Retraction: “A unified probability density function formulation to model turbulence modification in two-phase flow” [Phys. Fluids 21, 105101 (2009)]

2012 ◽  
Vol 24 (6) ◽  
pp. 069901
Author(s):  
Gaurav Anand ◽  
Patrick Jenny
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Turbulence Modification ◽  
Function Formulation

scholarly journals Flow Pattern and Resistance Characteristics of Gas–Liquid Two-Phase Flow with Foam under Low Gas–Liquid Flow Rate

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3722
Author(s):  
Bin Wang ◽  
Jianguo Hu ◽  
Weixiong Chen ◽  
Zhongzhao Cheng ◽  
Fei Gao
Keyword(s):  
Stainless Steel ◽  
Probability Density Function ◽  
Probability Density ◽  
Flow Pattern ◽  
Density Function ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Liquid Ratio ◽  
Two Phase ◽  
Foam Flooding

To reduce the cost of arranging air foam flooding equipment at each wellhead, a method of establishing centralized air foam flooding injection stations is proposed. The flow pattern and resistance characteristics of air foam flooding mixtures in different initial conditions are studied. Experimental results indicate that the probability density function of stratified flow is obtained by comparing stainless steel and transparent pipes. If the gas–liquid ratio is kept constant, then the shape of the probability density function remains unchanged in both stainless steel and transparent tubes. Meanwhile, the flow pattern under the gas–liquid ratio is determined by comparing the image recognition results with the probability density function, and a formula for calculating the resistance and pressure drop of the gas and liquid two-phase flow in the horizontal and upward pipes is established. Compared with the experiments, the error results of the calculation are small. Thus, the proposed equations can be used to predict the flow resistance of real air foam flooding.

scholarly journals Probability density function approach for modelling multi-phase flow with ganglia in porous media

2011 ◽  
Vol 688 ◽  
pp. 219-257 ◽  
Author(s):  
Manav Tyagi ◽  
Patrick Jenny
Keyword(s):  
Porous Media ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Transport Equations ◽  
Kolmogorov Equation ◽  
Phase Flow ◽  
Correlation Times ◽  
Multi Phase Flow ◽  
Multi Phase

AbstractA probabilistic approach to model macroscopic behaviour of non-wetting-phase ganglia or blobs in multi-phase flow through porous media is proposed. The key idea is to consider a set of stochastic Markov processes that can mimic the microscopic multi-phase dynamics. These processes are characterized by equilibrium probability density functions (PDFs) and correlation times, which can be obtained from micro-scale simulation studies or experiments. A Lagrangian viewpoint is adopted, where stochastic particles represent infinitesimal fluid elements and evolve in the physical and probability space. Ganglion mobilization and trapping are modelled by a two-state jump process with transition probabilities given as functions of ganglion size. Coalescence and breakup of ganglia influence the ganglion size distribution, which is modelled by a Langevin type equation. The joint probability density function (JPDF) of the chosen stochastic variables is governed by a high-dimensional Chapman–Kolmogorov equation. This equation can be used to derive moment (e.g. saturation, mean mobility etc.) transport equations, which in general do not form a closed system. However, in some special cases, which arise in the limit of one time scale being smaller or larger than the others, a closed set of moment transport equations can be obtained. For slowly varying and quasi-uniform flows, the saturation transport equation appears in closed form with the mean mobility fully determined, if the equilibrium PDFs are known. Furthermore, it is shown how statistical parameters such as mobilization and trapping rates and equilibrium PDFs can be obtained from the birth–death type approach, in which ganglia breakup and coalescence are explicitly considered. A two-equation transport model (one equation for the total saturation and one for the trapped saturation) is obtained in the limit of very fast coalescence and breakup processes. This model is employed to mimic hysteresis in relative permeability–saturation curves; a well known phenomenon observed in the successive processes of imbibition and drainage. For the general case, the JPDF-equation is solved using the stochastic particle method, which was proposed in our previous paper (Tyagi et al. J. Comput. Phys. 227, 2008, 6696–6714). Several one- and two-dimensional numerical simulation results are presented to show the influence of correlation times on the averaged macroscopic flow behaviour.

B206 Effect of Gas-Liquid Interface on Gas-phase Turbulence Modification in Annular Two-phase Flow

2001 ◽  
Vol 2001 (0) ◽  
pp. 391-392
Author(s):  
Kenji YOSHIDA ◽  
Hidenobu TANAKA ◽  
Tadayoshi MATSUMOTO ◽  
Tomio OKAWA ◽  
Isao KATAOKA
Keyword(s):  
Gas Phase ◽  
Two Phase Flow ◽  
Liquid Interface ◽  
Phase Flow ◽  
Two Phase ◽  
Turbulence Modification

STRUCTURAL STUDIES ON GAS-PHASE TURBULENCE MODIFICATION IN ANNULAR TWO-PHASE FLOW

2002 ◽  
Author(s):  
KENJI YOSHIDA ◽  
KEIZO MATSUURA ◽  
HIDENOBU TANAKA ◽  
MANABU KUCHINISHI ◽  
ISAO KATAOKA
Keyword(s):  
Gas Phase ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Structural Studies ◽  
Two Phase ◽  
Turbulence Modification
Sign in / Sign up

Export Citation Format

Share Document