Showing papers on "Viscous fingering published in 1995"

Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches

Abstract: Part 1 Continuum versus discrete models: a hierarchy of heterogeneities and length scales long-range correlations, fractals and percolation continuum versus discrete models. Part 2 The equations of change: the equation of continuity the momentum equation the diffusion and convective-diffusion equations. Part 3 Fractal concepts and percolation theory: box-counting method and self-similar fractals self-affine fractals multifractal systems fractional Brownian motion and long-range correlations percolation processes a glance at history. Part 3 Diagenetic processes and formation of rock: diagenetic and metasomatic processes continuum models of diagenetic processes geometrical models of diagenetic processes in granular rock a geometrical model of carbonate rock diagenetic processes of fractured rock. Part 5 Morphology of porous media and fractured rock: porosity, specific surface area and tortuosity fluid saturation, capillary pressure and contact angle pore size distribution topological properties of porous media fractal properties of porous media porosity and pore size distribution of fractal porous media morphology of fractured rocks. Part 6 Models of porous media: models of macroscopic porous media models of pore surface roughness models of megascopic porous media interpolation schemes and conditional simulation. Part 7 Models of fractured rock: continuum approach - the multi-porosity models network models simulated annealing model synthetic fractal models mechanical fracture models. Part 8 Flow and transport in porous media: the volume-averaging method and derivation of Darcy's law the Brinkman and Forchheimer equations predicting the permeability, conductivity and diffusivity fractal transport and non-local formulation of diffusion derivation of Archie's law relation between permeability and electrical conductivity relation between permeability and nuclear magnetic resonance dynamic permeability. Part 9 Dispersion in porous media: the phenomenon of dispersion mechanisms of dispersion processes the convective-diffusion equation measurement of dispersion coefficients dispersion in simple systems dependence of dispersion coefficients on the Peclet number models of dispersion in macroscopic porous media long-time tails - dead-end pores versus disorder dispersion in short porous media dispersion in porous media with percolation disorder dispersion in megascopic porous media dispersion in stratified porous media. Part 10 Flow and dispersion in fractured rock: flow in a single fracture - continuum and discrete models flow in fractured rock dispersion in a single fracture dispersion in fractured rock. Part 11 Miscible displacements: factors affecting miscible displacement processes viscous fingering continuum models of miscible displacements in Hele-Shaw cells continuum models of miscible displacements in porous media. (Part contents).

Phenomenology and kinetics of lipid bilayer spreading on hydrophilic surfaces

Abstract: We studied the spreading of phospholipid bilayer membranes and the conditions for the formation of continuous bilayers on rough (glass, glass-MgF 2 , glass-MgF 2 -SiO 2 ) and smooth (mica) solids using reflection interference contrast microscopy as an analytical tool. We show that two fundamentally different spreading mechanisms are possible : (i) The sliding of a single bilayer on a thin lubricating water film and (ii) the rolling of thin lobes of two juxtaposed bilayers in a tank tread type motion. In the first mechanism the spreading velocity of straight interface exhibits a square root behavior, υ ∼ t 1/2 , allowing an estimate of the frictional coupling of the membrane to the substrate. On smooth surfaces (e.g., freshly cleaved mica) the dissipation is dominated by shear flow in the ultrathin water film separating the bilayer from the substrate. On rough surfaces in contrast (e.g., glass) friction is caused by two-dimensional flow of pinning centers through the spreading membrane. In the latter case the advancing front exhibits a self-similar interface roughness which grows with time. The growth of the roughness is analyzed, and a static roughness exponent ζ = 0.61 ± 0.04 is found. The rolling of membranes occurs on dehydrated solid-bilayerinterfaces with the substrate adjacent bilayer being immobilized. In this case a viscous fingering type spreading pattern is observed. From a practical point of view the rolling motion results in separated lipid patches with intermediate uncovered spots, while spreading by membrane sliding leads to continuous substrate-supported bilayers.

Fingering instabilities in vertical miscible displacement flows in porous media

Abstract: The fingering instabilities in vertical miscible displacement flows in porous media driven by both viscosity and density contrasts are studied using linear stability analysis and direct numerical simulations. The conditions under which vertical flows are different from horizontal flows are derived. A linear stability analysis of a sharp interface gives an expression for the critical velocity that determines the stability of the flow. It is shown that the critical velocity does not remain constant but changes as the two fluids disperse into each other. In a diffused profile, the flow can develop a potentially stable region followed downstream by a potentially unstable region or vice versa depending on the flow velocity, viscosity and density profiles, leading to the potential for ‘reverse’ fingering. As the flow evolves into the nonlinear regime, the strength and location of the stable region changes, which adds to the complexity and richness of finger propagation. The flow is numerically simulated using a Hartley-transform-based spectral method to study the nonlinear evolution of the instabilities. The simulations are validated by comparing to experiments. Miscible displacements with linear density and exponential viscosity dependencies on concentration are simulated to study the effects of stable zones on finger propagation. The growth rates of the mixing zone are parametrically obtained for various injection velocities and viscosity ratios.

Viscous Finger Widening with Surfactants and Polymers

Abstract: We study the viscous fingering instability which results from a competition between capillary and viscous forces. We show that for two different systems the instability is modified drastically by changing the surface tension or viscosity by means of surfactants or polymers. For both systems the width of the finger can increase with increasing velocity before settling at a plateau value larger than half the channel width. A numerical study shows that the large deviations from the classical result can be attributed to a velocity dependence of the dynamic interfacial tension and viscosity.

The effects of permeability heterogeneity on miscible viscous fingering: A three‐dimensional magnetic resonance imaging analysis

Abstract: The three‐dimensional evolution of the viscous fingering instability has been visualized directly with magnetic resonance imaging (MRI). Miscible displacement of thin solute bands by aqueous solvent was investigated in packed beds of 30 μm chromatographic particles. Fingering behavior into samples of glycerol and a protein, bovine serum albumin (BSA), with viscosity ratios ranging from 1 to approximately 4, were compared. The three‐dimensional morphology and dynamics of fingers were monitored to approximately millimeter spatial resolution using MRI. Linear and nonlinear fingering behavior were observed. Permeability heterogeneities with length scales on the order of the finger wavelength induced complex three‐dimensional fingering patterns. Sample and column boundary effects on fingering dynamics were also noted. The differences in fingering behavior observed between albumin and glycerol samples are consistent with the wavelength predictions of linear stability analysis and the large differences in molecu...

Viscous fingering in complex fluids

Abstract: Viscous fingers form when in a thin linear channel a fluid pushes a more viscous fluid. The instability of the interface results from a competition between viscous and capillary forces. We show here by acting on the viscosity or the surface tension by means of surfactants or polymers that the instability can be modified drastically. For the two different systems, unlike in the classical system, the width of the finger can go through a minimum and increases with increasing velocity before settling at a plateau value larger than half the channel width. A numerical resolution of the relevant hydrodynamic equations reveals that these large deviations from the classical result can be interpreted in terms of a velocity dependent dynamic interfacial tension for the surfactant system and viscosity for the polymer solution.

Thermo-viscous fingering of flow in a thin gap: a model of magma flow in dikes and fissures

Abstract: Flow of a fluid with a strongly temperature-dependent viscosity in a finite-length slot is analysed as a model of magma flow in dikes. The slot walls are held at a fixed temperature, thus cooling and increasing the viscosity of the fluid as it moves along the gap. Poiseuille flow and temperature advection, averaged across the slot, are used to study the stability of this basic one-dimensional flow to lateral perturbations. A linear stability analysis shows that for sufficiently strong cooling and viscosity increase with decreasing temperature, the flow is unstable to a fingering instability. Warm fluid is focused into relatively fast flowing zones and suffers only modest cooling, while cold, slow flowing regions experience more cooling and an increase in viscosity, which acts to locally clog the slot. The necessary condition for instability is the presence of multiple solutions for velocity (fast, intermediate and slow branches) in the basic one-dimensional flow. The intermediate branch, where the thermal adjustment lengthscale is comparable to the slot length, is unstable and the analysis indicates that the instability continues onto the slow branch. The parametric regions of instability and the growth rates are dependent on the choice of boundary conditions at the slot entrance (i. e. the magma source): either uniform flux, or uniform pressure. The latter case is the more geophysically realistic and has the larger unstable region and growth rates. Numerical solutions of the nonlinear equations show that at finite-amplitude the hot, low-viscosity, fast-flowing fingers continue to speed up, while the slow, cold regions continue to cool and slow down. At the slot exit fluid issues from the gap in isolated hot, low-viscosity spouts separated by zones of cold, nearly still fluid. Application of the model to geophysical settings indicates that the instability is expected for realistic parameter values. The model may help explain the observed focusing of fissure eruptions.

Fingering of Dense Nonaqueous Phase Liquids in Porous Media: 2. Analysis and Classification

Abstract: Fingering of dense nonaqueous phase liquids (DNAPLs) as seen in three-dimensional experiments with saturated, homogeneous porous media was analyzed. A consistent geometrical quantification of finger configurations was obtained using concepts of fractal and multifractal scaling. Fractal patterns that determine the probabilistic distribution of the DNAPL were found to be representative for every experimental combination of sand and DNAPL. These patterns could be attributed to either capillary or viscous fingering regimes. With multifractal formalisms we were able to give a description of the underlying process kinetics. The generalized dimension D{sub q} relates results to diffusion-limited aggregation (DLA) or invasion percolation type models. The spectrum of singularities f({alpha}) is invariable for cross sections of an experiment and in turn can be used for a classification of the displacement system. The width of the f({alpha}) curve in the range of positive moments quantifies displacement instability. Phase transitions are indicated for the more stable displacement systems. 36 refs., 7 figs.

Spreading of giant vesicles on moderately adhesive substrates by fingering: A reflection interference contrast microscopy study.

Abstract: The spreading of giant vesicles of neutral phospholipids on avidin-covered solid substrates is studied by reflection interference contrast microscopy. Contact formation, bilayer-substrate separation distances, and edge profiles are evaluated. The spreading occurs in two steps: advancement of lobes of average thickness \ensuremath{\approxeq}70 nm by fingering, sometimes followed by thinning to \ensuremath{\approxeq}30\ifmmode\pm\else\textpm\fi{}10 nm, determined by interfacial forces, and resulting in a pancakelike shape. The average advancement speed of the fingers appears constant at early times (\ensuremath{\approxeq}0.2 \ensuremath{\mu}m/s) and slows down at a later stage. Locally, the bilayer advances stepwise owing to discontinuous water expulsion. The spreading is impeded by pinning centers resulting in fjord formation. The vesicle spreading is tentatively interpreted in terms of the classical theory of viscous fingering.

The primary and inverse instabilities of directional viscous fingering

Abstract: Consider two infinitely long cylinders of different radii with one inside the other but off-centred. The gap between the two cylinders is partially filled with a viscous fluid. As the cylinders rotate with independent velocities U 1 and U 2 , a thin liquid film coats each of their surfaces all the way around except in the region where the viscous fluid completely fills the gap. Interface conditions that connect solutions of averaged equations in the viscous fluid region with solutions in the thin film region are derived. For the two-interface problem analysed here, two types of instabilities occur depending on the amount of viscous fluid between the cylinders. For large fluid volume, the primary supercritical instability occurs when the front interface becomes unstable as the cylinder velocities are increased. For small fluid volume, the back interface passes through the region where the gap width is a minimum to the same side as the front interface. Steady state solutions with straight interface edges exhibit a turning point with respect to the cylinder velocities. The back interface becomes unstable at the turning point; this inverse instability is subcritical.

A Renormalisation-Based Upscaling Technique for WAG Floods in Heterogeneous Reservoirs

Abstract: A novel and rapid upscaling procedure is described in which: (1) pseudo-functions are generated for each block in a coarse grid; (2) a renormalization method is used to calculate the pseudo-functions; (3) an empirical viscous fingering model is used to allow for fluid instabilities in unfavorable mobility ratio displacements. Oil recovery predictions are shown to agree well with conventional simulations made on the fine (geological model) grid for unstable, first-contact miscible WAG floods with a range of permeability distributions. In all cases, the result is an improvement (usually a substantial one) over a conventional coarse grid model in which only the absolute permeability of each block is upscaled.

Transition of viscous fingering patterns in polymer solutions

Abstract: Viscous fingering patterns of aqueous hydroxypropyl methyl cellulose (HPMC) solutions pushed by air in the Hele–Shaw cell were observed as a function of isopropyl alcohol content under a constant pressure of 15 cm H2O. A morphological transition from side branching patterns to tip splitting ones with increasing isopropyl alcohol content, accompanied with a decrease in surface tension and an increase in viscosity is found. The observed morphology transition was correlated with the dimension of the fingering pattern, as well as the average tip velocity in the fingering.

Dynamics of viscous fingers and threshold instability

Abstract: We present a detailed weakly nonlinear analysis, along with a solvability analysis, of an instability in viscous fingering which we term the surface-tension-driven instability. This instability occurs when the surface tension is modified in proportion to the local curvature. It is an intrinsically nonlinear instability which always requires a finite-amplitude perturbation to trigger it. It is also distinctively different from those arising via subcritical bifurcation. Numerical simulations reveal that this instability leads to spiky cellular patterns and may suggest a possibility of leading to a finite time singularity.

The evolution of radial fingering in a Hele-Shaw cell using C1 continuous Overhauser boundary element method

Abstract: An ideal porous medium can be created by a Hele-Shaw cell, a laboratory device consisting of two parallel plates of glass separated by a thin gap. In this cell, in the flow of two immiscible fluids, when a fluid of higher viscosity is displaced by a fluid of lower viscosity, the less viscous fluid is observed to form fingers into the more viscious one due to the unstable interface. The main interest in this process is to accurately capture the evolution of the interface which may be continuously deforming creating complex curvatures boundaries, hence making boundary element methods a suitable choice. The growth dynamics of radial viscous fingering in a Hele-Shaw cell has been simulated using boundary element method with C1 elements which have continuous representation of boundary geometry and variables. This type of shape function removes the instability that is encountered with C0 constant, linear and quadratic shape functions and allows one to simulate unsynmmetric and complicated patterns that may result due to the fingering phenomena. The results are compared with experimental and theoretical results.

Tree patterns on viscous paste surfaces

Abstract: A simple method for producing tree-like patterns on a layer of highly viscous paste is reported. The patterns are found to be fractal. A computer simulation reproduces the principal characteristics of the patterns fairly well. Such studies may provide insights into complex processes of viscous fingering and invasion percolation.

Saffman-Taylor fingers with anisotropic surface tension

Abstract: We have qualitatively explained the experiments of McCloud and Maher for the viscous fingering problem in which an anisotropy in the surface tension parameter was imposed by engraving a grid in one of the plates of the Hele-Shaw cell. We approached the problem in an analytical form by extending solvability theory to incorporate the effect of anisotropy. For the case in which the surface tension has a maximum at the finger tip, our theory provides two possible solutions: one corresponding to the solution of the isotropic case and a new solution which, below a threshold of the surface tension parameter, predicts a wider finger than the isotropic solution. Intuitivelt, we expect the “old” solution, namely the one that does not differ from the isotropic case, to be the selected solution for large values of the surface tension parameter and we expect the new solution to be selected for small values of the surface tension parameter. This was confirmed by dynamical simulations of the interface. The simulations predict that for the case in which the surface tension has a maximum at the finger tip, anisotropy is irrelevant for large values of the surface tension parameter. Furthermore, below a threshold in this surface tension parameter, the selected finger width is systematically wider than the corresponding isotropic case.

A new model to predict steam override and viscous fingering in heterogeneous oil reservoirs

Abstract: Early steam breakthrough, often observed in practice, is usually attributed to steam override. In the paper we address the question whether viscous fingering and/or channelling have an additional effect on the time of steam breakthrough. We have developed a pseudo 3-D mathematical model for steam drives that can handle steam override, viscous fingering and Channelling in 3-D heterogeneous reservoirs. The model incorporates gravity and viscous forces as well as heat losses to the cap and base rock. Capillary forces are not included. We use an interface approach where we decouple heat and mass transfer. We simplify by the vertical equilibrium approximation and reduce the model equations to 2-D. The ensuing model equations are solved by the probabilistic method proposed by King which is designed to model viscous fingering. The method allows 3-D evaluation of steam drive projects in heterogeneous reservoirs without the necessity for expensive fine grid three dimensional simulations. Example calculations for a thin medium-viscosity oil field show that heat losses have a stabilizing effect on the displacement process. They completely suppress viscous fingering and reduce steam override. For the homogeneous cases, poor steam drive recoveries occur due to strong override and cusping towards the production well, as a result of the pattern geometry. For the heterogeneous cases, the additional effect of channelling through high permeable zones occurs.

Effect of Wettability on Adverse Mobility Immiscible Floods

Abstract: Many immiscible displacements in reservoirs occur at adverse mobility. Effect of wettability on these displacements is not well understood and often ignored in reservoir simulation. Recent macroscopic theories of viscous fingering treat adverse immiscible flows similar to miscible flows, the mixing in the fingered region being controlled by a Todd-Longstaff-type functional form. The wettability of the medium is taken into account only through the use of appropriate relative permeabilities. The goal of this paper is to understand the macroscopic bypassing in adverse mobility immiscible floods. Immiscible displacements are conducted in a quarter 5-spot model in both drainage and imbibition modes at similar effective mobility ratios and viscous-to-gravity numbers. The level of bypassing and gravity override is visualized and measured. Tertiary water-alternating-gas (WAG) displacements are also conducted at various WAG ratios and viscosity ratios. Fractional flow analysis and numerical simulation are used to understand these displacements. Experiments show that macroscopic viscous fingering is present in adverse viscosity immiscible displacements where no saturation shock is expected from 1-D fractional flow theory. Bypassing due to both fingering and gravity override is higher in the drainage mode than in the imbibition mode, with other key parameters being the same. Optimum WAG ratio in water-wetmore » rock is a function of oil/solvent viscosity ratio. The macroscopic flow theory needs to include capillarity and viscous fingering to match these experimental findings.« less

Fractal nature of capillary and viscous fingering in two-dimensional porous media

Abstract: A computer model of capillary and viscous fingering in a porous media is presented, which treats the media as a square lattice connected with randomly chosen radius. The fractal properties of the model are studied for shell-shell aggregation method by Monte Carlo simulation. The simulation results show that the dimension D increases along with increasing of M and decreasing of mu, where M and mu are the ratios of the viscosity of the two fluids and the most probable radius of the throat in porous media respectively. It is found that there exist foul regions for fluid.

Steady states for viscous fingers with anisotropic surface tension.

Abstract: Pattern selection is considered for the case of viscous fingering in rectangular Hele-Shaw geometry in the presence of anisotropic surface tension, using solvability analysis and a boundary-integral method. We find that anisotropy introduced as a sinusoidal perturbation with a fourfold symmetry is irrelevant for small driving velocities and the usual steady-state finger width in the absence of the anisotropy is obtained. For sufficiently large driving velocities a new steady-state width is selected when the anisotropy makes the local interfacial tension a maximum at the finger tip. This is in agreement with recent experimental observations.