Immiscible Liquid-Liquid Displacement in Capillary Tubes

2005 ◽  
Vol 127 (1) ◽  
pp. 24-31 ◽  
Author(s):  
E. J. Soares ◽  
M. S. Carvalho ◽  
P. R. Souza Mendes

We analyze the liquid-liquid displacement in capillary tubes. The goal is to determine the amount of displaced liquid that remains attached to the tube wall and the configuration of the liquid-liquid interface at different operating parameters. The study encompasses both numerical and experimental approaches. The finite element method is used to solve the governing equations and, in order to validate the predictions, visualization experiments are performed to capture images of the interface. The numerical results were obtained for the assumption of negligible inertia, and the effects of viscosity ratio and capillary number are investigated. The predictions and experimental observations are in good agreement.

1966 ◽  
Vol 6 (03) ◽  
pp. 247-253 ◽  
Author(s):  
Necmettin Mungan

Abstract A study was made of the effects of wettability and interfacial tension the immiscible displacement of a liquid by another liquid for porous media. The influence of viscosity ratio was also investigated. Porous media used were polytetrafluoroethylene (TFE) cores prepared by compressing TFE powder under different pressures. It is shown that displacement of a wetting by a nonwetting liquid is always less efficient than the displacement of a nonwetting by a wetting fluid, all other things being equal. In the former case, the recovery efficiency can be increased substantially by either reducing the interfacial tension or increasing the viscosity of the displacing fluid. A qualitative discussion is given on the implications of this work to the recovery of crude oil by waterflooding. Introduction The high cost of oil exploration and new recovery schemes makes it imperative that waterflooding be conducted under conditions favoring most efficient oil recovery. To improve oil recovery by waterflooding, it is essential that the role played by interfacial forces in the entrapment of residual oil be studied and understood. Interfacial phenomena in natural rock, connate water and crude oil systems are very complicated because of the complexity of the natural liquids found in petroleum reservoirs, because of our inability to adequately describe the geometrical structure of the porous media and because of a lack of understanding of physical and chemical interactions between the liquids and surface of the pores. The problem becomes further complicated when one tries to elucidate the role of interfacial phenomena in fluid flow. Numerous studies of the displacement of oil by water under different interfacial tension or wettability conditions have been made. These studies have been performed in silica, alundum or sandstone systems using water and paraffin oil and also some surface active material to control the interfacial tension or and the contact angle. Unfortunately, the high energies of various interfaces involved favor adsorption and orientation of the surface active material at the intrafaces. Also the surface active material concentration at the interfaces exceeds that in the bulk of the liquid phases. Such surface excess may cause the surfactant distribution, the contact angle and the interfacial tension to differ from their measured static equilibrium values and makes interpretation of the displacement experiments difficult. Furthermore, as changes in also lead to changes in cos, the role played individually by one of these parameters in the displacement becomes obscured by the effect of the other. To circumvent these difficulties, a low surface energy solid and true solutions or pure liquids should be used. Use of a low surface energy solid minimizes adsorption and orientation effects at the solid-liquid interfaces. By controlling and cos through use of selected pairs of pure liquids or true solutions rather than by surfactants, the adsorption effects at liquid-liquid interfaces are eliminated. In the present study TFE cores were used as me porous media. Liquids used were water sucrose solutions, paraffin oils and benzyl, n-butyl and isobutyl alcohols. The interfacial tension was varied from 40 to 1.1 dynes/cm by suitably choosing the liquid pair. A surface above material was added to the water-oil system only in the case where interfacial tension of 0.5 dynes/ cm was desired. No precise changes of cos were attempted. However, either the displaced or the displacing liquid could be made the one which preferentially wets the TFE surface. Using sucrose solutions and blends of paraffin oils proved to be a convenient way of changing the viscosity ratio between the displaced and displacing liquids. The present investigation examines the effect of interfacial tension, wettability and viscosity ratio on the immiscible liquid-liquid displacement from porous media. SPEJ P. 217ˆ


2009 ◽  
Vol 641 ◽  
pp. 63-84 ◽  
Author(s):  
EDSON J. SOARES ◽  
RONEY L. THOMPSON

The motion of two immiscible liquids in a capillary tube is analysed, theoretically and numerically, for the case in which a residual film confines the displacing liquid to the core of this tube. The theoretical analysis has shown that the three flow regimes predicted by Taylor (J. Fluid Mech., vol. 10, 1961, pp. 161–165), for the case of gas-displacement, can only be achieved when the ratio of the viscosity of the displaced fluid to that of the displacing one is greater than 2. An elliptic mesh generation technique, coupled with the Galerkin finite-element method, is used to compute the velocity field and the configuration of the interface between the two fluids. A map of cases in the Cartesian space defined by the capillary number (Ca) and the viscosity ratio (Nμ) is constructed in order to locate the different flow patterns the problem exhibits. The critical capillary number at which the flow enters the transition range between the bypass regime and the full-recirculating one is given. While a decrease of the fraction of mass attached to the wall is achieved by decreasing Ca or increasing Nμ, bypass flow patterns are formed as a consequence of high values of the capillary number and viscosity ratio.


Author(s):  
Yuan Mao Huang ◽  
Chien Liang Li

A rotary sliding vane compressor was redesigned with extended rods on both edges of each vane and guide slots on both cover plates to improve its performance. The governing equations were derived to obtain loads acting on vanes and the stress of vanes. The finite element method is used with a generated computer program to determine the stress of vanes based on the calculated loads and the measured loads acting on the vanes. The results were compared and show good agreement with those obtained by using an existing software IDEAS.


1992 ◽  
Vol 20 (4) ◽  
pp. 230-253 ◽  
Author(s):  
T. Akasaka ◽  
K. Kabe ◽  
M. Koishi ◽  
M. Kuwashima

Abstract The deformation behavior of a tire in contact with the roadway is complicated, in particular, under the traction and braking conditions. A tread rubber block in contact with the road undergoes compression and shearing forces. These forces may cause the loss of contact at the edges of the block. Theoretical analysis based on the energy method is presented on the contact deformation of a tread rubber block subjected to compressive and shearing forces. Experimental work and numerical calculation by means of the finite element method are conducted to verify the predicted results. Good agreement is obtained among these analytical, numerical, and experimental results.


2021 ◽  
Vol 2 (3) ◽  
pp. 542-558
Author(s):  
Mohammadmehdi Shahzamanian ◽  
David Lloyd ◽  
Amir Partovi ◽  
Peidong Wu

The effect of the width to thickness ratio on the bendability of sheet metal is investigated using the finite element method (FEM) employing the Gurson–Tvergaard–Needleman (GTN) model. Strain path changes in the sheet with change in the width/thickness ratio. It is shown that bendability and fracture strain increase significantly by decrease in the width/thickness ratio. The stress state is almost uniaxial when the stress ratio (α) is close to zero for narrow sheets. Stress ratio is nothing but the major stress to minor stress ratio. This delays the growth and coalescence of micro-voids as the volumetric strain and stress triaxiality (pressure/effective stress) decrease. On the other hand, ductility decreases with increase in α for wider sheets. Fracture bending strain is calculated and, as expected, it increases with decrease in the width/thickness ratio. Furthermore, a brief study is performed to understand the effect of superimposed hydrostatic pressure on fracture strain for various sheet metals with different width/thickness ratios. It is found that the superimposed hydrostatic pressure increases the ductility, and that the effect of the width/thickness ratio in metals on ductility is as significant as the effect of superimposed hydrostatic pressure. Numerical results are found to be in good agreement with experimental observations.


2018 ◽  
Vol 82 (2) ◽  
pp. 21001
Author(s):  
Grzegorz Tytko ◽  
Leszek Dziczkowski

The paper examines the problem of an axially symmetric I-cored coil located above a three-layered plate with a hole in the middle layer. A cylindrical coordinate system was applied, wherein the solution domain was truncated in the radial direction. The employment of the truncated region eigenfunction expansion (TREE) method resulted in deriving the final formulas for the change of the coil impedance with regard to the air space, and also pertaining to the test object without a flaw. Formulas for various configurations of the test object, among others for a surface hole, a subsurface hole and a through hole, have been presented. For the purpose of defectoscopy, the influence of the hole in the plate on the impedance components was investigated. The calculations were made in Matlab for frequencies from 100 Hz to 50 kHz. The obtained results were verified using the finite element method (FEM) in Comsol Multiphysics package. A very good agreement was observed in the case of both the resistance and reactance.


Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2152
Author(s):  
Przemysław Czumaj ◽  
Sławomir Dudziak ◽  
Zbigniew Kacprzyk

The designers of civil engineering structures often have to face the problem of the reliability of complex computational analyses performed most often with the Finite Element Method (FEM). Any assessment of reliability of such analyses is difficult and can only be approximate. The present paper puts forward a new method of verification and validation of the structural analyses upon an illustrative example of a dome strengthened by circumferential ribs along the upper and lower edges. Four computational systems were used, namely Abaqus, Autodesk Robot, Dlubal RFEM, and FEAS. Different models were also analyzed—two-dimensional (2D) and three-dimensional (3D) ones using continuum, bar, and shell finite elements. The results of the static (with two kinds of load—self-weight and load distributed along the upper ring) and modal analyses are presented. A detailed comparison between the systems’ and models’ predictions was made. In general, the spatial models predicted a less stiff behavior of the analyzed dome than the planar models. The good agreement between different models and systems was obtained for the first natural frequency with axisymmetric eigenmodes (except from the Autodesk Robot system). The presented approach to the verification of complex shell–bar models can be effectively applied by structural designers.


2014 ◽  
Vol 30 (6) ◽  
pp. 603-609 ◽  
Author(s):  
C.-H. Huang ◽  
Y.-Y. Chen

AbstractIn this paper the transverse vibration characteristics of piezoceramic circular plates with V-notches are investigated theoretically through use of the Ritz's method incorporated with the defined equivalent constants. The Ritz's method is employed with two sets of admissible displacement functions, algebraic-trigonometric polynomials and corner functions, to guarantee convergence sufficiently and represent the stress singularity, respectively. Moreover, the equivalent constants derived by comparing the characteristic equations of transverse vibration between isotropic and piezoceramic disks are applied to suspend the electrical field consideration regarding the piezoelectricity. With the aid of theoretical analysis, the non-dimensional frequency parameters of transverse vibration modes for completely free V-notching circular plates are exhibited; in addition, the frequency variations depending on various notch angles and depths are explored. Numerical calculations using the finite element method (FEM) are performed and the results are compared with the theoretical analysis. It is shown that the resonant frequencies predicted by theoretical analysis and calculated by FEM are in good agreement.


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