K. A. Narayan

Squeezing flow between parallel plates

SummaryThe flow between two parallel plates (rectangular or circular) approaching or receding from each other symmetrically is analysed. The Xavier-Stokes equations have been transformed into an ordinary differential equation using a similarity transformation and the resulting equations are solved numerically. Results for the velocity components, pressure distribution and shearing stress on the wall are presented. In the case of squeezing flow between two circular plates the load supporting capacity of the upper plate has been calculated.ÜbersichtUntersucht wird die Strömung zwischen zwei parallelen Rechteck- bzw. Kreisplatten, die sich einander nähern oder entfernen. Die Navier-Stokes-Gleichungen werden durch eine Ähnlichkeitstransformation in eine gewöhnliche Differentialgleichung überführt. Die Lösung erfolgt numerisch. Ergebnisse für die Geschwindigkeitskomponenten, die Druckverteilung und die Wandschubspannung werden vorgestellt. Für die Quetschströmung zwischen zwei Kreisplatten wird die Tragkraft bestimmt.

Rise velocity of a swarm of spherical bubbles through a non-Newtonian fluid: Effect of zero shear viscosity

Happels free surface cell model has been combined with the equations of continuity and motion for the creeping motion of an ensemble of spherical bubbles through a generalized Newtonian fluid. The resultant equations have been solved approximately, using the variational principles, and upper and lower bounds to the drag force experienced by a swarm of bubbles have been obtained. Wide ranges of gas contents and non-Newtonian fluid parameters have been covered in this study. A method for estimating the rise velocity of a swarm of bubbles is also presented.

Creeping fluid flow relative to an assemblage of composite spheres

Abstract Incompressible creeping flow of a Neewtonian fluid relative to an assemblage of composite particles has been examined analytically. An individual particle iomposed of a solid sphere of radius a embeddd in a porous spherical shell of thickness ( b — a . The relevant governing equations have been combined with the well knoown free surface cell model of Happel to incorporate interparticle interactions of o the analysis. Detailed streamline patterns are presented embracing wide ranges of combinations of the size, thicknesss of porous region, permeability of porous medium, and concentration tf th suspension or assemblage. An analytical expression for the drag force experienced by the assemblage is also given.

A mathematical analysis of unsteady flow and heat transfer in a porous medium

Abstract The unsteady two-dimensional free convective flow through a porous medium bounded by an infinite vertical plate is considered when the temperature of the plate is oscillating with time about a constant nonzero mean. The problem is solved by developing two asymptotic expansions in powers of the frequency parameter ω. For small values of ω, a regular expansion is obtained, and for a large frequency parameter the method of matched asymptotic expansion is used. The effects of the frequency parameter ω, the permeability parameter K and the amplitude parameter ϵ on the velocity and the temperature fields are discussed.

Visualization of water and surfactant floods in oil-saturated porous media

The flow of water and 1% surfactant solution displacing oil through homogeneous and non-homogeneous porous media have been studied experimentally. The results are shown by taking the photographs of unstable interface at regular interval of time. These photographs suggest that the spreading of the moving interface in lateral direction is more for 1% surfactant solution displacing oil than for water displacing oil and also the interface is more stable for surfactant flooding in the bed. The wavelengths of viscous fingers measured from the experiments are found to be in good agreement with the theoretical predictions for homogeneous bed. The percentage oil recovery at breakthrough is improved considerably with the use of surfactant solution. Effect of flow rate on recovery and breakthrough time has also been studied. Finally, the effect of non-homogeneous packing on the growth of fingers has been studied by creating non-homogeneous medium in an otherwise homogeneous porous medium.

An experimental investigation of hydrocarbon recovery from a porous medium by continuous steam injection

Abstract Experiments were carried out to recover oils by steam flooding a previously waterflooded core maintained at room temperature (21 °C), 71.5 °C and steam temperature (143 °C), using continuous steam injection in an unconsolidated core containing oils of different viscosity, Primol, light paraffin and heavy paraffin, under varying heat loss conditions. In an actual petroleum reservoir, the injection of steam results in heat loss situations represented by all of the conditions used in this investigation on a stage-wise basis. Results indicate that the steamflood residual oil saturation is a highly variable quantity and any estimate of it must take into account the prevailing heat losses. The overall recoveries of Primol, light paraffin and heavy paraffin were found to be 62, 31 and 65% of the waterflood residual oil saturations.

An experimental study of the stability of displacement of a cold fluid by a hot fluid in a porous medium

Abstract The stability of non-isothermal flow through porous media is investigated experimentally when both density and viscosity are functions of temperature. The instability phenomena are due to the buoyancy effect of an upward-directed density gradient and to the fingering effect of the displacement of a more viscous fluid by a less viscous one. A series of centre-line temperatures in a packed column have been obtained where hot fluid displaces the same cold fluid (miscible thermal displacement) in a vertically upward direction. Based on these temperatures a stability criterion has been established in terms of Rayleigh number. Results are compared with available theoretical data.

Stability of miscible fluid displacement in a porous medium

SummaryThe stability of miscible fluid displacement through porous media has been investigated when concentration induced density and viscosity gradients are present. The dependence of Rayleighs number on the horizontal planform of cellular motion is established and it is shown that the Rayleigh and wave numbers interact in a nonlinear fashion and hence have to be treated as two independent parameters in the analysis of stability process.ÜbersichtUntersucht wird die Stabilität der Bewegung mischbarer Flüssigkeiten durch ein poröses Medium bei konzentrationsbedingten Dichte- und Viskositätsgradienten. Der Zusammenhang zwischen der Rayleigh-Zahl und der horizontalen Planheit der Zellbewegung wird aufgezeigt und nachgewiesen, daß die Rayleigh-und Wellenzahlen sich nichtlinear beeinflussen und folglich als zwei unabhängige Parameter der Stabilitäts-analyse zu betrachten sind.

Natural convection flow over a vertical frustum of a cone for constant wall heat flux

Laminar natural convection flow and heat transfer over a vertical frustum of a cone has been studied. The governing boundary layer equations are solved using local non-similarity method for constant wall heat flux. The local similarity and the local non-similarity two and three-equation models are constructed and the resulting equations are solved numerically. Results obtained from two and three-equation models are in good agreement. The numerical values of the flow and temperature functions required to calculate the surface skin friction and heat transfer rate are reported for various values of Prandtl numbers.

Mass transfer from a highly soluble single cylinder in parallel flow

This work deals with the study of mass transfer rates from single cylinders of oxalic, succinic and boric acids placed in parallel flowing water stream. Due to high dissolution rates of acids, the surface area of the cylinder is continually changing with time and cannot be assumed constant. The hydrodynamic regimes through which mass transfer takes place from a cylinder are divided into three regions: (i) transfer from the bottom surface of the cylinder; (ii) transfer from the lateral surface; and (iii) transfer from the top surface. In the present work, appropriate correlations have been obtained experimentally for each of these cases, together with the overall mass transfer. The predictive equations proposed herein enable calculation of the overall mass transfer coefficient in a new application with an acceptable level of accuracy.