A Note on Mixture Density Using the Shannak Definition

2015 ◽  
Vol 1 (1) ◽  
Author(s):  
M. M. Awad
Keyword(s):  
Multiphase Flow ◽  
Pressure Gradient ◽  
Froude Number ◽  
Liquid Density ◽  
Dimensionless Numbers ◽  
Two Phase ◽  
Phase Density ◽  
Mixture Density ◽  
Circular Pipes ◽  
Definition Of

In this study, a note on mixture density using the Shannak definition of the Froude number is presented (Shannak, B., 2009, “Dimensionless Numbers for Two-Phase and Multiphase Flow,” Proceedings of the International Conference on Applications and Design in Mechanical Engineering (ICADME), Penang, Malaysia, Oct. 11–13, 2009). From the definition of the two-phase Froude number, an expression of the two-phase density is obtained. The definition of the two-phase density can be used to compute the two-phase frictional pressure gradient using the homogeneous modeling approach in circular pipes, minichannels, and microchannels. We cannot have gas density≤two-phase density≤liquid density for 0≤mass quality≤1. Therefore, attention must be paid when using the obtained expression of the two-phase density in this note at any x value.

CFD Simulation of Two-Phase Vertical Annular Flow in Both Upward and Downward Direction in a Small Pipe

2019 ◽  
Author(s):  
Ekhwaiter Abobaker ◽  
Abadelhalim Elsanoose ◽  
John Shirokoff ◽  
Mohammad Azizur Rahman
Keyword(s):  
Film Thickness ◽  
Multiphase Flow ◽  
Pressure Gradient ◽  
Annular Flow ◽  
Cfd Simulation ◽  
Flow Direction ◽  
Flow Behavior ◽  
Two Phase ◽  
Downward Flow ◽  
Disturbance Wave

Abstract Computational fluid dynamics (CFD) simulation is presented to investigate the annular flow behavior in the vertical pipe by using ANSYS Fluent platform 17.2. The study was analyzed complex behavior of annular flow in two cases (upward and downward flow) for different air superficial velocities and range of Reynolds number for water, in order to obtain the effect of orientation flow and increasing superficial gas and liquid velocities on the base film, mean disturbance wave thickness, the average longitudinal size of disturbance wave as well as pressure gradient. For multiphase flow model, the volume of fluid method (VOF) for two-phase flow modelling was used and coupled with RNG k-ε turbulence model to predict fully annular flow structures in the upward and downward flow direction. From CFD simulation results, it is clear to see how increases in air velocity result in reductions in film thickness and increase in pressure gradient. Additionally, the results showed monotonic enhancement of film thickness occurring in tandem with increases in the liquid flow rate. However, due to the effect of gravitational force and interfacial friction, the film thickness and pressure gradient are slightly larger for the upward flow than for the downward flow. The results agree with the recent experimental data that studied the annular flow behavior and pressure drop in the upward and downward flow direction. This study will be very helpful in understanding multiphase flow behavior in natural gas wells.

scholarly journals An Improved Hydrodynamics Formulation for Multiphase Flow Lattice-Boltzmann Models

1998 ◽  
Vol 09 (08) ◽  
pp. 1393-1404 ◽  
Author(s):  
D. J. Holdych ◽  
D. Rovas ◽  
J. G. Georgiadis ◽  
R. O. Buckius
Keyword(s):  
Multiphase Flow ◽  
Stress Tensor ◽  
Lattice Boltzmann ◽  
Effective Field ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Physical Parameters ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Definition Of

Lattice-Boltzmann (LB) models provide a systematic formulation of effective-field computational approaches to the calculation of multiphase flow by replacing the mathematical surface of separation between the vapor and liquid with a thin transition region, across which all magnitudes change continuously. Many existing multiphase models of this sort do not satisfy the rigorous hydrodynamic constitutive laws. Here, we extend the two-dimensional, seven-speed Swift et al. LB model1 to rectangular grids (nine speeds) by using symbolic manipulation (MathematicaTM) and compare the LB model predictions with benchmark problems, in order to evaluate its merits. Particular emphasis is placed on the stress tensor formulation. Comparison with the two-phase analogue of the Couette flow and with a flow involving shear and advection of a droplet surrounded by its vapor reveals that additional terms have to be introduced in the definition of the stress tensor in order to satisfy the Navier–Stokes equation in regions of high density gradients. The use of Mathematica obviates many of the difficulties with the calculations "by-hand," allowing at the same time more flexibility to the computational analyst to experiment with geometrical and physical parameters of the formulation.

Evaluation of a Close Coupled Slotted Orifice, Electric Impedance, and Swirl Flow Meters for Multiphase Flow

2013 ◽  
Author(s):  
Gerald Morrison ◽  
Sahand Pirouzpanah ◽  
Muhammet Cevik ◽  
Abhay Patil
Keyword(s):  
Multiphase Flow ◽  
Flow Rate ◽  
Swirl Flow ◽  
Response Curves ◽  
Flow Meter ◽  
Two Phase ◽  
Flow Meters ◽  
Mixture Density ◽  
Wide Range ◽  
Impedance Sensor

The feasibility of a multiphase flow meter utilizing closely coupled slotted orifice and swirl flow meters along with an impedance sensor is investigated. The slotted flow meter has been shown to exhibit well behaved response curves to two phase flow mixtures with the pressure difference monotonically increasing with mixture density and flow rate. It has been determined to have less than 1% uncertainty in determining the flow rate if the density of the fluid is known. Flow visualizations have shown that the slotted orifice is a very good mixing device as well producing a homogenous mixture for several pipe diameters downstream of the plate. This characteristic is utilized to provide a homogeneous mixture at the inlet to the swirl meter. This is possible since the slotted orifice is relatively insensitive to upstream and downstream flow disturbances. The swirl meter has been shown to indicate decreased flow rate as the mixture density increases which is opposite to the slotted orifice making the solution of the two meter outputs to obtain density and flow rate feasible. Additional instrumentation is included. Between the slotted orifice and swirl meter where the flow is homogenous a custom manufactured electrical impedance sensor is installed and monitored. This array of instrumentation will provide three independent measurements which are evaluated to determine which system of equations are robust enough to provide accurate density and flow rate measurement over a wide range of gas volume fractions using a very compact system.

Bounds on Two-Phase Flow: Part I — Frictional Pressure Gradient in Circular Pipes

2005 ◽  
Author(s):  
M. M. Awad ◽  
Y. S. Muzychka
Keyword(s):  
Turbulent Flow ◽  
Pressure Gradient ◽  
Published Data ◽  
Two Phase ◽  
Working Fluids ◽  
Circular Pipes ◽  
Mass Fluxes ◽  
Wide Range ◽  
Flow Part ◽  
Fanning Friction Factor

Simple rules are developed for obtaining rational bounds for two-phase frictional pressure gradient. Both the lower and upper bounds are based on the separate cylinders formulation. The lower bound is based on turbulent-turbulent flow that uses the Blasius equation to represent the Fanning friction factor. The upper bound is based on an equation that represents well the Lockhart-Martinelli correlation for turbulent-turbulent flow. The model is verified using published experimental data of two-phase frictional pressure gradient versus mass flux at constant mass quality. The published data include different working fluids such as R-12 and R-22 at different mass qualities, different pipe diameters, and different saturation temperatures. It is shown that the published data can be well bounded for a wide range of mass fluxes, mass qualities, pipe diameters and saturation temperatures. The bounds models are also presented in a dimensionless form as two-phase frictional multiplier (φl and φg) versus Lockhart-Martinelli parameter (X) for different working fluids such as R-12, R-22, air-oil and air-water mixtures.

Numerical and Experimental Investigation of Stratified Gas-Liquid Two-Phase Flow in Horizontal Circular Pipes

2006 ◽  
Author(s):  
J. L. H. Faccini ◽  
P. A. B. De Sampaio ◽  
J. Su
Keyword(s):  
Experimental Investigation ◽  
Pressure Gradient ◽  
Two Phase Flow ◽  
Stokes Equations ◽  
Experimental Results ◽  
Circular Pipe ◽  
Phase Flow ◽  
Two Phase ◽  
Interface Position ◽  
Circular Pipes

This paper reports numerical and experimental investigation of stratified gas-liquid two-phase flow in horizontal circular pipes. The Reynolds averaged Navier Stokes equations (RANS) with the κ-ω model for a fully developed stratified gas-liquid two-phase flow are solved by using the finite element method. A smooth and horizontal interface surface is assumed without considering the interfacial waves. The continuity of the shear stress across the interface is enforced with the continuity of the velocity being automatically satisfied by the variational formulation. For each given interface position and longitudinal pressure gradient, an inner iteration loop runs to solve the nonlinear equations. The Newton-Raphson scheme is used to solve the transcendental equations by an outer iteration to determine the interface position and pressure gradient for a given pair of volumetric flow rates. The interface position in a 51.2 mm ID circular pipe was measured experimentally by the ultrasonic pulse-echo technique. The numerical results were also compared with experimental results in a 21 mm ID circular pipe reported by Masala [1]. The good agreement between the numerical and experimental results indicates that the κ-ω model can be applied for the numerical simulation of stratified gas-liquid two-phase flow.

Analytical Study of Effects of Flow Rate, Capillarity, and Gravity on CO2/Brine Multiphase-Flow System in Horizontal Corefloods

SPE Journal ◽  
2013 ◽  
Vol 18 (04) ◽  
pp. 708-720 ◽  
Author(s):  
Chia-Wei Kuo ◽  
Sally M. Benson
Keyword(s):  
Steady State ◽  
Multiphase Flow ◽  
Flow Rate ◽  
Flow System ◽  
Rock Properties ◽  
Displacement Efficiency ◽  
Dimensionless Numbers ◽  
Two Phase ◽  
The Core ◽  
Wide Range

Summary This paper presents an approximate semianalytical solution for predicting the average steady-state saturation during multiphase coreflood experiments across a wide range of capillary and gravity numbers. Recently, the influences of flow rate, gravity, and subcore heterogeneity on brine displacement efficiency have been studied with the 3D simulator TOUGH2 (Kuo et al. 2010). These studies have demonstrated that the average saturation depends on the capillary and gravity numbers in a predictable way. The purpose of this paper is to provide a simple and approximate semianalytical solution for predicting the average saturation (during two-phase coreflood experiments across a wide range of flow rates) for different average rock properties and fluid pairs. A 2D analysis of the governing equations for the multiphase-flow system at steady state is used to develop the approximate semianalytical solution. We have developed a new criterion to identify the viscous-dominated regime at the core scale. Variations of interfacial tension (IFT), core permeability, and length of the core and the effects of buoyancy, capillary, and viscous forces are all accounted for in the semianalytical solutions. We also have shown that three dimensionless numbers (NB, Ngv, Rl) and two critical gravity numbers (Ngv,c1, Ngv,c2) are required to properly capture the balance of viscous, gravity, and capillary forces. There is good agreement between the average saturations calculated from the 3D simulations and the analytical model. This new model can be used to design and interpret multiphase-flow coreflood experiments, gain better understanding of multiphase-flow displacement efficiency across a wide range of conditions and for different fluid pairs, and perhaps even provide a tool for studying the influence of subgrid-scale multiphase-flow phenomena on reservoir-scale simulations.

Modeling of Two-Phase Frictional Pressure Gradient in Circular Pipes

2015 ◽  
Author(s):  
M. M. Awad ◽  
Y. S. Muzychka
Keyword(s):  
Pressure Gradient ◽  
Two Phase Flow ◽  
Effective Property ◽  
Theoretical Method ◽  
Phase Flow ◽  
Pressure Gradients ◽  
Two Phase ◽  
Asymptotic Modeling ◽  
Modeling Approach ◽  
Circular Pipes

In this article, three different methods for modeling of twophase frictional pressure gradient in circular pipes are presented. They are effective property models for homogeneous two-phase flows, an asymptotic modeling approach for separated two-phase flow, and bounds on two-phase frictional pressure gradient. In the first method, new definitions for two-phase viscosity are proposed using a one-dimensional transport analogy between thermal conductivity of porous media and viscosity in two-phase flow. These new definitions can be used to compute the two-phase frictional pressure gradient using the homogeneous modeling approach. In the second method, a simple semi-theoretical method for calculating two-phase frictional pressure gradient using asymptotic analysis is presented. Two-phase frictional pressure gradient is expressed in terms of the asymptotic single-phase frictional pressure gradients for liquid and gas flowing alone. In the final method, simple rules are developed for obtaining rational bounds for two-phase frictional pressure gradient in circular pipes. In all cases, the proposed modeling approaches are validated using the published experimental data.

scholarly journals Non-linear multiphase flow in hydrophobic porous media

2021 ◽  
Author(s):  
Yihuai Zhang ◽  
Branko Bijeljic ◽  
Martin Blunt
Keyword(s):  
Porous Media ◽  
Multiphase Flow ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Intermittent Flow ◽  
Pore Scale ◽  
Two Phase ◽  
X Ray Imaging ◽  
Non Linear ◽  
Flow Pathways

Multiphase flow in porous materials is conventionally described by an empirical extension to Darcy’s law which assumes that the pressure gradient is proportional to flow rate. Through a series of two-phase flow experiments, we demonstrate that even when capillary forces are dominant at the pore scale, there is a non-linear intermittent flow regime with a power-law dependence between pressure gradient and flow rate. Energy balance is used to predict accurately the start of the intermittent regime in hydrophobic porous media. The pore-scale explanation of the behaviour based on the periodic filling of critical flow pathways is confirmed through 3D micron-resolution X-ray imaging.

scholarly journals Study of High Viscous Multiphase Flow Using OLGA Flow Simulator

2019 ◽  
Vol 4 (2) ◽  
Author(s):  
Yahaya D Baba ◽  
Amina S Chat ◽  
Aliyu M Aliyu ◽  
Ndubuisi N Okereke ◽  
Adebayo Ogunyemi ◽  
...  
Keyword(s):  
Multiphase Flow ◽  
Pressure Gradient ◽  
Oil And Gas ◽  
Flow Characteristics ◽  
High Viscosity ◽  
Heavy Oils ◽  
Oil Viscosity ◽  
Liquid Holdup ◽  
Two Phase ◽  
Flow Simulator

The continuous depletion of conventional reserves of the world oil and gas has spurred investigation towards the exploration and production from unconventional sources of hydrocarbons such as heavy oil. However, heavy oils are known for their high liquid viscosities making them even more difficult and expensive to produce and transport in pipelines at ambient temperatures. As a consequence of this, a critical understanding of multiphase flow characteristics is vital to aid engineering design it has become imperative to investigate the rheology of high viscosity oils and ways of enhancing its production and transportation. In this study, the characteristics of high viscous oil flows were studied using OLGA flow simulator. A comparison between simulation results from the flow simulator and those of data acquired for high oil-gas viscosity experiments (i.e. for oil viscosity ranging from 0.7-5.0 Pa.s) for two phase flow parameters such liquid holdup and pressure gradient exhibited huge discrepancies and under prediction.    Keywords— High viscosity oil, Liquid holdup, OLGA, Pressure gradient

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