Showing papers on "Viscous fingering published in 1993"

A lattice Boltzmann model for multiphase fluid flows

Abstract: A lattice Boltzmann equation method for simulating multiphase immiscible fluid flows with variation of density and viscosity, based on the model proposed by Gunstensen et al. for two‐component immiscible fluids [Phys. Rev. A 43, 4320 (1991)] is developed. The numerical measurements of surface tension and viscosity agree well with theoretical predictions. Several basic numerical tests, including spinodal decomposition, two‐phase fluid flows in two‐dimensional channels, and two‐phase viscous fingering, are shown in agreement of experiments and analytical solutions.

A Lattice Boltzmann Model for Multi-phase Fluid Flows

Abstract: We develop a lattice Boltzmann equation method for simulating multi-phase immiscible fluid flows with variation of density and viscosity, based on the model proposed by Gunstensen {\em et al} for two-component immiscible fluids. The numerical measurements of surface tension and viscosity agree well with theoretical predictions. Several basic numerical tests, including spinodal decomposition, two-phase fluid flows in two-dimensional channels and two-phase viscous fingering, are shown in agreement of experiments and analytical solutions.

Dispersion, permeability heterogeneity, and viscous fingering: Acoustic experimental observations and particle-tracking simulations

Abstract: Stable and unstable displacement experiments were performed in millstone and limestone cores. Concentration histories at ten locations along the core samples were obtained by acoustic measurements. Particle‐tracking simulations of the displacements were also made utilizing permeability distributions measured with a permeameter. The combination of experimental observations and simulations indicate that superstable (M<1) displacements suppress the influence of heterogeneity; this suppression was reflected in smaller apparent dispersivities as the mobility ratio decreased below unity. In the millstone, which exhibited random heterogeneity, two‐dimensional particle‐tracking simulations reproduce with reasonable accuracy the growth of the fingered region in unstable displacements. In homogeneous porous media, concentration histories obtained in three‐dimensional simulations did not differ significantly from their two‐dimensional counterparts. In the more heterogeneous limestone, unstable displacements accentuated the influence of heterogeneity leading to longer transition zones. Two distinct flow regimes were observed in unstable displacements: (1) an initial period of rapid transition zone growth and (2) a subsequent period in which leading and trailing edges of the transition zone travel at nearly constant velocities.

Numerical simulation of miscible displacement processes in porous media flows under gravity

Abstract: The nonlinear evolution of the interface between two miscible fluids of different densities and viscosities is simulated numerically for flow in a two‐dimensional porous medium in which gravity is directed at various angles to the interface. Global velocities tangential to the interface are included in the analysis in addition to a normal displacing velocity. In unstable configurations, the viscous fingers that result translate as they amplify when nonzero tangential velocities are present. The increased stabilization by tangential shearing velocities reported in [A. Rogerson and E. Meiburg, Phys. Fluids A 5, 1344 (1993)] affects the growth and wavelength selection of the emerging fingers. Tangential shearing also breaks the symmetry in the shape and concentration distribution of emerging fingers. In addition to the fingering mechanisms reported in previous studies, new mechanisms of diagonal fingering, trailing‐lobe detachment, and secondary side‐finger instability, resulting from the presence of gravity and tangential velocities, have been identified. These phenomena are reflected in one‐dimensional averaged profiles of the concentration field. Also, how different density–concentration relations influence the interfacial evolution is investigated. When the dependence of viscosity and density on the concentration has different functional forms, the region of instability may be localized. The nature of the interfacial development is altered by varying the density relation and thereby changing the region of instability, suggesting that careful modeling of the density and viscosity relations is warranted.

3D Simulation of Viscous Fingering and WAG Schemes

Abstract: Water-alternating-gas (WAG) injection has been suggested as a way to reduce viscous-fingering. This paper presents 3D simulations to assess the combined effects of gravity segregation in the vertical plane and areal viscous fingering for miscible displacements with substantial viscous fingering and for WAG injection. The simulations illustrate variations in recovery with WAG ratio and viscous-to-gravity ratio. A procedure to recalibrate the Todd and Longstaff parameter for WAG schemes in which buoyancy forces have little effect is described. Use of this recalibration provided excellent agreement with results from detailed simulation. Where gravity is important, recalibration of the parameter is required; examples of recalibration coarse-grid calculations are presented

3D simulation of viscous fingering and WAG schemes

Abstract: Water-alternating-gas (WAG) injection has been suggested as a way to reduce viscous-fingering. This paper presents 3D simulations to assess the combined effects of gravity segregation in the vertical plane and areal viscous fingering for miscible displacements with substantial viscous fingering and for WAG injection. The simulations illustrate variations in recovery with WAG ratio and viscous-to-gravity ratio. A procedure to recalibrate the Todd and Longstaff parameter for WAG schemes in which buoyancy forces have little effect is described. Use of this recalibration provided excellent agreement with results from detailed simulation. Where gravity is important, recalibration of the parameter is required; examples of recalibration coarse-grid calculations are presented

Shear stabilization of miscible displacement processes in porous media

Abstract: The interface region between two fluids of different densities and viscosities in a porous medium in which gravity is directed at various angles to the interface is analyzed. Under these conditions, base states exist that involve both tangential and normal velocity components. These base states support traveling waves. In the presence of a normal displacement velocity, the amplitude of these waves grows according to the viscous fingering instability. For the immiscible case, it can easily be shown that the growth rate is not affected by the tangential velocities, while surface tension results in the usual stabilization. For the case of two miscible fluids, the stability of the base states using the quasi‐steady‐state approximation is investigated. The resulting equations are solved analytically for time t=0 and a criterion for instability is formulated. The stability of the flow for times t≳0 is investigated numerically using a spectral collocation method. It is found that the interaction of pressure forces and viscous forces is modified by tangential shear as compared to the classical problem, resulting in a stabilizing effect of the tangential shear. The key to understanding the physical mechanism behind this stabilization lies in the vorticity equation. While the classical problem gives rise to a dipole structure of the vorticity field, tangential shear leads to a quadrupole structure of the perturbation vorticity field, which is less unstable. This quadrupole structure is due to the finite thickness of the tangential base state velocity profile, i.e., the finite thickness of the dispersively spreading front, and hence cannot emerge on the sharp front maintained in immiscible displacements.

How to predict viscous fingering in three component flow

Abstract: In a WAG process (Water Alternate Gas), water and a miscible solvent (gas) are injected into a reservoir containing water and oil. The solvent will finger through the oil, leading to early breakthrough and poor recovery. Compared with a miscible flood, when only solvent is injected, fingering is supressed by the simultaneous injection of water, since this reduces the apparent mobility contrast between the injected and displaced fluids. The fingering in a miscible flood, with only hydrocarbon flowing, can be modelled successfully using a Todd and Longstaff fractional flow. In this paper, we demonstrate how to modify the effective Todd and Longstaff mobility ratio self-consistently to account for fingering in three component systems. The resultant empirical equations of flow are solved exactly in one dimension and are in excellent agreement with the averaged saturation and concentration profiles computed using two dimensional high resolution simulation, for a variety of injected water saturations, in both secondary and tertiary displacements.

Successive bifurcations in directional viscous fingering.

Abstract: Directional viscous-fingering experiments are reported which extend previous studies by Rabaud, Michalland, and Couder. With the external cylinder rotation speed Ve fixed at a small constant value, the counter-rotation speed of the inner cylinder V i , which is then the single control parameter of the experiment, was increased or decreased in small steps. Beyond the primary planar-cellular bifurcation of the air-oil interface, a secondary bifurcation was observed to a state with uniform space-filling traveling cells, followed by a spatial period-doubling bifurcation

Transition to chaos by spatio-temporal intermittency in directional viscous fingering

Abstract: We present a statistical description of the transition to chaos in a directional viscous fingering experiment. In this extended one-dimensional system the order-disorder transition follows a scenario of spatio-temporal intermittency and appears as a second-order transition. The critical exponents of the transition are determined and compared with other systems exhibiting a similar behaviour. The values of these exponents are discussed.

Pattern formation in noncohesive and cohesive granular media

Abstract: We studied pattern formation in granular media in two distinct states: in the dry and non-cohesive (powder) state, on the one hand, and in the wet and cohesive (paste) state, on the other. In the first case, we have shown that gas injection in a thin layer of powder within a Hele Shaw cell leads to fractal patterns remarkably similar to viscous fingering patterns obtained with complex fluids. In the second case, we have shown that the tensile cohesive viscoplastic fracture of a layer of paste leads to self-affine rough surfaces with a Hurst exponent close to 0.88, very close to the value obtained for fragile fracture by other authors.18 Our observations reinforce the universality of two fractal growth processes and add a new element to the ambivalent nature of the granular state of matter.

Viscous fingering with adverse anisotropy: A new Saffman-Taylor finger.

Abstract: Viscous fingering in a linear channel is investigated in the presence of anisotropy, when the directions of easy growth are at 45 o to the direction of the cell axis. Experimentally, when the velocity is increased, the stable fingers and the averaged unstable ones tend to occupy an increasing fraction of the cell width, in contrast with the standard situation. The numerical simulation and the analytical investigation reveal the existence of a new solution for the Saffman-Taylor finger which does not belong to the standard manifold

Interpretation of Laboratory Gasfloods With Multidimensional Compositional Modeling

Abstract: Corefloods were conducted and simulated to evaluate oil recovery from field cores by injection of hydrocarbon solvents. Heterogeneity and fingering were evaluated separately by conducting computed-tomography (CT)-aided single-phase stable and unstable floods. In the absence of bypassing, oil displacement by an equimolar mixture of C 2 , propane, and butane (C 234 ) is first-contact miscible and C 2 (C 2 ) flood is multicontact miscible. In corefloods, heterogeneity and fingering cause oil bypassing. Bypassed oil remains miscible with injectant C 234 but becomes immiscible with injectant C 2 . Two heaviest pseudocomponents drop out in the bypassed region to form a residual oil saturation (ROS) of ≃ 25%

Asymptotic behavior of viscous-fingering patterns in circular geometry

Abstract: An examination of the scaling structure along with some extensive simulations on viscous fingering in circular geometry strongly suggest that the asymptotic patterns are compact. Experiments and simulations are in a transient regime that may exhibit a reasonable range where apparent fractal growth may be found. Arguments to connect the case of viscous fingering with that of vanishing surface tension are made.

Non Linear Three Dimensional Miscible Viscous Fingering in Porous Media

Abstract: Viscous fingering resulting from unstable fluid displacements in porous media has been studied extensively over the last forty years since the pioneering experiments of Hill1. Recent reviews on this subject by Homsy2 and Yortsos3 are available as well as on the special issue of the Saffman-Taylor4 finger in a Hele-Shaw cell by Bensimon et al.5. Most of the papers on viscous fingering deal with immiscible fluids, but indeed the problem involving miscible fluids deserves at least as much attention as the immiscible case: as in the immiscible case, the unfavorable viscosity ratio (displacing fluid less viscous than the displaced one) generates the instability but here the stabilizing effect is due to the hydrodynamic dispersion which tends to spread out growing fingers. Dispersion is more subtle than interfacial tension. Further, it is anisotropic and flow dependent which leads to new predictions6–12 such as a cross-over between diffusive and linear growth regimes7, 12 and an enhancement of the instability due to the interplay between the large viscosity ratio and the velocity dependent hydrodynamic dispersion9. Experiments are scarce1, 13–18 and deal generally with a pseudo 2D geometry involving qualitative visualization. In this paper, we use a newly developed acoustic technique19–21 to carry out the first study of the profiles of viscous fingers in 3D porous media. Our experiments have been performed out on three different porous media with a wide range of viscosity ratios and flow rates. Both the diffusive and the linear growth are observed including the cross-over from one to the other. Taken together, our data are best understood in terms of a new instability parameter, that characterizes the main features of viscous fingering. Our determination of the dependence of this parameter on the viscosity ratio, the flow rate and on the porous medium when placed in the context of existing theory leads to new physical insights on this rich and varied problem.

Onset of viscous fingering for miscible liquid-liquid displacements in porous media

Abstract: The displacement of one fluid by another miscible fluid in porous media is an important phenomenon that occurs in petroleum engineering, in groundwater movement, and in the chemical industry. This paper presents a recently developed stability criterion which applies to the most general miscible displacement. Under special conditions, different expressions for the onset of fingering given in the literature can be obtained from the universally applicable criterion. In particular, it is shown that the commonly used equation to predict the stable velocity ignores the effects of dispersion on viscous fingering.

Natural Viscous Fingering

Abstract: The fingering phenomenon that occurs when a low-viscosity fluid displaces another with a higher viscosity1 has been extensively studied in the last few years from a fractal point of view. Excellent reviews of this phenomenon have been recently published2–4. Oil recovery is by far the most classical case of naturally occurring viscous fingering. I will discuss several features observed on an unplanned large scale “experiment” of viscous fingering and I will try to apply these new features to two natural cases for which a morphogenetical explanation linked to viscous fingering has been proposed.

Compact or fractal patterns in diffusion limited growth

Abstract: Fractal viscous fingering patterns are observed in an infinite Hele-Shaw cell at long times when the capillary forces become negligible. On the contrary, growth of monocrystals from a punctual seed shows dendrites growing independently in 4 or 6 directions, according to the crystal symmetry. A close comparison of numerical and experimental data explains first the origin of the tip-splitting instability in radial growth and shows that it can be inhibited by the anisotropy of surface tension.

Dynamics of immiscible radial viscous fingering: A numerical study

Abstract: In this paper we undertake a numerical investigation of the dynamics of the interface in the problem of immiscible radial viscous fingering in a Hele-Shaw cell when the areal flow rate is maintained constant. Comparison is made with experimental results to check if there is a need to introduce velocity-dependent boundary conditions and to incorporate the effect of thickness of the film left behind by the moving interface. Some new scaling results are suggested by the numerical data. These data, along with those available from laboratory experiments, provide support for a mean field theory for radial immiscible viscous fingering published recently [Phys. Rev. Lett. 65, 2680 (1990)].

Viscous Fingering and Surface Structure Formation in Porous Media

Abstract: Finger-like instability with immiscible displacement of one viscous fluid with the other from porous material has been studied experimentally for two main cases: transparent two-dimensional model of porous medium with chaotic distribution of volumetric pores and thin 1×20×66 sm sample of arenaceous quartz placed horizontally Data on selection of surface structures with instable displacement front in two-dimensional and three-dimensional pore systems has been obtained In porous materials occur various phenomena related with the stability of interphase boundary in random medium when the capillary forces govern interphase boundary motion in small scale and viscous forces in a large one As the result, capillary instability in small scale generating the noise with large amplitude and viscous instability in large scale are simultaneously developed Surface structures development with viscous fingergrowing when there is large noise has been in detail studied and the experimental data are discussed from the standpoint of well-known theoretical models of viscous fingergrowing

Topological Considerations on Finger Dynamics in the Saffman-Taylor Problem

Abstract: The study of viscous fingering in Hele-Shaw cells[1], has been playing an important role in the understanding of interfacial pattern formation. As a prototype system for the study of diffusion-controlled growth, it is relevant for a variety of non-equilibrium phenomena, such as dendritic growth, directional solidification, chemical electrodepo-sition and flame propagation [2].

Fibonacci Sequences in Diffusion-Limited Aggregation

Abstract: Pattern formation in systems far from equilibrium is a subject of considerable current interest1–6. Recently, much effort has been directed towards the study of fractal growth phenomena in physical, chemical and biological systems7,8. Unfortunately, the understanding of phenomena like viscous fingering in Hele-Shaw cells9 and electrochemical deposition10 is hampered by the mathematical complexity of the problem. Highly ramified structures are generally produced in the zero surface tension limit. In this limit, both processes are equivalent to a Stefan problem11 : a diffusion problem for the pressure or the electrochemical potential, with boundary values specified on the moving interface, whose local velocity is in turn determined by the normal gradient of the Laplace field. This highly nonlinear problem is not readily amenable even to modern numerical simulations. When solving the Stefan problem by direct means, the interface develops unphysical cusps in a finite time9. One is thus led to introduce some short-distance cutoff which in some sense mimics surface tension12,13. Thus far no computer simulations of the equations of motion achieve the necessary size to make definite conclusions about the deterministic character of the fractal patterns observed in the experiments1–6.