Modeling of the Critical Deposition Velocity of Cuttings in an Inclined-Slimhole Annulus

SPE Journal ◽  
2017 ◽  
Vol 22 (04) ◽  
pp. 1213-1224 ◽  
Author(s):  
Baojiang Sun ◽  
Hengfu Xiang ◽  
Hao Li ◽  
Xiangfang Li
Keyword(s):  
Fluid Velocity ◽  
Deposition Velocity ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Parameter Design ◽  
Navier Stokes ◽  
Dispersed Particles ◽  
Continuum Equation ◽  
Coupling Algorithm ◽  
Good Agreement

Summary A coupled computational-fluid-dynamics/discrete-element-method (CFD/DEM) theory is developed to simulate the transportation of cuttings in an inclined-slimhole annulus. In this theory, the liquid phase is governed by the Eulerian continuum equation and the Navier-Stokes momentum-conservation equation. The collisions between particle and wall, between particle and drillstring, and among particles are treated as the spring-damping system, and the particle-contact model is then established. The particle-governing equation based on Newton's second law is established by analyzing the forces on the particles. The CFD/DEM theory is developed by analyzing the forces on the dispersed particles per unit volume, which is the source term in the coupling. Using this CFD/DEM coupling algorithm, cuttings transportation in slimhole drilling is investigated, and the particle velocity and distributions are calculated. The calculated annular cuttings concentration is in good agreement with experimental data from the literature (Kim et al. 2014). The effects of the annular-fluid velocity, angle of inclination, cuttings concentration in feeding, and rotation speed of the drillstring on the annular cuttings concentration are also investigated. A correlation of critical deposition velocity has been proposed by use of dimensional analysis and nonlinear regression analysis. The correlation of annular cuttings concentration is also concluded. The new method proposed in this work is of great significance to hole-cleaning calculation and hydraulic-parameter design in slimhole drilling.

Mathematical Modelling of Thermo-Hydro-Mechanical Behaviour for Concrete under Elevated Temperature

2014 ◽  
Vol 670-671 ◽  
pp. 355-364
Author(s):  
Shao Bo Zhang ◽  
Xiao Chun Wang ◽  
Xin Pu Shen
Keyword(s):  
Elevated Temperature ◽  
Stokes Equations ◽  
Constitutive Relations ◽  
Gaseous Mixture ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Energy Conservation Equation

A hydro-thermo-mechanical model was presented for concrete at elevated temperature. Three phases of continuum were adopted in this model: gaseous mixture of water vapor and dry air, liquid water, and solid skeleton of concrete. Mass conservation equations, linear momentum conservation equation, and energy conservation equation were derived on the basis of the macroscopic Navier-Stokes equations for a general continuum, along with assumptions made for the purpose of simplification. Mathematical relationships between selected primary variables and secondary variables were given with existing data from references. Specifications of the constitutive relations were made for the kinetic variables and their conjugate forces.

scholarly journals Development and stability of gyrotactic plumes in bioconvection

1999 ◽  
Vol 400 ◽  
pp. 1-31 ◽  
Author(s):  
S. GHORAI ◽  
N. A. HILL
Keyword(s):  
Continuum Model ◽  
Stokes Equations ◽  
Conservation Equation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Existence And Stability ◽  
Conservative Finite Difference Scheme ◽  
Micro Organisms ◽  
Good Agreement ◽  
The Continuum

Using the continuum model of Pedley, Hill & Kessler (1988) for bioconvection in a suspension of swimming, gyrotactic micro-organisms, we investigate the existence and stability of a two-dimensional plume in tall, narrow chambers with stress-free sidewalls. The system is governed by the Navier–Stokes equations for an incompressible fluid coupled with a micro-organism conservation equation. These equations are solved numerically using a conservative finite-difference scheme. In sufficiently deep chambers, the plume is always unstable to both varicose and meandering modes. A linear stability analysis for an infinitely long plume predicts the growth rates of these instabilities, explains the mechanisms, and is in good agreement with the numerical results.

Thermocapillary Convection of Low Prandtl Number Fluids under Uniform Magnetic Fields

2014 ◽  
Vol 580-583 ◽  
pp. 2970-2973 ◽  
Author(s):  
Ru Quan Liang ◽  
Di Bei ◽  
Fu Sheng Yan ◽  
Dian Qiao Geng
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Thermocapillary Convection ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Conservation Equation ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Constant Frequency ◽  
Energy Conservation Equation

Numerical simulations on thermocapillary convection of low Pr number molten tin under uniform magnetic field have been conducted under microgravity. The Navier-Stokes equations coupled with the energy conservation equation are solved on a staggered grid, and the free surface is captured by using the level set method. The present results show that the transverse uniform magnetic field can restrain the thermocapillary convection, and the fluid velocity at the hot corner fluctuates with a constant frequency at the steady state.

scholarly journals New Necessary Conditions for the Well-Posedness of Steady Bioconvective Flows and Their Small Perturbations

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 205
Author(s):  
Aníbal Coronel ◽  
Fernando Huancas ◽  
Alex Tello ◽  
Marko Rojas-Medar
Keyword(s):  
Weak Solutions ◽  
Flow Problem ◽  
Necessary Conditions ◽  
Fluid Velocity ◽  
Conservation Equation ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Small Perturbations ◽  
The Galerkin Method ◽  
Bioconvective Flow

We introduce new necessary conditions for the existence and uniqueness of stationary weak solutions and the existence of the weak solutions for the evolution problem in the system arising from the modeling of the bioconvective flow problem. Our analysis is based on the application of the Galerkin method, and the system considered consists of three equations: the nonlinear Navier–Stokes equation, the incompressibility equation, and a parabolic conservation equation, where the unknowns are the fluid velocity, the hydrostatic pressure, and the concentration of microorganisms. The boundary conditions are homogeneous and of zero-flux-type, for the cases of fluid velocity and microorganism concentration, respectively.

On the Streamwise Development of Density Jumps

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
A. Regev ◽  
S. Hassid
Keyword(s):  
Energy Conservation ◽  
Software Package ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Entrainment Ratio ◽  
Layer Height ◽  
Energy Conservation Equation ◽  
Linear Expression ◽  
Momentum Conservation Equation ◽  
Good Agreement

The analysis of density jumps in two-layer channel flows of miscible fluids controlled by a downstream obstruction, in which one of the layers is infinitely deep and at rest, is extended to consider the dependence of its features on its streamwise dimension. The momentum conservation equation in the entrainment and roller regions, and the energy conservation equation after the jump are corrected to account for friction. The streamwise coordinate is related to the increase in the density layer height through a linear expression derived from CFD calculations. Three regimes are distinguished: (1) for short distances from the origin to the obstruction, only an entrainment region exists; (2) for medium distances, two regions can be distinguished, i.e., the entrainment region, and the roller region, in which no entrainment is assumed; and (3) for long distances, three regions can be distinguished—the entrainment, the roller, and the postjump regions, characterized by approximate energy conservation. It is shown that initially the dimensionless total entrainment ratio increases as the distance to the obstruction increases, until a roller region appears. A further increase in distance to the obstruction does not have a significant effect on the total entrainment, until the appearance of a postjump region, resulting in a gradual decrease in the total entrainment. These results are supported by numerical calculations using the FLUENT CFD software package, which are in good agreement with experimental results.

Modelling of the Wall Jet in a Direct Injection Diesel Engine

1992 ◽  
Vol 206 (3) ◽  
pp. 185-196 ◽  
Author(s):  
J M Desantes ◽  
M Lapuerta ◽  
J M Salavert
Keyword(s):  
Diesel Engine ◽  
Initial Conditions ◽  
Direct Injection ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Wall Jet ◽  
Jet Interaction ◽  
Direct Injection Diesel Engine ◽  
Free Jet ◽  
Good Agreement

As a part of a phenomenological model, a method for simulating the wall/jet interaction in a direct injection diesel engine is proposed. The method is based on the application of the momentum conservation equation in the different directions in which the wall jet is spread, and takes into account both the interaction with the combustion chamber geometry and with swirl. It takes as initial conditions the results of calculating the free jet, which is divided into packages. The predictions provide good agreement with those by other researchers.

Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

Numerical Modeling of Evolution of Boundary Between Incompressible Gas and Liquid in Two-Dimensional Region

2006 ◽  
Vol 4 ◽  
pp. 224-236
Author(s):  
A.S. Topolnikov
Keyword(s):  
Numerical Modeling ◽  
Interphase Boundary ◽  
Incompressible Liquid ◽  
Stokes Equations ◽  
Numerical Code ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Incompressible Media ◽  
Good Agreement

The paper is devoted to numerical modeling of Navier–Stokes equations for incompressible media in the case, when there exist gas and liquid inside the rectangular calculation region, which are separated by interphase boundary. The set of equations for incompressible liquid accounting for viscous, gravitational and surface (capillary) forces is solved by finite-difference scheme on the spaced grid, for description of interphase boundary the ideology of Level Set Method is used. By developed numerical code the set of hydrodynamic problems is solved, which describe the motion of two-phase incompressible media with interphase boundary. As a result of numerical simulation the solutions are obtained, which are in good agreement with existing analytical and experimental solutions.

scholarly journals Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Navier Stokes ◽  
Dean Flow ◽  
Continuity Equations ◽  
Riemann Sum ◽  
Flow Formation

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

On the Flow Fields of Inertial Impactors

1974 ◽  
Vol 96 (4) ◽  
pp. 394-400 ◽  
Author(s):  
V. A. Marple ◽  
B. Y. H. Liu ◽  
K. T. Whitby
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Relaxation Method ◽  
Water Model ◽  
Navier Stokes ◽  
Visualization Technique ◽  
Navier Stokes Equations ◽  
Theoretical Results ◽  
Plate Distance ◽  
Good Agreement

The flow field in an inertial impactor was studied experimentally with a water model by means of a flow visualization technique. The influence of such parameters as Reynolds number and jet-to-plate distance on the flow field was determined. The Navier-Stokes equations describing the laminar flow field in the impactor were solved numerically by means of a finite difference relaxation method. The theoretical results were found to be in good agreement with the empirical observations made with the water model.

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