Viscous Fingering Research Articles

Immiscible invasion of granular suspension by high-viscosity liquid

We investigate the morphology and dynamics of the pattern of immiscible invasion by injecting a high-viscosity liquid into a granular suspension consisting of movable solid grains in a low-viscosity liquid. Laboratory experiments conducted in a Hele–Shaw cell shed light on how the frictional forces of the grains and the viscous forces of the liquids affect the instability of the liquid–liquid interface and the formation of viscous fingers. The frictional force increases with an increase in either the volume fraction or the size of the grains, leading to higher resistance to the invading pattern. Upon changing the grain shape from spherical to irregular, both the frictional force and the rotational energy of the grains increase, resulting in more numerous but narrower fingers. Increasing either the injection rate or the viscosity of the injected liquid increases the viscous pressure within the fingers, promoting the splitting of the pattern. Although the defending liquid always has a lower viscosity than the invading liquid in this study, the former's viscous force becomes non-negligible as the viscosity ratio of the invading liquid to the defending liquid decreases to near unity, which destabilizes the fluid–fluid interface and causes a transition to an asymmetric pattern.

EOR of heavy oil polymer on Alaska's North Slope: History matching challenges and solutions in a significant long-term water cut reduction

In 2016, a pilot program in Alaska's Milne Point Field tested polymer flooding for heavy oil recovery. Using four wells in the Schrader Bluff reservoir, it aimed to assess its effectiveness in capturing heavy oil resources. Generally, polymer flooding can boost oil production by 10-15%, typically occurring 6-9 months after injection. However, in this case, it took over 24 months for a polymer breakthrough. The method proved highly effective, consistently reducing water content by over 40% and maintaining a low level below 20% for 18 months. Applying standard simulation methods, like history matching, became challenging due to this prolonged low water cut. The usual history-matching processes focus on relative permeability, permeability corrections, and skin effect modifications. Nevertheless, these alternatives proved ineffective. In response to the extended low water cut in Alaska's North Slope, a unique approach was suggested. This approach entails highlighting the low-end point (Krw) across multiple relative permeability curves and adjusting these values according to the water cut history. Additionally, the method takes into account permeability adjustments, Equation of State on analyzes of oil viscosity, J-function incorporation, and considers the potential for viscous fingering during the process. The pilot program displayed remarkable polymer flooding effectiveness, but its unique performance on the North Slope required a modified history-matching approach to simulate its success accurately.

Insights into Molecular Dynamics and Oil Extraction Behavior of the Polymeric Surfactant in a Multilayered Heterogeneous Reservoir.

Interlayer heterogeneity, an inevitable and complex challenge during water flooding, seriously constrains the spread of the sweep region and oil recovery enhancement in multilayered heterogeneous reservoirs. To overcome this challenge, a novel polymeric surfactant, having an excellent performance in the reduction of interfacial tension (IFT) and the increase of viscosity of displacing fluid, is applied for enlarging the sweep resonance and increasing the oil washing efficiency. Through the molecular dynamics (MD) simulation, the molecular distributing mechanisms of the polymeric surfactant at the oil-water interface are analyzed to provide the theoretical basis for explaining the microscopic mechanism of oil extraction. To directly reflect the microscopic behavior of oil extraction, multiple transparent sand-packed models are designed to investigate the flowing behavior of different fluids and the extracted mechanisms of the remaining oil in both pore and macroscales. The multilayered heterogeneous reservoirs consisting of high-, moderate-, and low-permeability layers are fabricated to represent a heterogeneous characteristic. The recognition from the visual experiment and MD simulation can study the performance control, the extracting performance of the remaining oil, and the expression of the displacing front from different perspectives. The results from MD simulation demonstrate that the polymeric surfactant can promote the disintegration of the remaining oil and enhance its mobility. The experimental results indicate that the sweep efficiency is restricted by viscous fingering and tongue advance. Through the analysis of mathematical models, the rising mobility ratio and the location of the displacing front have a strong positive relationship with viscous fingering and tongue advance, which can reasonably explain the plugging performance of the polymeric surfactant, greatly improving the sweeping effect of the whole reservoir. Moreover, the Marangoni effect generated by the IFT gradient can induce the transformation of interfacial energy to displacement kinetic energy by the emulsification of the oil-water interface so that the remaining oil in the blind-end pore can be effectively extracted. However, by comparing data from image quantification techniques and production dynamic performance, the sweep efficiency (484%) was significantly greater than that of oil recovery (300%), demonstrating that the expanded sweep effect still plays a dominant role in the extraction of remaining oil after polymeric surfactant flooding. This study provides a novel plugging and effective washing agent that is expected to be an excellent and comprehensive method for solving the problem of low oil recovery in multilayered heterogeneous reservoirs.

Dewatering Spent Ion-Exchange Resins with Supercritical CO2

ABSTRACT A process for dewatering spent ion exchange resins (gel and porous) used in nuclear power plants by supercritical CO2 (sCO2) is described. The amount of water removed by sCO2 is much higher than that expected from solubility considerations alone. Water from gel-type resins is both dissolved by and emulsified in sCO2. Emulsification also occurs in the absence of solids when water alone is contacted by sCO2. It is not a factor for microporous resins where an additional mechanism, viscous fingering, is involved. It appears that bulk water is emulsifiable but not if it is held in pores. Dewatering via viscous fingering has been previously invoked for matrices such as wood and sludge. The resins can be dewatered and dried with sequential batches of sCO2 at sub-boiling temperatures. The CO2 can then be potentially reused after expansion and separation from the entrained water. Partial decompression of the water-laden sCO2 would lead to cooling, which would drop the water solubility substantially. A reduction of temperature from 90 oC to 65oC reduces the solubility of water in sCO2 by a factor of five. The condensed water could then be separated with a hydrocyclone. The footprint of sCO2 is much smaller than the conventional drying process. The energy costs are also much lower because evaporation of water is avoided.

Pore-scale simulation of miscible displacement in an inclined porous medium

Introduction: This study investigates the displacement of two miscible fluids within an inclined porous medium at the pore scale, highlighting how the pore-scale microstructure, inclination angle, and viscosity ratio affect the interfacial instability between two fluids during displacement processes.Methods: The lattice Boltzmann Method (LBM) is employed to solve the governing equations. Two distribution functions are used to simulate the velocity field and the concentration field, respectively.Results and discussion: An increase in inclination angle exacerbates the interfacial instability between fluids and the viscous fingering phenomenon. This viscous fingering expands the sweep range of displacing fluids, which improves the displacement efficiency. When θ > 50°, further increase in inclination angle will not cause significant changes in displacement efficiency. In addition, the viscosity ratio is a key factor affecting displacement efficiency. The larger the viscosity ratio, the greater the displacement efficiency. Furthermore, the critical viscosity ratio has been found, and any increase in the viscosity ratio above the critical value will not affect the displacement efficiency.

Oil Shale In Situ Production Using a Novel Flow-Heat Coupling Approach.

Oil shale development, a significant global energy concern, involves the pyrolysis of kerogen, a process that can heat and contaminate groundwater with pyrolysis products. To address these challenges, this study introduces the ambient-temperature gas in situ heating (ATGIH) method as an alternative to traditional techniques. The ATGIH method establishes a low-temperature gas barrier to prevent water infiltration into the production zone by placing heating holes between the injection and production wells. The effectiveness of the ATGIH method in mitigating groundwater contamination during oil shale development is demonstrated through thermochemically coupled reservoir simulations. The study further discusses how gas injection enhances the flowability of mobile oil and gas phases into production wells and how controlling the Dykstra-Parsons coefficient, a measure of heterogeneity, can mitigate gravity segregation and aggregate viscous fingering issues. Our results show that well spacing is a critical factor in designing oil shale development, with a larger spacing resulting in higher energy efficiency but lower oil recovery rates. Furthermore, the study reveals that porosity decreases while permeability increases during pyrolysis due to thermal cracking and pore structure changes. It also highlights that heterogeneity-induced issues can be alleviated by increasing the correlation length to make the system more homogeneous. Therefore, the ATGIH method represents a key innovation in oil shale development, offering a solution that mitigates groundwater contamination while improving the energy efficiency.

Air invasion into three-dimensional foam induces viscous fingering instabilities

We conducted an experimental investigation to examine the immiscible radial displacement flows of air invading three-dimensional foam in a Hele-Shaw cell. Our study successfully identified three distinct flow regimes. In the initial regime, characterized by relatively low fingertip velocities, the foam underwent a slow displacement through plug flow. During this process, the three-phase contact lines slipped at the cell walls. Notably, we discovered that the air injection pressure exhibited a proportional relationship with the power of the fingertip velocity. This relationship demonstrated excellent agreement with a power law, where the exponent was determined to be 2/3. Transitioning to the second regime, we observed relatively high velocities, resulting in the displacement of the foam as a plug within single layers of foam bubbles. The movement of these bubbles near the cell walls was notably slower. Similar to the first regime, the behavior in this regime also adhered to a power law. In the third regime, which manifested at higher air injection pressures, the development of air fingers occurred through narrow channels. These channels had the potential to isolate the air fingers as they underwent a process of "healing." Furthermore, our results unveiled a significant finding that the width of the air fingers exhibited a continuous scaling with the air injection pressure, irrespective of the flow regimes being observed.

Extensive tip-splitting of injected organic liquid into an aqueous viscoelastic fluid

The injection of a fluid into another fluid causes a spatiotemporal pattern along the injection front. Viscous fingering is a well-known example when the replaced material is a viscous fluid. Notably, most fluids are, in reality, viscoelastic, i.e., they behave as an elastic solid over short timescales. For this reason, it is important to study the situation when the replaced fluid is viscoelastic. In this study, we observed a dynamics of fluids when an incompressible organic liquid was injected into an oleophilic Hele–Shaw cell filled with an aqueous viscoelastic fluid made of a wormlike micellar solution. We found extensive tip splitting of the injection front, which led to thin fingers with a characteristic size comparable to four times the cell thickness. We examined the material properties and suggest that the thin fingering pattern observed in our system is due to the delamination of viscoelastic fluid from the bottom substrate surface. Our result shows that the effect of interfacial energy in the existing solid layer should be considered in the injection process.

Coupled instability modes at a solvent/non-solvent interface to decorate cellulose acetate flowers

Dispensing a water drop on the thin film of a solution composed of cellulose acetate (CA) in dimethyl formamide (DMF) forms a thin and porous CA layer at the water–DMF interface. While a denser water drop on a rarer CA–DMF film manifests a Rayleigh–Taylor instability—RTI, the dynamically forming porous layer at the water–DMF interface triggers a Saffman–Taylor instability—STI. The combined effects of RTI and STI enable the formation, growth, coalescence, and branching of an array of periodic finger patterns to finally develop into a flower-like morphology. A general linear stability analysis (GLSA) of a thin bilayer composed of a Newtonian and incompressible water layer resting on a Darcy–Brinkman porous medium could predict the length and the time scales of such a finger formation phenomenon. The GLSA uncovers the crucial roles of pressure gradients originating from the gravitational effects, osmotic forces, the Marangoni effect, and capillary forces on the dynamics of the finger formation. While the density difference between water and CA–DMF layer plays a crucial role in deciding the initial finger spacing, the osmotic pressure dictates the formation, growth, branching, and coalescence of fingers. The length-FL and number-Navg of fingers are found to scale as FL∼We0.33Re−0.25 and Navg∼We0.33Re0.25. Further, an inverse relationship of the concentration of CA (C) with ∼We−0.3 and ∼Re−0.7 highlights its role in the formation and growth of fingers. The loading of CA in DMF, the viscosity and density of the CA–DMF film, and the curvature of the fingers are found to be other parameters that decide morphologies.

Interfacial instabilities in confined displacements involving non-Newtonian fluids

The growth of interfacial instabilities during fluid displacements can be driven by gradients in pressure, viscosity and surface tension, and by applying external fields. Since displacements of non-Newtonian fluids such as polymer solutions, colloidal and granular slurries are ubiquitous in natural and industrial processes, understanding the growth mechanisms and fully developed morphologies of interfacial patterns involving non-Newtonian fluids is extremely important. In this perspective, we focus on displacement experiments, wherein competitions between capillary, viscous, elastic and frictional forces drive the onset and growth of primarily viscous fingering instabilities in confined geometries. We conclude by highlighting several exciting open problems in this research area.

Controlling viscous fingering instabilities of complex fluids

Despite their aesthetic elegance, wavy or fingering patterns emerge when a fluid of low viscosity pushes another immiscible fluid of high viscosity in a porous medium, producing an incomplete sweep and hampering several crucial technologies. Some examples include chromatography, printing, coating flows, oil-well cementing, as well as large-scale technologies of groundwater and enhanced oil recovery. Controlling such fingering instabilities is notoriously challenging and unresolved for complex fluids of varying viscosity because the fluids’ mobility contrast is often predetermined and yet the predominant drive in determining a stable, flat or unstable, wavy interface. Here we show, experimentally and theoretically, how to suppress or control the primary viscous fingering patterns of a common type of complex fluids (of shear-thinning with a low yield stress) using a radially tapered cell of linearly varying gap thickness, h(r). Experimentally, we displace a complex viscous (PAA) solution with gas under a constant flow rate (Q), varied between 0.02 and 2 slpm (standard liter per minute), in a radially converging cell with a constant gap-thickness gradient, α=dh/dr<0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha = dh/dr < 0$$\\end{document}. A stable, uniform interface emerges at low Q and in a steeper cell (i.e., greater |α|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\alpha |$$\\end{document}) for the complex fluids, whereas unstable fingering pattern at high Q and smaller |α|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\alpha |$$\\end{document}. Our theoretical predictions with a simplified linear stability analysis show an agreeable stability criterion with experimental data, quantitatively offering strategies to control complex fluid-fluid patterns and displacements in microfluidics and porous media.

Optimal control of viscous fingering

The paper considers the problem of optimally filling a Hele-Shaw cell. The system is subject to viscous fingering effect. It is shown that, despite the threshold terms appearing on the right-hand side of the governing equations, the dynamics can be rewritten using several prime integrals. This allows reforming optimal control problems for the Fourier modes describing the fluid interface into smooth optimization problems, in the sense of Gâteaux derivative. Some numerical experiments illustrate the advantages of using the optimal solutions obtained using this reformulation instead of the currently known time-dependent injection rates.

Research on the Influence of Heterogeneity and Viscosity on the Fluid Intrusion Mechanism of the Water Flooding Process Based on the Microscopic Visualization Experiment.

The flow law of immiscible fluids in porous media plays an important role in the development of oil and gas fields. In the process of water flooding reservoir development, when the water phase displaces the oil phase, a fluid with higher viscosity, as a fluid with lower viscosity, the oil-water interface will always be unstable, resulting in different fingering effects. After water flooding, the distribution law of oil and water in the reservoir is mainly affected by the fluid intrusion mechanism. Due to the difference of capillary force, viscous force, and other microscopic forces, the fluid intrusion mechanism is mainly divided into two types: viscous fingering and capillary fingering. At the same time, due to the influence of reservoir heterogeneity, the fingering effect in the process of water displacement in porous media will be influenced to a certain extent. Based on the two-dimensional microscopic visualization experiment, this paper extracted the variance of the static parameter G in the capillary number calculation method of the two-dimensional microscopic model to represent the heterogeneity and conducted displacement experiments with different viscosities and flow rates to study the influence of the flow rate, viscosity, and heterogeneity on the results of water flooding. The experiments found that as for the influence of flow velocity, with the increase of flow velocity, that is, with the increase of capillary number, the recovery degree decreases first and then increases. As for the influence of viscosity, from a numerical point of view, the displacement efficiency and conformance coefficient of the low-viscosity group are higher than those of the high-viscosity group. From the trend, with the increase of the capillary number, the displacement efficiency of both the low-viscosity and high-viscosity groups increases, while the conformance coefficient decreases first and then increases, indicating that capillary fingering and viscous fingering can occur in different viscosity reservoirs. As for the influence of heterogeneity, the conformance coefficient of the water flooding decreases with the increase of heterogeneity, and the viscous pointing trend caused by heterogeneity is stronger, resulting in an uneven water injection sweep and higher oil displacement efficiency within the swept area. It can be seen from the fluid intrusion mechanism diagram that with the increase of heterogeneity, the viscous fingering trend becomes more obvious; with the increase of viscosity, the fluid intrusion mechanism boundary moves down and the viscous fingering trend becomes more obvious.

Numerical study on the characteristics of viscous fingering during the displacement process of non-Newtonian fluid.

This study uses numerical methods (ANSYS-Fluent) to investigate the viscous fingering of the displaced phase as a shear-thinning fluid in the classic three-dimensional Hele-Shaw cell. Comparing the behavior of fingerings with different properties on the upper and lower surfaces of a three-dimensional model, it was found that when the upper and lower surfaces are walls, under the combined action of moving contact lines and Saffman-Taylor instability, fingering splitting occurs at the tip, resulting in the appearance of two fingers at the interface. In addition, we have found that interfacial tension has a suppressive effect on short waves. As the interfacial tension increases, the velocity at the advancing tip decreases. Therefore, when the interface tension is 0, viscous fingering displacement reaches the farthest distance. We have also conducted research on the viscous fingering at different temperatures. The results indicate that increasing the temperature leads to a decrease in the viscosity of the displaced phase, making the flow more stable. As the temperature rises, the pressure gradient inside the flow path increases, pushing the viscous fingering further.

Comparison of velocity field characteristics of gas invasion via viscous fingering and elastic fracturing in visco-elasto-plastic fluids

Viscous fingering (VF) and elastic fracture (EFr) are prevalent phenomena when gas invades into the complex fluids. In this study, compressed nitrogen gas was injected into a complex fluid called...

Detachment forces during parallel-plate gap separation mediated by a simple yield-stress fluid.

In this work we have monitored the multiple stages of the normal traction force response of a yield-stress fluid confined between two circular parallel plates that are separated at constant velocity. At narrow initial gaps, the air-fluid interface suffers from the Saffman-Taylor instability, confirmed by visual inspection of fingering patterns imprinted on the fluid. At larger initial gaps, the fluid preserves the initially imposed circular symmetry of the confining plates, indicating the absence of instability. Due to the system characteristics and experimental environment, the multiple traction force contributions occurred in cascade, permitting us to isolate the adhesion responses associated with viscosity, capillarity, and yield stress. Employing a standard Herschel-Bulkley model, we assessed the scaling of the traction force in multiple regimes-specifically, evaluating the dependencies of the fingering to yield-stress transitions.

Momentum transport of morphological instability in fluid displacement with changes in viscosity.

Saffman-Taylor instability exhibits a stepwise unstable morphology from a stable interface to viscous fingering, eventually leading to tip splitting. The nonlinear dynamics of the destabilized interface depends on various flow properties. However, the physicochemical mechanism that determines the transition point of the flow state is unclear. We studied the interfacial instability transition in miscible displacement from a thermodynamic perspective by calculating the momentum transport and entropy production. Using numerical analysis based on Darcy's law coupled with the convection-diffusion equation, the observed flux-dependent flow state transitions were attributed to the selection of the flow state with a higher entropy production.

Drainage dynamics: From capillary to viscous fingering under different wettability

The displacement of two-phase fluids within porous media is a critical process in various engineering and industrial fields. However, the inherent instability of the fluid interface often leads to an irregular morphology of the displacement front, which can impact the efficiency of displacement and limit its application in engineering activities. In this study, the color gradient model based on the lattice Boltzmann method was employed to simulate displacement, with the aim of investigating the dynamic evolution of the displacement front under the combined effects of wettability and injection velocity, specifically during the capillary to viscous fingering transition. The results demonstrate that the impact of wettability on the displacement front morphology increases as the injection velocity decreases. The displacement process with the maximum fingering distribution range and compact morphology is found at the midpoint of the capillary-viscous fingering crossover zone. Furthermore, an in-depth analysis of the phase field evolution and pressure difference changes between the inlet and outlet unveiled the pore-filling mechanisms associated with the unique variation characteristics of the displacement front and the fluid topological structure. These comprehensive pore-scale findings offer theoretical insight supporting the engineering application of the two-phase flow in porous media from multiple perspectives.

Capillary waves and dendritic instability on radial Hele–Shaw displacements

The displacement of a fluid by another less viscous one in isotropic quasi-two-dimensional Hele–Shaw cells typically leads to viscous fingering patterns characterized by repeated tip-splitting and side-branching. When anisotropy is present, the viscous fingering patterns are replaced by dendritic instability. In isotropic cells, Couder et al. [“Dendritic growth in the Saffman-Taylor experiment,” Europhys. Lett. 2, 437 (1986)] induced the growth of a dendritic finger by placing a small isolated bubble in contact with the tip of a finger. Moreover, in rectangular displacements, Kopf-Sill and Homsy [“Narrow fingers in a Hele–Shaw cell,” Phys. Fluids 30, 2607–2609 (1987)] observed for specific ranges of modified capillary numbers, Ca, that narrow fingers develop into dendritic patterns after carefully cleaning the Hele–Shaw cell with a soap solution. In the current work, by injecting air to radially displace a lubricant oil with strong adsorption properties, we observe for the first time the growth of dendritic instability in displacements confined in isotropic Hele–Shaw cells in the absence of air bubbles driving the fingertip. These structures are driven by the formation of capillary waves inside the finger adjacent to the Hele–Shaw surfaces. Furthermore, we compare displacements of different materials at similar high Ca values and obtain significantly different morphological results, indicating the pattern formation may not scale with this parameter in this range. Discrepancies are explained based on both wetting and inertia effects.

Numerical study of viscous fingering patterns under annular boundaries based on the Hele-Shaw model

Numerical study of viscous fingering patterns under annular boundaries based on the Hele-Shaw model