Showing papers on "Viscous fingering published in 1987"

Viscous fingering in porous media

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

Radial viscous fingering patterns in Hele-Shaw cells

Abstract: Viscous fingering experiments were performed by injecting a liquid to radially displace a much more viscous liquid in a Hele-Shaw cell consisting of two parallel closely-spaced glass plates. Both smooth and etched plates were used to study the influence of plate roughness on the fingering mechanism. Effect of flow rate and interfacial tension was also demonstrated. The results show that symmetric dendritic finger patterns can form in the presence of anisotropy provided by an etched square network, for both miscible and immiscible fingers. Chaotic finger patterns can form both in a cell with smooth surfaces and in one having a network of randomly oriented channels etched on one plate. Due to interfacial tension, the immiscible finger patterns are less ramified than their miscible counterparts, are more sensitive to the flow rate and become compact as the flow rate decreases. Possible applications of two-phase displacement studies in Hele-Shaw cells are discussed, which include two-phase flow in porous media and acid fracturing of oil reservoirs.

Experimental and Theoretical Study of Polymer Flow in Porous Media

Abstract: In this paper, an extensive study is presented on the single-phase flow of xanthum/tracer slugs in a consolidated sandstone. The phenomena studied include polymer/tracer dispersion, excluded/inaccessible-volume effects, polymer adsorption, and viscous fingering. In some floods, there is also evidence of nonequilibrium effects. Macroscopic flow equations are derived that include terms to model all the behaviors listed above. A microscopic approach is also developed that describes certain features of polymer flow in porous media semiquantitatively.

Viscous fingering in liquid crystals

Abstract: We have studied the Saffman-Taylor instability in a Hele-Shaw cell containing the nematic liquid crystal 4,4'-n-octylcyanobiphenyl (8CB). Air injected into the center of the cell gives rise to viscous fingering patterns, which show a sequence of dense-branching, dendritic, dense-branching morphologies as a function of temperature. A qualitative explanation of these morphological transitions is given in terms of the flow alignment of the director field and the resulting anisotropic viscosity in the nematic phase of the liquid crystal. The fingering patterns were digitized; analysis of the resulting data shows that while the perimeter of the pattern is fractal, the pattern itself is not. The extent to which the pattern is space filling depends on the morphology and this quantity may serve to indicate the morphological transitions.

The fractal nature of viscous fingering in porous media

Abstract: Viscous fingering in porous media is an instability which occurs when a less viscous fluid displaces a more viscous one. An interface between the fluids is unstable against small perturbations and gives rise to a fingered configuration. In the oil industry viscous fingering can be a serious problem when displacing viscous oil by a more mobile fluid because it leads to poor recovery of the hydrocarbon. Recent work suggests an analogy between viscous fingering at an infinite viscosity ratio and diffusion-limited aggregation (DLA) and hence that the fingers may be fractal with a fractal dimension of around 1.7 (in two dimensions). This leaves unanswered the question of the nature of the fingered patterns at a finite viscosity ratio. To answer this a network model of the porous medium has been used. The rock is modelled as a lattice of capillary tubes of random radius through which miscible displacement occurs. At a high viscosity ratio and in the presence of a large amount of disorder the model reproduces DLA fingering patterns. The results of this model provide evidence that at a finite viscosity ratio the displaced area is compact with a surface fractal dimension between 1 and a DLA result of 1.7 with increasing viscosity ratio.

Viscous fingering with imposed uniaxial anisotropy.

Abstract: We study viscous fingering in the radial Hele-Shaw cell with a set of parallel grooves on one of the plates in order to obtain the morphological phase diagram of a system with imposed uniaxial anisotropy. Varying the pressure of air injected into glycerin and the distance between the plates, a rich variety of phases can be obtained corresponding to all of the possible combinations of stable or splitting tips in directions parallel and perpendicular to the grooves. We demonstrate that the effective anisotropy governing the stability of the tips is a result of a complex interplay between the local anisotropy and the driving force.

Viscous fingering on percolation clusters

Abstract: The physical phenomena that occur when a low-viscosity fluid is forced into a high-viscosity one, inside a porous medium (e.g. water pushing oil in a rock), are clearly of much practical interest. These phenomena became the center of much recent scientific interest when it was realized that under some conditions flow instabilities yield viscous fingers (VF) [1,2,3], that are fractal [4,5,6. Fractals are self-similar objects, which look the same at different magnifications [7].

Stability of viscous fingering patterns in liquid crystals.

Abstract: We present experimental data of viscous fingering patterns in a radial Hele-Shaw cell filled with the liquid crystal 4,4\ensuremath{'}-$n$-octylcyanobiphenyl (8CB) We observe a dense-branching-dendritic-dense-branching morphological phase sequence as a function of temperature The wave number of the fastest growing mode can be selected by varying experimental parameters, and the number of initially growing fingers on a circular interface is in good agreement with linear-stability analysis which includes the full kinetic term A mechanism is proposed for tip stabilization by anisotropic viscosity; the critical viscosity ratio for circular tips is \ensuremath{\simeq}2

Viscous fingering simulated by off-lattice aggregation

Abstract: An off-lattice version of the diffusion-limited aggregation model is used to simulate pattern formation in viscous flows. The patterns generated are very similar to those obtained in the experiments on fingering in the radial Hele Shaw cell. We find a crossover from compact to fractal structure as the length scale is increased. The effective fractal dimension of dusters obtained for low values of a parameter corresponding to the surface tension is about 1.74, which is dose to that of the diffusion-limited aggregates.

Quantitative test of solvability theory for the Saffman-Taylor problem.

Abstract: We report on a quantitative test of solvability theory in the case of pattern selection for viscous fingering in a rectangular Hele-Shaw cell. We construct an effective two-dimensional theory that properly takes into account the effect of film draining. In the parameter range where the theory is applicable we find excellent agreement between our predictions and the experimental data. This provides the first precise, quantitative assessment of microscopic solvability in a physical system.

Viscous fingering in a smectic liquid crystal

Abstract: To study the effects of a driving force on interfacial-pattern formation, we introduce a novel experimental system, a radial Hele-Shaw cell with nitrogen injected into a smectic liquid crystal. In the absence of initial alignment of the molecules a cross-over can be observed: the effective fractal dimension of the pattern changes from the value D ≈ 1.6 (low pressures) to D ≈ 2 (high pressures). If an external magnetic field is applied to achieve uniaxial ordering, a dramatic change in the direction of the easy growth takes place as a function of the increasing pressure. The results are discussed in terms of the internal structure of smectics.

The relationship between immiscible and miscible displacement in porous media

Abstract: Displacement processes in porous media share several common characteristics. Fundamental among them is the representation of the momentum balance via Darcy’s law and its multiphase extension (Bear, 1972). Such description leads to systems of equations the solution of which parallels the behavior of the solution of processes in multicomponent chromatography. For instance, it has been recognized that noncapillary, multiphase displacement in one-dimensional (rectilinear or radial) porous media can be solved by techniques identical to those used in chromatographic transport (Helfferich, I98 I; Rhee et al., 1986, and references therein). This similarity arises naturally for the case of one-dimensional flow geometries and in the absence of dissipative terms (diffusion, dispersion, or capillarity), where both multiphase and multicomponent chromatography processes are formulated by systems of first-order hyperbolic equations. In this note we pursue further this relationship in mathematical representation between multiphase flow and chromatographic processes in porous media. Specifically, we consider two-phase, immiscible displacement and single-phase, miscible displacement in the presence of equilibrium adsorption. It is demonstrated that the two problems are mathematically equivalent, regardless of the dimensionality of the flow system and the presence of dissipative effects. Such an analogy is of practical importance in the analysis of various process characteristics, for instance in describing the evolution of unstable two-dimensional disturbances during viscous fingering. The latter is a topic of active current investigations (Homsy, 1987, and references therein), and of fundamental importance in process performance. Any similarities between seemingly different processes would be of considerable help in an effort to reduce complexity and to uncover common mechanisms. An extension to multiphase immiscible displacement and multicomponent miscible displacement is also briefly discussed. Mathematical Description

Role of fluctuations in viscous fingering and dendritic crystal growth: a noise-driven model with non-periodic sidebranching and no threshold for onset

Abstract: A noise-driven model is developed to describe the role of fluctuations in side- branch phenomena in growth patterns for the fluid displacement problem and for dendritic crystal growth. Simulation results are compared with recent experiments on NH,Br den- drites. It is found that the RMS sidebranch amplitude is an exponential function of distance from the tip, with no apparent onset threshold. Moreover, the sidebranches are non-periodic (at all distances from the tip) with apparently random variations in amplitude. What is the physical mechanism whereby sidebranches 'spontaneorrsly' appear a short distance behind the growing tip of a dendritic form? For generations, this question has fascinated scientists in a variety of fields, ranging from metallurgy and crystal growth on the one hand to botany and embryology on the other. Recently interest has focused on extremely simple systems that spontaneously develop sidebranches. It has been found that, when a low-viscosity fluid displaces a high-viscosity anisotropic fluid under pressure, a sidebranch pattern develops that resembles dendritic crystal growth. For example, Buka et a1 (l) use air to displace a viscous solution of a nematic liquid crystal. The anisotropy can also be in the medium itself. Horvath er a1 (2) have shown that a single scratch in one wall of the confining Hele-Shaw cell is sufficient to produce a dendritic pattern. Similarly, Ben-Jacob et a1 (3) find dendritic fluid patterns when they scratch a triangular lattice onto the cell. Most surprising, perhaps, is the observa- tion of Couder et af (4) that dendritic growth patterns can occur when the anisotropy is provided by a simple bubble of air on the tip of the growing viscous finger. Can these similarities between diverse systems be understood in terms of underlying physical principles common to all? Here we tentatively suggest a physical model that seems to account for such sidebranch phenomena. Although fluid displacement phenomena are striking, a larger number of quantitative results is known for dendritic crystal growth. Hence we shall focus attention on the latter. In paiticular, Dougherty et a1 (5) have recently made a detailed analysis of photographs of growing NH4Br dendrites, taken at 20s intervals. They have found three surprising results: (i) sidebranch positions are non-periodic at any distance from the tip, with almost random variations in both phase and amplitude, (ii) sidebranches on opposite sides of the dendrite are essentially uncorrelated in position and length and (iii) the sidebranch amplitude is an exponential function of distance from the tip, with no apparent onset threshold distance.

Dynamics and Structure of Viscous Fingers in Porous Media

Abstract: The displacement of a high viscosity fluid by a low viscosity fluid in a porous medium is a process of both scientific and practical importance. It has recently been shown by Chen and Wilkinson1 and by Maloy et al.2 that viscous fingering in a random porous medium at high capillary numbers, Ca > >10−4, generates structures with a fractal3 geometry. This fractal structure closely resembles that obtained from the diffusion limited aggregation (DLA) model of Witten and Sander4. Similar structures have also been obtained by fluid-fluid displacement in radial HeleShaw cells using non-Newtonian viscous fluids5. The relationship between fluid-fluid displacement in porous media and DLA was first discussed by Paterson6 and a more detailed analysis has been presented by Kadanoff7.

Computer image processing: A new tool for studying viscous fingering in corefloods

Abstract: Computer image processing technology was used to study the pattern of viscous fingering in laboratory corefloods. The fingering patterns in unstable immiscible corefloods were captured and photographed with the aid of a fluorescent dye. The photographs were digitized and stored as computer image files for subsequent processing. A program was written to count the fingers, to determine their sizes, to compute the sweep efficiencies at the core cross sections, and to determine the frequency contents of the fingering patterns. The frequency contents were used in conjunction with stability theory to estimate the effective interfacial tension (IFT) required for calculating the stability numbers of the floods. Results show that computer image processing technology can be used to study the performance of laboratory corefloods quantitatively.

Pore‐scale difference between miscible and immiscible viscous fingering in porous media

Abstract: When one fluid displaces another in a porous medium, the displacement can be stable or unstable. Viscous fingering is an unstable phenomenon that occurs when a less viscous fluid displaces a more viscous one. During oil recovery viscous fingering results in a poor recovery due to the bypass of the resident oil by the displacing fluid. In an oil reservoir there is randomness of many different length scales, ranging from pore size to reservoir size. Viscous fingering can have many different length scales due to the randomness. It is important to understand how the randomness on different scales affects the development of fingering. In this note the authors report experiments on the displacement stability in two-dimensional network models of porous media. The purpose of this work is to better understand the pore-scale phenomena of displacement. Immiscible viscous fingering in a two-dimensional network model, with negligible effects of the interfacial tension, has been studied. Although qualitative agreement was found between simulations and experiments for the immiscible case, some fundamental difference was found for the miscible case. The cause of difference and other relevant experimental observations are discussed.

Diffusion-limited aggregation with radial bias

Abstract: The authors introduce radial bias into off-lattice diffusion-limited aggregation in order to simulate radial anisotropy present in experiments on viscous fingering in liquid crystals. For large cluster sizes the model is also expected to provide information about the asymptotic shape of the ordinary off-lattice diffusion-limited aggregates. They find that for large enough radial bias the overall shape of the clusters becomes star-like with a spontaneously selected number of main arms which is either four, or less frequently five. The crossover to this structure is accompanied by a change in the radius of gyration exponent which approaches the value 1.5 previously observed for systems with axial anisotropy or very large clusters grown on the square lattice.

Formation of Interfacial Patterns in Aggregation and Viscous Flows

Abstract: Computer simulations and experiments on viscous fingering are used to investigate the effects of fluctuations, driving force and anisotropy on the growth of two dimensional unstable interfaces. It is demonstrated that variations of the diffusion-limited aggregation model capture many of the most important features of Laplacian pattern formation. In the viscous fingering experiments carried out in a radial Hele-Shaw cell with nematic or smectic liquid crystals a number of unexpected morphological phase transitions can be observed including crossovers from tip splitting to dendritic growth and from fractal to homogeneous structures. The investigations reviewed here suggest that the role of noise, driving force and anisotropy is crucial in the formation of patterns and it is the complex interplay of these factors which produces the great variety of morphologies found in nature.

Studies of Critical Gas Saturation During Gas Injection

Abstract: Results of studies of critical gas saturation in a long, porous medium have been compared with those obtained in a short system. In general, the relationship of rate vs. critical gas saturation for gas flow into an oil-saturated core can be divided into two regions in which capillary forces and viscous forces govern flow, respectively. At low gas injection rates (below about 10/sup -3/ cm/sup 3//cm/sup 2/ . s (0.39 x 10/sup -3/ in./sup 3//in./sup 2/-sec) for oil of 1.4-mPa . s (1.4-cp) viscosity), capillary processes govern distribution of the gas and result in increasing critical gas saturation as the flow rate is increased from very low values. At high injection rates, viscous forces become prominent and result in very low critical gas saturation, probably as a result of viscous fingering. In a long system, the saturation distribution includes high gas saturation values (>8%) near the inlet end and low values (-- 2%) near the outlet. The latter are the critical gas saturation. For the case of 1.4-mPa . s (1.4-cp) oil in a short core, the increase of fingering with increasing flow rate produces more regions of low gas saturation. This tends to counterbalance the increase in saturation occurringmore » because of capillary forces, with the result that a maximum is eventually observed in average saturation for the short core. In very viscous (63-mPa . s (63-cp)) oil, no maximum is observed. Studies of saturation profiles during gas injection at high rates indicate that no stabilized zone is formed, but further work, probably with longer cores, could clarify the displacement mechanism.« less

Fluctuations, anisotropy and scaling in growth processes

Abstract: Some recent developments in the physics of two-dimensional growth processes are reviewed. The concept of effective anisotropy is used to explain tip stabilization and the non-trivial role of the driving force in Laplacian growth. Related experiments on viscous fingering are described. In diffusion-limited aggregation on a lattice, the anisotropy is suppressed by noise and very large clusters are needed to see its effect. By introducing the method of noise reduction, the asymptotic region is reached much earlier and a cross-over in the exponent of the radius of gyration takes place. In the case of the Eden model the anisotropy is no more relevant in the above sense but noise reduction is still useful because it improves the scaling behaviour and enables one to separate the contribution of the intrinsic width from the capillary waves.

Annual review of fluid mechanics. Volume 19

Abstract: The present evaluation of the status of fluid mechanical research gives attention to confined vortices in flow machinery, turbulent secondary flows, upstream blocking and airflow over mountains, critical point concept descriptions of eddying motions and flow patterns, viscoelastic flows through contractions, the theory of solute transport by groundwater, tsunamis, turbulent premixed flame behavior, and viscous fingering in porous media. Also treated are the computation of flows with shocks, the use of spectral methods in fluid dynamics, the dynamics of tornadic thunderstorms, thermocapillary instabilities, the behavior of magnetic fluids, Von Karman swirling flows, the use of isolated eddy models in geophysics, recent developments in rapid distortion theory, and rarefaction waves in liquid and gas-liquid media.

Fractal Flow Patterns in Porous Media

Abstract: The displacement of one fluid by another fluid in a porous medium is of importance in many processes, especially petroleum recovery. The purpose of this paper is to describe three types of displacements where patterns are very ramified: i) when a non-wetting fluid is injected at very low flow rate (capillary fingering), ii) when a low viscosity fluid pushes a more viscous fluid (viscous fingering), iii) when the porous matrix is etched by the invading fluid (reactive flow).

Fluid Dynamics at Pore Scale

Abstract: We discuss in detail simple statistical mechanical models of irmniscible displacement in porous media, with emphasis on the percolation and viscous fingering regimes where critical type behaviour is observed. The predictions of percolation models include the fractal nature of the non-wetting fluid configuration in drainage, and the size distribution of the residual non-wetting clusters in imbibition. At the macroscopic level it is suggested that percolation ideas are consistent with the usual multiphase darcy equations, and critical behaviours of the relative permeability and capillary pressure curves are obtained. In the case of viscous fingering, we focus on the effect of competition between anisotropy and disorder on the fingering process. The relation of viscous fingering to Diffusion Limited Aggregation is discussed.