scholarly journals HYPERBOLIC DESCRIPTION OF CONTAMINATED FLOW THROUGH AN UNSATURATED WELLBORE

2007 ◽  
Vol 6 (1) ◽  
pp. 11
Author(s):  
M. L. Martins-Costa ◽  
R. M. Saldanha da Gama ◽  
J. H. Carneiro de Araujo
Keyword(s):  
Newtonian Fluid ◽  
Nonlinear Partial Differential Equations ◽  
Operator Splitting ◽  
Mixture Theory ◽  
Porous Matrix ◽  
Theory Approach ◽  
Splitting Technique ◽  
Two Fluids ◽  
Nonlinear Hyperbolic System ◽  
Solid Liquid

This work studies the flow of a mixture of two fluids – a Newtonian fluid and a pollutant – through a rigid cylindrical shell porous matrix. Aiming to build a preliminary local model for the flow of a Newtonian fluid containing a pollutant through a wellbore, a mixture theory approach is employed. The mixture consists of four overlapping continuous constituents: one solid (porous medium), one liquid (Newtonian fluid), the pollutant (solid, liquid or gas) and an inert gas included to account for the compressibility of the mixture as a whole. Assuming the flow on radial direction only, a set of three nonlinear partial differential equations describes the problem. Combining Glimm’s scheme with an operator splitting technique to account for the non-homogeneous part of the hyperbolic operator, the resulting nonlinear hyperbolic system is numerically approximated. Representative results illustrating the numerical methodology are presented.

Forced Convection Flow Through an Unsaturated Wellbore

2003 ◽  
Author(s):  
Maria Laura Martins-Costa ◽  
Roge´rio M. Saldanha da Gama
Keyword(s):  
Nonlinear Partial Differential Equations ◽  
Operator Splitting ◽  
Mixture Theory ◽  
Porous Matrix ◽  
Convection Flow ◽  
Theory Approach ◽  
Splitting Technique ◽  
Nonlinear Hyperbolic System ◽  
Implicit Finite Difference Scheme ◽  
Flow Through

This work studies the dynamics of the filling up of a rigid cylindrical shell porous matrix by a Newtonian fluid and the heat transfer associated phenomenon. A mixture theory approach is employed to obtain a preliminary local model for nonisothermal flows through a wellbore. The mixture consists of three overlapping continuous constituents: a solid (porous medium), a liquid and an inert gas included to account for the compressibility of the mixture as a whole. Assuming the convection flow on radial direction only, a set of four nonlinear partial differential equations describes the problem. Its hydrodynamic part — a nonlinear hyperbolic system — is approximated by means of a Glimm’s scheme, combined with an operator splitting technique, while an implicit finite difference scheme is used to simulate the thermal part.

Structural Integrity of Flexible Piping Systems Conveying Liquids

2005 ◽  
Vol 128 (3) ◽  
pp. 341-347 ◽  
Author(s):  
Felipe BastosFreitas Rachid
Keyword(s):  
Structural Integrity ◽  
Mathematical Problem ◽  
Nonlinear Partial Differential Equations ◽  
Operator Splitting ◽  
Piping System ◽  
Damage Growth ◽  
Splitting Technique ◽  
Structure Interaction ◽  
Piping Systems ◽  
Fast Transients

This work presents a structural integrity model for piping systems conveying liquids which takes the axial fluid-structure interaction into account. The model is used to numerically investigate the influence of pipe motion on the degradation of the piping when fast transients are generated by valve slam. The resulting mathematical problem is formed by a system of nonlinear partial differential equations which is solved by means of an operator splitting technique, combined with Glimm’s method. Numerical results obtained for an articulated piping system indicate that high piping flexibility may induce a substantial increase in damage growth along the pipes.

Dynamic model of dehydration melting motivated by a natural analogue: applications to the Ivrea–Verbano zone, northern Italy

1996 ◽  
Vol 87 (1-2) ◽  
pp. 23-31 ◽  
Author(s):  
Scott A. Barboza ◽  
George W. Bergantz
Keyword(s):  
Numerical Model ◽  
Mixture Theory ◽  
Mafic Magma ◽  
Northern Italy ◽  
Porous Media Flow ◽  
Theory Approach ◽  
Dehydration Melting ◽  
Porous Flow ◽  
Crustal Rocks ◽  
Switching Functions

ABSTRACT:Dehydration melting of crustal rocks may commonly occur in response to the intrusion of mafic magma in the mid- or lower crust. However, the relative importance of melt buoyancy, shear or dyking in melt generation and extraction under geologically relevant conditions is not well understood. A numerical model of the partial melting of a metapelite is presented and the model results are compared with the Ivrea-Verbano Zone in northern Italy. The numerical model uses the mixture theory approach to modelling simultaneous convection and phase change and includes special ramping and switching functions to accommodate the rheology of crystal-melt mixtures in accordance with the results of deformation experiments. The model explicitly includes both porous media flow and thermally and compositionally driven bulk convection of a restitecharged melt mass. A range of melt viscosity and critical melt fraction models is considered. General agreement was found between predicted positions of isopleths and those from the Ivrea-Verbano Zone. Maximum melt velocities in the region of porous flow are found to be 1 × 10−7 and 1 × 10−1m per year in the region of viscous flow. The results indicate that melt buoyancy alone may not be a sufficient agent for melt extraction and that extensive, vigorous convection of partially molten rocks above mafic bodies is unlikely, in accord with direct geological examples.

Water–mineral interaction in hygromechanics of clays exposed to environmental loads: a mixture-theory approach

1992 ◽  
Vol 29 (6) ◽  
pp. 1071-1086 ◽  
Author(s):  
Tomasz A. Hueckel
Keyword(s):  
Mass Transfer ◽  
Mixture Theory ◽  
Adsorbed Water ◽  
Theory Approach ◽  
Environmental Loads ◽  
Fluid Fraction ◽  
Effects Of Temperature ◽  
Dynamics Simulations ◽  
Experimental Findings ◽  
Mineral Interaction

Water–mineral interaction in narrow interstices (<30 Å (1 Å = 0.1 nm)) in dense, saturated clays is discussed in view of recent experimental findings and molecular dynamics simulations. Consequences to the macroscopic behavior are considered. A mixture theory for two interacting constituents is developed. Effects of temperature and chemicals are discussed. A postulate of mass transfer of adsorbed water from solid to fluid fraction caused by thermal or chemical load is then discussed. Theory of plasticity of clays affected by heat or chemicals is developed to deal with the effects of thermal and chemical consolidation. Key words : hydraulic conductivity, effective stress, environmental loads, thermo-chemo-plasticity.

Study of Blood Flow in Micro-Channels Using Mixture Theory

2014 ◽  
Author(s):  
Wei-Tao Wu ◽  
Nadine Aubry ◽  
James F. Antaki ◽  
Mehrdad Massoudi
Keyword(s):  
Blood Flow ◽  
Newtonian Fluid ◽  
Mixture Theory ◽  
Shear Thinning ◽  
Characteristic Size ◽  
Navier Stokes ◽  
Two Phase ◽  
Plasma Skimming ◽  
Micro Channels ◽  
Complex Phenomena

It is known that in large vessels (whole) blood behaves as a Navier-Stokes (Newtonian) fluid; however, in a vessel whose characteristic dimension (e.g., a diameter in the range of 20 to 500 microns) is about the same size as the characteristic size of the blood cells, blood behaves as a non-Newtonian fluid, exhibiting complex phenomena, such as shear-thinning, stress relaxation, the Fahraeus effect, the plasma-skimming, etc.. Using the framework of mixture theory an Eulerian-Eulerian two phase model is applied to model blood flow, where the plasma is treated as Newtonian fluid and the RBCs are treated as shear thinning fluid.[5]

EFFECT OF STENOSIS SEVERITY ON SHEAR-INDUCED DIFFUSION OF RED BLOOD CELLS IN CORONARY ARTERIES

2019 ◽  
Vol 19 (05) ◽  
pp. 1950034 ◽  
Author(s):  
ABDULRAJAK BURADI ◽  
SUMANT MORAB ◽  
ARUN MAHALINGAM
Keyword(s):  
Red Blood Cells ◽  
Blood Cells ◽  
Mixture Theory ◽  
Theory Approach ◽  
Newtonian Viscosity ◽  
Maximum Fluctuation ◽  
Stenosis Severity ◽  
Flux Model ◽  
First Time ◽  
Arterial Endothelial Cells

In large blood vessels, migration of red blood cells (RBCs) affects the concentration of platelets and the transport of oxygen to the arterial endothelial cells. In this work, we investigate the locations where hydrodynamic diffusion of RBCs occurs and the effects of stenosis severity on shear-induced diffusion (SID) of RBCs, concentration distribution and wall shear stress (WSS). For the first time, multiphase mixture theory approach with Phillips shear-induced diffusive flux model coupled with Quemada non-Newtonian viscosity model has been applied to numerically simulate the RBCs macroscopic behavior in four different degrees of stenosis (DOS) geometries, viz., 30%, 50%, 70% and 85%. Considering SID of RBCs, the calculated average WSS increased by 77.70% which emphasises the importance of SID in predicting hemodynamic parameters. At the stenosis throat, it was observed that 85% DOS model had the lowest concentration of RBCs near the wall and highest concentration at the center. For the stenosis models with 70% and 85% DOS, the RBC lumen wall concentration at the distal section of stenosis becomes inhomogeneous with the maximum fluctuation of 1.568%. Finally, the wall regions with low WSS and low RBC concentrations correlate well with the atherosclerosis sites observed clinically.

scholarly journals Encapsulation of Droplets Using Cusp Formation behind a Drop Rising in a Non-Newtonian Fluid

Fluids ◽  
2018 ◽  
Vol 3 (3) ◽  
pp. 54 ◽  
Author(s):  
Raphaël Poryles ◽  
Roberto Zenit
Keyword(s):  
Critical Velocity ◽  
Newtonian Fluid ◽  
Formation Process ◽  
Critical Size ◽  
Long Tail ◽  
Capillary Effects ◽  
Velocity Discontinuity ◽  
Two Fluids ◽  
Viscous Solution ◽  
Surrounding Liquid

The rising of a Newtonian oil drop in a non-Newtonian viscous solution is studied experimentally. In this case, the shape of the ascending drop is strongly affected by the viscoelastic and shear-thinning properties of the surrounding liquid. We found that the so-called velocity discontinuity phenomena is observed for drops larger than a certain critical size. Beyond the critical velocity, the formation of a long tail is observed, from which small droplets are continuously emitted. We determined that the fragmentation of the tail results mainly from the effect of capillary effects. We explore the idea of using this configuration as a new encapsulation technique, where the size and frequency of droplets are directly related to the volume of the main rising drop, for the particular pair of fluids used. These experimental results could lead to other investigations, which could help to predict the droplet formation process by tuning the two fluids’ properties, and adjusting only the volume of the main drop.

Accuracy of the Operator Splitting Technique for Two-Phase Flow With Stiff Source Terms

2002 ◽  
Author(s):  
Iztok Tiselj ◽  
Andrej Horvat
Keyword(s):  
Two Phase Flow ◽  
Fluid Model ◽  
Operator Splitting ◽  
Splitting Method ◽  
Water Hammer ◽  
Phase Flow ◽  
Hydraulic Systems ◽  
Source Terms ◽  
Two Phase ◽  
Splitting Technique

Code for analysis of the water hammer in thermal-hydraulic systems is being developed within the WAHALoads project founded by the European Commission [1]. Code will be specialized for the simulations of the two-phase water hammer phenomena with the two-fluid model of two-phase flow. The proposed numerical scheme is a two-step second-order accurate scheme with operator splitting; i.e. convection and sources are treated separately. Operator splitting technique is a very simple and “easy-to-use” tool, however, when the source terms are stiff, operator splitting method becomes a source of a specific non-accuracy, which behaves as a numerical diffusion. This type of error is analyzed in the present paper.

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