Mecanisme de digitation visqueuse. Ecoulements de Hele Shaw. Deplacements non miscibles en cellules de Hele Shaw

Viscous fingering in porous media

In this paper, theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible and immiscible displacement processes in reservoir rocks are reviewed and discussed. Both macroscopically homogeneous and heterogeneous rocks are considered. The latter are characterized by large-scale spatial variations and correlations in their effective properties and include rocks that may be characterized by several distinct degrees of porosity, a well-known example of which is a fractured rock with two degrees of porosity---those of the pores and of the fractures. First, the diagenetic processes that give rise to the present reservoir rocks are discussed and a few geometrical models of such processes are described. Then, measurement and characterization of important properties, such as pore-size distribution, pore-space topology, and pore surface roughness, and morphological properties of fracture networks are discussed. It is shown that fractal and percolation concepts play important roles in the characterization of rocks, from the smallest length scale at the pore level to the largest length scales at the fracture and fault scales. Next, various structural models of homogeneous and heterogeneous rock are discussed, and theoretical and computer simulation approaches to flow, dispersion, and displacement in such systems are reviewed. Two different modeling approaches to these phenomena are compared. The first approach is based on the classical equations of transport supplemented with constitutive equations describing the transport and other important coefficients and parameters. These are called the continuum models. The second approach is based on network models of pore space and fractured rocks; it models the phenomena at the smallest scale, a pore or fracture, and then employs large-scale simulation and modern concepts of the statistical physics of disordered systems, such as scaling and universality, to obtain the macroscopic properties of the system. The fundamental roles of the interconnectivity of the rock and its wetting properties in dispersion and two-phase flows, and those of microscopic and macroscopic heterogeneities in miscible displacements are emphasized. Two important conceptual advances for modeling fractured rocks and studying flow phenomena in porous media are also discussed. The first, based on cellular automata, can in principle be used for computing macroscopic properties of flow phenomena in any porous medium, regardless of the complexity of its structure. The second, simulated annealing, borrowed from optimization processes and the statistical mechanics of spin glasses, is used for finding the optimum structure of a fractured reservoir that honors a limited amount of experimental data.

Flow phenomena in rocks : from continuum models to fractals, percolation, cellular automata, and simulated annealing

Viscoelastic instabilities are of practical importance, and are the subject of growing interest. Reviewed here are the fresh developments as well as earlier work in this area, organized into the following categories: instabilities in Taylor-Couette flows, instabilities in cone-and-plate and plate-and-plate flows, instabilities in parallel shear flows, extrudate distortions and fracture, instabilities in shear flows with interfaces, instabilities in extensional flows, instabilities in multidimensional flows, and thermohydrodynamic instabilities. Emphasized in the review are comparisons between theory and experiment and suggested directions for future work.

Instabilities in viscoelastic flows

This paper summarizes the field of static mixers including recent improvements and applications to industrial processes. The most commonly used static mixers are described and compared. Their respective advantages and limitations are emphasized. Efficiencies of static mixers are compared based both on theory and experimental results from the literature. The operations, which can benefit from the use of static mixers, are explored, namely, mixing of miscible fluids, liquid–liquid and gas–liquid interface generation, liquid–solid dispersion and heat transfer. Design parameters governing the performance of the various mixers in these applications are reported. The key parameters needed for the selection of a suitable mixer are highlighted.

Static Mixers in the Process Industries—A Review

Steps of membrane blocking in flux decline during protein microfiltration

Two- and three-dimensional boundary-layer equations have been developed for pseudoplastic non-Newtonian fluids which can be characterized by a power-law relationship between shear stress and velocity gradient. The types of potential flows necessary for similar solutions to the boundary-layer equations have been determined. For two-dimensional flow the results are similar to those obtained for Newtonian fluids. For three-dimensional flow, however, the possibility of similar solutions depends on the nature of the expression which describes effective viscosity of the fluid. At most, similar solutions are possible only for the case of flow past a flat plate where the potential velocity vector is not perpendicular to the leading edge of the plate; this is a much more restrictive condition than is obtained for Newtonian fluids.

The application of boundary-layer theory to power-law pseudoplastic fluids: Similar solutions

Trajectories have been computed for two equal sized spherical particles in simple laminar shearing and in uniaxial extensional flows. Effects of interparticle attraction, electrostatic repulsion, and hydrodynamics were included.

The results are pertinent to questions of colloidal stability under various conditions of flow. Particulate dispersions can react in several different ways as the intensity of shearing is increased from zero: the dispersion can remain stable; it can be redispersed, if it had been initially flocculated into a weak secondary minimum in the interparticle potential curve; it can be flocculated into a strong primary minimum in the potential curve; or, in extreme cases, it can be redispersed from the primary minimum. Results are presented which illustrate criteria for flocculation or stability to both laminar shearing and extensional flow. It is shown that hydrodynamic effects can significantly alter the criteria developed for stability of dispersions to Brownian coagulation.

Use of trajectory analysis to study stability of colloidal dispersions in flow fields

An iteration technique has been developed to solve the equations of motion for flow of an incompressible Newtonian fluid through circular tube with a radius which varies sinusoidally in the axial direction. The iteration is essentially geometric; one proceeds from a solution for flow through a tube in which the waveleneth of diameter chance in the axial direction is

Flow through tubes with sinusoidal axial variations in diameter

A tube with sinusoidal axial variations in diameter has been used as a first step toward modeling the flow channels of a porous medium in such a way that appreciable Lagrangian unsteadiness is present. Experiments with dilute aqueous solutions of a polyacrylamide (Dow Separan AP-30) show that the Lagragian unsteadiness gives rise to an increase in resistance to flow through the sinusoidal channel relative to that predicted for a purely viscous fluid. The increase in pressure drop can occur as a consequence of fluid elasticity, without any observable secondary flow. At sufficiently high flow rates, secondary flow appears. 20 references.

W. R. Schowalter

Papers

The application of boundary-layer theory to power-law pseudoplastic fluids: Similar solutions

Use of trajectory analysis to study stability of colloidal dispersions in flow fields

Flow through tubes with sinusoidal axial variations in diameter

Modeling the flow of viscoelastic fluids through porous media

Behavior of non-Newtonian fluids in the entry region of a pipe