Analysis of the Interchange Rate and Pressure Gradient of Annular Flow Based on a Probability Model

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Ri Zhang ◽  
Feng Zhang ◽  
Sheng Dong
Keyword(s):  
Pressure Gradient ◽  
Annular Flow ◽  
Phase Distribution ◽  
Probability Model ◽  
Interfacial Shear Stress ◽  
Flow Rates ◽  
Liquid Phases ◽  
Deposition Processes ◽  
Basic Equations ◽  
Relationship Of

The phase distribution and mechanical properties of annular flow have obvious, random characteristics because of the influence of turbulence. Thus, probability analysis is a suitable method for the study of annular flow. In the present work, the interchange rate and pressure gradient of fully developed annular flow are investigated in detail based on a probability model. The probability model tracks the atomization and deposition processes of a single particle to analyze the momentum and mass exchange between the gas and liquid phases. The interchange rate can be calculated by summing the generation or disappearance probability of droplets with different sizes. The pressure gradient can be obtained by solving the basic equations of the annular flow, which contains an improved relationship of interfacial shear stress. The predictions of the interchange rate and pressure gradient are well verified by comparison with experimental data available in the literature. Furthermore, the effects of the gas and liquid flow rates on the interchange rate and pressure gradient are discussed in detail.

A Probability Analysis of Atomization Rate for Fully Developed Annular Flow in Vertical Pipes

2017 ◽  
Author(s):  
Ri Zhang ◽  
Sheng Dong
Keyword(s):  
Annular Flow ◽  
Probability Model ◽  
Droplet Breakup ◽  
Probability Analysis ◽  
Breakup Process ◽  
Deposition Rates ◽  
Important Intermediate ◽  
Basic Equations ◽  
Random States ◽  
Development And Evolution

The phase distributions and mechanical properties of annular flow are constantly fluctuating, so they can be regarded as random states. The probability analysis of annular flow is an appropriate method to research the formation, development and evolution of the flow pattern. In the present work, the atomization and deposition rates of fully developed annular flow are investigated in detail by the method of a probability analysis. First, the basic equations of the probability model are applied to solve some important intermediate parameters of annular flow. Second, the atomization and deposition rates of any size droplets are closely related to the probabilities of droplet generation and disappearance. Third, the interchange rate of the whole liquid phase can be obtained by summing the generation and disappearance probabilities of arbitrary size droplets. The predictions of atomization rate are well verified by comparing with the experimental date of 71 cases from three sets of tests. It is demonstrated that the probability model can accurately calculate the atomization rate of the fully developed annular flow for most cases. The predicted deviation for some cases may be caused by the neglect of droplet breakup process. Furthermore, the effects on the atomization rate of seven parameters of annular flow are discussed in detail.

The Effect of Surfactants on Vertical Air/Water Flow for Prevention of Liquid Loading

SPE Journal ◽  
2016 ◽  
Vol 21 (02) ◽  
pp. 488-500 ◽  
Author(s):  
A. T. van Nimwegen ◽  
L. M. Portela ◽  
R. A. Henkes
Keyword(s):  
Surface Tension ◽  
Pressure Gradient ◽  
Water Flow ◽  
Annular Flow ◽  
Surfactant Concentration ◽  
Gas Flow ◽  
Liquid Loading ◽  
Dynamic Surface ◽  
Flow Rates ◽  
Churn Flow

Summary From field experience in the gas industry, it is known that injecting surfactants at the bottom of a gas well can prevent liquid loading. To better understand how the selection of the surfactant influences the deliquification performance, laboratory experiments of air/water flow at atmospheric conditions were performed, in which two different surfactants (a pure surfactant, sodium dodecyl sulfate, and a commercial surfactant blend) were added to the water. In the experiments, a high-speed camera was used to visualize the flow, and pressure-gradient measurements were performed. Both surfactants increase the pressure gradient at high gas-flow rates and decrease the pressure gradient at low gas-flow rates. The minimum in the pressure gradient moves to lower gas-flow rates with increasing surfactant concentration. This is related to the transition between annular flow and churn flow, which is shifted to lower gas-flow rates because of the formation of an almost stagnant foam substrate at the wall of the pipe. At high surfactant concentration, it appears that the churn flow regime is no longer present at all and that there is a direct transition from annular flow to slug flow. The results also show that the critical micelle concentration, the equilibrium surface tension, the dynamic surface tension, and the surface elasticity are poor predictors of the effect of the surfactant on the flow.

A Probability Model for Fully Developed Annular Flow in Vertical Pipes: Film Thickness, Interfacial Shear Stress, and Droplet Size Distribution

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Ri Zhang ◽  
Haixiao Liu ◽  
Sheng Dong ◽  
Mingyang Liu
Keyword(s):  
Shear Stress ◽  
Film Thickness ◽  
Size Distribution ◽  
Droplet Size ◽  
Annular Flow ◽  
Probability Model ◽  
Interfacial Shear Stress ◽  
Droplet Size Distribution ◽  
Interfacial Shear ◽  
Characteristic Parameters

The movement and distribution of each phase in annular flow can be considered as random events at a microscopic level. Hence, a probability analysis is appropriate to estimate the morphological features and mechanical characteristics of annular flow from a macroscopic scale. In the present work, three characteristic parameters including the film thickness, interfacial shear stress, and characteristic droplet size are predicted by a probability model as the statistical results of abundant samples. The film thickness can be directly calculated as one of the solutions to the basic equations of annular flow. The interfacial shear stress is estimated as a combination of the frictional and dragging components. The droplet size distribution is obtained using a method of undetermined coefficients. These characteristic parameters are well verified by comparing with the experimental data available in the literature. It is demonstrated that the probability model can accurately calculate the film thickness and maximum droplet size, but the predictions of the interfacial shear stress and mean droplet size are relatively coarse. Furthermore, the effects on the film thickness and Sauter mean diameter of other parameters are discussed in detail. Finally, some important phenomena observed in experiments are interpreted by the probability model.

scholarly journals One-Dimensional Vacuum Steady Seepage Model of Unsaturated Soil and Finite Difference Solution

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Feng Huang ◽  
Jianguo Lyu ◽  
Guihe Wang ◽  
Hongyan Liu
Keyword(s):  
Finite Difference ◽  
Unsaturated Soil ◽  
Vacuum Pressure ◽  
Vacuum Field ◽  
One Dimensional ◽  
Steady Seepage ◽  
Basic Equations ◽  
The One ◽  
Seepage Law ◽  
Relationship Of

Vacuum tube dewatering method and light well point method have been widely used in engineering dewatering and foundation treatment. However, there is little research on the calculation method of unsaturated seepage under the effect of vacuum pressure which is generated by the vacuum well. In view of this, the one-dimensional (1D) steady seepage law of unsaturated soil in vacuum field has been analyzed based on Darcy’s law, basic equations, and finite difference method. First, the gravity drainage ability is analyzed. The analysis presents that much unsaturated water can not be drained off only by gravity effect because of surface tension. Second, the unsaturated vacuum seepage equations are built up in conditions of flux boundary and waterhead boundary. Finally, two examples are analyzed based on the relationship of matric suction and permeability coefficient after boundary conditions are determined. The results show that vacuum pressure will significantly enhance the drainage ability of unsaturated water by improving the hydraulic gradient of unsaturated water.

Experimental Study of DRA for Vertical Two-Phase Annular Flow

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
R. L. J. Fernandes ◽  
B. A. Fleck ◽  
T. R. Heidrick ◽  
L. Torres ◽  
M. G. Rodriguez
Keyword(s):  
Pressure Gradient ◽  
Drag Reduction ◽  
Production Rate ◽  
Annular Flow ◽  
Liquid Holdup ◽  
Two Phase ◽  
High Production Rate ◽  
High Production ◽  
Feasibility Test ◽  
Main Effects

Experimental investigation of drag reduction in vertical two-phase annular flow is presented. The work is a feasibility test for applying drag reducing additives (DRAs) in high production-rate gas-condensate wells where friction in the production tubing limits the production rate. The DRAs are intended to reduce the overall pressure gradient and thereby increase the production rate. Since such wells typically operate in the annular-entrained flow regime, the gas and liquid velocities were chosen such that the experiments were in a vertical two-phase annular flow. The drag reducers had two main effects on the flow. As expected, they reduced the frictional component of the pressure gradient by up to 74%. However, they also resulted in a significant increase in the liquid holdup by up to 27%. This phenomenon is identified as “DRA-induced flooding.” Since the flow was vertical, the increase in the liquid holdup increased the hydrostatic component of the pressure gradient by up to 25%, offsetting some of reduction in the frictional component of the pressure gradient. The DRA-induced flooding was most pronounced at the lowest gas velocities. However, the results show that in the annular flow the net effect will generally be a reduction in the overall pressure gradient by up to 82%. The findings here help to establish an envelope of operations for the application of multiphase drag reduction in vertical flows and indicate the conditions where a significant net reduction of the pressure gradient may be expected.

scholarly journals Marangoni Convection of Dust Particles in the Boundary Layer of Maxwell Nanofluids with Varying Surface Tension and Viscosity

Coatings ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 1072
Author(s):  
Khaled S. AlQdah ◽  
Naseer M. Khan ◽  
Habib Ben Bacha ◽  
Jae-Dong Chung ◽  
Nehad Ali Shah
Keyword(s):  
Surface Tension ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Dust Particles ◽  
Physical Parameters ◽  
Temperature Dependent Viscosity ◽  
Liquid Phases ◽  
Variable Surface ◽  
Basic Equations ◽  
Dependent Viscosity

The flow of nanofluids is very important in industrial refrigeration systems. The operation of nuclear reactors and the cooling of the entire installation to improve safety and economics are entirely dependent on the application of nanofluids in water. Therefore, a model of Maxwell’s dusty nanofluid with temperature-dependent viscosity, surface suction and variable surface tension under the action of solar radiation is established. The basic equations of momentum and temperature of the dust and liquid phases are solved numerically using the MATLAB bvp4c scheme. In the current evaluation, taking into account variable surface tension and varying viscosity, the effect of dust particles is studied by immersing dust particles in a nanofluid. Qualitative and quantitative discussions are provided to focus on the effect of physical parameters on mass and heat transfer. The propagation results show that this mixing effect can significantly increase the thermal conductivity of nanofluids. With small changes in the surface tension parameters, a stronger drop in the temperature distribution is observed. The suction can significantly reduce the temperature distribution of the liquid and dust phases. The stretchability of the sheet is more conducive to temperature rise. The tables are used to explain how physical parameters affect the Nusselt number and mass transfer. The increased interaction of the liquid with nanoparticles or dust particles is intended to improve the Nusselt number. This model contains features that have not been previously studied, which stimulates demand for this model among all walks of life now and in the future.

Possible Reason of the Dependence of an Apparent Permeability on the Pressure Gradient at low Flow Rates in Laboratory Study

2021 ◽  
Author(s):  
Nikolay Baryshnikov ◽  
Evgeniy Zenchenko ◽  
Sergey Turuntaev
Keyword(s):  
Pressure Gradient ◽  
Pore Pressure ◽  
Pore Space ◽  
Low Flow ◽  
Pressure Gradients ◽  
Apparent Permeability ◽  
Flow Rates ◽  
Rock Samples ◽  
Pore Pressure Gradient ◽  
Filtration Properties

<p>Currently, a number of studies showing that the injection of fluid into the formation can cause induced seismicity. Usually, it is associated with a change in the stress-strain state of the reservoir during the pore pressure front propagation. Modeling this process requires knowledge of the features of the filtration properties of reservoir rocks. Many researchers note the fact that the measured permeability of rock samples decreases at low pressure gradients. Among other things, this may be due to the formation of boundary adhesion layers with altered properties at the interfaces between the liquid and solid phases. The characteristic thickness of such layer can be fractions of a micron, and the effect becomes significant when filtering the fluid in rocks with a comparable characteristic pore size. The purpose of this work was to study the filtration properties of rock samples with low permeability at low flow rates. Laboratory modeling of such processes is associated with significant technical difficulties, primarily with the accuracy limit of measuring instruments when approaching zero speed values. The technique used by us to conduct the experiment and data processing allows us to study the dependence of the apparent permeability on the pore pressure gradient in the range of 0.01 MPa/m, which is comparable to the characteristic pressure gradients during the development of oil fields. In the course of the study, we carried out laboratory experiments on limestone core samples, during which the dependencies of their apparent permeability on the pore pressure gradient were obtained. We observed a significant decrease in their permeability at low flow rates. In the course of analyzing the experimental results, we proposed that a decrease in apparent permeability may occur due to the effect of even a small amount of residual gas in the pore space of the samples. This has been confirmed by additional experiments. The possibility of clogging of core sample pore space must be considered when conducting when conducting laboratory studies of the core apparent permeability.</p>

scholarly journals Investigation on Nonlinear Flow Behavior through Rock Rough Fractures Based on Experiments and Proposed 3-Dimensional Numerical Simulation

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-34
Author(s):  
Xianshan Liu ◽  
Man Li ◽  
Nandou Zeng ◽  
Tao Li
Keyword(s):  
Pressure Gradient ◽  
Friction Factor ◽  
Flow Behavior ◽  
Nonlinear Flow ◽  
Wall Friction ◽  
Cloud Data ◽  
3 Dimensional ◽  
Relative Roughness ◽  
Seepage Characteristics ◽  
Relationship Of

Rock fractures as the main flow channels, their morphological features, and spatial characteristics deeply influence the seepage behavior. Reservoir sandstones as a case study, four splitting groups of fractures with different roughness were scanned to get the geometric features, and then the seepage experiments were taken to analyze the relationship of the pressure gradient ∇ P and flow rate Q , and the critical Reynolds number( Re c ) and wall friction factor ( f ) were determined to explain the translation of linear seepage to nonlinear seepage condition. Based on the scanning cloud data of different rough fractures, the fractures were reconstructed and introduced into the COMSOL Multiphysics software; a 3-dimensional seepage model for rough fractures was calibrated and simulated the seepage process and corresponding pressure distribution, and explained the asymmetry of flow velocity. And also, the seepage characteristics were researched considering aperture variation of different sample fractures; the results indicated that increasing aperture for same fracture decreased the relative roughness, the fitting coefficients by Forchheimer formula based on the data ∇ P ~ Q decreased, and the figures about the coefficients and corresponding aperture described nonlinear condition of the above rough fractures. In addition, the expression of wall friction factor was derived, and relationship of f , Re , and relative roughness indicated that f increased with increasing fracture roughness considering the same aperture, resulting in nonlinear flow more easily, otherwise is not, showing that f could be used to describe the seepage condition and corresponding turning point. Finally, it can be seen from the numerical results that the nonlinearity of fluid flow is mainly caused by the formation of eddies at fracture intersections and the critical pressure gradient decreases with increasing angle. And also, analysis about the coefficient B in the Forchheimer law corresponding to fracture intersections considering the intersecting angle and surface roughness is proposed to reveal the flow nonlinearity. The above investigations give the theoretical support to understand and reveal the seepage mechanism of the rock rough fractures.

A critique: relationship of the time derivative of pressure to blood flow

1965 ◽  
Vol 20 (6) ◽  
pp. 1141-1147 ◽  
Author(s):  
Joseph C. Greenfield ◽  
Donald L. Fry
Keyword(s):  
Blood Flow ◽  
Pressure Gradient ◽  
Time Derivative ◽  
Fluid Motion ◽  
Electromagnetic Flowmeter ◽  
Analog Computer ◽  
Aortic Blood Flow ◽  
Pressure Derivative ◽  
Time Constants ◽  
Relationship Of

The relationship of the time derivative of pressure to instantaneous aortic blood flow was studied in six dogs. Pressure was measured with calibrated high-fidelity manometry and flow with an electromagnetic flowmeter. The true time constants of the equation of fluid motion (relating blood flow to the pressure gradient) were calculated and compared to the magnitude of time constants necessary to produce flow contours computed from the pressure time derivative that empirically “matched” flows measured by the electromagnetic flowmeter. It was found that time constants which produced acceptable “matching” were approximately 20 times too large. This observation demonstrated that 1) the time derivative of pressure is not proportional to the pressure gradient and 2) the similarity of measured and computed flows, using the pressure derivative, depends not on the laws of fluid motion but rather on the accidental similarity of the final form of the equation of fluid motion (with pressure derivative substituted for pressure gradient) to an empirical equation describing the hydraulic input impedance to the aorta. pressure gradient technique; blood velocity; analog computer Submitted on September 30, 1964

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