Showing papers on "Herschel–Bulkley fluid published in 1987"

A macroscopic description of multiphase flow in porous media involving spacetime evolution of fluid/fluid interface

Abstract: A macroscopic description of a two-phase flow in a porous medium is given by writing, firstly, mass and momentum-balance equations and, secondly, phenomenological equations derived from the theory of irreversible thermodynamic processes. The main results are as follows: (i) the law of capillary pressure is extended to dynamic conditions, (ii) an extended formulation of Darcy's law is established for each fluid phase and also for fluid/fluid interface which is considered as a phase of the system, and (iii) a coupling may appear between fluid phases.

Flow through Porous Media of a Shear-thinning Liquid with Yield Stress

Abstract: Darcy's law for the laminar flow of Newtonian fluids through porous media has been modified to a more general form which will describe the flow through porous media of fluids whose flow behavior can be characterized by the Herschel-Bulkley model. The model covers the flow of homogeneous fluids with a yield value and a power law flow behavior. Experiments in packed beds of sand were carried out with solutions of paraffin wax in two oils and with a crude oil from the Peace River area of Canada. The model fitted the data well. A sensitivity analysis of the fitting parameters showed that the model fit was very sensitive to errors in the flow behavior index, n, of the Herschel-Bulkley model. A comparison of the “n” values calculated from viscometer measurements and from flow measurements agreed well. A more general Reynolds number for flow through porous media, which includes a fluid yield value, was developed. The data were fitted to a Kozeny-Carman type equation using this Reynolds number. The constant in the Kozeny-Carman equation was determined for the two packed beds studied using Newtonian oils. The data could all be represented, within the experimental error, by the relationship f* = 150/Re*. Since the mean volume to surface diameter of the packing was determined by the measurement of its permeability to a Newtonian oil, assuming C' = 150, the new definition of the Reynolds number allows the direct use of the Kozeny-Carman equation with Herschel-Bulkley type fluids.

Thermal shaft effects on load-carrying capacity of a fully coupled, variable-properties cryogenic journal bearing

Abstract: The purpose of this work was to perform a rather complete analysis for a cryogenic (oxygen) journal bearing. The Reynolds equation required coupling and simultaneous solution with the fluid energy equation. To correctly account for the changes in the fluid viscosity, the fluid energy equation was coupled with the shaft and bearing heat conduction energy equations. The effects of pressure and temperature on the density, viscosity, and load-carrying capacity were further discussed as analysis parameters, with respect to relative eccentricity and the angular velocity. The isothermal fluid case and the adiabatic fluid case represented the limiting boundaries. The discussion was further extrapolated to study the Sommerfeld number dependency on the fluid Nusselt number and its consequence on possible total loss of load-carrying capacity and/or seizure (catastrophic failure).

Orientation and rheology of rodlike particles with strong Brownian diffusion in a second-order fluid under simple shear flow

Abstract: An analysis of orientation in a dilute suspension of rodlike macromolecules in a second-order fluid is presented and the effect of the elasticity of the fluid on the orientation of the suspended particles is examined. Distributions of particle orientation under a simple shear flow have been obtained for small β where β is the ratio of the intrinsic relaxation time of the fluid to the rotational relaxation time of the particle, the latter being inversely proportional to the Brownian rotation diffusion coefficient Dr of the particle. The parameter β represents also the ratio of the Weissenberg number of the fluid to the non-dimensional shear rate, g/Dr. An expression of the stress tensor of the suspension is derived and used in conjuntion with the orientation distribution to obtain the rheological properties of the mixture subjected to a simple shear.

A note of the fundamental dynamical flow characteristics of magnetic fluids. Comparison between simple shear and constant pressure gradient flows

Abstract: When a homogeneous magnetic field is applied parellel to the flow direction, physical quantities such as velocity, angular velocities of fluid and suspended particles, shear stress and pressure are theoretically obtained for two fundamental magnetic fluid flows i.e., a simple shear flow and a constant pressure gradient flow between two parallel plates, under the consideration of the diffusion effect of internal angular momentum on the basis of governing equations for a magnetic fluid, in which is used the constitutive equuation of magnetization proposed by the authors in the previous report. The fundamental dynamical flow characteristics of a magnetic fluid are comprehensively clarified by investigation of the differences which some dimensionless numbers (micropolar effect parameter, magnetic effect parameter, size effect parameter and so on) have on these two kinds of flow. Furthermore a limit of range for the wall surface coefficient when the applied magnetic fields exist is given.

Excitation of Van Kampen-case waves

Abstract: The response of a fluid with a shear flow having a slightly curved profile to an external vertical impact force, harmonic with respect to the horizontal coordinate and concentrated in a narrow layer, is calculated. The cases of an ideal and a viscous fluid are considered.

Non-Newtonian fluid flow in a reservoir - An application to hydraulic fracturing

Abstract: A formulation for the flow of a power law non-Newtonian fluid in a porous-permeable medium represented by a nonlinear partial differential equation is presented. This governing equation is transformed into a nonlinear ordinary differential equation whose solution is expanded as a Lie series. As an application to hydraulic fracturing, the problem of a Newtonian reservoir fluid being displaced by an injected non-Newtonian fluid is discussed. The resulting moving boundary problem is solved, resulting in explicit solutions for the respective pressure distributions and the displacement of the moving interface. The presented solutions provide a firm theoretical basis for fluid loss characterization in the porous-permeable reservoir.