, nor do they require the construction of conditional averages on particle locations. A key benefit of this simplicity is that the stochastic slip velocity proposed here can be calculated equally well for laboratory, field and numerical experiments. The stochastic slip velocity allows the definition of a Reynolds number that should indicate whether large particles in turbulent flow behave (a) as passive tracers; (b) as a linear filter of the velocity field; or (c) as a nonlinear filter to the velocity field. We calculate the value of stochastic slip for ellipsoidal and spherical particles (the size of the Taylor microscale) measured in laboratory homogeneous isotropic turbulence. The resulting Reynolds number is significantly higher than 1 for both particle shapes, and velocity statistics show that particle motion is a complex nonlinear function of the fluid velocity. We further investigate the nonlinear relationship by comparing the probability distribution of fluctuating velocities for particle and fluid phases.

Two‐phase dynamic analysis by material point method

SUMMARYThis paper extends the material point method to analyze coupled dynamic, two‐phase boundary‐valued problems via a velocity formulation, in which solid and fluid phase velocities are the variables. Key components of the proposed approach are the adoption of Verruijt's sequence of update steps when integrating over time and the enhancement of volumetric strains. The connection between fractional step method and the time‐stepping algorithm presented in this paper is addressed.Enhancement of volumetric strains allows lower order variations in pressure and mitigates spurious pressure fields and locking that plague low‐order finite‐element implementations.A stress averaging technique to smoothen stress variations is proposed, and the local damping procedure adopted by FLAC is extended to handle two‐phase problems. Special Kelvin‐Voigt boundaries are developed to suppress reflections at artificial boundaries. Idealized examples are presented to demonstrate the capability of the proposed framework to accurately capture the physics of wave propagation, consolidation and wave attack on a sea dike. Copyright © 2012 John Wiley & Sons, Ltd.

Comparison of azimuthal ion velocity profiles using Mach probes, time delay estimation, and laser induced fluorescence in a linear plasma device

We compare measurements of radially sheared azimuthal plasma flow based on time delay estimation (TDE) between two spatially separated Langmuir probes, Mach probes and laser induced fluorescence (LIF). TDE measurements cannot distinguish between ion fluid velocities and phase velocities. TDE and Mach probes are perturbative, so we compare the results against LIF, a non-perturbative, spatially resolved diagnostic technique that provides direct measurements of the ion velocity distribution functions. The bulk ion flow is determined from the Doppler shift of the Argon absorption line at 668.6139 nm. We compare results from all the three diagnostics, at various magnetic fields, which acts as a control knob for development of drift wave turbulence. We find that while Mach probes and LIF give similar profiles, TDE measurements typically overestimate the velocities and are also sensitive to the drift wave modes being investigated.

Recovery of airflow resistivity of poroelastic beams submitted to transient mechanical stress

The airflow resistivities of air-saturated poroelastic slender beams submitted to transient mechanical stress are recovered using fluid and solid borne compressional mode phase velocity expressions drawn from a modified Biot theory. A point where the two dilatational modes intersect and their phase velocities equal is first sought. This point also corresponds to the Biot transitional frequency indicating the frequency at which the solid and the pore fluid start disassociating due to the weakening of the viscous forces by the thinning of the viscous boundary layer in the pores. A bilinear time–frequency (TF) distribution is used to represent on the time–frequency plane, the captured transient mechanical stress waves from which the point of intersection/separation of the two modes is located. The projection of the Eigenfrequencies obtained from a simple 3D finite element modeling of the thin poroelastic beam, on a (TF) diagram, facilitates the identification of the modes. The transition frequencies for the poroelastic beams thus retrieved are verified through the use of variable frequency, single cycle sine wave bursts. The anisotropy of the foams are also revealed by analyzing the transient responses of the poroelastic beam specimens cut from the same panel but in two perpendicular directions in orientation to each other.

Differential transform semi-numerical analysis of biofluid-particle suspension flow and heat transfer in non-Darcian porous media

The differential transform method (DTM) is semi-numerical method which is used to study the steady, laminar buoyancy-driven convection heat transfer of a particulate biofluid suspension in a channel containing a porous material. A two-phase continuum model is used. A set of variables is implemented to reduce the ordinary differential equations for momentum and energy conservation (for both phases) to a dimensionless system. DTM solutions are obtained for the dimensionless system under appropriate boundary conditions. We examine the influence of momentum inverse Stokes number (Skm), Darcy number (Da), Forchheimer number (Fs), particle loading parameter (pL), particle-phase wall slip parameter (Ω) and buoyancy parameter (B) on the fluid-phase velocity (U) and particle-phase velocity (Up). Padé approximants are also employed to achieve satisfaction of boundary conditions. Excellent correlation is obtained between the DTM and numerical quadrature solutions. The results indicate that there is a strong decrease in fluid-phase velocities with increasing Darcian (first-order) drag and the second-order Forchheimer drag, and a weaker reduction in particle-phase velocity field. Fluid and particle-phase velocities are also strongly affected with inverse momentum Stokes number. DTM is shown to be a powerful tool providing engineers with an alternative simulation approach to other traditional methods for multi-phase computational biofluid mechanics. The model finds applications in haemotological separation and biotechnological processing.

Numerical Investigation of the Effects of Nanoparticle Diameter on Velocity Field and Nanoparticle Distribution of Nanofluid Using Lagrangian-Eulerian Approach

This article studies the effects of nanoparticle diameter on the concentration distribution and velocity of nanoparticles in nanofluid are examined using Lagrangian-Eulerian. Moreover, the effects of nanoparticle diameter on the velocity of fluid phase affected by the particle movements are studied. In addition, the effects of the change of Brownian and thermophoretic forces with diameter on nanoparticles and fluid velocity as well as nanoparticles distribution are studied. The results indicate that particles are not uniformly distributed, as the concentration is higher in the vicinity of the pipe centerline than its wall. With the increase of nanoparticle size, the nanoparticle concentration in the vicinity of pipe wall is augmented. According to the results, with the increase of the nanoparticle diameter, the fluid and nanoparticle velocity is reduced. The reason for this is the reduction of Brownian forces with the increase of nanoparticle diameter.

Two-phase interactions through turbulent events as described by fluid–particle correlations

An experimental investigation of a vertical upward, two-phase pipe flow was undertaken to measure kinematic parameters of the fluid and solid phases. The kinematic parameters included Reynolds stress distributions based on quadrant analyses that provided insight in understanding the behavior of two-phase kinematic correlation profiles. The data collected was based on a two-color digital particle image velocimetry (DPIV) technique that simultaneously measured the velocity fields of the fluid and solid phases. From quadrant analysis results, differences in Reynolds stress quadrant profiles between the single- and two-phase conditions were observed near the wall in the range 0.8> r/R>0.55, corresponding to wall distances between 35 and 75 viscous lengths ( y+). Correlation coefficients between the two phases were then calculated, using the fluctuating velocity components of each phase. The extent of the interaction between the two phases was tracked by the changing correlation values versus distance from the wall. The correlation of the fluid and solid phase velocities was highest in the core region of the pipe ( y+∼120), where the effect of turbulent events is reduced; low correlation coefficient values were found at y+<75, where differences of magnitudes, inflection points, etc. of burst and sweep event quadrant analysis profiles were observed. The extent of the influence of wall dynamic turbulent events on the solid phase was observed both by the differences in the relative Reynolds stress quadrant profiles and, more readily, by the changing values of two-phase axial and radial correlation coefficients determined from the simultaneous fluid and solid fluctuating velocities measured by the two-color DPIV methodology. These changing values of the correlation coefficients across the tube reflect the different responses of low inertia (fluid tracers) and high inertia (solid phase glass spheres) particles to the turbulent events. Similar profiles of the axial and radial correlation coefficients were observed, indicating that for the geometry and flow conditions considered, one velocity component of each phase was sufficient to track the spatial extent of turbulent event effects and their interactions with the fluid and solid phases. It is found that the two-color DPIV methodology and two-phase correlation results can give critical insight into the performance of thermal-fluid processes, as burst and sweep events have a large impact on the kinematics and dynamics of particles in the two-phase flow.

An Enriched Biphasic Model for Solute Driven Degradation

AbstractTransport of solutes in porous materials plays an important role in many kinds of materials such as biological tissues, porous implants or even soils. In most of the cases the liquid phase in the pores acts as a solvent for one or more solutions. The motion of the solutions is driven by both, the advective and convective transport. The former is related to the fluid phase velocity whereas the letter follows the concentration gradient. The interactions between the solutes and the solid and liquid phase may influence the overall material behavior. Although the solutes often carry electrical charges this paper is focused on neutrally charged solutions. In this contribution the model to describe the solute transport in a fluid saturated porous material is based on the well founded Theory of Porous Media. We will present the basic framework and the governing equations. Finally, we will show a three dimensional numerical example of the solute driven degradation of a skull implant. (© 2009 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Soft-sphere soft glasses

Molecular dynamics simulations have been used to compute physical properties of model fluids in which the particles interacted via the soft-sphere pair potential (SSP) phi(r)=epsilon(sigma/r)(n), where epsilon and sigma are the characteristic energy and distance, respectively. The emphasis is on small values of n, tending to the lower theromodynamically allowed bound of 3+. An accurate equation of state for the SSP fluid is obtained, consisting of two terms, and as n-->3+, the compressibility factor, Z tends to Z=B(2)zeta(n/3) for zeta>0, where B(2) is the second virial coefficient, and zeta=piNsigma(3)/6V is a nominal packing fraction for N particles in volume V. A simple formula for the position of the first peak in the radial distribution function in the soft particle limit is proposed and shown to agree with the simulation data. The fluid phase velocity autocorrelation function at fluid-solid coexistence becomes more oscillatory as n decreases. Values for the self-diffusion coefficient D and shear viscosity eta were calculated as a function of n and density, and these were used to estimate the n-dependence of an ideal glass transition. The glass transition shifts relatively further into the solid part of the phase diagram as softness ( approximately 1/n) increases. D decreases by ca. 75% and eta increases by about a factor of 3 along the fluid-solid coexistence line from n=infinity to 3.25. Non-Gaussian behavior was calculated from the particle displacements as a function of particle softness. A screened soft-sphere potential, SSSP, was introduced to explore the effects for small n of the long range part of the potential in relation to the scale of the local structure. The SSSP with suitable analytic form and parameters can give statistically indistinguishable results from the full SSP for the static properties, D and eta.

Prediction of Solid Particle Erosive Wear of Elbows in Multiphase Annular Flow-Model Development and Experimental Validations

Erosion damage in the pipe wall due to solid particle impact can cause severe problems in fluid handling industries. Repeated impact of the suspended small solid particles to the inner wall of process equipment and piping removes material from the metal surface. The reduced wall thickness of high pressure equipment and piping can no longer withstand the operating pressure that they were originally designed for and may cause premature failure of the system components. This results in production downtime, safety, and environmental hazards with significant loss to the industry and economy. Prediction of erosion in single-phase flow with sand is a difficult problem due to the effect of different parameters and their interactions that cause erosion. The complexity of the problem increases significantly in multiphase flow where the spatial distribution of the liquid and gas phases and their corresponding velocities change continuously. Most of the currently available erosion prediction models are developed for single-phase flow using empirical data with limited accuracy. A mechanistic model has been developed for predicting erosion in elbows in annular multiphase flow (gas-liquid-solid) considering the effects of particle velocities in gas and liquid phases of the flow. Local fluid phase velocities in multiphase flow are used to calculate erosion rates. The effects of erosion due to impacts of solid particles entrained in the liquid and gas phases are computed separately to determine the total erosion rate. Erosion experiments were conducted to evaluate the model predictions. Comparing the model predicted erosion rates with experimental erosion data showed reasonably good agreement validating the model.

Two‐phase model for sand transport in sheet flow regime

We introduce a two‐phase model for sand transport in sheet flow regime. This model uses a collisional theory and a k – ɛ fluid turbulence closure to respectively model the sediment and fluid phase stresses. The sediment stress closure adopts a balance equation of sediment particle fluctuation energy based on kinetic theory that incorporates two‐way interactions between fluid and sediment phases. The fluid turbulence closure also considers the two‐way interaction between fluid turbulence and sand particles. Model‐data comparisons for the sheet layer for oscillatory flows in a U‐tube and for open channel flows demonstrate the model's predictive skill. For steady open channel flows the fluid phase velocity follows closely the law of wall (i.e., the log‐profile) in which the von Karman constant is reduced and the equivalent roughness is increased, compared to the clear fluid flow conditions. The model also provides information in the near‐bed region where the transition from the solid‐like to the fluid‐like behavior of sediment particles is resolved and both the bed load layer thickness and bed load transport rate can be evaluated. For unsteady flows, this model can predict time evolutions for sediment transport throughout the water column.

A second-order moment turbulence model for power law fluid with particles

The USM - θ model of power law fluid for dense two-phase turbulent flow was developed, which combines the unified second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. This model was used to simulate the turbulent flow of power law fluid single-phase in pipe. It is shown that the USM - θ model has better prediction result than the κ f - ɛ- f - k p - ɛ p - θ model. The USM - θ model was then used to simulate the dense two-phase turbulent up flow of power law fluid with particles. With the increase of the flow exponent, the velocities of power law fluid and particles increase near the pipe centre. Comparison between the two-phase flow of power law fluid-particle and of liquid-particle indicates that the axial fluctuation velocity of fluid phase and particle phase in liquid-particle two-phase flow is smaller than that in the power law fluid two-phase flow, but the two-phase velocities of power law fluid-particle and liquid-particle are close to each other.